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NOAA Technical Memorandum NWS HYDR0-38
IMPROVEMENT OF HYDROLOGIC SIMULATION BY UTILIZING
OBSERVED DISCHARGE AS AN INDIRECT INPUT
(COMPUTED HYDROGRAPH ADJUSTMENT TECHNIQUE--CHAT)
Silver Spring, Md.
February 1979
NATIONAL OCEANIC AND
ATMOSPHERIC ADMINISTRATION I National Weather
Service
NOAA TECHNICAL MEMOIWfDO~S
Rational Weather Service , Of f ice of HydrolO~f Series
The Office of Hydrolcgy (HYDRO) o f the National Weather Service (NWS) develops procedures for IIUlkin a
river aDd water supply foreca•ts , analyzes hydra.eteoroloaical data for plannina and design cr iteria for
oth.er aaencie•, and conducts pertinen t research and develos-nt.
IOAA Technical ~randU8S in the MWS HYDRO aerie• facilitate proapt di•tribut ion of scientific and
technical .. terial by ataff •embera, cooperatora , and contractora . Infor.ation presented i n this 1eries
.. y be preliminary in nature and .. y be publi~hed f ormally elsewhere at a later date. Publication 1 is
in tbe for.er aeriea, Weather Bureau Technical Notea (TH); publications 2 through 11 are in t ~e former
1erie1, ESSA Technical K£80randUJU, Weather Bureau Technical HellorandUJU (WBTM ). Beginning v i tb 12 ,
publications are nov part of the aeries , NOAA Technical HeiDOranduma, RWS.
Publication• liate d below a re available from the National Technical Information Service, o.s. Depart-
.ent of Commerce, Si lls Sldg •. 5285 Port Royal Road, Springfield, VA 22161. Pr ices on request. Order
by accession nuaber (g i ve n i n parentheaes). Infor.~tion on memorandums not listed below can be obtained
ftom Environmental Sc ience Inforaation Center (0822.1 , NOAA, 6009 Executive Boulevard , Rockville, MD
20852 .
TH 44 HYDRO 1
Weather Bureau Technical Notes
Infrared a.diation Pro• Air to Underlying Surface . Vance A. Myers, Kay 1966 , 35 pp.
(Pil-170 -664)
ESSA Technical MeaorandUIU
WBTH HYDRO 2 Annotated Biblioaraphy of ESSA Publication• of Hydrometeoroloaical Intereat. J . L. H.
Pau lbua, February 1967, 20 pp. (Superaeded by WBTK HYDRO 8 )
WBTM BYORO 3 The Role of Persistence , Instability, and Moisture in the Intense Ra i nstoras in !astern
Co l o rado, ~une 14-17, 1965. F. K. Schwarz, February 1967 , 21 pp. (PB-174-609)
WITH HYDRO 4 Elements of River Forecas ting. Marshall H. Richarda and Jose ph A. Strahl , October 1967 ,
61 PP• (Superaeded by WBTH HYDRO 9}
WBTK HYDRO 5 Meteoro logical Estimation of Extre.e Precipi tation for Spillway Deaign Floods . Vance A.
WBTH HYDRO 6
IIBTM HYDRO 7
WBTH HYDRO 8
_/' WBTM HYDRO 9
Hyers , October 1967 , 29 pp. (PB-177-687}
Annotated Bibliography of ESS& Publications of HydrOGieteorological Intereat. J . L. H.
Paulhus, Noveaber 1967, 27 pp. (Superseded by WBTH HYDRO 8}
K£.teorology of Major Stot"IIS in Western Colorack and Eastern Utah.
January 196a , 75 pp. (PB-177-491}
Robert L. Weaver ,
Annotated Bibliography of ESSA Publications of Bydra.eteorological I nte~est. J. L. B.
Paulhus , August 1968 , ?.5 pp. (Superseded by NWS HYDRO 22}
Elements of Rive r Forecasting (Rev ised }. Marshall H. Richards and Joaeph A. Strahl,
Karch 1969, 57 pp. (PB-185-969 )
WBTH HYDRO 10 Flood Warning Be nef it Evaluation--Susquehanna River Bas in (Urban Reaid~nces). Harold
J. Day, Karch 1970, 42 PP• (PB-19Q-984)
WBTH HYDRO 11 Joint Probability Method of Tide Frequency Analysis Applied to Atlantic City and Long
Beach Island, N.J. Vance A. ~yers , April 1970, 1C9 pp . (PB-192-745)
INS HYDRO 12
INS HYDRO l3
NWS HYDRO 14
NOAA Technic al Hemorand~
Direct Search Optiaization in Katbe .. tical Modeling and a Watershed Hodel Application.
John C. Monro , April 1971, 52 PP• (COH-71-00616)
Ti•e Diatribution of Precipi tation in 4-to 10-Day Storaa--Obio River Balin.
Killer and Ralph B. Frederic k , July 1972, 41 pp. (COM-72-11139}
National We•ther Service liver Forecast System Forecast Procedures. Staff,
!z • .:a.ch Laboratory , Deceaber 1972, 7 chaptera plus a ppendixes A through I.
10517)
John F.
isydrologic
(COH-73-
NWS HYDRO 15 Ti.e Dist ribution of Precipitation in 4-to lG-Day Storaa--Arkaaaaa-Canadiaa River Ba-
sina . Ralph H. ~ederick, June 197 3 , 4S pp. (COM-13-11169)
(Coatiaued on. iDaide back coftr)
.....
NOAA Technical Memorandum NWS HY DR0 -38
IMPROVEMENT OF HYDROLOGIC SIMULATION BY UTILIZI NG
OBSERVED DISCHARGE AS AN INDIRECT INPUT
(COMPUTE D HYDROGRAPH ADJUSTMENT TEC HNIQUE--CHAT)
Walter T. Sittner and Kay M. Kr o use
Silver Spring, Md.
Fe bruary 1979
t ,. ' • •--~<I II ... -, , . -. '\
IJITED STATES
DEI'ARTIIEJfT OF COMMBICE
Juall M. Kleps, SetrNry
/ NATIONAL OCEANIC AND / Natoonal Weatller
/ ATMOSPHERIC ADMINISTR ATION / ServiCe
/ AICI!ard A Frank Admm tSt rator George P Cressman . Duector
CONTENTS
List of f i gu r es
List of table s
Abstract
l. Introd u c t i on and bac k g r o und •
2. Status o f resea r ch
3 . Theory
4. Comp o nent parts .
Objective function
Tolerance • • • • •
Unit hydr o g raph adjustment ••••.
Adjust ment s trategy •••••
Observed hy drograph inte rpolation •
Blending r o utine
5 . Operational use .
6 . Examples . . . .
Examp le 1 (Bird Cr eek 7 /2/76)
Example 2 (Honocacy Rive r 6/19/58-single event) .
Example 3 (Nonocacy River 6/19/58-separate event s)
Example 4 (r1onocacy Rive r 8/11/55) . .
Example 5 (Monocacy River 8 /1 7/5 5)
Example 6 (Leaf River 11/12 /61) . . . . . .
7 . Sug gestions for f uture research • .
.
.
Phase 2 -Outflow from Indi~idual Cat c hments During
Run o ff Events in which Snow or Sno~elt
is involved ..... .
Phase 3 -Outflow from Individual Catchments During
Low Water Pe rio ds . . .
Phase 4 -An Adjustment Te c hnique App l i c able t o
Po ints in a River Sy stem that are not
at the Outlets of Indi v idua l Catchments
iii
. .
.
i v
vii
viii
1
5
6
9
9
15
17
28
39
40
41
54
56
71
85
92
98
1 05
11 7
117
119
122
Further Testing of Adjusted Soil Moisture Va riab l es • . 12 3
Application t o a Distributed Input Ca tchmen t Model 124
Reference s
App e ndix A. Su broutine listin8s
iv
125
A-1
Figure
4.1
4.2
4 .3
4.4
4.5
4 .6
4.7
4 .8
4.9a
4. 9b
5.1
6.1
6.2
6.3
6.4
6.5
6.6
6.7
LIST OF FIGURES
Variation of tolerance with discharge and
with time . • • • • • • •
Relationship of WARP su~routine to other
components
Effect on unit graph of varying vertical
warp coefficient--RV=l.l, RV=0.9
Effect on unit graph of numerically large
vertical warp coefficient--RV•2 .0
Effect on unit graph of numerically small
ve rtical warp coefficient--RV•0.7
Effect on unit g raph of varying horizontal
warp coefficient--RH-0 .7, RH•l.2 ••••
Effect on unit graph of varying both
coefficients simultaneously--RV=l.l, RHc0.8 •••..
Effect on unit graph of varying both
coefficients simultane ously--RV•O.S, RH•l.2 •
~~justment strategy (precipitation) •••
Adj ustment strategy (unit hvdrograph)
Schematic of forecast procedure with CHAT
adjustment strategy • • •••••••••
Example 1, NFORC=6 . . . . . . . . .
Example 1, NFORC=7 . . .
Example 1, NFORC=8 . . . .
Example 1, NFORC=9 . . . .
Example 1, NFORC=lO . . . . .
Example 1, NFORC=ll . . . . . . . . .
Example 1, NFORC=l2 . . . . . . . .
v
. .
.
.
. . . .
. . . .
. . . .
Page
18
19
25
25
26
26
27
27
32
33
46
58
59
60
61
62
63
64
Figure Page
6 .8 Example 1 • NF f\RC..'=l3 . . . . . . 6 5
6 .9 Ex..!mple l , NFOR C=l4 66
6 .10 Example l • ~FORC=l 5 67
6 .11 Example 1 , :\FORC=l6 68
6 . 12 Exampl~ 1 • NFORC=l7 69
6 .13 Example 1 , ~FORC=2 1 . . . . 70
6 .1 ... example ') .... . ~FOR C=1 73
6 .15 Example ') NFORC =4 74 -,
6 .16 Exampl~ 2 , t\FORC=S 7:
b . 17 ::'<amp le ') ::FORC =6 7f:. -. . . . .
6 .18 Example ) ~FORC= 7 77 -. . . . .
6.19 Example ") t-;FORC =8 78 -'
6 .20 Exam j)l e ') -. ~!FOR C=9 . . . . . 79
6 .21 t.xample 'I ~FORC=l O 30 -, . . . . . . . . .
6 . 22 Examp le 2 , ;-J FORC=ll . . . . . . 8 1
6.23 Example 2 , NF CJR C=l2 82
6 .24 Example 2 , ~FORC=l 3 . . . . 83
6 .25 Exampl e 2 ' NFI.RC=l4 . . . . . 84
6 .26 Example 3 , ~FORC=3 87
6 . 2 7 Ex ample 3 , NFORC=4 . . . . 88
6 . 28 Example 3 , NFORC=S 89
6 .29 Example 3 , NF OR C=6 90
6 .30 Exam ple 3 , ~FORC=7 91
Vl
Figure Page
6.31 Example 4, NFORC=7 94
6 .32 Example 4, N~ORC=8 . . . . 95
6.33 Example 4, NFORC=9 . . . . . . . . . 96
6 . 34 Example 4, NFORC =lO . . . . . . . . . . 97
6 .35 Example 5, NFORC=4 . . . . 99
6 .36 Example 5 , NFORC=S . . . . 100
6 .37 Example 5, NFORC=6 . . . . . . . . . 101
6 .38 Example 5 , NFORC =7 . . . . 10 2
6 .39 Example 5, NFORC =8 . . . . . . . . 103
6 .40 Example 5, NFORC =9 . . . . 104
6. 41 Example 6, NFORC=7 . . . . 108
6.42 Example 6, NFORC=9 . . . . 109
6 .43 Examp le 6, NFORC=ll . . . . . 110
6.44 Example 6, NFORC=l2 111
6 .45 Example 6, NFORC=14 . . . . . . . . . 112
6 .46 Example 6, NFORC=l5 . . . . . . 113
6 .47 Example 6, NFORCo:::16 . 114
6 .48 Example 6, NFORC=l7 . . . . . . 1 ~5
6 .49 Example 6, NFORC:ul8 . . . . . . 116
vii
Table
5.1
LIST OF TABLES
Page
List of CHAT parameter s • • . • • • . • • • • • • • • • 42
v ii i
IMPROVEMENT OF HYDROLOGIC SIMULAT ION BY UTILIZING OBSERVED
DISCHAR GE AS AN INDIRE CT INPUT
(COMPUTED HYDROGRAPH ADJUSTMENT TECHNIQUE--CHAT )
Walter T. Sittner and Kay M. Krouse
Office of Hydrology
National Weather Service, NOAA
ABSTRACT. A computerized tec hnique is presented
whereby the output of a conti nuous conceptual hydrologic
model is adj us ted in real time to agr ee with the obser-
vations of discharge. Since the discharge generated by
the model in response to a moisture input is dependent
upon the current values of the state variables of the
model, the procedure also adjusts the state variables
to correspond to the output. The technique is appli-
cable to ou t flow from headwater ca t c hments during
runoff events that result from liquid precipitation.
Its approach is to make adjusLments, iteratively and
simultaneously, to the precipitation and the shape of
the unit graph unti l the model produces a simulation
that agrees, within reasonable limits, with the
discharge observations. Examples of the performance
of the procedure under a variety of hydrologic condi-
tions are included.
1. INTRODUCTION AND BACKGROUND
River forecasting is a process in which hydrologic models, using
meteorological variables as their inputs, are used to c ompute streamflow
hyd rog raphs for a period into the future. Such a computed hydrograph,
or s i mula tion, is continuous from the time the meteorological observa-
tions are made up to, a nd probably beyond, some critica l time in
the future. In flood forecasting that c rit i c al time may be the time
of the crest or the time some lesser but signif icant stage is reached.
During the interim, which may be as short as a few hours, or as long
as several weeks, the forecaster normally has available a number
of observations of the quantity he has computed, stage or discharge.
He has the oppo rtunity t o compare t he observed quantities with the
values indicated by his simulation at the times the observations
were made. The comparison almost always discloses differences, some-
times very large ones. The next step in the forecas ting process
is to somehow revise, or adjust, the simulation so that it agrees
with the observations , and such an adjustment normally has some effect
on the portio n o f the simulation that defines the response of the
ri ve r during the critical time period in the future. The hydrologic
simulation, revised on the basis of observed river stage or discharge,
is what constitutes the forecast. Thus, observed river stage is
normally one of the i nputs t o a forecast, but it is not an input
to the hydro logic model since it has no effect on the output of that
model.
The problem of adjusting computed hydrographs to agree with river
o bservations has existed ever since river forecasting activities
began . Prior to the early 1960's, the computations involved in river
forecasting were done manually . The computed hydrograph was normally
dis played as a hand-drawn curve on a sheet of cross-section paper.
The observations were plotted on the same sheet and the adjustment
p r o cess consisted of sketching in a revised hydrograph that coincided
with the observations . The portion of the revised hydrograph subsequent
to the time of the latest observation was based in part on the computed
graph but could not, of course, be exactly equal to it. While the
making of the adjustment was a very simple procedure, the decision
a s t o how to make the adjustment was not simple. It was, of necessity ,
a highly subjective process and in cases where the discrepancies
were large, demanded a high degree of skill and judgment from the
forecaster.
When the practice of having computers perform the mathematical
c omputations involved in forecasting began, the adjustment problem
became a bit more complicated. There appeared to be two alternatives
available. The first, which has come t o be known as "manual" adjust-
ment, c onsists of the f o recaster v iewing some sort of machine-produced
display , which shows both the computed hydrograph and the observations,
then making a subjective decision as t o how the hydrograph should
be adjusted, and instructing the computer to make such an adjustment.
Thus, with this alternative, the decisions concerning adjustments
are made in precisely the same manner as in a wholly manual operation,
and the on ly additional programming required is a relatively simple
routine to permit the forecaster to input his adjustment decision
and have it executed.
The second alternative, c alled "automatic" :idjustment, consists
of programming the computer to make the adjustment decisions and
then carry them out . This involves no human intervention whatsoever.
The question of whether or not a computer can be programmed to satis-
factorily model the human thought process involved in such decisions
is highly debatable and has been debated at length over the years.
Suffice it to say that the adjustment routines that have been devised
and used for this purpose have been, almost without exception, rather
simple "blending" procedures that gradually merged the partial observed
hydrog raph into the computed graph in a pre-determined manner and
without any regard for the condition that caused them to differ
in the first place.
ln c omputerizing a river forecast o peration, the decision as to
whether to make the adjustments manually or automatic ally must be
2
based on the answers to two questions. First, ~a suitable automatic
technique be devised and programmed; second, shoulri this be done
by computer rather than manually. With the type of hydrologic models
used by the National Weather Service (NWS) prior to the early 1970's
(A.P. I.-type rainfall-runoff analysis), the answer t o the first question
was probably "no," thereby rendering the second question superfluous.
If the answer to the first question were in fa c t "yes," the second
question might be difficult to answer. The making of such decisions
manually involves rather complex mental processes, but they are not
very time consuming. There is no question that any coffiputerized
forecast operation must be designed in such a wa y as to permit the
forecaster to monito r various steps in the process rather than simply
observe the final result. Such monitoring helps him to assess the
nature of the situation at hand and to interpret the simulations
that the computer produces. Since provision for such monitoring
must be made, there is nc c ompelling reason not to also provide for
actual intervention by the f o re c aster at any step in the process.
The adoption by the NWS in 1971 of continuous conceptual hydrologic
models as the standard for forecasting casts an entirely different
light on this matter. The decision to make the change was based
on a number of factors, one of the most important being that the
conceptual models provide an accuracy advantage o ver the API method.
This advantage, when judged on the basis of statistical error summaries
of long simulations, appears to be slight. Closer examination, however,
reveals that the overall improvement results from vastly better a c curacy
being achieved in certain small portions of the simulation. That
is, there are some hydrologic regimes and some t y pes of events li1
whic h the conceptual models yield errors at least an order of magnitude
smaller than those obtained with ~~I . Thus, the adoption of conceptual
models can be expected to make only a small difference in the average
size of the discrepancy between computed and observed streamflow.
The maximum, or extreme discrepancies a f ,orecaster may expect to
enc ounter, however, should be greatly reduc ed . Since the making o f
hydrograph adjustments is ~ot particularly difficult when the dis-
crepancies are small, the adoption of a model that greatly reduces
the extreme simulation errors also simplifies the adjustment process.
For this reason, it seems logical to conclude tha t while an ac c eptable
computerized decision-making algorithm may have been an impossibility
when the raw simulations were being made with an API-type model,
it may well be possible to accomplish this when the adjustments
are to be applied to the output of a c onceptual mod•~!. Thus, in
the present era of river forecasting, the answer t o the first of
the two questions is probably "yes."
In regard to the sec ond questi on, the pic ture is also different
since the adjustment of the simulated hydrograph to agree with the
observations is no longer the only thing to be accomplished. The
nature of the accuracy advantage achieved with a conceptual model
has been explained . The rea son for it has not, but that reason i s
that the conceptual model has a longer "hydrolog i c memory" than does
the API sys tem. That is, the state variables inv olved in an API-
type rainfall-runoff relationship are virtually unaffected by any
3
hydrologic activity occurring more than about 1 month pri"r to the
time in question and so the model cannot duplicate the typ,~ of event
in which the actual response of the river is affected by occurrences
several months earlier. The conceptual model on the other hand involves
a rather complex soil moisture accounting system, which 1s capable
of reflecting events that took place months or even years earlier.
The Sacramento catchment model contains five state variables that
represent the quantity of water in storage in various parts of the
soil mantle. The discharge generated by the model in response to
a moisture input is dependent upon the current values of these five
variables. If at any time the simulated discharge is not in satis-
factory agreement with that being observed, it follows that one or
more of the state variables differ from their true values by an un-
acceptable amount. Because of the model's long memory, this condition
may have a harmful effect on the accuracy of simulation of the ~
runoff event and should therefore be corrected along with the model
output. The conclusion then is that in order to realize the accuracy
of which a conceptual model is capable, it is necessary to adjust
not only the model output to agree with the observed discharge but
also to adjust the state variables to correspond to the output.
Any procedure that can accomplish this must obviously have a complexity
comparable to that of the model itself, and it is therefore not realistic
to think in term& oi cxecucing the procedure manually. Since the
procedure requires voluminous computations, the answer to the second
question is also in the a~firmative.
What is required then for use with conceptual forecast models is
a computerized procedure that adjusts the state variables of the
model in such a way that they produce a model output that agrees,
within reasonable limits, with the observed discharge. Such a pro-
cedure, called CHAT (Ccmputed Hydrograph Adjustment Technique), is
being developed and if1 th~ subject of t!ds technical memorandum.
The two requirement~ that the procedure must fulfill are : the soil
moisture accotmting variables be adjusted along with the output
and the adjusted output be at least as good as that which might be
arrived at subjecti~·<>.ly by a skilled human forecaster.
4
I_
2. STATUS OF RESEARCH
The adjustment of computed hydrographs under all conditions encoun-
tered in a river forecasting operation requires the capability of
dealing with all of the hydrologic conditions and situations that
occur in a river system. The requirements for the technique as
described in the previous section and the method of approach to be
described in the next section indicate the definition of four problem
areas and the development of different but similar techniques applicable
to each. These four areas are associated with four phases of research
as follows:
Phase 1. Development of an adjustment technique applicable to
catchment outflow during runoff events resulting from liquid precip-
itation only.
Phase 2. Development of an adjustment technique applicable to
catchment outflow during runoff events in which snowmelt is involved.
Phase 3. Development of an adjustment technique applicable to
catchment outflow during low-water periods.
Phase 4. Development of an adjustment technique applicable to
points in a river system that are not at the outlets of individual
catchments.
Research work to date has been concerned only with the phase 1
problem, and the method presented in this technical memorandum is
intended to be applicable only to the phase 1 problem. In chapter 7,
"Suggestions for Future Research," some thoughts concerning possible
solutions of the phase 2, 3, and 4 problems are presented.
The solution to the phase 1 problem that is described in subsequent
sections, while not presented as an interim v ersion, at the same
time is not presented as a completely perfected technique either.
The distinction lies in the fact that the authors view this technique
as workable and ready for immediate operational use (without further
planned research) but with full realization that modifications and
improvements to the procedure will undoubtedly evolve from extended
use in the field.
5
3. THEORY
When a simulated hydrograph is compared with observed values of
diacharge, the discrepancy noted is the combined effect of four
error sources:
1. Errors in model input data
z. Errors in model )arameters
3. Errors in model structure
4. Errors in observed discharge
The basic concep t of CHAT is that if the true values of the input
data were known and were applied to the model, then the discrepancy
in the output would result only from error types 2, 3, and 4 and
that if this could be accomplished two conditions would then exist.
First, the values of the intermediate state variables would be about
as close to their true values as the model is c apable of making them
and therefore so close that the potential accuracy of the model could
be realized in the simulation of a future runoff event. Second,
the discrepancy resulting from erro r types 2, 3, and 4 would be small
enough that it could be either ignored or reconciled by a "blending"
algorithm . These contentions involve the assumptions that the model
parameters being used have been c arefully determined and are c lose
to their true values and that the errors in the o bserved discha~ge
are small compared to other errors in the modelling procedure .
The second contention involves the additional assumption that the
model structure is a good enough representation of the physical
process that it cannot in itself be responsible for gross errors
in simulated discharge. It was stated in the "Introduction and Back-
ground" section that an automatic adjustment technique for use with
an API forecast model may be an impossibility but could be feasible
when the simulations are made with a conceptual model. That statement
relies heavily on this assumption . An API-type model is capable
of yielding gross errors even with perfect parameters and per f ect
data. Hopefully, the con cep tual model is not. The re is, however,
an exception t o this which must be recognized and dealt with, and
that is the manner in whi ch the model converts runoff volumes to
the ordinates of a discharge hydrograph. This is accomplished through
the use of a unit hydrograph, which models a no nlinear time va riant
process with an algorithm which is both linear and time invariant.
There are available, of course , model modifications that make it
possible to apply a degree of flexibility and nonlinearity to th e
response function which the unit hydrograph models. The fact remains,
how tver , that even if the unit hydrograph, whi ch is a model parameter,
could be evaluated exactly, it would still represent an average runoff
distribution that may differ greatly from the dis tribution in a specific
event. This inability of the model to duplicate a hydrograph resulting
6
from an unusual runoff distribution is a limitation of the model
structure and can be the source of large discrepancies between the
simulated and true hydrographs. It follows then that in such cases
there must exist a unit hydrograph, somewhat different from the average,
that, if used by the model for the specific event, would produce
a simulated hydrograph in close agreement with the observed. CHAT,
as will be shown later, has the capability of detecting such anomalies
and modifying the unit hydrograph accordingly, thus eliminating the
gross discrepancy that would otherwise result.
The approach used to apply this concept is to make adjustments,
iteratively and simultaneously, tc both the input data and the shape
of the unit hydrograph until the model produces a simulation that
is in satisfactory agreement with the discharge observations.
"Satisfactory agreement," in this context. means that the discrepancy
is small enough to be reasonably attributable to error types 2, 3,
and 4 as defined above but not including gross errors resulting from
large differences between the actual runoff distribution and that
assumed by the unit hydrograph. For the phase 1 study, the only
input data types involved are liquid precipitation and potential
evaporation. Since the effect of the errors in evaporation data
during runoff events is thought to be negligible, only the precipitation
is adjusted. It might be noted at this point that the precipitation
input to the model c ·:>n sists of areal means (MAP) rather than point
amounts. These means are normally determined by analyzing the point
precipitation measu&:ed with rain gages. While sizeable simulation
erro rs c an be attributed to the precipitation input, they originate
mostly in the conversion of point amounts to areal means rather than
from errors in point measurement.
When satisfactory agreement has been achieved by adjusting both
the precipitation and the unit hydrograph 11 five conditions are assumed
to exist:
1. The adjusted precipitation data are a c loser approximation
to the true precipitation than was the original data derived from
rain gage observations.
2. The adjusted unit hydrograph expresses the runoff distribution
of the event more closely than does the average unit hydrograph
derived from historical records.
3. The values of the state variables are closer approximations
to the true values than those that would be genetated by applying
the original precipitation data to the model.
4 . The agreement between the simulated hydrograph and the observed
discharge is close enough that the difference can either be ignored
or resolved by "blending."
7
5 . The portion of the simulated hydrograph subsequent to the
time of the last discharge observation con tains all available infor-
ma tion conce rning the event and does in fact constitute a forecast.
To ttuly achieve these five condi tions requires that the adjustments
be mad e in a manner consistent with the underlying rationale. The
details of making the adjustments are explained in subsequent sections.
To appr eciate the reasons for performing the operations in the manner
descr ibed requires the unde rstanding of a numbe r of subtle but extremely
important aspects of the technique.
1 . CHAT utilizes an objective function as an indicator of the
extent of the disagreement between simula ted and observed discharge.
Const raints are used to limit the values that may be assigned to
the decision variable s. precipitation and the unit hydrograph a djustment
co !ficients. Thus, CH AT resembles a conventional optimizing procedure.
Unlike ·onventional optimizing howev er, CHAT does not seek to minimize
the obJecti .. •n f unc tion subject to the constraints oothe decision
va riables . Rather, it reduces the o bjective function to an acceptable
value while making the s mallest po ssible c hanges in the decision
variables .
2 . Adjustments applied to the ~it hydrograph affect the simulated
hyd r og raph but have no direct effect on the soil mcisture accounting
state variables . They do, however, affe c t these state variables
indirectly by influencing the adjustments t h at are made to the pre-
cipitation input.
3 . In mos t cases , it would probably be possible to make precip-
i t ation a djustments that would reduc e the objective function to a
value c on side rably smaller than tha~ which is considered acceptable.
To do so would be t o adjust the precipitation in order to minimize
discrepancies that originate from o ther factors. This would produce
values of adjusted precipitation, values of state variables, and
a f uture s i mulation tha t would be further from their true values
than those that result from stopping the adjustment procedure at
the app ropria t e point.
4 . CHAT will not necessarily always make adj ustments to the input
data . If, at a ny po int in the forecasting process, the difference
between the observed discharge a nd the simulation resulting from the
input data as adjusted at the previous forecast time is within
limits, CHAT will recognize this condi tion and make no adjustments.
8
4. COMPONENT PARTS
The application of the CHAT adjustment procedure involves six
mathematical algorithms in addition to the hydrologic model itself.
These can oe thought of as component parts of the CHAT package.
Each has been coded in the form of a computer subroutine and the
adjustment procedure is accomplished by calling those subroutines
and that representing the hydrologic model. The six parts and their
associated subroutine names are:
1. Objective function OBJEC
2. Tolerance TOL
3. Unit hydrograph adjustment WARP
4. Adjustment strategy STRAT
S o Observed discharge interpolation INTERP
6. Blending routine BLEND
In this section, the rationale and mathematical formulations involved
in each of these parts are discussed. Listings of the subroutines
themselves appear in Appendix A.
Objective Function
The objective function is a numerical measure of the difference
between a simulated hydrograph and a group of one or more discharge
observations. It serves two purposes in the technique. First, during
the iterative adjustment process, changes in the value of the objective
function indicate whether the fit is improving or degrading. Second,
when the objective function has been reduced to a pre-determined
acceptable value, the "tolerance," the agreement between the observat-
ions, and the computed hydrograph is considered satisfactory and
the adjustment process ceases.
The function compares an array of computed discharges, spaced 6 hours
apart, with a corresponding array of observed dis.~harge values.
The function involves the observed and computed discharge at each
6-hour ordinate, up to the latest observed discharge. If the latest
observation is not at the time of a 6-hour ordinate, the function
involves all ordinates up to the one immediately preceding that
observation and in addition that observation and the corresponding
computed discharge, which is obtained by linear interpolation.
9
The "observed" discharge values are, of course, in most caces,
obtained by applying stage observations to a stage-discharge relation-
ship. In practice, such observations often do not exactly coincide
with the 6-hour ordinates of the computed discharge array and missing
observations are coiiiDon. The observed discharge interpolation procedure
(subroutine INTERP) computes a matching array of observed discharge
ordinates based on whatever randomly spaced observations happen to
be available.
The basic equation for the objective function is:
OF •
where:
N~B WD(L) (WT(L)DQ(L)~t(L)QO(L))
L-1
NOB
1:
L•l
(4 .1)
NOB is the number, in the discharge arrays, of the ordinate at
the time of the latest observed discharge. If the latest
observation is not at the time of a 6-hour ordinate, then
NOB is the number of the ordinate immediately preceding that
observation.
WD(L) is a weight related to the time interval between ordinate,
L, and the latest observation. That is, the most recent
ordinates are considered more significant than the earlier
ones. The weight is given by:
WD(L) • (L/TLO)EX2. (4.2)
TLO is the time of the greatest observed discharge, referred
to the array indexing scale. During the rising limb of the
hydrograph, this is usually the latest observation. If this
discharge value coincides with an ordinate, then TLO is an
integer. If it is the largest observation and does not coincide
with an ordinate, then TLO • NOB plus some amount less than
unity. EX2 is an exponent that permits the variation of
the weight with time to be made nonlinear. The research
indicates that an appropriate value for EX2 is 2 or 3.
The rationale behind considering the most recent ordinates
more important than earlier ones involves the concept of
the forecast or future portion of the simulated hydrograph
being an extension of the earlier portion. While both portions
are generated by the model in the same way, the earller portion
is compared with, and directly controlled by, the observed
discharge. The future portion is controlled only indirectly.
10
DQ(L)
WT(L)
QO(L)
To avoid unrealistic discontinuities between the observed
partial hydrograph and the extension part of the simulation
and thereby reduce the chance of having large errors in the
forecast, it is necessary ~o achieve rather close agree-
ment in the vicinity of ~he transition.
This rationale applies only on the rising limb of the hydro-
graph. Once past the peak, the procedure is more concerned
with adjusting the volume under the entire hydrograph. There-
fore, ordinates further down the recession are not necessarily
any more significant than earlier ones. For this reason, the
value of WD(L) becomes unity at the peak and remains unity for
all L>TLO .
is the absolute value of the difference between the observed
and computed discharge at ordinate, L.
is a ~iming weight. It reflects the fact that discharge
observations are subject to errors in time as well as magnitude
and that, in addition, the structure of the model precludes
its being able to achieve a fine time discrimination in the
output. Thus, in a steep portion of the hydrograph, it is
possible to have large values of J>Q(L) when the only real
disagreement between the simulation and the observations
is a small timing error. The timing weight prevents such
discharge discrepancies from contributing heavily to the
objective function . The weight is computed by de~ermining
the value of DT, the time interv£.1 between ordinate L, and
the nearest simulated discharge equal to the observed discharge
at ordinate, L. Then,
If DT < 3 hours, WT(L) = 0
If DT ~ 12 hours, WT(L) = 1
If 3 < DT < 12, WT(L) = (DT-3)/9.
In order for a WT(L) of less than unity to be used, it must
result from matching discharges at points where the two
hydrographs have similar slopes. That :1..s, if the observed
hydrograph at ordinate, L, has a positive slope and if the
segment of the simulated hydrograph in which the matching
discharge is found has a negative slope, or if the reverse
is true, then that matching discharge is ignored.
is the observed discharge at ordinate, L.
11
WM(L) is a slope weight. Its p\.trpose is to increase the objective
function when the two hydrographs, at an ordinate, agree
closely in magnitude but have vastly different slopes.
In Eq. 4.1, the product of WM(L) and QO(L) is added to the
product of DQ (L) and 'WT(L). Thus, WM(L) must be computed
in ~uch a way that if the degree of mismatch expressed by
the first product is the same as the degree of miE~-match
expressed by the second, then the two produc t.s will be of
equal magnitude numerically. In regard to WT(L)DQ(L), the
"worst case" situation might be thought of as that in which
the discharge error is 100 percent of the observed discharge
and WT(L)=l. In this case, the product is equal to the observed
discharge, QO(L). This produc t is computed every 6 hours.
Consequently, an equally serious slope mis-match would be
the case in which the difference in slope of the two hydrograpbs
is such that in 6 hours, they diverge by an amount equal
to the observed discharge. In this case, the second product
must be equal to QO{L) and thus, WM(L) must be unity. WM(L)
is then given by:
WM(L) = ABS[(S -S )/QO(L)]
0 c (4. 3)
but no t greater than 1.0.
Where S and S are the slopes, in ems per 6 hours, of the
observe8 and simulated hydrographs. The slopes, at each
point, are computed in the manner described in regard to
Subroutine lNTERP (~age 39 ). The slope at the last point
on the observed bydrograph is, of necessity, computed as
a straight line slope. The slope of the simulated hydrograph
at the same point is, for the sake of consistency, computed
the same way, even though simulated points later in time
are available.
Note that the computation of WH(L) involves dividing by QO{L)
and that in Eq. 4.1, 'W!-I(L) is multiplied by QO (L). This
is not an unnecessary step since i .n the case where ~S -s )
is greater than QO(L) 11 the weight is "topped off" at RniEy.
Weight WM(L) is subject to one final adjustment. If, within
12 hours of the ordinate, the simulated hydrograph exhibits
a slope equal to that of the observed hydrograph at the or-
dinate, then WM(L) is reduced in value. The formulation
is identical to that used in computing weight, W!(L).
12
The objective function computed as described from Eq. 4 .1 i s valid
only for the case in which the latest observed discharge is a t the
time of ordinate, NOB. If this is not the c ase, the contribution
of the partial 6-hour period must be included and the function is
computed by:
:!:WD(L){WT(L)DQ(L)~(L)QO(L)]+ PJ[(WTLT)(DQLT);(WMLT)(QOLT)J
OF = =-;;;;_---------~---------------( 4. 4 ) NOB
whe r e:
E WD(L) + PJ
L•l
wr LT is the t i ming weight, WT, at the time of t he l a st observation.
DQ LT is the absolute discharge difference, DQ, at the time o f
the last observation.
WMLT is the slope weight, WM, at the time of the last obse rvation.
QOLT is the observed discharge at the time of the last observation.
PJ is one-sixth of the time interval f rom ordinate NOB to the
last observation. PJ must alwayt; be greater t h an zer o and
less than uni ty.
Eq. (4.4) is essentially the same as Eq. (4.1) but gives a weight
of PJ to the last ordinate and weights of unity to all previous or-
dinates. It should be noted that the second term of the numerator
of Eq. (4.4) is weighted not only by PJ but also b:' its value of
weight, WD. This weight, however, must be unity at this point and
hence does not appear in the equation. It should also be noted that
the summation of weights WD in the denominato r is f rom ordinate 1
to ordinate NOB and does not include the unit value of WD that occurs
at ordinate NOB + PJ.
The rationale and formulations described above are intended to
model, to some degree, the thought processes which a human forecaster
uses in judging the seriousness of a disagreement between the rising
limb of a simulated hydrogra ph and a group of disc harge observations.
The major objective in maki ng such a judg ement is to decide if a
future portion (the peak) of the simulated hydrograph represents
a valid forecast. After the peak has been observed, however, there
is no forecast to make, with the possible exception of a recession
forecast. CHAT however, as explained in Chapter 1, has a dual purpose:
to adjust the simulation to produce an a cceptable forecast and to
come out of the runoff event with a set of values for the s o il moisture
variables which are closer to the true values than thos e which would
13
be yielCed b y t:he "raw" simulation. To accomplish this l.atte~ puqr~
CHAT keeps ou working right down the r e c ession.
to/hen the entire hydrograph , o r a major port:ion of i t has been o b-
s erve d, it has been found that the use of a more statistically b ased
e rror func t ion to guide the adjusting process gives results s uperi.or
t.o those obtained with the function d escribed a bov e, as t:hat f unction
embodies c oncepts a ppropriate to fo recasting a peak. as opposed to
f itting an entire hydr og.raph . Conse quently , the subroutine also
compu tes the root mean square error of the 6 hourly discharges~ RMS.
Up to the time of the observed pe ak., the o bjectiv e f unction is equal
to the value computed from Eq. 4 .1 or 4 . 4 ; wh en the t ime f rom begi nning
of the event to the p resent i s g reater than twice the t ime f rom ~
beginning to the p e ak, the o bj e ctive function i s equal t o the RMS.
In the intervening period , i t i s a weighted average of the ~.
S ince the RMS may b e combined with the basic objectiv e function
and since it is compared with the tolerance, it must b e c omputed
in such a way that similar d egrees of ag-reement will yield a b asic
obj e c t ive function and an RMS of similar magnitude. Experience has
shown that this may b e accomplishe d by c omputing the true RMS and
then mu l tiplying i t by 0.25 .
The obj ective f unction then i s computed as follows:
Th e b asic v alue is determined f rom Eq. 4 .1 o r 4 .4 .
The RMS i s computed as :
[
NOB l RMS = 0.25 SQRT L (DQ(L)2 )/NOB .
1 =1
(4 .5)
If the last observation is a partial ordinate, it i s included, suitably
weighted .
Then, a weighting f actor , WF , i s d etermined;
WF = 2 -(PJ+NOB)/MPT (4 .6)
but not l ess than z e ro nor greater than u nity . PJ and NO B are as
p revio usly defined and HPT is the time of the p eak on the array inciexing
scale .
Finally:
OF= (OF)(WF) + (RMS)(l-WF). (4 . 7)
14
Tolerance
The tolerance is the maximum value the objective function may have
while representing a satisfactory agreement between the observed
and cou:.puted hydrographs. As such, it is a quantity that must have
the same dimensions as the objective function, and, in addition,
the manner in which it is computed must be related to the manner
in which the objective funct.ion is computed. The objective function
is essentially a weighted mean discharge, and so the tolerance is
also expressed in units of discharge. Its value is dependent upon
two factors, the magnitude of the discharge that is contributing
most heavily to the objective function and how far the runoff event
bas progressed at the time the computation is made.
The tolerance is related to discharge because both modelling errors
and errors in discharge observations tend to increase in magnitude
along with the discharge itself. Thus, if the tolerance is to be
thought of as a measure of error types 2, 3, and 4 as defined in
the section on "Theory," it must increase as the discharge increases.
As the runoff event progresses from the beginning of the rise,
past the peak and on down the recession, an ever greater portion
of the runoff can be thought of as being "observed." Typically,
at the time the peak occurs, only about 35 to 40 percent of the runoff
volume (upper level compo112nts) bas passed the gage. When just half
of the time from beginning of rise to peak has elapsed, the figure
ia 5 to 10 percent. It follows then that if an attempt is made to
obtain a close tit early in the rise, based on only a s~ll portion
of the observed runoff, that the effect of observational errors and
of imperfections in the method will be magnified. This is avoided
by using a very large tolerance at the beginning of the rise and
gradually "tightening" it as more of the observed hydrograph becomes
available.
The to 1 erance is computed by the fullowing equation:
TOL PCOB ---WP (4. 8)
where:
PCOB ~s a fixed percentage of either the latest observed discharge,
QO(NOB) or QOLT, or of the average observed discharge up
to that time, whichever is greater. The ·percentage to be
~sed. expressed as the coeffici ent, PCENT, depends on the
stability of the stage-discharge relationship. A typical
value would probably be about 5 to 10 percent. Values of
0.05, 0.075, and 0.1 have been used in the investigation.
15
!he middle iT al uc, 0 .0 75-, s eems to give the best resul.ts. All
c ases t ha ': were s tudied have inv ulved reasonably staiJle
stage-·aisch arge relationships. Normally, PCO:S i s based
ca the l ates t observed d ischarge up to a f ew in~e.rvals pasc
t he peak and t hen the average observed discha r ge begins to
exceed the lates t o bse.-ve d and become s the basis f or co~u t
ing t h e t o leranc e .
ifF expresses the relat ions hip, in time, between the c urrent time
and the sta ge of d evelopmen t o f the rwtoff event. I t i s
given by :
--rzz JEXl WP MP T , but no t g reater than unity. (4 .9)
ZZ i s the o r d inate number co rrespondi ng to the latest o bserved
d isch a r g e; t hat is , NOB + PJ.
HPT i s the o rdinate numb e r co rresponding to the p eak of the
hy drograph . Conceptua lly , this is the peak of the observed
hy drograph , bu t, in the c omputations, it is based o n the
s imulation . Th e reason is that p rior to the peak (ZZ<MP T),
i t bas not b een observed. Subsequent to the peak (ZZ>}~T ),
the two are e ssential ly the same . The s imulated hydrograph
f rom which MPT is d etermined is that which wa s obtained by
applying adjustments a t earlier time periods bu t b efore any
a d j ustments are made at t he time in question .
I n a case where the runo f f event begins on the recession of a
p revio us event , it is p ossible f or the latest simulated o rdinate to
be smaller t han the f irst o rdinate on t he observed/simulated hy dro-
g raph. Obviously , the f irst ordinate , whil e l argest in the array,
s hould not be considered t he pe a k f or purposes of computing MPT .
To p rev e nt it from being used t h is way, a t each time period the time
of t he center o f mass o f the observed p rec ipitation is d etermined
and the v alue o f MPT is constrained t o a v alue no less than this.
EXl i s an expo nent wh i c h permits t he v a riation of w~ with
t ime t o be made nonlinear. A value o f 2 has been used in
the investigation.
I t should be noted here that the q uan tity , WP , o r some o ther function
related to the de velopment of the event, c ould have been applied
to the objective function r ather than t o the tolera nce . Tha t is,
dec reasing the obj e c t ive function ear ly in the rise o r increasing
the tolerance would accomplish the same thing.
16
Another point, which has been noted earlier, is that the computation
of the objective function and the tolerance, or the execution of
CHAT itself, after the peak has passed is obviously unnecessary for
purposes of forecasting the peak. The reason for continuing to make
adjustments until the end of the event is to have the final adjusted
values of the soil moisture accounting state variables be influenced
by all of the observed discharge data. This is accomplished by fitting
the entire hydrograph to observed data rather than just the rising
limb.
Figure 4.1 illustrates the variation of the tolerance with time
and with discharge for a typically shaped hydrograph. Note that
at the beginning of the rise the tolerance is quite large. Up until
approximately the time of ordinate no. 3, the tolerance is so large
compared to the discharge values involved that it is very easily
satisfied and it is not likely that any adjustments would be made.
And none should be made on the basis of such a small part of the
observed hydrograph. As the rise develops, the tolerance follows
a generally downward trend in a c tual value and becomes much smaller
in relation to the magnitude of the discharge being experienced.
Finally, at ordinate no. 6, when t he peak and 37 percent of the runoff
have been observed, it is quite restrictive. Following the peak,
the tolerance drops off rather rapidly as each increment of time
produces a large increase in the percentage of runoff that has been
observed and, consequently , a large improvement in the reliability
of the adjustment procedure. At the time of ordinate no. 9, the
average observed discharge at:tains a value equal to the current dis-
charge. Prom that point on, PCOB is based on the average discharge
and the tolerance decreases much more slowly. This prevents it from
dropping off to very small values which would be virtually impossi.ble
to satisfy.
Un it Hydrograph Adjustment
As has been explained, the purpose of the unit hydrograph adjustment
algorithm is to convert the unit hydrograph representing average
runoff conditions to one that reflects the runoff distribution exhibited
by the specific event that is being simulated. Such a hydrograph
is assumed to be generally similar in shape to the average graph
but to differ somewhat in sharpness and in timing. This is to be
accomplished under the control of a numerical optimization strategy.
That is, the altered hydrograph must be related to the original by
a series of numerical values that are manipulated by the program
in a manner similar to the manipulation performed on the precipitation
input data.
17
0
N
~
...
v.
o-
.....
OCD
:ID
c
z-o
>
~
m ....
0
z
c
~
CD
m
:ID
N
(.)
~
"'
o-
.....
0
• ••
0
0
N
0
0
DISCHARGE
~
0
0
"' 0
0
• •• ••• •• ··r •• , ossERvEo
\ '-.,.
p '··· rt '······ ~ ······ .. I ... ····· ' .. 0 \ ······· I : ? ~
~
~
I '
~ ...,
" /i -I .... m
cb2 )(
I~ II 1: N
~~ 12~ 0 -
~~ I .CI»
~; I! I ~
<f.::.. /§ I
cJ)
I
&
I
WP
18
o-
0
0
....,
0
0
Q) e
..-4
""
.c
"" Tl
3
'0 .::
Ill
Q)
00 ....
<U .c
CJ
Ill
..-4
"0
.c
"" ""' 3
Q)
u
~
<U ....
Q)
r-i
0
"" ~
0
c
0
..-4
"" IU
..-4 ....
IU > I
I
....j ..
..;;r
Q) ....
:l
00
..-4
j:Z..
The algorithm that performs this transformation is the "unit hydro-
graph warping" algorithm and is expressed by Subroutine WARP. The
manner in which the alteration takes place is defined by two "warp
coefficients," RH and RV. That is, the input to Subroutine WARP
is the original unit hydrograph, defined by its ordinates, and the
two warp coefficients. The output is the adjusted, or warped, unit
hydrograph. Figure 4.2 illustrates how this portion of the adjus~nt
technique operates.
Tolerance-+!
i
Adjustment
strategy
Q) > c:: .... 0
~ ....
CJ~
Q) CJ c::
.0 :l 016-4
OBJEC
Warp coefficients
RH & RV
Adjusted
simulated
hydro graph
·-
WARP
Hydrologic
model
Figure 4.2. -Relationship of WARP subroutine to other components.
19
The adj ustment strategy s e l ects values of the warp coef£icienrs,
RB and RV , and p asses them to the WARP subroutine. Using thesa
c oefficients, WARP OI>erates on the o riginal unit hydrograph to p roduce
a warped unit hydrograph, which it passes to the hydrologic modeL
The model p r o duces an adjusted s imulated hydrograph which reflects
the changes made in the unit hydrograph on the b asis of the warp
coefficients . The simulation is compared with the observed hydrograph
by Subr outine OBJEC , which computes the obj ectiv e f unction. The
adjustment s crategy then examines the o b j e ctive function to d etermine
whether the v alues of RH and RV that it s e lecte d have improved o r
d egraded the simulation . If an improvement h as b een made, the o b-
j e c tive f unction i s compared wi th the tolerance to d etermine i f
the f it is sat isfactory. ~ote that t h e adjust.ment s trategy works
wit h the warp coe fficients as i t might work with any o ther numerical
quantity and that i t ne v er "sees" the u nit hydrograph. Note also
that the hydrologic mod el wo r ks with the warped unit hydrograph
j ust as i t works with the o riginal unit hydrograph and n ever "sees"
the warp coefficients .
The actual t ransfo rmation i s accomplished by using the two coeffi-
c ients, RH (horizontal warp c oe fficient) a nd RV (vertical warp co-
efficient), to d efine a new position for the peak of the unit hydro-
g rap h . The algorithm then g enerates a new set of o rdinates repre-
s enting a g raph that peaks at the point so defined, that has the
s ame g eneral shape as the o riginal g raph , and that, o f c ourse, encloses
unit runoff. The posit ion o f the new p eak is defined by:
and
TP = (TP)(RH) A
QMXA = (QMX)(RV)
where: TP and TP A a re the original. and adjusted time intervals
f rom o r d inate no. 1 (zero discharge) to the peak,
(4.10)
(4 .11)
QMX and QMXA a re the o r iginal and adjusted peak discharge
values .
Thus, v ~:ues of RH l ess than u nity cause the peak to move tc the
left and values greater than unity move it to the right. Values
of RV l ess than unity move the peak down and values g reater than
unity move it up . If RH and RV are both equal to unity, WARP makes
no change in the unit hydrograph.
20
Tbe horizontal portion of the warping procedure is accomplished
by simply translating the hydrograph right or left far enough to
move the peak to the time defined by RH. After the translation,
the first and last ordinates are set to zero. In some cases, this
results in a small amount of volume being lost. As will be shown
later, however, this is automatically restored by the vertical portion
of the procedure.
The vertical portion of the warping procedure is accomplished by
adjusting each of the ordinates with the following equation:
where:
Q • Q * RV (l+A(l-CRV))B (4.12)
A RV
Q and QA are the original and adjusted values of the ordinate
and A and B are coefficients. CRV is the curvature of the
hydrograph at the ordinate in question. It is given by :
CRV • Q(N)
[Q(N-1) + Q(N+l)]/2 (4.13)
That is, CRV is greater than unity where the graph is concave
downward, less than unity where concave upward, and equal
to unity at inflection points. CRV is normally less than
unity for the lower portions of the rise and recession and
greater than unity just before, at, and just after the peak.
Given a unit hydrograph defined by a series of ordinates, Q, Eq. (4.12)
will generate a family of adjusted hydrographs, each set of values of
A and B de!: .ling a different graph. The definition of the vertical
warp coefficient, RV, however, requires (Eq . (4.11)) that the adjusted
peak discharge be equal to the product of RV and the original peak
discharge. Applying Eq. (4.12) to the peak and letting CMX represent
the curvature at the peak, Eq. (4.12) becomes:
Q*RV • Q*RV [l+A(~;CMX) r (4.14)
or
(.1 +A(l-CMX)) B z
l 1 . RV (4 .15)
21
For any value of the exponent B, other than zero, the expression
[l+A(l-CMX)]/RV mu.st be equal to unity. Solving for coefficient
A then gives:
RV -l Aa •
l-CMX (4 .16)
Thus, there is only one value of A that will produce the required
peak adjustment and it is given by Eq. (4.16). Since the unit hydro -
graph mu.st always be concave downward at the peak, CMX ~ust be greater
than unity. Therefore, the sign of coefficient A depends on whether
the vertical warp coefficient is greater or less than unity. That
is:
If RV > 1, A < 0
If RV < 1, A > 0 .
Looking again at Eq. (4.12), if the v alue of exponent B is 1.0, the
equation becomes:
QA = Q(l+A(l-CRV)].
Then, for a warp coefficient greater than unity, which increases
the peak, RV > 1, A < 0, and:
If CRV < 1, Q < Q A
If CRV= 1, Q = Q !
If CRV > 1, QA > Q
(4.17)
Conversely, with a warp coefficient less than unity , which decreases
the peak, RV < 1, A > 0, and:
If
If
CRV < 1,
CRV = 1,
QA > Q
Q = Q A
If CRV > 1, QA < Q .
This demonstrates the properties of Eq. (4.12). If RV i s greater
than unity, the peak and all ordinates above the inflection points
are increased. All ordinates below the inflection points are decreased.
If RV is less than unity, the reverse is true. In either case, if the
increase exactly balances the decrease, unit volume is maintained.
22
If the exponent B is not equal to 1.0, then the effect will be similar
but the transition will occur somewhat above or below the inflection
points. Applying Eq. (4.12) then with various values of exponent B
and with coefficient A defined by Eq. (4.16) will produce a family
of hydrographs all of wbich pass through the newly defined peak but
only one of which will enclose unit volume. The value of the exponent
that will accomplish this is determined by iteration. If a unit
hydrograph is warped horizontally and loses volume in the process
as explained earlier, that volume is restored during the vertical
warp by selecting a value of B that causes the volume to match that
of the original unit hydrograph prior to the h~rizontal translation.
The mathematical characteristics of the WARP algorithm require
a rather fine time discrimination in the ordinates defining the unit
hydrograph . The catchment model used with CHAT utilizes a 6-hour
duration unit hydrograph defined by ordinates spaced b hours apart.
WARP requires that the ordinate spacing be 2 hours. The subroutine
is dimensioned for a time base of 210 hours. That is, the unit hydro-
graph used as input to WARP is defined by 106 ordinates, UGI(K),
covering the time base from 0 to 210 hours. The average unit hydrograph
for the catchment must be defined in this way in the input to any
forecast program using CHAT. Note that UGI is actually dimensioned
for 107 ordinates. UGI(l07), however, does not appear outside the
subroutine. The final opera t .ion in the subroutine is the computation
of the adjusted ordinates, which then appear in array UG. This array
is also dimensioned for 107 ordinates because it is used internally
with the 2-bour ordinates. At the end of the subroutine, however,
it contains 36 ordinates spaced 6 hours apart and covering the 0
to 210-hour time base. This presents the unit hydrograph in the
form used by the catchment model.
The values of the curvature, CRV, are actually computed in the
subroutine in a somewhat different manner than described above.
If the values of CRV as computed with Eq. (4.13) were used in Eq. (4.12),
the results could be erratic. This is because the computation is
very sensitive to the value of CRV where it is close to unity and
roundoff errors in the input ordinates can produce erratic values.
The alternate method consists of determining the curvature at each
ordinate, using Eq. (4.12), and from t.hese values locating all in-
flection points. The mean inflection point discharge is then computed,
but the computation involves only those points at which the discharge
is greater than 20 percent of the maximum discharge. Finally, the
curvature at each ordinate is computed as the ratio of the discharge
to the mean inflection point discharge. These values have properties
similar to the true curvature but result in a smooth adjusted hydro-
graph. Figures 4.3-4.8 show the effect of operating on the same
unit hydrograph with various combinations of RV and RH and demonstrate
23
the characteristics of the algorithm. Figure 4 .3 shows the a pplication
of RV slightly greater and slightly less than unity . Note that whe n
the peak increases, the lower portions of the g raph decrease and
that unit volume is always maintained. I n Figure 4 .4 , an extreme
value of RV (2. 0) is applied. No ,.... that the volume i s maintained
by pulling in the side& and shortenJ..Ug the base. Figure 4.5 shows
the effect of a numerically small v ertical warp coefficient, 0 .7.
No te that the peak has become very f lat. I n fact, in o rder t o maint ain
volume , the algorithm has generated ordinates to the left a nd right
of the "peak" that are slightly higher than the "peak." This illus-
trates the need for constraints on the values of the warp coe££icients
to be used with this algorithm. For this particular unit hy drograph,
a lower constraint on RV of slightly ove r 0 .7 would b e a ppropriate
and this is fairly typical. Figure 4 .4 demonstrates that the upper
constraint on RV may be much l ess res trictive .
Figure 4 .6 shows the effect of RH values greater and less than
unity, which produce pure translation. Note that where RB = U.7,
a small amount of volume (5 percent) h as been lost . This case, ~q < 1
a nd RV = 1, is the only situation in which the algorithm may not
ma intain unit volume. This is not particularly important since the
usual situation involve s values other than unity for bo th coe fficients.
Where RV # 1, the vertical warp op eration restores the v olume lost
dur ing a horizontal shift to the left . As will be noted later, the
op timization strategy always operates firs t on RV and then on RH .
So , wh::.le a situation of this type can occur , the chance of it is
minimal. In Figure 4. 7 , applica tion of RR = 0 . 8 reduces the volume
but the vertical warp with RV = l.l restores it, and the area under
both hydrographs shown is the same . Had the vertical warp coe fficient
been less than unity, the peak would have been reduced in magnitude, but
the lost volume would s till have been restored. Figure 4.8 illustrates
the effect of RV < 1 and RH > 1.
The previous examples show that the mathematical characteristics
of the warp sub routine impose the need for lower constraints of about
0.7 on both warp coefficients, but they impose no such requirement
with respect to upper constraints . As will be pointed out in the
section on optimization strategy, constraints are imposed on all
of the decision variables with which CHAT is involved, and these
c onstraints are related to the physical system being treated. Ex -
perience has shown that the physL:al constraints on the warp coef-
ficients are at least as restrictive as those just noted, thereby
rendering the mathema tical constraints redundant.
I t was stated above t hat the '7alue of the exponent B, which will
cause the volume of the warped unit hydrograph 'to equal that of the
original, is d etermined by iteration. In t his procedure, the volumes
corresponding to three different values of B are determined, and
24
-en
~
v -"" C) • ~
% v en -Q
-en
~ u -"" C) • ~
% v en
Q
t
20 ------AVERAGE UNIT HYDROGRAPH
-------RV=1 .1, RH=l .O
---RV=0.9,RH=1.0
15
10
-o#
oUL-L--L--L~~~~--~~a.~~
0 10 20 30 40 50 60 70 80 90 100
40
35
30
25
20
15
10
5
TIME(HRS)
Figure 4.3--Effect on unit graph of varying vertical
warp coefficient--RV=l.l, RV=0.9
1\ AVERAGE UNIT HYDROGRAPH I \
I \ ----RV--2 .0 .RH= 1.0 I \
I \
I \
I \
I \
\ I \ I
0~~~~--~--~--~~--~===---~~ 0 10 20 30 40 50 60 70 80
TIME(HRS )
Figure 4.4--Effect on unit graph of numerically large
vertical warp c oefficie nt--RV=2 .0
25
-en
~ u -t!t
Gl:
~
X u
!!!
Q
20 --AVERAGE UNIT HYDROGRAPH
---RV= 0.7, RH:l.O
15
10
5
o~-L--L-~--~-J--J-~~~~~~
0 10 20 30 AO 50 60
20
15
10
TIME (HRS)
Figure 4.5--Effect on unit graph of numeric ally s mall
vertical warp coefficient--RV=0.7
---AVERAGE UNIT HYDROGRAPH
\ ---·RV=l.O,RH=0.7
\ ---RV=1.0,RH=1.2
\
\
\
0 ~~--~~~~--L--L~~~~ .. ~
0 10 20 AO 50 60 70 80 90 100
TIME (HRS)
Figure 4.6--Effect on unit graph of varying horizo nta l
warp coefficient--RH=0.7, RH=l.2
26
-.
en
~ .
u -
"' C)
CIC
~
X
u
en -Q
-.
en .
~ .
u -
"' C)
• <(
:z:
v
en -Q
20
1 5
1 0
5
2T i' I \ AVERAGE UNIT
I HYDROGRAPH
I 1 5 1
I
I ---RV=1.1, RH=0 .8
I
I
1 0 I
I
I
I
5
0~~--~~L__L __ ~~-=~~a.~--~
0 10 20 30 40 50 60 10 80 90 100
TIME ( HRS }
Figure 4.7--Effect on unit graph of varying both coef-
ficients simultaneously--RV=l.l, RH•0 .8
' \
\
\
\
\
\
\
\
\
' ' ',
AVERAGE UNIT
HYOR OGR A PH
---R V = 0. 8 , R H.::l , 2
'~ o~--._ __ ._ __ ~--~---~---~----L-=~==~~~
0 10 20 3'0 40 50 60 10 80 90 100
TIME (HRS}
Figure 4.8--Effect on unit graph of varying both coef-
ficients simultaneous--RV=0.8, RH=1.2
27
a second-degree polynomial is f it to these thr.ee points. The polynomial
is then solved for the value o f the exponent where the value of the
function is unity. This process involves the solution of a quadrat~c
equation. If the d~scriminant o f this equation should be negat2ve,
indicating c omplex roots, a solution of the WARP algorithm would
not be possible. While the WARP subroutine has been executed thousands
of times without this happening and ev en though i t p robably never
will happen, it seems prudent to make provision f or such an eventuality
in the program, and this has he en done .
Within the WARP subroutine is a quant~ty IZZ . If the s ubr ou~e
ir> executed normally the return w~ll be made ~th IZZ = 0. If,
en the oth er hand, the discriminant in the quadratic equation is
negative , three things happen:
1. A message "ROOTS ARE COMPLEX" is printed.
2 . IZ Z is s et t o unity .
3 . A return from the subr outine is made.
The a dj ustment strategy subroutine, STRAT , interrogates ~ZZ after
the return from WARP, and , if WARP h as not completed execution, STRAT
takes suitable a c tion to prevent the adjustment procedure f rom being
aborted. The manner in which this is do ne is descr i bed in t he next
section.
The sequence of o perations in dealing with a negat.ive discriminant
is provided for entirely within the CHN: subroutines, and, when these
subroutines are inco rporated into an op era~ional or experimental
program, the only provision that must be made is t hat IZZ be collDDOn
to both subroutines STRAT and WARP and not be used elsewhere.
Of cours e, if the user wishes , IZZ can be interrogated in the main
program and be u sed to t rigger any a dditional dis1>lays.
Adj ustment Strategy
The adjus tment strategy i s the procedure by which changes are made
in the decision variables in an attempt to alter the simulation so
that the objective function will be smaller than the tolerance.
These decision v ariables consist of 6-hour mean areal precipitation
amounts and the two warp coefficients, RH and RV . At any particular
time in the forecast operation, either during the storm or after
its end, the number of precipitation amounts will normally be equal
to the number of 6-hour periods that have elapsed since the beginning
of the event. If QPF i s being used, there may be one o r two more.
The o bserved hydrograph, as explained earlier, is defined by a series
of o rdinates spaced 6 hours apart, although the time interval between
the last ordinate and the one preceding it may be less than b hours.
28
If the observational reporting system is operating in the prescribed
manner and if QPF is not being used, the last precipitation observation
will coincide, in time, with the end of the observed hydrograph.
The adjustment strategy does not, however, depend on the existence
of this condition. The last available discharge observation may
be at a time prior to the last precipitation observation either because
the river observations are not current or because some of the pre-
cipitation is based on QPF and is in the future. Or the forecast
might be p r epared 2 hours after precipitation observation time and
include in the observed hydrograph a river observation made just
a few minutes prior to forecast preparation. In any event, the strategy
works with all precipitation increments up to the latest available,
including QPF, if any. The objective function is computed up to
the end of the observed hydrograph. Neither the strategy nor the
objective function ~ecognizes, explicitly and directly, which of
the three possible conditions exists. What in fact happens is that
the strategy will not make any changes in a particular precipitation
period if none of the runoff resulting fro·m that precipitation has
been "seen" at the river gage. That is, adjustments will be made
only to precipitation that fell prior to the last discharge observation.
The reason the strategy will not change precipitation that fell,
or may fall, subsequent to the end of the observed hydrograph is
not that it knows it shouldn't, but that when it attempts to do so
it will find that it cannot possibly change the objective function,
and it will therefore not change the precipitation. This means,
among other things, that if one or more periods of QPF are included
in a forecast, it is not necessary to tell CHAT that this is forecast
rainfall. CHAT will make no changes in it. One possible exception
to this is the case where a river observation is made a few hours
after the last precipitation observation and QPF is being used in
that 6-hour period. Then, a change in the. precipitation for that
period can affect the objective function and such change may be made.
The adjustment process consists of making a number of "passes"
through the strategy. In each pass, a maximum of three changes can
be made. One 6-hour precipitation amount and only one can be increased
or decreased by an amount, ~, probably 1 mm. Either or both of the
warp coefficients can be increased or decreased by an amount, l!.W,
probably 0.01. At the completion of a pass, if an exit condition
has been reached, the adjustment process is terminated. If not,
another pass is made.
As stated, within a pass, only one precipitation amount can be
changed and that is the one that produces the greatest improvement
in the objective function. Furthermore , at the time this change
is made, in the first pass, a sensitivity term, STY, is co~uted.
STY is equal to 7.5 percent of the ratio of the improvement in the
objective function to the function itself. The value of the objective
29
\
f unction at this time is designated as OFBSE. On subsequent passes~
no change will be made unl ess the ratio of the change to OFBSE exceeds
STY .
The rationale behind this type of strategy is similar to that behind
the quant ity ~ WP ~ which is one of the comp onents of the tolerance.
It was pointed o ut~ in the section dealing with th~ ::olera:nce~ that
during the early p art of the rise~ when only a small portion of th.e
runoff v olume has been sampled~ there is l ittle j ustification for
making substantial changes in the decision variables. A similar
factor is involved in the adjustment procedure. The adjustment strategy ,
however, is dealing with a series of 6-hour precipitation increments .
The simulated hydrograph, as well as the observed~ i s a composite
of a s eries of contributions each one of which is in a different
s tage of d evelopment. Just as large changes in the simulation cannot
be j ustified on the basis o f what is seen early in the rise, ch.anges
in an individual 6-hour precipitation amount cannot be justified
wh en only a small part of the contribution o f tbat 6-hour amount
has bee.n seen. As an example, s uppose t h at at one point in time
during a forecast o pera tion, there are tbree precipitation periods
involved . Depending on a number of f actors, primarily the charact-er-
i stics ot the catchment, perhaps only a tiny portion of the runoff
r esul t i n g f rom period 3 has appeared at the gage. The rate of runoff
resulting f rom period 2 p recipi tation is at a maximum , however, and
the c ontribution of peri od 1 has already peaked and is in recession.
Under these circumstances, the desired s trategy would be to work
primarily with period 2 . Period 3 should be adjusted slightly if
a t all because its c ont ribution h as not yet been seen. Any necessary
adjustments to period 3 will be made at a subsequent time. Period 1
need not be adjusted substantially because it .!!! adjusted at some
previous time when it, rather than period 2, was the most critical.
It should be noted at this point that adj ustments t o period 1 or
3 will not affect the obj ective function as much as will changes
in period 2 . Period 1 wil~ have a slight e ffect because the portion
of the simulation it af f ects the most i s s ome period back from the
current time and weight, WD, in the objective function reduces the
effect of errors in tnat portion of the simulation. Period 3 will
h ave a slight effect because the portion of the simulation it affects
the most is in the future and i s not included in the objective function
at all . The reason for restricting adjustments to those precipitation
periods that are affecting the hydrograph the most at the time the
adjustment is being made i s to avoid making unrealistic and unjustified
c hanges in recent precipitation periods simply because they produce
an improvement in the fif th decimal place of the objective function.
Such adjustments can make substantial and unj ustified changes ~
the f uture portion of the simulation. While such.changes would pre-
sumably be rectified at a later time, they would work to the detriment
of the forecast issued at the time in question. Once again, the
30
aim is not to m.inimize the objective function subject to constraints
on the decision variables but ratber to reduce the objective function
to an acceptable value while making minimal changes in the decision
variables. This dictates a basically different strategy than would
be appropriate for a classic optimization procedure .
To accomplish this ~trategy requires a determ.ination of the relative
importance to the objective function of the various precipitation
periods at the time t he forecast is being made. It would be possible
to compute this intormation as a function of the model's parameters
and stete variables, but the complexity of such an analysis would
approach that of the model itself. Therefore, the actual simulations
are used for this purpose. Within each pass, increments or decrements
are applied to each precipitation period and the change in the obj ective
function noted . Then, all are reset to their starting values except
the one which prodru ced the maximum change . On subsequent passes,
further changes would probably be made in that period until it nears
i ts optimal value and then some other period may become the most
c ritical. The procedure continues until the maximum change that
can be produced i s less than the sensitivity figure, STY, rr until
the tolerance is reached or until some other exit condition is met.
The adjustmen ~ of the unit hy drograph is done in a different manner.
Adjustments are made to either RV, RH, or both if such adjustment
will improve t h e fit. Since the same adjusted unit hydrograph is
applied to the runoff from all precipitation periods, all necessary
controls are exercised by the objective function and the tolerance .
The simplifi ed flow c h art in Figures 4.9(a) and 4.9(b) illustrates
the adjustment process. When the proces s begins , at the box marked
"START," the following conditions exist.
A. The n umber of 6-hour periods that have elapsed since the
beginning of the runoff event is denoted by "N ." N may be any value
from 1 up to that which represents the entire hydrog raph base .
B. Six-b our mean areal precipitation amounts have been comp uted
from rain gage observations, radar, etc ., for p eriods 1 through N,
e>t \d some of these amounts may be zero.
C. Nonzero precipitation c\IIlounts for periods N+l, N+2, etc .,
may be involved in the simulation, but if so, they are QPF.
D. Discharge observations are available up to some point in
time no later than a couple o f hours after the end o t period N.
All computations of the objective func tion and tolerance will be
based on the hydrographs up to this time.
31
MXIMP =O
Figure 4 .9a --Adjustment strategy (precipita t i o n )
3 2
0 IG ~O
RV =RV +.:SW 2 >----~CALL WARP
CALl:. MODE
CALL OBJEC
RV =RV-2.:S
CALL WARP
~LMOOEL~--~~~
CALLOBJEC
RH=RH+dW
OFB =OF
IG =1
CALL WARP RV =RV t dW~----~~MODEL~~----------~
RH=RH -2dW
CALL WARP
CAUOBJEC
CALL MODELt--------l~<
CALL OB.JEC
YES
OFB =OF
IG =1
RH =RH +dW
~---------.-.~-------------CALL WARP
Figure 4.9b--A3justment strategy (uni t hydrograph)
33
\
E. At all time periods from 1 through N-1, simulations have
been made, and whatever adjustments necessary to satisfy the tolerance
or achieve some other exit condition have been accomplished.
F. At the current time period, that is, period N, a "base sim-
ulation" bas been made. The base simulation is that obtained by
applying to the model the following:
1. For periods 1 through N-1, the precipitation amounts
as adjusted at the end of period N-1.
2. For period N, the measured preciptation.
3. The unit hydrograph as adjusted at the end of period N-1.
If N = 1 or if no adjustments were made at any of the preceding
times, then the base simulation is a function of measured precipitation
and the average unit hydrograph.
G. The objective function corresponding to the base simulation
has been computed and, at the beginning of the adjustment process,
is denoted by the symbol, "OF."
H. The tolerance at the time of the base simulation has been
determined and is denoted by "TOL."
I. It has been determi.ned that OF > TOL .
When conditions A-I exist, then subroutine STRAT is called and
the adjustment process begins. If, instead of condition I, it is
determined that OF < TOL, then, of course, no adjustments are made,
and the forecast operation goes on to the next step, whatever that
may be.
Beginning at the top of Figure 4.9(a), the quantities ISTY and
MXIMP are set to zero, ISTY is used to indicate whether the pass
being made at this time is the first or a subsequent one. Later
in the pass, ISTY will be set to unity and remain at that value.
MXIMP will assume a value equal to the maximum improvement made to
the objective function, during the pass, by adjusting precipitation.
The quantity i is set to unity. It is the counter used to indicate
the 6-hour precipitation period being worked with and will be incre-
mented to "N" during this portion of the pass. The qwu1tity OFB
is set equal to OF, the objective function related to the base simulation.
For s ubsequent passes, both OFB and OF, at this point, will be those
values resulting from the previous pass.
34
With the initial~zation of the pass completed, adjustment of the
precipitation beg~ at point "A." P(i) is incremented by f)., and a
s~mulation is made by calling subroutine MODEL. This subroutine
is not one of the component parts of CHAT. Rather it u the means
by which CHAT is linked to any research or operational program that
uses CHAT. The function of subroutine MODEL ~ simply to call whatever
mainline program subroutines are needed to produce a simulation and
place the ordinates in the array utilized by subroutine OBJEC. Next,
the objective function is computed and the quantity CBNG, which
is the change in the objective function resulting from incrementi.ng
P(i). If the fit has been improved, CliNG will be positive; if it
has been degraded, CHNG will be negative.
Next, CHNG is compared with MXIMP. If i '"" 1, MXIMP will be zero.
If i > 1, MXIMP will probably be other than zero. It cannot be negative.
If CHNG > MXIMP, then the incrementing of P(i) has produced an improve-
ment in the fit, and it is the greatest improvement so far this pass.
If this condition exists, the statements in box "B" set MXIMP equal
to CHNG, reset P(i) to its previous value and set the quantity "CPR"
equal to i to "remember" which precipitation value produced MXIMP.
If, on the other hand, CHNG is not greater than MXIMP, the program
proceeds to point 11C," where a similar procedure takes place but
with P(i) being decremented by /).. If this produces a change greater
than MXIMP, a similar substitution is made, but now, CPR ~ set to
"-i, 11 indicating a decrementing of the precipitation rather than
incrementing. In any event, P(i) is reset to its previous value
and the program proceeds to point "D, 11 where "i" is incremented.
If i ~ N, a return is made to point "A·."
After all precipitation periods have been tested, the program proceeds
to point "E." At this point, all precipitation values have been
reset to the values they had at the beginning of the pass, MXIMP
shows the greatest improvement aC'.hie,ed, and CPR shows how it was
accomplished.
Next, MXIMP is tested against zero. If zero, it means that no
changes in precipitation have been made during the pass. In that
event, the program branches, via point "2," to the unit hydrograph
portion of the strategy. If MXIMP + 0 , it is then necessary to test
the improvement against the sensitivity, STY, as described earlier.
Or, if this is the first pass, (ISTY•O), STY is computed in box "F,"
and !STY is set to unity. Once STY i s computed, it is not changed.
If it is not the first pass and if the ratio of MXIMP to OFBSE is
less than STY, MXIMP is set to zero at point "G," and the program
proceeds to point "2" without adjusting precipitation. If an adjustment
is to be made, however, the path is through point ''H." The precip-
itation period that is associated with MXIMP is either incremented or
decremented, as indicated by the sign of CPR. Then, the statements in
box "I" create a new simulation and its corresponding objective
function, OF. At this point, OFB is se t equal to this value of OF
35
\
and the program proceeds to the unit hydrograph adjustment in the
portion of the chart shown in Figure 4.9(b).
This adjustment starts at point "J" by applying an increment, 6W,
to the vertical warp coefficient, RV, and producing a simulation.
If this simulation improves the fit, indic ated by the new objective
function, OF, being less than the previous value, OFB, then this
adjustment is retained, regardless of the size of the improvement,
and OFB is set equal to OF and the quantity, IG, which had been set
to zero in box "J," is set to unity to indicate that an adjustment
to the unit hydrograph has been made. If incrementing RV does not
produce an improvement, it is decreased by 26W, to its original value
minus 6W, and a similar test is made. If no improvement can be made,
RV is set to its original value.
Whether or not a change is made in RV, the program proceeds to
point '~e " where a similar procedure takes place involving the hor-
izontal warp coefficient, RH. At the completion of this procedure,
a test is made, at point "L," to determine if both MXIMP and IG are
equal to zero. If they are, it means that no adjustments were made
during the pass. It also mean.s that additional passes would achieve
the same result. Consequently, an exit condition has been reached.
This exit condition requires that some message or other indication
show that the adjustment procedure was terminated without reaching
the tolerance.
If either MXIMP or IG is other than zero, one or more changes has
been made during the pass. In this case, a test is made, at point
''M," to determine if the tolerance has been reached. If it has,
the normal exit occurs. If it has not, the routine branches back
to point "1" to begin another pass. When an exic takes place, all
decision variables have been set to their adj usted values, the sim-
ulation existing at that time corresponds to those values, and the
objective f unction corresponding to that simulation is that represented
by symbol OFB and also OF.
It should be noted at this point tha t if, in a pass, it is not
possible to improve the fit by adj usting precipitation but changes
to the unit hydrograph are =ude in that pass , it does not follow
that no changes to pre~ipitation will be made in subsequent passes.
It ~s quite possible tha t the change in simulation that results from
warping the unit hydrograpb will make it possible to improve the
fit by adjusting precipitation in later passes.
The flow chart is, as was noted earli er, a simplification. Tb@
subroutine has provision for an additional exit condition, not shown
on the chart. The maximum allowable number of passes, MAXN, is
specified by the user, and, if this number is made, the adjustment
procedure will terminate even if no other exit condi tion exists.
36
Also, not shown on the chart is the use of constraints on the
decision variables. If the various parameters used by CHAT are
properly defined and if the input data contain no gross errors in
observation or transmission, CHAT should operate quite nicely uncon-
strained. Since these conditions cannot be assumed to exist at
all times, however, it is prudent to constrain the variables. In
the great majority of cases, the constraints are not reached. Their
main function is to prevent gross data errors such as mis-punching
or misplaced decimal points from creating ridiculous results. Ap-
propriate constraints on the warp coefficients depend upon the shape
of the unit hydrograph and the characteristics of the catchment with
regard to typical storm movement and areal variation of precipitation.
Values of 0.7 and 1.5, however, for lower and upper constrains on
both warp coefficients are reasonable and should be adequate in the
majority of applications.
For precipitation adjustments, the lower constraint is simply a
multiple of the measured 6-hour value. The upper constraint can
take either of two forms, a multiple of the measured 6-hour value
or a fixed amount. The choice between the two forms is, in effect,
a user option. Actually, the parameters defining both forms are
specified in all cases. The values of these paramete.t"s cause the
program to select the form of constraint desired by the user.
That is, if it is felt that the precipitation computed from rain
gages must always bear some relationship to the true areal mean,
the user specifie s an upper constraint ratio such that the constraint
is equal to the product of the ratio and the measured areal precip-
itation. Under some climatic regimes, however, it is possible to
experience a rainfall amount so large as to be totally unrelated
to the mean computed from rain gage readings. In these circumstances,
it is more appropriate to simply constrain the HAP to a "non-preposter-
ous" value by the use of a fixed upper constraint which is not a
function of the measured precipitation. This constraint should be
a function of the region, of the size of the catchment, and of course,
of duration, which is always 6 hours. If thi6 option is to be exer-
cised, the recommended value is 50 percent of PMP (probable maximum
precipitation).
When the upper constraint is computed as a multiple of the measured
precipitation, a value measured as zero will have upper and lower
constraints of zero and consequently cannot be changed by the adjustment
technique. Since it is quite possible for a 6-hour MAP value to
be computed from rain gage observations as zero when in fact the
true MAP is not zero, it is necessary to place a lower limit on the
upper constraint. The value used for this limit is 20 percent of
the total accumulated 6-hour precipitation up to and including the
6-hour period in question.
37
Thus, to define the precipitation constraints for a catchment,
CHAT requires the definition of three parameters: ZLOW, the lower
constraint ratio; HIGH, the upper constraint ratio; and UCX, the
fixed upper constraint. The program computes the lower constraint
as:
LK (i)•ZLOW*P {i). (4.18)
It computes the upper constraint as the greatest of:
or
or
UK(i)•HIGH*P(i)
UK(i)•0.21:?(i)
UK{i)•UCX(i).
(4.19)
(4.20)
(4 ~,,
~L ......
If the user does not wish to exercise the fixed upper constraint
option, he simply specifies UCX as zero and the constraint will always
be related to the measured precipitation. If a very large value
of UCX is specified and if a storm occurs in which the true MAP actually
exceeds UCX, if the computed precipitation is reasonably close to
the true value, then the product, HIGH*P(i), will probably be greater
than UCX and UCX will not constrain. Should such a storm occur and
the measured precipitation be very small, CHAT may increase it up
to UCX without being able to match the observed hydrograph. The
program would then inform the forecaster of the circumstances and,
of course, this is a situation in which human intervention would
be desirable.
It should be noted once again that while constraints are necessary,
experience indicates that their actual values are not particularly
critical. In the research work already done, values of 2.0 and 0.5
have been llsed for HIGH and ZLOW in most cases. The adjustment pro-
cedure is capable of making substantial changes in the simulation
with surprisingly small changes in the decision variables.
In the discussion of the WARP subroutine, it wa s pointed out that
a quantity, I 2Z, is set equal to unity if a return from WARP occurs
without a new unit hydrograph having been generated. Subroutine
STRAT interrogates IZZ after every call to WARP. If IZZ•l, STRAT
does not attempt to create a new simulation and evaluate the objective
function related to it. It simply bypasses these steps and does
whatever it would normally do at that point if a change in RH or
RV resulted in a degradation of fit.
The flow chart in Figure 4.9 and the accompanyirtg discussion were
prepared for the purpose of explaining the procedure with a maximum
degree of clarity. The Fortran statements in subroutine STRAT were
written to execute the procedure in a computationally efficient manner.
Consequently, the symbols and the details of the operation as shown
in the flow chart do not correspond exactly with those in the subroutine .
38
Observed Hydrograph Interpolation
The purpose of this part of CHAT, and of Subroutine INTERP, is
as previously stated: to interpolate between discharge observations
made at random times and produce an array of "observed" discharge
values which coincide in time with the simulated ordinates. This
is accomplished by fitting a segment of the hydrograph between each
pair of successive observations. This segment is defined by a third-
order polynomial which is fit to the observation at each end of the
segment and to the slope at each end of segment. The slope is defined
prior to the fitting of the polynomial and is equal to the first
derivative of a second-order polynomial which passes through the
observation in question, the one immediately preceding it, and the
one immediately succeeding it. The slopes at the first and last
observations are special cases and are simply the straight line slopes
to the adjacent observation.
The segments combine to form a continuous smooth curve through
all of the observations. Each 6-hour ordinate is determined by solving
the appropriate third-order polynomial for the discharge at the time
of that ordinate. The technique is similar to the method of splines,
but unlike splines, will not develop unnatural oscillations.
The statements in Subroutine INTERP do not, upon cursory inspection,
appear to duplicate the computational procedure described above.
This is because the subroutine contains a number of mathematical
"short-cuts" which greatly increase its efficiency. The results,
however, are identical to those which would be obtained by following
that procedure.
While this algorithm is capable of doing an excellent job of inter-
polating between observations, it cannot crea~e data. The user
must therefore bear in mind that the program must be supplied with
enough observations to actually define the hydrograph. As noted
in the subroutine documentation, the first observation must always
be at time zero on the simulation scale. Since this time is prior
to the beginning of rainfall, the discharge will be the "base" discharge
for the event. There should be at least one observation fairly low
on the rise. If there is not, the time of beginning of the rise
is undefined and the interpolated hydrograph may start up too soon.
It is not particularly important to have an observation exactly at
the peak since INTERP will usually generate a peak between observations
and higher than the highest observation. It is important to supply
the progr.am with the very latest observation available, even if it
does not coincide with a 6-hour ordinate. Inclusion of such an ob-
servation not only helps to define the slope of the hydrograph at
the preceding ordinate but also the observation itself will be carried
over to Subroutine OBJEC as TILT and QOLT.
39
Blending Routine
As was pointed out in Chapter 3, the purpose of the blending routine
is to effect exact agreement between two hydrographs which differ from
each other by an amo unt wh!ch i s not hydrologically significant.
For t his reason , the routiile can be extremely simple.
Inpu t to the sub r outine consists of two discharge a rrays, QO, which is
the observed discharge, de fined up to the latest observed ordinat e,
NOB , and QS , wh ich is the simulated discharge, defined over the entire
time base . The blended hyd rograph appears in a rray QBL. From time 1
to time NOB, QBL-QO . From time (NOB+6) to the end of the simulation,
QBL=QS . The five ordinates from (NOB+!) to (N OB+S) are determined by
pro rating, linearly , the difference between QO and QS which exists at
time NOB . If a partial observed ordinate , QOLT, is available, then the
differen ce is computed between QOLT and QS(NOB) and suitably adjusted
by PJ, the fraction of the 6-hour period covered by TILT .
40
5. OPERATIONAL USE
The purpose of this chapter is to explain how to implement the
CHAT adjustment procedure in an operational forecast program.
The CHAT package is not an independent procedure but rnther consists
of six individual subroutines that must be interfaced with a forecast
program. The CHAT subroutines perform only those operations that
a re associated with the function of adjusting the computed hydrograph
to agree with the discharge observations. All other operations
that are necessary to produce a forecast, su,ch as I/0 routines,
MAP computations, rainfall-runoff computations, and runoff distribution,
must be supplied by the forecast program. The manner in which
the CHAT subroutines link with these other operations is described,
as well as the data and parameters that the CHAT procedure requires.
Subroutine listings can be found in Appendix A.
The CHAT procedure utilizes 13 parameters, each of which has
been discussed in previous chapters. Provision must be made in
the forecast program files for storage of these parameters. Because
many of them depend upon the hydrologic characteristics of the
catchment and of the gaging station and may therefore vary from
one area to the next, it may be necessary to store a unique set
for each headwater area. Table 5.1 lists these parameters, along
wi th a brief description of what they are, Where they are discussed
in this report, and the values that have been used for them in
t he research work. If necessary, the research values can be used
as initial values for most basins until the user acquires a better
unde rstanding of the effects they have on the performance of the
procedure. At that t ime , however, it would be advantageous to
suitably adjust them to the individual basins in order to obtain
optimal performance from the procedure. Som.e of the experiences
with parameter values that have been encountered in the research
are described in Chapter 6 and may provide some useful guidelines
for determining parameter values.
In addition to the parameters, CHAT requires the average basin
unit graph to be defined by 2-hour instantaneous ordinates as well
as by the usual 6-hour intervals, and to be placed in array UGI2 (107),
for use by the CHAT routines. All 107 values mu st be defined,
even if zero, and it must begin and end with zero. It is necessary
to define the unit graph in this manner for the computations inside
subroutine WARP. WARP, however, returns only the 6-hour ordinates
on the warped unit graph, UG6(36), so that the simulations continue
to be made with a unit graph defined by 6-hour ordinates. Since
adjustmen ts to the unit graph are reflected only in array UG6(36),
the average basin unit graph is always preserved in array UGI2 (.L07).
41
Parameter
EX2
PCENT
MAXN
DEL
WDEL
wm.
WVL
WVH
ZLOW
HIGH
ucx
Table 5.1. -List of CHAT parameters
Description
Exponent which permits the variation
of weight WP with time to be made
non linear in computing tolera nce
Exponent which permits the variation
of weight WD with time to be made
nonlinear in computing objectiv e
function
The fixed percentage for computing
PCOB in the tolerance
The maximum allowable number of passes
through the adjustment strategy
The fixed delta to be used for
precipitation adjustments in
subroutine STRAT
The fixed delta to be used for
adjustments to the warp coefficients,
RB and RV, in subroutine STRAT
Lower constraint on adjustments to RH
Upper constraint on adjustments to RH
Lower constraint on adjustments to RV
Upper constraint on adjustments to RV
The ratio for computing the lower
constraint on precipitation in
subroutine STRAT
The ratio for computing the upper
constraint on precipitation in
subroutine STRAT
The fixed upper constraint on
precipitation
42
Research
Value
2.0
2.0
0.075
100
lDDD
0.01
0.7
1.5
0.7
1.5
0.5
2.0
0.
Page
Referenc e
1 6
10
15
36
29
29
37
37
37
3 7
38
38
38
Other than standard input to the forecast, namely MAP computed
from point rainfall amounts, and discharge (stage) observations,
CHAT requires no additional data. However, the CHAT routines are
designed to operate in metric units; thus, the ~~ and discharge
observations must be expressed in Dillimeters (mm) and cubic meters
per second (ems), respectively.
All of the parameters, data, and variables required by the procedure
are passed between the CHAT routines and the forecast program through
the individual subroutine argument lists or by the following four
common blocks:
COMMON/MATOL/EXl,PCENT
COMMON/MAOBJ /EX2
COMMON/BLOT/QBL(53)
COMMON/MASTRA/UGI2(107)0FB,MAXN,DEL,WDEL,WHL,WHH,
1 WVL,WVH,ZLOW,HIGH,UCX,TOL,MSG,NJ,SUM,LK(53),UK(53)
These common statements must be inserted in the forecast prog:am
at the proper place; they have already been included in the appro-
priate CHAT subroutines. In addition, the variable LK must be
specified as type real. Also included in the CHAT routines are
all other necessary common statements that pass variables that
do not appear outisde the CHAT subroutines. Tile variables in each
of the subroutine argument lists will be described later in this
chapter.
As for dimensions, all variables currently dimensioned for 53
in the subroutine listings can be changed at the user's discretion.
This number is a function of the maximum duration, in intervals
of 6 hours, of runoff events in the user's forecast area. Every
time CHAT is used during a runoff event, it operates with the data
and hydrograph from the very beginning of the runoff event up through
forecast time. As CHAT is used for forecasts made down through
the recession, it deals with an ever increasing portion of the
runoff event until, at the very end, it is dealing with the entire
runoff event. Thus, the variables in the CHAT procedure, unless
specified otherwise, must be dimensioned for the entire duration
of the runoff event. The current value of 53 is carried over from
the research program, which was dimensioned to handle events that
extended up to a maximum of fifty-three 6-hour periods. The di-
mensions of the simulated and blended discharge arrays, QS and
QBL, must at least extend over the duration of the runoff event
to satisfy CHAT's requirements. Any additional dimensioning on
these variables will depend upon the design of the forecast program.
43
The noted exceptions to the dimensions thus far discussed are
variables TB, QB, and S in subroutine INTERP. They are dimensioned
to allow the usage of a maximum of 100 randomly spaced discharge
observations. Once again, this value can be changed as the user
deems appropriate for the observational reporting network in his
area. The only restriction on re-dimensioning applies to the var-
iables in subroutine WARP. They must remain as coded in the listings
in order for the subroutine to function properly.
In order to use CHAT, the beginning of the runoff event must
be defined. It is realized that there are no definitive guidelines
for doing this. The manner in which the runoff event is identified,
whether by the subjective judgement of the forecaster or by some
sort of objective criteria in the program, will depend upon the
user's oreference and his particular forecast operation. No attempt
has been made in this report to address the problem other than
by providing some insight through examples 2 and 3 of the next
chapter. Once the runoff event has begun, CHAT must be used for
every forecast made during the event. The forecaster does not
decide if adjustments, and hence CHAT, are necessary; the CHAT
procedure is always initiated during a runoff event, and it determines
if adjustments are required at that time. As will be shown later,
CHAT will make no adjustments if the hydrograph derived from the
data, as it is at the beginning of the forecast, agrees satisfactorily
with the observations.
Since the standard data and computing i.nterval for NWS forecast
programs is 6 hours, the CHAT adjustment procedure must also operate
on a 6-hourly basis. This means that, regardless of the time interval
between forecasts, during a runoff event each 6-hour period that
has elapsed since the last forecast must be regarded, in succession,
as the "current" time for CHAT's computations. Since this "current"
time will generally differ from forecast time, unless forecasts
are being made every 6 hours, CHAT provides its own indexing system
in the form of the variable "NFORC". NFORC represents the number
of 6-hour periods that have elapsed since the beginning of the
runoff event up to the period that is being regarded as the latest.
In other words, NFORC is always the "current" time for CHAT's compu-
tations. If forecasts are being made every 6 hours, then NFORC
and forecast time coincide. In the discussions in this report
so far, for the purpose of explaining the theory with as little
confusion as poss!ble, it has been assumed that forecasts are being
made every 6 hours, and thus the two terms have been used inter-
changeably. However, for the purpose of explaining how to use
CHAT in an operational framework, it becomes necessary to differ-
entiate between the two sine~ forecasts are not always made oper-
ationally every 6 hours.
44 .
Regardless of the value of NFORC, CHAT alway s operates from the
beginning of the runoff event. Its variables and data are, therefore,
i:ldexed from 1 to NFORC, where the first value is associated with
the first 6-hour period of the event . Any time a simulation is
made , the hydrograph is recompiled from this point. Con sequently .
only one set of carryover values needs to be saved, that being
the values of the soil moisture and channel flow variables going
into the first 6-hour period of the runoff event.
Figure 5.1 illustrates the way in which the CHAT routines link
to the normal forecast operations. The steps shown in the diagram
must be repeated for each successive 6-hour period that has occurred
since the last forecast. Th.is figure and the concepts discussed
in the last few pages are perhaps better explained through an example.
For instance, in a case in which forecasts are being made daily
at 12Z, four new 6-hour MAP values are available for input to the
forecast each time: the HAP of 18Z on the previous day (herewith
referred to as Day 1), and the MAPs of OOZ, 06Z, and 12Z of the
current day (Day 2). Starting at the top of the diagram, it is
assumed that all preliminary data processing (MAP computations)
has been completed prior to this point. Suppose 18Z is the first
period of a runoff event. NFORC is then set equal to 1 and becomes
associated with the time of 18Z; the values of the soil moisture
and channel flow variables at this time are saved as carryover,
and the program branches to the CHAT procedure.
The first step in the strategy is to call subroutine INTERP,
which interpolates between discharge observations made at random
times and determines the value at each 6-hour ordinate corresponding
to the ordinates of the simulated hydrograph. Three items must
be passed to the subroutine in the argument list:
CALL INTERP (NB, TB,QB)
where NB is the number of observations available for input at the
current time NFORC, TB(l) to TB(NB) are the times, in hours, of
the observations, and QB(l) to QB(NB) are the observed dis charges
at each of the times in the TB array. TB(l) must be zero or otherwise
it will be set to zero inside the subroutine, and it coincides
with the firs·t 6-hour ordinate on the simulated hydrograph. The
observations must be in chronological order. Even though, at forecast
time, discharge observations may be available up through 12Z, only
observations up to the time of NFORC are passed to the subroutine
for this pass through the strategy. The reason for this is to
prevent discharge observations that occur subsequent to the time
of the latest MAP value that is used in the soil-moisture computations
from being included in the computations of the objective func tion.
Otherwise, unjustified changes may be made to the ~~ values up
45
RO YES-use CHAT
Yo
\~';;.:j
....... INTE RP
TOLER
OBJEC l ...... ~oFB<TOL YES
SIMULATE MODEL r 1 ! •
-----------------n====!::==;t '--------...1------------__ _., --8 ----STRAT
Exit Condition
Reached
NO
NO ~----~~~~-------------------------------------~~ NFORC >4------------~ =F.T.
YES
'\OUTPUT~-.--------------------------------------i~IB_L_E•N-0~
Figure 5 .1--Schematic of forecast procedure with CHAT adjustment strategy
through the time of NFORC based on the degree of fit with observations
that include the effects of precipitation that the model has not
yet seen. While observations cannot be used subsequent to NFORC,
they need not necessarily be available up to the time of NFORC
either. INTERP computes the quantity NOB, which is the number
of the last 6-hour ordinate prior to, or at the time of, the last
discharge observation, and the objective function is computed only
as far as NOB. Situations will arise where the latest observation
was made more than a couple of hours later than time NFORC, but
the last observation prior to that one was made long before time
NFORC. In such a case, the forecaster should estimate the discharge
at time NFORC and include that estimate as the latest observation.
When, one or more periods later, the actual observation can be
used, any such estimates should be deleted from the QB array.
The next step is to make what is termed the "base" simulation.
This simulation is a result of using precipitation values PP(l)
to PP(NFORC-1), as adjusted during period (NFORC-1) plus the current
computed~~ value, PP(NFORC), and the unit graph ordinates, UG6(36),
as adjusted during period (NFORC-1). If no adjustments have been
made prior to period NFORC, then the PP array contains the original
computed MAP values, and the unit graph, UG6(36), is still the
average basi.n unit graph. (For this use, the average unit graph
must be defined by 6-hour instantaneous ordinates whereas for sub-
routine WARP, it has to be defined by 2-hour ordinates - a point
that was discussed earlier in this chapter.)
For the present example, with NFORC equal to 1 and no adjustments
having been made thus far in the event, the computed ~~ of 18Z .
is put into the PP(l) position and UG6(36) is set equal to the
average basin unit graph. If QPF is being used, its N values must
be placed in the PP(NFORC~l) to PP(NFORC+N) positions of the array.
As mentioned earlier, QPF can be used in conjunction with the CHAT
procedure but CHAT will make no adjustments to it. If no QPF is
used, the future precipitation is set equal to zero. The base sim-
ulation is then made by calling subroutine MODEL, passing to it
these input arrays:
CALL MODEL (PP,UG6,QS)
where PP and UG6 are as defined above and QS is the base simulation
array that MODEL returns. HODEL is not one of the six CHAT sub-
routines but instead is a subroutine that must be constructed by
the user for use with his particular forecast program. CHAT passes
the precipitation and unit graph arrays to it, MODEL calls whatever
forecast program modules are necessary to produce a hydrograph
from the respective input arrays, and places the ordinates of this
hydrograph in the array that is accessed by the OlAT procedure.
In this way CHAT remains independent of the particular hydrologic
model that is used to produce the hydrograph.
47
After HODEL returns the base simulation, the CHAT strategy decides
if it is in satisfactory agreement with the observations up through
ordinate NOB. This is determined by first calling subroutine TOLER
to compute the tolerance at the current time NFORC:
CALL TOLER(NFORC,QS,PP,TOL)
where NFORC,QS,PP are as defined earlier, and TOL is the tolerance,
and then by calling subroutine OBJEC to compute the objective function
for the base simulation:
CALL OBJEC(QS,OFB)
where OFB is the objective function for the base simulation. A
comparison must then be made between OFB and TOL: if OFB is less
than or equal to TOL, the base simulation agrees satisfactorily
with the observed hydrograph and adjustments by CHAT are not neces-
sary. On the other hand, if OFB is greater than TOL, the base
simulation is ~ satisfactory and CHAT must make adjustments to
the input arrays.
The adjustments are initiated by calling subroutine STRAT. A
detailed description of the adjustment strategy that is used by
this subroutine has already been presented in Chapter 4. It is
sufficient for the purposes of the present discussion to simply
describe the variables in its argument list:
CALL STRAT(NFORC,RH,RV,UG6,PP,QS)
where NFORC is the current 6-hour period, RH and RV are the horizontal
and vertical warp coefficients, UG6 is the unit graph, and PP is
the precipitation array. When STRAT is called, these variables ·
contain values that are associated with the base simulation. Since
NFORC is equal to 1, RH and RV must be initialized to the value
of 1.0 before being passed to the subroutine. When the return
is made from the subroutine, RH, RV, UG6, and PP have automatically
been updated inside STRAT to reflect the adjustments CHAT made,
and the adjusted hydrograph is returned in array QS.
In the diagram subroutine STRAT is connected to subroutines MODEL,
OBJEC, and WARP by dotted lines, whereas all the other connecting
lines are solid. This distinction is made to indicate that the
call statements to these subroutines are provided within subroutine
STRAT rather than by the forecast program. All operations associated
48
with making adjustments are handled automatically within this sub-
routine, and a return is not made from STRAT until one of three·
conditions exists:
MSG = 1: no reductions were made in the objective function on
the last pass through the adjustment strategy, and the
objective function is still greater than the tolerance
MSG = 2: the objective function is less than the tolerance
MSG = 3: the number of passes allowed through the adjustment
strategy MAXN, has been exceeded and the objective
function is still greater than the tolerance
The variable, MSG, is set within the subroutine to indicate which
exit condition is used and passed back to the forecast program
through a common block.
One more variable must be discussed in connection with subroutine
STRAT. The function of computing constraints on the precipitation
is performed within this subroutine. Thus, even if adjustments
are not necessary, STRAT must still be called to compute the con-
straints for the current MAP value, PP(NFORC), although this is
not shown on the diagram. Constraints for the MAPs of 6-hour periods
prior to NFORC will have been computed when each of those periods
was regarded as NFORC, and therefore, do not have to be recomputed.
If the subroutine is to be used only for this purpose, a flag,
NJ, must be set to zero prior to the call. Otherwise, NJ must
be set equal to 1 and the subroutine will be used to make adjustments
as well. The constraints, LK(S3) and UK(53), are used within STRAT,
but they are also commoned with the forecast program so that they
can be saved between forecasts.
At this point, CHAT has completed its operations for period NFORC,
or 18Z in this case. Let us assume that the base simulation for
18Z was not satisfactory and subroutine STRAT was called, with
NJ = 1, eo-make adjustments. The PP(l) position now contains the
adjusted MAP value of 18Z, UG6(36) is the revised unit graph based
on the adjusted values of RH and RV, and the QS(53) array contains
the adjusted hydrograph that corresponds to the new PP and UG6
arrays. If NFORC does not coincide with forecast time (llZ), as
it does not in this case, another pass is made through r:igure 5.1
with NFORC incremented to 2 and associated with the time of OOZ
of Day 2.
The first d1~cision on the second pass is to determine if OOZ
is still part of the runoff event. The use of the CHAT procedure
requires the definition of the end of the runoff event as well
as the beginning. Note in the schematic that if a 6-hour period
is not part of the runoff event, the forecast computations are
performed in the usual manner, using the compllted MAPs and the
average basin unit graph, and are unaffected >. the CHAT routines.
49
\
Assuming the nmoff event has not ended by OOZ of Day 2, INTERP
is once again called with the observations that are available up
to time NFORC, taking into account the fact that NFORC is now six
hours later. INTERP must always be called even if the discharge
observations coincide with 6-hour ordinates because it computes
quantities that are used by subroutine OBJEC.
Next, the base precipitation array is constructed by placing
the computed MAP of OOZ into the PP(NFORC), or PP(2), position.
PP(l) contains the 18Z MAP value as adjusted during the previous
pass. This array along with the adjusted unit graph, UG6, is then
passed to subroutine MODEL for computing the base simulation at
time OOZ. The user is reminded that when using CHAT, all simulations
are recomputed from the beginning of the runoff event. Therefore,
when MODEL calls the appropriate forecast program modules to produce
the hydrograph, the computations in these modules must originate
from the set of carryover values that were saved at the beginning
of the event.
The remainder of the steps in the diagram are executed for NFORC = 2
in the same manner as described for NFORC • 1. If the base simulation
is not satisfactory, STRAT is called and given the opportunity
to once again adjust UG6 and PP, with PP now containing two MAP
values. As before, these arrays are updated upon return from the
subroutine and are subsequently used as input for the base simulation
of the next 6-hour period, 06Z.
This process is repeated for each remaining 6-hour period until
NFORC coincides with forecast time, at which point a forecast must
be issued. In this example NFORC coincides with forecast time,
12Z on Day 2, when it reaches the value of 4. At that time, the
forecasted hydrograph from the CHAT procedure is located in array
QS, and the PP and UG6 arrays contain respectively the four MAP
values and the unit graph ordinates that produce this hydrograph.
Presumably, this hydrograpb agrees more closely with the partial
observed bydrograpb than would have the hydrograph derived from
the original data. To resolve the remaining difference, hopefully
minor, that might exist be tween the adjusted hydrograph and the
observations, subroutine BLEND is called, which merges the two
hydrographs within a pre-determined number of ordinates.
CALL BLEND(QS)
where QS is the adjusted nydrograph. The output from BLEND is
the blended hydrograph, QBL, which is the actual forecast from
the forecast program and OBAT combined.
50
The output routines of the forecast program are used to display
the CHAT-adjusted hydrograph. The user must program to bring out
whatever additional CHAT information he wishes to examine. In
the research work the following displays and information were found
to be useful at each forecast time (which was every 6 hours):
1. "raw" simulation from original data
original precipitation data
objective function for raw simulation
2. base simulation
RH and RV for base simulation
precipitation for ba se simulation
objective function for base simulation
tolerance at time NFORC
3. adjusted simulation
adjusted RH and RV values
adjusted precipitation
objective function for adjusted simulation
4. a message based on the value of MSG to indicate which exit
condition from STRAT was used
It is imperative that the for~cast program interrogate MSG.
In the case where MSG equals 1 or 3, CHAT is unable to produce,
by adjustments to the input, a hydrograph that agrees within accept-
able limits with the observations. It may not be desirous to route
this hydrograph downstream, and therefore, some sort of forecaster
intervention must be permitted at this time. Whatever type of
revision is used, the forecaster must refrain from interfering
with CHAT's function--that of adjusting the precipitation. CHAT
presumably has adjusted it in the best manner possible, and the
forecaster should not attempt to change it and re-run the model.
If he chooses to revise the simulation, using any rationale that
seems appropriate, he should revise only the output hydrograph
and not change the state variables of the model.
One more point concerning forecaster intervention should be men-
tioned. The CHAT output is a hydrologic analysis of what has happened
on the catchment as a result of rainfall that has already occurred
rather than what appears is going to happen if the rainfall continues.
If the forecaster thinks that there is going to be more rain, he
should not raise the forecast; he should, instead, enter QPF in
the PP array and allow CHAT to handle it.
51
After each forecast is made, the following CHAT variable~ must
be saved, in addition to the carryover, for input to the next forecast:
NFORC,PP(53),UG6(36),RH,RV,SUM,LK(S3),UK(S3).
Suppose the next forecast is made at 12Z on Day 3. If the runoff
event is still continuing, the CHAT variables listed above (values
at forecast time 12Z-Day 2) are retrieved from storage and used
to begin the next pass through Figure 5.1. NFORC, currently equal
to 4, is incremented to 5 and becomes associated with the time
of 18Z on Day 2. The base precipitation array is prepared by in-
serting the computed ~~ of 18Z-Day 2 into the PP(S) position;
the first four positions, PP(l) to PP(4), contain 6-bour MAP values
from the beginning of the event (18Z-Day 1) as adjusted when NFORC
was equal to 4. Likewise, UG6, RB, and RV contain the final adjusted
values from the previous pass. With this data, the base simulation
is made for NFORC • 5, and so forth on through the strategy. Once
again, the simulation originates from the beginning of the ru.noff
event, and STRAT has the option of adjusting precipitation values
1 through NFORC.
The forecast operations continue in this manner until the forecaster
flags the end of the runoff event, at which t .ime control t:eturns
to the normal forecast procedure. The values of the soil moisture
variables at the end of the last pass through the CHAT procedure
reflect all the changes that were made to the input, and thus the
hydrograph, during the runoff event, and these values are carried
into future simulations. Therefore, CHAT has fulfilled its require-
ments of adjusting the model's state variables as well as the model's
output.
It has been stated that each 6-hour period during the runoff
event must be regarded, in turn, as the current period for CHAT's
computations, but the reason for this bas not been explained.
One of the unique features of the CHAT adjustment strategy is that
it will adjust only those precipitation periods that are contributing
most heavily to the runoff at the current time. (This feature has
been discussed at length on pages 30-31.) As "current" time pro-
gresses through the runoff event, the critical precipitation periods
change also, so that at one point or another each 6-hour precip-
itation period will have been in the "critical" position and been
able to be adjusted. However, if "current" time progresses at inter-
vals larger than 6 hours, one or more of the 6-hour precipitat.ion
periods will never be in the criticd position in relation to "current
time," and consequently, will not be properly adjusted. Hence,
the reason for each 6-hour period being treated, in succession,
as the "current time."
52
It is hoped that the discussions of this chapter will provide the
necessary guidelines for implementing the CHAT adjustment procedure
in the user's forecast program. Only those specifications that are
crucial to the proper use of the procedure have been provided in
order to allow as much freedom as possible in adapting this procedure
to the user's particular forecast program.
53
6. EXAMPLES
During the research phase of the project, the CHAT procedure
has been tested on many runoff events from various headwater basins.
The analyses are of a conceptual rather than a statistical nature;
thus, no attempt has been made to study a "statistically significant"
number of events. The pr~mary purpose of the studies has been
to acquire a knowledge of the characteristics of the CHAT procedure.
It is believed that this type of knowledge is transferable to other
events as well. From these studies, six examples have been selected
for this report to illustrate the manner in which the procedure
operates. These particular events were chosen because they demon-
strate CHAT's performance under a variety of conditions on several
basins of highly different characteristics.
To test the CHAT procedure, the CHAT routines were linked to
a hydrologic model consisting of the Sacramento soil moisture account-
ing routine and a unit graph operation for distributing the runoff
in time. For each runoff event, forecasts were made with this
model every six hours as ~n a real-time forecasting operation.
Thus, each example cons~sts of a series of plots that illustrate
the behavior of the procedure at various forecast times. The vertical
dashed line identifies the forecast time, NFORC, for each plot.
The ordinates along the abscissa are successive 6-hour periods
from the beginning of the runoff event. In the legend, the "raw"
simulation refers to the hydrograph produced by the hydrologic
model using the reported data without any adjustments from CHAT.
The "adjusted" hydrograph is the product of the CHAT strategy.
The actual forecast from the forecast program in conjunction with
the adjustment procedure is the "blended" hydrograph, obtained
by merging the available portion of the observed hydrograph into
the adjusted hydrograph within a pre-determined number of ordinates.
The rainfall profile for the event is displayed in the upper
left corner of the illustration. Accumulative amounts, in mm.,
are plotted every six hours up to current time, NFORC, for both
the "raw" and "adjusted" precipitation. The number on each 6-hour
segment is the precipitation that occurred during that 6-hour period,
or in the case of the adjusted graph, the ~alue to which CHAT adjusted
the 6-hour amount. No QPF was used in any of the examples presented
in this report.
Directly beneath the precipitation plot are the adjusted values
of the warp coefficients, RH and RV, that were used to warp the
average unit graph. The warped unit graph resulting from these
values was used in producing the adjusted hydrograph.
5 4
Each example is accompanied by discussions at each forecast time
of the hydrologic conditions and the subsequent behavior of the
CHAT procedure. The decisions made by CHAT have been analyzed
according to a philosophy in decision-making theory expressed by
Tribus (1969). If any decision involves risk, it is always possible
that a good decision can lead to a bad outcome and that a bad decision
can lead to a good outcome. Therefore, it is necessary to evaluate
a decision on the basis of whether or not it represents a logical
analysis of the information available to the decision maker at
the time, and not on the outcome of the decision. It is with this
philosophy that the CHAT adjustment procedure must be evaluated.
The rationality of its decisions should be determined by comparing
the CHAT adjustment to what an intelligent and experienced, but
not clairvoyant, forecaster would have done under the same circum-
stances. Verifications of the peaks of the CHAT-adjusted hydrographs
cannot be used as an effective measure until the rainfall for the
runoff event has stopped. If the adjustment results in a good
forecast, so much the better, but this is not the principal criterion
in judging the performance of the technique. As stated earlier
in Chapter 1, the two requirements the CHAT procedure must fulfill
a re that the soil moisture accounting variables be adjusted along
wi t h the output, and that the adjusted output be at least as good
as that which a skilled human forecaster could produce subjectively.
55
Example 1
Example 1 is a runoff event that occurred on Bird Creek near
Sperry, Oklahoma, on July 2, 1976. It illustrates the performance
of the CHAT procedure for a case in which the raw simulation and
the observations differ greatly.
NFORC 6: The raw simulation is rising in response to 33 mm of
precipitation but the observations are not. CHAT lowers
and delays the rise somewhat.
NFORC 7: An additional 31 mm of rain has fallen in the past 6 hours,
and the raw simulation is rising rapidly. The river is
still not responding, and CHAT lowers the simulation to
agree with the observations.
NFORC 8: The rain has stopped. The raw simulation is showing a
rise froru 7 ems to 180 ems, an increase of 2500 percent,
and has been continually rising for the last 18 hours.
Yet, the observations show no rise at all. CHAT concludes
that there has been no precipitation in the catchment,
an unlikely but not impossible condition in Oklahoma in
July. The action is drastic, but not ridiculous. A
prudent forecaster might well reason similarly and would
certainly refrain from issuing a forecast of e sizeable
rise.
NFORC 9: The rain has started again and the river begins to rise
slightly. CHAT acknowledges that a small rise is
probable at this time.
~70RC 10-12: During these periods the river continues to rise. An
additional 37 mm of rain has occurred in the past 24 hours .
The CHAT simulations are repeatedly increased at the
successive forecast times, partly in response to the
additional rainfall, and partly because the observations
indicate that the downward revisions made earlier may
have been too drastic . The initial burst of 64 mm had
been reduced to 0 at NFORC 8, but by the end of the
event, CHAT restored 19 mm.
~WORC 13-17: There has been no additional preci pitation. CHAT con-
tinues minor upward adjustments to the simulations in
response to a continued rise in the observations to a
peak 24 hours past the time that the raw simulation
indicates the peak should have occurred.
56
NFORC 23: The CHAT procedure continues to operate past the peak
and on down the recession so that the soil moisture
variables will be updated at the end of the runoff
event. By the end of the event, the total surface run-
off for the raw simulation was 46.1 mm, which CHAT
adjusted downward to 20.7 mm . The actual observed
surface runoff was 22.6 mm.
In summation, early in the rise CHAT over-reacted somewhat in
the early downward revision and had to revise upward in light of
future events. However, CHAT was dealing with an event in which
the raw simulation was predicting a major flood 7 feet above flood
stage. The highest stage reached, in fact, was slightly below
flood stage. CHAT, at all times, produced adjusted hydrographs
which peaked below flood stage. It is felt that a human forecaster
cou ld not have handled this situation in a more apt manner, and
consequently, CHAT has satisfied the requirements that were estab-
lished for the procedure.
57
VI
00
w
(!)
700
600
500
a:: 300 ~
(.)
(/)
0
200
100
a.
(.)
LLJ a:: a.
2:V'
/ / ,.
4 --~"": /l6 ~,... ___ _
3
1 1
RH • 1.14
RV s 1.16
5
I
14.0 FT
7 9 11 13
TIME (PERIODS)
Figure 6.1--Example 1, NFORC=6
15 17
LEGEND
---OBSERVED
·-- -BLENDED
---RAW
··•••••••• ADJUSTED
RAW PRECIP
-·-·-ADJUSTED PRECIP
19 21
" (f)
~
() ._,
w
\JI (!)
\0 a::
~
~
0
700
600
500
-400
300
200
100
100-
" ~
~
9::
() w a:: a..
50 ..
" 31/
/
/
23// /
/ /
6 / *31 " --/ 0 ........... -::::-.-. --· 0 0 0
/27.3FT
r"--....
I "' I '\
I \ ·---BLENDED
I \ ---RAW
••••••••• ADJUSTED
-F~ ~L ~F~ I I ' ~== ~~~s~;~CI;RECIP
I I \,
I
I,;' ................ L .. :~:~.:.T \ .. ... '
.••. ······ ·············· \ .... ·····
/ ' I •••• •• ~· •••
RH a 1.20
RVa 0.86
LEGEND
---OBSERVED
, ~ , ~ ,/ I ... ··· ~·· ..
/ ,, 0--------~----~~·----------~----------~----------~----------~----------~----------~~~=··~ 2 3 5 7 9 11 13
TIME <PERIODS)
Figure 6.2--Example 1, NFORC=7
15 17 19 21
@
~
0 -
700 100.
9
600 ~50.
0 ,.---
3y/
/
/
l:V/
/
~-"
500 "--0~---·---·-·-·---0 0 0 0 0
400
RHa1 .17
RV a 0.89
w
(!)
0:: 300
~
0
UJ
i5
200
100
FLOOD lEVEl -21 FT -----
3 7 9 11 13
TIME <PERIODS)
Figure 6 .3--Example 1, NFORC=8
15 17
LEGEND
---OBSERVED
·---BlENDED
---RAW
•••••••••• ADJUSTED
----RAW PREOP
-·-·-ADJUSTED PRECIP
19 21
-en
::1!
0 -LU
(!)
0\ 0::: -<(
:I:
0 en
0
100
600
500
~00
300
200
100-
g
~50•
Q..
0
f
0 10,. _,. /---
3J/
/
/
/ 2Y
/ ,..
6 J' -·,o .. -·-·-· ~ ---·-0 ow....-:-·-·-4 ~ 0 0
RH a 1.09
RV a 0.81
/'27.4 FT
, -......
"' "" ( '\ I , l \,
I I \ FLOOD lEVEL -21 fT
----~
LEGEND
---OBSERVED
---BLENDED
---RAW
•••••••••• ADJUSTED
·---· RAW PREOP
-·-· AD.lJSTED PIECIP
I I '\
;' I '\
I I ~~~ .. ~ .... ~~~_..'."'., .. ~~~!t··:·:··:··:·~_ .. _=_·~~··_·~_ .. _~_.-_ .. _.m~~~~--Wft __ ··_··_··-~~~-:_.~_-·_··_··_··_··~··~··_··_··_··_:_.~~-·=·~··:~:-~:··:··:··:··~·~
2 3 5 11 13 15 17 19 21
TIME (PERIODS)
Figure 6.4--Example 1, NFORC=9
,..... en
~
0 -w
0\ (!)
N a:: <t
:I:
0 en
0
700
600
500
~00
300
200
100
100•
so-a..
0 w a:: a..
10,.. ,..
10,.. .... 0 _ .... /----
31/
/
// ·' / 27.6 fT
23 / ........... 1 0
I ____ ..... 10
, • 0 ~ . I
~ 6-/ ·' o..r:-::~:=---~· ..... 13 /------~ ~H. 1~00 1 ,\
RV: 0.86 1
I \ LEGEND
I \ OBSERVED
---BLENDED
I I ' ---RAW
I
I I \, ~==: ~~s;:~ciP
-·-· ADJUSTED PRECIP I I \
FLOOD lEVEl - 2 1 FT -----
/ I 8 .2 FT '\
;' '-----.::::::.£,. .... -............. '\.,
/ ····· ······ ~ / ···t·········· ················· -/ ······
0~--~----~--------~~~~--~----~------L-----~----~----~ 2 3 5 7 9 11 13 15 17 19 21
TIME (PERIODS)
Example 6.5--Example 1, NFORCclO
@
~
0
~
w
(.!)
600
500
400
0:: 300 ~
0 en
0
200
100
RH= 0 .95
RV a 0.91
/27.6FT
J--~ / I ,
( I '\,
II \ ~~~ I ' ----OBSERVED
---BLENDED
I I \ ---RAW
I •••••••••• ADJUSTED
I \ ---· RAW PRECIP
I \ ·-·-ADJUSTED PREOP
I I ,
FLOOD LEVEL - 2 1 FT -----
;' I /'3.0 fT \,
I -----=====~~--\ ········ ·······b.._ I I ····· ······ r .. ... , ·········· . . .......... ,
/ ~~
7 9 11 13 15 17 19 2 1
TIME <PERIODS)
Figur e 5 .6--EA~w ~l~ l, NFOR C=ll
700
500
.400 ,..... en
~
0 v
w
0\
(.!) a: 300 ~ ~ g
0
200
100
0 2
1 s,
2 411'7
10----,..
1 0 411'411'
0 --,. .... ---~
/ -~ 3~ -~s
/ -·-/ ,..,... 2 I / 27.7 FT
/ ~· 13 23/ ~
100•
6
// .,.--·o-· ..... ·10 1-........
RH•0.95
RV: 0.91
(). f:--=c;::..-:;. ,.. 1 s ,!" /11 -"""'\
LEGEND
I I \\ ---O&SERVEO
~:::. ~~:OED
II I '\:········· ADJUSTED
I ---RAW PRECIP
·-· AOJJSTEO PREOP
\
/ I
I
I
I
I
/
FLOOD LEVEL -2 1 FT -----../15.6fT \,
------" ----fiiiiii'J •••••••••••••••• ....... ' I ······ ······· !till... ••• ••q ····· ..... ' .... ······ .... ······~ ~ ~~ .... 1 ..... ...
~ ~ .. ········· I
3 5 7 9 11 13 15 17 19 21
T~ME <PERIODS)
Fi g ure 6.7--Examp l e 1, NF ORC=l 2
...
w
(!)
700
600
500
n:: 300 ~ :t:
(.)
C/)
0
200
100
0 2
100-
RH& 0 .94
RVa 0.92
1__/21.1 FT
.,---~
~ I ,
,/ I "., LEGEND
---OBSERVED
---BLENDED
---RAW
••••••••· AD.lJSTED
----RAW PRECIP / I \, I I \, ··-·-ADlJSTED PRECIP
FLOOD LEVEL -21 FT / : /17.1 FT\\ -------
I -------\ I ............. :.:............. ' ····· .... .... ' r····· ······· ~ ···~"' I I ··············~ .•• ,_.~ •..••.... ~~
~ ~ ~ ' ..
I •••• ...
~ I
3 5 7 9 J1 13 15 17 19 21
TIME <PERIODS)
Figure 6.8--Example 1, NFORC •l3
" en
::E
0
\,J
0\ w
C> 0\ a::
<{ :z:
0 en
0
700
500
AOO
300
200
100
100-
so-
RH• 0 .94
RV: 0.92
FLOOD LEVEL - 2 1 FT
----~-
27 .7 FT _/J ,/ I',
( I \
LEGEND
---OBSERVED
·---BLENDED
---RAW
••••••••• AD.lJSTED
---·RAW PRECIP
-·-· AD.lJSTED PRECIP I I '\,
I I 17.9 >-, / --~, \
I l ,, \ ················ ', ~ I ······ ... ·········· ', ······ I ·······, ... ···-~ ........ ' ... ···7.' I •• ·• ~.,
I ······ I ······~ ~~ .
... / ····· ······ I ...
0 2 ~ .... 3 .. ~ .. ~~5 -'MM~··•···-~~··;·;··~··.··~~9~------~1~1-------1~3~--~--~15~----~1~7~----~~;9------~21
TIME <PERIODS)
Figur e 6.9--Example 1. NFORC=l4
,
w
(.!) a:
700
600
<X 300 :r
()
(/)
0
200
100
50-
0 0 0
15,. ...... --------~
2 /
10_,---/
10 --
0 --
____ .,.
/ ~--·-·-·-·-31 / .,..5 o o o
/ ~--·' / • 2
23// , ..... ·~15
/ ---· 10 / .~· 0
.. 6-~ ~ 15
/27.7 FT
_........ --· 0....,.,-___ ._.. A
0 0
,.,.----... I
(" "'J LEGEND
---OBSERVED RH a 0 .93
RV• 0.93
FLOOD LEVEL -21 FT -----
I
I
I
I f\ I I '
I I \
/ I
- - -• BLENDED
---RAW
••••••••• AD.lJSTED
----RAW PRECIP
-·-· AD.lJSTED PRECIP
I
i
I
--\ t .................. \
······ ········· ' ~ .... ······ ' ... ... '
.. ···· J ········ ' ... ·· ···· .. ""', ~ ' .. .. ~ ' .... I ... ..
/ ~ .. ., ..
11 13 15 17 19 21
TIME (PERIODS)
Figure 6.10--Example 1 , NFORC=l5
700
600
500
200
100
0 2
0 0 0 0
15 ~------------
2 ~~
10-----to-~
0 --,---~·-·a·-a-·-o·-·o-·
3 v/ · 1s // ,."t:·l·-/ '2 7.7 FT
50-
/ .i. 0 2~/ -----1o ~ I
_. ~-/ ,·rs ~---~ ....... o~:Z::o--·7'"· // '-, I
I \1
LEGEM:>
---OISERVED
3
RHe 0.92
RV•0.9-'
5
---• IUNOED
I ~ ·········· ADAJSTED I ~ ----RAW PREOP i \ ·---· AD.liSTED PRECIP
I I \
I I \~20 .5FT
I ~·~~ I ············t ,~
I I •••• ••·•·•••········ ~·················· •••• :',, .. . ... ~ '
I I ..• ••••··•• I ·····~~ ...... ~
/ ·~~ ....
I
---RAW
7 9 11 13 15 17 19 21
TIME <PERIODS)
Figure 6.11--Figure 1, NFORC•l6
700 100-
" ~
~
600 50-
500
w
~ 300
Q_
C3 w
0:::
Q_
RH• 0.93
RV a 0 .95
FLOOD LEVEL -21 FT
/27.7FT
~----.. ....
/ " ;I' , I
I " I I '\
I \
LEGEND
---OBSERVED
---BLENDED
---RAW
•••••••••• ADJUSTED
----RAW PRECIP
ADJUSTED PRECIP
~
(.)
C/)
-----~--~~----20.7 FT
I
I
0
200
100
3 5
I
I
I
I
I .. .. ······ ·················
7 9
I,~
·················· ,, ······· .... ,.. '' ... ···· ········ ~',
/ ' ' / ' ' ~ ~ ' .. · ' ' ... ·· '-. ', ~ ~ .
/ ' ..
11 13 15 17 19 21
TIME <PERIODS)
Figure 6.12--Example 1, NFORC=l7
w
(!)
700
600
5 00
4 0 0
a:: 300
<!
I
() en
0
200
100
100 -
\J 50 -
Q.
(3
w a::
Q.
1 ~/------fi~~~-~-------------
2 /
I0----10 __ _
0 --/___ ·"'·-·-.-"I'p".;t,8iiM .. -·-.-.-.-.-.-.-.
/ ."Is 3 ~ -·-/ ,-2
/ ,·
23 / ,. 17
/ ---·,....io / • 0 • .!:..-, /. 1'5
~27 .7FT
__ ...-~· o----·-· • 0 0
~-...
/ "' LEGEND
---OBSERVED
RH r: 0 .9 6
RV= 0.9 8
5
I ,\ I ,
I \ I ,
I
I
I
I . .. . · ... ····
... ······ I
I
7 9
.. .. .. ...
II
TIME (PER IOD S)
13
F i gu r e 6.1 3--Exam ple 1 , NFO RC=2 3
15 17
---• BLENDED
---RAW
•••••••••· ADJJSTED
----RAW PRECI P
-·-·•AD.lJSTED PRECIP
19 21
Example 2
Example 2 occurred on the Monocacy River near Frederick, Maryland,
on June 19-23, 1958. Even th ough it is a double-peaked event, it
is treated as a single runoff event in this example. In an effort
to shed some light on what constitutes a runoff event, this same
rise is rerun in Example 3 as two separate runoff events.
NFORC 3:
NFORC 4:
NFORC 5:
NFORC 6:
NFORC i:
NFORC 8:
NFO RC 9:
NFORC 10 :
NFORC 11:
After 30 mm of pr~cipitation, both the observations and the
raw simulation exhibit slight rises. Since they are in close
agreement, CHAT makes no adjustments. It is an insignificant
rise, but CHAT does not know this and is, therefore, not
influenced by it when making the decision.
There is a 30-percent disagreement at the latest ordinate,
but CHAT ooes not adjust. Since it is still 12 hours before
the forecast peak, this is a reasonable decision.
The rain has stopped and the observed graph is levelling off.
The agreement between the raw simulation and the observations
is reasonable and no adjustments are made.
No more rain has occurred in the past 6 hours but there is a
sudden and unexpected rise in the river. CHAT makes upward
adjustments to the simulation to agree with the observations.
At NFORC 5, there was absolutely no indication that the river
might suddenly rise 6 hours later; consequently, the decision
CHAT made at NFORC 5 is still logical.
The observations continue t o rise sharply and CHAT increases
the precipitation by 5 mm more and alters RH and RV. It
concludes that the latest observed is the peak. The raw
simulation p~aked 6 hours earlier at a stage 2 feet below the
latest observation.
The river is recedin g at this time, which verifies CHAT's
assumption at NFORC 7 c oncerning the peak.
After 24 hours. the rain begins again. The simulations
forecast another rise, and the additional rainfall justifiE·s
such a forecast.
It is still raining, but t he observations are showing no
rise.
The raw simulation indicates that the river should have
been rising for the pas t 18 hours, but the observed is still
falling. The adjustments that CHAT makes are minimal even
though the agreement during the second rise is not good.
CHAT is apparently being influenced by the agreement with
the observations during the fi rst rise. This suggests
that the procedure might operate in a better manner if the
second rise were treated as a separate runoff event.
71
\
NFORC 12:
NFORC 13:
NFORC 14:
The simulation now appears to agree more closely because the
observed is finally rising. Even though the results are
good at this time period, CHAT, nevertheless, made a bad
decision at NFORC 11; the agreement was not acceptable and
CHAT should have attempted to improve it.
The observed is still rising. The adjusted simulation and
the observations are almost identical except for a 6-hour
displacement in time. However, the idea of treating this
example as separate runoff events is still logical.
The stage of 6 feet at NFORC 13 was the peak and the
hydrograpb is now in recession.
In summary, the highest stage reached by this event was 6 feet,
which is 8 feet below flood stage. The rise was insignificant through-
out the entire event, but CHAT was unaware of this and operated
in the same manner as it would have on an event of flood proportions.
During the early part of the second rise, CHAT's decisions were
not good, apparently due to the influence from the first rise.
Therefore, it seems advisable to treat this example as two separate
runoff events.
72
90 oo-,.....
~
~ -a..
0
80 50• w a: a..
2 8//
2 _/28 7 0
RH & 1.00
RV a 1.00
6 0 LEGEND
OBSE RVED
'"' ---BLENDED
CJ) ---RAW ~
(.) 50 ••••••••• AD.lJST ED
'-'
---· RA W PR ECIP w -·-· A DJJST ED PRECIP (.!)
a::
<( ::r
(.) 40 CJ)
0
3 0
I 2 .6 FT
I ~--/ ~ 1 .5 FT
.,,___~
, ~-1 -___ .......:;;_ ... __ _
2 0
10
I
0~--~------~------~------~------~------~------~------~ 1 2 6 8 10 12 14 16
TIME CPERIOOS)
Figure 6.14--Example 2, NFORC•3
73
\
Q..
()
80 so-w
Q..o:: 6 40' --28/""" 6
i128
70 ~-/ 2
60
w 50
(!)
0::
<(
J:
()
(j)
0 40
30
20
10
RH: 1 .00
RV a 1.00
LEGEND
---OBSERVED
---BLENDED
---RAW
•••••••••• AD.lJSTED
---·RAW PRECIP
·-·-· AD.lJSTED PRECIP
-----
0~-~----~------~------~-------L------~------~------~ 1 6 8 10 12 16
TIME (PERIODS)
Figure 6.15--Example 2, NFORC=4
74
90 oo-,....
~
~ .......
a..
0
80 5 0-w g: 6 __ ..J_
,-0
70
,.... 60 en
~
() .......
w
~ 5 0
<t
I
() en
0
28/ 6
/
2_//28
RH: 1.00
RV: 1.00
TIME (PERIODS )
Figure 6.16--Examp le 2, NFORC=S
75
LEGE ND
---OBSERVED
---BLEN DED
---·P.AW
···•·••••• ADJUSTED
----RAW PRECIP
·-·-·AD.lJSTED PRE CIP
\
l
w
(.!)
a:
<{
J:
()
C/)
a
90 10~
:E
a..
()
80 5~ 0 0
a.. ~~-----· I-" 0 0 76
2 /28
70 &--2
60
50
40
30
20
RH a 1.00
RV ~ 1.02
4 .1 FT
I
..... 1··········\.. ', . . \ .... I ...... \ / 3.3 FT
J ~·"(\ /1'-' .. , !/ '\. \ .. '\ ..... / I " ..... , // I , ···-.. ~,
.y '·· .. ' ... ~ "'··· .. ',
LEGEND
---OBSERVED
·---BLENDED
---RAW
·••••••••• ADJUSTED
----RAW PRECIP
-·-·AD.lJSTED PRECIP
10 ... '..::.;, ... -::-, I _..,.., ______ _
I
0~---~---------~----------L--------~~---------L------~---~---~
1 2 4 6 8 10 12 14 1 6
TIME <PERIODS)
Figure 6.17--Example 2, NFORC•6
76
-60 (/)
~
0 -w
(!) 50 a:
<{
I
0
(/)
0
40
30
20
10
RH • 1.05
RV c 1.07 I'\
1 \
5.3 FT
.. ·. \ .. . .1.. \
: ... \
I .... \ .. \ \ :.. ... \ : I \ ' ! \ \
! I .... ' : \ \
! \ \
! I \ ', : . : ~ \ ! L,3.3 FT \ \
i ~ .. \
. '~I \ '
:/ 1', ... ' . \ \
r ... ?/ I "' \ ... ',
LEGEND
--OBSERVED
---• BLENDED
---RAW
··········ADJUSTED
----RAW PRECIP
-·-·-ADJUSTED PRECIP
v I , ·· .... ', ~ " ··. ' , .. ' -········ ..... I -----··-··.;.;·~;.:.~ ... ,... ......... ___ _
I oL1---L2------~4 ------~6--~--~e~----~~~o------~~~2------~~~4------~~6
TIME CPERIODS)
Figure 6.18--Example 2, NFORC=7
77
w
Q_
()
80 so.w 3 0 0 0 ~ 9 .~--·-·-·-·-·-CL. ........... __________ _
.-..--0 0 0 0
29;' 6
/
2 /28
70 ~-"" 5.3 FT
2
RH = 1.05
RV : 1.07
.. . . . . . . . . . . . . . .
LEGEND
---OBSERVED
·---BlENDED
---RAW
•••••••••. AD.lJSTED
(!) 50 a::
~
~\ I' ----RAW PRECIP
-·-· AD.lJSTED PRECIP <t
I
()
(/)
0
40
30
20
10
. . :· . : . . : . . . . . : . . . . . : : . . . . . . . .
\ \ 1 \
~~ \
1
\ \
\ \
I \ \
\ \
\ \ /3.3 FTI \\
: /-""' I \.. ',
I ' \ ' : / ,, ... ' ~~ " \~ ', v I , ··.. ' .....
i1 " •••• '-..... .. ' .... -....._ ········· ....... ...... I --...... ,..,. ...... __ --
I 0~~~------L-------~------~------~-------L------~-------J
1 2 6 8 10
TIME <PERIODS)
Figure 6.19--Example 2, NFORC m8
78
12 1 4 16
Cl.
(.) 12 ·' 80 so-w 3 o o o .ii'.,
0:: 9 ..,.. ..... ------·-·-·-.,...,
2 6
Cl.L(t--·---o--'0--o---a--12
2/28 5 .3 FTI
70 ~-I
RH : 1.05
5 .2 FT
\
LEGEND
--OBSERVED
·---BLENDED
~--, ---RAW
'"' 60
(J)
~
(.)
'-"
w
(.!) s 0
0::
<t
:I:
(.)
(f)
0
~0
30
20
10
RV = 1.07 I
I
I
I \ .......... ADJJSTED
I \---·RAW PRECIP
/ \..-·-ADJJSTED PRECIP
I ········~ \ f \ \
I : ~\-'-~.6 FT
I fr---...,.\\
! /J !/ '\\ \ : I fJ \ ', : . .
I ,I /I '\\\ f \ /1 \\
f \~ ./I \ \\ I .(I \~,
: I \ ·.\
:/ ' \·~ j /-~ y \··~~ I" '\._ ,·\. ~·. I ~ ... ,.:
I
I
0~--~---------~--------~-------~---------~---------~---------~--------J 1 2 6 8 10 12 1~ 16
TIME (PERIODS)
Figure 6.20--Example 2, NFORC~9
79
a.. 4
12 .-·-
(.) ·""' ---80 so-w 3 o o o , __ 4
Q: 9 ·-·-·-·-·-·-· ,_,..
,;v-5 .7 FT
1\
I \
70
r. 60
CJ)
~
(.)
'-J
w
(.!) so a::
<{
I
(.)
CJ)
Q
30
20
10
I ~: \ I ..
a.. ~. =-------------,_... 1 2 F-'1,-o o o o 2v •
2_/28 I I f\\ /5.3 FT
I 1 •\/
I t//S,\
I lrf, \\\
2
RH = 1.05
RV: 1.07
I If \ \\ I • •\ I~~ \~
f,/, ,,~ . \\ : . .
! \ ! '\\\
f \ fi ~ ! ... .. \\
. \ I '~
i ·. .. \~' f \/ I LEGEND \~
f I I OBSERVED ~~ i ---BLENDED \ ~~
.... 1/,............_, I I ---RAW \~~,
"' •••••••••• AD.AJSTED -a J ·---·RAW PRECIP
1/ ' I -·-·-AD.lJSTED PRECIP '\> .. ~~ "---I ~
I
I oll---2L-----~4~------~6~----~8~------~1~o-------~12~-----~14~----~~6
TIME (PERIODS)
Figure 6.21--Example 2, NFORC =lO
80
w
9o oo-,..,.
~
~ -~ 12 _1-·-0
·-
8 0 50-w 3 0 0 0 • .,. • ----0:: 9 ..... .-·-·-·-·-·---4JIIII">~~ 0 .,.. -~ a. ~. -----------------' 12 29, 6 0 0 0 0
.(a 2 ,
70 ~-2
RH e 1.09
RV • 1.06
. : . .
!
f :
!
0 :
! . . .
5.3 FT
. /5.3 FT
: ... 'o/"'
I ~\ 1/ '\\
{
• \.,... ~.8 FT . J1J~
: 1\ \~
(!) 50 a:::
:
0 . :
/1 /\ \
!, I : \ '~\ <X:
I u
(/)
0
~0
30
20
. . . .
! . : : : . : . . : .
: I \ ~ . \ . . I ~ . \ ~
\ ••••. .}/ I \~ \ ·; \\
II I '\\
• LEGEND \\\
•••
• ·/-............. I I OBSERVED ,~ ... " I ---BLENDED \ \
!/ ' ~---RAW \ \
,(
: '--_,. •o••o ••o•• ADJJSTED ',, \.
----RAW PRECIP ,, '
1
··-·-ADJUSTED PRECIP-,", /.··· .. .. 1 0 •• ~Mil.,-..... 0. I
I 0~---~---------~---------~---------~---------~---~----L----------L--------J 1 6 8 10 12 1~ 16
TIME (PERIODS)
Figure 6.22--Example 2, NFORC=ll
81
0... 4 _ • ..Q._?_.
11 .-· 0 0 0 0 ·" --------80 so-w 1 ·-·-·---·-·-,.-4 o o a:: 9 .-,.
70
,... 60
(/)
~
0
'-./
w
(.!) so a::
<(
:c
0
(/)
Cl
40
30
20
10
0... -.:..":"------------1 2 L';~ 0 0 0 0
S.3 FT 2~" 6
2 /.1'28 -S.3FT J lf . . . .
2 . .
I '~. . ,, .
j \\ I I\\
I I ~~ : I ,, \
1 \~ \ ~ I '\\
\ \,\ \ : I ''\ ······ ,, I \\~
) I \'~,
II LEGENd \'~.
--OBSERVED \ •
---·BLENDED \~:\
:/~ ~ )/ ::::::: ~~~STED \~··· •••
/ ' ·---RAW PRECIP \ •.
)/ "--··-·-A,AISTED PRECIP "':
/.~ I .. ..
~ I -····· ........... ~
RH: 1.09
~v = 1.06
o~--~------4--------~---------~·-------~------~'------~·------~ 1 6 c 10
TIME (PERIODS)
Figure 6 .23--Example 2, NFORC=l2
82
12 1 4 16
,.... 60
en
~
()
'-'
w
(!) so a::
<3:
I
() en
0
40
0~--~------~------~------~------~-------L------~-------J
1 2 6 8 10 12 16
TIME <PERIODS)
Figure 6.24--Example 2, NFORC =l 3
83
90 oo·-:E
:E
'-"
a.. .5 ___ o_.-P.-. ..2.-.it.
11 .-·
(.) 0 0 0 ., .~ ---~-----------~-80 50• w 7 ·-·-·-·-·-· --4 0 0 0 0 0::: 9 -·--.-__ ..._ 5 .7 FT a.. • .,-_ ~----------.~ 1 2
70
"" 60
(/)
:E u
'-"
w
(!) so a:::
<t
I u
(/)
0
30
20
10
-_n-0 0 0 0
2!f'
RHa1.10
RV: 1.07 . : : : : : . . : . . : : : : . . . . . . . . : . . . . . . : . . • . • • : . • . :
'"· ·. ·· ..
•·· ... •. .. .\ . .
~
~ . .
~ .
\ . . .
\ . . . .
········]
I
I
/ ,~ I i/ , I }' "--
~ .· .. .. .. .. ....
LEGEND
--O&SEAVED
•---BLENDED
---RAW
•••••••••• ADJUSTED
·---·RAW PRECIP I
-·-··AD.USTED PRECIP '
QL-~-------L------~-------~----~------~------._----~ 1 2 6 8 10 12 16
TIME <PERIODS)
Figure 6.25--Example 2, NFORC•l4
84
Example 3
Example 3 treats the rise of Example 2 as two separate runoff
events. As one would expect, the first rise is exactly the same
as in the previous example and will not be illustrated again. The
beginning of the second rise, NFORC 1 in this example. corresponds
to NFORC 8 in Example 2.
NFORC 3:
NF ORC 4:
Because the second rise begins on the recession of the
previous rise, the first ordinate is the highest at
this time. However, CHAT does not treat it as the peak
in its computations of MPT for the tolerance. This
feature is discussed in detail in Chapter 4. The raw
simulation is much higher than what it was in the previous
example due to CHAT operating on the first rise, thus
rendering the soil-moisture contents much higher at
the beginning of this rise. CHAT overreacts and tries
to lower it too much to effect an agreement with the
observations. This situation would not have occurred
wit •. a smaller !::. on the precipitation adjustments.
The adjustment on the last pass put the objective function
well inside the tolerance. As stated earlier, this
adjustment strategy is not intended to minimize the
objective function but rather to reduce it to a sat-
isfactory value with as minor modifications to the
input as possible. With a smaller !::. the adjustment
would have put the objective function just inside
the tolerance and not way below it. This !::. size is
a CHAT parameter whose value must be supplied by the
user. It is not necessarily being suggested that the
!::. size be changed, but this example does illustrate
the effect the !::. size can have on the performance of
the procedure.
The raw simulation indicates that the river sho•:ld have been
rising for the last 12 hours. more than dou~!~ng the
discharge in that time. Yet, the observed has been
falling steadily during the period. The on ::.y logical
conclusion is that the simulation should be reduced
drastically, which is the course of action CHAT takes.
In light of the information available at this time,
this decision is logical even if one is "over one's head "
in water the next 6 hours. In comparison with Example
2, note that at the corresponding time, NFORC 11,
CHAT made only minimal adjustments because it was taking
into account the fit of the first rise as well.
85
NFORC 5:
NF!JRC 6-7:
The hydrograph is now rising. CHAT responds by adding 6 mm
of precipitation, thereby increasing the peak. Note
that at this point the adjusted precipitation totals
15 mm -the same as in Example 2. Now that the river
is finally rising, both examples are behaving similarly.
Prior to the rise, however, they were operating quite
differently . In comparison, CHAT in Example 2 made
a bad decision at NFORC 11 but was fortunate in that
the results were good at NFORC 12: at the corresponding
periods in Example 3, its decision at NFORC 4 was logical
even though the results were poor at NFORC 5.
CHAT makes only minor adjustments from this point on through
to the end of the event. The major point has already
been illustrated at periods 4 and 5.
In summary it is felt that the decisions made in this example
were more logical decisions than those made at the corresponding
periods in Example 2, even though the results were not as good.
Since CHAT must be evaluated on the basis of the rationality of
its decisions rather than the outcome of the decisions, the conclusion
is inescapable: the CHAT procedure does what it is supposed to
do better when the two rises are treated separately than when they
are treated as one runoff event.
The usage of the CHAT procedure requires the identification of
the beginning and the end of the runoff event. It is hoped that
this example has provided some insight into the problem of defining
runoff events. It is an age-old problem for the forecaster and no
attempt has been made to solve it in this study.
86
w
(!)
a::
<l:
I
()
(/)
0
100
80
60
40
20
1 oo-.
£l.
5~
a::
£l.
LEGEND
---OBSERVED
---BLENDED
---RAW
12 ---~-_-:J -~· 9 FT ........ ------· I .,.. ....... s·-· • I ,/ '
RH~0.79 I / "
··········ADJUSTED
----RAW PRECIP
-·-·-ADJUSTED PRECIP
RV:0.80 / r4.8 FT '
1/ _,.,JOUIIM'IM·-~.., "
; ,, ' ,~ ' " ._-~~~ '··. ··. ··. ' ····... ' ··. ""' ··.. ' .. ······ .... ...
0 1L-------~2------~3~--·----~4--------sL-------~6------~7~----~8
TIME <PERIODS)
Figure 6.26--Example 3, NFORCmJ
87
w
(!)
a::
<{
I
(.)
(f)
0
100
60
20
100·
RH:0.78
RV:0.80
,. ____ ·············· .... _ ····· ---.. .
LEGEND
---OBSERVED
---· BLENDED
---RAW
···········ADJUSTED
----·RAW PRECIP
-·-··ADJUSTED PRECIP
I
I
...... ...... ·· ... ...............
.....:~ .. ... ········· ·········· ·····
I oL--------L---------~------~---------~----~------~--~s l 2 3 .. 5 6 7
TIME <PERIODS)
Figure 6.27--Example 3, NFORC=4
88
w
(!) a::
<t
I
(.) en
0
LEGEND
-----OBSERVED
---• BLENDED
~
100 so-~ a:: ~ 5.9 FT ---RAW
12 _!-----:-~-=-,_._._.Q,._;i( __. .... .-.-;-_.__..-·-3 0
80 ~.;:::.-·-6 ""'
6 // l '
RH:0.95 I .. · ···---~ . . ..
RV:-0.85 , ••••••• / \---~··· ••• / .. ····· I 5 3 FT ".:·· ••• --"--!,.c.:.~__ .... ······ I . '"'' ~~---. .. · \ ·•. '·.
I '~> I ~
···········ADJUSTED
----·RAW PRECIP
-·-·-ADJUSTED PRECIP
60
40
20 I
I 0~------~~------~----------L---------~----------L-------~--~
1 2 3 5 6 7 8
TIME <PERIODS)
Figure 6.28--Example 3, NFORC=S
89
w
(!)
a::
<t :r:
0
(/)
0
100-
100
CL 5 .9 FT
50·0 * ~ • ----L-:~..rA..-::-r :a:.~:r.
12 --------·-· 0 1 ____ _.. ---·-3 , =~---· 7 ~ '
6 ~ , •••••••
RH:0.96 /~ •••• •• ..
RV:0.86 •••• •••••
~ .. ·· ~/ .......... ....
----~~:;... ...... ..::._.·
80
20
LEGEND
---OBSERVED
---·BLENDED
---RAW
•••••••••• ADJUSTED
----RAW PRECIP
-·---ADJUSTED PRECIP
5.8 FT
' ' ... ' i .. ' ··· ... ' .. '
I ·· ... ' · .. ' ' ·· .. '
I " ···-~~'
I '\··.~
I '·
I
I oL---------~~------~----------L---------~R------~6------~7~---~8
1 2 3 4 ~
TIME (PERIODS)
Figure 6.29--Example 3. NFORC•6
90
w
i..!)
a::
<t:
:I:
0
(/)
Q
0~------~----~~----~------~------~------~------~ 1 2 3 .. 5 6 7 8
TIME <PERIODS)
Figure 6.30--Example 3, NFORC•7
91
Example 4
Example 4 is a rise that occurred on the Monocacy River near Frederick,
Haryland, on August 11, 1955. This storm, better remembered as
hurricane "Connie," produced a major flood as this example illustrates.
NFORC 7:
NFORC 8:
NFORC 9:
NFORC 10:
After an insignificant rise at the very beginning, the
observed hydrograph is now rising sharply. The raw
simulation is much lower and rising less steeply.
CHAT revises the hydrograph upward and earlier - a
perfectly logical adjustment at this time.
There is an additional 28 mm of precipitation. The river
is at flood stage, 14 feet, and is rising rapidly.
The raw simulation is very low. As a result of CHAT's
adjustments at period 7, the base hydrograph and the
observations agree very nicely, and CHAT makes no further
adjustments.
Another 25 mm of rainfall has occurred in the last 6 hours,
but the observations are beginning to level off. CHAT
again accepts its base simulation, which when blended
with the observed hydrograph, indicates that the river
is going to rise for another 6 hours from the current
stage of 16 feet to 17 feet.
The flow is rec eding, verifying that 16 feet at period 9
was the peak.
In summary, this was a major flood in which there was fairly poor
agreement between the raw simulation and the observations. Early
in the rise CHAT made adjustments to reduce the differences. These
adjustments were sufficient to keep the simulation in satisfactory
agreement with the observations at later forecast times without
additional adjustments.
One of the underlying assumpti~ns of the technique is that when
satisfactory agreement has been achieved, the adjusted precipitation
data are a closer approximation to the true precipitation t h an was
the original data. At any one forecast time, there probably are
a number of combinations of precipitation values that could suffi-
ciently reduce the discrepancy between the simulation and the obser-
vations, and most any classical optimization procedure could arrive
at such a set of values. However, if the values are not representative
of the true precipitation, even though they may resolve the discrepancy
apparent at the time, they may unduly alter the future portion of
the simulation. Unlike most ordinary curve-fitting techniques,
92
the CHAT adjustment strategy is designed to account for the physical
significance of the decision variables, thereby increasing the
likelihood of finding a set of adjusted values that are truly a
closer 3pproximation to the actual precipitation. At the same time,
it can resolve the difference between the simulation and the obser-
vations without unjustified modifications to the future portion
of the hydrograph.
For the most part, the examples are evidence that the CHAT procedure
is behaving in this manner. Adjustments to each precipitation amount
are not fluctutating widely from one forecast time to the next as
they quite possibly would if the procedure were simply curve fitting.
Oftentimes, as in this example, a few adjustments early in the rise
resolve the current disagreement and also produce a future simulation
that agrees with the observations at later forecast times without
further adjustments. This kind of result is possible only if the
adjustments are indeed producing a data set that better represents
the true precipitation.
·93
800
700
,... 600
(J)
~
(.)
'J
w
~ 500
<(
:I:
(.)
(J)
0
400
300
200
100
47.
IJ
i 147 .'I
II a•'l .. ,'//
3 ~.-/ 8 ·-·-·-/16 21_.-·-..,-'
~ --/. ----8
# ~---4 0
1 1
RH=0.79
RV= 1.30
FLOOD LEVEL -1 4 FT _, ___ _
'::·
I
I
I
I ~13 .0 FT ,,
I '~· ...... , If •• ••. \ /10.5 FT
li ··. ' I . . 1: • •• \ r: ·.:,
I} I •
It/ I \~~
: I ··~\\
.I I ..... ~.~~'
LEGEND
---OBSERVED
·---BLENDED
----RAW
.......... AD.USTED
-----RAW PRECIP
-·--· AD.USTED PRECIP
.. 1, .:.~~
........ _,/ ·-~~~'
'!.:: ........... ,._.,,,,, ••• • / I ... ,~..... a s --ob:~~=s~~~~~~--~----L-==~==~
1 2 4 6 8 10 12 u 16
.;
TIME <PERIODS)
Figure 6.31--Example 4, NFORC=7
94
900 150•""
~
~
'-"
a..
(.)
8oo 1 oo-~
a..
700 50-
""' 600
(J)
~
(.)
'-"
w
~ 500
<{
:X:
(.)
(J)
0
RHa 0 .79
RVm 1.30
28
I I 117.1FT
I ~ 1\ 1 f. I I \ 14.9 FT
LEGEND
--OBSERVED
---BLENDED
---RAW
··········AD.lJSTED
----RAW PRECIP
-·-··AD.lJSTED PRECIP
1/ }(
FLOOD LEVEL-14 FT li / f. \ ------i. I \,
'1/ \\
<&00
300
I' \ ,
! ,Y \\
.Ill \~\
I ~. ' :I ~. ' .·i)i ~~~
I , .. ~~
/ ·-~ .... , 0~~~~-~~~~~~-----1------~------L------L----~
200
100
1 2 4 6 ·e 1 o 1 2 1 4 1 6
TIME (PERIODS)
Figure 6.32--Example 4, NFORC=8
95
\
900 150-'"'
~
~
Q..
(.)
800 10()-~
Q..
700
600
w
(!) 500
0::
<{
I
(.)
(/)
0
AOO
30 0
200
100
RH:0.79
RVz1.30
FLOOD LEVEL-14 FT -----
I
I .. · ~
••• ~ 17.8 FT ~··· \I
17.1 FT ~:4 f~
': :' : ~ ~'
LEGEND
-----OBSERVED
----BLENDED
---RAW /1/'\\\
: II \ ~ ----RAW PRECIP
f v \ \ \ ---··AD.lJSTED PRECIP
••••••••• ADJUSTED
! \ \ \ . .
; I \ ~
f Jl \ \ '\ \ \ . I ' \
II \ \ \\ I \ \ \ ....
II I \"······· .. \ I , ·. ,
:I ' \\. ! I I ',, ......... ' .: I ', ·· ... ~ )' ~-·::. ....... ~
0 ~1~~2~·=··=--~~~--=··=·-~:~··=··~~~ .. ~ .. ~-~~~=··i::~-~----~8~~1~--1~0-------.~2~----~.:4------~.6
TIME (PERIODS)
Figure 6.33--Example 4, NFORC=9
96
,.... en
~
(.)
"-J
w
~ a::
<{
:I:
(.) en
0
900
a..
(.)
800 100~
a..
600
500
400
300
200
100
RH: 0.79
RV: 1.30
... ·i 17.9 FT .·· ~; r· ~\ . . : ~
15 .• FT j ;' I \.\
LEGEND
---08SERVED
---8LENDED
---RAW
•••••••••• ADAISTED
·---·RAW PRECIP I i\ \ \ -----ADlJSTED PREC1P
I '~\,\\ I \ \
i I I \ \\ I I \\,\\
! ;' I \ ......... :\_ : I \..... ·· ... ',
: I '' ·•···· •. ~
~ ------...... I I ' ······:;; ....
.,
0~~~~~~=··:••3••=··~·K~·~~~-------L------~------~~------~----~
l 2 6 8 10 12 16
TIME (PERIODS)
Figure 6 .34--Example 4, NFORC=lO
97
Example 5
Example 5 is s runoff event that, within hours, succeeded hurricane
"Connie" on the Monocacy River on August 17, 1955, as a result of
hurricane "Diane." The conceptual model performs quite well under
the saturated soil conditions this situation creates, and, consequently,
the raw fit is fairly good. This example illustrates the performance
of the CHAT procedure when the disagreement between the raw simula t .ion
and the observations is great enough to require adjusting by CHAT,
but the raw fit is not totally unacceptable as in the case of Example 1.
NFORC 4 -6:
NFORC 7:
NFORC 8 :
NFORC 9 :
I t is continually raining during these periods and the
river is rising mor~ quickly than the raw simulation
indicates. CHAT revises the hydrograph upward by adding
5 mm of precipitation to the first two periods. At
period 6 the blended hydrograph forecasts a peak j ust
slightly under a flood stage of 14 feet .
The precipitation is diminishing and the observations are
beginning to level off. CHAT accepts its base simulation,
which indicates the river will rise for another 6 hours
to a stage of 13.5 £eet.
I t is now apparent that the river peaked at the previous
period at 13 .2 feet, just under flood stage.
As the forecast time moves into the recession, the simulation
is adjusted more heavily on the basis of the RMS error.
The adjusted and observed hydrographs are almost identical
at this point.
In summary, this ~ise was an ordinary, uncomplicated runoff event.
In response to continuous rainfall from Diane on a lready saturated
soil conditions, the river rose quickly to flood proportions and
then receded . The raw simulation was somewhat low and late, but
not totally unacceptable as in the Bird Creek example. CHAT made
the necessary adjustments to reduce the discrepancies .
98
w
<!)
0::
<t
I
()
(/)
0
1 o ...
~--a.. 9~;,41' u 1 o_. ,.;.., 1 o
w ·-9 0:: ~7
a.. FLOOD lEVEL-14 FT -----
300
250
200
150
100
RH 0 .97
RV 1.03
I I ~9 .0 FT
I , ,
I / '
// ', ,/ 7.5 FT
I I .. ······-~\ .·• """' ··... \
II ··;· -~· .. \
I ; '' \ ... , .... '
I :;/I ~~
: ~'
LEGEND
--OBSERVED
----BlENDED
---RAW
··········ADJUSTED
----RAW PRECIP
··---ADJUSTED PRECIP
Y./~ ~-. , ..... . ~-.... . · ~::..····· . I ~····· .. ··/ ------. ~. :.;: ....... so
!!!?/I
ol------L--~--A-----~------~----~------~---~
1 3 s 7 9 11 13 15
TIME <PERIODS)
Figure 6.35--Example 5, NFORC=4
99
w
(!) a:
<t :r::
0
(j)
Cl
~ so~ 16, ~ . .., ~ 0 -~ -1 ..... ...,,6 a. 11.,·~--
.-10 0 10 -~-w Jl"-9 a: (/"7 a.
FLOOD LEVEl-14 FT
300
250
-----
RH:0.97
RVa 1.05
~12 .7 FT
/~\
/ \
LEGEND
I \ OBSERVED I / \
I \ ----BLENDED
I / ... \/10.6 F! ---RAW
I ...... -/\ ......... ADJUSTED
I • ··~ \
: •• \ ··-·-ADJUSTED PRECIP
: ~··. ---· RAW PRECIP
... ·•. \ I I I '\ \
I I I ~· .. .\
i I \\ \
1/ I \~\
:I \" •• \ r '=:·.~. !1./ ~~~ . ~ ~· /.Iii ~· ... 1/l ,~,
/I I ~-~··· / ~······· ... . .
50 ....... -:;:a.o~d} I
o-----------~---------~---------._---------~---------~---------~----------
200
150
100
1 3 5 7 9 1 1 13 15
TIME (PERIODS)
Figure 6.36--Example 5, NFORC•S
100
w
(.!) a::
<{
J:
()
(/)
0
/t_/ 13.9 FT
--r-r \
I / \
/ \ /12.2 FT
I \ ....... ·N' ... ·· ~·· ' I//~...,\
I !;:' ''\\ . ·. \
t.! ...... \ ·----RAW PRECIP : ~ \ / ' \ -·---ADJUSTED PRECIP
;1V \\ .. v'
!;' 1 \\
! I 'X·.' : ,.,
: ··~
/I I '· !/I ~,.
// I ~, ..
: ~
FLOOD LEVEL-14 FT -----·-
RHc0 .97
RV•1 .05
300
·•••••h• .. ADJUSTED
LEGEND
---OBSERVED
---BLENDED
---RAW
250
200
150
100
.:::· I I
. ..:/ I .· /
""~ I
50
0~--~~------~---------~-----~------~~-----~----_.
1 3 5 7 9 " 15 1 3
TIME (PERIODS)
Figure 6.37·--Exarnpl e 5 , NF ORC=6
1 0 1
\
" so• :i
:i .....,
FLOOD LEVEL-1.C FT -----/13.5 FT
300
2SO
200
1SO
100
so
RH:0.97
RV: 1.0S
I "' " ' ' 12 • .c FT .. \ ~ J ••• •• •• •• ~,...........-
~···· /II •••• \ ·; , .... ' IJ "\' ~A~· '~\
: ~· \
.:! I I ~-~··· ... ', ----RAW PRECIP
• • \ -·-··ADJUSTED PRECJP !J I ······'
! \~~1
! I I \' If I ·~~ ! ,.~~
• I ·~ II I ~~ I I ~. . ~ ! I ~·.
··········ADJUSTED
LEGEND
---OBSERVED
---BLENDED
---RAW
: , .. . . !j I '··.
//I I .... r; I . ,
~ I
0~------~------~--------------~------~------~------~ 1 3 s 7 9 1 1 13 1S
TIME <PERIODS)
Figure 6.38--Example 5, NFORC•7
102
w
(!) cr:
<t
I
()
(f)
a
FLOOD LEVEL-l~ FT -----13.2 FT
..... J.\ / 12 •• FT
... ~-. . . . : ·. . .: /' ·· .. : I ' V·.
I;' 1 '<:\,
l ' ~· f; I \\
;/, l '\\
! I '~~~ j I \\~
i I I ~~ ; I ~,-...... . . ~
: I '
IJ I ''·· I ~:
l I
/) I ... / I C/ ~ I
RV•l.07
300
250
200
150
100
50
LEGEND
---OBSERVED
---BLENDED
---RAW
··········ADJUSTED
----RAW PRECIP
·---·ADJUSTED PRECIP
o~-----~---------~---------~----------L-------~---._ ___ ~
1 3 5 7 9 1 1 1 3 15
TIME (PERIODS)
Figure 6.39--Example 5, NFORC=8
103
w
(.!) a::
<!
I
(.)
(J)
0
6 1
___ o ___ o __ ---.,.. _...----~---
16 ·""'. ..,-"'j 0 0 i' ~ 15 ,. /.., 12 ,. ..,""
16/ • .., 16 a.. • ""-""
(.) 10 ·""'--10 w ~-9 a::~ a..
FLOOD LEVEL·1.c FT
--~--
•• ~13.2 FT
.. ·. I
••••• •• •• ~12 . .c FT . . . . . . . . : ·.
f / .... \ .. 1
I \ •.. 1\ I ~ \
t. \ ----RAw PREC10
I \.... -·-··ADJUSTED PRECIP
I 1.\_'\ I \ ............... ~\ I I \, ······· ... :~
• I I ',, ·· .... '~
f I I '..... ········... '
! ,, ·····~ . ..... ... ___ .
. ··)' I
~ , I ~··-::.~ I
oL-----~----~------~----~----~~----~----~ 1 3 5 7 9 11 13 15
RH::0 .7 8
300 LEGEND
200
.......... ADJUSTED
---OBSERVED
·---BLENDED
---RAW
250
150
100
50
TIME (PERIODS)
Figure 6.40--Example 5, NFORC=9
104
Example 6
Example 6 occurred on the Leaf River near Collins, Hississippi,
on November 12, 1961. This example demonstrates the use of the
CHAT procedure on an event that is a result of a nonuniform rainfall
distribution over the catchment.
NFORC 7:
NFORC 9:
NFORC 11:
After 130 mm of precipitation, the raw simulation is some-
what higher than the observed hydrograph, and CHAT
lowers it slightly. Since it is still very early in
the rise, large adjustments would not be justifiable
at this time.
For the last 12 hours the rain has essentially stopped, but
the river has been rising very rapidly. There is a
41% disagreement betl.reen the base :.:limulation and the
latest observation, which already exceeds the forecasted
peak. Yet, CHAT assesses the fit to be satisfacto ry
and makes no adjustments. In light of the above facts,
it appears that the tolerance is being too easily sat-
isfied. Consequently, CHAT's decision to make no adjust-
ments is not good.
No significant precipitation has occurred in the past
12 hours and the o bserved hydrograph is beginning to
level off. There is still a large discrepancy between
the simulated and t he observed hydrographs, and CHAT
makes adjustments tv the pre cipitation and the unit
graph until the tolerance is reached. These adjustments
reduce the difference somewhat, but probably not to
the extent that a human forecaster would judge sufficient.
There are two questions to consider at this time:
first of all, why is the CHAT procedure accepting sim-
ulations that for the most part are not suitable, and
secondly, if the adjustment process were allowed to
continue further, could CHAT indeed produce a hydrograph
that more closely resembles the observed hydrog raph
of this example? In ansl.rer to the first question,
the tolerance is still quite large at this time because
it is a function of the stage of development of the
runoff event, and NFORC 11 in this example is still
quite early in the rise. However, the research for
the tolerance was performed on catchments having a
much shorter time to peak than the Leaf River. This
example indicates that when dealing with slower responding
catchments, it may be necessary to tighten the tolerance
at the earlier periods in order for CHAT to adequately
adjust the input at those times. This is accomplished
105
\
by decreasing the exponent EXl in the WP weight. (Note
that even though the tolerance could be decreased by re-
ducing PCOB, the change should not be made in this
manner. PCOB represents the degree of confidence in
the stage-discharge relationship and that has not had
reason to change in this case.)
In regard to the second question, CHAT was re-run on
this example without any restraint from the tolerance;
the adjustments were allowed to continue as long as they
could still produce improvements in the objective
function. CI~T was able to produce simulations at
the earlier per~ods that more closely matched the partial
observed hydrographs, but in doing so, produced future
portions of the simulations that were far too high
and, consequently, had to be revised downward at later
forecast times. It appears that the model may not be
capable of closely duplicating the river's response in
this event with a lumped input. It would therefore not
be prudent to force a very close fit at these ~eriods
at the expense of the data. Indications are tha~ an
EXl value around 0.5 would be appropriate.
NFORC 12: The rain has stopped and the observations are beginning
to fall. CHAT ~s slowly increasing the simulation
in an effort to match the observations. Although not
shown on the plot, the simulation with EXl equal to
0.5 is higher at this time as a result of the adjustment
process having been carried out further at earlier
periods, and is, therefore, closer to the observations.
NFORC 14-17: In response to 26 mm of additional rainfall in the past
24 hours, the observed hydrograph is beginning to rise
again. Now that the river is rising once more, the
CHAT simulations and the observations at· these times
agree very nicely. The blended hydrographs are predict-
ing, on the average, a peak of approximately 17.5 feet
at period 16.
NFORC 18: It is observed that the rise peaked at 17.6 feet at
period 17. Now that the rain has ceased, the volume
under the CHAT simulation is very good and far better
than that of the raw simulation.
In summary, this event occurred as the result of a very nonuniform
rainfall pattern over the catchment. The CHAT procedure can compensate
for some degree of nonuniformity by altering the temporal distribution
function (unit graph) on an event basis. However, this does not
106
preclude the idea of using a distributed input for events such as
this one. Although CHAT is not currently designed to operate on
a catchment that has been sub-divided, some thought has been given
to such a modification. Further ideas on this topic are discussed
in Chapter 7 "Suggestions for Future Research". When using CHAT
on an event such as this one, where the discrepancy might originate
from the use of a lumped input rather than the data itself, it is
concluded that a very close fit should not be forced by un.realistic
adjustments to the input since this may cause harmful effects in
the future portion of the simulation. In spite of a few difficulties
with CHAT's simulations on the rising limb, the procedure still
performed its function of adjusting the volumes by the end of the
runoff event very nicely. Consequently, the forecast~r could have
a fair amount of confidence in the soil moistun.~ variables going
into the next event.
This example also provided some insight into choosing parameter
values. The research value for EXl was found to be inappropriate
for slower responding catchments such as the Leaf River near Collins,
and as a result, did not permit the adjustment process to be carried
out far enough during the earlier periods in this riae. This problem
was corrected by decreasing the value of the exponent, thereby tighten-
ing the tolerance at the earlier periods.
107
\
300
250
RH•l.O 1
200 RV•l.O 1
,....., en
~
0
\,J
w
(!) 150
0:::
,_ <(
0 J:
00 (.) en
0
100
50
JV 15.3 FT
I #,_-...... \··==-~ .... ······~ ... ~
I 4.~JI~ 15.2 FT ·····~
~ ~~
··~
I ~-~··;/ ... ""
--=···· ,. ,. ,. '
I . : ,.,. "\ ... ,. LEGEND
/.~·>" . ---~~:~~~~D
• / ··········ADJUSTED
/ ----RAW PRECIP 1
!.·//i" ---RAW
1
,. -·-··ADJUSTED PRECIP
~
8 10 12 14 16 18 20
TIME (PERIODS)
Figure 6.41 --Exampl e 6, NFORC=7
.....
0
\D
250
,.... 200
CJ)
::E
()
'-'
w
(.!)
0:: 150 <(
:I:
()
CJ)
0
100
50
RK:l.O 1
RV=l.O 1
6
I 16 .• 0 FT
------------~1~3 FT
.,.. ............ ~ ····· ·····~ . ··~ #~···· ~ ~ ~~ . ·· .. ~ .. , ~···· ·· .. ,~·· ·······~
~~ ~ . -~······, LEGEND .
•• •••• 08SERVED
8 10 12
TIME <PERIODS)
Figure 6.42--Example 6, NFORC •9
16
• ---8LENDED
---RAW
···········ADJUSTED
----RAW PRECIP
-·-·-ADJUSTED PRECIP
18 20
--0
" ~
300~ 100-
250
" 200 C/)
~
()
'J
UJ
(!) J 50 0:
~
I
()
C/)
0
100
50
RH:1>.97
RV.0.97
;-/17.5FT
-------..... , I ................. ,
·········• ~
I .... ····· ' .. ·· ····· ' .. . .. ~
l ... ······/,~-,. ···· ... .... ··· / \ ,, ...
•••••••• • .... ]/' 15.3 FT ':::-· ••••
.... ·····~,/ I LEGEND '~~
~/ I OBSERVED
---·BLENDED
I
I
I
---RAW
···········ADJUSTED
·----RAW PRECIP
··-·-ADJUSTED PRECIP
I ot=~====~~~L---~-----L~~~----~--~~--~----~
1 2 6 8 10 12 1 .. 16 18 20
TIME <PERIODS)
Figu re 6 .43--Example 6, NFORC =ll
,....
(/)
~
(.)
'J
w
(.!)
0:::
<{ -I -(.) -(/)
0
,......
~ 0 1 1 1 0
3 00~ I 00-•s ; r~==-;;=:=-f=.:..T=..;f.:..-=-1;=1
(.) /? 17.5 FT ~ //45 _[
200
150
100
50
a.. 46 ~· ~ 2 5 -1-~~6 ------........... 1'-1 ... ~ • -..... 2 4 1 ..... ,
RH:0.94
RV::().94
' ·••·····••• ~ ······ ······· ~ .. ··t········· ·······~~~
~ ~
.. ·························· I,/ ... -~ -.............. ~········· ...
.. A 15.3 FT ' • ••
,..,.., ... ' I "··· ... /~ ' ', / LEGEND , I
I
I
I
--OBSERVED
---BLENDED
---RAW
········ADJUSTED
·---RAW PRECIP
··-·-ADJUSTED PRECIP
0~1==~2========!4~==::~~6--------~8--------~------~~~----~~-------L--------L-------~ 10 12 14 16 18 20
-TIME <PERIOD S )
Figur e 6.44--Exam p l e 6, NFORC=l 2
--N
w
(!) a::
~ :r:
:..:> :n
r.. 0 I I 0 4 • -_7_ ~ 3 9 • -• -• -• -• -• -.-• -• -.--.___..----~ ~ ~---------------7 ~ ~-0 I I I 0 4
300 '""'100-45 ,..,.....-31
t3 /-;?s g: .c~
2 5 ~-"'F.c6
250 --.----"'"-· 2 4 I
RH:0 .93
RV:0 .95
--------~~-·-············
.... ··········1 15. ::~······ ••• .. · f ··. . ~ __ ... ~ J,---····-.... .... ·· ---............. ... . , .... ~ ·· ...
... ···················· /// : ",,:·· ..
; ' ,~ I
,/ I
LEGEND
---OBSERVED
----BLENDED
---RAW
::l 100 I
I
I
··········ADJUSTED
50
2 6 8 10 12
TIME (PERIODS)
Figure 6.45--Example 6, NFORC•J 4
----RAW PRECIP
·-·-·ADJUSTED PRECIP
I
l.C 16 18 2 0
,.....
(J)
~
0
~
w
<.!)
0:::
<l:
I .... 0 ...... (J) w
0
250
200
150
100
50
7 1.C ..
0 1 1 l 0 ~----·-..:.--
39 ---·-·---·-·-·-·-·-· __ ..... ....-...... J'--o---,---1--1--o--;--1 '"
~~"31
45# '······ !."·· Fl .. __ {~ ,/..·s .. ~
2 5 1 / 46 •---""-2 .. 1
Rtu0.93
RVa0 .95
------.~.~ ~~ ... ··········· I r'6.0 fT ......... , ....
.... ········· /t-----~ ~.
... ··················· /' I .. ,~:
.. · .. /' I
~~ I
,/ I
I
I
I
LEGEND
---OBSERVED
·---BLENDED
---RAW
··········ADJUSTED
----RAW PRECIP
·-·-·ADJUSTED PREC I P
I 0~~====~~~~--~----~----~----~~~-----~--~ 1 2 6 8 10 12 16 18 20
TIME (PERIOD S)
Figu r e 6.46--Example 6, NFORC=l5
w
(.!) a:
<{
:::t:
{)
(/}
0
I '"' -·-· 7 .-· --~ 0 I I I 0 -~---·=---1 ---·-------· ..,....-I" , ' .~~~~·--·-·-_..,.._.. 7 .. ~ 3 9 , ______________ "'
~ ,,.. 0 1 1 I 0 3oo ;;::too-45 ., ... 31
/I'
17.5 FT
{) ~-..5 ~ .c6.,-~"
0..2 5 ~/..6
250 --t-,_..
2 "' '
100
50
RHaQ .93
RV:0.95
.. .. .. .. .. ·
.. .. .. .. .. .. · .. .. .. ·
.. .. .. .. ..
.. .. .. .. .. ..
........ ... ······ ........... ....... ' .. ~
-fl6.0 FT ·····~
··~ ··~ ·· . ·~ -.............._ -~ ~-~..... ····~ / "' "•:\
;' " · .. /~ I , /" I ,
~/~ I
.. ~ I
LEGEND
---OBSERVED
----BLENDED
---RAW
···········ADJUSTED
----RAW PRECIP
I
I
I
-·-·-~DJUSTED PREC l l
ob:==~========~==::==-L--------~8 ----~1~0~---~12~--~,~ .. ~-----~,6~------~,~8----~2~o
' 2 "' 6
TIME (PERIODS)
F'·i g u r e 6.47--ExampJ e 6 . NFORC •1 6
"""' (/)
~
(.)
'-'
w
....-(.!)
....-0::
1../1 <t
J:
(.)
(/)
a
"""' ~
~
1~ 1 0
0 1 1 1 0 .. 7 ------·-·-·· -------·-·-·-·----~----~~~~~~-~-· 3 9 /.. ..... -------~---------------7 14 1 0
Joo '-' 1 oo-/""-0 1 1 1 0 ..
AS, 31
~6/-s
250
~· 1 5 1 _/. ~6 .... .-..-~.':/
2 ~ 1
RH:0 .93
RV: 0 .95
200
150
100
5 0
.. ···
/ . . : .
... . : . •
.. .. .. ...
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
.. .. , . .. .. ..
LEGEND
---OBSERVED
----BLENDED
---RAW
··········ADJUSTED
·---·RAW PRECIP
······ I ..... , ····· ' ~ 6 .0 FT
1
·········.:>'
1 ··. ' -............._ ·· .. ' I ~ ·· .. ' '""'-. '•< I ,
I
I
I
I
I
I
'
·-·-·ADJUSTED PREC IP I 0~~====~==~----~----~--~----~----~~~~--~ 16 18 2 0 1 2 6 8 10 12
TIME (PERIODS)
Figure 6.48--Example 6, NFORC =l7
200-
1 0 0
14 ------------0 I 1 1 0
4 7 ---· ______ , __ _
---· --0 0 ·-·-·-·-·-·-·---·~· ~~~1 I 39~~~--~~-~~~------~~7 ~ ~., 0 I 1 1 0 4
45 ? 31 ~ 17.5FT
Q
46 ,. 45
a. ~
2 5 1_? 46 250 -~...,.._.,.. __
2 4 1
"' 200 en
~
0 -
lJJ
(.!) 150 a::
<{ ::r:
0
!a
0
100
50
RH=0.93
RV:0.95
.. .. .. •
.. .. .. .. .. ..
.. .. .. .. .. ..
.. .. .. .. .. •• ..
.. .. .. .. ' ' .. ' j16.0 FT •••• 1..... ',
i .. '
----I ····... '·
LEGEND
---'OBSER'.'ED
·---BLENDED
---RAW
~ ·· ... I ," ..
' I
I
I
··········ADJUSTED
----RAW PRECIP J
-·-··ADJUSTED PRECI
I
I
I 0~~====~~~----~----L---~----~----~---l----~ I 2 6 8 10 12 16 18 20
TIME (PEBIODS)
Figure 6.49--Example 6, NFORC=l8
7. SUGGESTIONS FOR FUTURE .RESEARCH
As was pointed out in Chapter 2, the complete solution to the
problem of adjusting simulated hydrographs to agree with river ob-
servations must involve a number of techniques, each associated
with a different flow regime or a different type of flow point.
These techniques were associated with four phases of research and
it was further pointed out that the present effort has been concerned
only with phase 1, the outflow from an individual catchment during
runoff events resulting from liquid precipitation.
It was also explained in an earlier section that the phase 1 solution
may be subject to some modification in light of experience with
the method, and that certain types of additional research on the
phase 1 problem may be worthwhile.
The purpose of this chapter is to present the thoughts and recommen-
dations of the authors in regard to the phase 2, 3, and 4 problems,
and to possible future research on, and modification of, the phase 1
solution. This chapter contains no answers or solutions; those
can r~sult only from further research. It contains the authors'
recommendations on how that research should be approached, based
on their understanding of the problems and their experience with
phase 1.
Phase 2
Outflow from Individual Catchments During Runoff
Events in which Snow or Snowmelt is Involved
Runoff events of this type may involve three types of input, liquid
precipitatic·n (rain), solid precipitation (snow), or the melting
of an existing snow cover. Representing these by the symbols R,
S and M, there are seven possible types of occurrences, R, S, M,
R-l-1, R-S-M, S-H and R-S. It should be noted that when R and S are
both involved, this may be because the precipitation changes character
during the event, or because snow is falling at the higher elevations
and rain at lower levels. Of the seven combinations noted above,
two need not be considered here. The "R" event is phase 1 and the
"S" event produces no runoff. The remaining five will be discussed
individually.
M event:
This situation involves the melting of an existing snow cover
as the result of heat transfer from the atmosphere or from the soil,
but not from rainfall. If the discrepancy between the simulated
and the observed hydrograph is assumed to result from errors in
the input to the catchment model, that input is the computed snowmelt.
The solution then would be similar to the phase 1 solution, but
the adjusted values of snowmelt would have to be carried back into
117
the snow ablation model and suitable adjustments made to the remaining
snow cover. It is likely that changes should be made in the constraints
and in the size of the tolerance.
R-tt event:
In this situation, the rain may be falling only on the snow cover
and slightly accelerating the melt process, or it may be falling
on bare ground in portions of the catchment. This type of evE:.lt
t y pically produces somewhat greater runoff volumes than the pure
melt situation described above. Most of the additional r1moff results
from the rain itself; additional snowmelt caused by heat transfer
from the rain is slight. This also appears to be a case in wh.ich
the phase 1 technique is basically applicable but the adjustments
to the input data must be distributed between the rain and the melt.
The development of a rationale for doing this will probably involve
additional research. In addition, such situations typically result
in areal distributions of runoff wh.ich differ greatly from those
exhibited by pure rain events. Thus, it may be necessary to widen
the constraints on the unit hydrograph warp coefficients.
R-S-~f event:
This is a situation in which snow falls during a portion of the
event a.td then turns to rain; or, parts of the catchment may receive
only rain. There may or may not be a pre-existing snow cover. If
there is no pre-existing cover, the situation is very similar to
the phase 1 problem and the phase 1 solution should be able to handle
it. Sizeable simulation errors may result from incorrect classifi-
cation of precipitation as rain or snow, but the ability of CHAT
to shift precipitation input from one period to another should make
it capab.le of dealing with this. If there is a pre-existing cover,
the situation is then practically the same as the R-M case discussed
above.
S-M event:
This situation usually involves a snowfall followed by a warming
trend. It can be thought of and treated as two events, both of
which have been discussed.
R-S event:
Since melt is not involved in this type of event, it is pretty
well limited to the case in which a storm consists of rain at low
elevations and snow at higher levels, and the portion of the catchment
receiving rain is free of snow cover prior to the event. Thia then
is the same problem as is encountered in phase 1 when a rainfall
event is highly nonuniform. The only modifications necessary would
be either wider constraints on the warp coefficients or a subdivided
catchment approach. The latter has been alluded to in Chapter 6
and will be explored further in this chapter.
118'
The above discussions are not intended to imply that the phase 2
technique should consist of five separate procedures corresponding
to the five types of events discussed. The recoDmlendation is that
the research on this phase should investigate the five types indi-
vidually and when an understanding of what is required for each
has been acquired, then it should be possible to combine these into
one procedure capable of handling any event involving snow or snowmelt.
It appears likely that this procedure would be similar to the phase 1
solution, but would involve an interaction with the snow accumulation
gnd ablation model. The need for a distributed catchment approach
is a strong possibility.
Phase 3
Outflow from Individual Catchments During Low Wa ter Periods
Discussion of the phase 3 problem should probably begin by defining
what is meant by a "low water period." 'nle most direct definition
is that it is any time that a flow regime of the type handled by
the phase 1 solution is not occurring. During the dis~ussion of
the phase 1 problem in previous chapters, the term "runoff ·e:vent"
was never objectively defined; it was assumed that a forecaster
would know when he was involved in such an event and would then
operate his forecast program in the "CHAT mode" until the end of
the event. This is a valid assumption. At some future time however,
when the combination of techniques, phases 1 and 3, are operating
so as to continuously keep a model in line, it will probably be
necessary to have an objective and hydrologically based criterion
to indicate when to switch back and forth betw .. ~en the two methods.
Such a criterion would have to be of the "either or" type. That
is, if the model is doing certain things, ~ if the river is doing
certain things, then a runoff event is occurring. Perhaps the model
indication woul~ be the exceedance of a particular threshold value
of runoff from the upper three components. A suitable threshold
value would have to be determined by study and it may vary regionally.
The river indication might be an increased flow such that the net
disr.harge above an estimated base flow corresponds to that threshold
value of upper level runoff. The occurrence of either of these
indications would put the procedure in the phase 1 mode, and it
would remain in that mode up to a point in time equal to the end
of upper level runoff plus the length of the unit hydrograph base.
At all other times, it would be in the phase 3, or low water, mode.
With such a definit:f.on, the model input during a low water period
would consist of pr~cipitation and potenti~l evapotranspiration
just as it does in phase 1. In this case. howevP.r.. ~.t appears that
the principal source of simulation error would be the PE. Errors
in the determination of mean areal rainfall during such a period
would probably not affect the long-term tracking of the model ap-
preciably. Or, if they did, perhaps the slack could be taken up
by the adjusting of the evapo transpiration computations.
119
In some applications, the model uses a normal PE curve rather
than actual values and, even when actual values are used, a time-
invariant adjustment curve is involved. Both normal PE and the
adjus tment curve a r e subject to sizeable errors, especially during
long-term departures from climatic normals. It therefore appears
that the adjustment of model output during low water periods m.ight
best be accomplished by adjusting the observed/computed/normal PE
and/or the adjustment curve. Or, perhaps just the figure representing
ca tchment demand could be adjust~d.
If this approach is used, a question which arises is bow far back
in time to go . Since the pertine n t mechanisms in the model a re
slow ac ting , it may be necessary to iteratively change the input
over an extended period, perhaps t hirty days or longer. On the
o t her hand , since the ajjustment proc edure will be a pplied every
day , what is done on any single day may involve only a short period
o f i nput, the earlier periods h aving been adjusted previously .
This concep t is similar to that behind the phase 1 strategy which
op era tes every six hours and c oncentrates on the few precipitation
periods which have a substantial effect on the objective function
a t that particular time . In any event, adjustment o f input c ould
no t go further back in time than the end o f the last runof f event.
~~tever pe riod i s invol v ed, the decision variables, in the case
of PE, might be the only ac tual daily values. This could present p roblems
since the s erial correlation of such values is high enough that
they should not be conside:.:ed independent •rariables. Also, if t he
period being adjusted is lon g , their great n umber could make the
process unwieldy. Perhaps some sort of warping operation performed
on the whole series would be preferable .
If the ad ju.:;tment curve is t o be c hanged, no obvious problem exists
as this is norma l ly defined by j ust a f ew points.
The objective funct ion in the phase 3 problem should be based
on daily volumes, perhaps:
L I (QO -QS ) I
where QO and QS are the observed and simulated mean daily discharg es
and the summation is made over a period of perhaps the last f ive
days.
In determining the o bserved mean dailies, some problems may arise
due to diversion and regulation. Diversions not noticeable d uring
runoff events may involve substantial portions of the flow d uring
low water periods. Artificial regula tion during s u ch periods may
cause the instantaneous flow a t the time of an o bservation to differ
from the mean daily by an. order of magni tude. And, since such reg-
ulation often exhibits a diurnal pattern, the differences a re not
1 20
always random. These problems, wnere they exist, must be solved.
To detect, analyze, and treat these matters will involve investigating
aspects of the flow regime in wnich Weather Service offices have
not traditionally been interested. Nevertheless, if these factors
are ignored or if they are treated by expanding the tolerance to
such magnitudes, any effort to keep the model's moisture accounting
in line will be rend~red totally meaningless • ..
In the case of forecast points subject to excessive regulation,
a solution to the problem may lie in the use of the U. S. Geological
Survey's "Data Relay" system if the gage is part of that system.
The stages at such stations are relayed in real time, via satellite,
to the U.S.G.S. computer in Reston, Va. There they are available,
within a few hours, for interrogation by any high-speed term.inal.
The frequency of observation is the same as the frequency of on-site
tape punching.
At the present time, less than 300 stations have this capability,
but the system is expanding and o~e of the criteria is user need.
Further details may be found in U.S.G.S. Circular 756, "Collection,
Storage, Retrieval and Publication of Water Resources Data."
The tolerance should reflect primarily the accuracy of the low
water rating and the effect of both the accuracy and the precision
involved in observing and telemetering stages. The tolerance may
have to be somewhat larger just after runoff events and some sort
of transition from a type 1 tolerance to a type 3 may be needed.
Finally, if the adjustment is to be accomplished solely by manip-
ulating PE input, one cannot exclude from consideration the unhappy
situation in which such input has been reduced to zero and the model
still generates too little water. If this happens, and if it is
real rather than observational, there are three possible causes.
They are, in order of likelihood:
1. Errors in model parameters, particularly maximum storages
and depletion coefficients.
2. A need to adjust precipitation values during the low water
period.
3. Erroneous storages at the end of the last runoff event; a
deficiency of the phase 1 operation.
121
Phase 4
An Adjustment TeChnique Applicable to Points in a River
System that are not at the Outlets of Individual Catchments
The hydro graph at a downstream point is modelled by the execution
of one or more catchment analyses and one or more channel routing
operations. The errors in such a simulation reflect the combined effect
of errors in both types of computation. The accuracy of a channel
routing operation is very muc h higher than that of a catchment model.
Further, it is probably safe to assume, tentatively, that if errors
in the catchment analyses could be eliminated, the residual discrepancy
in the simulation, reflecting only routing errors, would be small
enough that it could be reconciled by a blending procedure. It
is therefore recommended that initially no thought be given to making
CHAT type adjustments to the routing operation. One possible exception
to the foregoing is the case of channels which involve substantial
bank losses at high flows. Whatever type of model is used to analyze
this phenomenon may indeed generate large errors and may require
some type of real time adjustment. It should also be noted here
that, with the possible exception of the bank loss problem. channel
routing models do not involve soil moisture accounting and the problem
of correcting soil moisture variables along with the model output
does not exist.
If then the adjustment of hydrographs at downstream points is
to be accomplished by malring phase 1 type adjusti:lents to the con-
tributing catchments, phase 4 should consist only of a variation
of the phase 1 solution·. If it can be further 1.5sumed that all
upstream forecast points have been observed and ea.djusted, and this
is admittedly a ten~us assumption, then the only catchment which
should be adjusted t s the "local" area immediately above the forecast
point. What is involved then is basically a phase 1 type operation
in that area. If, due to a poorly operating operat.ional network,
one or more headwater points have B£1 been observed and adjusted,
they will have to be treated along with the local area. Because
of the time lag in the channel system, and because of the nature
of the phase 1 strategy, such a procedure should be workable even
though the number of decision variables appears to be large.
For this type of solution it will probably be necessary to make
some changes in the method of computing both the objective function
and the tolerance. 'The development of these was based on concepts
appropriate to catchment simulation. The simulation of a downstream
point may well require the changing of some of those concepts.
For instance, the method of computing the timing weight in phase 1
is based on the assumption that timing errors of less than three
hours should be ignored. In phase 4, where it is desired to ignore
routing errors completely, some other interval based on the accuracy
of the routing procedure may be more appropriate. Further, it may
122
be necessary to recognize that the early part of the hydrograph,
which consists primarily of local catchment outflow, may have to
be treated differently than the later part which consists mainly
of routed upstream flow.
This completes the discussion of the phase 2, 3 , and 4 problems .
The remainder of this chapter is devoted to possible further work
with phase 1, specifically further testing of the adjusted soil
moisture vari~bles and application to a distributed input catchment
model.
Further Testing of Adjusted Soil Moisture Variables
In Chapter 1 it was explained that CHAT is intended to serve two
purposes; adjustment of the model output, and adjustment of the
soil moisture variables, so a.s to produce a more accurate simulat.ion
of the next runoff event. This latter purpose is also implied by
the title of this report. In the research so far, all of the veri-
fication of CHA'! was based on an analysis of the adjusted model
output, and no at:.;empt was made to determ.:ine if the adjustments
actually would improve the model's performance for a period into
the future. Such an invest.igation would be a worthwhile research
effort.
To accomplish this would require the simulation of a long period
of streamflow in two different modes. The first mode would be a
normal simulation in which no adjustment to the model's output is
made. In the second mode, each runoff event would be adjusted using
the CHAT phase 1 technique. The model would then advance to and
through the next event, making a raw s i mulation. After determining
the error statistics for that simulation, it would back up, re-nJD
the event making CHAT adjustments, proceed to the next event, and
so on. The comparison of error statistics would be between ~h~
simulations made in the first, free-wheeling mode ·and those resulting
from the raw simulations in the second mode when the soil moisture
variables in the preceding runoff event have been adjusted by CHAT.
The statistics should be based on the error in the total runoff
volume and the analysis should relate the errors t o the time which
has elapsed since the last event.
Of the events studied in the research, there was only one which
might have shed some light on this aspect o f CHAT's performance
and that was the closely spaced Conn.ie-Diane storms in the Monocacy
basin. Unfortunately, the raw simulat.ion of the Connie event was
quite good and the slight changes made by CHAT during that event
did not produce large changes in the values of the soil moisture
variables at the end. Consequently, the raw simulation of the Diane
storm was about the same whether or not Connie had been adjusted.
123
Application to a Distributed Input Catchment Model
All of the research on alAT phase 1 has been based on the use
of a lumped catchment t10del. Investigations into the use of distributed
input -distributed para .. ter applications of conceptual c atchment
mo dels have taken place concurrently with that research (Morris,
1975, 1 977). It appears at this writing that the use o f d istribu ted
mo dels in certain types of catcluuots may not be far off, and i t
i s therefore appropriate to consider how the CHAT technique might
be a pplied to them.
Basically, such an application would consist of having a s epa r a te
s et of six hourly mean areal precipitation values for e ach zone
within the catchment, and perhaps a set of warp coefficients f or
each zone. The only obvious problem is that this may increase t he
number of decision variables to an unmanageable quantity . For in-
s tance, with three zones and a two-day storm, there would be 30
v ariables to be manipulated. This would probably not be a p roblem ~
howe ve r , since at any particular forecast time, only two or t hree
of the precipitation periods in each zone would be in a "working
po sition." Further, the uae of the distributed input model may
we ll eliminate the need to manipulate the unit hydrograph. This
wo uld mean that the warp coefficients and the warp s ubrout ine c o uld
be r emoved f rom the operation.
A question which arises is just how the CHAT strategy wou ld operate
in such an application. Tbat is, would the change in precipitation
be limited to one per paaa, or would it be one per zone. per pass ?
Would the changes be controlled by one beginning sensitiv ity figure
f or the ca~chment, or would there be a separate sensitivity f i gure
f or each zone?
The answers to these questions can be determined only t hrough
r esearch. At this time, however, there seems to be n o reason to t hink
that CHAT cannot be used succesafully with a distributed model i f
a pplied along the linea deacribed above.
124
REFERENCES
1. Tribus, Myron, 1969: Rational Descriptions, Decisions and Design,
Pergamon Press, Inc., Elmsford, N. Y., 478 pp.
2. Morris, David, 1975: "The Use of a Multizone Hydrologic Model with
Distributed Rainfall and Distributed Parameters in the National
Weather Service River Forecast System", NOAA Technical Memorandum
NWS Hydro-25, U.S. Dept. of Commerce, Silver Spring, Md., 15 pp.
3 . Morris, David, 1977: "Streamflow Synthesis in Employing a
:Hulti-zone Hydrologic Hodel with Distributed Rainfall and Distrib-
uted Parameters ", Ph.D. Dissertation, Oklahoma State University ,
Stillwater, Okla.
125
APPENDIX A
SUBROUTINE LISTINGS
Subroutines are available to IBM 360/195 users in the following library:
NWS.RFS.ARCHIVE.SOURCE(CHATTERP)
NWS.RFS.ARCHIVE.SOURCE(CHATTOLR)
NWS.RFS.ARCHIVE.SOURCE(CBATOBJC)
NWS.RFS.ARCHIVE.SOURCE(CHATSTRT)
NWS.RFS.ARCHIVE.SOURCE(CHATWARP)
NWS.RFS.ARCHIVE.SOURCE(CHATBLND)
A-1
SUBROUTINE INTER~C NB tTBtWH) c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c•••••••••••••••••••••••••••••••••••••••••***********************•••••••
THIS SUBHOUTINE 1NTE"P0LATES ~ETWEl N DISCHARGE (OH S TAGlJ
OBSEHVATlO~S MADl AT RA N DO~ Tl~ES AND DETER MIN ES TH E VALUl
AT EACH SIX HOUR ORDINATE CORRESPONDING TO THE oRO l ~A TES
OF THE SlMULATEO HYOkOGRAPH.
SUBROUTINE lhPUT •
NB
TBClJ
QBllJ
-IHE NU~BR OF OBSERVATIO NS CMAXIMU~ 100)
TO TBCNB> -THl TI~E• IN HOUH St OF EACH OB SERVATIO N•
LERO OF lHE TIME SCALE MUST CORRESPOND TO THE
~IRST ORUINATE OF THE SI ~U LATEU HYORUGRAPH. TBClJ
~UST BE LERO ANO ~ILL BE SET TO lERO IF IT IS ~or.
fBCNB) M~Y NOT EXCEED 23~ HOURS. 08SERVAT10 NS M U~T
APPEAR I~ CHHONOLOGICAL ORDER.
TO QBCNBJ • TH~ OBSERVED DISCHARGE COR STAGEJ AT
EACH OF THE TIMES SHOWN IN THE PRlVIOUS ARRAY.
SUBROUTINE OUTPUI •
~OB
TILT QOLT
PJ QOMX zz
QOCNJ
SUBROUTINE COMPUTES iHESE QUANTITIES AS
D~FINlO I ~ SUBROUTINE OBJEC
-THE lhTERPOLATEC C~SER :Q DIS CHARGE S
AT ORUINATES 1 TO NOB.
c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c•••••••••••••••••~•••~••••••••••••••••••••••••••••••••••••·•••••••••••• DIMENSION TB l 100J,QBC100 J tS(l00)
c c c c
7
9
C0M~ON/ALL/NOB,T1 LT•QOLT•PJ,Q0(53),QOMX,ZZ
IF O~SERVATIO NS ARE AT S IX•HOUR OHUINATES AND
ONLY TH (HE, SKIP THE INTlRPOLATI ~G S TATE MENTS
rBcl>=o.
TlLl=O. QOLl:QBCNBJ
N OB=TBC~~)/6e+l.U1
IFtNOB.NE.NBJ GO TO 9
00 7 K=l•NB
T0:ABSCT~CKJ+6.·6.*K)
IF(TO.GT •• 001) G~ TO 9
QOCK):QBCKJ
GO IO 1~
TlLT:TBcNB)+b,·&••NOa
QOLT:QBCNBJ $C 1):CQBC2l·QBC1JJ/T BC2 )
K=NH•l uO 10 J:2,K
A-2
10
11
12
13
c
14
15
16
A-3
SUBHOUTINE IOLERtNFORCtQS,PR•TOL) c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c c c c c c c c c c c c c c c c c c c c c c c c c c c
IHIS SUBHQUTINE COMPUTES THE TOLEHANCE•THE MAXIMUM
VALUl THl OBJECTiVE FUNCTION MAY HAVE WHILE REPRE•
SENTiNG A SATISFACTOMY FIT BETWEEN THE OBSERVED ANO
COMPUTED HYUROGRAPHS•
SUB HOUTINE INPUT •
NF ORL
QS C5j )
EXl
PCE NI
• THE CURRENT SlX•HOUR PEHIOD, NUMBEREU
SEQUENTIALLY fROM THE BEGINNING OF THE
RU~OF~ EV~N T
-lHE AHRAY OF SIMULATED &·HOUR DISCHARGES
• THE EXPONENT ~SED IN COMPUTING WEIGHT WP
• PERCENTAG~ USED I~ COMPUTING TOL(SEE SECT.~.~)
AS CO ~PUTEO IN INTERP ANO
DlFINEU IN OBJEC
SUBHOUTINE OUTPUI •
TOL • TOLERANCE FOR FORECAST TIME NFORC
MPT -l iME OF THE SIMULATED PEAK
c•~••••••••••••••••••••••••••••••••••••••••••••••••••••••••••*•••••••••• c•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••
c c c c c
5
s
7
1 0 c
DIMENSION QS(53>•PR(53) .
COMMON/MATOL/ EXl,PCENT
C0M~O N /ALL/N 0BtT1LT•QOLT•PJ,Q0(5~)tQOMX,ZZtMPT
FINO CENIER OF MASS UF PMECIPCCMPJ.
DC TEH MINE TI ME OF MA~ DISCHARGE, BUT IT
CAN~UT OLCUR BEFORE C~P.
CM P=o.
sPR=o . DO 5 K=l•NfOHC CMP:CMP+PRCKJ*(K+,Q5)
SPR:SPH+PRCKJ
IF(SPR,GT.a.J GO TOG
cMP=o. GO TO 7 CMP=CMP/SPR
~~x=o. DO 10 I:l,53
IFlGS<l>•LE.YMXl GO TO l U
x =I IFlX.LT,CMPl GO TO 10
~M X=QS<IJ
MPT=I
CONTINUE
A-4
c c c c
c c c c c
20
CO~~UTE ~EIGHT WP••AASED oN THE TI~E DISTA NCE BETWEE N THE LAST OBSERVEU DISCHARGE ~NO THE SI~ULATEO PEAK.
•P=CCPJ+N08)/~PTJ••EX1
tFC~P.GT•l•» WP:l.
PCOB IS A PERCE~TAGECI N PUT•PCENT) OF THE LAST OBSERVED DISCH4RGE, ·oR THE ~EA N DISCHARGE
UP TO THE LATEST OBSlRVEC, W ~ICHEVER IS GREATER.
~go~o 0 l:l,No~
PCO~=PC08+Q0Cl) pCQB:CPCOB+QULT•PJ)/(PJ+NOB»
IFCQOLT.GT.P~OB) PCOB:QOLT TOL=CPCOB•PCENTI/WP --
RETURN
END
A-5
SUBROUTINE OHJECCNFORCtQStOFJ c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c c c c c c c c c c c c c c c c c c c c c c c c c c
~ c c c c c c c c c c c c c c c c c c
THIS SUBROUTINE COMPUTES THE OBJECTIVE FUNCTION WHICH REFLECTS T~E GOODNESS OF FIT BETWEEN THE COMPUTED HYDROGR.PH AND THE OBSERVED DISCHARGES UP TC THE TIME Of THE LAST OBSERVED DISCHARGE,
THE LAST OBSERVEU DISCHARGE N£ED NUT COINCIDE WITH
ONE OF T~E SIX•HOURLY COMPUTED ~RUINATES.
SUBROUTINE INPUT •
NFORC
QSCSJ)
NOB
TILT
QOLT
PJ
QOCNJ
MPT
EX2
• THE CURRENT SlX•HOUR PERIOD, NUMBERED SEQUENTIALLY FROM THE BEGINNING OF THE RUNOFF EVENT
• lHE ARRAY OF SIMULATED 6-HOUR DISCHARGES
• NUMBEH OF THE LAST ORDINATE PRIOR TO, OR AT THE TIME OF , THE LAST DISCHARGE OBSERVATION
• THE llMEt IN HOURSt FROM ORDINATE NOB TO THE LAST UISCHARGE OBSERVATIO N. IF TH LAST OBSERVATION COINCIDES WITH ORDINATE NOB,
THE~ TILT=O,
• VALUE OF UISCHARGE AT THE LAST OBSERVATioN. IF TILT IS ZERO, THEN QOLT:QOCNOB) .
• FRACTION OF THE SIX•HOUH PERIOD COVERED BY TILT AND lS EQUAL TO TILT/6,
• MAXIM~H OHSER~EO OISC HAHGE I NCLUSIVE OF QOLT•
• NUMBEH OF THE ORDINATE AT WHICH QOH~ OCCURS, IF QOMX:JOLTt zz:NOB+Pw•
• OBSERVES UISCHARGE ARRAY AS COMPUTED IN INTERP,
• TIME OF THE SIMULATED PlAK, AS COMPUTED I N TOLER•
• EXPONENT USED IN COMPUTING WEIGHT WD,
SUBROUTINE OUTPUT •
OF • lHE OHJECliVE FU N CTIO~ c c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• DI~ENSION QSC53)tWDC53)t~MC5~)tWTC53JtOQ(53)tSOC5~),SSC53)
c
C0MMON/ALL/NOBtTlLT•QOLTtPJ,Q0(53),QOMX,ZZ•MPT COMMON/MAOHJ/EX2
c IN=O
A-6
c c c c c c c c
c c c c
c c c c
c c c c c c c c c c c
2
3
8
11
'3
COMPUTE THE SLOPE AI EACH OBSERVED OISC~ARGE SOClJ••SO(NOBJ AND T EAC~ SI"ULATED DISCHARGE ORUI~ATE SSfl)••SSCNOB+2)
COMPUTE ~LOPES BASED ON WALUES OF 0R81NATE
AT TlM£ L AND AT PRECEDING AND SUCCE NG ORDINATES.
LAST SEG~ENT USES ONLY PRECEDING ORDINATE.
IFCNOB.N£.1) GO IO 2 Q0(2):QOLT
QO(~):QOLT
IFCNOB.N£.2) GO TO 3 Q0(3):QOLT
S0(l):(Q0(2)•QO(l))*•S
SSC1):(QSC2)•QS(l))*.S
J:NOB•1
IFf~.LT.l) J=l
DO '+ L=2•J S0CL):fU0CL+1)•QU(L•1))*0•5
SSCL):CQS(L+l)·Q~CL•1))*U•5 SOCNOBl:fQOCNOB)•QO(J))
J=NOB+3 DO 8 L=NOBeJ xS:QSCl)
IFCL.N£.1) XS=QSlL•l)
SSCL):QSCL)•XS
tFCTILT.LTe u.O~J GO TO ~ xO:QO C1)
xS:QSfl)
IFCNOB,£Q,1) GO fO 11
xO:QOCNOB·1) XS:QS(NOB•1)
SOCNOBl:CQOC~OB)*CPJ•PJ•l,)•XO•PJ•PJ+QOLTJICPJ•CPJ+l,))
SSCNOS):(QS(~OB+l)•XSJ••~ S0Ll=CQOLT•QUCN0~))/PJ
RMS=o,
COMPUTE fHE OBJECTIVE FUNCTION TERMS FOR OROI~ATE NOS~ 1 10 NOB.
no '+'+ L:l,NO~
COMPUTE IHE DIFFEKENCE BETWEEN SIMULATED AND OBSERVED DISCHARGES AT EACH OHDINATE 0Q(l)••DQ(N0~)
OQCL):ABSCQOCL)•QS(L))
RMS=RMS+DQ(LJ•DQfL)
COMP~TE liMING WEIGHIS W~(l)••WTCNOB)
OT IS THt TIME 0~ OCCURRENCE OF A SIMULATED DISCHARGE EQUAL TO THE OBSERVED DISCHARGE
AT OHDINATE Le
IF IF IF
01 eL~. 3 HOUHSt WT:O
D f • G f • 12 HOURS, WT:l
Dl .Gf. 3 HOURS BUT .LE• 12HOURS, WT RANGES
LINEARLY FR~M 0 TO 1,
A-7
10
12
c c c c c c c c c c c
c2,
28
AO:SOCL)
STE=12. oo '2 J:1, .. K=L+J•3 1(1<:1<+1
KKK=K+2 IFct<.LT 1) K=1 IFCKK.Lfe1) KK:1
IFCKKK.LT.1) KKK=1 AA:SSCKl AB:SSCKK)
I FClN.EQeOe) GO TO 30 A:AA+PJ*CAB•AA) AB:AB+PJ*CSSCKKKJ•AB)
A-8
c c c c c c
30
32 ~~
36
38
40
~2
IFCCABSCAO•AA),Ll,,0001)•ANO•CABSCAO•AB),Ll,,0001)) GO TO 36 IFCCABSCAA•AB)),LT,•OOOlt GO TO ~2 IFCAO•AA) 32t38tj~
IFCAO•ABJ~2,j8,~8
IFCAO•A8)38t38t~~
OEL=18e•l5•*~+3,*J•J GO TO ~0
OEL=ABSC18e•6,•J•6,*CAO•AA)/CAB-AA)) IFCOEL.LT,STE)STl:OEL
CON.T INUE SWT=CSTE•3e)ICJ,
tFCSWT,LTiO,)SWT=O£ IF(IN,EQ, ) ij0 TO ~0
WMCL):ABSCCSOCL)•SSCL))/gO(Lt) IFCWMCL)eGT,l,OlWM(L):t,u
WMCLJ:WMCLJ•SWT
COMPUTE UISTANCE WEIGHTS WDC1)••WDCNOB) WHICH ARE BASED ON THE TIME OISTA~CE BETWEEN ORDINATE L AND THE MAXI~¥"' OBSERVED DISCHARGECQOMX)~ lF L IS GREATER THAN HE TIME OF QOMX••CZZ)• THE N WOCL):l,
WDCL):(L/ZZ)**EX2
IFCWDCL)eGT,l,O)WD(L):t,O
~I+ CONTINUE c
C CO~PUTE IHE PORTION OF THE OBJECTIVE FUNCTION C UP TO THl TIME OF ORUINATE NU~. c
c c c c
1+6
48
50
52
WSUP\:0,
PRSUM:O,
00 1+6 L:l,NOB
pRSUM=PRSUM+WOCLJ•CCWTCLt•DQCL)+~MCL)*QOfL))/2,) WSUM:WSU .. +WDCL)
oF:PRSUM/WSUP\ IFCTILT,LT,Ue05) GO TO 5~
IF THE LAST OBSE"VATION FALLS BETWEEN SIX•HOUR ORDIN~TE~t
ADJUST ThE FUNCTION ~OR THE FRACTIO NAL CONTRIBUTION,
A-9
53
A-10
SUBRgUTINE SlRATINFORCtRHtRV•UG6tPPtQA0J) c••••••••• ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c c c c c c c c c c c c c c c c
~ c c c c c c
~ c c c c c c c c c c c c c c c c c c c c c c c c c c c c c
THIS SUBHOUTINE "AKES THE ADJUSTMENTS TO THE PHECIP AND TO THE UNIT GRAPHCTHROUGH SUBROUTINE WARP) oN
SUCC~SSIVE PASSES~ A RETURN IS ~ACE FROM THE SU6ROUTINE WHEN ONE OF 3 CONuiTIONS EXIST: THE VALUE OF THE O~JECTlV~ FUNCTION IS LESS THAN THE TOLERANCE, NO IMPROVE~ENTS WEKE ~ACE DURING A PASSt OR THE NUMBER OF PASSES ALLO~ED HAS BEEN EXC~EOEO, THE SUBROUTINE RETUHNS THE ADJUSTEU SET OF PHECIP AND UN1T GRAPH VALUES ANO THE CORRESPONDING ADJUSTED HYDROGR~PH.
SUBHOUTINE INPUT ••
NFORC
TOL
NJ
UGI2t1071
MAXN
DEL WDEL WHL WHH WVL WVH
ZLOW
HIGH
ucx
RH
RV
UG6 (3~)
• THE CURRENT SIX•HOUH PEKIOOt NUMBERED SEQUENTIALLY FROM THE BEGINNING OF THE RUNOFF EVENT
• THE TOLERANCE
• :o ORlGINAL SiMULATION SATISFACTORYtNO ADJUST• MENTS NECESSARY. SUBROUTINE USED ONLY FOR CO"PUTlNG ~ONSTRAINTS ON LATESTCNFO~C) PRlCIP VALOE.
=1 CO"~UTE CONSTRAINTS AND BEGIN ADJuSTMENTS
ORIGINAL UNIT GRAPHt 8HOINATES SPACEU EVERY 2 HOUHSt ~EGINNING AN ENOING WITH Z~ROtTO BE
PASSE~ ON TO ~ARPI -
• "AXI"U" NUMBER OF PASSES ALLOWED THROUGH THE ADJUSTMENT STRATEGY.
• OELTA J APPLIED TO PRECIP • DELTA APPLIED TO RH A~D RV • LOWER CONSTRAINT ON RH • UPPER CONSTRAINT UN RH • LOWER CONSTRAINT UN RV • UPPER CONSTRAINT ON RV
• THE CONSTANT MULTIPLIER FOR THE LOWER PRECIP CONSTRAINT.
• THE CUNSTANT ~ULTIPLIEH FOH THE UPPER PRECIP CONSTRAINT•
• THE 'FIXED' UPPER PRECIP CONSTRAINT.
• HORIZUNTAL WARp COEFFICIENT AT END OF PR~VIOUS FORECAST TIME
-VERTICAL WARP COEFFICIENT AT END OF PREVIOUS FORECAST TIME
• WARPED UN~T GRAPHCOROINATES SPACEU
A-ll
\
c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c
PPC5~J
OF8
EVERY 6 HOURS) RESULTING FROM THE ABOVE RH ANO RV VALU~S
• PRECIP VALUES 1 THHU CNFORC•lJ, AS ADJUSTED DURING PREVIOUS FORECAST TIME PLUS . CURRENT REPORTED VALUEtPPCNFORC)
• OBJECIIVE FUNCTION FOR THE BASE SIM• ULATION AT TIME NFORCt WHICH USES THE PRECIP ANU UNIT GHAPH A"RAYS DESCRIBED ABOVE
SUBROUTINE OUTPUf -·
RH RV
UG6C~6)
PPCS~)
• THE ADJUSTED HORIZONTAL WARP COEFFICIENT • THE AUJUSTEO VERTICAL WARP COEFFICIE~T
• WARPED UNlT GRAPHCORDINATES SPACED EVERY 6 HOURS) RESULTING FROM THE ABOVE RH AND RV VALUES
• THE ADJUSTED ~RECIP VALUES• 1 THRU NFORC
QADJl53) • THE AUJUSTED HyDROGRAPH RESULTING FROM THE PRECIP ANU UNIT GRAPH ARRAYS DESCRIBED ABOVE
OFB • THE O~JECTIVE FUNCTION FOR THE ADJUSTED HYDROijRAPH
C MSG • INOIC•TES WHICH EXIT CONDITION WAS USED•
C =1 NO-IMPROVEM~NTS WERE MACE ON LAST PASS C =2 OB~ECTIVE f NCTION IS LESS THAN TOLERA NCE C =3 NU~BER OF ~ SSES HAS BEEN EXCEEDED c••••••••••••••••••••••••••••••••••••••••~•••••••••••••••••••·~···•••••• c c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• REAL LK,MXIMP ·
c c c
c
c c
DIMENSION PPl53)tUG6C36)•QAO~C53) COM~ON/STWARP/ IZZ
C0M~ON/MASTRA/UG12(107)tOFBt~AXNtOELtWDELtWHLtWHHt
1 WVLtWVH•ZLOWtHIGHtUCX•TOL•MSG•N~•SUMtLKC53)tUKC53J
COMPUTE CONSTRAINt ON PRECIP VALUE OF NFORC
tFCNFORCeEQ 1) suM:O ,
UKCNFORC):HfGH•PPCNFORCJ LKCNFORCJ=ZLOW•PPCNFORCJ SUM=SUM+PPCN FORCJ UMN=,2•SUM IFCUMN.LT UCX)UM~:UCX IFCUKCNFOAC)eLT,U"N) UK(NFORCJ:U~N IF(NJ,EQ.OJ "ETUHN
IPASS=l
~EGIN PA~S
A-12
c c c
5
8
20
12
15
10 c c c c c c
APPLY A + AND • DELTA TO EACH PRECIP VALUEtONE AT A TI~E. CO~PUTE CHITERION FOR EACH AOJUST~ENT,
IST=O
~SG=o
MXI~P:O, 00 10 I:1,NF0RC ICON:O PP C I) :pp C I J+UEL
IFCPPCl)eLE,UKCIJ) GO TO 8 ICOI\:1
p:PP C U PPCIJ:UKCIJ CALL ~OOELCP~tUG6tQAOJJ CALL OBJECCNFORC•QADJtOFJ CHNG:OFB•OF IFCCHNG,LEeMXIMPJ GO TO 20
HXI~P=CHNG CPR= I eP:PPCI) tFCICON,EQelJ PPCIJ=P PPC.l):PPCIJ•UEL GO TO 10 IFC1CON,EQ,1JPPC!):P
ICON:O pP(l):PPCI)•2,•0EL tFCPPCIJeGE,LKCIJ) GO TO 12 ICON:1 . p:ptl ( u
pP(l):LKCIJ CALL ~ODELCPPtUG6tQA0J) CALL OBJECCNFORC•QAOJ,OFJ CHNG:OFB•OF
IFCCHNG,LE.~XI~PJ GO TO 15
~XI~P=CHNG CPR= I aP:PPCI> IFC!CON,EQ.1JPPC1J:P pP(l):PPCI>+UEL CONTINUE
COMPUTE ~ENSITIV1TY TERM ONCE FRO,.. THE FIRST "AXI~UM
I~PROVEHENT• FINALIZ~ THE IMPROVE~ENT WHICH "OSI IMPROVED THE CRIIERIONCONLY IF THE I~PROVEHENT S SIGNlFICANTti,E.-751 OF THE SENSITIVITY)
IFC~XI~P•LE,O,) GO TO 50 IFCIST.EQ,l) GO ro 30
xsT=1 OFBSE:OFB STY=,075*CMX1MP/UFBJ
C30 tFCCMXI~P/OF~SE>•LTtSTYJ GO TO ~0
PPCCPR):BP CALL ~OOELCPPtUG6tQAOJ)
CALL OBJECCNFORC•QAOJ,OFJ oFB=OF GO TO 50
A-13
\
~0 MXI"P=O• ~ ADJUST U"'IT GRAPt; c IG:O 50
LCON=O
t<CO"'=O RV:RV+WOEL
IFCMV.LTeWVHJ GO TO 52
~CON:l ALL WARP<RH•WVH•UGl2tUG6J
GO TO 53 52 fALL WARPCRH•RVtUGI2tUG6) 53 FCIZZ.NE.l) GO TO 5~
xzz=o GO TO 60
~~ ~ALL HOOELtPPtUG&tQAOJ) ALL OBJEC<NFORC•QAOJ,QF)
IFCOF~GE•OFBJ GO TO 60 oFa:o
IG=l tFtLCON.EQ.tJ RV=WVH
GO TO 70 60 RV:RV•2 *WOEL
IF<RV.Gf.WVLJ GO TO 62
t<CON:l
CALL WARPtRM•WVL•UG12tUG6)
GO TO 63 62 CA~L WARP<RH•RVtUGI2tUG6J 63 IF lZZ.NE.lJ GO TO 6~
xzz=o GO TO 65
6~ CALL MOOELCPPtUG&tQAOJ) CALL OBJEC<N ~ORC•QAOJ,OFJ
IFCOFFGE.OFBJ GO TO 65 oFs=o IG:l
IFCKCON.EQ~lJRV:WVL
GO TO 70 65 RV:HV+ .. OEL c 70 LCON:O t<Cor.:o
RH:HH+WOEL
IFCRH.LT•WHHJ GO TO 72
LCON:l
CALL WARP I WHMtRV•UGI2tUG6) .;O TO 73 72 CALL WARP<RHtRVtuGI2tUG6' 73 IF<lZZ.NE,l) GO TO 7~ .
IZZ=O GO TO 80
7~ CALL MOOELCPPtUGatQAOJJ
CALL OBlECCNFORC•QAUJ,OFJ
IF<OF.G eOFBJ GO TO 80 QFB=OF
tG=l RH=WHH IF<LCON,EQ.tJ
A-14
ao
a2 a!
a ..
GO TO 90 RHzRH•2.*WDEL IFCHH{GT.WHLJ GO TO a2 KCON:
CALL WARPCWHLtRV•UG12t U G~) GO TO 83
CALL WARPCRH•RV,UGI2,UG6J
tFCIZZ.NE.lJ GO tO a .. xzz=o GO TO a5
CALL "OOELCPPtUG6tQAOJ) CALL OBJECCNFORCtQADJtOFJ ~~~2~,GE.OFBJ GO TO 85
IG:l
a5 c
IFCKCON 1 EQ.1J RH=WHL GO TO 9u RH:HH+.OEL
c c c c c c c c
c
90
PASS COMt'LETE
IF NO PEKTUHBATIONS IMPROVED CHITlHIO Nt KETUK N. IF A PERlURBATIO~ I"PROVEO CRITERIO N TO AN ACCEPTABLE TOLEHANCt, HETUR~.
OTHEHWISE, CONTI"UE OPTI ~IZAT10N WITH ANOTHER PA~St IF NVP18EH OF PASSES HAS NOT tXCEEDEO THE LIMIT.
IF(CP1XIP1P.LE•O•J•AND.CIG•EQ.U)) P1SG:1
~~[~F:1~~(~~~~v~e~~~.UG6J
I~:~~Xs~~t~!"X~N !0 G~1 ¥o 1oo IPASS:IPASS+l
GO TO S
100 "SG=3
110 CALL P100ELCPPtUGbtQAOJJ RETURN
END
A-15
SUBROUTINE WARPCHHtRVtUGltUG6) c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c .
C THIS SUBHOUTINE ALTERSCWARPS) THE UNIT GRAPH C ACCOHDING TO THE VALUES ASSIGNED TO THE HORIZONTAL C WARP COEFFICIENT RH AND THE VERTICAL WARP
C COE~FICI~NT RV c c c c c c c c c c c c c c c c
SUBROUTINE I~PUT •
RH RV
UGIC107)
-HORIZONTAL WARp COEFFICIENT. VERTICAL WARP COEFFIC ENTe
-UNIT ijRAPH To eE WARPED. oRBJNATES EvERY TWO HOURS• BEGINNING ANU EN NG WITH ZERO.
SUBROUTINE OUTPUT •
UG6C.56)
IZZ
• WARPED UNIT GRAPHtORDINATES SPACED EVERY SIX HOURS• BEGINNING WITH FIRST NON·Z~RO VALUE•
• PASSED BAC~ TO STRAT WHERE IT IS INTERRO· GATED TO SEE 1F CO"PLEX ROOTS ENCOUNT~RED, c c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c
c
~ c
(.; c c
50
DIMENSION UGl107JtUGIC107J,CC106),UG6C36) COMMON/STWARP/ IZZ
UGIC107):0. oo 50 1:1,107 UG(l):UGICI)
cOMPUTE RO VOLUMEt GRO AND HORIZONTAL SHIFT, SHFT,
GRO=o. QMAX:O, oo 1 ~=1t107 GRO::GRO+UGCKJ
IFCUGC~)eLE,QMAXJ GO TO 1
J=K QMAX:UGCK)
1 CONTINUE GPT=2•CJ•1) SHFT:RH•GPT·~PT
SHIFT HYDROGHAPH RIGHT OR LEFT
tFCSHFT)2,13t8 2 SHFT:SHFT•C•1,) 3 tFCSHFT•2,)6t~t~
~ 00 5 K=lt106
5 UG(I'):UGCK+lJ UGC107):0, SHFT:SHFT•2, GO TO 3
A-16
' SHFT:SHFT•.S
00 1 K=~•106 7 UG(K):U (K)+SHFT*CUGCK+11•UGCK)) uGC1):0.
uGC107>=o. GO TO 13
8 IfCSHFT-2.»11,9,9
9 00 10 K:l,l06
J=108•K 10 UGCJJ:UGCJ•1J uGC1):0
sHFT=SHFT·2• GO TO 8
11 SHFT:SHFTe.5
00 12 K:1,106
J=108•K
12 UGCJ):UGCJ)+SHFT*CUGCJ•1)•UGCJ)) c c WARP HYOROGRAPH VERTICALLY. c CO~PUTE CURVATURE, CCK»• c 13 Q .. AX:O uGCl):o.
u&ClO&J:o.o
U6Cl07>=0• CO l ct K:1,106
tFCUGCK)tGT.QMAXJQMAX:UGlK)
x=o. IFCK.GT.l»X=UGCK•1) Y=X+UGCK+l)
CCK>:o.
IFCY.EQ.O.»GO TO l't
C C K) :2 • •UG C K J/Y
l't CONTINUE tFCCRV.LT •• 999)•0R.CRV•GT.1·0001J) GO TO 16 CO 15 K:1,10&
1!5 CCKJ:l.
e=l· GO TO 26 c c LOCATE INFLECTIO~ POINTS• c 16 NT=O
x=o
Q .. AX:QMAXe.2 00 21 K:2dU6
IFCUGCK)eLT.QMAXJ GO TO ~1
IFCCCK)•l.117t19•20
17 IFCCCK+l>.L i •1.JijO TO 21
18 NT=~T+l x=X+UGCKJ+CUGCK+l)•UGCK))e(l••CCK)J/CCCK+1J-CCKJJ
GO To 21
19 NT:NT+l
x=X+UGCKJ
GO TO 21
20 IFCCIK+1>-l.J18t21t21
21 CONT NUE y:NT
A-17
x:Y/X c C X IS AVEHAGE OF ALL INFLECTION POINT DISCHARGES, RE•CO"pUTE C(KJ
C AS A LI NEAR FU NCTION OF OISCHA~GE SO THAT WHEN UG:O, CCK):O AND
C wHE~ UG:X, ClK):l, c 00 ~2 K:1,106
22 CCKJ:UGCKJ*X c C VERTICAL WARP EQUATION I~-Q(K)=QCK)*HV•l(le+A•Cle•CCK)))/RV)•*B
C COMPUTE COlFFICilNTe A, -
CMX=QMAX*X*5• ATS=CRV•1,)/(1,•CMX)
QO 23 K:l,lOb
cCK):(l,+ATS*Cle•CfK)))/RV
IFCCCKl,LTeOe)CCK):O,
23 cONTINUE c C BY ITERAliON• DEIERMINE A VALUE FOR THE EXPONENT• Be WHICH WILL C CAUSE THE VOLUHE OF THE ADJUSTED HYDROGRAPH TO BE [QUAL TO GRO, c
A-18
R1=C•ZB·Z7)/C2,•tC) R2=CZ7•Z8)/(2,•ZC)
J=3 e=Rl GO TO 2 .. 3 .. TR1=R
J= .. e=R2 GO To 2 ..
35 TR2=R
IFCABSCTR1•1e),GT,ABSCTR2•1,J)G0 TO 36 e=Rl
R=THl 36 IFCN .GTe15)G0 TU 26
[R:ABSCR•l•l IFClR.LT •• O JGO TO 26 RA:HB .
RB:HC
RC=H BA:BB
BB=BC eC:B
GO TO 37 c CO"PUTE AOJU~TEO c HYOROGRAPH c
26 00 "C7 K:l,35
27 J=3•K+1 UG6lK):UG(J)*RV•CCCJ))**H UG6C36):0.
RETURN
END
A-19
SUBROUTINE BLENDCQS) . c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••
THIS SUBHOUTINE HESOLVES THE ~INOR RE~AINING DIFFERENCE BETWEEN THE FI~AL ADJUST£0 SI~ULATION AND THE OBSERVED DISCHARGl BY BLENDIN~•
SUBHOUTINE INPUT •
QSC5~) -THE AHRAY OF ADJUSTED 6•HOUR SIMULATED DISCHARGES.
NOH,QOLT•PJ•OOC~J -A~ CO~PUTED I N INTERP AND
OEFIN~D IN OBJEC.
SUBROUTINE OUTPUT -
c c c c c c c c c c c c c c C QBLC~3) -THE BLENDED HYDROGHAPH• WHICH IS THE FORECASf c c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• c .
c
10
20
30
DIMENSION Q~l53) C0MIIION/BLOT/QBL(53)
tOM~ON/ALL/NCBeTllT•QOLTtPJeWOC53)eQOMX
DO 10 K:l,NOH QBL( K) :QO ( K)
OELQ:QOLT•QS(NOBJ-PJ*(QSlNOB+l)•QSCNCBl)
L=NOB+l "''=NUB+6 QO 20 K:L,III
QBLCK):QSCKl+CDELQ/6e)*f"•K+PJ)
L=N08+7 QO .50 K:L,53 JBL(K):QS(K)
RETURN
END
o u .S . GOVERN MENT PA INTING OF FICE • 1 979 -2ee·067 /11
A-20
(Continued froa inside front cover)
NWS HYDRO 16 A Dynamic Model of Stage-D ischarge Relations Affected by Changing Discharge. D. L.
Fread, November 1973 (revised, October 1976), 38 pp. plus appendixes A and S . (COK-74-
10818)
NWS HYDRO 17 National Weather Service River Forecast System--Snow Accumulation and Ablation Hodel.
Eric A. Anderson, November 1973, 5 chapters plus appendixes A through .H. (COK-74-10728)
NWS HYDRO 18
NWS HYDRO 19
NilS HYDRO 20
NWS HYDRO 21
Numerical Properties of Implicit Four-Point Finite Difference Equations of Unsteady
Flow. D. L. Fread, March 1974, 38 pp. (COM-74-11691)
Storm T•de Frequency Analysis for the Coast of Ceorgia .
28 pp . (CO M-74 -11746/AS)
Francis P. Ro, Septec~er 1974,
Sto rm Tide Frequency Analysis for the Gulf Coast of Florida From Cape San Bias to St.
Petersburg Beach . Francis P. Ho and Robert J. Tracey, April 1975, 34 pp . (COM-75-10901
/AS)
Storm TidP. Frequency Analysis for the Coast of North Carolina, South of Cape Lookout.
Francis P. Ro and Robert J. Tracey, Hay 1975, 44 pp. (CO M-7 5 -11000/AS)
NWS HYDRO 22 Annotated Bibliography of NOAA Publications of Hydrometeoro1ogical Interest.
Miller, May 1975, 50 PP• (Superseded by NWS HYDRO 34)
John F.
NWS HYDRO 23 Storm Tide Frequency Analysis for the Coast of Puerto Rico .
43 PP• (COM-11001/AS)
Francis P. Ho, May 1975,
NWS HYDRO 24
NWS HYDRO 25
NWS HYDRO 26
NWS HYDRO 27
NWS HYDRO 28
NWS HYDRO 29
NWS HYDRO 30
NWS HYDRO 31
NWS HYDRO 32
NWS HYDRO 33
The Flood of April 1974 i n So uthern Mississippi and Southeastern Lo uisiana.
Chin, August 1975, 45 pp. (COM-75-11387/AS)
Edwin H.
1he Use of a Mu1tizone Hydrologic Model With Distributed Rainfall and Distributed Par-
amete r s in the National Weather Service River Fore~ast System. David G. Morris, Aug ust
1975, 15 pp. (COM-75-11361/AS)
Moisture Sou r ce for Three Extreme Loca. Rainfalls in the Southern Intermountain Region.
E. Marshall Hansen, November 1975, 57 pp . (PB-248-433)
Storm Tide Frequency Ana lysis for the Coast of North Carolina, No~th of Cape Lookout .
Francis P . Ho and Robert J. Tracey, November 1975, 46 pp. (PR-247-900)
Flood Dam.age Reduction Potential of River Forecast Services
Rasin. Harold J. Day and Kwang K. Lee, February 1976, 52 pp.
in t he Connecticut
(PR-256 -758)
River
Water Available f~c Runoff for 4 to 15 Days Du ration in the Snake River Rasin in Idaho .
Ralph H. Freder~ck and Robert J. Tracey, June 1976, 39 pp . (P&-258-427)
Meteor Rurst Communication System--A:aska Winter Field Test Program.
ford, March 1976, 51 pp. (PR-260-449)
Hen r y S. Sante-
Catchment Modeling and Initial Parame ter Estimation for the National Weather Service
River Forecast System. Eugene L, Peck, June 1976, 9 pp. plus a ppendixes A through D.
(PB-264.-154)
Storm Tide Frequency Analysis for the Open Coast of Virginia,
Francis P. Ho, Robert J. Tracey, Vance A. Myers, and Normalee
52 pp. (PB261969)
Maryland,
S . Foat,
and Delaware.
August 1976,
Greatest Known Areal Storm Rainfall DepthB fo~ the Contiguous United States. Albert P.
Shipe and Juhn T . Riedel, December 1976, 174 pp . (PR-268-87 1)
NwS HYDRO 34 Annotated Bibliography of NOAA Publications of Hyd r ometeorological Interest. John F.
NWS HYDRO 35
Miller, April 1977, 65 pp. (PB-268-·846)
Fi7e-to 60-Hinute Precipi tation Frequency for the Eastern and Central United States .
Ralph H. Frederick, Vance A. Myers, and Eugene P. Aucie l lo, June 1977, 36 rp.
NWS HYDRO 36 Determination of Flood Forecast Effectiveness by the Use of Mean fo recast Lead Time.
NilS HYDRO 3 7
Walter T. ~ittner, August 1977, 22 PP •
Derivation of Initial Soil Moisture Accounting Parameters From Soil Propertiess for the
National Weather Service River Forecast System. Bobby L . Armstrong, March 1978, 53 pp .
(PB-280-710)
\
NOAA--S/T 79 -39