Development and testing of updated curve number models for efficient runoff estimation in steep-slope watersheds.

• Developed computationally efficient three new variants of the CN model. • Introduced flexible initial abstraction to avoid sudden jumps in runoff estimation. • New weighted score-based statistical indicators for the models' evaluation. • The proposed models outperformed in almost all watersheds. The globally adopted and computationally efficient curve number (CN) model fills an active hydrological professional niche and has a well-documented history. However, it is structurally inconsistent and fails to reliably estimate runoff from rainfall. This is mainly due to the much-debated fixed initial abstraction (λ) and associated sudden jumps in runoff based on CN obtained from the documented tables. In this study, three new variants (M4, M5, M6) of the CN model are proposed that consider the hydrological imbalance between pre-storm soil moisture and initial abstraction after a rainfall event. A total of 1837 rainfall-runoff events were analyzed from 41 steep-slope watersheds in South Korea to test the robustness of the proposed CN models. The results were compared to the recently updated original CN model (M1) and two other recent variants (M2, M3) of this model. These models were evaluated using root mean squared error (RMSE), Nash-Sutcliffe efficiency (NSE), percent bias (PB), Kling-Gupta efficiency (KGE), a proposed overall weighted score, 1:1 line graph, and the FITEVAL tool. Using data from 41 watersheds, the lowest mean (median) RMSE of M5, M6, M4 [15.54(16.56), 15.84(11.45), 18.00(16.56)], PB for M4, M6, M5 [−1.28(−1.03), 1.29(0.03), −7.06(−7.27)]; the highest mean (median) NSE for M5, M6, M4 [0.86(0.87), 0.85(0.87), 0.81(0.83)], KGE for M6, M5, M4 [0.81(0.84), 0.79(0.81), 0.79(0.81)] and other graphical assessments show a better agreement between the observed and the runoff estimated by the proposed models. The corresponding mean (median) of RMSE, PB, NSE, and KGE statistics for M2 [19.26(17.69), 9.50(10.34), 0.78(0.80), 0.77(0.79)], and M3 [19.99(18.47), 05.56(7.17), 0.76(0.79), 0.77(0.79)] models show comparatively inferior results. Based on the same statistics, the M1 [24.60(22.48), 33.62(32.77), 0.63(0.68), 0.60(0.64)] model yields unrealistic results. It is inferred that both λ and CN should be kept flexible for a systematic and region-specific revision of the CN model to improve runoff estimation. In addition, a structurally consistent model with a stable soil moisture accounting (SMA) procedure is vital to get more reliable runoff estimates without compromising the simplicity and applicability to ungauged watersheds. [ABSTRACT FROM AUTHOR]