Create Presentation
Download Presentation

Download Presentation

Modified Rational Method for Texas Watersheds

Download Presentation
## Modified Rational Method for Texas Watersheds

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Runoff coefficients from Land use**• 90 watersheds in Texas for us to estimate standard (table) rational runoff coefficient using ArcGIS • From a previous TxDOT project, we had a geospatial database containing watershed boundaries for 90 Texas watersheds, which were delineated using 30-meter Digital Elevation Model (DEM). • National Land Cover Data (NLCD) for 2001 were obtained for the Texas from the USGS website http://seamless.usgs.gov/. • The first task was to cut out the NLCD layer using watershed boundary for a particular watershed and find out areas of different classes of land cover within that watershed. • Clipping polygon method was used using original NAD_1983_Albers projected coordinate system.**Runoff coefficient contd..**• For clipping polygon method Raster NLCD layer converted into the polygon feature layer. • The “Clip” function of the Arc Toolbox used by selecting “Analysis Tools”, then “Extract”. • “Input Features” should be 2001 NLCD panel containing selected watershed, “Clip Features” should be the layer containing selected watershed boundary, and “Output Feature Class” is to provide a shape file name for storing clipped NLCD area. • The attribute table was opened, “Area” field added and then Calculate Geometry function was used to determine the areas for different grid (land cover) codes. • Using the Statistics and Summarize functions, the total area as well as the individual area of each land cover class for the watershed was obtained.**Runoff coefficient contd..**• Each different watershed has different land cover classes distributed inside its watershed boundary. • It was found that there were total 15 land cover classes involved for the 90 watersheds studied. • Our next task was to assign runoff coefficient for particular land cover class. • From different literature sources studied, typically we do not find runoff coefficients for most of 15 NLCD land-cover classes, but we identified similar land use types to match them. • Assuming that all of the rainfall is converted into runoff for open water and wetlands, the value of C assigned to these land-cover classes is 1. • For the other land cover classes a range of C values are available in the mentioned sources under similar land use types. • Average values were assigned for them after determining under which land use type the particular class falls or closely matches.**Runoff coefficient contd..**• A weighted C value was calculated in excel spreadsheet for each watershed using the following equation: • Weighted C value compared with “Table C” values and observed runoff coefficient values from Kirt Harle (2003) and from another TxDOT project supervised by Dr. David B. Thompson for 36 watersheds.**Future work for runoff coefficient**• Our rainfall and runoff data were in the range of date from 1960-1980. • True Land cover conditions of that time will be represented by the older NLCD. • Reliable NLCD as old as 1992 is found. • Repetition of the work for runoff coefficient calculation using the NLCD 1992 has started.**Modified Rational Method**• For MRM three different possible types of hydrograph can be developed for the given sub-basin. When rainfall duration = tc(from Wanielista, Kersten and Eaglin)**When rainfall duration > tc**Assumptions of rainfall distribution and rainfall loss: (1). Uniform rainfall distribution (2). No initial loss (3). Constant rainfall loss over the duration**(“Urban Surface Water Management” by Walesh, 1989)**• When rainfall duration < tc • MRM can be extended to applications for nonuniform rainfall distribution. • The runoff hydrograph from the MRM for the rainfall event with the duration less than the time concentration can be converted to a unit hydrograph (UH). • UH generated can be used to obtain runoff hydrographs for any nonuniform rainfall events using unit hydrograph theory (convolution).**Rational Hydrograph Method (RHM) proposed by Guo (2000,**2001) for continuous nonuniform rainfall events. • RHM was used to extract runoff coefficient and time of concentration from observed rainfall and runoff data through optimization. • Considered the time of concentration as the system memory (Singh 1982) and used a moving average window from (T-tc) and T to estimate uniform rainfall intensity for the application of the rational method to determine hydrograph ordinates. • For 0 ≤ T < tc • For tc ≤ T ≤ Td (the rainfall duration) • For Td ≤ T ≤ (Td+Tc), Guo (2001) adopted linear approximation for a small catchment**A hypothetical non-uniform rainfall event tested with**5-min MRM unit hydrograph and then with Guo’s RHM . • DRH predicted by the two methods show some differences after the rainfall ceases. • Guo’s RHM (2002, 2001) used a linear approximation from the discharge Q(Td) at the end of the rainfall event to zero at the time Td + Tc. • For nonuniform rainfall events this approximation is not correct because this will result the violation of the conservation of volume for the rainfall excess and the runoff hydrograph.**Huo et al. (2003) extended the rational formula to develop**design hydrographs for small basins for nonuniform rainfall inputs using the following design rainfall intensity formula: • Used an extended rational formula proposed by Chen and Zhang (1983) to compute the design peak flow (Qm,p) with design frequency of p and time of concentration (tc): • V. P. Singh and J. F. Cruise (1982) used a systems approach for the analysis of rational formula. • Watershed represented as a linear, time-invariant system . • Nash (1958) equation used to obtain instantaneous unit hydrograph (IUH). • for 0 ≤t ≤Tc . • for t≥ Tc • Used the convolution to derive the D-hr unit hydrograph.**A symmetric trapezoidal shape unit hydrograph obtained for**D<Tc . • for 0 ≤t ≤D • for D ≤t ≤Tc • for Tc ≤t ≤Tc + D • Concluded probability density function (PDF) of the rational method is a uniform distribution with entropy increasing with the increasing value of Tc.**MRM UH development and convolution**• For all the 90 watersheds the unit hydrograph duration (d) used is 5 minutes. • Time of concentration obtained from the square root of area of the watersheds. • We also have Tc developed using Kirpich method from three other sources: LU, UH and USGS. • We have runoff coefficients obtained from two methods Cvlit and Cvbc. • Fortran code is developed to calculate the rainfall excess and finally perform convolution to get DRH. • Different combinations of runoff coefficient and time of concentration used to get different simulated results of DRH.**Seventeen error parameters between observed and predicted**DRHs were calculated after applying MRM UH to each event. • Average/SD error parameters were estimated for all events in the same station. • Some of the events were selected randomly to plot the observed and modeled DRH. • Plot was made between the peak value of the modeled and observed discharges. • Plot was made between the relative time to peak between the modeled and observed data.**Statistical error parameters Nash - Sutcliffe efficiency**(ME) and the coefficient of determination (R2) were calculated for each run. • Gamma UH was also developed using the regression equations with MRNG Optimized Qp and Tp (Pradhan 2007) of UH. • Mean Gamma UH developed were applied to all the events corresponding to the same station to generate DRHs by convolution. • Two runs were made one with Cvbc and then with Cvlit .**Statistical summary of peak discharge results using Cvbc and**different Tc**Statistical summary of time to peak results using Cvbc and**different Tc**Statistical summary of peak discharge results using Cvlit**and different Tc**Statistical summary of time to peak results using Cvlit and**different Tc**Statisticalsummary of peak discharge results using Gamma UH**and different C**Statistical summary of time to peak results using Gamma UH**and different C