Forecast error growth: A dynamic-stochastic model

TL;DR

This paper introduces a nonlinear stochastic differential equation model for forecast error growth in weather prediction, capturing key properties and fitting well to operational data, with potential applications across sciences involving prediction.

Contribution

A novel scalar dynamic-stochastic model for forecast error growth that incorporates multiplicative noise and aligns with operational NWP error data.

Findings

Model accurately fits error growth curves

Captures both mean and probabilistic error features

Proves well-posedness and positivity of solutions

Abstract

There is a history of simple forecast error growth models designed to capture the key properties of error growth in operational numerical weather prediction (NWP) models. We propose here such a scalar model that relies on the previous ones and incorporates multiplicative noise in a nonlinear stochastic differential equation (SDE). We analyze the properties of this SDE, including the shape of the error growth curve for small times and its stationary distribution, and prove well-posedness and positivity of solutions. Next, we fit this model to operational NWP error growth curves, and show good agreement with both the mean and probabilistic features of the error growth. These results suggest that the dynamic-stochastic error growth model proposed herein and similar ones could play a role in many other areas of the sciences that involve prediction.