This paper further modifies soil conservation service curve number (SCS-CN) based on the concept of adjusting the rainfall in accordance with rain duration and considering the initial abstraction (Ia) as a fraction of rainfall for runoff estimation. The former yields Model M3 and its explicit form with constant parameter λ = 0.2 is designated as Model M4. Model M5 couples both the concepts and thus all these models are the advanced versions. The applicability of all the five models is tested using a large number of rainfall-runoff events (25,502) derived from 53 U.S. Department of Agriculture-Agricultural Research Service watersheds. Models M3–M5 performed better than Models M1 and M2. Model performance is evaluated by employing six statistical measures, namely, root mean square error, mean absolute error, normalized root mean square error, Nash–Sutcliffe coefficient (%), percent Bias, RSR, n(t), and several grading criteria. Results show Model M5 to have performed the best of all in both calibration and validation largely due to its incorporating the impact of rain duration and allowing Ia to vary with rainfall, which is close to reality and not accounted for in any other models considered in this study.

  • An enhanced mathematical SCS-CN model for estimating direct surface runoff by storm duration and rainfall-based initial abstraction is suggested in this study.

  • Performance of the model is also evaluated by different indicators and compared with existing models.

  • The proposed model shows robust performance in surface runoff prediction.

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