arXiv subjects

Annette Möller

Publications and source records attributed to Annette Möller.

17 recordsLinked to original sources

arXiv2026

Bivariate Postprocessing of Wind Vectors

To quantify the uncertainty in numerical weather prediction (NWP) forecasts, ensemble prediction systems are utilized. Although NWP forecasts continuously improve, they suffer from systematic bias and dispersion errors. To obtain well calibrated and sharp predictive probability distributions, statistical postprocessing methods are applied to NWP output. Recent developments focus on multivariate postprocessing models incorporating dependencies directly into the model. We introduce three novel bivariate postprocessing approaches, and analyze their performance for joint postprocessing of bivariate wind vector components for 60 stations in Germany. Bivariate vine copula based models, a bivariate gradient boosted version of ensemble model output statistics (EMOS), and a bivariate distributional regression network (DRN) are compared to bivariate EMOS. The case study indicates that the novel bivariate methods improve over the bivariate EMOS approaches. The bivariate DRN and the most flexible version of the bivariate vine copula approach exhibit the best performance in terms of verification scores and calibration.

stat.AP↗

arXiv2025

Operational convection-permitting COSMO/ICON ensemble predictions at observation sites (CIENS)

We present the CIENS dataset, which contains ensemble weather forecasts from the operational convection-permitting numerical weather prediction model of the German Weather Service. It comprises forecasts for 55 meteorological variables mapped to the locations of synoptic stations, as well as additional spatially aggregated forecasts from surrounding grid points, available for a subset of these variables. Forecasts are available at hourly lead times from 0 to 21 hours for two daily model runs initialized at 00 and 12 UTC, covering the period from December 2010 to June 2023. Additionally, the dataset provides station observations for six key variables at 170 locations across Germany: pressure, temperature, hourly precipitation accumulation, wind speed, wind direction, and wind gusts. Since the forecast are mapped to the observed locations, the data is delivered in a convenient format for analysis. The CIENS dataset complements the growing collection of benchmark datasets for weather and climate modeling. A key distinguishing feature is its long temporal extent, which encompasses multiple updates to the underlying numerical weather prediction model and thus supports investigations into how forecasting methods can account for such changes. In addition to detailing the design and contents of the CIENS dataset, we outline potential applications in ensemble post-processing, forecast verification, and related research areas. A use case focused on ensemble post-processing illustrates the benefits of incorporating the rich set of available model predictors into machine learning-based forecasting models.

physics.ao-ph↗

arXiv2024

Gradient-Boosted Generalized Linear Models for Conditional Vine Copulas

Vine copulas are flexible dependence models using bivariate copulas as building blocks. If the parameters of the bivariate copulas in the vine copula depend on covariates, one obtains a conditional vine copula. We propose an extension for the estimation of continuous conditional vine copulas, where the parameters of continuous conditional bivariate copulas are estimated sequentially and separately via gradient-boosting. For this purpose, we link covariates via generalized linear models (GLMs) to Kendall's $τ$ correlation coefficient from which the corresponding copula parameter can be obtained. Consequently, the gradient-boosting algorithm estimates the copula parameters providing a natural covariate selection. In a second step, an additional covariate deselection procedure is applied. The performance of the gradient-boosted conditional vine copulas is illustrated in a simulation study. Linear covariate effects in low- and high-dimensional settings are investigated for the conditional bivariate copulas separately and for conditional vine copulas. Moreover, the gradient-boosted conditional vine copulas are applied to the temporal postprocessing of ensemble weather forecasts in a low-dimensional setting. The results show, that our suggested method is able to outperform the benchmark methods and identifies temporal correlations better. Eventually, we provide an R-package called boostCopula for this method.

stat.ME↗

arXiv2024

The zero degree of freedom non-central chi squared distribution for ensemble postprocessing

In this note the use of the zero degree non-central chi squared distribution as predictive distribution for ensemble postprocessing is investigated. It has a point mass at zero by definition, and is thus particularly suited for postprocessing weather variables naturally exhibiting large numbers of zeros, such as precipitation, solar radiation or lightnings. Due to the properties of the distribution no additional truncation or censoring is required to obtain a positive probability at zero. The presented study investigates its performance compared to that of the censored generalized extreme value distribution and the censored and shifted gamma distribution for postprocessing 24h accumulated precipitation using an EMOS (ensemble model output statistics) approach with a rolling training period. The obtained results support the conclusion that it serves well as a predictive distribution in postprocessing precipitation and thus may also be considered in future analyses of other weather variables having substantial zero observations.

stat.AP↗

arXiv2024

Time Series based Ensemble Model Output Statistics for Temperature Forecasts Postprocessing

Nowadays, weather prediction is based on numerical weather prediction (NWP) models to produce an ensemble of forecasts. Despite of large improvements over the last few decades, they still tend to exhibit systematic bias and dispersion errors. Consequently, these forecasts may be improved by statistical postprocessing. This work proposes an extension of the ensemble model output statistics (EMOS) method in a time series framework. Besides of taking account of seasonality and trend in the location and scale parameter of the predictive distribution, the autoregressive process in the mean forecast errors or the standardized forecast errors is considered. The models can be further extended by allowing generalized autoregressive conditional heteroscedasticity (GARCH). Last but not least, it is outlined how to use these models for arbitrary forecast horizons. To illustrate the performance of the suggested EMOS models in time series fashion, we present a case study for the postprocessing of 2 m surface temperature forecasts using five different lead times and a set of observation stations in Germany. The results indicate that the time series EMOS extensions are able to significantly outperform the benchmark EMOS and autoregressive adjusted EMOS (AR-EMOS) in most of the lead time-station cases. To complement this article, our method is accompanied by an R-package called tsEMOS.

stat.AP↗

arXiv2023

D-Vine GAM Copula based Quantile Regression with Application to Ensemble Postprocessing

Temporal, spatial or spatio-temporal probabilistic models are frequently used for weather forecasting. The D-vine (drawable vine) copula quantile regression (DVQR) is a powerful tool for this application field, as it can automatically select important predictor variables from a large set and is able to model complex nonlinear relationships among them. However, the current DVQR does not always explicitly and economically allow to account for additional covariate effects, e.g. temporal or spatio-temporal information. Consequently, we propose an extension of the current DVQR, where we parametrize the bivariate copulas in the D-vine copula through Kendall's Tau which can be linked to additional covariates. The parametrization of the correlation parameter allows generalized additive models (GAMs) and spline smoothing to detect potentially hidden covariate effects. The new method is called GAM-DVQR, and its performance is illustrated in a case study for the postprocessing of 2m surface temperature forecasts. We investigate a constant as well as a time-dependent Kendall's Tau. The GAM-DVQR models are compared to the benchmark methods Ensemble Model Output Statistics (EMOS), its gradient-boosted extension (EMOS-GB) and basic DVQR. The results indicate that the GAM-DVQR models are able to identify time-dependent correlations as well as relevant predictor variables and significantly outperform the state-of-the-art methods EMOS and EMOS-GB. Furthermore, the introduced parameterization allows using a static training period for GAM-DVQR, yielding a more sustainable model estimation in comparison to DVQR using a sliding training window. Finally, we give an outlook of further applications and extensions of the GAM-DVQR model. To complement this article, our method is accompanied by an R-package called gamvinereg.

stat.ME↗

arXiv2023

Some Additional Remarks on Statistical Properties of Cohen's d from Linear Regression

The size of the effect of the difference in two groups with respect to a variable of interest may be estimated by the classical Cohen's $d$. A recently proposed generalized estimator allows conditioning on further independent variables within the framework of a linear regression model. In this note, it is demonstrated how unbiased estimation of the effect size parameter together with a corresponding standard error may be obtained based on the non-central $t$ distribution. The portrayed estimator may be considered as a natural generalization of the unbiased Hedges' $g$. In addition, confidence interval estimation for the unknown parameter is demonstrated by applying the so-called inversion confidence interval principle. The regarded properties collapse to already known ones in case of absence of any additional independent variables. The stated remarks are illustrated with a publicly available data set.

stat.ME↗

arXiv2023

Effect Size Estimation in Linear Mixed Models

In this note, we reconsider Cohen's effect size measure $f^2$ under linear mixed models and demonstrate its application by employing an artificially generated data set. It is shown how $f^2$ can be computed with the statistical software environment R using lme4 without the need for specification and computation of a coefficient of determination.

stat.ME↗

arXiv2022

A Note on Cohen's d From a Partitioned Linear Regression Model

In this note we introduce a generalized formula for Cohen's $d$ under the presence of additional independent variables, providing a measure for the size of a possible effect concerning the location difference of a variable in two groups. This is done by employing the so-called Frisch-Waugh-Lovell theorem in a partitioned linear regression model. The generalization is motivated by demonstrating the relationship to appropriate $t$ and $F$ statistics. Our discussion is further illustrated by inference from a publicly available data set.

stat.AP↗

arXiv2022

Predicting school transition rates in Austria with classification trees

Methods based on machine learning become increasingly popular in many areas as they allow models to be fitted in a highly-data driven fashion, and often show comparable or even increased performance in comparison to classical methods. However, in the area of educational sciences the application of machine learning is still quite uncommon. This work investigates the benefit of using classification trees for analyzing data from educational sciences. An application to data on school transition rates in Austria indicates different aspects of interest in the context of educational sciences: (i) the trees select variables for predicting school transition rates in a data-driven fashion which are well in accordance with existing confirmatory theories from educational sciences, (ii) trees can be employed for performing variable selection for regression models, (iii) the classification performance of trees is comparable to that of binary regression models. These results indicate that trees and possibly other machine learning methods may also be helpful to explore high-dimensional educational data sets, especially where no confirmatory theories have been developed yet.

stat.AP↗

arXiv2019

Probabilistic Temperature Forecasting with a Heteroscedastic Autoregressive Ensemble Postprocessing model

Weather prediction today is performed with numerical weather prediction (NWP) models. These are deterministic simulation models describing the dynamics of the atmosphere, and evolving the current conditions forward in time to obtain a prediction for future atmospheric states. To account for uncertainty in NWP models it has become common practice to employ ensembles of NWP forecasts. However, NWP ensembles often exhibit forecast biases and dispersion errors, thus require statistical postprocessing to improve reliability of the ensemble forecasts. This work proposes an extension of a recently developed postprocessing model utilizing autoregressive information present in the forecast error of the raw ensemble members. The original approach is modified to let the variance parameter depend on the ensemble spread, yielding a two-fold heteroscedastic model. Furthermore, an additional high-resolution forecast is included into the postprocessing model, yielding improved predictive performance. Finally, it is outlined how the autoregressive model can be utilized to postprocess ensemble forecasts with higher forecast horizons, without the necessity of making fundamental changes to the original model. We accompany the new methodology by an implementation within the R package ensAR to make our method available for other researchers working in this area. To illustrate the performance of the heteroscedastic extension of the autoregressive model, and its use for higher forecast horizons we present a case study for a data set containing 12 years of temperature forecasts and observations over Germany. The case study indicates that the autoregressive model yields particularly strong improvements for forecast horizons beyond 24 hours.

stat.AP↗

arXiv2018

Vine copula based post-processing of ensemble forecasts for temperature

Today weather forecasting is conducted using numerical weather prediction (NWP) models, consisting of a set of differential equations describing the dynamics of the atmosphere. The output of such NWP models are single deterministic forecasts of future atmospheric states. To assess uncertainty in NWP forecasts so-called forecast ensembles are utilized. They are generated by employing a NWP model for distinct variants. However, as forecast ensembles are not able to capture the full amount of uncertainty in an NWP model, they often exhibit biases and dispersion errors. Therefore it has become common practise to employ statistical post processing models which correct for biases and improve calibration. We propose a novel post processing approach based on D-vine copulas, representing the predictive distribution by its quantiles. These models allow for much more general dependence structures than the state-of-the-art EMOS model and is highly data adapted. Our D-vine quantile regression approach shows excellent predictive performance in comparative studies of temperature forecasts over Europe with different forecast horizons based on the 52-member ensemble of the European Centre for Medium-Range Weather Forecasting (ECMWF). Specifically for larger forecast horizons the method clearly improves over the benchmark EMOS model.

stat.AP↗

arXiv2016

Spatially adaptive, Bayesian estimation for probabilistic temperature forecasts

Uncertainty in the prediction of future weather is commonly assessed through the use of forecast ensembles that employ a numerical weather prediction model in distinct variants. Statistical postprocessing can correct for biases in the numerical model and improves calibration. We propose a Bayesian version of the standard ensemble model output statistics (EMOS) postprocessing method, in which spatially varying bias coefficients are interpreted as realizations of Gaussian Markov random fields. Our Markovian EMOS (MEMOS) technique utilizes the recently developed stochastic partial differential equation (SPDE) and integrated nested Laplace approximation (INLA) methods for computationally efficient inference. The MEMOS approach shows good predictive performance in a comparative study of 24-hour ahead temperature forecasts over Germany based on the 50-member ensemble of the European Centre for Medium-Range Weather Forecasting (ECMWF).

stat.AP↗

arXiv2015

Probabilistic temperature forecasting based on an ensemble AR modification

To address the uncertainty in outputs of numerical weather prediction (NWP) models, ensembles of forecasts are used. To obtain such an ensemble of forecasts the NWP model is run multiple times, each time with different formulations and/or initial or boundary conditions. To correct for possible biases and dispersion errors in the ensemble, statistical postprocessing models are frequently employed. These statistical models yield full predictive probability distributions for a weather quantity of interest and thus allow for a more accurate assessment of forecast uncertainty. This paper proposes to combine the state of the art Ensemble Model Output Statistics (EMOS) with an ensemble that is adjusted by an AR process fitted to the respective error series by a spread-adjusted linear pool (SLP) in case of temperature forecasts. The basic ensemble modification technique we introduce may be used to simply adjust the ensemble itself as well as to obtain a full predictive distribution for the weather quantity. As demonstrated for temperature forecasts of the European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble, the proposed procedure gives rise to improved results upon the basic (local) EMOS method.

stat.AP↗

arXiv2015

Bivariate ensemble model output statistics approach for joint forecasting of wind speed and temperature

Forecast ensembles are typically employed to account for prediction uncertainties in numerical weather prediction models. However, ensembles often exhibit biases and dispersion errors, thus they require statistical post-processing to improve their predictive performance. Two popular univariate post-processing models are the Bayesian model averaging (BMA) and the ensemble model output statistics (EMOS). In the last few years increased interest has emerged in developing multivariate post-processing models, incorporating dependencies between weather quantities, such as for example a bivariate distribution for wind vectors or even a more general setting allowing to combine any types of weather variables. In line with a recently proposed approach to model temperature and wind speed jointly by a bivariate BMA model, this paper introduces a bivariate EMOS model for these weather quantities based on a truncated normal distribution. The bivariate EMOS model is applied to temperature and wind speed forecasts of the eight-member University of Washington mesoscale ensemble and of the eleven-member ALADIN-HUNEPS ensemble of the Hungarian Meteorological Service and its predictive performance is compared to the performance of the bivariate BMA model and a multivariate Gaussian copula approach, post-processing the margins with univariate EMOS. While the predictive skills of the compared methods are similar, the bivariate EMOS model requires considerably lower computation times than the bivariate BMA method.

stat.AP↗

arXiv2014

Joint probabilistic forecasting of wind speed and temperature using Bayesian model averaging

Ensembles of forecasts are typically employed to account for the forecast uncertainties inherent in predictions of future weather states. However, biases and dispersion errors often present in forecast ensembles require statistical post-processing. Univariate post-processing models such as Bayesian model averaging (BMA) have been successfully applied for various weather quantities. Nonetheless, BMA and many other standard post-processing procedures are designed for a single weather variable, thus ignoring possible dependencies among weather quantities. In line with recently upcoming research to develop multivariate post-processing procedures, e.g., BMA for bivariate wind vectors, or flexible procedures applicable for multiple weather quantities of different types, a bivariate BMA model for joint calibration of wind speed and temperature forecasts is proposed based on the bivariate truncated normal distribution. It extends the univariate truncated normal BMA model designed for post-processing ensemble forecast of wind speed by adding a normally distributed temperature component with a covariance structure representing the dependency among the two weather quantities. The method is applied to wind speed and temperature forecasts of the eight-member University of Washington mesoscale ensemble and of the eleven-member ALADIN-HUNEPS ensemble of the Hungarian Meteorological Service and its predictive performance is compared to that of the general Gaussian copula method. The results indicate improved calibration of probabilistic and accuracy of point forecasts in comparison to the raw ensemble and the overall performance of this model is able to keep up with that of the Gaussian copula method.

stat.ME↗

arXiv2012

Multivariate probabilistic forecasting using Bayesian model averaging and copulas

We propose a method for post-processing an ensemble of multivariate forecasts in order to obtain a joint predictive distribution of weather. Our method utilizes existing univariate post-processing techniques, in this case ensemble Bayesian model averaging (BMA), to obtain estimated marginal distributions. However, implementing these methods individually offers no information regarding the joint distribution. To correct this, we propose the use of a Gaussian copula, which offers a simple procedure for recovering the dependence that is lost in the estimation of the ensemble BMA marginals. Our method is applied to 48-h forecasts of a set of five weather quantities using the 8-member University of Washington mesoscale ensemble. We show that our method recovers many well-understood dependencies between weather quantities and subsequently improves calibration and sharpness over both the raw ensemble and a method which does not incorporate joint distributional information.

stat.AP↗