Generative machine learning methods for multivariate ensemble post-processing

Abstract

<p>Statistical post-processing of ensemble forecasts has become a common practice in research to correct biases and errors in calibration. While many of the developments have been focused on univariate methods that calibrate the marginal distributions, practical applications often require accurate modeling of spatial, temporal, and inter-variable dependencies. Copula-based multivariate post-processing methods, such as ensemble copula coupling, have been proposed to address this issue and proceed by reordering univariately post-processed ensembles with copula functions to retain the dependence structure. We propose a novel multivariate post-processing method based on generative machine learning where post-processed multivariate ensemble forecasts are generated from random noise, conditional on the inputs of raw ensemble forecasts. Moving beyond the two-step strategy of separately modeling marginal distributions and multivariate dependence structure, the generative modelling approach allows for directly obtaining multivariate probabilistic forecasts as output. The flexibility of the generative model also enables us to incorporate additional predictors straightforwardly and to generate an arbitrary number of post-processed ensemble members. In a case study on the surface temperature and wind speed forecasts from the European Centre of Medium-Range Weather Forecasts at weather stations in Germany, our generative model that incorporates additional weather predictors substantially improves upon the multivariate spatial forecasts from copula-based approaches. And the model shows competitive performance even with state-of-the-art neural network-based post-processing models applied for the marginal distributions.</p>

Assessing the calibration of multivariate probabilistic forecasts

“…Though the multivariate post-processing frameworks employed in this study are commonly applied in operational post-processing suites, the multivariate rank histograms in Figure 5 suggest that these forecast still exhibit significant biases, particularly related to the dependence between the wind speed at nearby grid points. An interesting avenue for future work would therefore be to compare these results with those obtained using state-of-the-art machine-learning models that have recently been introduced for multivariate post-processing (e.g., Chen et al, 2022;Dai & Hemri, 2021;Horat & Lerch, 2023).…”

Lead‐time‐continuous statistical postprocessing of ensemble weather forecasts

“…Furthermore, with upcoming machine learning and artificial intelligence postprocessing methods (Rasp and Lerch, 2018; Kirkwood et al, 2021; Haupt et al, 2021; Chen et al, 2022) there is a need for larger data sets to train and evaluate models. As Hamill (2018) notes, due to the cost of generating reforecasts and practical constraints such as frequent model updates, data sets available in practice can often be of nonideal quality and may not have considerable size.…”

“…Parameters of postprocessing methods but also NWP forecasting skill tend to vary depending on the time of year, which means that methods like EMOS need to account for seasonality. This is usually done by fitting models in a running window—as originally proposed by Gneiting et al (2005)—or by including terms in the model that adjust for seasonal cycles as in Gebetsberger et al (2018); Lang et al (2020), and Chen et al (2022). Dabernig et al (2017b) and Messner et al (2017) instead work on standardized anomalies to which they fit EMOS models.…”

Comparison of multivariate post‐processing methods using global ECMWF ensemble forecasts

“…Though these advanced post‐processing methods can serve as building blocks of multivariate post‐processing schemes, incorporating additional predictor information in the second, copula‐based step is challenging, calling for the development of tailored approaches to machine‐learning methods for multivariate post‐processing. There have been first studies in this direction focusing on obtaining spatially coherent forecast fields via generative adversarial networks (Dai and Hemri, 2021) and multivariate post‐processing using scoring‐rule‐based generative models that allow for incorporating additional predictors (Chen et al ., 2022).…”