water Article Effect of Time-Resolution of Rainfall Data on Trend Estimation for Annual Maximum Depths with a Duration of 24 Hours Renato Morbidelli 1, * , Carla Saltalippi 1 , Jacopo Dari 1,2 and Alessia Flammini 1   Citation: Morbidelli, R.; Saltalippi, C.; Dari, J.; Flammini, A. Effect of Time-Resolution of Rainfall Data on Trend Estimation for Annual Maximum Depths with a Duration of 24 Hours. Water 2021, 13, 3264. https://doi.org/10.3390/w13223264 Academic Editor: Ataur Rahman Received: 11 October 2021 Accepted: 16 November 2021 Published: 17 November 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Department of Civil and Environmental Engineering, University of Perugia, via G. Duranti 93, 06125 Perugia, Italy; carla.saltalippi@unipg.it (C.S.); jacopo.dari@unipg.it (J.D.); alessia.flammini@unipg.it (A.F.) 2 National Research Council, Research Institute for Geo-Hydrological Protection, via Madonna Alta 126, 06128 Perugia, Italy * Correspondence: renato.morbidelli@unipg.it; Tel.: +39-075-5853620 Abstract: The main challenge of this paper is to demonstrate that one of the most frequently con- ducted analyses in the climate change field could be affected by significant errors, due to the use of rainfall data characterized by coarse time-resolution. In fact, in the scientific literature, there are many studies to verify the possible impacts of climate change on extreme rainfall, and particularly on annual maximum rainfall depths, H d , characterized by duration d equal to 24 h, due to the significant length of the corresponding series. Typically, these studies do not specify the temporal aggregation, t a , of the rainfall data on which maxima rely, although it is well known that the use of rainfall data with coarse t a can lead to significant underestimates of H d . The effect of t a on the estimation of trends in annual maximum depths with d = 24 h, H d=24 h, over the last 100 years is examined. We have used a published series of H d=24 h derived by long-term historical rainfall observations with various temporal aggregations, due to the progress of recording systems through time, at 39 representa- tive meteorological stations located in an inland region of Central Italy. Then, by using a recently developed mathematical relation between average underestimation error and the ratio t a /d, each H d=24 h value has been corrected. Successively, commonly used climatic trend tests based on different approaches, including least-squares linear trend analysis, Mann–Kendall, and Sen’s method, have been applied to the “uncorrected” and “corrected” series. The results show that the underestimation of H d=24 h values with coarse t a plays a significant role in the analysis of the effects of climatic change on extreme rainfalls. Specifically, the correction of the H d=24 h values can change the sign of the trend from positive to negative. Furthermore, it has been observed that the innovative Sen’s method (based on a graphical approach) is less sensitive to corrections of the H d values than the least-squares linear trend and the Mann–Kendall method. In any case, the analysis of H d series containing potentially underestimated values, especially when d = 24 h, can lead to misleading results. Therefore, before conducting any trend analysis, H d values determined from rainfall data characterized by coarse temporal resolution should always be corrected. Keywords: rainfall data measurements; rainfall time resolution; extreme rainfall; annual maximum rainfall depths; trend analysis 1. Introduction It is well known that climate change is mainly due to greenhouse gas emissions from human activities [1]. One of the most important consequences is the modification of the hydrologic cycle with significant implications for water resources [2–5]. In the last century, mean global surface temperatures showed an increase of approximately 1.1 ◦ C[6] and, based on the Clausius–Clapeyron relation, for each 1 ◦ C increase in global temperature, the precipitable water increases by ~7% [7,8], even though relative humidity appears to decrease at high temperatures [1,8–10]. Moreover, it is expected that temperature will increase near to the surface and will decrease in the upper troposphere, favoring Water 2021, 13, 3264. https://doi.org/10.3390/w13223264 https://www.mdpi.com/journal/water