Explore the vast range of titles available.

Statistical postprocessing techniques are nowadays key components of the forecasting suites in many national meteorological services (NMS), with, for most of them, the objective of correcting the impact of different types of errors on the forecasts. The final aim is to provide optimal, automated, seamless forecasts for end users. Many techniques are now flourishing in the statistical, meteorological, climatological, hydrological, and engineering communities. The methods range in complexity from simple bias corrections to very sophisticated distribution-adjusting techniques that incorporate correlations among the prognostic variables. The paper is an attempt to summarize the main activities going on in this area from theoretical developments to operational applications, with a focus on the current challenges and potential avenues in the field. Among these challenges is the shift in NMS toward running ensemble numerical weather prediction (NWP) systems at the kilometer scale that produce very large datasets and require high-density high-quality observations, the necessity to preserve space-time correlation of high-dimensional corrected fields, the need to reduce the impact of model changes affecting the parameters of the corrections, the necessity for techniques to merge different types of forecasts and ensembles with different behaviors, and finally the ability to transfer research on statistical postprocessing to operations. Potential new avenues are also discussed.

Seasonal forecasts of variables like near-surface temperature or precipitation are becoming increasingly important for a wide range of stakeholders. Due to the many possibilities of recalibrating, combining, and verifying ensemble forecasts, there are ambiguities of which methods are most suitable. To address this we compare approaches how to process and verify multi-model seasonal forecasts based on a scientific assessment performed within the framework of the EU Copernicus Climate Change Service (C3S) Quality Assurance for Multi-model Seasonal Forecast Products (QA4Seas) contract C3S 51 lot 3. Our results underpin the importance of processing raw ensemble forecasts differently depending on the final forecast product needed. While ensemble forecasts benefit a lot from bias correction using climate conserving recalibration, this is not the case for the intrinsically bias adjusted multi-category probability forecasts. The same applies for multi-model combination. In this paper, we apply simple, but effective, approaches for multi-model combination of both forecast formats. Further, based on existing literature we recommend to use proper scoring rules like a sample version of the continuous ranked probability score and the ranked probability score for the verification of ensemble forecasts and multi-category probability forecasts, respectively. For a detailed global visualization of calibration as well as bias and dispersion errors, using the Chi-square decomposition of rank histograms proved to be appropriate for the analysis performed within QA4Seas.

Statistical postprocessing is commonly applied to reduce location and dispersion errors of probabilistic forecasts provided by numerical weather prediction (NWP) models. If postprocessed forecast scenarios are required, the combination of ensemble model output statistics (EMOS) for univariate postprocessing with ensemble copula coupling (ECC) or the Schaake shuffle (ScS) to retain the dependence structure of the raw ensemble is a state-of-the-art approach. However, modern machine learning methods may lead to both a better univariate skill and more realistic forecast scenarios. In this study, we postprocess multimodel ensemble forecasts of cloud cover over Switzerland provided by COSMO-E and ECMWF-IFS using (i) EMOS + ECC, (ii) EMOS + ScS, (iii) dense neural networks (dense NN) + ECC, (iv) dense NN + ScS, and (v) conditional generative adversarial networks (cGAN). The different methods are verified using EUMETSAT satellite data. Dense NN shows the best univariate skill, but cGAN performed only slightly worse. Furthermore, cGAN generates realistic forecast scenario maps, while not relying on a dependence template like ECC or ScS, which is particularly favorable in the case of complex topography.

This paper presents an approach to postprocess ensemble forecasts for the discrete and bounded weather variable of total cloud cover. Two methods for discrete statistical postprocessing of ensemble predictions are tested: the first approach is based on multinomial logistic regression and the second involves a proportional odds logistic regression model. Applying them to total cloud cover raw ensemble forecasts from the European Centre for Medium-Range Weather Forecasts improves forecast skill significantly. Based on stationwise postprocessing of raw ensemble total cloud cover forecasts for a global set of 3330 stations over the period from 2007 to early 2014, the more parsimonious proportional odds logistic regression model proved to slightly outperform the multinomial logistic regression model.

Many practical applications of statistical post-processing methods for ensemble weather forecasts require accurate modeling of spatial, temporal, and inter-variable dependencies. Over the past years, a variety of approaches has been proposed to address this need. We provide a comprehensive review and comparison of state-of-the-art methods for multivariate ensemble post-processing. We focus on generally applicable two-step approaches where ensemble predictions are first post-processed separately in each margin and multivariate dependencies are restored via copula functions in a second step. The comparisons are based on simulation studies tailored to mimic challenges occurring in practical applications and allow ready interpretation of the effects of different types of misspecifications in the mean, variance, and covariance structure of the ensemble forecasts on the performance of the post-processing methods. Overall, we find that the Schaake shuffle provides a compelling benchmark that is difficult to outperform, whereas the forecast quality of parametric copula approaches and variants of ensemble copula coupling strongly depend on the misspecifications at hand.

Statistical postprocessing is applied in operational forecasting to correct systematic errors of numerical weather prediction models (NWP) and to automatically produce calibrated local forecasts for end-users. Postprocessing is particularly relevant in complex terrain, where even state-of-the-art high-resolution NWP systems cannot resolve many of the small-scale processes shaping local weather conditions. In addition, statistical postprocessing can also be used to combine forecasts from multiple NWP systems. Here we assess an ensemble model output statistics (EMOS) approach to produce seamless temperature forecasts based on a combination of short-term ensemble forecasts from a convection-permitting limited-area ensemble and a medium-range global ensemble forecasting model. We quantify the benefit of this approach compared to only postprocessing the high-resolution NWP. The multimodel EMOS approach (“mixed EMOS”) is able to improve forecasts by 30% with respect to direct model output from the high-resolution NWP. A detailed evaluation of mixed EMOS reveals that it outperforms either one of the single-model EMOS versions by 8%–12%. Temperature forecasts at valley locations profit in particular from the model combination. All forecast variants perform worst in winter (DJF); however, calibration and model combination improves forecast quality substantially. In addition to increasing skill as compared to single-model postprocessing, it also enables us to seamlessly combine multiple forecast sources with different time horizons (and horizontal resolutions) and thereby consolidates short-term to medium-range forecasting time horizons in one product without any user-relevant discontinuity.

The special issue on advances in post-processing and blending of deterministic and ensemble forecasts is the outcome of several successful successive sessions organized at the General Assembly of the European Geosciences Union. Statistical post-processing and blending of forecasts are currently topics of important attention and development in many countries to produce optimal forecasts. Ten contributions have been received, covering key aspects of current concerns on statistical post-processing, namely the restoration of inter-variable dependences, the impact of model changes on the statistical relationships and how to cope with it, the operational implementation at forecasting centers, the development of appropriate metrics for forecast verification, and finally two specific applications to snow forecasts and seasonal forecasts of the North Atlantic Oscillation.

An influential step in weather forecasting was the introduction of ensemble forecasts in operational use due to their capability to account for the uncertainties in the future state of the atmosphere. However, ensemble weather forecasts are often underdispersive and might also contain bias, which calls for some form of post-processing. A popular approach to calibration is the ensemble model output statistics (EMOS) approach resulting in a full predictive distribution for a given weather variable. However, this form of univariate post-processing may ignore the prevailing spatial and/or temporal correlation structures among different dimensions. Since many applications call for spatially and/or temporally coherent forecasts, multivariate post-processing aims to capture these possibly lost dependencies. We compare the forecast skill of different nonparametric multivariate approaches to modeling temporal dependence of ensemble weather forecasts with different forecast horizons. The focus is on two-step methods, where after univariate post-processing, the EMOS predictive distributions corresponding to different forecast horizons are combined to a multivariate calibrated prediction using an empirical copula. Based on global ensemble predictions of temperature, wind speed and precipitation accumulation of the European Centre for Medium-Range Weather Forecasts from January 2002 to March 2014, we investigate the forecast skill of different versions of Ensemble Copula Coupling (ECC) and Schaake Shuffle (SSh). In general, compared with the raw and independently calibrated forecasts, multivariate post-processing substantially improves the forecast skill. While even the simplest ECC approach with low computational cost provides a powerful benchmark method, recently proposed advanced extensions of the ECC and the SSh are found to not provide any significant improvements over their basic counterparts.

Accurate and reliable probabilistic forecasts of hydrological quantities like runoff or water level are beneficial to various areas of society. Probabilistic state-of-the-art hydrological ensemble prediction models are usually driven with meteorological ensemble forecasts. Hence, biases and dispersion errors of the meteorological forecasts cascade down to the hydrological predictions and add to the errors of the hydrological models. The systematic parts of these errors can be reduced by applying statistical post-processing. For a sound estimation of predictive uncertainty and an optimal correction of systematic errors, statistical post-processing methods should be tailored to the particular forecast variable at hand. Former studies have shown that it can make sense to treat hydrological quantities as bounded variables. In this paper, a doubly truncated Bayesian model averaging (BMA) method, which allows for flexible post-processing of (multi-model) ensemble forecasts of water level, is introduced. A case study based on water level for a gauge of river Rhine, reveals a good predictive skill of doubly truncated BMA compared both to the raw ensemble and the reference ensemble model output statistics approach.

Statistical postprocessing is routinely applied to correct systematic errors of numerical weather prediction models (NWP) and to automatically produce calibrated local forecasts for end-users. Postprocessing is particularly relevant in complex terrain, where even state-of-the-art high-resolution NWP systems cannot resolve many of the small-scale processes shaping local weather conditions. In addition, statistical postprocessing can also be used to combine forecasts from multiple NWP systems. Here we assess an ensemble model output statistics (EMOS) approach to produce seamless temperature forecasts based on a combination of short-term ensemble forecasts from a convection-permitting limited-area ensemble and a medium-range global ensemble forecasting model. We quantify the benefit of this approach compared to only processing the high-resolution NWP. We calibrate and combine 2-m air temperature predictions for a large set of Swiss weather stations at the hourly time-scale. The multi-model EMOS approach ('Mixed EMOS') is able to improve forecasts by 30\\% with respect to direct model output from the high-resolution NWP. A detailed evaluation of Mixed EMOS reveals that it outperforms either single-model EMOS version by 8-12\\%. Valley location profit particularly from the model combination. All forecast variants perform worst in winter (DJF), however calibration and model combination improves forecast quality substantially.