Regional Characteristics of Unit Hydrographs and Storm Hyetographs Theodore G. Cleveland, Ph.D.,...
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Transcript of Regional Characteristics of Unit Hydrographs and Storm Hyetographs Theodore G. Cleveland, Ph.D.,...
Regional Characteristics of Unit Hydrographs and Storm
HyetographsTheodore G. Cleveland, Ph.D., P.E.
Instantaneous Unit Hydrograph Approach
• Unit hydrograph is one of several methods examined in this research.
• University of Houston has focused exclusively on this technique.
• Two major components– Analysis (Find IUH from rainfall-runoff data)– Synthesis (Estimate IUH from watershed
character)
Storm Analysis
• Central Texas Database• Analyze all storms using five different IUH model
equations.• Pick a “good” model• Aggregate model parameter values by station.• Re-run each storm using the aggregated values.• Test these results for acceptability• Interpret results• Conclusions and Recommendations
Different Unit Hydrograph Models
• Five IUH Models– Gamma– Rayleigh– Weibull – NRCS (DUH as an IUH)– Commons
Gamma-family
• Gamma, Rayleigh, and Weibull are all generalized gamma-distributions. The IUH model equation is
• Gamma when p=1; Rayleigh when p=2
)exp()( 1 p
pNp
pNp
p
p
t
t
t
t
t
tp
A
tq
NRCS DUH
• NRCS DUH as an IUH. Using a Gamma-type functional representation is
pt
t
pp
et
t
Aq
tq 88.381.3)(5387.37
)(
NRCS Curve-Fitting Using Gamma function
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6
t/Tp
q/qp
NRCS-Tabulation Equation
Commons Model
• Commons’ Hydrograph– Empirically derived for large watersheds
Figure 1. Hydrograph developed by trial to cover a typical flood. from: Commons, G. G., 1942. “Flood hydrographs,” Civil Engineering, 12(10), pp
571-572.
0
10
20
30
40
50
60
0 10 20 30 40 50 60 70 80 90 100
Units of Time
Uni
ts o
f Flo
w
Approximation Original
p
p
p
t
t
p
t
t
p
t
t
p
et
t
et
t
et
t
A
tq
641.5132.0
694.2965.0
707.4176.0
)641.5
()288.0(
88.3
)694.2
()925.0(
58.7
)707.4
()118.0(
001.77)(
Analyze Each Storm
• Supply observed precipitation data to the hydrograph function.
• Convolution of sequence of the IUH models to create a DRH.
• Compare observed runoff with DRH, adjust parameters in IUH to minimize some error function.
Typical Result
0
1
2
3
4
5
6
7
100 600 1100 1600 2100
Time (minutes)
Cu
mu
lati
ve D
epth
(in
ches
)
0.00E+00
1.00E-02
2.00E-02
3.00E-02
4.00E-02
5.00E-02
6.00E-02
Rat
e (i
nch
es/m
in)
ACC_PRECIP(IN) ACC_RUNOFF(IN)
ACC_MOD_RUNOFF(IN/MIN) RATE_PRECIP(IN/MIN)
RATE_RUNOFF(IN/MIN) RATE_MODEL(IN/MIN)
Figure 7.4 Plot of Observed and Model Runoff, Ash Creek, June 3, 1973 storm using the Weibull IUH model.
Typical Result
0
1
2
3
4
5
6
7
0 500 1000 1500 2000
Time (minutes)
Cu
mu
lati
ve D
epth
(in
ches
)
0.00E+00
1.00E-02
2.00E-02
3.00E-02
4.00E-02
5.00E-02
6.00E-02
Rat
e (i
nch
es/m
in)
ACC_PRECIP(IN) ACC_RUNOFF(IN)
ACC_MOD_RUNOFF(IN/MIN) RATE_PRECIP(IN/MIN)
RATE_RUNOFF(IN/MIN) RATE_MODEL(IN/MIN)
0
1
2
3
4
5
6
7
0 500 1000 1500 2000
Time (minutes)
Cu
mu
lati
ve D
epth
(in
ches
)
0.00E+00
1.00E-02
2.00E-02
3.00E-02
4.00E-02
5.00E-02
6.00E-02
Rat
e (i
nch
es/m
in)
ACC_PRECIP(IN) ACC_RUNOFF(IN)
ACC_MOD_RUNOFF(IN/MIN) RATE_PRECIP(IN/MIN)
RATE_RUNOFF(IN/MIN) RATE_MODEL(IN/MIN)
0
1
2
3
4
5
6
7
0 500 1000 1500 2000
Time (minutes)
Cu
mu
lati
ve D
epth
(in
ches
)
0.00E+00
1.00E-02
2.00E-02
3.00E-02
4.00E-02
5.00E-02
6.00E-02
Rat
e (i
nch
es/m
in)
ACC_PRECIP(IN) ACC_RUNOFF(IN)
ACC_MOD_RUNOFF(IN/MIN) RATE_PRECIP(IN/MIN)
RATE_RUNOFF(IN/MIN) RATE_MODEL(IN/MIN)
0
1
2
3
4
5
6
7
0 500 1000 1500 2000
Time (minutes)
Cu
mu
lati
ve D
epth
(in
ches
)
0.00E+00
1.00E-02
2.00E-02
3.00E-02
4.00E-02
5.00E-02
6.00E-02
Rat
e (i
nch
es/m
in)
ACC_PRECIP(IN) ACC_RUNOFF(IN)
ACC_MOD_RUNOFF(IN/MIN) RATE_PRECIP(IN/MIN)
RATE_RUNOFF(IN/MIN) RATE_MODEL(IN/MIN)
Commons
NRCS
Rayleigh
Gamma
Choosing a Model
• Establish acceptance criteria:– Averages
• Bias
• Fractional Bias
• Fractional Variance
• Normalized Mean Square Error
– Peak• Peak Relative Error:• Peak Temporal Bias:
PmPo ttTB
PoPmPo QQQQB /
N
iimiomo QQ
NQQBias
1,,
1
mo
mo
QQFB 2
qmqo
qmqoFV
22
22
2
mo
mo
QQNMSE
2
Acceptance AnalysisC r i t e r i a ( B a s e f l o w
S e p a r a t e d ) G a m m a R a y l e i g h W e i b u l l N R C S C o m m o n s
A c c e p t e d % - A c c e p t e d A c c e p t e d % - A c c e p t e d A c c e p t e d % - A c c e p t e d A c c e p t e d % - A c c e p t e d A c c e p t e d % - A c c e p t e d
S t o r m s A n a l y z e d 1 6 4 2 - - 1 6 4 2 - - 1 6 4 2 - - 1 6 4 2 - - 1 6 4 2 - -
2
1NMSE
1 5 5 6 9 4 . 8 % 6 9 5 4 2 . 3 % 1 5 6 9 9 5 . 6 % 3 4 7 2 1 . 1 % 7 0 . 4 %
21
21 FB
1 5 3 1 9 3 . 2 % 5 2 9 3 2 . 2 % 1 5 4 5 9 4 . 1 % 2 9 7 1 8 . 1 % 5 0 . 3 %
21
21 FV
1 4 3 2 8 7 . 2 % 8 3 7 5 1 . 0 % 1 4 7 1 8 9 . 6 % 2 5 1 1 5 . 3 % 2 0 . 1 %
45
43 MG
1 6 4 2 1 0 0 . 0 % 1 6 4 2 1 0 0 . 0 % 1 6 4 2 1 0 0 . 0 % 1 6 4 2 1 0 0 . 0 % 1 6 2 4 9 8 . 9 %
45
43 VG
1 6 4 2 1 0 0 . 0 % 1 6 4 2 1 0 0 . 0 % 1 6 4 2 1 0 0 . 0 % 1 6 4 2 1 0 0 . 0 % 1 6 4 1 9 9 . 9 %
41
41 QB
4 0 3 2 4 . 5 % 5 6 3 3 4 . 3 % 5 5 1 3 3 . 6 % 9 3 5 . 7 % 0 0 . 0 %
3030 TB 8 9 2 5 4 . 3 % 5 4 3 3 3 . 1 % 9 1 1 5 5 . 5 % 5 7 9 3 5 . 3 % 1 9 4 1 1 . 8 % N M S E M a x i m u m 1 . 3 3 E + 1 4 1 2 4 0 0 2 2 5 1 8 1 0 0 1 8 1 0 0 0 0 N M S E M i n i m u m 2 . 2 7 E - 0 9 8 . 5 5 E - 0 6 2 . 3 3 E - 0 9 2 . 1 4 E - 0 8 0 . 0 0 0 4 2 3 N M S E A v e r a g e N M S E M e d i a n 0 . 1 4 2 5 0 . 7 7 8 0 . 1 3 4 5 4 . 4 5 1 6 5 C r i t e r i a ( B a s e f l o w I n c l u d e d )
G a m m a R a y l e i g h W e i b u l l N R C S C o m m o n s
A c c e p t e d % - A c c e p t e d A c c e p t e d % - A c c e p t e d A c c e p t e d % - A c c e p t e d A c c e p t e d % - A c c e p t e d A c c e p t e d % - A c c e p t e d
S t o r m s A n a l y z e d 1 6 4 2 - - 1 6 4 2 - - 1 6 4 2 - - 1 6 4 2 - - 1 6 4 2 - -
2
1NMSE
1 5 4 1 9 3 . 5 % 8 4 8 5 1 . 6 % 1 5 6 9 9 5 . 6 % 8 3 3 5 0 . 7 % 1 2 9 5 7 8 . 9 %
21
21 FB
1 5 1 2 9 1 . 7 % 6 9 9 4 2 . 6 % 1 5 3 9 9 3 . 7 % 7 6 0 4 6 . 3 % 1 1 5 4 7 0 . 3 %
21
21 FV
1 4 4 8 8 7 . 8 % 1 0 2 5 6 2 . 4 % 1 4 7 2 8 9 . 6 % 7 7 6 4 7 . 2 % 1 2 8 2 7 8 . 1 %
45
43 MG
1 6 4 2 9 9 . 6 % 1 6 4 2 1 0 0 . 0 % 1 6 4 2 1 0 0 . 0 % 1 6 4 1 9 9 . 9 % 1 6 4 1 9 9 . 9 %
45
43 VG
1 6 4 2 9 9 . 6 % 1 6 4 2 1 0 0 . 0 % 1 6 4 2 1 0 0 . 0 % 1 6 4 1 9 9 . 9 % 1 6 4 1 9 9 . 9 %
41
41 QB
4 4 2 2 6 . 8 % 5 6 4 3 4 . 3 % 6 8 3 4 1 . 6 % 2 1 0 1 2 . 8 % 3 0 9 1 8 . 8 %
3030 TB 9 5 2 5 7 . 7 % 6 7 4 4 1 . 0 % 9 4 1 5 7 . 3 % 1 6 2 9 . 9 % 4 5 0 2 7 . 4 % N M S E M a x i m u m 4 E + 5 6 2 . 6 6 E + 3 5 1 . 6 2 E + 8 2 9 3 4 0 0 0 1 1 8 0 N M S E M i n i m u m 2 . 0 4 E - 0 8 3 . 6 7 E - 0 7 2 . 4 2 E - 1 2 6 . 4 1 E - 0 8 4 . 1 5 E - 0 9 N M S E A v e r a g e N M S E M e d i a n 0 . 0 1 7 7 0 . 4 2 4 0 . 0 1 3 9 0 . 4 5 0 . 0 8 2 8
Acceptance Analysis
• Aggregate model parameter values by station.– Test if parameter values depend on station or are
independent. (Dependent)
• Re-run each storm using the aggregated values.– (In-Progress)
• Test these results for acceptability– (Pending)
Interim Conclusions
• Parameter values vary by station and module. (Jonnalagadda, 2003)
• Weibull model is reasonable IUH model (He, 2004).References: Xin, He. 2004. Comparison of Gamma, Rayleigh, Weibull and NRCS Models with Observed Runoff Data for Central Texas Small Watersheds. Master's Thesis. Department of Civil and Environmental Engineering, University of Houston, Houston, Texas. 90p.Jonalagadda, Krishna, 2003. Determination of Instantaneous Unit Hydrographs for Small Watersheds of Central Texas. Master's Thesis. Department of Civil and Environmental Engineering, University of Houston, Houston, Texas. 132p.
Synthesis
• Evaluate methods to synthesize hydrographs in absence of data.
• Fundamental assumption: Watershed characteristics (slope, length, etc.) are predictors of hydrologic response and thus are predictors of IUH parameter values, and that there exists a UH.
Synthesis
• Determine watershed characteristics– Area, perimeter, slopes, lengths, etc.
• Relate regression models to IUH parameters to selected watershed characteristics.
• Use regression model to determine parameter values by station.
• Run each storm using these values.• Test results for acceptability• Interpret results• Make Conclusions and Recommendations
Watershed Characteristics
• These are measurements that can be made from a map, air photo, or possibly field visit.– Area, slope, etc.– Manual determination (University of Houston,
checked and corrected by Lamar)– Automated determination (USGS)
Regression Models• Power Law Model (representative)
• Weights determined by minimization of RMS error between “observed” IUH parameters and the power law model.
• Predict values of IUH model (t_bar,p,N) from watershed characteristics, then use resulting IUH.
SlopeStreamx
ShapeRatiox
PerimeterAreax
SlopeRawx
RatioAspectx
Areax
resNy
py
barty
xxxxxxwy wi
wi
wi
wi
wi
wioi
_
/
_
_
_
_
6
5
4
3
2
1
3
2
1
,6,5,4,3,2,1654321
Typical Interim Results
Tp(hrs) versus SQRT(Area)All Watersheds
0.1
1
10
100
0.1 1 10 100
SQRT(Area (mi 2))
Tim
e (h
rs)
Tp = 0.64*SQRT(Area)
Interim Conclusions
• Analysis of selected small, medium, and large watersheds in each module was used to test feasibility of approach
– The power-law model can produce parameter values that, when used as the IUH model could match peak discharge rates to within 15% of observed values, and match the arrival time of the peak within an hour.
References
Lazarescu, Ioana, 2003. Correlation of Geometric Properties of Small Watersheds in Central Texas with Observed Instantaneous Unit Hydrographs Master's Thesis. Department of Civil and Environmental Engineering, University of Houston, Houston, Texas. 84p.
Remaining Work
• Storm analysis– Aggregate results, perform comparisons and
acceptance tests. (in-progress)– Interpret results in raw form and transform into
conventional Qp,Tp,Tc format. (pending above)– Write research report. (in-progress)
Remaining Work
• Regionalization– Power-law model of entire data set (not just subset used
in Lazarescu’s thesis).– Interpret results, select most meaningful watershed
characteristic combinations. – Test with all storms, apply acceptance criteria.– Compare with NRCS methods to synthesize Unitgraphs
• 90 TR-20 models to be created this summer.
– Write research report with methodology and guidelines for use (Report started, quite empty).