A Probabilistic Model for Maximum Rainfall Frequency Analysis

As determining the probability of exceedance maximum precipitation over a specified duration is critical to hydrotechnical design, particularly in context climate change, model was developed perform frequency analysis duration. The PMAXΤP (Precipitation MAXimum Time (duration) Probability) harbors pair computational modules fulfilling different roles: (i) statistical series, and (ii) estimation for its exceedance. input data consist homogeneous 30-element series values 16 durations: 5, 10, 15, 30, 45, 60, 90, 120, 180, 360, 720, 1080, 1440, 2160, 2880, 4320 min, obtained through Annual Maximum Precipitation (AMP) Peaks-Over-Threshold (POT) approaches. includes: detecting outliers using Grubbs-Beck test; checking random variable’s independence Wald-Wolfowitz test Anderson serial correlation coefficient (iii) stationarity nonparametric tests, e.g., Kruskal-Wallis Spearman rank trends mean variance; (iv) identifying trend variables regression analysis, including an evaluation form function; (v) internal autocorrelation test. To estimate precipitations with exceedance, three-parameter theoretical distributions were used: shifted gamma distribution (Pearson type III), log-normal distribution, Weibull (Fisher-Tippett log-gamma as well two-parameter Gumbel distribution. best selected by: likelihood parameters; tests hypothesis goodness fit function empirical Pearson’s χ2 selection best-fitting within each according criterion minimum Kolmogorov distance; most credible from set various types functions Akaike information criterion; verification single-dimensional fit: Kolmogorov-Smirnov test, Anderson-Darling Liao-Shimokawa Kuiper’s PMAXTP tested on two meteorological stations northern Poland (Chojnice Bialystok) drawn digital database high-resolution records period 1986 2015, available 100 (i.e., Polish Atlas Rainfall Intensities (PANDa)). Values compared probabilistic Bogdanowicz-Stachý model. comparative based standard error fit, graphs density estimated quantile errors. errors lower For both stations, smallest quantiles determined basis POT PMAXTP.