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DOCUMENT CON T ROL Cllfllllllll
RESPONSE TO COMMENTS BY
HARZA-EBASCO SUSITNA JOINT VENTURE
ON AEIDC'S REPORT ENTITLED
"STREAM FLOW AND TEMPERATURE MODELING
IN THE SUSITNA BASIN, ALASKA."
Cllfllllllll
By: AEIDC
1983
TK
1425
.S8
A23
no.2627
Response to Comments by Harza-Ebasco Susitna Joint Venture
on AEIDC's Report Entitled "Stream Flow and Temperature
Modeling in the Susitna Basin, Alaska"
This document is numbered "APA 2627", and is the edition not containing original comments.
Alaska Resources Library and Information Services (ARLIS) is providing this table of contents.
Table of Contents
Response to general comments.
Response to specific comments.
Attachment 1 - SNTEMP mathematical model description.
Attachment 2 - Heat flux components for average mainstem Susitna conditions.
Attachment 3 - Weather wizard data.
Attachment 4 - Daily Indian River temperatures versus Devil Canyon air temperatures.
Cllfllfllll( RESPONSE TO GENERAL COMMENTS Cllfltfmlr
We feel that, although the AEIDC report entitled "Stream Flow and
Temperature Modeling in the Suai.tna Basin, Alaska" is written for a technical
audience, a detailed description of the SNTEMP model would be unnecessary
since the temperature model description is available from the !nat ~am Flow
Group , U.S. Fish and Wildlife Service (the reference Theurer et al. 1983 in
the draft report). The description is lengthy and its inclusion in the AEIDC
report would detract from the purpose of the report: a description of the
modifications of the stream temperature model, the techniques used for data
genesis, and the methods employed fo r validation and calibration.
Attachment 1 of this memo is a copy of the mathematical model description frO.
a draft of the Theurer et al. 1983 paper which we hope will be useful in
providing background to the AEIDC report.
The decision to investigate other methods of determining subbasin flow
contributions was made at a March 15, 1983, mee t ing between Harza-Ebasco and
AEIDC personnel. We agreed t hen to examine more sophisticated approaches
which included the effects of precipitation distribution, and to respond in a
letter report to Dr. B.K. Lee in April.
The decision to test the three weighting methods using a large set of
subbasins rather than one or two individual subbasins was based on a number of
reasons. The resolution of the precipitation and water yield distribution
maps used to determine weighting coefficients are low enough to allow
substantial miscalculation of coefficients for any single subbasin. By
testing on a composite set of subbasins, higher basinwide accuracy would be
expected. Additionally the largest set of flow data available to test these
coefficients was on the mainstem river rather than on individual tributaries .
-1-
CDifllllllll
Th i s i s important as the weighting co effic ients were derived from maps
repr esenting average trends ; anomalous runoff even ts on small subbasins could
easily lead to unrepresentative short-term flow records . Finally, delineation
and planimetry o.f all subbasins was necessary· for watershed area weighting.
Once this and the additional work transferring precipitation and water yield
isopleths onto the base map was done, little extra time was required to
calculate water yield and precipitation coefficients for all subbasins.
As described later in this memo, alternate techniques could be used in
predicting tributary temperatures. The technique chosen should be physically
based to insure reasonable predictions when the model is used to extrapolate
tributary t emperatures. We have discovered that the tributaries have a major
influence on the mainstem temperature in simulations of postproject
conditions. We also feel that accurate tributary temperature predictions may
be neces sary to a ddress thermal shock effects on spawners traveling from the
mainstem into the tributaries.
We are presently organizing the data necessary to simulate daily stream
temperatures. Our initial effort will be validation of the stream tempera ture
model predictions using 1982 data. A coordinated approach will be necessary
for determining which periods should be simulated and for defining the purpose
of daily simulations.
p. 1, para. 2
RESPONSE TO SPECIFIC COMMENTS
Note that ADF&G and USFWS have undertaken studies of
temperature effects on salmonid egg incubation.
-2-
The introduction to this temperature report paper was not intended to be
all inclusive concerning the literature on temperature effects on the various
fish life stages. We are aware of t he studies being done by ADF&G and USFWS.
Their respective reports are due out during the month of August 1983 and we
will utilize the informat i on as it becomes available.
p. 8, Par. 1 and
p. 11, Pa r. 2
Since subjectiveness is involved in areal precipitation
weighting (method 2), is using this method more
appropriate than using the drainage area method?
Since Method (2) yields a higher Watana discharge, we
recommend this method not be used at this time . The
high discharge implies additional econamic benefits.
For economic runs, we need to be conservative. However,
a final decision on the sele ted method will be made by
H/E in the near future.
The subjectiveness of the precipitation weighting coefficients is d\le
both to the methods used to arrive at those coefficients from the
precipitation distribution map, and to the inherent "art" i nvolved in
developing that isohyetal map from the paucity of data available for the
Susitna basin. Method 2 was chosen solely on the merit of its better
agreement in predicting Watana streamf l ows than the other two methods. l.Je
think this method has merit and could be improved by refining the basin
isohyetal map with the additional data that is being collected.
However, in the short term, we agree that the simpler drainage area
method can be used. It should be clarified, though, that no matter: which
method is used, we have been running SNTEMP using the available monthly data
sets provided in Exhibit E (ACRES 1983) (with the exception of the Sunshine
data set). Flows at Watana (or at Devil Canyon for the two-dam scenario) and
at Gold Creek are input to the water balance program , and are thus consistent
with those used by ACRES and Harza-Ebasco. It is only the apportionment of
water between gage sites that differs etween t hese methods.
-3-
p. 9, Fig. 3 Mean annual water yield for several subbasins appears
to be greater than the mean annual precipitat i on
(Tsusena, Fog, Devil, Chin-Chee, Portage).
This is true. Mean annual precipitation values were developed using the
map of Wise (1977), and mean annual water-yield values using the map of Evan
Merril of the Soil Conservation Service (1982). These numbers are clearly in
dispute. This figure was included to demonstrate the differences between
those weighting methods.
p. 10, Bottom Calculate d C for Method (1) is 0.5104. ACRES used
0.515. Why Is there a difference? Were these areas
replanimetered?
The basin between Cantwell and Gold Creek was divided into ten subbasins
(Clarence through Indian, Figure 4 of the draft report), four upstream from
the Watana dam site, and six downstream. The area of each subbasin was found
by planimetry; the areas of the basin above and t he basin below Watana were
arrived at by summing the appropriate subbasin areas. Discrepancies in basin
area measurements are expected when those basins are delineated and
planimetered independently. Moreover, our pro.:edure incorporates possible
errors from a number of individual planimetry measurements, and compounding
errors can occur. However, the agreement of these two figures is to less than
one-half percent (0.0046) of the area between Cantwell and Gold Creek. This
difference corresponds to an area less than 9 mi 2 in a watershed (defined at
Watana) larger than 5000 m1 2 •
-4-
Once again nd most importantly, these coefficients are defined for the
Cantwell to Gold Creek basin. 'When running SNTE){P, only the flow
ap~ortionment between basin sites having input data is affected. Thus
mainstem f lows at Watana. Gold Creek and Susitna Station are consistent with
those flows used by other groups.
p. 18, Par. 1 We suggest us ng solar radiation measurements when
available rather than calculated values. We would
also like to see daily comparisons of observed versus
computed solar radiation. Please provide descriptions
of the six SNTEMP submodels.
We have decided to use pr edicted solar radiation rather than observed
values so that we would be able to simulate water temperatures for perio.ds
when there was no data co llected. This is useful for predicting average and
extreme conditir'!la .. :~!.ch did not necessarily occur during the 1980 to 1982
periods. We have made an effort to calibrate the solar model to observed
solar radiation data to make our predictions as representative as possible.
As Figure 22 indica tes predicted solar radiation values are
represe tative of bas in for monthly average conditions. This figure
demonstrates a tendency to overpredict Watana and underpredict Devil Canyon
insolations. Thus. the solar model is predicting an average basin insolation.
Since the current implementation of SNTEMP allows for only one meteorc · gical
data station, basin average solar radiations would have to be estimated from
alternative means or · area weighted averages. The solar JDOdel essentially
averages conditions for us.
Calculated solar radiation is also necessary for simulating topographic
shade effects. The solar model track~ the sun during the day and accounts for
the time the stream surface is in shade due to the adjacent topography.
-s-
We will produce a plot similar to Figure 22 but with daily values if it
becomes necessary to predict daily water temperatures.
Attachment 1 contains pertinent pa a from the paper by Theurer et al.
(1983) which describes the six SNTEHP submod~ s. These pages Will be useful
in clarifying some of the comments to other section o f AEIDC's draft flow and
temperature report.
p. 19, Bottom More discussion on heat flux would be helpful. Statements
regarding the relative importance of heat inputs and
outputs should be made. Please provide all heat sources
and sinks considered.
Attachment 1 discussed in the previous response should clarify how the .
heat flux components (atmospheric, t o.,ographic, and vegetative radiation;
so~.ar radiation; evaporation; free and forced convection; stream friction;
stream bed conduction; and water back radiation) are simulated by SNTEHP. We
are working on a graphic presentation to demonstrate the values of the
individual heat flux compo nents for average mont h ly conditions but do not feel
it will be available for the final version of this report. Preliminary plots
of the heat flux components are presented in Attachment 2. The relatively
high friction heat input is interesting and will probably be a major influence
in f all and winter simulations.
p. 20 . In Eq. (9), how wasT (Equilibrium temperature)
estimated? What are !he parameter values of K1 and K2?
The values of the equilibrium temperature (Te) and 1st (K 1) and 2nd
(K 2) thermal exchange coefficients are computed within SNTEMP. To visualize
-6-
the technique used, it is necessary to realize that the net beat flux (EH) is
an analytical but nonlinear function of the stream temperature (due to the
back radiation, evaporation, and convection beat components); i.e. tB •
where t is w stream temperature. When stream temp er ture equals
equilibrium temperature, the net beat flux is zero (tH • f (T •T ) • 0). w e
Newton's method is used to iterate to the equilibrium temperature with the air
temperature being the initial estimate of Te. The values for K1 and K2
follow since the first and second derivations of the beat flux are also
analytical functions and:
d{t'H ) d~ dfK
• 1 2 • Kl ~ ~ dT T • T w w w w e
d2 (tH) d2f d 2f
• K2 K2 • K2
dT 2 dT 2 dT 2 T • T w w w w e
Average values of Te' K1 , and K2 will be presented in a subsequent
report which will include 1983 data/SNTEMP simulation validation.
p.21 There are potential problems with using temperature lapse
rat es at Fairbanks and Anchorage. Both sites are
subject to temper~ture inversions because of topography.
This may not occur along the Susitna River. We
recommend that the existing Weather Wizard data be
reviewed.
-7-
No long term upper air data are available for Talkeetna. Anchorage and
Fairbanks vertical temperature (and humidity) data averaged over a six-year
period (1968, 1969, 1970, 1980, 1981, and 1982) are felt to be the best
available representation of verti~al air temperature profiles for the Susitna
River basin. Examination of numerous winter daily synoptic weather maps for
surface, 850 mb, and 500 mb levels verifies the assumption that inversion
strength and thickness in the Susitna River basin are roughly halfway between
those observed in Anchorage and Fairbanks.
The Susitna basin is surrounded by mountains on the north, east and west.
To the south it is open to the Cook Inlet and Gulf of Alaska. In winter, the
Alaska range blocks most low level interior air from reaching and influencing
the Susitna basin and Anchorage. However, radiative processes in concer~ wfth
topography are responsible for producing a strong, well documented low level
inversion in the Susitna valley (Comiskey, pers. co111111.). This inversion is
not as severe as in Fairbanks, but more severe than in Anchorage. Data from
both stations are retained since upper air temperatures for all three regions
are relatively uniform.
Topographic variability will introduce loc 1 systematic error in the
vertical profiles. Cold air flows downhill where radiative cooling in the
valleys further reduces air temperatures. Weather Wizard data gathered at
stations wi bin the basin may reflect highly localized weather activity.
Within the mountain walls vertica and lateral air mass extent and movement is
limited compared to that of the synoptic scale events governing the major air
mass properties. Local topographic effects cannot be reliably incorporated
into the larger scale vertical lapse rate regime.
-8-
This strong inversion is not just a statewide phenomena, but occurs
throughout the high latitudes in winter. Due to the small heat capacity of
the land surface its temperature is highly dependent upon absorption of solar
radiation. Minimal radiation is absorbed in Alaaka (i.e., the Susitna River
basin) in winter for the following four reasons: (1) a high albedo, (2) short
hours of daylight, (3) the oblique angle of the sun's rays, and (4) screening
by clouds of ultraviolet rays. Consequently, a warm maritime air mass flowing
from the North Pacific or Bering Sea over Alaska will be strongly cooled at
the earth's surface. When subsequent air masses move onshore they are forced
to flow aloft by the previously cooled. dense stable surface layer. Daytime
heating at the earth's surface is usually not strong enough to destroy the
inversion. Over a 24-hour cycle no well-defined mixed layer remains and
fluxes of latent and sensible heat are very small. The inversion's longevity
is enhanced whe n the wind speeds are low and corresponding momentum trancfer
is weak. Talkeetna is typified by comparatively low average wind speeds, on
the order of 5 mph during the winter months. A single strong wind event can
disperse the inversion temporarily; however, it will occur frequently each
winter and is considered a semi-permanent feature.
Translocating average temperatur e profiles from Anchorage and Fairbanks
in the spring, summer, and fall to the Susitna River basin is well within
acceptable limits. The temperature profiles generated by this method fall
precis.ely within the . moist adiabatic lapse rate, as predicted by standard
theory. The temperature data gathered from upper air National Weather Service
radiosonde instruments is highly correlated with temperatures measured in the
basin by the Weather Wizard. This argument further substantiates use of large
scale data to predict local temperature patterns.
-9-
p.24, Par. 4 How have we demonstrated that t opographic shading has an
important influence on the Susitna River? While we do not
dispute this, we would like to see this verified with a
sensitivity run.
Our statement is in error since we have not demonstrated that topographic
shading has an important influence on Susitna stream temperatures. Initial
sensitivity simulations without to agraphic shade have shown that the
corresponding increase in solar radiation has only a small effect on the
stream t snperatures. The significance of the shade effects bas only been
tested for average natural June through September conditions where an increase
of less than 0. 2 C was simulated without shade from Cantwell to S · shine.
Based on the solar path plots in Appendix A of the draft report, we would
expect that the shading effects in other months would be greater but still
relatively small. The wording of this paragraph will be changed to reflect
the new knowledge gained from this sensitivity study.
p. 27 , Par. 2 Stream surface area is necessary to compute heat flux.
According to Figure 26, we are considering only ten (10)
reaches. How representative are these reaches for
determining stream width and hence surface areas for the
river segment between Watana and Sunshine? While Append ix B
illustrates the representativ eness of the ten (10) reaches,
it appears t hat we may have l ost some of the refinement
of the Acres model with its a pproximately sixty (60) reaches.
We feel that increasing the number of simulated reaches would improve the
representativeness of t he stream temperature model as would any increase in
data detail. Ba sed on our familiarity with SNTEMP, we did not originally feel
that this many reaches were necessary. Nevertheless, we can increase the
number of reaches for simulation purposes; the data i s already available and
the only increase in the client's costs will be the manpower to add them to
SNTEMP data files and the increased computa t ional time .
-10-
We are not familiar with the ACRES stream temperature model and do not
know the model's stream width or hydraulic data requirements.
p. 29, Par. 1 To compute daily minimum and maximum tmperatures, we
suggest the use of HEC-2 velocit i s r a h er than
obtaining Manning's n values to compute s t ream velocities.
To reduce client costs, we must be conscious of the
information that is available and no t redo computations
wh .re they are not warranted.
There would be two objections to using HEC-2 velocities as input to
SNTEMP: ( 1) HEC-2 simulations would be required for all water temperature
simulations where the minimum and maximum water temperatures were desired; and
(2) SNTEMP would have to be modified to accept velocities.
Velocity input is not curren tly necessary to .m SNTEMP for minimum and
maximum temperatures since it is computed internally. This allows us to. use
SNTEMP for simulating any i ~--free period from 1968 to 1982 (or later, when
the required data are r eceived). Thus, we can determine the extreme
meteorological/fl ow periods for simulating maximum and minimum average daily
temperatures and the diurnal variati on around these extreme daily
t emperatures. If the HEC-2 velocity estimates are required, this flexibility
would be lost. If the Susitna Aquatic Impact Study Team could agree on the
periods for minimum and maximum temp erature predictions , this first problem
could be eliminated.
Modifying SNTEMP to accept velocitie s , howeve r , would be a major
undertaking. The explanation for this would be lengthy; we would prefer to
discuss this potential modification at a technical meet ing to explain the
amount of work necessary and to help decide if SNTEHP should be modified or
alternate techniques used.
-11-
Figure 12 This figure i s xcellent. It should probably be expanded
to include the months of May and October.
We agree that Figure 12 is bo t h useful and usable ~nd should be expanded
to include May and October data as well as 1983 data. However, due to
budgetary and time constraints , we will not be able to revise this figure
until after the October 14 report.
p. 39, Par 3 We suggest that AEIDC discontinue its literature search
for techniques to improve the resolution of the (ground
temperature) model.
This is not an intensive literature search. We are limiting our search
to the journals and reports we normally read within the course of our
professional maintenance and to conversations with other professionals who may
have experience and knowledge of lateral flows and temperature in general and
Susitna conditions specifically. The last sentence of this paragraph will be
replaced with 1 AEIDC believes this ~del currently provides the best available
approximation of the physical conditions existing in the Susitna basin and
will be applied without validation until better estimates of existing
conditions are obtained."
p. 40, Par 2 I s the Talkeetna climate station representative of
conditions further north in the basin? Presumably Fig. 19
is a comparison of monthly observed versus precicted
which appears to be a good comparison. However, Fig. 19
does not show the comparison of Talkeetna temperatures
with other basin temperatures. Thus, if Talkeetna data
are to be ~~ed in the model, are they representative of
basin cot'.ditions?
-12-
Talkeetna climate data would not be representative of conditions within
the basin if applied without adjustment. The last two sentences of this
paragraph will be changed to "This period of record allows stream temperature
simulati ons under extreme and normal meteorology once these data a re adjusted
to better repres~nt conditions throughout the Susitna basin. We used
meteorologic data collected specifically for the Susitna e tudy to validate
this meteorologic adjustment and the solar model predictions." We hope this
will clarify that we are not blindly applying Talke e t n a data without
adjustmen t.
Apparently Figure 19 bas been misunderstood. The predicted temperatures
are based on observed temperatures at Talkeetna and the laps rates which we
have developed (Figure 7 in the report). Given the observed temperature at
the Talkeetna elevation , the lapse rate equations are used to predict
temperatures at any elevation. The air temperatures predicted for the
elevations of the Sherman, Devil Canyon, Watana, and Kosina Weather Wizards
were compared to the air temper tures observed by R&M (Figure 19 in the
report).
p. 41, Bottom Since monthly average wind speeds are used in the model,
we fail to see th justification for obtaining wind speeds
directly over the water surface. We could understand this
for a lake, but for a river?
A·s Figure 21 suggests, the wind speed data collec ted at Ta lkeetna
represents average basin wind as collected at the four R&M sites (at least
the data at Talkeetna is not extremely different). What these wind spee~ data
represent, however, is not fully understood. The evaporative and convective
heat flux is driven by local (2 m above t he water surface) wind speeds. The
Watana, Devil Canyon, and Kosina stations are located :1igh above the wa ter
-13-
surface ( 3 we understand, we have not visited the sites). This implies that
the d t a collect ed do not meet the model's require111ents; however, we agree r
that it is no t necessary to collect additiona l data if this would be very
expens ive. In ou r initial conversation with Jeff Coffin of R&M Consultants,
we inquired if it would be possible to obtain this data easily as part of
their existing collect ion effort. He felt it would be possible. A return
cal from Steve Bredthauer informed us that equipment necessary to collect
this data was not available and would have to be purchased. Our response was
that t is data would improve our understanding of in-canyon winds but wou l d
not be necessary at the expense envisioned. We have replaced this la t
sentence on Page 41 with "Since it appears to be impr ctical to collect wind
speed data within the canyons below the existing meteorological deta sit"ea
(Bredthauer 1983), the wind speed data collected at Talkeetna will be used as
repr esentative of average basin winds."
p. 44 Top figure. Is the value (9.3° C predicted, 2° C observed)
for Watana correct?
SNTEMP did pr {1 ct an air temperature of 9. 3 C and an average air
temperature of 2 C was observed for Augus t 1981 at the Wat ana weather station.
The observed Watana data is obviously in error (e.g., a temperat ure of -30.9 C
was recorded for 15 August 1981) and p~obably should not have been included
for v alidation of the .air temperature lapse mode l in this plot. As stated in
the report, none of the Weather Wizard data were used in the water temperature
simulations but are presented as a v alidation of the adjustment of the
observed Talkeetna data. Careful review of the Weather Wizard data
(especially humid~ties) would be nece ssary if these data were to be used in
-14-
water temperature simulations. This data point will be remo v ed from the plot
in the final draft.
p. 45, 46 There appears t~be something seriously wrong here. We
believe more work is necessary to underst and what the
problem is. For example, how do the observed relative
humidities at the stations compare with one another?
The large variability in observed Weadler Wizard data gives rise to
doubts of its relia ility. Data which are smoothed by monthly averaging are
not expected to exhibit the year to year range of humidities which was
observed at the Weather Wizard stations. The entire data set is characterized
by irregular large annual changes in average relative humidities on the ord~r
of 30% to 40%. Talkeetna relative humidity values, measured by the National
Weather Service, are cons1.stently greater by approximately 20% throughout the
data. Talkeetna values are in agreement with the large scale picture
generated by averaged Anchorage and Fairbanks data. For this reason, and
those enumerated on Page 41 in the draft report, AEIDC maintains that the
pre dictive scheme derived for input into the stream temperature model is the
best representation of relative humidity with height for input in the surface
flux calculati~ns.
Five sample figures from the R&M raw data are presented for inspection
(Attachment 3). Figures 1 and 2 present summer (June 1981) and winter
(November 1980) situations where the correlation betwe en Weather Wizard data
at two stations is illustrated . In both instances the relative humidity data
is in good agreement from one station to another. These were chosen as
exemplary months; they are not, however, typical. Figure 3 indicates two
common errors, missing days of data and an unvarying upper limit. Another
common error discussed in the report is illustrated by Figure 4. Erratic
-15-
daily swings from zero to 100 percent exist throughout the data. Figure 5
illustrates simultaneous comparison of Watana Weather Wizard data and surface
relative humidities measured at Talke t na by the National Weather Service.
The correlation between the two is poor.
Attempts to explain the erratic swings in the data (daily, monthly and
annually) as highly localized topographic or microscale weather events is also
unsatisfactory. OVer time, monthly averaging woul d smooth anomalies.
However, a three-year average for each month still retains a high variability
with elevation (see Figure 6, Attachment 3). From year to year topography
requires that highly localized atmospheric events be fairly consistent,
thereby giving rise to identifiable trends in the data. Such is not the case.
AEIDC meteorologists concur that instrument calibration problem& ar~ the
probable explanation for t he high variability in the data.
The best way to verify these conclusions regarding the reliability of the
relative humidity data collected in the Susitna basin would be to perform a
spot calibration of the Weath er Wizards. A wet bulb-dry dry bulb sling
psy chrometer could be carried to the remote wea t her stations where the
relative humidities measured by each method can be compared.
p. 51-54 The predicted temperatures in Appendix C generally
indicate increasing temperature with distance downstream
except for the Chulitna confluence. We are not convinced
that the observed data show this. Thus, can we say the
model is calibrated? To apply the model to postproject
condition~ may not be valid.
We have some problems in believing the observed data, especially the
variation in downstream temperatures observed in August 1981, September 1981,
and August 1982. We do not understand what would cause the types of
variations ir.dicated unless there were tributary impacts which we ere not
-16-
considering. e feel, however, that we have made a thorough attempt at
modeling tributary flows and temperatures.
We are not thoroughly familiar with the techniques used by ADF&G to
verify. and calibrate their thermograph&. Their techniques are not published
in any Susitna reports.
We recommend that data verification be performed. Wayne Dyok, H-E, has
collected some longitudinal temperature data which tends to support the
downstream increase in temperature which we have predicted. Wayne's effort
vas helpful but does not identify which thermographs or data sets may be in
error. Until faulty data sets are identified (if any) we do not feel we
should attempt to increase the degree of fit of the model.
As to applying the model to postproject conditions, we feel that, •t the
very least, it is necessary that some initial estimates of project impacts be
made at this time. It may be necessary to label these simulations as
preliminary results until tempe rature data is verified.
p. 55, Future
Applications
1) Normal and extreme flow regimes for the 32-year record
should be defined in coordination with H-E. (See
general comments).
Our intent here is to identify the natural range of flow regimes in the
Susitna basin, not to necessaril y "define" representative flow years for more
detailed study. We agree tha identifying such years should be done by AEIDC
and H-E together, insuring the most thorough results for the efforts of each.
p. 55 2) Please explain what is meant by "This will identify
the area facing possible hydrologic/hydraulic impacts?"
-17-
If possible, we will determine the location downstream from the project
where operational flows become statistically indistinguishable from natural
flows. This will vary on a month-by-month basis. If project flows downstream
from a given location are insignificantly different from natural flows, we
reason that flow-related impacts must also be indistinguishable, and,
therefore, need not be examined further.
p. 55 3) Good, but do in coordination with H-E, as this is
necessary for other models.
We have met with Wayne Dyok of Harza-Ebasco and discussed our approach in
simulating normal and extreme stream temperature changes. The periods we
selected were not the same as the periods selected by Harza-Ebasco. Since ve
bad a deadline to meet in producing a stream temperat re effects paper, there
was insufficient time for a more coordinated approach . We feel that more
coordination will be of mutual benefit in the future.
p. 55 8) Techniques for improving the groundwater temperature
should not be pursued at this time.
We have found that the influence of the tributaries on the mainstem is
significant, especially in postproject simulations. The distributed flow
temperature model was developed to improve the tributary temperature
predictions with a ph,sically reasonable model. There are other approaches to
predicting tributary temperatures but the technique used will have to meet
several requirements: (1) it must be general enough to apply to June-September
periods without observed tributary temperatures, (2) it must be applicable to
winter conditions for future ice simulations, and (3) any technique used
cannot depend on more data than is available. The technique which you have
-18-
suggested (relating tributary temperatures to air temperatures) may be
possible when the 1983 field data becomes available, although we would
rec~nd a regression model based on C'omputed equilibrium temperatures.
There is not enough monthly tributary data currently available for any
regression approach. Daily air temperature and tributary te.perature data
suggests a correlation (Att~cbaent 4 is a scattergraa of recorded Indian River
temperatures versus air temperatures) but we believe that a regression model
baaed on daily data would result in a tributary temperature model which would
not be as capable as the distributed flow temperature model • .
As you request, we will not pursue techniques for improving the
distributed flow temperature model at this t1111e. This model will be used u
is for all silL ations until the 1983 tributary teaperature data b~cOIIias
available. When the 1983 data are available, we will look at possibl e
regression models for predicting tributary temperatures. We will then select
the beat approach. Harza-Ebasco's involvement in this selection process would
be appreciated.
-19-
Cllfllllllll
AttacbMnt 1
SNTEMP MATB!MATICAL MODEL DESCRIPTION
INTRODUCTION
This part is to explain each of the physical processes affecting instream
w&ter temperatures and their mathematical descriptions so that the responsible
engineer/scientist can understand the behavior of the model. It will enable
the responsible engineer/scientist to determine the applicability of the
model, the utility of linking the model with other models, and the validity of
results.
The instream water temperature model incor rates: (1) a complete solar
model including both topographic and riparian vegetation shade; (Z) in
adi a bat 1 c meteoro 1 ogi ca 1 correction mode 1 to account for the change in air
temperature, relative humidity, and atmospheric pressure as a function of
e 1 evat ion; ( 3) a comp 1 ete set of heat flux components to account for a 11
signif i cant heat sources; (4) a heat transport model to determine longitudinal
water temperature changes; (5) regression models to smooth or complete known
water temperature data sets at measured points for starting or interior
validation/calibration temperatures; (6) a flow mixing model at tributary
s junctions; and (7) calibration models to eliminate bia~ and/or reduce the
probable errors at interior calibration nodes.
23
SOLAR RAD I ATION
The solar radiation model has four parts: (l) extra-terrestrial radia-
tion, (Z) correction for atmospheric conditions, (3) correction for cloud
cover, and (4) correction for reflection from wate r s ur·race. The extra-
terrestrial radiation, when corrected for both the atmosphere and cloud cover,
predicts the average daily solar radiation received at the ground on a hori-
zontal surface of unit area:-Therefore, it is the total amount of solar
energy per unit area that projects onto a level surface in a 24-hour period.
It is expressed as a constant rate of heat energy flux over a 24-hour period
even though there is no sunshine at night and the actual solar radi.atfon
varies from zero at sunrise and sunset to a maximum intensity at solar noon.
EXTRA-TERRESTRIAL RADIATION
The extra-terrestrial radiation at a site is a function of the latitude,
general topographic features, and time of year. The general topographic
features aff~ct the actual time of sunrise and sunset at a site. Therefore,
the effect of so 1 ar s hading due to hills and canyon wa 11 s can be measured.
The time · of year directly predicts the angle of the sun above or below the
equator (declination) and the di stance between the earth and the sun (orbital
position). Th l atitude is a measure of the angle between horizontal surface s
along the same longitude at the equator and the site.
")If _,
The extra-terr estr i a l so l ar radiation equation is
where:
H sx,i
q 1 solar constant= 1377, J/m 2/sec. s
e 1 orbital eccentricity = 0.0167238, dimen sionless.
ei 1 earth orbit position about the sun, radians.
f 1 site latitude for day i , radians.
6i 1 sun declination for day 1, radians.
h 1 sunrise/sunset hour angle for day i, radians. s,f
(
H 1 average daily extra-terrestrial solar radiation for day 1,
sx,i J/m2/sec.
) .
The extra-terrestrial solar radiation may be averaged over any time
period according to
where:
N = [ I H i]/[N-n + 1] i=n sx,
H ! extra-terrestrial solar radiation for day i, J/m 2 /sec. sx,i
N! last day in t im e period, Julian days.
n 1 first day in time period, Julian days.
:day counter, Juli a n days.
extra-terrestrial solar radiation averaged over time
period n to N, J/m 2 /sec.
,,
( )
The earth orbit position and sun declination as a fun ction of the day of year
are
( )
61 = 0.40928 cos [(2~/365) (172-01)] ( )
where: 01 ! day of year, Julian days; 0 1=1 for January 1 and Oi=365
for December 31 . ~
/~~.
e1 ! earth .orbit position for day 1r, Julian days.) tZ'
6i 1 sun declination for day f, Julian days.
The sunrise/sunset hour angle is a measure of time, expressed as an angle,
between solar noon and sunrise/sunset. Solar noon fs when the sun fs at its
zenith. The time from sunrise to noon f s equa 1 to the time from noon to
sunset only for symeterical topographic situations. However, for simplicity,
this model will assume that an average of the solar attitudes at sunrise/
sunset is used. Therefore, the sunrise/sunset hour angle is
h s, i ( )
N
hs = [ t hs,i]/(N-n + 1]
i=n
( )
where: f 1 s ite latitude, rad i ans.
61 ! sun declination for day f, radians.
as ! average solar altitude at sunrise/sunset, radians; a = 0
for flat terrian, as > 0 for hilly or canyon terrian~
26
,,
9-
')
0
0 ,
,,
LEVEL PLANE ON
E ARTH'S SURFACE
s
figure 2.1. Solar angultr aeasure.ents.
LATITUDE
EQUATOR
h :sunrise/sunset hour angle for day i, radians
S 1 i
n !
average sunrise/sunset hour angle over the time period n to
N, radians.
first day of time pe ri od, Julian days.
N 5 last day of time period, Julian days.
5 day counter, Julian days.
I t is possible for t e sun to be completely shaded during winte r months
at some sites. This i s why snow me~ts last on the north slopes of hillsides.
Therefore, certain restrictions are imposed on c 5 ; i.e., cs s (w/2)-f + 61 .
The average solar atti ude at sunrise/sunset is a measure of the obstruc-' .
tion of topographic feature s. It is determined by measuring the average angle
from the horizon to the point where the sun rises and sets. Therefore, the
resulting prediction of extra-terrestrial solar radiation includes only the
solar rad i ation between the estimated actual hours of sunrise and sunset.
SUNRISE TO SUNSET DURATION
The sunrise to sunset duration at a specific s ite i s a function of
l atitude, time of year,_ and topographic features. It can be computed directly
from the sunrise/suuset hour angle h .. The average sunrise to sunset duration
Sl
over the time period n toN is .....
·-~ · .... .-.... \,/'?
~ ( )
/
\ 27
where: S
0
: average sunrise to sunset duration at the specific
site over the time period n to N, hours.
hs 1 average sunrise/sunset hour angle over the time
period n to N, radians.
ATMOSPHERIC CORRECTION
The extra-terrestrial solar radiation is attenuated on its path through
the atmosphere by scattering and absorbtion when encountering gas molecules,
water vapor, and dust particles. Furthermore, radiation is reflected from the
ground back into the sky where it is again scattered and reflected back again
to the ground.
The attenuation of solar radiation due to the atmosphere can be approxi-
mated by Beer's law
where:
( )
Hsx -average daily e t ra-terrestrial solar radiation; J/m:/sec.
: average daily solar radiation corrected for atmosphere
only, J/m:/sec.
~ : absorbtion coe f ficient, 1/m.
z : path length, m.
While Beer's law is valid on ly for monochromatic radiation, it is useful
to predict the form of and significant variables for the atmospheric correction
equation. Repeated use of Beer's law and recognition of the importance of the
28
optical air mass (path length), atmospheric moisture content (water vapor),
dust particles, and ground reflectivity results in a useful emperical atmos-
pheric correction approximation.
where:
e-z =[a" • (l-a'-d)/2]/[1-R (1-a'+d)/2] ( ) g
a' ! mean atmospheric transmission coefficient for dust free
moist air after scattering only, dimensionless.
a" 1 mean distance transmission coefficient for dust free moist
air after scattering and absorbiton; dimensionless.
d : total depletion coefficient of the direct solar radiation
by scattering and absorbtion due to dust, dimensionless.
R 1 total reflectivity of the ground in the vicinity of the
g site, dimensionless.
The two transmission coefficients may be calculated by
a' = exp {-(0.465 • 0.134 w] [0.129 + 0.171 exp (-0.880 mp)] mp} ( )
a"= exp {-[0.465 + 0.134 w] [0.179 • 0.421 exp (-0.721 mp)] mp} ( )
where: w : precipitable water content, em.
mp -optical ~.ir mass, dimensionless.
The precipitable water content, w, of the atmosphere can be obtained
using the following pair of formulas.
T T
(1.0640 d)/(Td+273.16) = (Rh1.0640 a)/(Ta+273.16) ( )
w = 0.85 exp (0.110 + 0.0614 Td) ( )
29
where: T -average daily air temperature, C. a
Rh = relative humidity, dimensio~less.
Td -mean dew point, C.
w : precipitable water content, em.
The optical air mass is the measure of both the path length and absorb-
tion coefficient of a dust-frl'e dry atmosphere .. It is a function of the sit&
elevation and instantaneous solar altitude. The solar altitude varies accord-
ing to the latitude of the site, time of year, and t~me of day. For practical
application, the optical air mass can be time-averaged over the same t ime
period as the extra-terrestrial solar radiation. The solar alti t ude f nction
is
where:
ai = arcsin ((sin~ si n61] + (cos8 (cos~ coscS i)]}
N h -( t (( J s ,i dh)/h i]}/[N-n + 1] a = ai i=n c s.
~ = site latitude, radians.
61 : sun declination on day i, radians.
h : instantaneous hour angle, radians.
h 1 s unrise/sunset hour angle for day i, radians. s. i
n; first day in time period, Julian days.
N ; last day in time period, Julian days.
1 day counter, Julian days .
a 1 1 instantaneous solar al t t ude during day i, radians.
( )
( )
a = average solar altitude over time period n to N, radians .
.,,.
Equation A14 can be solved by numerical integration to obtain a precise
solution. However, if the time periods do not exceed a month, a reasonable
approximation to the solution is
N -
~ 2 ( I ~1 ]/(N-n + 1]
1=n
where: ~i i average solar altitude during day i, radians.
remaining parameters as previously defined.
The corresponding optical air mass is
where:
m = {((288-0.0065Z)/238]5 ·256 }/{sin ; p
+ 0 .15((180/v) ; + 3.885]-1·253 }
Z: site elevation above mean sea 1evel, m.
~ 1 average solar altitude for t im e peri od n to N, radians.
mp : average optical air mass, dimens i onles s .
( )
( )
The · d u st coefficient d and the ground reflectiv ity Rg may be estimated
from Tables A1 and A2 respectively or they can be c a librated to published
solar radiation data (Cinquemani et. al, 1978 ) a ft er cl ou d cover corrections
have been made.
31
Table A1. Oust coefficient d.1
Season Washington, DC Madison, Wisconsin
m =1 p m =2 p m =1 p m =2 p
Winter 0.13 0.08
Spring 0.09 0.13 0.06 0.10
Summer 0.08 0.10 0.05 0.07
Fall 0.06 0.11 0.07 0.08
1 Tennessee Valley Authority 1972, page 2.15.
Table A2. Gr ound reflectivity Rg.1
Ground condition
Meadows and fields
Leave and needle forest
Dark, extended mixed forest
Heath
Flat ground, grass covered
Flat ground, rock
Sand
Vegetation early summer leaves with
high water content
Vegetation late summe~eaves with
low water content
Fresn snow
Old snow
1 Tennesee Valley Authority 1972, page 2.15 .
.,.,
Li nco 1 n, Nebraska
m =1 p m =2 p
0.06
0.05 0.08
0.03 0.04
0.04 0.06
Rg
0.14
0.07 -0.09
0.045
0.10
0.25 -0.33
0.12 -0.15
0.18
0 .1 9
0.29
0.83
0.42 -0.70
Seasonal variatio ns appear to occur in both d and Rg. Such seasonal
variations can be predicted resulting in reasonable estimates of ground solar
radiation.
The dust coefficient d of the atmosphere can be seasonally distributed by
the following empirical relationship.
where: d 1 : minimum dust coefficient occurring in late July -early
August, dimensionless.
( )
dz i maximum dust coefficient occurring in late January -early
February, dimensionless.
Di :day of year, Julian days; Di=1 for Janua ry 1 and Di=365
for December 31 .
The ground reflectivity Rg can be seasonally distributed by the following
empi r ical relationship.
where: R -minimum ground reflectivity occurring in mid-September,
g 1 dimensionle s .
R gz -maximum gr ound reflectivity occurring in mid-March,
dimens i onless.
-day of year, Julian days; Di=l for January 1 and 01=365
for December 31.
( )
The average minimum-maximum val ue for both the dust coefficient and
ground reflectivities can be calibrated to actual recorded solar radiation
data. Summaries of recorded solar radiation can be found in Cinquemani,
et al. 1978 .
13
CLOUD COVER CORRECTION
Cloud cover significantly reduces direct solar radiation and somewhat
reduces diffused solar radiation. The preferred measure of the effect of
cloud cover is the "percent possible sunshine" recorded value (S/S 0 ) as
published by NOAA. It is a direct measurement of solar radiation duration.
( )
where: H59 1 daily solar radiation at ground level.
Hsa i solar radiation corrected for atmosphere only.
S 1 actual sunshine duration on a cloudy day.
S0 1 sunrise to sunset duration at :he specific site.
If direct S/S 0 values are not available, then S/S 0 can be obtained from
estimates of cloud cover C1 .
SIS = 1-C 513
0 t ( )
where : C1 -cloud cover , dimensio nless.
DIURNAL SOLAR RADIATION
Obviously, the solar radiation intensity varies throug hout the 24-hour
daily per i od. It is zero at ni ght, increases from zero at sunrise to a maximum
at noon, and decreases to zero at sunset. This diurnal variation c n be
approximated by:
where:
Hnite = 0
Hnite 1 average nighttime solar radiation, J/m 2 /sec.
Hd 1 average daytime solar radiation, J/m 2 /sec. ay
Hsg 1 averag~ daily solar radiation at ground level, J/m 2 /sec.
h5 1 average sunrise/sunset hour angle over the time
period n to N, radians.
SOLAR RADIATION PENETRATING WATER
( )
( )
Solar or shortwave radiation can be reflected from a water surface. The
relative amount of solar radiation reflected (Rt) is a function of the solar
angle and the proportion of direct to diffused shortwave radiation. The
average solar angle a is a measure of the angle and the percent possible
sunshine S/S 0 reflects the direct-diffused proportions.
where:
B(S/S )
Rt .= A(S/S 0 ) [c(l80/~)] 0 0 s Rt s 0.99 ( )
Rt -solar-water reflectivity coefficient, dimensionless.
a ! average solar altitude, radians.
A(S/S 0 ) 1 coefficient as a function of S/S 0 .
B(S/S 0 ) 1 coefficient as a function of S/S 0 .
S/S 0 : percent possible sunshine, dimensionless.
35
Both A(S/S 0 ) and B(S/S 0 ) are based on values given in Table 2.4 Tennessee
Valley Authority, 1972. The following average high and low cloud values were
selected from this table to fit the curves.
where:
c,
0
0.2
1
S/S 0
1
0.932
0
A
1.18
2.20
0.33
A' = dA/dC and B' = dB/dC r. r.
A'
0
B
-0.77
-0.97
-0.45
B'
0
The resulting curves are:
A(S/S 0 ) = [a, + a 1 (S/S 0 ) + az (S/S 0 )z]/[1 + a,(S/S0 )] ( 1
B(S/S 0 ) = [b 0 + b1 (S/S 0 ) + bz (S/S 0 )z]/[1 + b, (S/S 0 )] ( )
where: ao = 0.3300 b0 = -0.4500
a1 = 1.8343 b1 = -0.1593
az = -z .1528 bz = 0.59 86
a, = -0.9902 b, = -0.9862
The amo unt of solar radiation actually penetrating an un haded water
surface is:
where:
H = (1-R ) H sw t sg
Hsw J daily solar radiation entering water, J/m 1 /sec
Rt 1 solar-water reflectivity, dimensionless
Hsg 1 daily solar radiation at ground level, J/m 1 /sec
36
( )
SOLAR SHADE
The solar shade factor is a combination of topographic and riparian
vegetation shading. It is a modifaction and extension of Quigley's (1981)
work. It distinguishes between topographic and riparian vegetation shading,
and does so for each side of the stream. It was modified to include the
intensity of the solar radiation throughout the entire day and is completely
consistent with the heat flux components used with the water temperature
model.
Topographic shade dominates the shading effects because it determines the
local time of sunrise and sunset. Riparian vegetation is mportan for shading
between local su nr ise and sunset only if it casts a shadow on the water
surface.
Topographic shade is a function of the: (1) time of year, (2) stream
reach latitutde, (3) general stream reach azimuth, and (4) topographic altitude
an g 1 e. The ri pari an vegetation is a function of the topographic shade p 1 us
the riparian vegetation parameters of : (1) height of vegetation, (2) crown
measurement, ( 3) vegetation off set, an ( 4 ) vegetation density. The mode 1
allows for different conditions on opposite sides of the stream.
The time of the year (D 1 ) and stream reach latitude (~) parameters were
explained as a pa r t of the solar radiation section. The remaining shade
parameters are peculiar to determination of the shading effects.
37
The general stream reach azimuth (Ar) is a measure of t he average depa r -
ture angle of the stream reach from a north-south ( N-S) reference 1 i ne when
looking south. For streams oriented N-S, the azimuth is 0°; streams oriented
NW-SE, the azimuth is less than 0°; and streams oriented NE-SW, the azimuth is
greater than 0°. Therefore, all stream reach azimuth angles are bounded
between -90° and +90°.
The east side of the strelm is always on the left-hand side because the
azimuth is always measured looking south for streams located in the north
latitudes. Note that an E-W oriented stream dictates the east or left-hand
side by whether the azimuth is a -90° (left-hand is the north side) or +~0°
(left-hand is the south side).
The topographic altitude angle (at) is the vertical angle from a level
line at the streambank to the general top of the local terrian when looking 90°
from the general str eam reach azimuth. There are two altitude angles --one
for for the lef~-hand and one for the right-hand sides. The altitude is 0 for
level plain topography; at> 0 for hilly or canyon terrian. The altitudes for
pposite sides of the stream are not necessarily identical. Sometimes streams
tend t o one side of a valley or may be flowing past a bluff line.
The height of vegetation (V~) is the average maximum existing or proposed
height of the overstory riparian vegetation above the water surface. If the
height of vegetation changes dramatically--e.g., due to a change in type of
vegetation --then sudividing the reach into smaller subreaches may be
warranted.
38
----
At
J---SOUTH ----------------------
--------
Figure 2 .2. local solar and strea• orientation angular uure.ants .
Crow n measurement (Vc) i s a funct i on of the crown d i ameter and accounts
f or over ha ng . Crown measuremen for hardwoods 1 s the crown diamete r , soft-
woods i s t he crown radius .
Vegetat i on offset (V 0 ) is the average distance of the tree tru nks from
th e waters edge . Together with crown measurement, the net overhang is deter-
mi ned . Th i s net overhang, (V/2) -V 0 , must always be equal to or greater
than zero .
Vegetat i on dens i ty (Vd) i s a measure of the screening of sunlight that
woul d oterhwise pass t hru the shaded area determined by the riparian vege~a
t i on. I t accounts for both the continuity of ri pari an vegetation a 1 ong the
stream ba nk and the fil t ering effect of leaves and stands of t rees along the
stream. For example , if on l y 50% of the left side of the stream has riparian
vegetation (trees) and if t hose trees actually screen only 50: of the sunlight,
then the vegetation density for the le f t-hand (east side) is 0 .25 . Vd must
a l ways be be ween 0 and 1.
The solar shade model al l ows for separate topographic a l titudes and
r i parian vegetation parameters for both the eas t (left-hand) and west (right-
hand) side s of the stream .
The solar shade model i s calculated in two steps . First the topographic
shade i s determined according to the local sunrise and sun set tim es f or the
spec ifi ed time of y ear. Then the r i parian shade i s calculated between the
l oca l sunr i se and su nset times.
7Q
.
)
'
Vc = d i ameter, hardwoods
= radius, softwoods
Vd = ratio of shortwave
radiation eliminated
t lnco lng over entire
reach shaded area
f1gure 2.3. R1par1an vegetat1on shade para.eters.
Topographic shade is defined as the ratio of that portion of so l ar radia-
tion excluded between level-plain and local sunrise/sunset to the solar radi a-
tion between level-p l ain sunrise and sunset.
Riparian vegetation shade is defined as the ratio for that portion of th
solar radiation over the water surface intercepted by the vegetation between
1 oca 1 sunrise and sunset to the solar radiation between 1 eve 1-p 1 a in sunrise
an d sunset.
The following math models are based upon the previous rationals. There
are five groupings of these models: (1) level-plain sunrise/sunset hour angle
and azimuth (h and A ), (2) local sunrise/sunset altitude (~sr and ~.,5'), s so -
(3) topograp .. ic sh cde (St), (4) riparian vegetation shade (Sv), and (5) total
solar shade (Sh). The order is suggested for direct solutions.
Indicator function notation, I(•], is used. If the relationship shown
within the brackets are true, the value of the indicator function is 1; if
false, the value is 0. Definitions for each variable is given after the last
groupting of math models.
The global conditions of latitude and time of year determine the rel at ive
~ovements of the sun which affect all subsequent ca l culations. They were
explained in the solar radiation section. The time of year directly determines
the solar decl in ation, which is the starting point for the following math
models.
40
LEVEL-PLAIN SUNRI SE/SUNSE T HOUR ANG LE AND AZIM UTH
The leve l -plain sunrise/sunset gr • p of math models are to determ in e t he
hour ang l e and corresponding solar azimuth a su nrise and sunset. The solar
movements are symetrical about solar noon; i .e., the absolute val ues of the
sunri se nd su set parameters are identical, they differ only in sign. The
math model is:
5 = 0.40928 cos[(Z~/365) (172 - 01 )]
hs = arccos [-(sin • sin 5)/(cos • cos 5)]
Aso =\arcsin (cos 5 sin h ) \ ~ f, ¢ l if'-G\rC.'::\Y\ ( c...o~ &s !;~"" '-":.) \ ~ ~ ~
The level-plain sunrise hou r angle is equal to -hs; the sunset hour angle
is hs . The hour angles are referenced to solar noon (h = 0). Therefore, the
duration from sunrise to solar noon is the same as from solar noon to sunset.
One hour of time is equal to 15° of hour angle.
The solar azimuth at sunrise is -As 0 ; the sunset azimuth is Aso· Azimu t hs
are referenced from the north-south line looking south for streams located in
the north latitudes.
LOCAL SUNRISE/SUNSET ALTITUDES
Local sunrise and sunset is a function of the local topography as well as
t~e glo t al conditions . Furthermore, the local terrain may not be identical on
oppos ite sides of ~he stream . Al so, some streams are oriented such that the
41
sun may r ~se and set on the same side of the stream during part or even all of
the year. The following local sunrise/sunset models prope r ly accoun1: for the
relative location of the sun with respect to each side of the stream.
The model for the local sunrise is:
atr = ate I[-Aso s Ar] + atw I[As o > Ar]
hsr = -arccos {(sin asr -(sin .J~ sin 6)]~:cos ; cos 6]}
Asr = -arcsin [cos 6 sin hsr)/[cos asr)]
asr =arctan [(tan atr) (siniAsr-Arl)]
but, sin asr s (sin ; sin 6) + (cos ; cos 6)
The model for the local sunset is:
ats = ate I[Aso s Ar] + atw I[Aso > Ar]
hss = arccos {[sin ass -(sin ~.sin 6)]/[cos; cos 6]}
."· .. , I • •
Ass = arcsin [cos 6 sin hss~/(cos ass)]
ass = arctan [(tan a s s) (siniAss -Arl)]
but, sin ass s (sin ; sin 6) + (cos ; cos 6)
The reason for the restriction on the sin asr and sin ass is that the sun
never raises higher in .the sky than indicated for that latitude and time of
year regardless of the actual topographic altitude. For example, an E-W
oriented strgam in the middle latitudes could be flowing through a deep canyon
which fs casting continuous shade for a portion of the winter months.
4?
TCPCGRAP~IC SHAD~
Once ~he 1evei-plain and ocal sunsrise and suns.H times are :C.nown, ~h!
topographic shade can be computed direct i y in closed form . The def ini t i on fo·
topographic sh ade 1eads to the following:
' = -. ...
I ;.. .. s s ~~ di1 I :
I -n s
s .. = 1 -l [ rn -n ) (s~n 9 ' ss s:-
~in ci)] -[(sin "ss -sin
(cos 0 ·:os ;) ] / iz [en, sino s<n O) • (sin n, :os • cos I) 11
RI?ARIAN VEGETATION SHADE
The riparian vegetation shade requires keeping track of the shadows ccst
thr~ugnout the sunl~ght time because only that portion over the water surface
is of interest. The model must account for sun side of the stream and t1e
length of the shadow cast over the water. The model is:
43
but,
vd = v . I(A s A ] + v . i(A > A 1 ae s r aw s r·
vh = vhe I[A :S Ar] + v T'"A > A ] s hw -L s r
v = v ! [As s Ar] + v ![A > A ]
0 oe ow s r
-a = sin 1 [(sin ~ sin 6) + (cos ~ cos 6 cos h)]
A5 = sin 1 [(cos 6 sin h) I (cos a)]
;, ss s -I ).-
v -I :"1.~
~·
s~n -)'"' .. -'-'I
~=~~~~::ly. so a r.~~~;i:~1 -.
s = 'I r
;,
;,
-·----.: ... ···= •. ·--. .:.
.,.
~ ..
! (I/~ 35
~:"'
_:),_.,;_:t~ . --.... -...
:)l•J jl ~3 s ~ n
J L l
r< h L s
Si:"l 9 sin 0 ~ (sin h s ~=s 9
E~uations __ t h:--ough __ are used to determine the jth value of Vd'
3s, and a for h.= h + jdh. J sr Sixteen int~rvals, or dh = (h - h )/16 will "' ss sr •
give better :han !~ jrgcision when using the ~:--apezoidal rule and better than
.81~ pr2c i s ~on when using Simpson's rule for functions without discontinuities.
t.4
_J c:s :) I ,
J
~owever, ::,e ::u~c~i on will have a discont i nu i ty if i:.he stream becomes fu l;y
shaded du~ :o r i par i an vegetat i on after sunrise or before sunset.
SOL~R SHADE FACiOR
The so~ar shade factor is s i m ly the sum of the topographic and riparian
vegetation shades. It is:
S~nce the solar declinition and subsequent solar related parameters
cepend upon the time of year, it will be necessary to calculate the various
shade fac:ors for each day of the time period to obtain :he average factor for
..
the time ~eriods . This will result in shade factors completely compatibie
with the heat flux components. This is done by :
(St . +
I 1
OEF!NITICNS
The · following definitions pertain to all the variables used in this solar
sr.ace sec~io:1 :
~ -solar altitude, radians
a -sr local sunrlse solar altitude, radians
45
i
i
i
local sunset solar altitude, radians
eastside topographic altitude, radians
sunrise side topographic altitude, radians
sunset side topographic altitude, radians
Cllfllflllll
~tw 1 westside topographic altitude, radians
I stream reach azimuth, radians
I local azimuth at tima h, radians
I level-plain sunset azimuth, radians
I local sunrise solar azimuth, radians
I local sunset solar azimuth, radians
~ 1 . average stream width, meters
n
N
I
I
-..
:
stream solar shade width, meters
time of year, Julian day
solar declination, radians
solar hour angle, radians
level-plain hour sunset hour angle, radians
local sunrise hour angle, radians
local sunset hour angle, radians
1 day counter, Julian days
1 first day in time period, Julian days
1 last day in time period, Julian days
1 stream reach latitude, radians
: total solar shade, decimal
1 topodraphic shade, decimal
1 riparian vegetation shade, decimal
I riparian vegetation crown factor, meters; crown diameter for
hardwoods, crown radius for soft·~oods
vee ! eastside crown factor, meters
vcw I westside crown factor, meters
vd I riparian vegetation density factor, decimal
vde I eastside density, decimal
vr:t.t I westside density, decfmil
vh I riparian vegetation height above water surface, meters
vhe I eastside height, meters
vnw I westside height, meters
vo I riparian vegetation waterline offset distance, meters
voc I eastside offset, meters
V 1 westside offset, meters ow
•
METEOROLOGY
There are five meteorological parameters used in the instream water
temperature model: (1) air temperature, (2) humidity, (3) sunshine ratio/cloud
cover, (4) wind speed, and (S) atmospheric pressure. The first four are
expected as input data for a specific elevation in the basin. The meteroology
model assumes adiabatic conditions to transpose the air temperature and
humidity vertically throughout the basin. Atmospheric pressure is calculated
directly from reach elevations. Sunshine ratio/cloud cover and wind speed is
as~umed constant throughout the basin.
ADIABATIC CORRECTION MODEL
The atmospheric pressure for each reach can be computed with sufficient
accuracy directly from the respective reach elevations~ The formula is:
' i-:lv~ .,. , ..... ~.-~
P = 1013[(288-0.00GbZ)/288]5 ·256 ( )
where: P : atmospheric pressure at elevation Z, mb.
Z : average reach elevation, m.
Air temperatures gen~rally decrease 2°F for every 1000 ft. increase in
ele vation. Therefore, correcting for the meter1c system, the following formula
is used:
48
I
I
I
I
I
iii
1!1
1 00 •.•
n c!
0
I
I
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I
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I
I
l
0
=
' . . l.
~
·'·""' 0
...
J ·-· ,_.
., .. 'i
I
I
iii
1!1
;:~ ---
===
.. I -
( Ae :. ( ,, (: ,_
!I
ea -= 1 ... •
:
f-t =
....... : •. \ 4
~ .............
··~ '"" t-r ,...._, _____
I'--·
"f : Y • .jp ... +
~ht ~ 4 h ; ::
~
(. ,. ... (?:'( -~---t. --
f r-
<:t :. e.tf -Pr
t2~,. = \(~.-. 9"
-. ((.l. 6 K:..-i
'2.: = t;.~o . r; '· ~,.,,
( \ - 0 -~ 1 8
~, '\ 0 •1'
' ;--...--
"~fi. v v.~,, ~ (J-n--\
f 2..~ e,_
Pr -o. :78 t'f
07L. e.:/
( \,-.)~ .~ \\ '-. ~N"Dr~~
·.,, ~ r .~ •m\-"')
...... b2..2. e!d ,...,
.-\ ..... ~
,..... ,..... c,zz. e.-i-
e ~ . 0' ~ 7 '] f~ P-"'·
~/~-'
p2
P~
'P-L --fe~
(:.8S -o.oo"S" i!.., /z.&a)
(l.'&~ -o.oo6S"'i-AJ/~S8)~·'
I
I
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iii
1!1
e.a •·/ f.' ~i: ::
<?oo(Ec.o
~r e~} :.
e."t. eu
....,..... , -
I -=2. ·-L i ~
-r.. .. (.-, ·:.
<2:. ... '~ ~ 2.1 ~
e .. .. ~ lo ~ 2. 71
~ I.e-~-2-7 ~
.y lo ~-2-1~
iii
1!1
~
I
I
..
I
I
w:' ··.;,
l 'i 0 1)
~
It>!)~
~:J \)
.
i
l
I
i
I
I
I
I
I
I
I
1
o.s
tB~ -0 . oC(:,~ (to!")
'2 -5 5
-··
. . , ~ •, .. p...
~ -, • '! ~ {' ..
r -J (.',.~~"
~.,,_ ..
....
C-r .
~· .. \ .........
o. ~ o.; o.s
R\..
.• ,.
,
o+i' ~v-C
o.-, 1.1)
where:
Ta a T0 -CT (Z-Z 0 )
T I I air temperature at elevation
To 1 air temperature at elevation
Z 1 aver ag elevation of reach, •
Z 1 elevation of station, • 0
: (
E, C
~-o ·• c
CT 1 adiabatic temperature correction coefficient a 0.00656 C/m
)
Both the mean annual air temperatures and the actual air temperature for
the de si red t ime period must be corrected.
T e relative humidity can also be corrected for elevation assu.ing that
the tota moisture content fs the same over the basin and the station. There-
fore, the formula is a function of th~. original relative humidity and the two
different a i r temperatures. It is based upon the ideal gas law.
where:
(T -T )
Rh = R0 {[1.0640 ° a ] [(Ta+273.16)/(T0 +273.16)]} ( )
Rh 1 relative humidity for temperature Ta, dimensionless·.
R 1 relative humidity at station, dimensionless. 0
Ta 1 air temperature of reach ~ C.
T 1 afr temperature at station, C. 0
0 s Rh s 1.0
The sunshine factor is assumed to be the same over the entire basin as
over the station. There is no known way to correct the windspeed for transfer
to the basin . Certainly local topographic features will influence the wfnd-
speed over the water . However, the sta t ion windspeed fs, at least, an
indicator of the basin win dspeed. Since the windspeed affects only the con-
vecti on and evaporation heat flux components and these components have the
least reliable coefficients in these models, the windspeed can be used as an
important calibration parameter when actual water temperature data is avail-
able.
AVERAGE AFTERNOON METEOROLOGICAL CONDITIONS
The average afternoon air temperature is greater than the daily air
temperature because the maximum air temperature usually occurs during the
middle of the afternoon . This model assumes that
where: fax : average daytime air temperatur between noon/sunset, C.
Tax :maximum air tem perature during the 24-hour period, C.
( )
Ta 1 average daily a ir temperature during the 24-hour period, C.
A regression model was selected to incorporate the significant daily
meteorological parameters to estimate the incremental increase of the average
daytime air temperature above the daily . The resulting average daytime air
temperature model is
Tax = T + (a 0 + a 1 H + a 1 Rh + a, (S/S )] ( ) a sx o
sc
wnere: T 1 maximum air temperature, C. ax
T 1 daily air temperature, C. a
H 1 extra-terresterial sol a r radiation, J/m 2 /sec. sx
Rh 1 relative humidity , decimal.
SIS 1 percent possib l e sunshine, decimal. 0
a0 thru a, 1 regression coefficients.
Some regression coefficients were determined for the "normal• meteor-
ological conditions at 16 selected weather stations. These coefficients and
their respective coefficient of multiple correlations R, sta~dard dev1ation of
maximum air temperatures S.Tax' and probable differences 5 are given fn
Table 81 .
The corresponding afternoon average ~elative humidity is
(T -T )
Rhx = Rn [1.0640 a ax ][(T1 x+273.16)/(Ta+273.16)] ( )
where: Rnx 1 average afternoon relative humidity, dimensionless.
Rh 1 average daily relative humidity, dimensionless.
Ta 1 daily air temperature, C.
Tax =average afternoon air temperature, C.
51
Table 81
c c
S.Tax
Regression coef f icients
SUtion name R 5 ao 11 lz a,
Phoenix, AZ .936 0 .737 0.194 11.21 -.00581 -9.55 3.72
Santa Maria, CA .916 0.813 0.243 18.90 -.00334 -18 .85 3.18
Grand Junction, co .987 0.965 0.170 3.82 -.00147 -2.70 5.57
Washington, DC .763 0.455 0.219 6.64 -.00109 -7.72 4.85
M1u1, FL .934 0.526 0.140 29.13 -.00626 -24.23 -7.45
Dodge City, KA .888 0.313 0.107 7.25 -.00115 -5.24 4.40
Caribou, ME .903 0.708 0.226 0.87 .00313 0.09 7.86
Columbia, MO .616 0.486 0.286 4.95 -.00163 -2.49 4.54
Great Fa 11 s, MT .963 1.220 0.244 9.89 .00274 -9.56 1.71
Omaha (North), NE .857 0.487 0.187 9.62 -.00279 -9.49 6.32
Bismark., NO .918 1.120 0.332 11.39 -.00052 -13.03 5.97
Charleston, SC .934 0.637 0.170 9.06 -.00325 -8.79 7.42
Nashville, TN .963 0.581 0.117 5.12 -.00418 -4.55 9.47
Brownsville , TX .968 0.263 0.049 9.34 -.00443 -4.28 0 .}2
Seattle, WA .985 1.180 0.153 -9.16 .00824 12.79 3.86
Madison, WI .954 0.650 0.145 1.11 .00219 1.80 3.96
ALL .867 1.276 0.431 6.64 -.00088 -5.27 4.86
52
HEAT FLUX
THERMAL PROCESSES
There are five basic thermal processes recognized by the heat flux rela-
tionships: (l) radiati~, (2) evaporation, (3) convection, (4) conduction,
&nd (5) the conversion from other energy forms to heat.
THERMAL SOURCES
The various relationships for the individual heat fluxes will be discussed
here. Each is considered mutually exclusive 1nd when added together account
for the heat budget for 1 single column of water. A heat budget analysis
would be applicable for a station&ry tank of continuously mixed body of water.
However, the transport model 1s necessary to account for the spatial location
of the column of water at any point in time.
RADIATION
Radiation 1s an electomagnetic mechanism, which allows energy to be
transported at the speed of light through regions of space that are devoid of
matter. The physical phenomena causing radiation 1s sufficiently well-
understood to provide very dependable source-component models. Radiation
mode 1 s have been theoret 1 ca lly derived from both thermodynamics and quantum
53
'" '.)
;"J
ALSO: (I) HEAT LOS DUE T
EVAPOO ATI
(2) HEAT OAIH DUE TO
flUID FRICTION
(3) ttEAT EXCitAHOE DUE TO
AIR CIRCULATION (COI.VE C TIOH
I
A TMOSPtiERIC RADIA liON
STREAMBED CONDUCTION
ftgure 2.4. Heat flux sources.
··o··'''/,~ -: . .
_.. -·/ ,. /,''·"'
CONfiDIIIIAl
~~ phy s i c s and ha ve been e xp er im en t a ll y ve ri fied with a h~gh degree of pr ec is i on
an d r e li ab il ty . I t pr ov i de s th e most depen dab l e components of th e he at flux
I
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I
I
s ubmodel and, f ortunate l y, is a l so the most i mportant sour ce of hea t exc hange.
So l ar, back. radia t ion fr om the wate r, atmospheric , riparian ve ge tat i on , and
topograp hi c features are the major sources of rad i at i on heat flux. There is
an i nter-act i on between these va r ious sources; e.g ., r iparian vegetati on
sc r eens bot h solar and atmospheric radiation whi1e replacing it with its own.
SO L)q RADIATION CORRECTED FOR SHADING
The solar radiation penetrating the water must be further modi fi ed by t he
local s hading due to riparian vegetation, etc. The resulting model is:
where :
•
H = (1-S ) H s h sw ( )
sh -solar shade factor, decimal.
H -avera ge da i ly solar radiatio n entering unshaded water , J /m%/s ec. sw
Hs -average dai ly o lar radiation entering shaded water, ~/ml /sec.
ATMOSPHERIC RADIATION
The atmosphere emits longwave rad i at i on (heat). There are five factors
J affecting t he amount of 1 ongwave rad i at i on entering the w ter: (1) the air
temperature i s the pr i mary fac~or; (2) the atmos pheric vapor pressure affect s
t he em i ss i vity ; (3) t he c l oud cover converts the shortwave so l ar radiation
I
r,h in t o additiona l longwave radiation, sort of "hot spots 11 in the atmosphere;
(4) t he reflection of longwave radiation at the water-air interface; and
I
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I
(5) the interception of longwave rad ia tion by vegetative canopy cover or
shading. An equation which approximates longwave atmospheric radiation enter-
ing the water is:
where: c, = [1-(S/S 0 )~15
= cloud cover, decimal
S/S 0 -sunshine ratio, decimal
k i type of cloud cover factor, 0.04 s k s 0.24
ta = atmospheric emissivity, decimal
sa -atmospheric shade factor, decimal
rt -longwave radiation reflection, decimal
T -air temperature, C a
a = 5.672•10-, J/m 1 /sec/K~ : Stefen-Boltzman constant.
The preferred estimate oft is: a
ta = a+b lea, decimal
a = 0.61
b = 0.05
/'•a ·• vapor pressure ... -~:c;60(!.0640) T •]. mb I
I
I
I
I
I
•.
~-);c.,)··.,.. -t.·r::..,
. '
( -
' \ -' ' I =
HuM•'-': ~J~l£:.~ • 1 \.:>o~ ··"DI) ·(I--vT I (,A.,~tJ ... ?.7--: .. ~))
~~ : -, A If(_~ -'DI
O .O ~bS'S.· (G'LE.V -t..LE.VP)
\-4 l)t'\ I 0 :. 0 . I ' '-
.,--P<\ (L ~ 2 \ . c,
( .. ..
I
I
I
I
I
~
I
I
An alter nate estimate of ta is:
The preferred estimate accounts for water vapor which also absorbs so l ar
radiation which, in turn, is converted into lon gwave radiation. If the
absorbtion of solar is overpredicted, then some o the overprediction is
returned as longwave and vice versa. Therefore, errors in one (solar) tend to
be compensated by the other (atmospheric). The alternate form is mentioned in
the literature as a simpler model and possibly a better predictor of longwave
radiation alone. However, for purpose of predicting water temperatures, ·it
ultimately makes little difference as to the form of radiation (short or
~ .
longwave) as long as the total heat exchange is accurately predicted. The
alternate form i s only used when the solution technique requires simple steps.
Assuming k = 0.17, r1 = 0.03, and using the preferred estimate of ta,
this equation reduce s to:
( )
The ·atmospheric shade factor (Sa) is assumed to be identica l to the solar
shade factor (Sh).
c:-... o
~ TO POGRAPHIC FEAT URES RADIATION
I
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..
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Currently, the radiation from topographic features is assumed to be
included as a part of the riparian vegetation radiation. Therefore, no
separate component model i s used.
RIPARIAN VEGETATION RADIATION
The riparian vegetation intercepts all other forms of radiation and
radiates its own. Essentially it totally eliminates the estimated shade
amount of solar, but replaces the other longwave sources with its own lorrgwave
source. The difference is mostly in the emissivity between the different
longwave sources. The model is:
(
where: tv -vegetation emissivity = 0.9526 de ci mal
a -Stefan-Boltzman constant= 5.672·10-. J/m:/sec/K ..
H ! riparian vegetation radiation, J/m:sec v
s ! riparian vegetation shade factor , decimal v
T ! riparian vegetation temperature, assumed to be the ambient a air temperature, C
The r i parian vegetation shade factor (Sv) is assumed to be identical to the
solar shade factor (Sh) .
.JI
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WATER RADIATION
The water emits radiation and t his is the major balancing heat fl ux which
prevents the water temperat ure f rom in c r easing without bounds. The mode l i s:
A
H = £ o(T +273.16)~ w w w ( )
where: "' radiation, J/~z/sec Hw -water
T :: w water temperature, c
t w ! water emissivity= 0.9526 decimal
o -Stefan-Boltzman constant = 5.672•10-, J/mz/sec/K~
A first-or der approximation to equation A36 with less than ± 1 .8% error
of predicted radiation for OC s T s 40C is: w
where:
" Hw = 300 + 5.500 Tw
I'
H -approximate water radiation, J/mz/s ec w
T -water temperature, C w
STREAM EVAPORATION
( )
Evaporation, and its counterpart condensa t on, requires an exchange of I heat. The isothermal (same temperature) conversion of liquid water t o va por
1 requires a known fixed amount of heat energy ca l led the heat of vaporizat i on .
Conversely, condensat i on releases the same amount of heat . The rate of evapora-
~ t1on --the amount of liquid water converted to vapor--is a function of both
I
I 58
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I
~ the c ircu lation and vapor pressure (relative humidity) of the surrou ndi ng a ir.
If the surrounding air were at 100% relative humidity, no evaporation would
occur. If there were no circ ulation of air, then the air immediately above
the water surface would qui cK ly become saturated and no further net evaporat ion
would occur.
Evaporation, while second i n importance to radiation, is a s i gnificant
form of heat exchange. Most a vailable models are derived from lake environ-•
ments and are probably the least reliable of the thermal processes modeled.
However, one model was derived from a single set of open channel flow data.
Both model types are offered. They differ only in the wind function used.
The wind function for the flow-type model was adjusted by approximately 3/4 'to
better match recorded fiel data .
Two ev ap oration models are available. They differ only in the wind
function assumed. The first is the simplest. It was obtained la r gely from
lake data, and is used only for small hand held calculator solutions tech-
niques . The second is the preferred. It was obtained from open channel flow
data, and is used for all but the simplest solutions technique.
The 1ake-type model is:
T
He= (26.0Wa)[Rh(l.0640) a
T
( 1. 0640) w] ( )
I
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I
The flow-type model is:
T T
He= (40.0 + 15.0Wa)[Rh(l.0640) a -(1.0640) w] ( )
where: He i evaporation heat flux, J/m 1 /sec
wa = wind speed, m/sec
Rh -relative humidity, decimal
Ta i air temperature, c
Tw -water temperature, c
CONVECTION
Convection can be an important source of he at exchange at the air-water
interface. Air is a poor conductor, but the ability of the surrounding air to
circulate, either under forced conditions from winds or freely due to t emp er-
ature differences, constantly exchanges the a~r at the air-water interface.
Convection affects the r ate of evaporation and, the re fore, the model s are
re 1 a ted. But the actua 1 heat exchange due to the two different sources are
mutually exclus i ve. Convection is not quite as important a s eva poration as a
source of heat flux but is still significant. The available models suffer
from the same defects since both use the same circulation model.
The heat exchange at the air-wa t er int e rface is due mainly to convection
of the air. Air is a poor conductor, but the ability of the atmosphere to
convect freely constantly exchanges the air at the air-water interface. The
current mode ls are l argely based upon l ake models but will be used here. The
50
. u
~ convection model is based upon the evaporation model using what is called the
6owen ratio; i.e.
I
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•
Bowen ratio= Bf P(Tw-Ta)/(es-ea) ( )
where: p -atmosphe r ic pressure, mb
T -water temperature, c w
T ! air temperature, c a
es i saturation vapor pressure, mb
ea 5 air vapor pressure, mb
Bf -Bowen ratio factor
Air convection heat exchange is approximated by the product of the Bow~n
ratio and the evaporation heat exchange:
where: He -air convection heat flux, J/m 1 /sec
R : Bowen ratio, decimal
He -evaporated heat flux, J/m 1 /sec
( )
Since the air convection heat flux is a function of the evaporation heat
flux, two models are offered. The first, the simplest, is a lake-type model.
The second, the preferred, is a flow-type model.
The lake-type model is:
( )
61
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The flow-t y pe model is :
He= (3 .75•10-, + 1.40•10-3 W) P(T -T ) ( ) a w a
where : He = air convect i on heat flux, J/m 2 /sec
wa -wind speed, m/sec
p = atmospher i c pressure, mb
T = water temperature, c w
Ta :: air temperature, c
STREAMBED CONDUCTION
.
Conduction occurs when a temperature gradient a temperature difference
between two po i nts --exists in a material medium in which there is molecu l ar
contact. The on 1 y important conduct; on eat flux component is throug h the
streambed . The thermal processes are r easonably well-understood although some
of the necessary data may not be easily obtained without certain assump t ions .
I However, the importance of this component, while not negilible, does allow fo r
some li berties and suitable predictions can be made for most applications.
Streambed conduction is a function of the difference in t emperature of
the streambed at the water-streambed interface and the streambed at an equ i l i b-
rium ground temperature at some depth be 1 ow the streambed e 1 evat ion, this
equilibrium depth, and the thermal condu c t i vity of the streambed mater i al.
The e Jation i s :
( )
62
I
I
where : H = conduction heat flux , J/m~/sec d
Kg-thermal conductivity of the streambed material, J/m/sec/C
Tg -
T = w
streambed equilibrium temperature, C
streambed temperature at the water-streambed interface,
assumed to to be the wate r temperature, C
AZg-equilibrium depth from th ·~ water-streambed interface, m
Kg = 1.65 J/m/sec/C for water-saturated sands and gravel
mixtures (Plukowskf~ 1970)
STREAM FRICTION
Heat is generated by fluid frictifln, either as work done on the boundaries . I or as internal fluid shear, as the water flows downstream. That portion of
the potential energy (elevation) of the flowing water that is not converted to
other uses (e.g., hydroelectric generation) is converted to heat. When ambient
co nditions are below freezing and the water in a stream is still flowing, part
of the reason may be due to this generation of heat due to friction. The
I available model is straight-forward , simple to use, and solidly justified by
basic physics. However, fluid friction is the least significant source of
heat flux, but it can be noticeable for steep mountain streams.
The stream friction model is:
where: Hf : fluid friction heat flux, J/m 1 /sec
sf -rate of heat energy conversion, generally the stream
gradient, m/m.
63
( )
I
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I
I
I .
I
.... .
r_ :. r-.. 'I \c.--. "" .. :: c r-I . L I -r--. .. '-\ "" ... ... :::-.. , \:. . :... ) ...
•
I
I ,
I
I
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I
I
I .,
I
Q : discharge, ems.
B : average top width, m
NET HEAT FLUX
The various heat flux components, when added together, form the net heat
flux equation, i.e.,
H = H + H + Hd + H + H + H - H n a c e ·s v w
where: Ha, etc. are as previously defi~ed
Hn 1 net heat flux
( )
When the equations for the separate components are substituted into
equation 01, it can be reduced to:
where:
T
Hn = A(Tw+273.16)• + BTw + C (1.0640) w-0
B = (Cr • Ce P) + (K9/AZg)
C = (40 .0 + 15.0Wa)
0 = Ha + Hf + Hs + Hv + (Cr • Ce PTa) +
C = I + bW + C 1-w-e a a
Cr = Bf/6.60
64
( )
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I
The equilibrium water temperature Te is defined to be the wa t er tempera-
ture when the net heat flux is zero for a constant set of input parameter ;
i . e. ,
T
A(Te+273.16)• + BTe + C (1.0640) e-0 = 0
where: A, 8, C, and 0 are as define~ above.
( )
The solution of equation 03 forTe, given A,.B, C, and 0, is the equilib-
rium water temperature of the stream for a fixed set of meterologic, hydro-
logic, and stream geometry conditions. A physical analology 1s that as a
constant discharge of water flows downstream in a prismatic stream reach under
a constant set of meterolog1c conditions, then the water temperature w"ll
asymptoti~ally approach the equilibrium water temperature regardless of the
initial water temperature.
The first order thermal exchange coefficient K1 is the firs~ derivative
of equation 02 taken at Te .
T
K1 = 4A(Te+273.16)2 + B + [Cln (1.0640)] (1.0640) e
where : Te, A, B, and C are as defined above .
•
( )
The second order therma 1 exchange coefficient is the coefficient for a
second order term that collocates the actual heat flux at the initial water
temperature {T 0 ) with a first-order Taylor series expansion about Te.
T
Ka = ([A{T 0 +Z73.16)• + BT + C(1.0640) 0 -O]-[K 1 {T -T )]l/[{T -T )1 ] ( ) o o e o e
65
~ where: A, B, C, 0, K1 , T0 , and Teare as defi1ed before.
I
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..
Therefore, a first-order approximation of equation 02 with respect to the
equilibrium temperature is
Hn = K1 (T - T ) e w )
And a second order approximation of equation 02 with respect tc • the
equilibrium temperature is
)
HEAT TRANSPORT
The heat transport model fs based upon the dynamic temperature -steady
~ flow equation. This equation, when expressed as an ordinary differential
equation, is identical fn form to the less general steady-state equation.
However, ft. is different fn how the input data 1s defined and in that the
dynamic equ ;1tfon r equires tracking the mass movement of water downstream. The
simultaneous use of the two identical equations with different sets of input
1s acceptable since the actual water· temperature passes through the average
daily water temperature twice each day --once at night and then again during
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the day. The steady-state equation assumes that the input parameters are .
constant for each 24-hour period. Therefore, the solar radiation, metero-
logfcal, and hydrology parameters are 24-hour averages. It follows, then,
that the predicted water temperatures are also 24-hour averages. Hence, the
term "average daily!' means 24-hour averages -from midnight to midnight for
each parameter.
The dynamic model allows the 24-hour period to be divided into night and
day times. While the solar radiation and meterological parameters are
different between night and day, they are still considered constant during the
cooler nighttime period and different, but still constant, during the warmer
daytime p·eriod. Since it is a steady flow model, the discharges are constant
over the 24-nour perf od.
It can be vf~ualfzed that the water temperature would be at a minimum at
sun r ise, continually rise during the day so that the average daily water
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temperature would occur near noon and be maximum at sunset, and begin to cool
so that average daily would again occur near midnigh~ and return to 1 minimum
just before sunrise where the cycle would repeat itself.
The steady-state equation, with input based upon 24-hour averages, can bt
used to predict the average daily water t111peratures throughout the entire
stream system network. Since these average daily values actually occur near
m.id-night and mid-day, the dynamic model can be used to track the column of
water between mid-night and sunrise and between noon and su"~•t to determine
the minimum nighttime and maximum daytime water temperature respectively. Of
course, the proper solar radiation and me ·"'erological parameters reflecting
night and daytime conditions must be used for the dynamic model.
ihe minimum/maximum simulation requires that the upstream average daily
water temperature stations at mid-night/mid-day for the respective sunrise/
sunset stations be simulated. This step 1s a simple hydraulic procedure
requiring only a means to estimate the average flow depth.
DYNAMIC TEMPERATURE -STEADY FLOW
A control volume ;or the dynamic temperature -steady flow equation is.
shown in Figure Al. It allows for lateral flow. To satisfy the fundamental
laws of physics regarding conservation of mass and energy, the heat energy in
the incoming waters less the heat energy in the outgoing water plus the net
h•at flux across the control volume bounoaries must equal the change in heat
se
,..
eQ c: ... •
N .
"' .
CJ '<
:I ..
B
~
n
• :I • ...
~
n
0
:I
r+ ...
0
< 0
c B ,. .
r
t----8-·--t
cp(OT)1
iiiliilii . ~ lWJ
PCp(OT)0 = pcp(OT)I t
PCp(8QT /Ctx)Ax
• I
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energy of the water within the control volume. The mathematical expression
is:
where:
[(BIH) ~x]}~t = {(pcp(a(AT)/at)]~t}~x
p 1 water density, M/L 1
c 1 specific heat of water, E/M/T p
Q ~ discharge, L1 /t
T 1 • temperature, T
q1 1 lateral flow, L1 /t
r, I lateral flow temperature, T
X ! distance, L
t I time, t
A I flow area, Lt
i inflow index
0 I outflow index
B 1 stream top width, L
IH = net heat flux across control volume, E/L 1 /t
note: units are
M -mass
T -temperature
L -length
t -time
E -heat energy
( )
I
-I
Equation A38 reduces to:
( )
J Assuming steady flow (aA/at=O), letting Hn = BtH, recognizing q1 1 aQ/ax, and
dividing through by Q, leads to:
<
<
dynamic >l <---s-t.-.aa ... d;;;;.!ly._-_s_t_a t.-e ....... e.g...,u_a t-i_o_n._ __ >
term
dynamic temperature -steady flow equation >
( :. )
If the dynamic temperature term is neglected (aT/at a 0), then the steady-
state equation is left. Since the steady-state equation contains only· a
single independent vari ble x, it converts directly into an ordinary differ-
if~' · ential equation with no mathematical restrictions:
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( )
If the dynamic temperature term is not neglected (aT/at ; 0), then equa-
tion A40 can still be solved using the classical mathematical technique known
as the "Method of Characteristics". If, for notional purposes only, we
substitute
(:: )
fnto equation A40 and use the definition of the total derivative for the
dependent variable T, a resulting pair of dependent simultaneous first-order
partial differential equations emerge
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••
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It
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(A/Q) (aT/at) + (1) (aT/ax) = + ( )
(dt) (aT/at) + (dx) (aT/ax) = dT ( )
Since the equations are dependent, the solution of the coefficient matrix fs
zero; 1. e.,
[
(A/Q)
dt
-
1]:: 0
dx
which leads to the characteri$t1c line equation,
dx = (Q/A)dt
For the same reason, the solution matrix is also zero; i.e.,
1
] = 0 dx
which leads to the characteristic integral equation,
when t fs replaced by its original terms of equation A4Z.
( )
( )
Equation A46 is identical fn form to equation A41, and is valid for
dynamic temperature conditions when solved along the characteristic line
equation (equation A4 5). This presents no apecial problem since equation A45
simply tracts a column of water downstre1m --!n easily simulated task.
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Closed-form solutions for the ordinary different i al equation forms
(equations A4l and A46) of the dynamic temperature-steady flow equations are
possible with two important assumptions : (1) uniform flow exists, and
(Z) first and/or second order approximations of the heat flux versus water
temperature relationships are valid.
FIRST-ORDER SOLUTIONS
First-order solutions are possible for all three cases of o1 : Case 1,
q1 >0; Case Z, q1 <0; and Case 3, q1=0.
The ordinary differential equation wi ~h the first-order substitution is:
( )
Since Q = Q0 + q1 x, equation 08 becomes
-.'l
[Q 0 + ~1 x] dT/dx = ((q 1 T1 ] + [(K 1 B)/(pcp)]Te} -(q 1 + [(K 1 W)/(pcp)]lT ( )
let, a = (q 1T1 ] + [(K 1 ~)/(pcp)]T 1
73
I
Then 09 becomes
I ( )
I Using separation of variables,
( )
and the solution is
Case 2, q 1 < 0:
If q 1 < 0, then T1 = T and equation 08 becomes
( )
The so 1 uti on fs
( )
Case 3, q1 = 0:
If q1 = 0, then Q ~ Q(x) and equation 08 becomes
74
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~
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( )
The solution fs
( )
SE COND-ORDER SOLUTIONS
A second-order solution for ~ase 3 is as follows.
Let q1 = 0 and using equation A4S results in
( )
The solution is
( )
Using the first-order solution and mak i ng second-order corrections according
to the form suggested by equation Dl8 results in
75
lt where: a= (q 1T1 ] + ((K 18)/(pcp)]Te
I b = q1 + (K1B)/(pcp)
I Case 1. q>O:
I
I T = a/b e
(-b/q )
I R = [1 + (qtxo/Qo)] 1
I Case 2. q<O:
I
T = T e •
((q -b)/q ]
R = (1 + (q X /Q )] f. f. f. 0 0
p Case 3. q=O:
I
T = T e e
I R = exp [-(bxo)/Qo]
76
-r --
w a:
::>
1-
c(
a: w
Q.
:E w
1-
::E
c(
w a:
1-m
- ----,.,---
EQUILIBRIUM TEMPERATURE
"--INITIAL WATER TEMPERATURE
0
LONGITUDINAL DISTANCE
Figure 2 .6. Typtca 1 lony ttudtna 1 water. te•perature profile
predicted by heat transport equation.
TIME PERIODS
The basic math model for the overall basin network. is a steacy-state
I model because it assumes that the input is a constant over an indefinite
period of time. Conceptually it assumes that the input conditions exist
sufficiently long for the steady-state results to reach the! lowest point in
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tne network.. If the travel time from the upstream most point to the down-
stream end of the network. becomes significant compared to the time period,
then the results become less reliable.
If the travel time to the lowest point is 30 days, it should be
recognized that the water passing this point on the first day of the 30 day
period originated upstream 30 days prior. Therefore, the meterological condi-
tions that determine downstream daily water temperatures on the first day are
not included in the time period averages. In fact, only the last day•s water
column was influenced entirely by the meterologic data used in the input for
the time period.
One way to overcome this prob 1 em is to redefine the time periods to
smaller increments (as small as a day if necessary) and track. each day•s water
column movement using the previous day•s results as the initial conditions for
the current day.
7i
~ DIURNAL FLUCTUATIONS
The following relationships can be solved explicitly at any study site or
I point of interest to determine the maximum temperature rise of the water above
the average. It fs base j upon the fact that the water temperature passes
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through the average values twice each day. That the average water temperature
occurs approximately half way through the day. That the remainder of the day
the water t emperature increases steadily to a maximl!lll close to sunset. The
same logic is used for determining the minimum water temperature by subst1tu-
ting nighttime conditions in lieu of daytime.
where: d -average flow depth, m.
n ! Man ~ing's n-value.
0 1 discharge, ems.
B I average top width, m.
S · I energy gradient, m/m. e
tx 1 travel time from noon to sunset, sec.
so 1 duration of possible sunshine from sunrise to sunset,
Ted I equilibrium temperature for average daily conditions,
hours.
c.
T i equilibrium temperature for average daytime c nditions, C. ex
78
( )
( )
( )
( )
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--
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: average daily water temperature (at so l ar noon) at point of
interest, C.
T
0
x ! average daily water temperature at travel time distance upstream
f om point of interest, C.
Twx 1 average maximum daytime water temperature (at sunset) at po · nt
of interest, C.
Kd 1 first order thermal exchange coefficient for daily conditio1s,
J/m 1 /sec/C.
Kx 1 first o~er thermal exchange coefficient for daytime cond i tions ,
J/m 1 /sec/C.
p 1 density of water= 1000 kg/m 2 •
cp 1 specific heat of water = 4182 J/kg/C.
Because of the symmetery assumed for the daytime conditions, it is only
necessary to cal culate the difference between the maximum daytime anc average
daily water temperatures to obtain the minimum water temperature.
where: T wn
Twx
( )
: average minimum nightime water temperature (at sunri ;e) at
point of interest, C.
: av!rage maximum daytime' water temperature (at sunset at
point of interest, C.
Twd 1 average daily water temperature (at solar noon) at pc ir•t of
interest, C.
79
FLOW MIXING
The equation for determining the final downstream water temperature when
II flows of different temperatures and discharges met at junctions, etc. fs:
II
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~
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~
where: TJ 1 water temperature below junction
T8 1 water . temperature abov-junction on the mafnstem
(branch node)
TT 1 water temperature above junction on the tributary
(terminal node of the tributary)
08 1 discharge above junction on the mainstem (branch node)
Or 1 discharge above junction on the tributary (terminal
node on the tributary)
( )
REGRESSION MODELS
Regression modesl are commonly used to smooth data and /or fill-in missing
data. They are used as a part of the instream water temperature model:
first, to provide ini tial water temperatures at headwaters or point sources to
start the transport mode; and second, as an independent prediction of water
temperatures at interior network points for purposes of validation and calibra-
tion. Obviously, regression models are only useful at the points of analysis
and cannot be used in lieu of longitudinal transport. Two regression models
are included in the instream water temperature model package : (1) a standard
regression model, and (2) a transformed regression mode l . Each requires
measured or known water temperatures as the dependent variable along with
associated meteorological, hydrological, and stream geometry independent
parameters. However, the standard regression model requires less detail than
the transformed. The standard model i s satisfactory for most appl i cations,
but the transformed version has a b~tter physica l bas i s. Th e cho i ce becomes a
matter of judgement by the responsible engineer/sc i entist.
STANDARD REGRESSION MODEL
IFG studies during the model development have shown that the following
simple linear multiple regression model provides a high de~ree of correlat i on
for natural condit i ons . The model is:
1\ T = a, + a 1 T + a 1 W + a 1 Rh + a~ (S I S ) + a, H + a, Q w a a · o sx
81
where:
A
T 1 estimate of water temperature, C w
a,-a, 1 regression coefficients
Ta I air temperature, C
Wa 1 wind speed, mps
Rh 1 relative humidity, decimal
SIS 1 sunshine rat i o, decimal
0
H 1 extra terrestrial solar radiation, J/m 2 /sec sx .
Q 1 discharge, ems
It is recommended that the meterologica ~ parameters and the solar radiation at
the meterological station be used for each regression anal y sis. Obviously,
the discharge, Q, and the de pendent variable water temperatures must ~e
obtained at the point of analysis.
These six independant variables are readily obtainable and are also
necessary for the transport model . A minimum of seven data sets are necessary
to obtain a solution . However, a greater number is desirable for statistical
validity. Also, it needs to be emphasized that the resulting regression model
is only valid at the point of analysis and only if upstream hydrologic condi-
tions do not change. For example, if a reservoir has been constructed upstream
subse quent to the data set, the model is not likely to be valid because the
release temperatures have been affected.
TRANSFORMED REGRESSION MODEL
The best regression mode 1 would be one that not only uses the same
parameters as the best phys i cal-process models; but has the same, or near l y
the same, mathematical form. That 1s, the regression model equat i on uses
physical-process transformed parameters as the independent variables . Thi s
transformed regression model uses all of the input parameters used i n the
transport model except for stream distance and init1 1 water temperatures.
The f1 rst-ordtr approximation of the constant-discharge heat transport
model was chosen as the b sis for the physical-process regression model.
Water temperature and discharge data at the specified location together with
the corresponding time period meterolog1c data from a nearby station are
needed . The meteoro 1 ogi c data . is used to determine the equi 11 bri um tempera-
ture (Te) and first-order thermal exchange coefficient (K 1 ). The Te and K1
are combined with the corresponding time period discharges as inde~endent
variables to determine the regression coefficients for estimating the corre-
sponding time period water temperature dependent variable. An estimate of the
average stream width W above the site location 1s necessary as an arbitrary
constant in the regression. The resulting regression coefficients are tant-
amount to synthetically determining an upstream source water temperature as a
function ·of time and the .distance to the source.
The constant discharge heat transport model is:
( )
where: Te I equilibrium water temperature, C
T, 1 initial water temperature, C
Tw 1 water temperature at x0 , C
K1 1 first-order thermal exchange coefficient, J/m 1 /sec/C
~ 1 average stream width, m
x, 1 distance from T,, m
p 1 water density • 1000 kg/mJ
cp 1 specific heat of water • 4182 J/kg
Q 1 discharge, ems
X
The definition of exp (x) • e fs
( )
If T, is a function of the time period only, then it can be approximated
as
r. = T. + 6T, cos[(Zw/365) (01-213)] ( )
where: T, 1 average initial water tempera tu re over all tim• periods; c
6T 1 1 half initial temperature range over all time periods; c
of 1 average Julian day for fth time period; January 1 = 1 and
December 31 = 365.
Let, Z1 = -(Kl§)/(pcPQ) ( )
Za = -i e ( )
z, = cos [(Zw/365) (0 1 -213)] ( )
84
If equations C2 throu gh CS are subst i tuted into equat i on Cl and the te rms
rearranged, then Tw can be expressed as:
Tw • T, + (6T,)Z, + (T,x,)Z 1 + (6T 1 x1 )Z 1 Z,
+ (x,)Z,Za + (T,1 x,lf2)Z 1
1 + (6T,x 1 /2)Z 1
1 Z,
+ (x,1 /2)Z 1
1 Z1 + (T,x,1 /6)Z 1
1 + (6T,x,1 /6)Z,'Z,
+ (x,'/6)Z 1
1 Z1 + (T,x,'/24)Z 1 ' + (6T,x,'/24)Z 1 'Z,
( )
If the converging power series is truncated after the final fourth-orde r I !"Ill
and the following substitutions are made, then I possible multiple linear
regression model results.
Let, '• = T,
a, = 6T, x, = Z,
&a = T,x, X a = z,
a, • 6T 0 X1 X, = z,z,
It = x. X, = ZaZa
'• = T,x,1 /2 x, • z,a
'• = 6T,x,1 /2 X, = Z,1 Z,
a, = x,1 /2 X,.= Z1
1 Z1
'• = T,x,1 /2 X, = z,,
a, = 6T,x,1 /6 X, = z, 1 Z,
&u = x,'/6 Xu = Z, 'Za
lu = T,x,'/2 Xu = Z,'
85
a 12 a f.T,x,'/24
au = x,'/24
If the resulting independent transformed variab l es X1 , through Xu are
regressed on the dependent variable Tw, then the following regression equation
results
The best estimates of the synethic physical-process parameters are
T, = a,
x, = a,
86
( )
( )
( )
( )
Attachment 2
HEAT FLUX COMPONENTS FOR AVERAGE
MAINSTEM SUSITNA CONDITIONS
4(\\)
300
1977 200
t?ZT/141 100
.1"0
8
rZZZI
-ue
-288
-380
-488
1970
3()0
r.z .vv.;-~~
IH7 200
rz;·/z.z-ca tOO
ueo
0
E/ / LJ
-IQO
-298
-:S\10
-~\)\)
_, ,. ... ('
ATI10 SPH£RIC
". ' / · ...
I '• '
J
S U S IT N ~ RI VER HE ~T FLit ':·:' -''
SOLAR
J UII(
rRICTlOH _ CONDUCTION [Yj;PORATIO H
COHPOHEHT
SUSITNR RIVER HE~T FLUX
JUL Y
l ACK RA li
1970
1977
t?2?2?23
1911
rZZZI
1971
l'i77
rzzvm
1981
f ZZZI
<4 00
300
200
108
•
-tee
-lit
-308
-481
ATI'IOSPHEP.IC
388 -
200 ~
180 -
0
-100 ~
-200 1-
-300 ~
. l , .. i ·-( • t
I
) /
SU S ITNR RIV ER HE~T FLU X
SOLAR
Au ~u:r
rRICTION -CONDUCTION EVAPORATION
COI'IPONEHT
SUSITNR -RIVER HERT FLUX
$EPT£11BER
non
' .......
-,~...~ .:
JACK ltAD
~-
.... · ~:. ~--. ; ........... _
~---------------------------------------------------------------_; ~OL.wP rF':'-TICIII
COMPI)II[IIT
Attachment 3
WEATHER WIZARD DATA
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:1: B
R&H CONSULTANTS, INC.
SUSITNA HYDROELECTRIC PROJECT
WATANA WEATHER STATION
August, 1981
::l
::l
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88 c
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28 .... ~L-~~~--~=:~--~~~~--~~--~--~--~~~98 ~
tJ
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n
t---~,.~~~~~~--~~~~~r---~~--~~r-~Oi~r-~3681:
288 .... t~ 216 ~
144 tJ
72 M ~--~~L-~------------------------~~------~----~--,8 ~
From R&M Processed Climatic Data , Vol. 5, Watana Station
Figure 4
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From R&K Processed Climatic. Data, Vol. 5, Watana Station
Figure 5
From Local
Climatolog ical
Data Summa r y
for Talkeetna
Nov. 1980
'
Figure 6. Monthly averaged observed relative and absolute humidity data
from R&M Weather Wizzards in Susitna basin.
JUNE
10 5 JULY
X 10 5 AUG
X 10 5 SEPT
Rh p X Rh Pv Rh Pv Rh Pv X v
(decimal) (kg/11 3) (decimal) (kg/11 3) (decimal) (kg/11 3) (decimal)
1 Talkeetna ~
105 11
1980 .785 8.2 .810 10.0 .8 3 9 .0 .813 6 •. ,
1981 .713 7.7 .805 9.4 .835 9.1 .785 6:'
1982 .755 8.6 .790 9.4 .820 9.4 .903 7. •)
3-year average .751 8.2 .802 9.6 .829 9.2 .834 6.~
Sherman
198.0 11
1980
1981
1982 .40 4.0 .44 4.9 .22 1. 8 .35 2 .8
3-year average .40 4.0 .44 4.9 .22 1.8 .35 2.8
Devil Canyon
457.0 11
1980 .65 7.6 .54 6.0
1981 .67 6.4 .78 7.1 .82 7.6 .66 4.2
1982 .37 3.5 .43 4.2 .35 3.5 .52 3.9
3-ye r average .52 5.0 .62 6.3 .57 5.7 .59 2.7
Watana
671.0 11
1980 .50 4 .5 .47 5.0 .71 5.0
1981 .29 2.7 .37 3.4 .26 1.6 .30 2.0
1982
3-year average .40 3.6 .42 4.2 .26 1.6 .50 3.5
Koaina Creek
792.5 •
1980 .66 5.2 .10 0. ti
1981 .51 4.3 .65 6.1 .56 5.0 .46 2. ~·
1982 .29 2.5 .35 3.4 .26 2.3 .53 3.t
3-year average .40 3.4 .so 4.8 .49 4.2 .36 2.3
1 Data from National Weather Service Local Climatological Data Summary
10 5
3 (kg/11 )
Figure 7 . Monthly averaged observed temperature <•c>
from R&M Weather Wizzard.
JUNE JULY AUG SEPT
Talkeetna 1
105.0 m
1980 11.9 14.7 12.1 7.7
1981 12.2 13.5 12.4 7.7
1982 11.7 13.7 13.2 7.8
3-year average 11.9 14.0 12.6 7.7
Shenaan
198.0 11
1980
1981
1982 10.7 12.8 11.6 7.1
3-year average 10.7 12.8 11.6 7 .1
Devil Canyon
457.0 m
1980 13.7 12.5
1981 10.0 9.3 9.2 3.3
1982 9.9 11.7 10.8 6.0
3-year average 10.0 11.6 10.8 4.7
Watana
671.0 m
1980 9.1 11.9 4.8
1981 9.3 9.3 2.0 4.0
1982 8.6 10.8 10.0 5.0
3-year average 9.0 10.7 6.0 4.6
Koaina Creek
792.5 •
1980 6.8 3.1
1981 8.0 9.7 9.0 2.9
1982 8.4 10.4 9.1 4.4
3-year average 8.2 10.1 8.3 3.5
1 Data from National Weather Service Local Climatological Data Summary
Attachment 4
DAILY INDIAN lliVD. TEMP!llATUllES VD.SUS
DEVIL CANYON Alll TEMPDATUllES
c. 1
H-J~-H-H-H -· l-U+~-+H-J+I.J+H-J.J+I.J+U-1+1-1-U t+t+t++++t+t+H+H-H-f Hf
ll• •I 1 I . I~ l 'j I:)
-r ;.;,. 0 ·~)..;,\.. r " .. (c) c,:.-
'"
...