Two universal runoff yield models: SCS vs. LCM

Abstract

Runoff calculation is one of the key components in the hydrological modeling. For a certain spatial scale, runoff is a very complex nonlinear process. Currently, the runoff yield model in different hydrological models is not unique. The Chinese LCM model and the American SCS model describe runoff at the macroscopic scale, taking into account the relationship between total actual retention and total rainfall and having a certain similarity. In this study, by comparing the two runoff yield models using theoretical analyses and numerical simulations, we have found that: (1) the SCS model is a simple linear representation of the LCM model, and the LCM model reflects more significantly the nonlinearity of catchment runoff. (2) There are strict mathematical relationships between parameters (R, r) of the LCM model and between parameters (S) of the SCS model, respectively. Parameters (R, r) of the LCM can be determined using the research results of the SCS model parameters. (3) LCM model parameters (R, r) can be easily obtained by field experiments, while SCS parameters (S) are difficult to measure. Therefore, parameters (R, r) of the LCM model also can provide the foundation for the SCS model. (4) The SCS model has a linear relationship between the reciprocal of total actual retention and the reciprocal of total rainfall during runoff period. The one-order terms of a Taylor series expansion of the LCM model describe the same relationship, which is worth further study.