ALBERT

Description: In this paper, we present a detailed evaluation of cross wavelet analysis of bivariate time series. We develop a statistical test for zero wavelet coherency based on Monte Carlo simulations. If at least one of the two processes considered is Gaussian white noise, an approximative formula for the critical value can be utilized. In a second part, typical pitfalls of wavelet cross spectra and wavelet coherency are discussed. The wavelet cross spectrum appears to be not suitable for significance testing the interrelation between two processes. Instead, one should rather apply wavelet coherency. Furthermore we investigate problems due to multiple testing. Based on these results, we show that coherency between ENSO and NAO is an artefact for most of the time from 1900 to 1995. However, during a distinct period from around 1920 to 1940, significant coherency between the two phenomena occurs.

Description: We study the inference of long-range correlations by means of Detrended Fluctuation Analysis (DFA) and argue that power-law scaling of the fluctuation function and thus long-memory may not be assumed a priori but have to be established. This requires the investigation of the local slopes. We account for the variability characteristic for stochastic processes by calculating empirical confidence regions. Comparing a long-memory with a short-memory model shows that the inference of long-range correlations from a finite amount of data by means of DFA is not specific. We remark that scaling cannot be concluded from a straight line fit to the fluctuation function in a log-log representation. Furthermore, we show that a local slope larger than α=0.5 for large scales does not necessarily imply long-memory. We also demonstrate, that it is not valid to conclude from a finite scaling region of the fluctuation function to an equivalent scaling region of the autocorrelation function. Finally, we review DFA results for the Prague temperature data set and show that long-range correlations cannot not be concluded unambiguously.

Description: To assess potential impacts of climate change for a specific location, one typically employs climate model simulations at the grid box corresponding to the same geographical location. But based on regional climate model simulations, we show that simulated climate might be systematically displaced compared to observations. In particular in the rain shadow of moutain ranges, a local grid box is therefore often not representative of observed climate: the simulated windward weather does not flow far enough across the mountains; local grid boxes experience the wrong airmasses and atmospheric circulation. In some cases, also the local climate change signal is deteriorated. Classical bias correction methods fail to correct these location errors. Often, however, a distant simulated time series is representative of the considered observed precipitation, such that a non-local bias correction is possible. These findings also clarify limitations of bias correcting global model errors, and of bias correction against station data.

Description: We investigated the influence of atmospheric noise on the generation of interannual El Niño variability. Therefore, we perturbed a conceptual ENSO delay model with surrogate windstress data generated from tropical windspeed measurements. The effect of the additional stochastic forcing was studied for various parameter sets including periodic and chaotic regimes. The evaluation was based on a spectrum and amplitude-period relation comparison between model and measured sea surface temperature data. The additional forcing turned out to increase the variability of the model output in general. The noise-free model was unable to reproduce the observed spectral bandwidth for any choice of parameters. On the contrary, the stochastically forced model is capable of producing a realistic spectrum. The weakly nonlinear regimes of the model exhibit a proportional relation between amplitude and period matching the relation derived from measurement data. The chaotic regime, however, shows an inversely proportional relation. A stability analysis of the different regimes revealed that the spectra of the weakly nonlinear regimes are robust against slight parameter changes representing disregarded physical mechanisms, whereas the chaotic regime exhibits a very unstable realistic spectrum. We conclude that the model including stochastic forcing in a parameter range of moderate nonlinearity best matches the real conditions. This suggests that atmospheric noise plays an important role in the coupled tropical pacific ocean-atmosphere system.

Description: Much of our knowledge about future changes in precipitation relies on global (GCM) and/or regional climate models (RCM) that have resolutions which are much coarser than typical spatial scales of precipitation, particularly extremes. The major problems with these projections are both climate model biases and the gap between gridbox and point scale. Wong et al. developed a model to jointly bias correct and downscale precipitation at daily scales. This approach, however, relied on pairwise correspondence between predictor and predictand for calibration, and thus, on nudged simulations which are rarely available. Here we present an extension of this approach that separates the downscaling from the bias correction and in principle is applicable to free running GCMs/RCMs. In a first step, we bias correct RCM-simulated precipitation against gridded observations at the same scale using a parametric quantile mapping approach. To correct the whole distribution including extreme tails we apply a mixture distribution of a gamma distribution for the precipitation mass and a generalized Pareto distribution for the extreme tail. In a second step, we bridge the scale gap: we predict local variance employing a vector generalized linear gamma model (VGLM gamma) with the bias corrected time series as predictor. The VGLM gamma model is calibrated between gridded and point scale (station) observations. For evaluation we adopt the perfect predictor experimental setup of VALUE. Precipitation is in most cases improved by (parts of) our method across different European climates. The method generally performs better in summer than in winter and in winter best in the Mediterranean region with a mild winter climate and worst for continental winter climate in mid & eastern Europe or Scandinavia. A strength of this two-step method is that the best combination of bias correction and downscaling methods can be selected. This implies that the concept can be extended to a wide range of method combinations.