Title: Can singular vectors reliably describe the distribution of forecast errors?

Author: Martin Leutbecher (ECMWF)
Simon Lang (ECMWF)

One of the main goals for ensemble prediction is to provide reliable forecasts of the distribution of forecast errors. Here, reliability is to be understood in the sense of statistical consistency with the actual forecast errors. The representation of uncertainties will influence how well this goal can be achieved. Singular vectors have been and are still used in some operational ensemble prediction systems to represent uncertainties in the initial conditions. The main theoretical justification for doing so is a property of the leading singular vectors: They evolve into the leading eigenvectors of the forecast error covariance matrix. Thus, the subspace spanned by the leading n singular vectors is the n-dimensional subspace that describes most forecast error variance. It seems obvious that it is important to adequately represent initial uncertainties in the subspace of the leading singular vectors in order to obtain an ensemble that reliably samples the distribution of forecast errors.

The main issues addressed by the talk revolve around the consequences that arise for the reliability of the ensemble forecasts if the distribution of initial uncertainties is represented by a sample from a distribution that is confined to a subspace of the leading n singular vectors. Examples based on experiments with ECMWF's medium-range ensemble will be used to illustrate the issues. Therefore, the talk will focus on global numerical weather prediction. However, the raised issues are thought to be generic and similar results are expected across a range of different applications.

GMAO Head: Steven Pawson Global Modeling and Assimilation Office NASA Goddard Space Flight Center

Curator: Nikki Privé Last Updated: Feb 9 2015