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

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  • 1 Department of Civil, Environmental and Architectural Engineering, University of Cagliari, via Marengo 2, Cagliari, Italy.
  • 2 Department of Civil Engineering, University of Patras, Patras, Greece
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Abstract

We develop a non-parametric procedure to assess the accuracy of the normality assumption for annual rainfall totals (ART), based on the marginal statistics of daily rainfall. The procedure is addressed to practitioners and hydrologists that operate in data poor regions. To do so we use: 1) goodness-of-fit metrics to conclude on the approximate convergence of the empirical distribution of annual rainfall totals to a normal shape, and classify 3007 daily rainfall timeseries from the NOAA-NCDC Global Historical Climatology Network (GHCN) database, with at least 30 years of recordings, into Gaussian (G) and non Gaussian (NG) groups, 2) logistic regression analysis to identify the statistics of daily rainfall that are most descriptive of the G/NG classification, and 3) a random-search algorithm to conclude on a set of constraints that allows classification of ART samples based on the marginal statistics of daily rainrates. The analysis shows that the Anderson-Darling (AD) test statistic is the most conservative one in determining approximate Gaussianity of ART samples (followed by Cramer-Von Mises, CVM, and Lilliefors’ version of Kolmogorov-Smirnov, KSL), and that daily rainfall timeseries with fraction of wet days fwd < 0.1 and daily skewness coefficient of positive rainrates skwd > 5.92 deviate significantly from the normal shape. In addition, we find that continental climate (D) exhibits the highest fraction of Gaussian distributed ART samples (i.e. 74.45%, AD test at α = 5% significance level), followed by warm temperate (C, 72.80%), equatorial (A, 68.83%), polar (E, 62.96%), and arid (B, 60.29%) climates.

Correspondence: Dario Ruggiu (dario.ruggiu@unica.it)

Abstract

We develop a non-parametric procedure to assess the accuracy of the normality assumption for annual rainfall totals (ART), based on the marginal statistics of daily rainfall. The procedure is addressed to practitioners and hydrologists that operate in data poor regions. To do so we use: 1) goodness-of-fit metrics to conclude on the approximate convergence of the empirical distribution of annual rainfall totals to a normal shape, and classify 3007 daily rainfall timeseries from the NOAA-NCDC Global Historical Climatology Network (GHCN) database, with at least 30 years of recordings, into Gaussian (G) and non Gaussian (NG) groups, 2) logistic regression analysis to identify the statistics of daily rainfall that are most descriptive of the G/NG classification, and 3) a random-search algorithm to conclude on a set of constraints that allows classification of ART samples based on the marginal statistics of daily rainrates. The analysis shows that the Anderson-Darling (AD) test statistic is the most conservative one in determining approximate Gaussianity of ART samples (followed by Cramer-Von Mises, CVM, and Lilliefors’ version of Kolmogorov-Smirnov, KSL), and that daily rainfall timeseries with fraction of wet days fwd < 0.1 and daily skewness coefficient of positive rainrates skwd > 5.92 deviate significantly from the normal shape. In addition, we find that continental climate (D) exhibits the highest fraction of Gaussian distributed ART samples (i.e. 74.45%, AD test at α = 5% significance level), followed by warm temperate (C, 72.80%), equatorial (A, 68.83%), polar (E, 62.96%), and arid (B, 60.29%) climates.

Correspondence: Dario Ruggiu (dario.ruggiu@unica.it)
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