A Foray of Dynamics into the Realm of Statistics: A Review of Ensemble Forecasting
- 1NOAA Research, Global Systems Laboratory, Boulder, CO, United States of America (zoltan.toth@noaa.gov)
- 2Department of Atmospheric and Oceanic Sciences and Institute of Atmospheric Sciences, Fudan University, Shanghai, China
- 3Shanghai Typhoon Institute, China Meteorological Administration, Shanghai, China
- 4Department of Civil and Environmental Engineering, University of Connecticut, Storrs, CT, USA
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 are 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 on any direction, including the error in the best estimate, therefore consistently degrading it. 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 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?
How to cite: Toth, Z., Feng, J., Zhang, J., and Pena, M.: A Foray of Dynamics into the Realm of Statistics: A Review of Ensemble Forecasting, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-6791, https://doi.org/10.5194/egusphere-egu24-6791, 2024.
