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INTRA-OFFICE MEMORANDUM
LOCATION Denver/Anchorage DATE _--=:.Oc:::..t:::...:.......:l:.::2:..1,--=l~9.:.84-'--_
TO
Bv)FROM
E.J.Gemperline
D.W.Beaver
NUMBER
SUBJECT Slough Discharge Regression Relations
8
In our continuing review of Susitna slough groundwater conditions,we have
reexamined statistical relations between slough discharge and other hydraulic
parameters (mainstem discharge,mainstem stage,and mainstem stage minus
slough stage).In performing these revised calculations,we have used slough
discharge data provided by R&M Consultants,mainstem discharge data provided
by the U.S.Geological Survey,and stage-discharge relations at selected cross
sections inferred from rating curves given in the Harza-Ebasco draft report
entitled "Sus i tna Hydroelec tricProject,Lower Susi tna River,Water Surface
Profiles and Discharge Rating Curves",dated October,1983.
The derived relationships are summarized on Attachment 1 (slough discharge vs •.
mainstem discharge),Attachment 2 (slough discharge vs.mainstem stage),and
Attachment 3 (slough discharge vs.head difference).In general,these
relationships differ but little from relationships previously presented.The·
differences that do appear can be attributed to minor corrections in the data
base,as well as the use of rating curves at different river cross sections.
Some general co~nents can be made.Regression relations using all values
generally have a higher coefficient o£determination (R2)than those which
exclude dates when upstream berms were overtopped.This is to be expected,
since the sloughs will behave essentially as side channels under overtopping
conditions.However,in many instances the correlations are improved when
both dates of overtopping and dates when slough discharge is relatively high
are excluded,particularly at sloughs 8A and 9.This suggests that other
sources,such as localized surface runoff,can be important contributors to
slough discharge at some sloughs,such as 8A and 9.(Note that excluding
dates when slough discharge is relatively high tends to dramatically increase
R2,while resulting in relatively little change in the slope of the
regression line.)Furthermore,these refined analyses confirm previous
conclusions regarding the apparent uniqueness of each of the four sloughs
studied in detail so far.It remains unlikely that any general 'relationships
applicable to all sloughs can be developed.
The relationships presented in the Attachments should be applied with
caution.They are not necessarily accurate predictors of absolute slough
discharge under all flow conditions.However,the slopes of the regression
lines with higher R2 values may provide reasonably accurate order of
magnitude estimates of changes in apparent groundwater upwelling over the
ranges in flow considered.Thus,the indicated relationships may be accurate
predictors of relative changes in groundwater upwelling with changes in other
parameters,if not accurate predictors of absolute slough discharge.
cc:B.H.Wang,Harza,Chicago
S.D.Simmons,Ebasco,Seattle
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ATTACHMENT 1.LINEAR REGRESS ION EQUATIONS
FOR SIDUGH DISCHARGE VS.MAINSTEH DISCHARGE
<..J
SLOUGH
8A
9
11
21
YEAR
1983
1983
1983
1982.
1982
REGRESSION EQUATION
S =-3.83 +0.000526 G
S =5.10 +0.0000377G
5 =0.15)+0.000117 G
5 =-0.627 +0.000128 G
5 =-149.7 +0.010008 G
5 =2.94 +0.000307 G
5 =1.97 +0.000351 G
5 =1.51 +0.000102G
S =2.15 +0.000104 G
5 =-7.62 +0.00105 G
5 = -0.570 +0.000445 G
S =-2.71 +0.000803 G
R2
0.103
0.001
0.086
0.631
0.264
0.089.
0.805
0.766
0.504
0.543
0.405
0.916
COHMENTS
All values
Exc 1uding overtopping flows,G'>30,000
June 6 -Aug.7 only;excluding G730,000
June 6 -Aug.7 only;excluding G730,000,573
All values
Excluding overtopping flows,G~16,000
Excluding G;7 16,000,S'7 8
All values
All values
All values
Exc1ud ing overtopping flows,G "724,700
Sept.22 -Oct.22 on1Yi excluding G'724,700
Notes:5 =510ugh discharge,cfs;G =Hainstem discharge at Gold Creek,cfs
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ATTACHMENT 2.LINEAR.REGRESSION EQUATIONS
FOR SLOUGH DISCBAR.GE VS.HAINSTEM STAGE
SLOUGH YEAR REGRESS ION EQUATION R2 COMMENTS
8A 1983 S •-2149.8 +3.698W l 0.065 All values
S •-92.3 +0.1683WI 0.000 Excluding overtopping flows,G)30,000
S •-695.45 +1.1966Wl 0.091 June 6 -Aug.1 only;excluding G)30,OOO
S '"-740.96 +1.2737Wl 0.626 June 6 -aug.7 only;excluding G)30,000,S>3
9 1983 S '"-32,801 +54.380W2 0.228 All values
S ..-769.1 +1.2871W 2 0.085 Excluding overtopping flows,G>16,000
S •-877.21 +1.4658W2 0.755 Excluding G>16,000,S>8
11 1983 S '"-367.04 +0.54004W3 0.783 AI"values
1982 S ..-327.05 +0.48278W3 0.531 All values
21 1982 8 '"-4400.2 +5.8554W4 0.491 All values
8 ..-1810.6 +2.4130W4 0.391 Excluding overtopping flows,G>24,700
,8 ..-3244.1 +4.3212W4 0.938 8ept.22 -Oct.22 only;excluding G>24,700
Notes:8"Slough discharge,cfs;G •Mainstem dischrage at Gold Creek,cfs
WI.'Mainstem stage at RM 127.1,ft.;W2 •Mainstem stage at RM 129.3,ft.;
W3 •Mainstem stage at RM 136.68,ft.;W4 •Mainstem stage at RM 142.2,ft.
421051/10
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ATTACl~ENT 3.LINEAR REGRESSION EQUATIONS
FOR SLOUGH DISCHARGE VS.HEAD DIFFERENCE
\-.J
SWUGH
8A
9
11
21
YEAR
1983
1983
1983
1982
1982
REGRESSION EQUATION
S =-11.2 +1.25 AH
S =26.1 -1.39 ~H
S =-6.26 +0.603 ~H
S =-17.3 +1.31 ~H
S="-158 +19.8 AH
S =-0.187 +0.670 AH
S =-9.22 +1.53 AH
S =-4.74 +0.550 AH
S =-3.23 +0.483 l)H
S =-35.9 +5.60 ~H
S =-11.4 +2.19 ~H
S =-30.5 +5.11 AH
R2
0.007
0.027
0.021
0.564
0.011
0.021
0.720
0.771
0.519
0.296
0.270
0.910
COMMENTS
All values
Excluding overtopping flows,G730,OOO
June 6 -Aug.7 onlYi excluding G~30,OOO
June 6 -Aug.7 onlYi excluding G >30,000,S73
All values
Excluding overtopping flows,G~16,OOO
Excluding G:>16,000,S>8
All values
All values
All values
Exc luding overtopping flows,G>24,700
Sept.22 -Oct.22 on1Yi excluding G,724,700
Notes:S =Slough discharge,cfs;G =Mainstem discharge at Gold Creek,cfs
AH =Mainstem stage minus slough stage