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.
Highlights
For simulations and forecasts numerical weather generators require amongst others precipitation data as an input
We exemplify our fitted model for three of the data sets we present in the appendix, namely for the (a) Fichtelberg, 1916–2018, in Germany (Deutscher Wetterdienst (DWD) 2018), the (b) Bordeaux, 1946–2018, in France
Graphical visualizations of the results are very similar for all stations in Table 2, so that based on Table 3 any of the stations would illustrate well our modeling approach and so do the three chosen ones
Summary
For simulations and forecasts numerical weather generators require amongst others precipitation data as an input. On that account, truncated-Gaussianpower transformations of short-range correlated Gaussian processes have been used to model the distribution of precipitation amounts and their dynamics (Sanso and Guenni 1999; Ailliot et al 2009; Sigrist et al 2012). An appropriate data model for daily precipitation time series should cover both the non-Gaussianity of the data and their short- and long-range temporal correlations. We thoroughly validate our findings that the marginal distribution of the empirical data sets in terms of daily mean, annual totals and maxima, the short- and long-term correlations and the waiting-time distribution of the empirical data is well modeled by a truncated-Gaussian-power of a long-range correlated ARFIMA process. Properties of the process like the mean will be indexed by X
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