Identifying efficient ensemble perturbations for initializing subseasonal-to-seasonal prediction

The prediction of weather at subseasonal-to-seasonal (S2S) timescales is affected by both initial and boundary conditions, and as such is a complicated problem that the geophysical community is attempting to address in greater detail. One important question about this problem is how to initialize ensembles of numerical forecast models to produce reliable forecasts¹, i.e. initialize each member of an ensemble forecast such that their statistical properties are consistent with the actual uncertainties of the future state of the physical system.

Here, we introduce a method to construct the initial conditions to generate reliable ensemble forecasts. This method is based on projections of the ensemble initial conditions onto the modes of the model's dynamic mode decomposition (DMD), which are related to the procedure used for forming Linear Inverse Models (LIMs). In the framework of a low-order ocean-atmosphere model exhibiting multiple different characteristic timescales, we compare the DMD-oriented method to other ensemble initialization methods based on Empirical Orthogonal Functions (EOFs) and the Lyapunov vectors of the model², and we investigate the relations between these.

References:

1. Leutbecher, M., & Palmer, T.N. (2008). Ensemble forecasting. Journal of Computational Physics, 227, 3515–3539.

2. Vannitsem, S., & Duan, W. (2020). On the use of near-neutral Backward Lyapunov Vectors to get reliable ensemble forecasts in coupled ocean–atmosphere systems. Climate Dynamics, 55, 1125-1139.