An ARFIMA-based model for daily precipitation amounts with direct access to fluctuations
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ORIGINAL PAPER
An ARFIMA-based model for daily precipitation amounts with direct access to fluctuations Katja Polotzek1
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Holger Kantz1
Ó The Author(s) 2020
Abstract Correlations in models for daily precipitation are often generated by elaborate numerics that employ a high number of hidden parameters. We propose a parsimonious and parametric stochastic model for European mid-latitude daily precipitation amounts with focus on the influence of correlations on the statistics. Our method is meta-Gaussian by applying a truncated-Gaussian-power (tGp) transformation to a Gaussian ARFIMA model. The speciality of this approach is that ARFIMA(1, d, 0) processes provide synthetic time series with long- (LRC), meaning the sum of all autocorrelations is infinite, and short-range (SRC) correlations by only one parameter each. Our model requires the fit of only five parameters overall that have a clear interpretation. For model time series of finite length we deduce an effective sample size for the sample mean, whose variance is increased due to correlations. For example the statistical uncertainty of the mean daily amount of 103 years of daily records at the Fichtelberg mountain in Germany equals the one of about 14 years of independent daily data. Our effective sample size approach also yields theoretical confidence intervals for annual total amounts and allows for proper model validation in terms of the empirical mean and fluctuations of annual totals. We evaluate probability plots for the daily amounts, confidence intervals based on the effective sample size for the daily mean and annual totals, and the Mahalanobis distance for the annual maxima distribution. For reproducing annual maxima the way of fitting the marginal distribution is more crucial than the presence of correlations, which is the other way round for annual totals. Our alternative to rainfall simulation proves capable of modeling daily precipitation amounts as the statistics of a random selection of 20 data sets is well reproduced. Keywords Data model for daily precipitation Non-Gaussian long-range correlated processes Nonlinear transformation of ARFIMA
1 Introduction For simulations and forecasts numerical weather generators require amongst others precipitation data as an input. The occurrence and intensity of precipitation is affected by a multitude of atmospheric processes, which evolve on many different temporal and spatial scales. Stochastic precipitation generators are, hence, convenient to capture the outcome of such highly complex physical dynamics. & Katja Polotzek [email protected] Holger Kantz [email protected] 1
Max Planck Institute for the Physics of Complex Systems, No¨thnitzer Str. 38, 01187 Dresden, Germany
Two essential aspects of the statistics of precipitation amounts are their distribution and temporal correlations. There is ongoing discussion on the most appropriate choice of a model distribution for daily precipitation amounts. In particular, their tail behavior is crucial for the estimation of large precipitation events. Most glo
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