Post-processing of wind gusts from COSMO-REA6 with a spatial Bayesian hierarchical extreme value model

Abstract

The aim of this study is to provide a probabilistic gust analysis for the region of Germany that is calibrated with station observations and with an interpolation to unobserved locations. To this end, we develop a spatial Bayesian hierarchical model (BHM) for the post-processing of surface maximum wind gusts from the COSMO-REA6 reanalysis. Our approach uses a non-stationary extreme value distribution for the gust observations, with parameters that vary according to a linear model using COSMO-REA6 predictor variables. To capture spatial patterns in surface wind gust behavior, the regression coefficients are modeled as 2-dimensional Gaussian random fields with a constant mean and an isotropic covariance function that depends on the distance between locations. In addition, we include an elevation offset in the distance metric for the covariance function to account for the topography. This allows us to include data from mountaintop stations in the training process. The training of the BHM is carried out with an independent data set from which the data at the station to be predicted are excluded. We evaluate the spatial prediction performance at the withheld station using Brier score and quantile score, including their decomposition, and compare the performance of our BHM to climatological forecasts and a non-hierarchical, spatially constant baseline model. This is done for 109 weather stations in Germany. Compared to the spatially constant baseline model, the spatial BHM significantly improves the estimation of local gust parameters. It shows up to 5 % higher skill for prediction quantiles and provides a particularly improved skill for extreme wind gusts. In addition, the BHM improves the prediction of threshold levels at most of the stations. Although a spatially constant approach already provides high skill, our BHM further improves predictions and improves spatial consistency.

Figures (18)

• Figure 1: Directed acyclic graph for SpatBHM with predictand $y_{ik}$, covariates $x_{j,ik}$ and station coordinates $\vec{r}_i$, for location $i$ and time $t$. $m_{\mu/\varsigma}$ refer to the respective number of covariates for location and scale. Please refer to Table \ref{['tab:notation']} for a comprehensive notation reference.
• Figure 2: (a) Spatial distribution of the skill of LocMod against climatology for exceedances of the 14 m s^-1 threshold (BSS 14). Blue colors indicate positive skill, red colors indicate negative skill. Each dot is one SYNOP station used for training. (b) Mean $\mathrm{FX}$ value used for training. (c) Mean $V_\mathrm{m}$ value used for training.
• Figure 3: Spearman rank correlation coefficient between various variables and LocMod skill against climatology, shown for exceedance probabilities of the 14 m s^-1 (BSS 14) and 18 m s^-1 (BSS 18) threshold, and the 0.75 to 0.999 quantiles (QSS 0.75 to QSS 0.999). Correlations are shown (a) for the gust observations $\mathrm{FX}$, (b) the maximum wind speed $V_\mathrm{max}$ and (c) the mean wind $V_\mathrm{m}$. Boxes represent the interquartile range and whiskers extend to the 0.01 and 0.99-quantiles. Uncertainty estimates are based on 5000 bootstrap iterations. In each iteration, both the dates for the calculation of the mean wind and the stations to calculate the correlation are resampled.
• Figure 4: Cross-validated skill scores of ConstMod and LocMod against climatology, and ConstMod against LocMod for exceedance probabilities of the 14 m s^-1 (BSS 14) and 18 m s^-1 (BSS 18) thresholds, and the 0.75 to 0.999 quantiles (QSS 0.75 to QSS 0.999). Each box plot contains skill scores at 109 locations. Boxes represent the interquartile range and whiskers extend to the $0.01$ and $0.99$-quantiles. Bold lines mark the median skill scores. Median score values are given in Table \ref{['tab:ConstmodOverview']}.
• Figure 5: Miscalibration of SpatBHM with and without the elevation offset in the covariance function. Each data point represents the miscalibration at one station. The coloring represents station altitude of the station in question. Miscalibration values are shown for (a) BS 14, (b) QS 0.75, and (c) QS 0.99. The gray line represents the identity function. Note that the axes are scaled logarithmically, so that smaller values are overrepresented.