Water 2023, 15, 128. https://doi.org/10.3390/w15010128 www.mdpi.com/journal/water Article An Area-Orientated Analysis of the Temporal Variation of Extreme Daily Rainfall in Great Britain and Australia Han Wang 1,2,3 and Yunqing Xuan 3, * 1 China Institute of Water Resources and Hydropower Research, Beijing 100038, China 2 Research Center on Flood & Drought Disaster Reduction of the Ministry of Water Resources, Beijing 100038, China 3 Department of Civil Engineering, Swansea University Bay Campus, Fabian Way, Swansea SA1 8EN, UK * Correspondence: y.xuan@swansea.ac.uk Abstract: This paper presents an analysis of the temporary variation of the area-orientated annual maximum daily rainfall (AMDR) with respect to the three spatial properties: location, size and shape of the region-of-interest (ROI) in Great Britain and Australia using two century-long datasets. The Maximum Likelihood and Bayesian Markov-Chain-Monte-Carlo methods are employed to quantify the time-varying frequency of AMDR, where a large proportion of the ROIs shows a non-decreasing level of most frequent AMDR. While the most frequent AMDR values generally decrease with larger-sized ROIs, their temporal variation that can be attributed to the climate change impact does not show the same dependency on the size. Climate change impact on ROI-orientated extreme rain- fall is seen higher for rounded shapes although the ROI shape is not as significant as the other two spatial properties. Comparison of the AMDR at different return levels shows an underestimation by conventionally used stationary models in regions where a nonstationary (i.e., time-varying) model is preferred. The findings suggest an overhaul of the current storm design procedure in view of the impact of not only climate change but also spatial variation in natural processes. Keywords: extreme rainfall; spatial variation; return period; GEV; climate change; nonstationarity 1. Introduction Applications of extreme value (EV) theory in modelling meteorological and environ- mental processes have been widely practised in designing and validating many infra- structure systems [1]. A classical analysis approach adopted in these applications is to use historical hydro-climatic data, such as rainfall, temperature, river flows, etc., to estimate the parameters of the required EV model which would offer probability distributions of the natural phenomenon in question, so as to address its occurrence or exceedance prob- ability at given thresholds. Since Jenkinson [2] proposed a generalized approach to ana- lysing the frequency distribution of annual maxima, many efforts have been made to quantify natural phenomena at extreme levels using the Generalized Extreme Value (GEV) models whose parameters are often fitted by using the Maximum Likelihood (ML) method and L-Moments (LM) method, especially in designing and planning water engi- neering systems [3–7]. Recently, there has been a growing interest in studying natural events from a climate- change perspective, given that the key hydroclimatic variables, such as precipitation, tem- perature and streamflow, are indeed changing due to the impact of climate change [8,9]. To address the reliability of infrastructure designs based upon extreme value analysis, stationary risk analyses have been re-assessed from a new adaptive perspective where Sarhadi [10] proposed a multivariate time-varying risk framework for all stochastic mul- tidimensional systems under the influence of a changing environment. For the commonly used nonstationary GEV models, this means that their scale and location parameters can Citation: Wang, H.; Xuan, Y. An Area-Orientated Analysis of the Temporal Variation in Extreme Daily Rainfall in Great Britain and Australia. Water 2023, 15, 128. https://doi.org/10.3390/w15010128 Academic Editor: Aizhong Ye Received: 24 November 2022 Revised: 23 December 2022 Accepted: 28 December 2022 Published: 29 December 2022 Copyright: © 2022 by the authors. Li- censee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and con- ditions of the Creative Commons At- tribution (CC BY) license (https://cre- ativecommons.org/licenses/by/4.0/).