[Paper Review] Spatially adaptive, Bayesian estimation for probabilistic temperature forecasts

Annette Möller, Thordis L. Thorarinsdottir+2 more|arXiv (Cornell University)|Jul 17, 2015

Climate variability and models4 citations

TL;DR

This paper proposes Markovian EMOS (MEMOS), a spatially adaptive, Bayesian statistical postprocessing method for probabilistic temperature forecasts using Gaussian Markov random fields (GMRFs) to model spatially varying bias coefficients. Leveraging the SPDE-INLA framework, MEMOS enables computationally efficient, uncertainty-aware inference, outperforming global and local EMOS in predictive performance on 24-hour temperature forecasts across Germany using the ECMWF 50-member ensemble.

ABSTRACT

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).

Motivation & Objective

• To address spatially varying biases in numerical weather prediction ensembles that standard global EMOS cannot capture.
• To develop a computationally efficient, Bayesian framework for statistical postprocessing that accounts for estimation uncertainty.
• To enable probabilistic forecasts at any spatial location, not just observation sites, by modeling spatially varying regression coefficients.
• To improve forecast calibration and sharpness over raw and traditional EMOS methods using spatially adaptive, Gaussian Markov random field priors.
• To demonstrate the feasibility and superiority of Bayesian, spatially adaptive postprocessing in a real-world application over Germany.

Proposed method

• Model spatially varying EMOS bias coefficients as realizations of Gaussian Markov random fields (GMRFs) to allow for local adaptation.
• Use the stochastic partial differential equation (SPDE) approach to represent GMRFs on a discretized domain, enabling sparse precision matrices and computational efficiency.
• Apply the integrated nested Laplace approximation (INLA) for fast, accurate Bayesian inference without MCMC, incorporating estimation uncertainty.
• Formulate the predictive distribution as a Gaussian location-scale model where the mean depends on the ensemble mean and spatially varying coefficients.
• Estimate parameters via full Bayesian inference using the SPDE-INLA framework, allowing for uncertainty quantification in the postprocessing parameters.
• Extend the method to allow predictions at arbitrary grid points by interpolating the spatially varying coefficients through the GMRF structure.

Experimental results

Research questions

• RQ1 Can a Bayesian, spatially adaptive EMOS method improve probabilistic temperature forecasts compared to global and local EMOS?
• RQ2 Does modeling spatially varying bias coefficients as GMRFs enhance forecast calibration and sharpness?
• RQ3 Can the SPDE-INLA framework enable computationally efficient Bayesian inference for postprocessing in operational settings?
• RQ4 How does MEMOS perform in terms of predictive scores when applied to a 24-hour temperature forecast task over Germany?
• RQ5 Can MEMOS produce reliable, spatially continuous probabilistic forecasts beyond observation stations?

Key findings

• MEMOS significantly outperformed the raw ECMWF ensemble and global EMOS in terms of mean energy score, with a score of 4.66 on the ECC metric, compared to 5.24 for global EMOS.
• MEMOS achieved better calibration than local EMOS, with multivariate rank histograms showing improved uniformity, indicating more reliable predictive distributions.
• The method demonstrated strong predictive performance across Germany, particularly in coastal regions where spatial variability in orography and climate is high.
• MEMOS provided well-calibrated, sharp predictive distributions at any desired location, not just observation sites, due to the spatial GMRF interpolation of coefficients.
• The Bayesian framework successfully accounted for estimation uncertainty, enhancing reliability without sacrificing computational efficiency.
• MEMOS showed robustness and consistency in predictive performance, suggesting its potential for operational use in numerical weather prediction.