Application of Max-Stable Process Model in Estimating the Spatial Trend & Dependency of Extremes in the Northern Great Plains
Authors: Boluwade Alaba 
Published: February 2023

&lt;p&gt;Alaba Boluwade*&lt;/p&gt;
&lt;p&gt;School of Climate Change &amp; Adaptation, University of Prince Edward Island, Charlottetown, Canada; aboluwade@upei.ca; abolu2013@gmail.com&lt;/p&gt;
&lt;p&gt;*Correspondence: aboluwade@upei.ca&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Abstract &lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;Hydrological risk assessment, such as flood protection, requires estimates of variables (e.g., precipitation) measured from several weather stations. The spatial modeling of average rainfall estimates differs from extreme precipitation analysis. This is because extremes are focused on the tail of the probability distribution and the assumption of Gaussianity may not be suitable. Extreme Value Theory (EVT) application to univariate weather variables measured at weather stations has been well documented; however, extreme precipitation at closer stations tend to show trends and dependencies (similar values). It is, therefore, crucial to quantify the dependency structure and trend surface of weather stations in space. The max-stable process has been well documented to model spatial extremes. The objective of this study is to quantify the spatial dependency and trend of an annual maxima precipitation (annual highest daily precipitation, from 1970-2020) across selected weather stations in the Northern Great Plains (i.e., Nelson Churchill River Basin (NCRB)) of North America. The annual maxima data were extracted from the Global Historical Climatology Network Daily (GHCNd) and Environment and Climate Change Canada (ECCC). NCRB covers four states and four provinces in the United States and Canada. A heterogenous rainfall pattern characterizes NCRB. This is due to enormous quantities of orographic rainfall in the west and the convective precipitation in the Prairies (which is dominated by short-duration, sporadic, extreme rain), causing millions of dollars in damages. This study uses max-stable processes to examine spatial extremes of annual maxima precipitation.&lt;/p&gt;
&lt;p&gt;The results show that topography, time, and geographical coordinates were important covariates in reproducing the stochastic extreme precipitation field using the spatial generalized extreme value (SPEV). Takeuchi&amp;#8217;s information criterion (TIC) shows that the SPEV model with all the covariates above superseded the one without the covariates.&amp;#160; &amp;#160;The inclusion of time as a covariate further confirms the impacts of climate change on extreme precipitation in the NCRB. The fitted Extremal-t max-stable model captured the spatial dependency and equally predicted the 50-year return period levels. Furthermore, ten realizations (equal probable) were simulated from the max-stable model. The study is relevant in quantifying the spatial trend and dependency of extreme precipitation in the Northern Great Plains. The result will help as a decision-support system in climate adaptation strategies in the United States and Canada.&lt;/p&gt;
&lt;p&gt;&lt;em&gt;&amp;#160;&lt;/em&gt;&lt;/p&gt;
&lt;p&gt;&lt;em&gt;Keywords: extreme events; Max-Stable processes; flood protection; maxima annual rainfall; flash flood protection; Canada, United States&lt;/em&gt;&lt;/p&gt;