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By the end of 2021, the renewable energy share of the global electricity capacity reached 38.3% and the new installations were dominated by wind and solar energy, showing global increases of 12.7% and 18.5% respectively. However, both wind and photovoltaic energy sources are highly volatile, making planning difficult for grid operators; thuss, accurate forecasts of the corresponding weather variables are essential for reliable electricity predictions. The most advanced approach in weather prediction is the ensemble method, which opens the door for probabilistic forecasting. However, ensemble forecasts are often underdispersive and subject to systematic bias. Hence, they require some form of statistical post‐processing, where parametric models provide full predictive distributions of the weather variables at hand. We propose a general two‐step machine‐learning‐based approach to calibrating ensemble weather forecasts, where, in the first step, improved point forecasts are generated, which then together with various ensemble statistics serve as input features of the neural network estimating the parameters of the predictive distribution. In two case studies based on 100 m wind speed and global horizontal irradiance forecasts of the operational ensemble prediction system of the Hungarian Meteorological Service, the predictive performance of this novel method is compared with the forecast skill of the raw ensemble and the state‐of‐the‐art parametric approaches. Both case studies confirm that, at least up to 48 hr, statistical post‐processing substantially improves the predictive performance of the raw ensemble for all forecast horizons considered. The variants of the proposed two‐step method investigated outperform in skill their competitors, and the suggested new approach is well applicable for different weather quantities and for a fair range of predictive distributions. [ABSTRACT FROM AUTHOR]

Current practice in predicting future weather is the use of numerical weather prediction (NWP) models to produce ensemble forecasts. Despite of enormous improvements over the last few decades, they still tend to exhibit bias and dispersion errors and, consequently, lack calibration. Therefore, these forecasts may be improved by statistical postprocessing. In this work, we propose a D‐vine‐copula‐based postprocessing for 10 m surface wind speed ensemble forecasts. This approach makes use of quantile regression related to D‐vine copulas, which is highly data driven and allows one to adopt more general dependence structures as the state‐of‐the‐art zero‐truncated ensemble model output statistic (tEMOS) model. We compare local and global D‐vine copula quantile regression (DVQR) models to the corresponding tEMOS models and their gradient‐boosting extensions (tEMOS‐GB) for different sets of predictor variables using one lead time and 60 surface weather stations in Germany. Furthermore, we investigate which types of training periods can improve the performance of tEMOS and the D‐vine‐copula‐based method for wind speed postprocessing. We observe that the D‐vine‐based postprocessing yields a comparable performance with respect to tEMOS if only wind speed ensemble variables are included and to substantial refinements if additional meteorological and station‐specific weather variables are integrated. As our main result, we note that, in the global setting, DVQR is able to provide better scores than tEMOS‐GB in general, whereas the local DVQR is able to substantially outperform the local tEMOS‐GB at particular stations admitting nonlinear relationships among the variables. In addition, we remark that training periods capturing seasonal patterns perform the best. Last but not least, we adapt a criterion for calculating the variable importance in D‐vine copulas and we outline which predictor variables are due to this approach the most important for the correction of wind speed ensemble forecasts. [ABSTRACT FROM AUTHOR]

An influential step in weather forecasting was the introduction of ensemble forecasts in operational use owing 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 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 non‐parametric 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 ensemble model output statistics 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. In general, compared with the raw and independently calibrated forecasts, multivariate post‐processing substantially improves the forecast skill. Although even the simplest ECC approach with low computational cost provides a powerful benchmark method, recently proposed advanced extensions of the ECC and the Schaake shuffle are found to not provide any significant improvements over their basic counterparts. [ABSTRACT FROM AUTHOR]

Probabilistic forecasting of electricity demand (load) facilitates the efficient management and operations of energy systems. Weather is a key determinant of load. However, modelling load using weather is challenging because the relationship cannot be assumed to be linear. Although numerous studies have focussed on load forecasting, the literature on using the uncertainty in weather while estimating the load probability distribution is scarce. In this study, we model load for Great Britain using weather ensemble predictions, for lead times from one to six days ahead. A weather ensemble comprises a range of plausible future scenarios for a weather variable. It has been shown that the ensembles from weather models tend to be biased and underdispersed, which requires that the ensembles are post-processed. Surprisingly, the post-processing of weather ensembles has not yet been employed for probabilistic load forecasting. We post-process ensembles based on: (1) ensemble model output statistics: to correct for bias and dispersion errors by calibrating the ensembles, and (2) ensemble copula coupling: to ensure that ensembles remain physically consistent scenarios after calibration. The proposed approach compares favourably to the case when no weather information, raw weather ensembles or post-processed ensembles without ensemble copula coupling are used during the load modelling. [ABSTRACT FROM AUTHOR]

Ensemble prediction systems (EPSs) serve as a popular technique to provide probabilistic precipitation prediction in short- and medium-range forecasting. However, numerical models still suffer from imperfect configurations associated with data assimilation and physical parameterization, which can lead to systemic bias. Even state-of-the-art models often fail to provide high-quality precipitation forecasting, especially for extreme events. In this study, two deep-learning-based models—a shallow neural network (NN) and a deep NN with convolutional layers (CNN)—were used as alternative post-processing approaches to further improve the probabilistic forecasting of precipitation over China with 1–7 lead days. A popular conventional method—the censored and shifted gamma distribution-based ensemble model output statistics (CSG EMOS)—was used as the baseline. Re-forecasts run using a frozen EPS—Global Ensemble Forecast System version 12—were collected as the raw ensembles spanning from 2000 to 2019. The re-forecast data were generated once per day and consisted of one control run and four perturbed members. We used the calendar year 2018 as the validation period and 2019 as the testing period, and the remaining 18 years of data were used for training. According to the results, in terms of the continuous ranked probability score (CRPS) and the Brier score, the CNN model significantly outperforms the shallow NN model, as well as the CSG EMOS approach and the raw ensemble, especially for heavy or extreme precipitation events (those exceeding 50 mm/day). A remarkable degradation was seen when reducing the size of training samples from 18 years of data to two years. The spatial distribution of the CRPS shows that the stations in central China were better calibrated than those in other regions. With a lead time of 1 day, the CNN model was found to be superior to the other models (in terms of the CRPS) at 74.5% of the study stations. These results indicate that deep NNs can serve as a promising approach to the statistical post-processing of probabilistic precipitation forecasting.

In the last decades, wind power became the second largest energy source in the EU covering 16% of its electricity demand. However, due to its volatility, accurate short range wind power predictions are required for successful integration of wind energy into the electrical grid. Accurate predictions of wind power require accurate hub height wind speed forecasts, where the state-of-the-art method is the probabilistic approach based on ensemble forecasts obtained from multiple runs of numerical weather prediction models. Nonetheless, ensemble forecasts are often uncalibrated and might also be biased, thus require some form of post-processing to improve their predictive performance. We propose a novel flexible machine learning approach for calibrating wind speed ensemble forecasts, which results in a truncated normal predictive distribution. In a case study based on 100m wind speed forecasts produced by the operational ensemble prediction system of the Hungarian Meteorological Service, the forecast skill of this method is compared with the predictive performance of three different ensemble model output statistics approaches and the raw ensemble forecasts. We show that compared with the raw ensemble, post-processing always improves the calibration of probabilistic and accuracy of point forecasts, and from the four competing methods, the novel machine learning based approach results in the best overall performance. [ABSTRACT FROM AUTHOR]

In recent years, ensemble weather forecasting has become a routine at all major weather prediction centers. These forecasts are obtained from multiple runs of numerical weather prediction models with different initial conditions or model parametrizations. However, ensemble forecasts can often be underdispersive and also biased, so some kind of postprocessing is needed to account for these deficiencies. One of the most popular state of the art statistical postprocessing techniques is the ensemble model output statistics (EMOS), which provides a full predictive distribution of the studied weather quantity. We propose a novel EMOS model for calibrating wind speed ensemble forecasts, where the predictive distribution is a generalized extreme value (GEV) distribution left truncated at zero (TGEV). The truncation corrects the disadvantage of the GEV distribution‐based EMOS models of occasionally predicting negative wind speed values, without affecting its favorable properties. The new model is tested on four datasets of wind speed ensemble forecasts provided by three different ensemble prediction systems, covering various geographical domains and time periods. The forecast skill of the TGEV EMOS model is compared with the predictive performance of the truncated normal, log‐normal and GEV methods and the raw and climatological forecasts as well. The results verify the advantageous properties of the novel TGEV EMOS approach. [ABSTRACT FROM AUTHOR]

Statistical post-processing is an indispensable tool for providing accurate weather forecasts and early warnings for weather extremes. Most statistical post-processing is univariate, with dependencies introduced via use of an empirical copula. Standard empirical methods take a dependence template from either the raw ensemble output (ensemble copula coupling, ECC) or the observations (Schaake Shuffle, SSh). There are drawbacks to both methods. In ECC it is assumed that the raw ensemble simulates the dependence well, which is not always the case (e.g. 2-meter temperature in The Netherlands). The Schaake Shuffle is not able to capture flow dependent changes to the dependence and the choice of observations is key. Here we compare a reshuffled standard ensemble model output statistics (EMOS) approach with two multivariate bias adjustment approaches that have not been used before in a post-processing context: 1) the multivariate bias correction with N-dimensional probability density function transform (MBCn) and 2) multivariate ranks that are defined with optimal assignment (OA). These methods have the advantage that they are able to explicitly capture the dependence structure that is present in the observations. We apply ECC, the Schaake Shuffle, MBCn and OA to 2-m and dew point temperature forecasts at seven stations in The Netherlands. Forecasts are verified with both univariate and multivariate methods, and using a heat index derived from both variables, the wet-bulb globe temperature (WBGT). Our results demonstrate that the spatial and inter-variable dependence structure is more realistic in MBCn and OA compared to ECC or the Schaake Shuffle. The variogram score shows that while ECC is most skilful for the first two days, at moderate lead times MBCn is most skilful and at the longest lead times OA is more skilful than both ECC and MBCn. Overall, we highlight the importance of considering the dependence between variables and locations in the statistical post-processing of weather forecasts.

• A hybrid approach to probabilistic solar irradiance forecasting is studied. • We propose a post-processing model for numerical weather prediction ensembles. • Two case studies cover distinct weather models, domains and temporal resolutions. • Significant improvement compared to the ensemble for lead times up to at least 2 days. In order to enable the transition towards renewable energy sources, probabilistic energy forecasting is of critical importance for incorporating volatile power sources such as solar energy into the electrical grid. Solar energy forecasting methods often aim to provide probabilistic predictions of solar irradiance. In particular, many hybrid approaches combine physical information from numerical weather prediction models with statistical methods. Even though the physical models can provide useful information at intra-day and day-ahead forecast horizons, ensemble weather forecasts from multiple model runs are often not calibrated and show systematic biases. We propose a post-processing model for ensemble weather predictions of solar irradiance at temporal resolutions between 30 min and 6 h. The proposed models provide probabilistic forecasts in the form of a censored logistic probability distribution for lead times up to 5 days and are evaluated in two case studies covering distinct physical models, geographical regions, temporal resolutions, and types of solar irradiance. We find that post-processing consistently and significantly improves the forecast performance of the ensemble predictions for lead times up to at least 48 h and is well able to correct the systematic lack of calibration. [ABSTRACT FROM AUTHOR]

Abstract The main approach to probabilistic weather forecasting has been the use of ensemble forecasting. In ensemble forecasting, the probability information is generally derived by using several numerical model runs, with perturbation of the initial conditions, physical schemes or dynamic core of the numerical weather prediction (NWP) models. However, ensemble forecasting usually tends to be under‐dispersive. Statistical post‐processing has, therefore, become an essential component of any ensemble prediction system aiming to improve the quality of numerical weather forecasts as they seek to generate calibrated and sharp predictive distributions of future weather quantities. Different versions of the ensemble model output statistics (EMOS) and the Bayesian model averaging (BMA) post‐processing methods are used in the present paper to calibrate 24, 48 and 72 hr forecasts of 24 hr accumulative precipitation. The ensemble employs the weather and research forecasting (WRF) model with eight different configurations which were run over Iran for six months (September 2015–February 2016). The results reveal that the BMA and EMOS‐censored, shifted gamma (CSG) techniques are substantially successful at improving the raw WRF ensemble forecasts; however, each approach improves different aspects of the forecast quality. The BMA method is more accurate, skilful and reliable than the EMOS‐CSG method, but has poorer discrimination. Moreover, it has better resolution in predicting the probability of high‐precipitation events than the EMOS‐CSG method.

Probabilistic weather forecasts from ensemble systems require statistical postprocessing to yield calibrated and sharp predictive distributions. This paper presents an area-covering postprocessing method for ensemble precipitation predictions. We rely on the ensemble model output statistics (EMOS) approach, which generates probabilistic forecasts with a parametric distribution whose parameters depend on (statistics of) the ensemble prediction. A case study with daily precipitation predictions across Switzerland highlights that postprocessing at observation locations indeed improves high-resolution ensemble forecasts, with 4.5 % CRPS reduction on average in the case of a lead time of 1 day. Our main aim is to achieve such an improvement without binding the model to stations, by leveraging topographical covariates. Specifically, regression coefficients are estimated by weighting the training data in relation to the topographical similarity between their station of origin and the prediction location. In our case study, this approach is found to reproduce the performance of the local model without using local historical data for calibration. We further identify that one key difficulty is that postprocessing often degrades the performance of the ensemble forecast during summer and early autumn. To mitigate, we additionally estimate on the training set whether postprocessing at a specific location is expected to improve the prediction. If not, the direct model output is used. This extension reduces the CRPS of the topographical model by up to another 1.7 % on average at the price of a slight degradation in calibration. In this case, the highest improvement is achieved for a lead time of 4 days. [ABSTRACT FROM AUTHOR]

In this paper we propose some parametric and non-parametric post-processing methods for calibrating wind speed forecasts of nine Weather Research and Forecasting (WRF) models for locations around the cities of Valparaíso and Santiago de Chile (Chile). The WRF outputs are generated with different planetary boundary layers and land-surface model parametrizations and they are calibrated using observations from 37 monitoring stations. Statistical calibration is performed with the help of ensemble model output statistics and quantile regression forest (QRF) methods both with regional and semi-local approaches. The best performance is obtained by the QRF using a semi-local approach and considering some specific weather variables from WRF simulations. [ABSTRACT FROM AUTHOR]

The main approach to probabilistic weather forecasting has been the use of ensemble forecasting. In ensemble forecasting, the probability information is generally derived by using several numerical model runs, with perturbation of the initial conditions, physical schemes or dynamic core of the numerical weather prediction (NWP) models. However, ensemble forecasting usually tends to be under-dispersive. Statistical post-processing has, therefore, become an essential component of any ensemble prediction system aiming to improve the quality of numerical weather forecasts as they seek to generate calibrated and sharp predictive distributions of future weather quantities. Different versions of the ensemble model output statistics (EMOS) and the Bayesian model averaging (BMA) post-processing methods are used in the present paper to calibrate 24, 48 and 72 hr forecasts of 24 hr accumulative precipitation. The ensemble employs the weather and research forecasting (WRF) model with eight different configurations which were run over Iran for six months (September 2015-February 2016). The results reveal that the BMA and EMOScensored, shifted gamma (CSG) techniques are substantially successful at improving the raw WRF ensemble forecasts; however, each approach improves different aspects of the forecast quality. The BMA method is more accurate, skilful and reliable than the EMOS-CSG method, but has poorer discrimination. Moreover, it has better resolution in predicting the probability of highprecipitation events than the EMOS-CSG method. [ABSTRACT FROM AUTHOR]

Abstract Modelling forecast uncertainty is a difficult task in any forecasting problem. In weather forecasting a possible solution is the use of forecast ensembles, which are obtained from multiple runs of numerical weather prediction models with various initial conditions and model parametrizations to provide information about the expected uncertainty. Currently all major meteorological centres issue forecasts using their operational ensemble prediction systems. However, it is a general problem that the spread of the ensemble is too small compared to observations at specific sites resulting in under‐dispersive forecasts, leading to a lack of calibration. In order to correct this problem, various statistical calibration techniques have been developed in the last two decades. In the present work different post‐processing techniques were tested for calibrating nine member ensemble forecasts of temperature for Santiago de Chile, obtained by the Weather Research and Forecasting model using different planetary boundary layer and land surface model parametrizations. In particular, the ensemble model output statistics and Bayesian model averaging techniques were implemented and, since the observations are characterized by large altitude differences, the estimation of model parameters was adapted to the actual conditions at hand. Compared to the raw ensemble, all tested post‐processing approaches significantly improve the calibration of probabilistic forecasts and the accuracy of point forecasts. The ensemble model output statistics method using parameter estimation based on expert clustering of stations (according to their altitudes) shows the best forecast skill.

Wind shear can occur at all flight levels; however, it is particularly dangerous at low levels, from the ground up to approximately 2000 feet. If this phenomenon can occur during the take-off and landing of an aircraft, it may interfere with the normal altitude change of the aircraft, causing delay and cancellation of the aircraft, as well as economic damage. In this paper, to estimate the probabilistic forecasts of low-level wind shear at Gimpo, Gimhae, Incheon and Jeju International Airports, an Ensemble Model Output Statistics (EMOS) model based on a left-truncated normal distribution with a cutoff zero was applied. Observations were obtained from Gimpo, Gimhae, Incheon and Jeju International Airports and 13 ensemble member forecasts generated from the Limited-Area Ensemble Prediction System (LENS), for the period December 2018 to February 2020. Prior to applying to EMOS models, statistical consistency was analyzed by using a rank histogram and kernel density estimation to identify the uniformity of ensembles with corresponding observations. Performances were evaluated by mean absolute error, continuous ranked probability score and probability integral transform. The results showed that probabilistic forecasts obtained from the EMOS model exhibited better prediction skills when compared to the raw ensembles.

We investigate the effect of statistical post‐processing on the probabilistic skill of discomfort index (DI) and indoor wet‐bulb globe temperature (WBGTid) ensemble forecasts, both calculated from the corresponding forecasts of temperature and dew point temperature. Two different methodological approaches to calibration are compared. In the first case, we start with joint post‐processing of the temperature and dew point forecasts and then create calibrated samples of DI and WBGTid using samples from the obtained bivariate predictive distributions. This approach is compared with direct post‐processing of the heat index ensemble forecasts. For this purpose, a novel ensemble model output statistics model based on a generalized extreme value distribution is proposed. The predictive performance of both methods is tested on the operational temperature and dew point ensemble forecasts of the European Centre for Medium‐Range Weather Forecasts and the corresponding forecasts of DI and WBGTid. For short lead times (up to day 6), both approaches significantly improve the forecast skill. Among the competing post‐processing methods, direct calibration of heat indices exhibits the best predictive performance, very closely followed by the more general approach based on joint calibration of temperature and dew point temperature. Additionally, a machine learning approach is tested and shows comparable performance for the case when one is interested only in forecasting heat index warning level categories. [ABSTRACT FROM AUTHOR]

• Ensemble modeling for 1-min diffuse fraction is discussed. • The raw ensemble is post-processed using ensemble model output statistics (EMOS). • EMOS outperforms the best stand-alone models such as Yang2 and Engerer2. • EMOS is superior to simple model blending in terms of CRPS and ignorance score. Separation models split diffuse and direct components of solar radiation from the global horizontal radiation. At the moment, all separation models only issue predictions that are deterministic (as opposed to probabilistic). Since the best prediction is necessarily probabilistic, a parametric post-processing framework called the ensemble model output statistics (EMOS) is introduced in this paper, to make probabilistic predictions. EMOS takes the diffuse fractions predicted by an ensemble of existing 1-min separation models, and outputs a predictive distribution, with parameters optimized by maximum likelihood estimation. Clearly, the EMOS-based separation modeling goes beyond the current literature, in terms of uncertainty quantification. Eight popular separation models from the literature, with different architectures, are used to demonstrate the predictive power of EMOS. Using 1-min high-quality radiometric data from seven stations in the USA and four stations in Europe, it is found that Y ang2 is the best stand-alone model with an average RMSE of 21.8%, in terms of direct normal irradiance prediction, contrasting the 26.3% of the previously reported best model, namely, E ngerer2. On the other hand, the EMOS post-processed predictions have an average RMSE of 20.8%, which is lower than that of the best stand-alone model. Moreover, EMOS is shown superior to simple model averaging, in terms of continuous ranked probability score and ignorance score. [ABSTRACT FROM AUTHOR]

The main goal of this study is to assess the performance of the analog‐based post‐processing method applied to the Austrian ALADIN‐LAEF wind speed ensemble predictions through a set of sensitivity experiments. Evaluation of several analog‐based configurations using various meteorological variables as predictors is therefore conducted. The results of those experiments are compared to the ensemble model output statistics (EMOS) baseline model. The hypothesis further investigated is that using summarized measures, such as mean and standard deviation of an ensemble for several meteorological variables, is comparable to the analog post‐processing using all of the ensemble members. Results show that both analog‐based and EMOS experiments considerably improve the raw model forecast. Even though the improvement over raw model forecast is evident, large differences among nearby stations are noticed in the highly complex terrain. The processes at lower stations seem to be better represented by the raw model, which leads to a better input forecast to the post‐processing and a better overall result than for the mountain stations. The analog‐based method is overall comparable to or even outperforms the EMOS. Assessing the post‐processing performance for high wind speeds shows that the analog experiments can improve the raw forecast, exhibiting significantly higher skill than the EMOS. The difference among all analog experiments is less pronounced, especially the experiment using all of the raw model ensemble members and the one using summarized measures. Furthermore, it is demonstrated that the usage of summarized ensemble measures is an optimal way to improve the forecast skill, compared to the other analog‐based experiments and the EMOS model. Therefore, it is suggested that it is not necessary to increase the computational costs by using the full input spectrum of a raw probabilistic model, that is, all ALADIN‐LAEF members as predictors, as the summarized metric suffices. [ABSTRACT FROM AUTHOR]

Modelling forecast uncertainty is a difficult task in any forecasting problem. In weather forecasting a possible solution is the use of forecast ensembles, which are obtained from multiple runs of numerical weather prediction models with various initial conditions and model parametrizations to provide information about the expected uncertainty. Currently all major meteorological centres issue forecasts using their operational ensemble prediction systems. However, it is a general problem that the spread of the ensemble is too small compared to observations at specific sites resulting in under‐dispersive forecasts, leading to a lack of calibration. In order to correct this problem, various statistical calibration techniques have been developed in the last two decades. In the present work different post‐processing techniques were tested for calibrating nine member ensemble forecasts of temperature for Santiago de Chile, obtained by the Weather Research and Forecasting model using different planetary boundary layer and land surface model parametrizations. In particular, the ensemble model output statistics and Bayesian model averaging techniques were implemented and, since the observations are characterized by large altitude differences, the estimation of model parameters was adapted to the actual conditions at hand. Compared to the raw ensemble, all tested post‐processing approaches significantly improve the calibration of probabilistic forecasts and the accuracy of point forecasts. The ensemble model output statistics method using parameter estimation based on expert clustering of stations (according to their altitudes) shows the best forecast skill. [ABSTRACT FROM AUTHOR]

The implementation of statistical postprocessing of ensemble forecasts is increasingly developed among national weather services. The so-called Ensemble Model Output Statistics (EMOS) method, which consists of generating a given distribution whose parameters depend on the raw ensemble, leads to significant improvements in forecast performance for a low computational cost, and so is particularly appealing for reduced performance computing architectures. However, the choice of a parametric distribution has to be sufficiently consistent so as not to lose information on predictability such as multimodalities or asymmetries. Different distributions are applied to the postprocessing of the European Centre for Medium-range Weather Forecast (ECMWF) ensemble forecast of surface temperature. More precisely, a mixture of Gaussian and skewed normal distributions are tried from 3- up to 360-h lead time forecasts, with different estimation methods. For this work, analytical formulas of the continuous ranked probability score have been derived and appropriate link functions are used to prevent overfitting. The mixture models outperform single parametric distributions, especially for the longest lead times. This statement is valid judging both overall performance and tolerance to misspecification.

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 postprocessing. For a sound estimation of predictive uncertainty and an optimal correction of systematic errors, statistical postprocessing 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 postprocessing of possibly multimodel ensemble forecasts of water level, is introduced. A case study based on water levels 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. Using rolling training periods, BMA considerably outerperforms ensemble model output statistics. However, this gap shrinks drastically when using analog‐based training periods. Key Points: Doubly truncated Bayesian model averaging (BMA) is introduced as a postprocessing methodThe proposed BMA approach, which is tailored to bounded variables, outperforms an ensemble model output statistics reference methodThe benefit from BMA is considerable for rolling training periods but shrinks drastically for analog‐based training periods [ABSTRACT FROM AUTHOR]

The computational cost as well as the probabilistic skill of ensemble forecasts depends on the spatial resolution of the numerical weather prediction model and the ensemble size. Periodically, e.g. when more computational resources become available, it is appropriate to reassess the balance between resolution and ensemble size. Recently, it has been proposed to investigate this balance in the context of dual‐resolution ensembles, which use members with two different resolutions to make probabilistic forecasts. This study investigates whether statistical post‐processing of such dual‐resolution ensemble forecasts changes the conclusions regarding the optimal dual‐resolution configuration. Medium‐range dual‐resolution ensemble forecasts of 2 m temperature have been calibrated using ensemble model output statistics. The forecasts are produced with ECMWF's Integrated Forecast System and have horizontal resolutions between 18 and 45 km. The ensemble sizes range from 8 to 254 members. The forecasts are verified with SYNOP station data. Results show that score differences between various single‐ and dual‐resolution configurations are strongly reduced by statistical post‐processing. Therefore, the benefit of some dual‐resolution configurations over single‐resolution configurations appears to be less pronounced than for raw forecasts. Moreover, the ranking of the ensemble configurations can be affected by the statistical post‐processing. [ABSTRACT FROM AUTHOR]

Bayesian model averaging (BMA) and ensemble model output statistics (EMOS) were used to improve the prediction skill of the 500 hPa geopotential height field over the northern hemisphere with lead times of 1–7 days based on ensemble forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF), National Centers for Environmental Prediction (NCEP), and UK Met Office (UKMO) ensemble prediction systems. The performance of BMA and EMOS were compared with each other and with the raw ensembles and climatological forecasts from the perspective of both deterministic and probabilistic forecasting. The results show that the deterministic forecasts of the 500 hPa geopotential height distribution obtained from BMA and EMOS are more similar to the observed distribution than the raw ensembles, especially for the prediction of the western Pacific subtropical high. BMA and EMOS provide a better calibrated and sharper probability density function than the raw ensembles. They are also superior to the raw ensembles and climatological forecasts according to the Brier score and the Brier skill score. Comparisons between BMA and EMOS show that EMOS performs slightly better for lead times of 1–4 days, whereas BMA performs better for longer lead times. In general, BMA and EMOS both improve the prediction skill of the 500 hPa geopotential height field.

In this study, the statistical post-processing methods that include bias-corrected and probabilistic forecasts of wind speed measured in PyeongChang, which is scheduled to host the 2018 Winter Olympics, are compared and analyzed to provide more accurate weather information. The six post-processing methods used in this study are as follows: mean bias-corrected forecast, mean and variance bias-corrected forecast, decaying averaging forecast, mean absolute bias-corrected forecast, and the alternative implementations of ensemble model output statistics (EMOS) and Bayesian model averaging (BMA) models, which are EMOS and BMA exchangeable models by assuming exchangeable ensemble members and simplified version of EMOS and BMA models. Observations for wind speed were obtained from the 26 stations in PyeongChang and 51 ensemble member forecasts derived from the European Centre for Medium-Range Weather Forecasts (ECMWF Directorate, 2012) that were obtained between 1 May 2013 and 18 March 2016. Prior to applying the post-processing methods, reliability analysis was conducted by using rank histograms to identify the statistical consistency of ensemble forecast and corresponding observations. Based on the results of our study, we found that the prediction skills of probabilistic forecasts of EMOS and BMA models were superior to the biascorrected forecasts in terms of deterministic prediction, whereas in probabilistic prediction, BMA models showed better prediction skill than EMOS. Even though the simplified version of BMA model exhibited best prediction skill among the mentioned six methods, the results showed that the differences of prediction skills between the versions of EMOS and BMA were negligible. [ABSTRACT FROM AUTHOR]

This study focuses on an objective comparison of eight ensemble methods using the same data, training period, training method, and validation period. The eight ensemble methods are: BMA (Bayesian Model Averaging), HMR (Homogeneous Multiple Regression), EMOS (Ensemble Model Output Statistics), HMR+ with positive coefficients, EMOS+ with positive coefficients, PEA_ROC (Performance-based Ensemble Averaging using ROot mean square error and temporal Correlation coefficient), WEA_Tay (Weighted Ensemble Averaging based on Taylor's skill score), and MME (Multi-Model Ensemble). Forty-five years (1961-2005) of data from 14 CMIP5 models and APHRODITE (Asian Precipitation- Highly-Resolved Observational Data Integration Towards Evaluation of Water Resources) data were used to compare the performance of the eight ensemble methods. Although some models underestimated the variability of monthly mean temperature (MMT), most of the models effectively simulated the spatial distribution of MMT. Regardless of training periods and the number of ensemble members, the prediction skills of BMA and the four multiple linear regressions (MLR) were superior to the other ensemble methods (PEA_ROC, WEA_Tay, MME) in terms of deterministic prediction. In terms of probabilistic prediction, the four MLRs showed better prediction skills than BMA. However, the differences among the four MLRs and BMA were not significant. This resulted from the similarity of BMA weights and regression coefficients. Furthermore, prediction skills of the four MLRs were very similar. Overall, the four MLRs showed the best prediction skills among the eight ensemble methods. However, more comprehensive work is needed to select the best ensemble method among the numerous ensemble methods. [ABSTRACT FROM AUTHOR]

Two seemingly unrelated postprocessing concepts retaining inter-variable, spatial and temporal rank dependence structures from raw ensemble forecasts are compared and unified. The first concept combines ensemble model output statistics (EMOS), which fits and adjusts a parametric probability density function, with the ensemble copula coupling (ECC) reordering notion. The second concept is the member-by-member postprocessing (MBMP), based on a direct parametric adjustment of the raw ensemble members. It is shown that MBMP can be interpreted as a specific EMOS-ECC variant. In an application to ensemble forecasts for temperature, EMOS-ECC and MBMP succeed in outperforming the raw ensemble and conserving correlation structures. [ABSTRACT FROM AUTHOR]

Weather forecasts are typically given in the form of forecast ensembles obtained from multiple runs of numerical weather prediction models with varying initial conditions and physics parameterizations. Such ensemble predictions tend to be biased and underdispersive and thus require statistical post-processing. In the ensemble model output statistics approach, a probabilistic forecast is given by a single parametric distribution with parameters depending on the ensemble members. The paper proposes two semilocal methods for estimating the ensemble model output statistics coefficients where the training data for a specific observation station are augmented with corresponding forecast cases from stations with similar characteristics. Similarities between stations are determined by using either distance functions or clustering based on various features of the climatology, forecast errors and locations of the observation stations. In a case-study on wind speed over Europe with forecasts from the 'Grand limited area model ensemble prediction system', the similarity-based semilocal models proposed show significant improvement in predictive performance compared with standard regional and local estimation methods. They further allow for estimating complex models without numerical stability issues and are computationally more efficient than local parameter estimation. [ABSTRACT FROM AUTHOR]

Recently, all major weather prediction centers provide forecast ensembles of different weather quantities, which are obtained from multiple runs of numerical weather prediction models with various initial conditions and model parametrizations. However, ensemble forecasts often show an underdispersive character and may also be biased, so that some post-processing is needed to account for these deficiencies. Probably the most popular modern post-processing techniques are the ensemble model output statistics (EMOS) and the Bayesian model averaging (BMA), which provide estimates of the density of the predictable weather quantity. In the present work, an EMOS method for calibrating ensemble forecasts of precipitation accumulation is proposed, where the predictive distribution follows a censored and shifted gamma (CSG) law with parameters depending on the ensemble members. The CSG EMOS model is tested on ensemble forecasts of 24-h precipitation accumulation of the eight-member University of Washington mesoscale ensemble and on the 11-member ensemble produced by the operational Limited Area Model Ensemble Prediction System of the Hungarian Meteorological Service. The predictive performance of the new EMOS approach is compared with the fit of the raw ensemble, the generalized extreme value (GEV) distribution-based EMOS model, and the gamma BMA method. According to the results, the proposed CSG EMOS model slightly outperforms the GEV EMOS approach in terms of calibration of probabilistic and accuracy of point forecasts and shows significantly better predictive skill than the raw ensemble and the BMA model. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

State-of-the-art weather forecasts usually rely on ensemble prediction systems, accounting for the different sources of uncertainty. As ensembles are typically uncalibrated, they should get statistically postprocessed. Several multivariate ensemble postprocessing techniques that additionally consider spatial, inter-variable and/or temporal dependences have been developed. These can be roughly divided into two groups. The first group comprises parametric, mainly low-dimensional, approaches that are tailored to specific settings. The second group involves non-parametric reordering methods that impose a specific dependence template on univariately postprocessed forecasts and are suitable in any dimension. In this article, these different strategies are combined, with the aim of exploiting the benefits of both concepts. Specifically, a high-dimensional postprocessing problem is divided into multiple low-dimensional instances, each of which is postprocessed via a suitable multivariate parametric method. From each postprocessed low-dimensional distribution, a sample is drawn, which is then reordered according to the corresponding multidimensional rank structure of an appropriately chosen dependence template. In this context, different ranking concepts for multivariate settings are discussed. Finally, all reordered samples are aggregated to obtain the overall postprocessed ensemble. The new approach is applied to ensemble forecasts for temperature and wind speed at several locations from the European Centre for Medium-Range Weather Forecasts, using a recent bivariate ensemble model output statistics postprocessing technique and a reordering based on the raw ensemble forecasts similar to the ensemble copula coupling method. It shows good predictive skill and outperforms reference ensembles. [ABSTRACT FROM AUTHOR]

Ensemble model output statistics (EMOS) is a statistical tool for post-processing forecast ensembles of weather variables obtained from multiple runs of numerical weather prediction models in order to produce calibrated predictive probability density functions. The EMOS predictive probability density function is given by a parametric distribution with parameters depending on the ensemble forecasts. We propose an EMOS model for calibrating wind speed forecasts based on weighted mixtures of truncated normal (TN) and log-normal (LN) distributions where model parameters and component weights are estimated by optimizing the values of proper scoring rules over a rolling training period. The new model is tested on wind speed forecasts of the 50 member European Centre for Medium-range Weather Forecasts ensemble, the 11 member Aire Limitée Adaptation dynamique Développement International-Hungary Ensemble Prediction System ensemble of the Hungarian Meteorological Service, and the eight-member University of Washington mesoscale ensemble, and its predictive performance is compared with that of various benchmark EMOS models based on single parametric families and combinations thereof. The results indicate improved calibration of probabilistic and accuracy of point forecasts in comparison with the raw ensemble and climatological forecasts. The mixture EMOS model significantly outperforms the TN and LN EMOS methods; moreover, it provides better calibrated forecasts than the TN-LN combination model and offers an increased flexibility while avoiding covariate selection problems. © 2016 The Authors Environmetrics Published by JohnWiley & Sons Ltd. [ABSTRACT FROM AUTHOR]

Hydrologic ensemble forecasts driven by atmospheric ensemble prediction systems need statistical postprocessing in order to account for systematic errors in terms of both location and spread. Runoff is an inherently multivariate process with typical events lasting from hours in case of floods to weeks or even months in case of droughts. This calls for multivariate postprocessing techniques that yield well-calibrated forecasts in univariate terms and ensure a realistic temporal dependence structure at the same time. To this end, the univariate ensemble model output statistics (EMOS) postprocessing method is combined with two different copula approaches that ensure multivariate calibration throughout the entire forecast horizon. The domain of this study covers three subcatchments of the river Rhine that represent different sizes and hydrological regimes: the Upper Rhine up to the gauge Maxau, the river Moselle up to the gauge Trier, and the river Lahn up to the gauge Kalkofen. In this study, the two approaches to model the temporal dependence structure are ensemble copula coupling (ECC), which preserves the dependence structure of the raw ensemble, and a Gaussian copula approach (GCA), which estimates the temporal correlations from training observations. The results indicate that both methods are suitable for modeling the temporal dependencies of probabilistic hydrologic forecasts. [ABSTRACT FROM AUTHOR]

Ensembles of forecasts are obtained from multiple runs of numerical weather forecasting models with different initial conditions and typically employed to account for forecast uncertainties. However, biases and dispersion errors often occur in forecast ensembles: they are usually underdispersive and uncalibrated and require statistical post-processing. We present an Ensemble Model Output Statistics (EMOS) method for calibration of wind-speed forecasts based on the log-normal (LN) distribution and we also show a regime-switching extension of the model, which combines the previously studied truncated normal (TN) distribution with the LN. Both models are applied to wind-speed forecasts of the eight-member University of Washington mesoscale ensemble, the 50 member European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble and the 11 member Aire Limitée Adaptation dynamique Développement International-Hungary Ensemble Prediction System (ALADIN-HUNEPS) ensemble of the Hungarian Meteorological Service; their predictive performance is compared with that of the TN and general extreme value (GEV) distribution based EMOS methods and the TN-GEV mixture model. The results indicate improved calibration of probabilistic forecasts and accuracy of point forecasts in comparison with the raw ensemble and climatological forecasts. Further, the TN-LN mixture model outperforms the traditional TN method and its predictive performance is able to keep up with models utilizing the GEV distribution without assigning mass to negative values. [ABSTRACT FROM AUTHOR]

All numerical weather prediction models used for the wind industry need to produce their forecasts starting from the main synoptic hours 00, 06, 12, and 18 UTC, once the analysis becomes available. The 6-h latency time between two consecutive model runs calls for strategies to fill the gap by providing new accurate predictions having, at least, hourly frequency. This is done to accommodate the request of frequent, accurate and fresh information from traders and system regulators to continuously adapt their work strategies. Here, we propose a strategy where quasi-real time observed wind speed and weather model predictions are combined by means of a novel Ensemble Model Output Statistics (EMOS) strategy. The success of our strategy is measured by comparisons against observed wind speed from SYNOP stations over Italy in the years 2018 and 2019. • First attempt to couple in an efficient and economic way real-time data and ensemble predictions. • First assessment of the added value of real-time observations in a wind calibration. • Real-time data can be easily and economically ingested in an EMOS-based calibration. • Ingestion of real-time data produces noticeable benefits vs. static calibrations. • Real-time data provide added value to the whole wind predictive probability density. [ABSTRACT FROM AUTHOR]

Wind shear can occur at all flight levels; however, it is particularly dangerous at low levels, from the ground up to approximately 2000 feet. If this phenomenon can occur during the take-off and landing of an aircraft, it may interfere with the normal altitude change of the aircraft, causing delay and cancellation of the aircraft, as well as economic damage. In this paper, to estimate the probabilistic forecasts of low-level wind shear at Gimpo, Gimhae, Incheon and Jeju International Airports, an Ensemble Model Output Statistics (EMOS) model based on a left-truncated normal distribution with a cutoff zero was applied. Observations were obtained from Gimpo, Gimhae, Incheon and Jeju International Airports and 13 ensemble member forecasts generated from the Limited-Area Ensemble Prediction System (LENS), for the period December 2018 to February 2020. Prior to applying to EMOS models, statistical consistency was analyzed by using a rank histogram and kernel density estimation to identify the uniformity of ensembles with corresponding observations. Performances were evaluated by mean absolute error, continuous ranked probability score and probability integral transform. The results showed that probabilistic forecasts obtained from the EMOS model exhibited better prediction skills when compared to the raw ensembles. [ABSTRACT FROM AUTHOR]

The implementation of statistical postprocessing of ensemble forecasts is increasingly developed among national weather services. The so-called Ensemble Model Output Statistics (EMOS) method, which consists of generating a given distribution whose parameters depend on the raw ensemble, leads to significant improvements in forecast performance for a low computational cost, and so is particularly appealing for reduced performance computing architectures. However, the choice of a parametric distribution has to be sufficiently consistent so as not to lose information on predictability such as multimodalities or asymmetries. Different distributions are applied to the postprocessing of the European Centre for Medium-range Weather Forecast (ECMWF) ensemble forecast of surface temperature. More precisely, a mixture of Gaussian and skewed normal distributions are tried from 3- up to 360-h lead time forecasts, with different estimation methods. For this work, analytical formulas of the continuous ranked probability score have been derived and appropriate link functions are used to prevent overfitting. The mixture models outperform single parametric distributions, especially for the longest lead times. This statement is valid judging both overall performance and tolerance to misspecification. [ABSTRACT FROM AUTHOR]

Ensemble verification of low-level wind shear (LLWS) is an important issue in airplane landing operation and management. However, there have been few studies on the probabilistic forecasts of LLWS obtained from ensemble prediction system. In this study, we analyzed a reliability analysis to verify LLWS ensemble member forecasts and observation based on the limited grid points around Jeju International Airport in Jeju. Homogeneous and non-homogeneous regression models were used to reduce the bias and dispersion existing ensemble prediction system and to provide probabilistic forecast. Prior to applying probabilistic forecast model, reliability analysis was conducted by using rank histogram to identify the statistical consistency of LLWS ensemble forecasts and corresponding observations. Based on the results of our study, we found that LLWS ensemble forecasts had a consistent positive bias, indicating over-forecasting, and were under-dispersed for all seasons. To correct such biases, homogeneous regression and non-homogeneous regressions as EMOS (Ensemble Model Output Statistics) and EMOS exchangeable model by assuming exchangeable ensemble members were applied. The prediction skills of the methods were compared by the mean absolute error and continuous ranked probability score. We found that the prediction skills of probabilistic forecasts of EMOS exchangeable model were superior to the bias-corrected forecasts in terms of deterministic prediction. [ABSTRACT FROM AUTHOR]

Bayesian model averaging (BMA) and ensemble model output statistics (EMOS) were used to improve the prediction skill of the 500 hPa geopotential height field over the northern hemisphere with lead times of 1–7 days based on ensemble forecasts from the European Centre for Medium-Range Weather Forecasts (ECMWF), National Centers for Environmental Prediction (NCEP), and UK Met Office (UKMO) ensemble prediction systems. The performance of BMA and EMOS were compared with each other and with the raw ensembles and climatological forecasts from the perspective of both deterministic and probabilistic forecasting. The results show that the deterministic forecasts of the 500 hPa geopotential height distribution obtained from BMA and EMOS are more similar to the observed distribution than the raw ensembles, especially for the prediction of the western Pacific subtropical high. BMA and EMOS provide a better calibrated and sharper probability density function than the raw ensembles. They are also superior to the raw ensembles and climatological forecasts according to the Brier score and the Brier skill score. Comparisons between BMA and EMOS show that EMOS performs slightly better for lead times of 1–4 days, whereas BMA performs better for longer lead times. In general, BMA and EMOS both improve the prediction skill of the 500 hPa geopotential height field. [ABSTRACT FROM AUTHOR]