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Modified Rational Method for Texas Watersheds11Runoff coefficients from Land use90 watersheds in Texas for us to estimate standard (table) rational runoff coefficient using ArcGISFrom 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.22Runoff 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.

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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.

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5Runoff coefficient contd..A weighted C value was calculated in excel spreadsheet for each watershed using the following equation:

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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.

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8Future 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.

9 Modified Rational MethodFor MRM three different possible types of hydrograph can be developed for the given sub-basin.

10When rainfall duration = tc

(from Wanielista, Kersten and Eaglin)

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Assumptions of rainfall distribution and rainfall loss:(1). Uniform rainfall distribution(2). No initial loss(3). Constant rainfall loss over the duration

When rainfall duration > tcMRM 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). 12When rainfall duration < tc

(Urban Surface Water Management by Walesh, 1989)

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

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A hypothetical non-uniform rainfall event tested with 5-min MRM unit hydrograph and then with Guos RHM .DRH predicted by the two methods show some differences after the rainfall ceases.Guos 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.1414Huo 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.

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15A symmetric trapezoidal shape unit hydrograph obtained for D