Estimates of confidence intervals in extreme value models by parametric and nonparametric bootstrap were compared in terms of simulation experiments, with several combinations of "true" and fitted probability distributions. For small to moderate sample sizes (n<=60), the nonparametric bootstrap (i.e. resampling with replacement from the given sample and calculating the required statistic from a large number of repeated samples) should be interpreted with caution since it leads to confidence intervals that are too narrow and underestimate the real uncertainties involved in frequency models. Although the parametric bootstrap (based on randomly generated samples from a parametric model fitted to the data) yields confidence intervals that are slightly too liberal as well, it improves uncertainty estimates in most examined cases, even under conditions when an incorrect parametric model is adopted for the data. We recommend that the parametric bootstrap should be preferred whenever inferences are based on small to moderate sample sizes and a suitable model for the data is known or can be assumed, including applications to confidence intervals related to extremes in global and regional climate model projections (Kyselý, 2008a).

Regional frequency analysis was applied to improve estimates of probabilities of extreme precipitation in the Czech Republic. The delimitation of homogeneous regions was based on cluster analysis of site characteristics and subsequent tests for regional homogeneity; however, the regions reflect also synoptic patterns causing heavy precipitation. The regional approach lessens the between-site variation of estimates of the shape parameter of the distribution of extremes compared to at-site procedures, and estimates of high quantiles (e.g. 50-yr return values) are more reliable and climatologically consistent. Noteworthy is the heavy tail of distributions of multi-day events, reflected also in the inapplicability of the L-moment estimators for the general 4-parameter kappa distribution utilized in Monte Carlo simulations in regional homogeneity and goodness-of-fit tests. We overcome this issue by using the maximum likelihood estimation (Kyselý and Picek, 2007a, 2007b).


Methods of nonlinear time series analysis were used to detect oscillations hidden in the noise. Time series of climatic, geomagnetic and solar data were analysed using the extension of Monte Carlo Singular System Analysis (MCSSA). The so-called enhanced MCSSA is based on evaluating and testing regularity of dynamics of the SSA modes against the coloured noise null hypothesis. Several statistically significant oscillatory modes with the period in the range from 2 to 11 years were detected in the tested time series (Paluš and Novotná, 2008).


In statistical downscaling, which consists in identifying statistical relationships between large-scale upper-air variables with the local surface ones, and applying them to coarse-scale outputs from GCMs, we proceeded by comparing the performance of two families of downscaling methods, the linear and non-linear ones, for daily temperature. The linear methods include multiple linear regression and canonical correlation analysis, the nonlinear approaches include neural networks and linear models conditioned by a stratification by circulation types. The linear methods, and multiple regression in particular, perform better in most aspects, including the variance explained, and temporal and spatial structure of the downscaled series. On the other hand, neural networks are better at reproducing the properties of statistical distributions (Huth et al., 2008b).


In the examination of classifications of circulation patterns, we contributed to the inventory of classifications and their applications that have been available in Europe. For two subjective catalogues of circulation types, Brádka"s and Hess-Brezowsky, which have been widely used in both synoptic and climatological studies in the Czech Republic, we studied their possible inhomogeneities. Both catalogues suffer from unrealistic changes in the lifetime of the types, resulting in a sharp shortening of types in Brádka"s catalogue in the mid-1970s and a lengthening of types in the mid-1980s for Hess-Brezowsky. In the Hess-Brezowsky catalogue, changes of types are signifantly more frequent at the edge of months and years than elsewhere, which is also apparently an undesirable and unrealistic feature. This suggests that these two catalogues must be used in climate change studies very carefully (Huth et al., 2008a; Cahynová and Huth, 2007a, 2007b).