Hydrologists need to predict extreme hydrological and meteorological events for design purposes, whose magnitude and probability are estimated using a probability distribution function (PDF). The choice of an appropriate PDF is crucial in describing the behavior of the phenomenon and the predictions can differ significantly depending on the PDF. So, the success of the probability distribution function in representing the data of extreme value series of natural events such as hydrology and climatology is of great importance. Depending on whether the series consists of maximum or minimum values, the theoretical probability density function must be appropriately fit to the right or left tail of the extreme data, which contains the most critical information. This study includes a combined evaluation of the performance of four different tests for selecting the appropriate probability distribution of maximum rainfall in Türkiye: Kolmogorov–Smirnov (KS) test, Anderson–Darling (AD) test, Probability Plot Correlation Coefficient (PPCC) test, and L-Moments Z^DIST test. Within the scope of the study, maximum rainfall series of seven rainfall durations from 15 to 1440 min, at rain gauge stations in 81 provinces of Türkiye, were examined. Goodness of fit was performed based on ranking using a combination of four different numerical tests (KS, AD, PPCC, Z^DIST). The probabilistic character of maximum rainfall was evaluated using a large dataset consisting of 567 time series with record lengths ranging from 45 to 80 years. The goodness of fit of distributions was examined from three different perspectives. The first is an examination considering rainfall durations, the second is a province-based examination, and the third is a general country-based assessment. In all three different perspectives, the Wakeby distribution was determined as the best fit candidate to represent the maximum rainfall in Türkiye.

The fact that 2023 and subsequently 2024 were the hottest years in history makes it even more important to monitor temperature changes over time. In this study, trends in the mean, maximum, and minimum temperature data of 81 provinces in Türkiye were examined using three traditional methods (Mann–Kendall, Linear Regression Analysis and Sen’s slope), one innovative method (ITA), and the QuarTrend (QT) method proposed in this study, which uses quartiles of the data series. The objectives of this research are (1) to determine and evaluate the long-term temperature trends in Türkiye (1960–2022) and (2) to comparatively evaluate the trend results of the proposed QT method, traditional trend detection methods, and ITA. In the study, a statistically significant (p < 0.05) increasing trend was found in the mean (0.027 °C/year), maximum (0.031 °C/year), and minimum (0.038 °C/year) annual temperatures of Türkiye. While traditional trend tests detected similar trends with ITA and QT for mean temperatures; ITA and QT detected more trends than traditional methods for maximum and minimum temperatures. The results have direct implications for the impacts of climate change in the study region. The results have the potential to support the development of climate-resilient and adaptive policies for effective water resource planning and management to sustain the environment and agricultural productivity in Türkiye.