Ensemble Bayesian Model Averaging Research Articles

Bayesian typhoon precipitation prediction with a mixture of ensemble forecast-based and historical event-based prediction functions

Statistical post-processing has been widely adopted in probabilistic forecasting, especially when a predictive distribution of weather variables is of interest. Among the available post-processing methods, a common tool is the ensemble Bayesian model averaging. Challenges arise when it is applied to heavy rain prediction, including the precipitation produced by tropical cyclones. The issues are related to the rare extreme event and limited available data for model training. To address this, we propose in this research a Bayesian mixture model, Bmix, based on information from forecast members and historical tropical cyclones, rather than solely on immediately observed precipitation data. This approach provides a grid-specific Bayesian predictive distribution and an easy-to-derive probabilistic forecast with posterior samples generated from the Markov chain Monte Carlo algorithm. This post-processing procedure can be executed on each grid simultaneously, reducing the computational time significantly. In addition, a categorized Bmix (C.Bmix) is implemented to accommodate different scenarios such as heavy or torrential rain in applications. The proposed approaches are demonstrated on the 24-hour accumulated precipitation forecast of a category 4-equivalent super typhoon Dujuan landing in Taiwan in 2015; while two others, Matmo and Soudelor, are adopted to provide historical information. Over the Taiwan main island, a total of 1282 grids are considered, each with a resolution of 5 km and 20 ensemble member forecasts from the Weather Research and Forecasting Ensemble Prediction System (WEPS) at a 6-hour interval during the typhoon period. The analyses show that the proposed mixture approaches present larger percentages of positive CRPSS values than traditional BMA. For instance, at the time when Dujuan made landfall, the percentages are 92.2 % for Bmix, 95.2 % for C.Bmix, and 15.4 % for BMA when the true precipitation amount exceeds 200 mm/24 h. The proposed methods outperform in the probability prediction and the overall pattern of precipitation.

Probabilistic seasonal precipitation forecasts using quantiles of ensemble forecasts

Seasonal precipitation forecasting is vital for weather-sensitive sectors. Global Circulation Models (GCM) routinely produce ensemble Seasonal Climate Forecasts (SCFs) but suffer from issues like low forecast resolution and skills. To address these issues in this study, we introduce a post-processing method, Quantile Ensemble Bayesian Model Averaging (QEBMA). It utilises quantiles from a GCM ensemble forecast to create a pseudo-ensemble forecast. Through their reasonable linear relationships with observations, each pseudo-member connects a hurdle distribution with a point mass at zero for dry months and a gamma distribution for wet months. These distributions are mixed to construct a forecast probability distribution with their weights, proportional to the quantiles’ historical forecast performance. QEBMA is applied to three GCMs, including GloSea5 from the United Kingdom, ECMWF from Europe and ACCESS-S1 from Australia, for monthly precipitation forecasts in 32 locations across four climate zones in Australia. Leave-one-month-out cross-validation results illustrate that QEBMA enhances forecast skills compared to raw GCMs and other post-processing techniques, including quantile mapping and Extended Copula Post-Processing (ECPP), for forecast lead time of 0 to 2 months, based on five metrics. The skill improvements achieved by QEBMA are often statistically significant, particularly when compared to raw GCM forecasts across the 32 study locations. Among these post-processing models, only QEBMA consistently outperforms the SCF benchmark climatology, offering a promising alternative for improving seasonal precipitation forecasts.

Predicting Iran's achievement to Sustainable Development Goal 3.2: A systematic analysis of neonatal mortality with scenario-based projections to 2030.

Sustainable Development Goal 3.2 (SDG 3.2) is to reduce Under-5 and neonatal mortality rates (U5MR and NMR), two major health systems' performance indicators, globally by 2030. We aimed to report Iran's U5MR and NMR status during 2010-2017 and its achievement of SDG 3.2 by 2030, using scenario-based projection. To estimate the national and subnational levels of U5MR and NMR, we applied an Ensemble Bayesian Model Averaging (EBMA) with Gaussian Process Regression (GPR) and Spatio_temporal models. We used all available data sources including: 12-year data from the Death Registration System (DRS), two censuses, and a demographic and health surveys (DHS). This study employed two approaches, Maternal Age Cohort (MAC) and Maternal Age Period (MAP), to analyze summary birth history data obtained from censuses and DHS. In addition, we calculated the child mortality rate directly from DHS using the complete birth history method. National and subnational NMR was projected up to 2030 with a scenario-based method using average Annual Rate of Reduction (ARR) introduced by UN-IGME. In 2017, national U5MR and NMR were 15·2 (12·4-18·0) and 11·8 (10·4-13·2), with an average ARR of 5·1% (2·1-8·9) and 3·1% (0·9-5·8) during 2010-2017, respectively. According to our projection scenarios, 17 provinces have not fulfilled SDG 3.2 for NMR yet, and the current trend (the current trend of NMR improvement in Iran) will not result in reaching SDG for some provinces by 2030; However, if each province has the same neonatal mortality annual reduction rate as the best-performing province in the same region, besides achieving SDG, the national NMR will be reduced to 5·2, and almost 92,000 newborn lives will be saved. Iran has achieved SDG3.2 regarding U5MR and NMR; however, there are provincial inequalities. For all provinces to reach SDG3.2, health policies should focus on reducing provincial inequalities by precise planning for neonatal health care.

Bayesian Model Averaging Ensemble Approach for Multi-Time-Ahead Groundwater Level Prediction Combining the GRACE, GLEAM, and GLDAS Data in Arid Areas

Accurate groundwater level (GWL) prediction is essential for the sustainable management of groundwater resources. However, the prediction of GWLs remains a challenge due to insufficient data and the complicated hydrogeological system. In this study, we investigated the ability of the Gravity Recovery and Climate Experiment (GRACE) satellite data, the Global Land Evaporation Amsterdam Model (GLEAM) data, the Global Land Data Assimilation System (GLDAS) data, and the publicly available meteorological data in 1-, 2-, and 3-month-ahead GWL prediction using three traditional machine learning models (extreme learning machine, ELM; support vector machine, SVR; and random forest, RF). Meanwhile, we further developed the Bayesian model averaging (BMA) by combining the ELM, SVR, and RF models to avoid the uncertainty of the single models and to improve the predicting accuracy. The validity of the forcing data and the BMA model were assessed for three GWL monitoring wells in the Zhangye Basin in Northwest China. The results indicated that the applied forcing data could be treated as validated inputs to predict the GWL up to 3 months ahead due to the achieved high accuracy of the machine learning models (NS > 0.55). The BMA model could significantly improve the performance of the single machine learning models. Overall, the BMA model reduced the RMSE of the ELM, SVR, and RF models in the testing period by about 13.75%, 24.01%, and 17.69%, respectively; while it improved the NS by about 8.32%, 16.13%, and 9.67% for 1-, 2-, and 3-month-ahead GWL prediction, respectively. The uncertainty analysis results also verified the reliability of the BMA model in multi-time-ahead GWL predicting. This highlighted the efficiency of the satellite data, satellite-based data, and publicly available data as substitute inputs in machine-learning-based GWL prediction, particularly for areas with insufficient or missing data. Meanwhile, the BMA ensemble strategy can serve as a powerful and reliable approach in multi-time-ahead GWL prediction when risk-based decision making is needed or a lack of relevant hydrogeological data impedes the application of the physical models.

Bayesian model averaging to improve the yield prediction in wheat breeding trials

Accurate pre-harvest prediction of wheat yield through secondary traits helps to facilitate plant breeding and reduce costs. Machine learning (ML) algorithms are increasingly applied to grain yield with remote sensing data. However, the performance of individual ML algorithms varies for different species in different environments due to different sources of uncertainty. This study proposed a novel wheat yield prediction framework based on canopy hyperspectral reflectance (350–2500 nm) and adopted the ensemble Bayesian model averaging (EBMA) method to improve model performance. To develop the yield prediction models, important bands extracted by the Boruta feature selection method were fed into four linear ML models and four nonlinear ML models. Meanwhile, Bayesian model averaging (BMA) weights obtained based on model cross-validation performance were used to combine the predictions of individual ML models. Compared to the best-performing individual model, the EBMA models obtained a weak accuracy improvement by integrating only the linear models or the nonlinear models. Additionally, the integration of two linear models and two non-linear models simultaneously was analyzed. Results indicate that most EBMA combinations of mixed linear and non-linear models achieved higher prediction accuracy than those integrating a single type of model and the best-performing individual model. The advantage of the EBMA method is that it produces a prediction distribution that reflects the uncertainty associated with deterministic predictions. With full consideration of the model diversity of ensemble members, the EBMA modeling framework provides an alternative method for predicting grain yield in plant breeding trials.

Multi-model Evaluation and Bayesian Model Averaging in Quantitative Air Quality Forecasting in Central China

There has been much interest in air pollution and the forecasting skill of air quality models in China since winter 2013. Different air quality models use different parameters (e.g., meteorological fields, emission sources and the initial concentrations of pollutants) and therefore their forecast results tend to have large systematic and random errors. We evaluated the concentrations of six pollutants in Henan Province predicted by three air quality models—the China Meteorological Administration Unified Atmospheric Chemistry Environment (CUACE) model, the Nested Air Quality Prediction (NAQP) model and the Community Multiscale Air Quality (CMAQ) model. We then established multi-model ensemble Bayesian model averaging (BMA). The prediction effect for PM2.5 and O3 was ranked as CUACE > CMAQ > NAQP and the prediction effect for SO2, NO2 and CO was CMAQ > NAQP > CUACE. All the models systematically underestimated O3 and heavy PM2.5 pollution events. For PM2.5 concentrations with a 24-h lead time, the root-mean-square error of BMA decreased by 35, 37, 68 and 50%, respectively, in winter, spring, summer and autumn relative to the CUACE model, whereas the normalized mean bias of BMA decreased by 67, 83, 94 and 55%, respectively, for O3 in the four seasons. Compared with the CMAQ model, the root-mean-square error of the SO2, NO2 and CO forecasts by BMA were reduced by 29, 33 and 39%, respectively. The evolution of the concentrations of the six pollutants during a heavy pollution event predicted by BMA was consistent with the observations.

Empirical Bayes Model Averaging with Influential Observations: Tuning Zellner’s [formula omitted] Prior for Predictive Robustness

The behavior of Bayesian model averaging (BMA) for the normal linear regression model in the presence of influential observations that contribute to model misfit is investigated. Remedies to attenuate the potential negative impacts of such observations on inference and prediction are proposed. The methodology is motivated by the view that well-behaved residuals and good predictive performance often go hand-in-hand. Focus is placed on regression models that use variants on Zellner's g prior. Studying the impact of various forms of model misfit on BMA predictions in simple situations points to prescriptive guidelines for “tuning” Zellner's g prior to obtain optimal predictions. The tuning of the prior distribution is obtained by considering theoretical properties that should be enjoyed by the optimal fits of the various models in the BMA ensemble. The methodology can be thought of as an “empirical Bayes” approach to modeling, as the data help to inform the specification of the prior in an attempt to attenuate the negative impact of influential cases.

Accounting for uncertainty in complex alluvial aquifer modeling by Bayesian multi-model approach

Alluvial aquifers by nature are complex caused by varied depositional environments. Developing a reliable groundwater model to represent an alluvial aquifer is non-trivial. Also, relying on a single best calibrated model may not be sufficient because of an inadequate choice of model parameter values. To better understand groundwater dynamics and improve model prediction reliability, this study presents a Bayesian multi-model uncertainty quantification (BMMUQ) framework to account for model parameter uncertainty in complex alluvial groundwater modeling. The methodology was applied to the agriculturally intensive Mississippi River alluvial aquifer (MRAA), Northeast Louisiana. An aquifer architecture was first constructed using 7,259 well logs in the MRAA area which covers three fluvial deposits (alluvium, braided-stream terrace, and braided-stream terrace-loess). A 12-layer MODFLOW model was then developed to address the alluvial aquifer complexity and well calibrated through a genetic algorithm. This study quantified model parameter uncertainty in hydraulic conductivity and specific storage of sand facies. Bayesian model averaging (BMA) with the Expectation Maximization (EM) algorithm was adopted to derive posterior model weights and head variances of 50 alternative conceptual groundwater flow models, and thereby obtains BMA ensemble model predictions instead of only relying on the best calibrated conceptual model. Results show that an estimated around 950 million m3 of groundwater storage loss occurs in 2015 with respect to the beginning of 2004, due to high groundwater demand for irrigation in the MRAA area. Explicitly quantifying model uncertainty can produce more reliable groundwater level predictions from BMA ensemble model. The presented groundwater modeling framework improves our understanding of the MRAA and provides a valuable tool to assist agricultural water management.

Forecast and uncertainty analysis of extreme precipitation in China from ensemble of multiple climate models

Global climate change is expected to have a major impact on the hydrological cycle. Understanding potential changes in future extreme precipitation is important to the planning of industrial and agricultural water use, flood control, and ecological environment protection. In this paper, we study the statistical distribution of extreme precipitation based on historical observation and various global climate models (GCMs), and predict the expected change and the associated uncertainty. The empirical frequency, generalized extreme value (GEV) distribution, and L-moment estimator algorithms are used to establish the statistical distribution relationships and the multi-model ensemble predictions are established by the Bayesian model averaging (BMA) method. This ensemble forecast takes advantage of multi-model synthesis, which is an effective measure to reduce the uncertainty of model selection in extreme precipitation forecasting. We have analyzed the relationships among extreme precipitation, return period, and precipitation durations for 6 representative cities in China. More significantly, the approach allows for establishing the uncertainty of extreme precipitation predictions. The empirical frequency from the historical data is all within the 90% confidence interval of the BMA ensemble. For the future predictions, the extreme precipitation intensities of various durations tend to become larger compared to the historic results. The extreme precipitation under the RCP8.5 scenario is greater than that under the RCP2.6 scenario. The developed approach not only effectively gives the extreme precipitation predictions, but also can be used to any other extreme hydrological events in future climate.

Ensemble Downscaling of Soil Moisture Data Using BMA and ATPRK

Soil moisture is essential information for meteorological and hydrological analyses. To date, many efforts have been made to achieve the two goals for soil moisture data, i.e., the improvement of accuracy and resolution, which is very challenging. We presented an ensemble downscaling method for quality improvement of gridded soil moisture data in terms of the accuracy and the spatial resolution by the integration of BMA (Bayesian model averaging) and ATPRK (area-to-point regression kriging). In the experiments, the BMA ensemble showed a 22% better accuracy than the data sets from ESA CCI (European Space Agency-Climate Change Initiative), ERA5 (ECMWF Reanalysis 5), and GLDAS (Global Land Data Assimilation System) in terms of RMSE (root mean square error). Also, the ATPRK downscaling could enhance the spatial resolution from 0.25o to 0.05o while preserving the improved accuracy and the spatial pattern of the BMA ensemble, without under- or over-estimation. The quality-improved data sets can contribute to a variety of local and regional applications related to soil moisture, such as agriculture, forest, hydrology, and meteorology. Because the ensemble downscaling method can be applied to the other land surface variables such as temperature, humidity, precipitation, and evapotranspiration, it can be a viable option to complement the accuracy and the spatial resolution of satellite images and numerical models.

Multi-model ensemble simulated non-point source pollution based on Bayesian model averaging method and model uncertainty analysis.

Watershed models are cost-effective and powerful tools for evaluating and controlling non-point source pollution (NPSP), while the reliability of watershed models in a management context depends largely on inherent uncertainties in model predictions. The objective of this study is to present the use of multi-model ensemble applied to streamflow, total nitrogen (TN), and total phosphorus (TP) simulation and quantify the uncertainty resulting from model structure. In this study, three watershed models, which have different structures in simulating NPSP, were selected to conduct watershed monthly streamflow, TN load, and TP load ensemble simulation and 90% credible intervals based on Bayesian model averaging (BMA) method. The result using the observed data of the Yixunhe watershed revealed that the coefficient of determination and Nash-Sutcliffe coefficient of the BMA model simulate streamflow, TN load, and TP load were better than that of the single model. The higher the efficiency of a single model is, the greater the weight during the BMA ensemble simulation is. The 90% credible interval of BMA has a high coverage of measured values in this study. This indicates that the BMA method can not only provide simulation with better precision through ensemble simulation but also provide quantitative evaluation of the model structure through interval, which could offer rich information of the NPSP simulation and management.

Optimization of Multi-Ecosystem Model Ensembles to Simulate Vegetation Growth at the Global Scale

Process-based ecosystem models are increasingly used to simulate the effects of a changing environment on vegetation growth in the past, present, and future. To improve the simulation, the multimodel ensemble mean (MME) and ensemble Bayesian model averaging (EBMA) methods are often used in optimizing the integration of ecosystem model ensemble. These two methods were compared with four other optimization techniques, including genetic algorithm (GA), particle swarm optimization (PSO), cuckoo search (CS), and interior-point method (IPM), to evaluate their efficiency in this article. Here, we focused on eight commonly used ecosystem models to simulate vegetation growth, represented by the growing season leaf area index (LAIgs), collected globally from 2000 to 2014. The performances of the multimodel ensembles and individual models were compared using the satellite-observed LAI products as the reference. Generally, ensemble simulations provide more accurate estimates than individual models. There were significant performance differences among the six tested methods. The IPM ensemble model simulated LAIgs more accurately than the other tested models, as the reduction in the root-mean-square error was 84.99% higher than the MME results and 61.50% higher than the EBMA results. Thus, IPM optimization can reproduce LAIgs trends accurately for 91.62% of the global vegetated area, which is double the area of the results from MME. Furthermore, the contributions and uncertainties of the individual models in the final simulated IPM LAIgs changes indicated that the best individual model (CABLE) showed the greatest area fraction for the maximum IPM weight (32.49%), especially in the low-lalitude to midlatitude areas.

Using Bayesian Model Averaging to Calibrate Temperature Forecast Ensembles in Hawassa Town, Ethiopia

Bayesian model averaging (BMA) is a statistical way of post-processing forecasts ensembles to create predictive probability density functions (pdfs) for weather quantities. BMA has been proposed as way of correcting underdispersion in ensemble forecasts. The output of ensemble BMA is a weighted average of pdfs centered on the individual bias-corrected ensemble forecast. The BMA weights are posterior probabilities of the models generating the forecast, and show the relative contribution of the component models to the prediction over the training period. This paper focuses on short range forecasting of daily maximum temperature. Forecasting temperature, we have approximated the conditional pdf by normal distribution centered at a linear function of the forecast. Since we are not able to get an ensemble of forecasts for Ethiopia, we have used the previous eight years from 2003 to 2010 data as ensemble and 2011 as observation. The BMA approach yields predictive distribution for temperature thatwere much better calibrated than those based on naive averaging of the forecasts.

On the incidence of meteorological and hydrological processors: Effect of resolution, sharpness and reliability of hydrological ensemble forecasts

Meteorological and hydrological ensemble prediction systems are imperfect. Their outputs could often be improved through the use of a statistical processor, opening up the question of the necessity of using both processors (meteorological and hydrological), only one of them, or none. This experiment compares the predictive distributions from four hydrological ensemble prediction systems (H-EPS) utilising the Ensemble Kalman filter (EnKF) probabilistic sequential data assimilation scheme. They differ in the inclusion or not of the Distribution Based Scaling (DBS) method for post-processing meteorological forecasts and the ensemble Bayesian Model Averaging (ensemble BMA) method for hydrological forecast post-processing. The experiment is implemented on three large watersheds and relies on the combination of two meteorological reforecast products: the 4-member Canadian reforecasts from the Canadian Centre for Meteorological and Environmental Prediction (CCMEP) and the 10-member American reforecasts from the National Oceanic and Atmospheric Administration (NOAA), leading to 14 members at each time step. Results show that all four tested H-EPS lead to resolution and sharpness values that are quite similar, with an advantage to DBS + EnKF. The ensemble BMA is unable to compensate for any bias left in the precipitation ensemble forecasts. On the other hand, it succeeds in calibrating ensemble members that are otherwise under-dispersed. If reliability is preferred over resolution and sharpness, DBS + EnKF + ensemble BMA performs best, making use of both processors in the H-EPS system. Conversely, for enhanced resolution and sharpness, DBS is the preferred method.

Performance and parameterization of the BMA model applied in the Huaihe River Basin

以淮河流域吴家渡水文站作为试验站点，采用基于贝叶斯平均法（BMA）的集合预报模型处理来源于马斯京根法、一维水动力学方法、BPNN（Back Propagation Neural Network）的预报流量序列，通过分析BMA的参数以及其预报结果，对各方法在淮河典型站点流量预报中的适用性进行验证与分析.经2003-2016年19场洪水模拟检验可知，BMA模型能够有效避免模型选择带来的洪水预报误差放大效应，可以提供高精度、鲁棒性强的洪水预报结果.通过进一步比较各模型统计最优的频率与BMA权重值之间的相关性，发现权重值不适用于对单场洪水预报精度评定，而适用于描述多场洪水预报中，模型为最优的统计频率；基于大量先验信息，提前获取BMA的权重等参数，将是指导模型选择、降低洪水预报不确定性、改进洪水预报技术的有效手段.;In this study, the BMA (Bayesian Model Averaging) method is used to deal with forecasts derived from three different flood routing models, i.e. the Muskingum, the one-dimensional hydrodynamic routing model and the BPNN (Back Propagation Neural Network). The numerical experiments are processed at the Wujiadu hydrological station in the Huaihe River Basin as a test site. By studying the BMA method parameters and ensemble forecast results the applicability of each method in the Huaihe River station flow forecast is verified and analyzed. According to the results from our experimental tests among 19 flood events, from 2003 to 2016, it is concluded that the BMA ensemble forecasting method can effectively avoid the flood forecast error amplification caused by uncertainty underlying in model selection and can provide high accuracy and robust flood forecasting result. After comparing the statistically optimal frequency and BMA weight value of each model, it is concluded that the BMA weight parameter reflects the probability that the model is optimal in the mean sense and is not suitable for evaluating the technicity of the model in one single flood event. It is an effective method to guide the model selection, reduce the uncertainties of flood forecasting and improve the flood forecasting techniques.

Improving microwave brightness temperature predictions based on Bayesian model averaging ensemble approach

The choices of the parameterizations for each component in a microwave emission model have significant effects on the quality of brightness temperature (Tb) simulation. How to reduce the uncertainty in the Tb simulation is investigated by adopting a statistical post-processing procedure with the Bayesian model averaging (BMA) ensemble approach. The simulations by the community microwave emission model (CMEM) coupled with the community land model version 4.5 (CLM4.5) over mainland China are conducted by the 24 configurations from four vegetation opacity parameterizations (VOPs), three soil dielectric constant parameterizations (SDCPs), and two soil roughness parameterizations (SRPs). Compared with the simple arithmetical averaging (SAA) method, the BMA reconstructions have a higher spatial correlation coefficient (larger than 0.99) than the C-band satellite observations of the advanced microwave scanning radiometer on the Earth observing system (AMSR-E) at the vertical polarization. Moreover, the BMA product performs the best among the ensemble members for all vegetation classes, with a mean root-mean-square difference (RMSD) of 4K and a temporal correlation coefficient of 0.64.

Blending of satellite SST products using ensemble Bayesian model averaging (EBMA)

ABSTRACTSea surface temperature (SST) is an important parameter in understanding atmosphere–ocean circulation processes and monitoring global climate change. In addition to in situ observations of SST, a series of satellite-borne instruments provide global coverage of SST through infrared and microwave remote sensing. This study was the first application of the ensemble Bayesian model averaging (EBMA) method to the blending of satellite SST products to minimize inherent uncertainties and improve the validation statistics. Monthly SST products from moderate resolution imaging spectroadiometer, Advanced Very High Resolution Radiometer and Advanced Microwave Scanning Radiometer-EOS were used as ensemble members. The mean bias and root-mean-square error (RMSE) of the EBMA method were better than those of the individual members or generic methods such as ensemble mean and median. This is because the weighting scheme adjusted by the expectation–maximization algorithm was based on the suitability of each member derived from training procedures. The errors of EBMA in our experiment had almost no spatial and temporal autocorrelation with regard to the latitude and month, which implies that the EBMA method can serve as a viable option for blending of satellite SST, although more experiments are necessary to determine its feasibility in more detail.

Limitations of Ensemble Bayesian Model Averaging for forecasting social science problems

We compare the accuracies of simple unweighted averages and Ensemble Bayesian Model Averaging (EBMA) for combining forecasts in the social sciences. A review of prior studies from the domain of economic forecasting finds that the simple average was more accurate than EBMA in four studies out of five. On average, the error of EBMA was 5% higher than that of the simple average. A reanalysis and extension of a published study provides further evidence for US presidential election forecasting. The error of EBMA was 33% higher than the corresponding error of the simple average. Simple averages are easy both to describe and to understand, and thus are easy to use. In addition, simple averages provide accurate forecasts in many settings. Researchers who are developing new approaches to combining forecasts need to compare the accuracy of their method to this widely established benchmark. Forecasting practitioners should favor simple averages over more complex methods unless there is strong evidence in support of differential weights.

Spatial Postprocessing of Ensemble Forecasts for Temperature Using Nonhomogeneous Gaussian Regression

Abstract Statistical postprocessing techniques are commonly used to improve the skill of ensembles from numerical weather forecasts. This paper considers spatial extensions of the well-established nonhomogeneous Gaussian regression (NGR) postprocessing technique for surface temperature and a recent modification thereof in which the local climatology is included in the regression model to permit locally adaptive postprocessing. In a comparative study employing 21-h forecasts from the Consortium for Small Scale Modelling ensemble predictive system over Germany (COSMO-DE), two approaches for modeling spatial forecast error correlations are considered: a parametric Gaussian random field model and the ensemble copula coupling (ECC) approach, which utilizes the spatial rank correlation structure of the raw ensemble. Additionally, the NGR methods are compared to both univariate and spatial versions of the ensemble Bayesian model averaging (BMA) postprocessing technique.

Calibrating ensemble forecasting models with sparse data in the social sciences

We consider ensemble Bayesian model averaging (EBMA) in the context of small-n prediction tasks in the presence of large numbers of component models. With large numbers of observations for calibrating ensembles, relatively small numbers of component forecasts, and low rates of missingness, the standard approach to calibrating forecasting ensembles introduced by Raftery et al. (2005) performs well. However, data in the social sciences generally do not fulfill these requirements. In these circumstances, EBMA models may miss-weight components, undermining the advantages of the ensemble approach to prediction. In this article, we explore these issues and introduce a “wisdom of the crowds” parameter to the standard EBMA framework, which improves its performance. Specifically, we show that this solution improves the accuracy of EBMA forecasts in predicting the 2012 US presidential election and the US unemployment rate.