Forecast error growth: a dynamic–stochastic model

Bach, E. ORCID: https://orcid.org/0000-0002-9725-0203, Crisan, D. and Ghil, M. (2025) Forecast error growth: a dynamic–stochastic model. Chaos: An Interdisciplinary Journal of Nonlinear Science, 35 (7). 073118. ISSN 1089-7682 doi: 10.1063/5.0248102

Abstract/Summary

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.

Item Type	Article
URI	https://centaur.reading.ac.uk/id/eprint/123533
Identification Number/DOI	10.1063/5.0248102
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > National Centre for Earth Observation (NCEO) Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher	American Institute of Physics
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