Calibrating 2-m Temperature of Limited-Area Ensemble Forecasts Using High-Resolution Analysis

Abstract

Although the quality of numerical ensemble prediction systems (EPS) has greatly improved during the last few years, these systems still show systematic deficiencies. Specifically, they are underdispersive and lack both reliability and sharpness. A variety of statistical postprocessing methods allows for improving direct model output. Since 2007, Aire Limité e Adaptation Dynamique Dé veloppement International Limited Area Ensemble Forecasting (ALADIN-LAEF) has been in operation at the Central Institute for Meteorology and Geodynamics (ZAMG), and its 2-m temperature model output subject to calibration. This work follows the approach of nonhomogeneous Gaussian regression (NGR) that addresses a statistical correction of the first and second moment (mean bias and dispersion) for Gaussian-distributed continuous variables. It is based on the multiple linear regression technique and provides a predictive probability density function (PDF) in terms of a normal distribution. Fitting the regression coefficients, a minimum continuous ranked probability score (CRPS) estimation has been chosen instead of the more traditional maximum likelihood technique. The use of high-resolution analysis data on a 1 km 3 1 km grid as training data improves the forecast skill in terms of CRPS by about 35%, especially on the local scale. The percentage of outliers decreases significantly without loss of sharpness. Sensitivity studies confirm that about half of the total improvement can be attributed to the effect of a bias correction. The training length plays a minor role, at least for the chosen verification period. A rescaling of the predictive PDF is important in order to obtain sharp forecasts, especially in the short range. Applying the same method to the global ensemble from the European Centre for Medium-Range Weather Forecasts (ECMWF) gives improvements of similar magnitude. However, the calibrated 2-m temperature of ALADIN-LAEF still remains slightly better than the 2-m temperature from calibrated ECMWF-EPS, which leads to the conclusion that statistical downscaling of EPS cannot replace dynamical downscaling. Finally, an advanced version of NGR, the so-called NGR-TD, which uses timeweighted averaging within minimum CRPS estimation, is able to yield a further improvement of about 5% in terms of the CRPS.

Combining 2-m temperature nowcasting and short range ensemble forecasting

“…The operational INCA run is used as ensemble mean and its RMSE over the past 30 training days is used as ensemble spread. The generation of 18 ensemble members is achieved by taking the quantile values from the Gaussian cumulative distribution function (CDF) centred about the mean in such way that the ensemble spread of the new, re-scaled ensemble is limited by a fractional amount (f re−scale = 3/4) of the root mean squared error of the training data (Kann et al, 2009). Formally the distribution can be expressed by the Gaussian CDF…”

“…The value of z, representing the re-scaled area around ensemble mean, is obtained iteratively, satisfying the constraint σ re−scaled ≤ f re−scale × RMSE INCA (Kann et al, 2009), where σ re−scaled denote the standard deviation of the re-scaled ensemble. In other words, z determines the amount of reduction of the standard deviation of the Gaussian distribution.…”

“…The INCA temperature analysis and forecast methodology has been described elsewhere (Kann et al, 2009;Haiden et al, 2011), so only a short summary is given here. Hourly analyses on a 1 km × 1 km grid are generated from a combination of numerical weather prediction (NWP) model output, surface station data, and high-resolution topographic data.…”

On the skill of various ensemble spread estimators for probabilistic short range wind forecasting

“…cut off at zero) Gaussian cumulative distribution function (CDF) centralized about the mean in such a way that the ensemble spread is determined by a fraction of the relative (i.e. with respect to the observed average) RMSE of the training data (Kann et al, 2009). Several experiments with varying rescaling factors revealed a value of 3/4 to perform best in terms of the Continuous Ranked Probability Score (CRPS) (not shown).…”

“…The EPS dyn is further calibrated by applying a cut-off variant of the nonhomogeneous Gaussian regression (NGR) technique (Thorarinsdottir and Gneiting, 2010;Gneiting et al, 2005;Hagedorn et al, 2008;Kann et al, 2009). This technique statistically calibrates the mean and the ensemble variance by minimizing the Continuous Ranked Probability Score (CRPS) within a certain training period.…”