For our analyses we use the precipitation reconstructions from Pauling et al. (2006). This dataset is seasonally resolved back to 1500 covering all European land areas (30W– 40 E/30 N–71 N) on a 0.5×0.5 grid. It has been developed using precipitation-sensitive proxies including long instrumental series, indices based on documentary evidence and natural proxies (tree-rings, ice cores, coral and speleothem data). These proxies served as input to a Principal Component Regression (PCR) technique which seeks to reconstruct large-scale fields (e.g. Mann et al., 1998, 2005; Jones and Mann, 2004; Luterbacher et al., 2004; Br¨onnimann and Luterbacher, 2004; Casty et al., 2005; Rutherford et al., 2005; Xoplaki et al., 2005; Pauling et al., 2006). As dependent variable the Mitchell and Jones (2005) gridded precipitation dataset has been used for calibration. Throughout our analyses we use this dataset for the 1901–2000 period and the Pauling et al. (2006) dataset for the 1500–1900 period. This approach allows to study seasonal precipitation patterns and extremes over whole Europe during 1500–2000. We restrict our analyses to the winter (here defined as the sum of December, January and February) season, as this allows dynamic interpretation and may contribute most to the understanding of the climate system. Additionally, reconstructive skill is highest for the winter season (Pauling et al., 2006). For illustration, Fig. 1 gives some examples of recent and historic precipitation anomaly patterns including their reconstructive skill which is measured by the Reduction of Error (RE) values. Any reconstruction with RE>0 can be considered as skilful (e.g. Cook et al., 1994; Pauling et al., 2006).
We selected recent winters that were anomalously dry in Fig. 2. Time series of winter precipitation over parts of Ireland (10– 5 W/54–56N) and the corresponding Gamma distributions for 5 different subperiods of the 500-year data set by Pauling et al. (2006).
northern Ireland, southern Spain, eastern and central Europe (left panels of Fig. 1) and compared them with winters taken from the reconstruction period (1500–1900; middle panels of Fig. 1) that were drier than normal in the same region. These regions are marked by the black rectangles in Fig. 1. The right panels show the spatial distribution of the associated RE values. In general, the anomaly pattern of the historic examples presented in Fig. 1 are similar to the modern ones. We define climate extremes as k-year return values (RVs) of seasonal sums of precipitation as estimated from Gamma distributions fitted to the data (Paeth and Hense, 2005; Xoplaki et al., 2005; Luterbacher et al., 2006). The return period (RP) k associated with a given RV is defined as the inverse of the probability that the RV is reached or exceeded assuming Gamma distribution. Seasonal precipitation is generally believed to follow this distribution (Dunn, 2004). We also calculated RPs assuming normal distribution. The results were very similar (not shown).
To investigate the changing RPs we selected the four areas mentioned above (see black rectangles in Fig. 1). Figure 2 shows exemplary the time series of winter precipitation over northern Ireland and the corresponding Gamma distributions for five different subperiods of the 500-year dataset. Ireland has been chosen because it is subject to a strong trend in the mean as well as in the extremely wet and dry years. Many more time series of the reconstructions can be found in Pauling et al. (2006). The figure illustrates the link between the long-term changes in mean precipitation and changes in the location and shape of the Gamma distributions. The negative rainfall trend between 1500 and 1900 is reflected by a shift of the Gamma distribution towards a lower mean. The increase in variability results in a broadening of the distribution. The anomalously wet years after 1970 lead to positive skewness for the 1950–2000 period. It is obvious from this figure that changes in the Gamma distributions are coming along with changes in the occurrence of extremely dry and wet years. Table 1 shows the corresponding parameters of the Gamma distributions and their 90% confidence intervals. They are estimated using the Monte Carlo method which is described in more detail below.
Climate reconstructions tend to lose variability during early periods when only few predictors are available (see Fig. 2; Pauling et al., 2006). This leads to biased estimations of the return periods of extremes. Hence, when analyzing changes of the return periods of extremes, which is the main purpose of this article, it is mandatory that the available predictors are able to realistically reconstruct not only the mean (which is often the case) but also the extremes (which is more difficult).
We addressd this issue by reconstructing precipitation during 1901–1983 using just the predictors that are available in 1500 for the four regions (northern Ireland, southern Spain, eastern and central Europe). The consideration of the time period 1901–1983 is motivated by the predictor availability. The reconstruction methods included multiple regression (for fitting) and cross-validation (for achieving the predictions). Then we compared these predictions (reconstructions) with the data from Mitchell and Jones (2005) to verify if there are significant differences between 20-year return values (RVs) of dry/wet extremes of the time series. No significant difference implies correct reconstruction of the RVs by the predictors available in 1500. For estimating the significance we used the Monte Carlo technique that is described in more detail below. We repeated this procedure using the predictor sets available in 1700 and 1800 (the predictors available for 1600 are identical with the ones available for 1500). Figure 3 shows the upper and lower 20-year return values of winter precipitation in the four regions using the three predictor sets and the corresponding return values of the Mitchell and Jones (2005) dataset. Significance was estimated using the Monte Carlo method (for details see below). For the predictor set available in 1500 significant differences were detected for all regions while the predictors available in 1700 and 1800 are able to realistically reconstruct the RVs except for the dry extremes in eastern Europe. However, in eastern Europe the dry extremes were hardly significantly different from the reference period 1951–2000 during the last 300 years anyway (Fig. 5). Therefore, we exclude all data prior to 1700 from our analyses concerning the changes of return periods. We estimated the RVs for several RPs for a moving 50- year-window over the period 1700–2000. These results provide insight in how variable the recurrence of extreme seasonal winter precipitation has been over the last 300 years (Figs. 4 and 6). As the changes of extremes prior to 1700 may be due to predictor availability, the significance of the changes in extremes is estimated for data after 1700 (Figs. 5 and 7).
To analyse the spatial differences of the change in RPs, we performed the following experiment (Figs. 8 and 9): First, we selected all gridpoints that have reconstructive skill (Pauling et al., 2006). Second, we determined the RVs that have a RP of 20 years for every gridpoint during 1951–2000 assuming Gamma distribution. By means of a Kolmogorov goodness of fit test it has been ensured that the Gamma distribution represents a reliable description of the seasonal precipitation data. For most regions and time periods after 1650, the Nullhypothesis, saying that the sample is taken from a Gamma distribution, has been accepted at an error level of 1%. An alternative way would be to start from a non-parametric estimate of the probability distribution, for instance by using kernel density estimators. The results do not substantially change if other RPs are calculated (not shown). Third, using these RVs we estimated the RPs based on Gamma distributions whose parameters were estimated using 50-year periods back to 1700. We chose periods of 50 years to ensure that 20-year-events are likely to occur. Fourth, the significance of these changes were estimated by applying a Monte Carlo sampling approach (Paeth and Hense, 2005).
When fitting a theoretical distribution like the Gamma distribution to a sample of limited size, the estimate of the distribution parameters, in this case shape (alpha) and scale (beta) parameter, is subject to uncertainty. This particularly affects the calculation of extreme values with return periods beyond the length of the original time series. Therefore, we construct an uncertainty range for each parameter of the Gamma distribution using a parametric bootstrap approach with 1000 iterations (Kharin and Zwiers, 2000; Paeth and Hense, 2005; Xoplaki et al., 2005). The Monte Carlo method is based on random samples which are drawn from the fitted Gamma distribution. One basic assumption is that the individual winter values are independent of each other. Therefore, we have computed the autocorrelation function for all time series and found that the autocorrelation coefficients with time lags of one year and longer are not significantly different from zero at an error level of 1% (not shown). Each random sample leads to a new set of parameters and RVs which are normally distributed over the 1000 bootstraps (Park et al., 2001). Thus, the standard error of the new random sample of Gamma parameters and RVs is a measure of uncertainty of the extreme value estimate. Accordingly, the confidence intervals can be estimated at a given error level. We will use the Monte Carlo method for two issues: First, the confidence intervals of the parameters of the Gamma distribution are estimated (see Table 1). It is obvious that the uncertainty range is considerable. Therefore, the subsequent analysis of extreme values is based on the mean parameters from the bootstrapping rather than on the parameters directly derived from the data. Second, the confidence intervals of return values for different subperiods between 1700 and 2000 are compared with each other in order to decide whether a change in the mean RV estimate is statistically significant at a given error level. These confidence intervals are based on the standard deviation and the quantiles of the bootstrap samples. A change of RPs significant at the 1% level is reached if the 90% confidence intervals of the associated RVs do not overlap between two subperiods (Kharin and Zwiers, 2000; Park et al., 2001).
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