A mathematical model for estimating surface runoff from small watersheds

Linking normalized antecedent precipitation index(NAPI) with the antecedent soil moisture content (AMC) and AMC to the losses of precipitation that abstain runoff, a process based rainfall-runoff model for predicting runoff yields from a watershed has been developed using the basic water balance equation. The mathematical structure of the model is described by the rainfall dependent derived variable “NAPI’ and three watershed specific parameters. The ‘NAPI’ of a rainfall event for which runoff is to be predicted can be determined from its 5-antecedent days rainfall events, and the parameters can be estimated from the historical time-series data of rainfall-runoff events of that watershed using the least squares optimization. Performance of the proposed model has been compared with the Soil Conservation Service-Curve Number (SCS-CN) model. The proposed model has resonance with the SCS-CN model, and explained the CN associated physical processes more convincingly. For a known value of CN, the model parameters can also be obtained using the mapped parametric relationships. The proposed model has been tested with the field data of three watersheds located in the semi-arid region of India. The results exhibited a better match to the field data by the proposed model than the SCS-CN model. Unlike necessity of substantial auxiliary data which mostly found missing for small watersheds as required by the SCS-CN model to determine CN, the proposed model needs minimum database and less skills to simulate rainfall-runoff events.