# Multivariate postprocessing methods for high-dimensional seasonal weather forecasts

## TL;DR

This paper introduces a multivariate postprocessing method for high-dimensional seasonal weather forecasts that improves accuracy by handling complex error patterns and trends, using covariance tapering and PCA for efficiency.

## Contribution

It presents a novel multivariate postprocessing approach combining covariance tapering and PCA, capable of managing non-stationary, non-isotropic, and negatively correlated errors on a global scale.

## Key findings

- Outperforms existing methods in global sea surface temperature forecasts
- Handles non-stationary and non-isotropic error patterns effectively
- Adapts to bias trends caused by global warming

## Abstract

Seasonal weather forecasts are crucial for long-term planning in many practical situations and skillful forecasts may have substantial economic and humanitarian implications. Current seasonal forecasting models require statistical postprocessing of the output to correct systematic biases and unrealistic uncertainty assessments. We propose a multivariate postprocessing approach utilizing covariance tapering, combined with a dimension reduction step based on principal component analysis for efficient computation. Our proposed technique can correctly and efficiently handle non-stationary, non-isotropic and negatively correlated spatial error patterns, and is applicable on a global scale. Further, a moving average approach to marginal postprocessing is shown to flexibly handle trends in biases caused by global warming, and short training periods. In an application to global sea surface temperature forecasts issued by the Norwegian Climate Prediction Model (NorCPM), our proposed methodology is shown to outperform known reference methods.