Flood Routing for Continuous Simulation Models

Transcription

1 Improving Life through Science and Technology Flood Routing for Continuous Simulation Models J. Williams, W. Merkel, J. Arnold, J. Jeong 11 International SWAT Conference, Toledo, Spain, June 15-17, 11

2 Contents Introduction Motivation Flood Routing Methods Routing Tests and Results Analysis Conclusion and Future Work

3 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

4 Project Goals Develop reliable routing methods in HYMO model Muskingum-Cunge (M-C) Variable Storage Coefficient () Storage with Variable Slope () 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

5 Saint-Venant Equations Continuity Momentum equation q t S t A x Q x v g v t v g x h S S f 1 Kinematic wave Diffusion wave Dynamic wave

6 Muskingum-Cunge (M-C) Method A diffusion wave model I 1 I t O 1 O t S S 1 S K X I 1 X O K and X determined from hydraulic properties of the reach K is a timing parameter, seconds X is a diffusion parameter, no dimensions X f ( peak inflow, bottom width, slope, wavecelerity, x) Based on NRCS WIN TR- Program

7 Variable Storage Coefficient () Method A diffusion wave model I 1 I t O 1 O t S S 1 T S / O Storage routing is calculated using a dimensionless storage coefficient (SC) Every time step, SC is updated iteratively SC f ( wetted area, channel length, water surface slope, normal velocity ) Based on Williams (1969)

8 Storage with Variable Slope () Method A variation of the method in which the continuity equation is directly solved with no coefficients O t I t O I j Oj j The storage term is equal to the average water volume in the channel S t RCHL AI t AO t St S t An iterative solution is used to solve these equations considering variable water surface slope 1

9 Test Configuration River: cs44 Reach: cs44 RS: 3 Legend Flow ( m3/s) Flow J an11 Date Q in Q out Rectangular (T1, T3) Trapezoidal (T) Channel flow Trapezoidal (T4,T5,T6) Floodplain flow (A-A)

10 Hydraulic Properties of Test Cases Test 1 Test Test 3 Test 4 Test 5 Test 6 Channel Length (km) Top Width (m) Bottom Width (m) Depth (m) Slope (m/ m) Manning s n Floodplain Width (m) Depth (m) Manning s n Routing Reaches Time interval (h)

11 Routing Result: Test 1 Flow (m3/s) Time (hr) INFLOW M-CCC HEC-RAS Q p (m3/s) t p (hr) Error (%) M-C HEC n/a (L=.335km, S=.6, Rectangular shape, Channel flow)

12 Routing Result: Test Flow (m3/s) INFLOW M-CCC HEC-RAS Q p (m3/s) t p (hr) Error (%) M-C Time (hr) HEC n/a (L=5.8km, S=.1, Trapezoidal shape, Channel flow)

13 Routing Result: Test 3 Flow (m3/s) INFLOW M-CCC HEC-RAS Q p (m3/s) t p (hr) Error (%) M-C Time (hr) HEC n/a (L=1.83km, S=., Rectangular shape, Channel flow)

14 Routing Result: Test 4 Flow (m3/s) 15 1 INFLOW M-CCC HEC-RAS Q p (m3/s) t p (hr) Error (%) M-C Time (hr) HEC n/a (L=13.6km, S=.1, Trapezoidal shape, Floodplain flow)

15 Routing Result: Test 5 Flow (m3/s) 4 3 INFLOW M-CCC HEC-RAS Q p (m3/s) t p (hr) Error (%) 1, , M-C, Time (hr) HEC 1,99 4. n/a (L=5km, S=.1, Trapezoidal shape, Floodplain flow)

16 Routing Result: Test 6 Flow (m3/s) 4 3 INFLOW M-CCC HEC-RAS Q p (m3/s) t p (hr) Error (%) M-C Time (hr) HEC n/a (L=5km, S=.1, Trapezoidal shape, Floodplain flow)

17 Routing Result: Summary Test 1 Test Test 3 Test 4 Test 5 Test 6 Rank M-C

18 Correlation Analysis % Error Q p -Length 4 6 R² =.89 R² =. R² =.83 M-C % Error Q p -Slope.1..3 R² =.3 R² =. R² =.9 M-C Length, km Slope % Error Q p -Inflow 4 Peak Inflow, m3/s R² =.9 R² =.8 R² =.75 M-C 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?

19 Correlation Analysis % Error t p -Length 4 6 Length, km R² =.1 R² =.13 R² =.5 M-C % Error t p -Slope.1..3 Slope R² =.67 R² =.55 R² =.6 M-C % Error t p -Inflow 4 Peak Inflow, m3/s R² =. R² =.17 R² =.5 M-C and show similar patterns while M-C behaves differently and use the same algorithm for calculating flow velocity and travel time

20 Conclusion All methods (M-C,, and ) 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 method performed superior on combined flow (channel flow + floodplain flow) in long channels The 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 showed similar patterns in responding to hydraulic properties. The time to peak of and showed similar patterns to hydraulic properties. Both use the same equations to compute flow velocity

21 Flow Rate (m3/s) 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 5 REACHES L=1km DT=.5h S=.1 CHFP Inflow MCCC MCVC HEC-RAS Time (hr) (Test 5)

22 Questions?