Statistical Postprocessing of Ensemble Forecasts with Bayesian Inference and Markov Chain Monte Carlo Sampling Methods

Ensemble predictions of sensible weather variables often manifest coherent patterns of forecast error. While the numerical weather prediction (NWP) community has traditionally focused on model improvements that affect “upstream” components – that is, the sophistication of various data assimilation schemes, more detailed mathematical descriptions of the governing dynamics, advanced numerics, and improved fidelity in parameterizing subgrid-scale processes via model physics – comparatively little attention has been given to “downstream” postprocessing techniques that directly interact with large samples of ensemble estimates to diagnose and calibrate systematic errors. In this way, statistical postprocessing exploits correlations between forecasts and their corresponding observations to improve the quality of current predictions. This study will explore the efficacy of the statistical postprocessing approach in tropical cyclone track and intensity forecasts made by the Coupled Ocean/Atmosphere Mesoscale Prediction System for Tropical Cyclones (COAMPS-TC).
To this end, Bayesian data analysis (BDA) will be exploited to condition subjective a priori forecast beliefs on past model performance and available ensemble guidance. More specifically, a hierarchical Bayesian joint probability model will be constructed to simulate the analytical relationships that influence the intrinsic data structure of observable forecast variables and unobservable model parameters and hyperparameters. An adaptive multiparameter variant of the Metropolis algorithm will be used within a Markov chain Monte Carlo (MCMC) framework to draw samples from analytically intractable Bayesian posterior distributions. Bayesian posterior predictive distributions (PPD) will be formed from current ensemble guidance to produce forecast estimates with improved quality – especially in the context of distributions-oriented scoring rules. In this way, this study will explore three principle hypotheses: 1) Bayesian probability models provide a viable method of statistical postprocessing in operational applications; 2) the Bayesian postprocessing approach provides meaningful improvements in forecast skill – for both measures-oriented and distributions-oriented scoring rules – when compared with the canonical components (e.g., the consensus solution) of the parent ensemble model(s); and 3) the Bayesian PPDs provide forecast distributions that have intuitive uncertainty interpretations that are appropriate for lay consumers and decision-makers. This Bayesian analysis should result in a family of predictive performance surfaces (PPS) that describe the joint and marginal probabilities of observable weather variables rigorously conditioned on a suitable combination of available forecast data.