A Probabilistic Model for Maximum Rainfall Frequency Analysis

Abstract

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

Effectiveness of Measures to Reduce the Influence of Global Climate Change on Tomato Cultivation in Solariums. Case Study: CrișUrilor Plain, Bihor, Romania

“…Comparing the ETRo values of tomatoes, obtained starting from the assurance of the air temperature of 80 %, with those obtained in the period 1999-2001, using the Piche evaporimeter [63], they are lower than 7153.1 m 3 ha -1 for WM and 6958.3 m 3 ha -1 respectively, for MBF. If we take into account the ETRo of tomatoes grown in solariums, estimated in 2018, starting from the insurance of not exceeding the precipitation, of 80 % [69], they are higher than those determined from the insurance air temperature, with: 597.5 m 3 ha -1 for the WM variant and 668.4 m 3 ha -1 , respectively, for the MBF variant.…”

“…The agricultural year for which the average outside temperature, of vegetation period (Apr-Sep), exceeds the insurance of 20 % was established using the data recorded at the Oradea Meteorological Station in the period 1970-2018. The Pearson type III function [69] was used to determine the probability of exceeding the air temperature, having the relation (1):…”

Flood Management Issues in Hilly Regions of Uttarakhand (India) under Changing Climatic Conditions

“…Now, the rainfall events of the monsoon season (JJAS) are considered to estimate the number of extreme monthly flood events. The probability of exceedance, i.e., the Weibull method [36], is applied to estimate the suitable threshold. For this estimation, it is necessary to sort all the rainfall data in decreasing order and assign a serial order number ranging from 1 to n. The formula is given by, 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑒𝑥𝑐𝑒𝑒𝑑𝑎𝑛𝑐𝑒 𝑃𝐸 (6) where m = rank order and n = number of events The probability of exceedance value of 5% is selected as a threshold to estimate the number of extreme flood events.…”

“…Now, the rainfall events of the monsoon season (JJAS) are considered to estimate the number of extreme monthly flood events. The probability of exceedance, i.e., the Weibull method [36], is applied to estimate the suitable threshold. For this estimation, it is necessary to sort all the rainfall data in decreasing order and assign a serial order number ranging from 1 to n. The formula is given by,…”

Modeling the Semivariogram of Climatic Scenario around Rivers by Using Stream Network Mapping and Hydrological Indicator

“…There is no doubt that climate changeability has given rise to harsh meteorological circumstances and has uninterruptedly disturbed the flow pattern of seas, rivers, and oceans together with the quality of surface water, particularly rivers and streams [1,2]. With the initiation of more flooding or overflowing and famines, warmer air is produced and excessive water content is held, which in turn makes precipitation styles extreme [3,4].…”