# Trajectory learning for ensemble forecasts via the continuous ranked probability score: a Lorenz '96 case study

## TL;DR

This study explores trajectory learning for ensemble forecasts using CRPS as a loss function, demonstrating improved accuracy and calibration in the Lorenz '96 model, especially for short-term predictions.

## Contribution

It introduces a CRPS-based trajectory learning method for stochastic parametrizations that outperform traditional derivative-fitting approaches in ensemble forecasting.

## Key findings

- CRPS-based parametrizations are more accurate and sharp.
- The approach simplifies calibration of ensemble models.
- Outperforms derivative-fitting methods in short-term forecasts.

## Abstract

This paper demonstrates the feasibility of trajectory learning for ensemble forecasts by employing the continuous ranked probability score (CRPS) as a loss function. Using the two-scale Lorenz '96 system as a case study, we develop and train both additive and multiplicative stochastic parametrizations to generate ensemble predictions. Results indicate that CRPS-based trajectory learning produces parametrizations that are both accurate and sharp. The resulting parametrizations are straightforward to calibrate and outperform derivative-fitting-based parametrizations in short-term forecasts. This approach is particularly promising for data assimilation applications due to its accuracy over short lead times.