Statistical Post-processing of High-resolution Marine Stratus Cloud Forecast Data with Bayesian Estimation and Markov Chain Monte Carlo Sampling Methods

Mesoscale model predictions of sensible weather variables, such as marine stratus, often manifest diagnosable patterns of forecast error. While the numerical weather prediction community has traditionally focused on improvements to “upstream” model 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 post-processing techniques that identify and calibrate systematic errors in objective guidance “downstream” of the model(s). In this way, statistical post-processing exploits correlations between forecast variables and contemporary observations to mitigate undesirable biases in the mean and spread of ensemble forecast distributions. This study will explore the efficacy of statistical post-processing in short timescale forecasts of near-surface marine stratus cloud fields using a now-cast framework to combine high-resolution (1 km) model data from the Weather Research and Forecasting (WRF) system with observations from the NOAA GOES 15 meteorological satellite.

To this end, a multivariate hierarchical Bayesian probability model has been developed to invert the canonical probability statement and stochastically parametrize observable forecast variables with unobservable model parameters and hyperparameters within a generalized linear model (GLM). In this way, a priori forecast beliefs will be conditioned on a time series of previous model forecasts (i.e., predictors) and their corresponding observations (i.e., predictands) to train a Bayesian predictive model that will statistically post-process current model predictors. A k-means clustering analysis will be similarly employed to heuristically classify forecast samples according to latent data structure observed between available training features. Finally, an adaptive multiparameter variant of the Metropolis algorithm has been developed within a Markov chain Monte Carlo (MCMC) sampling framework (Figure 1) to generate Bayesian posterior densities for unobservable model parameters and posterior predictive distributions (PPD) for observable predictands; these Bayesian posteriors will explicitly characterize the uncertainty of the parameter inference and corresponding forecast though probability density functions conditioned on available training data.

In this way, this study will explore three principle issues: 1) Whether Bayesian estimation and MCMC sampling techniques provide a computationally viable method of statistical postprocessing in operational now-cast cloud prediction applications; 2) whether the Bayesian/MCMC post-processing approach provides meaningful improvements in forecast skill when compared with suitable reference forecasts (e.g., climatology or traditional linear regression techniques vis-à-vis model output statistics); and 3) whether the Bayesian PPDs provide sharp, reliable forecast distributions with probabilistic interpretations that correspond to the observed frequency and variability of the observable predictands. This Bayesian estimation approach should result in a family of joint and marginal probability distributions that can be converted into intuitive performance surfaces (i.e., filled, two-dimensional contour plots of relevant forecast quantities) associated with near-surface cloud prediction.