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.

日降水量模型中的相关性通常是由采用大量隐藏参数的精细数值生成的。我们提出了欧洲中纬度日降水量的简约和参数随机模型，重点是相关性对统计的影响。通过将截断的高斯功率（tGp）变换应用于高斯ARFIMA模型，我们的方法是亚高斯方法。这种方法的特长是ARFIMA（1，  d，0）进程提供具有长（LRC）的合成时间序列，这意味着所有自相关的总和是无限的，而短程（SRC）相关仅每个参数一个。我们的模型仅需对五个参数进行总体拟合即可得出清晰的解释。对于有限长度的模型时间序列，我们得出样本均值的有效样本大小，其方差由于相关性而增加。例如，德国Fichtelberg山的103年日记录的平均日数量的统计不确定性等于约14年的独立日数据之一。我们有效的样本量方法还可以得出年度总量的理论置信区间，并可以根据经验平均值和年度总量的波动进行适当的模型验证。我们评估日数量的概率图，基于日均值和年总数的有效样本量的置信区间以及年最大值分布的马氏距离。为了再现年度最大值，拟合边际分布的方法比相关性的存在更为关键，后者与年度总数相反。由于可以很好地复制20个数据集的随机选择的统计信息，因此我们的降雨模拟替代方案证明了能够对每日降水量进行建模。这与年度总数相反。由于可以很好地复制20个数据集的随机选择的统计信息，因此我们的降雨模拟替代方案证明了能够对每日降水量进行建模。这与年度总数相反。由于可以很好地复制随机选择的20个数据集的统计信息，因此我们的降雨模拟替代方法证明了能够对每日降水量进行建模。