[Paper Review] Vine copula based post-processing of ensemble forecasts for temperature

Annette Möller, Ludovica Spazzini+3 more|arXiv (Cornell University)|Nov 6, 2018

Climate variability and models3 citations

TL;DR

This paper proposes a D-vine copula-based post-processing method for probabilistic temperature forecasts that explicitly models the non-Gaussian dependence between observed temperatures and ensemble forecasts. By using data-driven pair-copula constructions and quantile regression, the method improves calibration—especially for longer forecast horizons—outperforming standard EMOS models in both PIT histogram uniformity and predictive scoring rules.

ABSTRACT

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.

Motivation & Objective

• Address the limitations of traditional ensemble model output statistics (EMOS) in capturing non-Gaussian and nonlinear dependencies between observations and ensemble forecasts.
• Improve forecast calibration and reliability, particularly for extended forecast horizons where EMOS models often exhibit underdispersion.
• Develop a flexible, data-adapted statistical post-processing framework that does not assume Gaussian margins or dependence structures.
• Incorporate a novel rolling training period that combines multiple years of data to better capture seasonal effects and improve model robustness.

Proposed method

• Employ D-vine copulas to model the joint dependence structure between observed temperature and ensemble forecasts, enabling flexible, non-Gaussian dependence modeling.
• Use the D-vine quantile regression approach (Kraus and Czado, 2017) with forward predictor selection to identify relevant ensemble members and predictors.
• Estimate the predictive distribution via quantile regression using pair-copula constructions, allowing for asymmetric and heavy-tailed marginal distributions.
• Implement a new rolling training period that aggregates data from multiple years within a fixed window to enhance model stability and seasonal adaptation.
• Utilize the R package vinereg for efficient implementation of the D-vine quantile regression model.
• Compare performance against standard EMOS (station-wise) and refined EMOS (with extended training period) using proper scoring rules and PIT histograms.

Experimental results

Research questions

• RQ1 Can a D-vine copula-based post-processing model improve forecast calibration compared to standard EMOS models, especially for longer forecast horizons?
• RQ2 How does the D-vine approach perform in capturing complex, non-Gaussian dependence structures between observed temperature and ensemble forecasts?
• RQ3 To what extent does the proposed rolling training period enhance model performance compared to fixed or standard training windows?
• RQ4 Does the D-vine model reduce underdispersion and overdispersion issues commonly observed in EMOS forecasts?
• RQ5 Can the D-vine method be effectively applied to non-Gaussian weather variables like temperature without requiring distributional assumptions?

Key findings

• The D-vine model significantly improves calibration, as evidenced by PIT histograms that are closest to uniformity across all forecast horizons, especially at 120- and 240-hour leads.
• For 24- and 48-hour forecasts, the D-vine model shows only weak signs of overdispersion, whereas EMOS-S exhibits clear underdispersion and EMOS-R shows pronounced overdispersion.
• The D-vine model outperforms EMOS-S and EMOS-R in both the Continuous Ranked Probability Score (CRPS) and the Logarithmic Score (LS), with the largest performance gains observed at longer forecast horizons.
• In 70% of the 35 stations, the D-vine model ranks as best or second-best in terms of predictive performance across all horizons, demonstrating robust and consistent superiority.
• The novel rolling training period improves model performance, particularly when combined with the D-vine approach, by better capturing seasonal variability.
• The D-vine method is highly flexible and does not require parametric assumptions about marginal distributions, making it suitable for non-Gaussian variables like wind speed or precipitation.