Proficiency of probability distributions in unit hydrograph derivation

Abstract

The probability distribution function (PDF)-based unit hydrographs (UHs) are gaining momentum in an application for more accurate rainfall-runoff transformation. Employing seven statistical performance indices, R2, NSE, MSE, RMSE, MAE, MAPE, and SE in generalized reduced gradient nonlinear programming (GRG-NLP) optimization, 18 known and 12 adaptable PDF-based UHs were assessed against UHs derived from 18 storms in 7 basins across the United States, Turkey, and India. To this end, 27 Maple codes were proposed for UH-application requiring only peak discharge (qp), time to peak (tp), and time base (tb) for derivation. The introduced PDFs, such as Dagum, Generalized Gamma, Log-Logistic, Gumbel Type-I, and Shifted Gompertz, replicated the observed data-derived UHs more closely than did the known PDFs, like Inverse Gaussian, two-parameter gamma distribution (2-PGD), Log-Normal, Inverse-Gamma, and Nagakami. Among the three-parameter (6 nos.), two-parameter (21 nos.), and single-parameter (3 nos.) PDFs, the Dagum, Log-Logistic, and Poisson consistently outperformed their respective counterparts in replication. HIGHLIGHTS The present study evaluates the adequacy of 30 (18 old +12 new) probability density functions (PDFs) for unit hydrograph development.; The novel PDFs are more promising than existing PDFs in the literature.; Proposed PDFs with simple formulaic structures are easily adaptable as executables using a calculator.; The incomplete-Gamma distribution has the highest ability for qp and tp.; Maple codes are provided for 27 PDFs.;

Keywords

• maple code
• peak discharge
• probability distribution function-pdf
• time base
• time to peak
• unit hydrograph-uh