Comparing Probabilistic Forecasting Systems with the Brier Score

2007 ◽  
Vol 22 (5) ◽  
pp. 1076-1088 ◽  
Author(s):  
Christopher A. T. Ferro
Keyword(s):  
Confidence Intervals ◽  
Brier Score ◽  
Ensemble Size ◽  
Probabilistic Forecasting ◽  
Probabilistic Forecasts

Abstract This article considers the Brier score for verifying ensemble-based probabilistic forecasts of binary events. New estimators for the effect of ensemble size on the expected Brier score, and associated confidence intervals, are proposed. An example with precipitation forecasts illustrates how these estimates support comparisons of the performances of competing forecasting systems with possibly different ensemble sizes.

scholarly journals Evaluating probabilistic forecasts of football matches: the case against the ranked probability score

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Edward Wheatcroft
Keyword(s):  
Scoring Rules ◽  
Brier Score ◽  
Sporting Events ◽  
Forecast Performance ◽  
Scoring Rule ◽  
Probability Score ◽  
Probabilistic Forecasts ◽  
Non Local ◽  
Evaluating Forecasts ◽  
Non Locality

Abstract A scoring rule is a function of a probabilistic forecast and a corresponding outcome used to evaluate forecast performance. There is some debate as to which scoring rules are most appropriate for evaluating forecasts of sporting events. This paper focuses on forecasts of the outcomes of football matches. The ranked probability score (RPS) is often recommended since it is ‘sensitive to distance’, that is it takes into account the ordering in the outcomes (a home win is ‘closer’ to a draw than it is to an away win). In this paper, this reasoning is disputed on the basis that it adds nothing in terms of the usual aims of using scoring rules. A local scoring rule is one that only takes the probability placed on the outcome into consideration. Two simulation experiments are carried out to compare the performance of the RPS, which is non-local and sensitive to distance, the Brier score, which is non-local and insensitive to distance, and the Ignorance score, which is local and insensitive to distance. The Ignorance score outperforms both the RPS and the Brier score, casting doubt on the value of non-locality and sensitivity to distance as properties of scoring rules in this context.

scholarly journals Verification of Ensemble-Based Uncertainty Circles around Tropical Cyclone Track Forecasts

2011 ◽  
Vol 26 (5) ◽  
pp. 664-676 ◽  
Author(s):  
Thierry Dupont ◽  
Matthieu Plu ◽  
Philippe Caroff ◽  
Ghislain Faure
Keyword(s):  
Tropical Cyclone ◽  
Large Error ◽  
Ensemble Prediction ◽  
Probabilistic Forecasting ◽  
Cyclone Track ◽  
Ensemble Prediction System ◽  
Weather Forecasts ◽  
Probabilistic Forecasts ◽  
Medium Range ◽  
Uncertainty Information

Abstract Several tropical cyclone forecasting centers issue uncertainty information with regard to their official track forecasts, generally using the climatological distribution of position error. However, such methods are not able to convey information that depends on the situation. The purpose of the present study is to assess the skill of the Ensemble Prediction System (EPS) from the European Centre for Medium-Range Weather Forecasts (ECMWF) at measuring the uncertainty of up to 3-day track forecasts issued by the Regional Specialized Meteorological Centre (RSMC) La Réunion in the southwestern Indian Ocean. The dispersion of cyclone positions in the EPS is extracted and translated at the RSMC forecast position. The verification relies on existing methods for probabilistic forecasts that are presently adapted to a cyclone-position metric. First, the probability distribution of forecast positions is compared to the climatological distribution using Brier scores. The probabilistic forecasts have better scores than the climatology, particularly after applying a simple calibration scheme. Second, uncertainty circles are built by fixing the probability at 75%. Their skill at detecting small and large error values is assessed. The circles have some skill for large errors up to the 3-day forecast (and maybe after); but the detection of small radii is skillful only up to 2-day forecasts. The applied methodology may be used to assess and to compare the skill of different probabilistic forecasting systems of cyclone position.

scholarly journals Probabilistic forecasting of wind power production losses in cold climates: a case study

2018 ◽  
Vol 3 (2) ◽  
pp. 667-680 ◽  
Author(s):  
Jennie Molinder ◽  
Heiner Körnich ◽  
Esbjörn Olsson ◽  
Hans Bergström ◽  
Anna Sjöblom
Keyword(s):  
Wind Power ◽  
Energy Production ◽  
Spatial Representation ◽  
Forecast Skill ◽  
Cold Climates ◽  
Probabilistic Forecasting ◽  
Probabilistic Forecasts ◽  
Forecasting System ◽  
Production Losses

Abstract. The problem of icing on wind turbines in cold climates is addressed using probabilistic forecasting to improve next-day forecasts of icing and related production losses. A case study of probabilistic forecasts was generated for a 2-week period. Uncertainties in initial and boundary conditions are represented with an ensemble forecasting system, while uncertainties in the spatial representation are included with a neighbourhood method. Using probabilistic forecasting instead of one single forecast was shown to improve the forecast skill of the ice-related production loss forecasts and hence the icing forecasts. The spread of the multiple forecasts can be used as an estimate of the forecast uncertainty and of the likelihood for icing and severe production losses. Best results, both in terms of forecast skill and forecasted uncertainty, were achieved using both the ensemble forecast and the neighbourhood method combined. This demonstrates that the application of probabilistic forecasting for wind power in cold climates can be valuable when planning next-day energy production, in the usage of de-icing systems and for site safety.

scholarly journals Probabilistic forecasting of wind power production losses in cold climates: A case study

2017 ◽  
Author(s):  
Jennie P. Söderman ◽  
Heiner Körnich ◽  
Esbjörn Olsson ◽  
Hans Bergström ◽  
Anna Sjöblom
Keyword(s):  
Wind Power ◽  
Energy Production ◽  
Cold Climate ◽  
Forecast Skill ◽  
Cold Climates ◽  
Probabilistic Forecasting ◽  
Probabilistic Forecasts ◽  
Forecasting System ◽  
Production Losses

Abstract. The problem of icing on wind turbines in cold climates is addressed using probabilistic forecasting to improve next- day forecasts of icing and related production losses. A case study of probabilistic forecasts was generated for a two- week period. Uncertainties in initial and boundary conditions are represented with an ensemble forecasting system, while uncertainties in the spatial representation are included with a neighbourhood method. Using probabilistic forecasting instead of one single forecast was shown to improve the forecast skill of the ice-related production loss forecasts and hence the icing forecasts. The spread of the multiple forecasts can be used as an estimate of the forecast uncertainty and of the likelihood for icing and severe production losses. Best results, both in terms of forecast skill and forecasted uncertainty, were achieved using both the ensemble forecast and the neighbourhood method combined. This demonstrates that the application of probabilistic forecasting for wind power in cold climate can be valuable when planning next-day energy production, in the usage of de-icing systems, and for site safety.

scholarly journals A Transformed Lagged Ensemble Forecasting Technique for Increasing Ensemble Size

2007 ◽  
Vol 135 (4) ◽  
pp. 1424-1438 ◽  
Author(s):  
Andrew R. Lawrence ◽  
James A. Hansen
Keyword(s):  
Prediction Models ◽  
Weather Prediction ◽  
Ensemble Forecast ◽  
Ensemble Forecasting ◽  
Limited Area ◽  
Ensemble Size ◽  
Probabilistic Forecasting ◽  
Ensemble Forecasts ◽  
Chaotic Model ◽  
The Impact

Abstract An ensemble-based data assimilation approach is used to transform old ensemble forecast perturbations with more recent observations for the purpose of inexpensively increasing ensemble size. The impact of the transformations are propagated forward in time over the ensemble’s forecast period without rerunning any models, and these transformed ensemble forecast perturbations can be combined with the most recent ensemble forecast to sensibly increase forecast ensemble sizes. Because the transform takes place in perturbation space, the transformed perturbations must be centered on the ensemble mean from the most recent forecasts. Thus, the benefit of the approach is in terms of improved ensemble statistics rather than improvements in the mean. Larger ensemble forecasts can be used for numerous purposes, including probabilistic forecasting, targeted observations, and to provide boundary conditions to limited-area models. This transformed lagged ensemble forecasting approach is explored and is shown to give positive results in the context of a simple chaotic model. By incorporating a suitable perturbation inflation factor, the technique was found to generate forecast ensembles whose skill were statistically comparable to those produced by adding nonlinear model integrations. Implications for ensemble forecasts generated by numerical weather prediction models are briefly discussed, including multimodel ensemble forecasting.

scholarly journals Designing Multimodel Applications with Surrogate Forecast Systems

2020 ◽  
Vol 148 (6) ◽  
pp. 2233-2249
Author(s):  
Leonard A. Smith ◽  
Hailiang Du ◽  
Sarah Higgins
Keyword(s):  
Bayesian Model Averaging ◽  
Weather Forecasting ◽  
Model Averaging ◽  
Probabilistic Forecasting ◽  
Single Model ◽  
Forecast System ◽  
Mathematical System ◽  
Probabilistic Forecasts ◽  
Perfect Model ◽  
Seasonal Weather

Abstract Probabilistic forecasting is common in a wide variety of fields including geoscience, social science, and finance. It is sometimes the case that one has multiple probability forecasts for the same target. How is the information in these multiple nonlinear forecast systems best “combined”? Assuming stationarity, in the limit of a very large forecast–outcome archive, each model-based probability density function can be weighted to form a “multimodel forecast” that will, in expectation, provide at least as much information as the most informative single model forecast system. If one of the forecast systems yields a probability distribution that reflects the distribution from which the outcome will be drawn, Bayesian model averaging will identify this forecast system as the preferred system in the limit as the number of forecast–outcome pairs goes to infinity. In many applications, like those of seasonal weather forecasting, data are precious; the archive is often limited to fewer than 26 entries. In addition, no perfect model is in hand. It is shown that in this case forming a single “multimodel probabilistic forecast” can be expected to prove misleading. These issues are investigated in the surrogate model (here a forecast system) regime, where using probabilistic forecasts of a simple mathematical system allows many limiting behaviors of forecast systems to be quantified and compared with those under more realistic conditions.

Evaluation of a Probabilistic Forecasting Methodology for Severe Convective Weather in the 2014 Hazardous Weather Testbed

2015 ◽  
Vol 30 (6) ◽  
pp. 1551-1570 ◽  
Author(s):  
Christopher D. Karstens ◽  
Greg Stumpf ◽  
Chen Ling ◽  
Lesheng Hua ◽  
Darrel Kingfield ◽  
...  
Keyword(s):  
Hazard Identification ◽  
Control Test ◽  
Test Bed ◽  
Probabilistic Forecasting ◽  
Test Experiment ◽  
Tornado Warnings ◽  
Probabilistic Forecasts ◽  
Verification Methodology ◽  
Convective Weather ◽  
Hazardous Weather

Abstract A proposed new method for hazard identification and prediction was evaluated with forecasters in the National Oceanic and Atmospheric Administration Hazardous Weather Testbed during 2014. This method combines hazard-following objects with forecaster-issued trends of exceedance probabilities to produce probabilistic hazard information, as opposed to the static, deterministic polygon and attendant text product methodology presently employed by the National Weather Service to issue severe thunderstorm and tornado warnings. Three components of the test bed activities are discussed: usage of the new tools, verification of storm-based warnings and probabilistic forecasts from a control–test experiment, and subjective feedback on the proposed paradigm change. Forecasters were able to quickly adapt to the new tools and concepts and ultimately produced probabilistic hazard information in a timely manner. The probabilistic forecasts from two severe hail events tested in a control–test experiment were more skillful than storm-based warnings and were found to have reliability in the low-probability spectrum. False alarm area decreased while the traditional verification metrics degraded with increasing probability thresholds. The latter finding is attributable to a limitation in applying the current verification methodology to probabilistic forecasts. Relaxation of on-the-fence decisions exposed a need to provide information for hazard areas below the decision-point thresholds of current warnings. Automated guidance information was helpful in combating potential workload issues, and forecasters raised a need for improved guidance and training to inform consistent and reliable forecasts.

scholarly journals Probabilistic photovoltaic power forecasting model based on deterministic forecasts

2020 ◽  
Vol 152 ◽  
pp. 01003
Author(s):  
L. Alfredo Fernandez-Jimenez ◽  
Sonia Terreros-Olarte ◽  
Pedro J. Zorzano-Santamaria ◽  
Montserrat Mendoza-Villena ◽  
Eduardo Garcia-Garrido
Keyword(s):  
Genetic Algorithm ◽  
Forecasting Model ◽  
Probabilistic Forecasting ◽  
Deterministic Models ◽  
Conditional Quantile ◽  
Normal Distributions ◽  
Probabilistic Forecasts ◽  
Mixture Of Normal Distributions ◽  
Quantile Regression Method ◽  
Power Forecasting

This paper presents an original probabilistic photovoltaic (PV) power forecasting model for the day-ahead hourly generation in a PV plant. The probabilistic forecasting model is based on 12 deterministic models developed with different techniques. An optimization process, ruled by a genetic algorithm, chooses the forecasts of the deterministic models in order to achieve the probability distribution function (PDF) for the PV generation in each one of the daylight hours of the following day in a parametric approach. The PDFs, which constitute the probabilistic forecasts, are a mixture of normal distributions, each one centred in the forecasts of the selected deterministic models. The genetic algorithm chooses the deterministic forecasts, the variance of the normal distributions and their weights in the mixture. In a case study the proposed model achieves better forecasting results than the obtained with the conditional quantile regression method applied to the same data used to develop the deterministic forecasting models.

Tracking bits of information through forecasting systems: from source to decision

2020 ◽  
Author(s):  
Steven Weijs ◽  
Hossein Foroozand
Keyword(s):  
Information Theory ◽  
Monitoring Network ◽  
Sources Of Information ◽  
Probabilistic Forecasting ◽  
Good Decision ◽  
Monitoring Network Design ◽  
Information Monitoring ◽  
Maximum Value ◽  
Probabilistic Forecasts ◽  
Forecasting System

<p>Probabilistic forecasts are essential for good decision making, because they communicate the forecaster's best attempt at representation of both information available and the remaining uncertainty of a variable of interest. The amount of information provided, which can be measured in bits using information theory, would then be a natural measure of success for the forecast in a verification exercise. On the other hand, it may seem rational to tune the forecasting system to provide maximum value to users. Somewhat counter-intuitively, there are arguments against tuning for maximum value. When the design of the forecasting system also includes the choice of the sources of information, monitoring network optimization becomes part of the problem to solve.  <br>In this presentation, we give a brief overview of the different roles information theory can have in these different aspects of probabilistic forecasting. These roles range from analysis of predictability, model selection, forecast verification, monitoring network design, and data assimilation by ensemble weighting. Using the same theoretical framework for all these aspects has the advantage that some connections can be made that may eventually lead to a more unified perspective on forecasting. </p>

scholarly journals A methodology for optimizing probabilistic wind power forecasting

2018 ◽  
Vol 45 ◽  
pp. 289-294
Author(s):  
Christos Stathopoulos ◽  
George Galanis ◽  
Nikolaos S. Bartsotas ◽  
George Kallos
Keyword(s):  
Wind Power ◽  
Reference Method ◽  
Wind Farms ◽  
Atmospheric Model ◽  
Optimization Techniques ◽  
Probabilistic Forecasting ◽  
Time Data ◽  
Confidence Levels ◽  
Probabilistic Forecasts ◽  
Error Distributions

Abstract. Deterministic wind power forecasts enclose an inherent uncertainty due to several sources of error. In order to counterbalance this deficiency, an analysis of the error characteristics and construction of probabilistic forecasts with associated confidence levels is necessary for the quantification of the corresponding uncertainty. This work proposes a probabilistic forecasting method using an atmospheric model, optimization techniques for addressing the temporal error dependencies and Kalman filtering for eliminating systematic errors and enhancing the symmetry-normality of the shaped error distributions. The method is applied in case studies, using real time data from four wind farms in Greece. The performance is compared against a reference method as well as other common methods showing an improvement in the predictive reliability.

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