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Improving Life through Science and Technology
Flood Routing for Continuous Simulation Models
J. Williams, W. Merkel, J. Arnold, J. Jeong
2011 International SWAT Conference, Toledo, Spain, June 15-17, 2011
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Contents
Introduction
Motivation
Routing Tests and Results
Analysis
Conclusion and Future Work
Flood Routing Methods
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Motivation
Continuous simulation models like APEX and SWAT operate on a daily time step and offer options for simulating some processes on shorter time steps.
However, they are not adequate for applications like designing flood control structures or estimating flood damages.
Computationally efficient and robust flood routing methods can provide flood analysis capabilities as well as other potential advantages like more accurate sediment and pollutant transport
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Project Goals
Develop reliable routing methods in HYMO model Muskingum-Cunge (M-C)
Variable Storage Coefficient (VSC)
Storage with Variable Slope (SVS)
Test these methods for accuracy, efficiency and reliability on various hydraulic conditions Various channel lengths and slopes
Channel flow, channel flow + floodplain flow
Rectangular and trapezoidal cross sections
Compare results with the Dynamic Wave Flow routing method (HEC-RAS) as a test of accuracy
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Saint-Venant Equations
Continuity
Momentum equation
0
q
t
S
t
A
x
Q
x
v
g
v
t
v
gx
hSS f
10
Kinematic wave
Diffusion wave
Dynamic wave
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Muskingum-Cunge (M-C) Method
A diffusion wave model
K and X determined from hydraulic properties of the reach
K is a timing parameter, seconds
X is a diffusion parameter, no dimensions
Based on NRCS WIN TR-20 Program
OXIXKS 1
),,,,( xceleritywaveslopewidthbottomowinflpeakfX
122121
22SSt
OOt
II
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Variable Storage Coefficient (VSC) Method
A diffusion wave model
Storage routing is calculated using a dimensionless storage coefficient (SC)
Every time step, SC is updated iteratively
Based on Williams (1969)
OST /
)
,,,(
velocitynormal
slopesurfacewaterlengthchannelareawettedfSC
122121
22SSt
OOt
II
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Storage with Variable Slope (SVS) Method
A variation of the VSC method in which the continuity equation is directly solved with no coefficients
The storage term is equal to the average water volume in the channel
An iterative solution is used to solve these equations considering variable water surface slope
t
SSOIOIO t
t
j
jjt
11
2
11 22
2
ttt
AOAIRCHLS
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Test Configuration
2400 0200 0400 0600 0800 1000 1200 140001J an2011
0
50
100
150
200
River: cs44 Reach: cs44 RS: 30
Date
Flo
w (m
3/s
)
Legend
Flow
Qin Qout
(A-A)
Rectangular (T1, T3) Trapezoidal (T2)
Channel flow
Trapezoidal (T4,T5,T6)
Floodplain flow
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Hydraulic Properties of Test Cases
Test 1 Test 2 Test 3 Test 4 Test 5 Test 6
Channel
Length (km) 0.335 5.785 1.830 13.635 50.000 50.000
Top Width (m) 12.2 12.6 12.2 9.7 30.0 30.0
Bottom Width (m) 12.2 6.6 12.2 7.6 18.0 18.0
Depth (m) 2.8 1.6 3.1 1.0 3.0 3.0
Slope (m/ m) 0.0006 0.001 0.002 0.001 0.001 0.0001
Manning’s n 0.04 0.04 0.04 0.04 0.05 0.05
Floodplain
Width (m) 0.0 0.0 0.0 92.7 1900.0 1900.0
Depth (m) 0.0 0.0 0.0 1.0 6.0 6.0
Manning’s n 0.0 0.0 0.0 0.049 0.15 0.15
Routing
Reaches 1 4 2 10 50 50
Time interval (h) 0.083 0.167 0.1 0.1 0.5 0.5
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Routing Result: Test 1
Qp
(m3/s)
tp
(hr)
Error
(%)
VSC 24.8 4.25 0.3
SVS 24.8 4.33 0.3
M-C 24.8 4.32 0.2
HEC 24.9 4.33 n/a
(L=0.335km, S=0.0006, Rectangular shape, Channel flow)
Time (hr)
0 2 4 6 8 10 12
Flo
w (
m3
/s)
0
5
10
15
20
25
30
INFLOW
VSC
SVS
M-CCC
HEC-RAS
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Routing Result: Test 2
(L=5.8km, S=0.001, Trapezoidal shape, Channel flow)
Qp
(m3/s)
tp
(hr)
Error
(%)
VSC 11.0 5.0 4.5
SVS 12.4 5.2 3.3
M-C 13.0 4.9 5.2
HEC 12.0 5.0 n/a
Time (hr)
0 2 4 6 8 10 12
Flo
w (
m3
/s)
0
2
4
6
8
10
12
14
INFLOW
VSC
SVS
M-CCC
HEC-RAS
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Routing Result: Test 3
(L=1.83km, S=0.002, Rectangular shape, Channel flow)
Qp
(m3/s)
tp
(hr)
Error
(%)
VSC 17.8 2.16 8.5
SVS 17.9 2.23 6.7
M-C 18.0 2.03 10.6
HEC 18.4 2.50 n/a
Time (hr)
0 2 4 6 8 10
Flo
w (
m3
/s)
0
5
10
15
20
25
INFLOW
VSC
SVS
M-CCC
HEC-RAS
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Routing Result: Test 4
(L=13.6km, S=0.001, Trapezoidal shape, Floodplain flow)
Qp
(m3/s)
tp
(hr)
Error
(%)
VSC 70 5.8 24.7
SVS 114 5.4 1.9
M-C 137 4.7 14.9
HEC 116 5.3 n/a
Time (hr)
0 2 4 6 8 10 12 14 16 18
Flo
w (
m3
/s)
0
50
100
150
200
INFLOW
VSC
SVS
M-CCC
HEC-RAS
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Time (hr)
0 20 40 60 80 100 120
Flo
w (
m3
/s)
0
1000
2000
3000
4000
INFLOW
VSC
SVS
M-CCC
HEC-RAS
Routing Result: Test 5
(L=50km, S=0.001, Trapezoidal shape, Floodplain flow)
Qp
(m3/s)
tp
(hr)
Error
(%)
VSC 1,943 41.7 1.6
SVS 2,359 40.0 11.7
M-C 2,891 35.0 30.9
HEC 1,990 42.0 n/a
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Time (hr)
0 50 100 150 200
Flo
w (
m3
/s)
0
1000
2000
3000
4000
INFLOW
VSC
SVS
M-CCC
HEC-RAS
Routing Result: Test 6
(L=50km, S=0.0001, Trapezoidal shape, Floodplain flow)
Qp
(m3/s)
tp
(hr)
Error
(%)
VSC 454 81.7 3.8
SVS 619 82.5 15.6
M-C 606 50.4 31.5
HEC 482 80.3 n/a
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Routing Result: Summary
Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Rank
VSC 0.3 4.5 8.5 24.7 1.6 3.8 2
SVS 0.3 3.3 6.7 1.9 11.7 15.6 1
M-C 0.2 5.2 10.6 14.9 30.9 31.5 3
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Correlation Analysis
R² = 0.89R² = 0.02
R² = 0.83
-100
1020304050
0 20 40 60
% E
rro
r
Length, km
Qp-Length
SVS
VSC
M-C
R² = 0.32
R² = 0.00
R² = 0.09
-20
0
20
40
60
0 0.001 0.002 0.003
% E
rro
r
Slope
Qp-Slope
SVS
VSC
M-C
R² = 0.92R² = 0.08R² = 0.75
0
10
20
30
40
50
0 2000 4000
% E
rro
r
Peak Inflow, m3/s
Qp-Inflow
SVS
VSC
M-C
SVS shows typical responses of kinematic wave models (e.g. error increases as slope decreases or with larger inflow-meaning higher surface slope) M-C shows similar trends to SVS ?
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Correlation Analysis
SVS and VSC show similar patterns while M-C behaves differently
SVS and VSC use the same algorithm for calculating flow velocity and travel time
R² = 0.67
R² = 0.55
R² = 0.06
-10
0
10
20
30
40
0 0.001 0.002 0.003
% E
rro
r
Slope
tp-Slope
SVS
VSC
M-C
R² = 0.01R² = 0.13
R² = 0.52
0
10
20
30
40
0 20 40 60
% E
rro
r
Length, km
tp-Length
SVS
VSC
M-C
R² = 0.00R² = 0.17R² = 0.52
0
10
20
30
40
0 2000 4000
% E
rro
r
Peak Inflow, m3/s
tp-Inflow
SVS
VSC
M-C
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Conclusion
All methods (M-C, VSC, and SVS) were computationally stable and maintained mass balance in all of the tests
No prevailing advantage was found for the diffusion models over kinematic wave model
The VSC method performed superior on combined flow (channel flow + floodplain flow) in long channels
The SVS method was reliable in routing short channels, but showed marginal error on long channels
The M-C method showed limited performance. The errors were significant in tests with floodplain flow on long channels
The peak flows of M-C and SVS showed similar patterns in responding to hydraulic properties.
The time to peak of VSC and SVS showed similar patterns to hydraulic properties. Both use the same equations to compute flow velocity
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Future work
The routing methods will be integrated into APEX and SWAT for continuous simulation
The routing methods within APEX/SWAT will be tested on complex channel networks at the watershed scale
A preliminary study of the Muskingum-Cunge with Variable Coefficient method shows promising results, so it will be included in the future study
0
500
1000
1500
2000
2500
3000
3500
4000
0 50 100 150
Flo
w R
ate
(m3
/s)
Time (hr)
50 REACHES L=1km DT=.5h S=.001 CHFP 20110412
Inflow
MCCC
MCVC
HEC-RAS
(Test 5)
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Questions?