A non-parametric procedure to assess the accuracy of the normality assumption for annual rainfall totals, based on the marginal statistics of daily rainfall: An application to NOAA-NCDC rainfall database

In an effort to assess the accuracy of the normality assumption for annual rainfall totals (ART) in data-poor regions, we develop a non-parametric procedure based on the marginal statistics of daily rainfall. In doing so we start by using three goodness-of-fit metrics to conclude on the approximate convergence of the empirical ART distribution to a normal shape, and classify daily rainfall timeseries into Gaussian (G) and non-Gaussian (NG) groups. At a second step, we apply logistic regression analysis to identify the statistics of daily rainfall that are most descriptive of the G/NG classification. In the third and final step, we use a random-search algorithm to conclude on a set of constraints to classify ART samples based on the marginal statistics of daily rainrates. The analysis is conducted using 3007 daily rainfall timeseries from the NOAA-NCDC Global Historical Climatology Network (GHCN) database, and aims at developing a statistical tool towards informed decision making for water management purposes. The conducted analysis highlights that the Anderson-Darling (AD) test statistic is the most conservative one in determining approximate Gaussianity of ART samples (followed by Cramer-Von Mises and Kolmogorov-Smirnov), while daily rainfall timeseries with fraction of dry days in excess of 90% and skewness coefficient of positive rainrates that exceeds 5.92 deviate significantly from the normal shape. Further, our results indicate that continental climate exhibits the highest fraction of Gaussian distributed ART samples, followed by warm temperate, equatorial, polar, and arid climates.