SCS-CN METHOD REVISITED USING ENTROPY THEORY Academic Article uri icon

abstract

  • The SCS-CN method is one of the most popular methods for computing runoff from small watersheds (agricultural, forest, rural, and urban) for individual rainfall events. This study revisits the method using the entropy theory, which provides insights into the structure of the method and permits derivation of the probability distributions of the variables (CN = curve number, S = maximum soil moisture retention, P = precipitation, J = cumulative infiltration, I a = initial abstraction, and Q = surface runoff) inherent in the method if they are assumed random. If the variables are continuous, then the derivation of the distributions is based on the maximization of the Shannon entropy, subject to given constraints, and the derived distributions are non-parametric. If the variables are discrete, then the derivation is based on the maximization of cross entropy, subject to fractile constraints, wherein prior probability distributions are derived by Shannon entropy maximizing. The derived distributions are tested using field data. It is found that the SCS-CN method requires no information for the probability distribution of runoff associated with it, other than obeying the total probability law. Employing four statistical measures, including Akaike information criterion (AIC), Bayesian information criterion (BIC), bias (BIAS), and root mean square error (RMSE), to determine the goodness-of-fit of probability distributions to 100-CN, Q, P, S, Q/(P-Ia), and J/S, it is found that the gamma distribution, on the whole, is the preferred distribution. 2013 American Society of Agricultural and Biological Engineers.

published proceedings

  • TRANSACTIONS OF THE ASABE

author list (cited authors)

  • Singh, V. P.

citation count

  • 5

complete list of authors

  • Singh, VP

publication date

  • November 2013