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Establish Effective Lower Bounds of Watershed Slope for Traditional Hydrologic Methods

Establish Effective Lower Bounds of Watershed Slope for Traditional Hydrologic Methods. Manoj KC and Xing Fang May 11-13, 2009 For TxDOT project 0-6382. DIFFUSION HYDRODYNAMIC MODEL(DHM). It couples two-dimensional overland flow and one-dimensional open channel flow.

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Establish Effective Lower Bounds of Watershed Slope for Traditional Hydrologic Methods

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  1. Establish Effective Lower Bounds of Watershed Slope for Traditional Hydrologic Methods Manoj KC and Xing Fang May 11-13, 2009 For TxDOT project 0-6382

  2. DIFFUSION HYDRODYNAMIC MODEL(DHM) It couples two-dimensional overland flow and one-dimensional open channel flow. It is based on the diffusion form of the St. Venant equation dominated by pressure, gravity, and friction forces. It is a numerical model based on an explicit, integrated finite-difference scheme. It accommodates several important hydraulic effects like backwater effects, channel overflow, combined overland flow and storage effects, and ponding which are neglected by kinematic methods. The catchment is represented by topographic elevation and geometric data.

  3. DIFFUSION HYDRODYNAMIC MODEL(DHM) Some previous applications of the model include: - rainfall-runoff modeling, - development of synthetic S-graphs for unit hydrograph studies, - modeling of the flooding of the watershed due to open channel deficiencies, - large scale flood plain dam-break analysis, - small scale flood plain dam-break analysis, - temporary flood control debris-basin failure onto a broad plain.

  4. GOVERNING EQUATION OF DHM The 1-D governing equation of DHM: - where Qx is the flow rate; x and t are spatial and temporal coordinates; Ax is the flow area; H is water surface elevation; n is manning’s roughness coefficient, R is hydraulic radius; and mx is the momentum quantity defined as follows.

  5. GOVERNING EQUATION OF DHM For convective acceleration model For local acceleration model For coupled model For DHM

  6. COMPUTER PROGRAM FOR DHM DHM computer code consists of 2-D flood plain model, 1-D channel model, and an interface sub-model. The interface model updates the water surface elevations of grid (flood plain) and channel elements at specified time intervals. The kinematic routing technique can also be revoked by setting KMODEL to 1 for the comparison between two models. Variable time step algorithm used in the model dramatically reduces the computational time.

  7. INPUT FILE FOR DHM Separate program has been developed for the creation of input data file for DHM by researcher at Auburn University - the input file contains the following information: - minimum and maximum allowable time step - decrement and increment time step - total simulation time and output time - tolerance for depth change and surface detention - number and dimensions of grids in floodplain and channel - north, east, south and west cells, manning’s roughness coefficient, elevation and depth of the grid surrounding - similar data for channel elements - rainfall data, critical output node and output node for discharge

  8. TESTING OF DHM DHM was tested for channel-floodplain model of a hypothetical watershed. It was also tested for 5 other catchments for -sensitivity of DHM S-graph to effective rainfall intensity -sensitivity of DHM S-graph to watershed area and slope -sensitivity of DHM S-graph to manning’s friction factor -sensitivity of DHM S-graph to catchment shape DHM was also used to verify results for 2-D overland simulations by Su and Fang (2003).

  9. TESTING OF DHM Discharge variation for different excess rainfall intensity The outflow node is indicated by the arrow.

  10. TESTING OF DHM Sensitivity of DHM S-Graph to effective rainfall intensity S-Graph varied depending upon the effective rainfall intensity. When it is normalized with respect to maximum discharge and lag, the S-graphs became nearly coincident indicating the dominance of lag value in this technique (lag from 0 to 50% Qp)

  11. TESTING OF DHM Sensitivity of DHM S-graph to watershed area For this case the nodal elevations are held constant, as the grid size is increased catchment size is increased but the slope is decreased. Watershed lag differed depending upon area and slope but when normalized produced similar graphs.

  12. TESTING OF DHM Sensitivity of DHM S-graph to watershed slope For this case the nodal elevations are changed accordingly as the cross -fall slope while the grid size is held constant. Watershed lag differed depending upon slope but when normalized produced similar graphs.

  13. TESTING OF DHM Sensitivity of DHM S-graph to Manning’s friction factor Manning’s friction factor was varied to get the identical S-graph for constant effective rainfall. Watershed lag differed depending upon manning’s roughness factor, lag was directly proportional to the roughness factor.

  14. Sensitivity of DHM S-graph to the combination of catchment area and effective rainfall intensity Area = 5 miles 2 Area =10 miles 2

  15. TESTING OF DHM From these tests it can be inferred that DHM produced S-graphs are relatively insensitive to constant effective rainfall intensity, watershed area and slope, and the Manning’s roughness factor. The S-graphs so produced changed very slightly to the combination of changing rainfall intensity and catchment area. The watershed lag decreases with increasing constant effective rainfall intensity.

  16. The watershed lag and the constant effective rainfall intensity, i are related by Lag(i)=k1*ik2 k1, k2 are constants for a watershed. From regression analysis, k2 = -0.401 for each watershed. The watershed lag varied highly for low effective rainfall.

  17. For low-effective rainfall intensity the catchment behaved as non-linear system in terms of watershed lag values. For high intensity of effective rainfall, the variation in lag values is small and the watershed is expected to behave as a linear system.

  18. TESTING OF DHM When the backwater effects are neglected (i.e., when flows are all free draining) the kinematic and diffusion hydro- dynamic models produce similar results as shown in the figure aside.

  19. TESTING OF DHM The S-Graph from kinematic model when it is normalized produces similar results as that of DHM.

  20. The figures show the resulting hydrographs for the three storm patterns of variable rainfall input

  21. The hydrographs from the diffusion and kinematic wave models are similar. The hydrograph from the linear unit hydrograph method gives different result mostly in peak discharge depending on the type of storm pattern.

  22. The figure shows the hydrographs produced by the diffusion and the kinematic wave models for the different values of Manning’s friction factors. The peak discharge decreases as the Manning’s friction factor is increased significantly.

  23. TESTING OF DHM The DHM model was also tested for Su-Fang 2-D numerical model of the overland flow: The model was tested in a rectangular watershed (basin) of length 35 m and width 10 m with grid size of 5 m with constant effective rainfall over 12 hours. The traveling time was calculated from the relationship of discharge versus time at the point of 95.5% of the maximum discharge. The maximum discharge calculated from DHM model for various tests as given in the following table is in good agreement with the value by the Rational Method.

  24. Recreation of the Table 1 from Dehui Su and Xing Fang-2003 showing the simulated Travel Time from DHM.

  25. The figure shows the variation of discharge with time for the test T1-n1 as given in the table for each mesh. The travel time is directly proportional to the travel length of the flow in the water- shed. The travel time is also directly proportional to the Manning’s roughness coefficient.

  26. The figure shows the variation of discharge with time for the test for smaller and even zero slope. The travel time is inversely proportional to the basin slope of the watershed. The tests in table t2-i shows that travel time decreases with increase in rainfall intensity.

  27. Testing DHM for Small Scale Testing Plots Rainfall Test: The figure shows one of the testing plots (6 ft wide by 30 ft long) for the Rainfall Test performed by Dr. Ming-Han Li and his students through the TxDOT project 4404-2.

  28. Series-1 : gross rainfall intensity for total storm period Series-2: gross rainfall intensity considering initial abstractions for the first six minutes. Series-3: Effective rainfall intensity considering initial abstractions (TR = 0.6545”, initial loss = 0.187”, excess = 0.076”) Series-4: Field data from Ming-Han Li’s experiment.

  29. Discussion • “Infiltration rate = 0.0358 – 0.0598 in/hr” • Antecedent soil moisture (on bare clay, lawn and pasture): 8 – 54% • Resulting infiltration loss will be 0.0125 – 0.0209” over 21 rainfall input <<< estimated from runoff hydrograph.

  30. The figures show the comparisons of runoff variation between the field tests performed by Dr. Ming-Han Li (TxDot-4404-2) and the result from DHM. The rainfall loss affected the peak discharge to a greater extent than the travel time.

  31. Impulse Runoff Test The figure shows one of the testing plots (6 ft wide by 30 ft long) for the impulse runoff test performed by Dr. Ming -Han Li and his students through the TxDOT project 4404-2. The hydroseeder was used as the water source for the reservoir and the overflow from a weir as inflow hydrograph.

  32. “Measure travel time after water overtopped the weir until the waterfront reaches the outlet” –(Cahill and Li, 2005) The overflow from the reservoir through the weir at t = 0 is not equal to the flow from the hydroseeder, the inflow hydrograph as input for the DHM model was delayed. The calculation shows the overflow from the weir equals the inflow from the hydroseeder takes 10 seconds (approximately) after the water overtopped the weir for the flow rate of 41.2 gpm.

  33. The series-1 in the above graph is the recreation of the figure F.1 from Ming-Han Li’s Report TX-04/0-4404-2. Q starts at 1 minutes

  34. The series-2, 3, 4 in the above graph are the results produced from DHM model which show the variation of travel time with ending flow rates. The input discharge is delayed by 1 min. The travel time for series-2 is the time when flow just starts to appear at the outlet of the plot; for series-3 and -4, they are the travel times corresponding to 80% and 100% of peak discharge at the outlet respectively. (hydroseeder)

  35. The flow line in green shows the shortest path for travel time in the test plot (Ming- Han Li’s experiment). The travel time is the time when the flow starts to occur at the outlet. The flow line in black shows the longer path for travel time in the test plot since the water can only flow out from the middle node. The travel time therefore is longer than that of green flow line.

  36. FUTURE TAKS Integration of rainfall loss process in the model. Verification Ming-Han Li other test results -Rainfall tests -Impulse runoff tests Testing of the model with real watershed’s data. Testing of the model from the data collected for the current project by Ming-Han Li.

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