Petra Friederichs

Statistical Downscaling of Extreme Precipitation Events Using Censored Quantile Regression

Abstract A statistical downscaling approach for extremes using censored quantile regression is presented. Conditional quantiles of station data (e.g., daily precipitation sums) in Germany are estimated by means of the large-scale circulation as represented by the NCEP reanalysis data. It is shown that a mixed discrete–continuous response variable, such as a daily precipitation sum, can be statistically modeled by a censored variable. Furthermore, a conditional quantile skill score is formulated to assess the relative gain of a quantile forecast compared with a reference forecast. Just like multiple regression for expectation values, quantile regression provides a tool to formulate a model output statistics system for extremal quantiles.

Multivariate—Intervariable, Spatial, and Temporal—Bias Correction*

AbstractStatistical methods to bias correct global or regional climate model output are now common to get data closer to observations in distribution. However, most bias correction (BC) methods work for one variable and one location at a time and basically reproduce the temporal structure of the models. The intervariable, spatial, and temporal dependencies of the corrected data are usually poor compared to observations. Here, the authors propose a novel method for multivariate BC. The empirical copula–bias correction (EC–BC) combines a one-dimensional BC with a shuffling technique that restores an empirical multidimensional copula. Several BC methods are investigated and compared to high-resolution reference data over the French Mediterranean basin: notably, (i) a 1D BC method applied independently to precipitation and temperature fields, (ii) a recent conditional correction approach developed for producing correct two-dimensional intervariable structures, and (iii) the EC–BC method.Assessments are realiz...

Stochastic parameterization: Towards a new view of weather and climate models

AbstractThe last decade has seen the success of stochastic parameterizations in short-term, medium-range, and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to represent model inadequacy better and to improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing long-standing climate biases and is relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups that show that the stochastic representation of unresolved processes in the atmosphere, oceans, land surface, and cryosphere of comprehensive weather and climate models 1) gives rise to more reliable probabilistic forecasts of weather and climate and 2) reduces systematic model bias. We make a case that the use of mathematically stri...

Forecast verification for extreme value distributions with an application to probabilistic peak wind prediction

Predictions of the uncertainty associated with extreme events are a vital component of any prediction system for such events. Consequently, the prediction system ought to be probabilistic in nature, with the predictions taking the form of probability distributions. This paper concerns probabilistic prediction systems where the data are assumed to follow either a generalized extreme value (GEV) distribution or a generalized Pareto distribution. In this setting, the properties of proper scoring rules that facilitate the assessment of the prediction uncertainty are investigated, and closed form expressions for the continuous ranked probability score (CRPS) are provided. In an application to peak wind prediction, the predictive performance of a GEV model under maximum likelihood estimation, optimum score estimation with the CRPS, and a Bayesian framework are compared. The Bayesian inference yields the highest overall prediction skill and is shown to be a valuable tool for covariate selection, while the predictions obtained under optimum CRPS estimation are the sharpest and give the best performance for high thresholds and quantiles. Copyright

Spatial kinetic energy spectra in the convection-permitting limited-area NWP model COSMO-DE

1 Kinetic energy spectra derived from commercial aircraft observations of horizontal wind 2 velocities exhibit a k−5/3 wavenumber dependence on the mesoscale that merges into a 3 k−3 dependence on the macroscale. In this study, spectral analysis is applied to evalu4 ate the mesoscale ensemble prediction system using the convection-permitting NWP model 5 COSMO-DE (COSMO-DE-EPS). One-dimensional wavenumber spectra of the kinetic en6 ergy are derived from zonal and meridional wind velocities, as well as from vertical velocities. 7 Besides a general evaluation, the model spectra reveal important information about spin-up 8 effects and effective resolution. 9 The COSMO-DE-EPS well reproduces the spectral k−5/3 dependence of the mesoscale 10 horizontal kinetic energy spectrum. Due to the assimilation of high-resolution meteorologi11 cal observations (mainly rain radar), there is no significant spin-up of the model simulations 12 within the first few hours after initialization. COSMO-DE-EPS features an effective reso13 lution of a factor of about 4 to 5 of the horizontal grid spacing. This is slightly higher in 14 comparison to other limited area models. Kinetic energy spectra derived from vertical ve15 locities exhibit a much flatter wavenumber dependence leading to relatively large spectral 16 energy on smaller scales. This is in good agreement with similar models and also suggested 17 by observations of temporal variance spectra of the vertical velocity. 18

A probabilistic analysis of wind gusts using extreme value statistics

The spatial variability of wind gusts is probably as large as that of precipitation, but the observational weather station network is much less dense. The lack of an area-wide observational analysis hampers the forecast verification of wind gust warnings. This article develops and compares several approaches to derive a probabilistic analysis of wind gusts for Germany. Such an analysis provides a probability that a wind gust exceeds a certain warning level. To that end we have 5 years of observations of hourly wind maxima at about 140 weather stations of the German weather service at our disposal. The approaches are based on linear statistical modeling using generalized linear models, extreme value theory and quantile regression. Warning level exceedance probabilities are estimated in response to predictor variables such as the observed mean wind or the operational analysis of the wind velocity at a height of 10 m above ground provided by the European Centre for Medium Range Weather Forecasts (ECMWF). The study shows that approaches that apply to the differences between the recorded wind gust and the mean wind perform better in terms of the Brier skill score (which measures the quality of a probability forecast) than those using the gust factor or the wind gusts only. The study points to the benefit from using extreme value theory as the most appropriate and theoretically consistent statistical model. The most informative predictors are the observed mean wind, but also the observed gust velocities recorded at the neighboring stations. Out of the predictors used from the ECMWF analysis, the wind velocity at 10 m above ground is the most informative predictor, whereas the wind shear and the vertical velocity provide no additional skill. For illustration the results for January 2007 and during the winter storm Kyrill are shown. Zusammenfassung

Generating and Calibrating Probabilistic Quantitative Precipitation Forecasts from the High-Resolution NWP Model COSMO-DE

AbstractStatistical postprocessing is an integral part of an ensemble prediction system. This study compares methods used to derive probabilistic quantitative precipitation forecasts based on the high-resolution version of the German-focused Consortium for Small-Scale Modeling (COSMO-DE) time-lagged ensemble (COSMO-DE-TLE). The investigation covers the period from July 2008 to June 2011 for a region over northern Germany with rain gauge measurements from 445 stations. The investigated methods provide pointwise estimates of the predictive distribution using logistic and quantile regression, and full predictive distributions using parametric mixture models. All mixture models use a point mass at zero to represent the probability of precipitation. The amount of precipitation is modeled by either a gamma, lognormal, or inverse Gaussian distribution. Furthermore, an adaptive tail using a generalized Pareto distribution (GPD) accounts for a better representation of extreme precipitation. The predictive probabil...

A Probabilistic Forecast Approach for Daily Precipitation Totals

Abstract Commonly, postprocessing techniques are employed to calibrate a model forecast. Here, a probabilistic postprocessor is presented that provides calibrated probability and quantile forecasts of precipitation on the local scale. The forecasts are based on large-scale circulation patterns of the 12-h forecast from the NCEP high-resolution Global Forecast System (GFS). The censored quantile regression is used to estimate selected quantiles of the precipitation amount and the probability of the occurrence of precipitation. The approach accounts for the mixed discrete-continuous character of daily precipitation totals. The forecasts are verified using a new verification score for quantile forecasts, namely the censored quantile verification (CQV) score. The forecast approach is as follows: first, a canonical correlation is employed to correct systematic deviations in the GFS large-scale patterns compared with the NCEP–NCAR reanalysis or the 40-yr ECMWF Re-Analysis (ERA-40). Second, the statistical quant...

A Gaussian graphical model approach to climate networks

Distinguishing between direct and indirect connections is essential when interpreting network structures in terms of dynamical interactions and stability. When constructing networks from climate data the nodes are usually defined on a spatial grid. The edges are usually derived from a bivariate dependency measure, such as Pearson correlation coefficients or mutual information. Thus, the edges indistinguishably represent direct and indirect dependencies. Interpreting climate data fields as realizations of Gaussian Random Fields (GRFs), we have constructed networks according to the Gaussian Graphical Model (GGM) approach. In contrast to the widely used method, the edges of GGM networks are based on partial correlations denoting direct dependencies. Furthermore, GRFs can be represented not only on points in space, but also by expansion coefficients of orthogonal basis functions, such as spherical harmonics. This leads to a modified definition of network nodes and edges in spectral space, which is motivated from an atmospheric dynamics perspective. We construct and analyze networks from climate data in grid point space as well as in spectral space, and derive the edges from both Pearson and partial correlations. Network characteristics, such as mean degree, average shortest path length, and clustering coefficient, reveal that the networks posses an ordered and strongly locally interconnected structure rather than small-world properties. Despite this, the network structures differ strongly depending on the construction method. Straightforward approaches to infer networks from climate data while not regarding any physical processes may contain too strong simplifications to describe the dynamics of the climate system appropriately.

Statistical Inference in Canonical Correlation Analyses Exemplified by the Influence of North Atlantic SST on European Climate

Abstract To encourage the use of the standard parametric test procedures in canonical correlation analysis, the tests are applied to investigate the influence of northern Atlantic SST on the Euro–Atlantic atmospheric circulation. A comparison with a Monte Carlo testing procedure shows that the parametric tests perform properly given that at least one of the two multivariate variates is normally distributed. In this case the parametric tests are even superior to a Monte Carlo test procedure, when the estimation of the error level relies on relatively small Monte Carlo samples, which is often the case in climate studies. Even if the parametric test procedures fail due to departures from the independency assumption, they provide qualified variables to perform the more costly Monte Carlo testing procedure. A significant influence of the northern Atlantic tripole on the atmospheric circulation was detected in ensemble simulations with the Hamburg ECHAM3 model forced with prescribed SST. Another signal already ...