A Mechanism for the Skew of Ensemble Forecasts

Abstract It is often not appreciated that forecast ensembles are generally skewed. The skew can arise from the state dependence of chaotic system dynamics responsible for ensemble spread. Generation by this mechanism be demonstrated in even simplest dynamical with state‐dependent noise, and when initial asymptotic (i.e., “climatological”) distributions both symmetric. Indeed, systems noise tendencies must general skewed heavy tailed, implications forecasting extreme anomaly risks. Ensemble misrepresent such have errors their probability distributions. Because depend on condition lead time, they cannot removed simple a posteriori bias corrections standard deviation used as metric spread distribution Gaussian. In similar spirit, S may difference D between ensemble‐mean most likely forecast, well risk ratio R positive negative deviations forecast. This motivated facts (1) many geophysical quantities approximately stochastically generated (SGS) distributions, which analytical relationships exist these quantities, (2) Gaussian sub‐class SGS However, serve useful strictly