Advanced pattern techniques in weather and climate science

This presentation discusses two examples of the use of advanced pattern techniques in weather and climate science. Firstly, optimal mode decomposition (OMD) is employed for linear inverse modelling of large-scale atmospheric flow. The OMD technique determines a low-rank approximation to a high-dimensional dynamical system in terms of a linear empirical model; a set of patterns and a system matrix are identified simultaneously by maximising the explained predictive variance. The method is exemplified on a quasi-geostrophic atmospheric model with realistic mean state and variability. Considerable improvements in prediction skill are observed compared to the traditional approach based on principal components or dynamic mode decomposition (DMD). Secondly, nonlinear principal prediction patterns are used for stochastic subgrid-scale modelling. Pairs of predictor-predictand patterns are determined in the space of the resolved variables and the space of the subgrid forcing, respectively, and linked in a predictive manner. The predictor patterns may contain nonlinear functions of state variables. On top of this deterministic subgrid model the predictand patterns are forced stochastically. The approach is demonstrated on the two-scale Lorenz 1996 system.