Forecast error growth: A stochastic differential equation model

There is a history of simple error growth models designed to capture the key properties of error growth in operational numerical weather prediction models. We propose here such a scalar model that relies on the previous ones, but captures the effect of small scales on the error growth via additive noise in a nonlinear stochastic differential equation (SDE). We nondimensionalize the equation and study its behavior with respect to the error saturation value, the growth rate of small errors, and the magnitude of noise. We show that the addition of noise can change the curvature of the error growth curve. The SDE model seems to improve substantially the fit to operational error growth curves, compared to the deterministic counterparts.