Ensemble forecasting: A foray of dynamics into the realm of statistics

Abstract

Uncertain quantities are often described through statistical samples. Can samples for numerical weather forecasts be generated dynamically? At a great expense, they can. With statistically constrained perturbations, a cloud of initial states is created and then integrated forward in time. By now, this technique has become ubiquitous in weather and climate research and operations. Ensembles are widely used, with demonstrated value. The atmosphere evolves in a multidimensional phase space. Does a cloud of ensemble solutions encompass the evolution of the real atmosphere? Theoretically, random perturbations in high‐dimensional spaces have negligible projection in any direction, including the error in the best estimate, therefore consistently degrading that. As the bulk of the perturbation variance lies in the null space of error, samples in multidimensional space do not contain reality. An evaluation suggests that initial and short‐range forecast error and ensemble perturbations are random draws from a high‐dimensional domain we call the subspace of possible error. Error in any initial condition is partly a result of stochastic observational and assimilation noise, while perturbations explore other, mostly independent directions from the subspace of possible error that may have resulted from other configurations of stochastic noise. What benefits may arise from the deterministic projection of such noise? Consistent with theoretical expectations, ensemble members consistently degrade the skill of the unperturbed forecast until medium range. The mean and all other products derived from ensembles suffer an 18‐hour loss in forecast Information. Since Information is a sufficient statistic, any rational user can benefit more from the unperturbed, than from an ensemble of weather forecasts. Furthermore, case‐dependent variations in the distribution or spread of ensembles have no impact on commonly used metrics. Can alternative, statistical applications provide comparable, or even higher‐quality probabilistic and other products, at the fraction of the cost of running an ensemble?