Proficiency of probability distributions in unit hydrograph derivation

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, R-2, NSE, MSE, RMSE, MAE, MAPE, and SE in GRG-NLP optimization, 18 known and 12 adaptable 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 (q(p)), time to peak (t(p)), and time base (t(b)) 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 closed than did the known PDFs, like Inverse Gaussian, 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 center dot The present study evaluates the adequacy of 30 (18 old +12 new) probability density functions (PDFs) for unit hydrograph development. center dot The novel PDFs are more promising than existing PDFs in the literature. center dot Proposed PDFs with simple formulaic structures are easily adaptable as executables using a calculator. center dot The incomplete-Gamma distribution has the highest ability for q(p) and t(p). center dot Maple codes are provided for all PDFs.