Modified CN Method for Small Watershed Infiltration Simulation

Infiltration is an essential process in watershed hydrology. The curve number (CN) method has been widely used to calculate watershed infiltration for a given rainfall input but does not consider steady infiltration. This study develops a modified CN (MCN) method that included a term for the steady infiltration amount ($F_c$). Observed rainfall–runoff data for 14 rainfall events from a typical small watershed on the Loess Plateau of China were used to derive the watershed final infiltration rate ($f_c$). Watershed infiltration after runoff initiation was then calculated by both the MCN and CN methods using initial abstraction values that were either observed ($I_{a-obs}$) or calculated ($I_{a-0.2S}$) based on the calibrated $f_c$. Three criteria [relative error ($E_r$), model efficiency coefficient ($E$), and root mean square error (RMSE)] and visual assessments of graphed results were used to evaluate the methods’ simulation performances. The MCN method generally outperformed the CN method when using either of the initial abstractions for infiltration calculations. Moreover, infiltration calculated by the MCN method was more accurate when using $I_{a-\mathrm{obs}}$ ($E=0.9$; $\mathrm{RMSE}=24.4\%$) than when using $I_{a-0.2S}$ ($E=0.8$; $\mathrm{RMSE}=30.8\%$). The CN method using either initial abstraction tended to underestimate infiltration, especially higher values, which were always lower than the MCN method estimates. In addition, watershed runoff was calculated by both methods using only $I_{a-\mathrm{obs}}$. The MCN method ($E=0.4$ and $\mathrm{RMSE}=78.1\%$; excluding 3 outliers) outperformed the CN method ($E=-23.8$ and $\mathrm{RMSE}=506.8\%$; excluding 3 outliers) but not to the same extent as when calculating infiltration. The theoretical analyses and practical application results indicated that the MCN method is more appropriate than the CN method for predicting infiltration in small watersheds on the Loess Plateau.