Revisiting Modified Rational Method

Abstract

The rational method was originally developed to estimate peak discharges for sizing drainage structures, such as storm drains and culverts. The modified rational method (MRM) is an extension of the rational method to produce simple runoff hydrographs. The MRM is often called the rational hydrograph method. Application of the MRM produces a runoff hydrograph and runoff volume in contrast to application of the rational method, which produces only the peak design discharge ( Q p ). The hydrograph developed from application of the MRM is a special case of the unit hydrograph method and will be termed the modified rational unit hydrograph (MRUH) in this paper. Being a unit hydrograph, the MRUH can be applied to nonuniform rainfall distributions. Furthermore, the MRUH can be used on watersheds with drainage areas in excess of the typical limit for application of the rational method (a few hundred acres). The MRUH method was applied to 90 watersheds in Texas. Application of the MRUH method involved two steps: (1) determination of rainfall loss using rational method concept, that is, use of the runoff coefficient, and (2) determination of the MRUH using drainage area ( A ) and time of concentration ( T c ) as input parameters, in addition to applying the procedure of unit hydrograph convolution. Time of concentration was estimated using two methods: (1) the Kirpich method and (2) the square root of watershed drainage area. Runoff coefficients for application of the MRUH were estimated using two methods: The first estimate of the runoff coefficient was a watershed composite literature-based runoff coefficient ( C lit ) derived using the land-use information for the watershed and published C lit values for various land-uses. The second estimate of the runoff coefficient was a back-computed volumetric runoff coefficient, C vbc , determined by preserving the runoff volume and using observed rainfall and runoff data. Time interval used for unit hydrograph convolution was 5 minutes. Both predicted and observed discharge hydrograph ordinates were reported and compared using the same time interval. The MRUH method performed about as well as other unit hydrograph methods including the Gamma unit hydrograph and HEC-1 unit hydrograph in predicting the peak discharge of the direct runoff hydrograph, when the same rainfall loss model was used.