Title: Representing model error in Ensemble Data Assimilation

Authors: Carla Cardinali (ECMWF)
Roberto Buizza (ECMWF)
Gabor Radnoti (ECMWF)
Nedjeljka Zagar(Lubjana University)

The paper investigates a method to represent model error in an ensemble assimilation (EDA) system. The ECMWF operational EDA simulates the effect of both data and model uncertainties. The data errors are represented by adding perturbations with statistical characteristics implied by the observation error covariance matrix whilst the model uncertainties are represented by adding stochastic perturbations to the physical tendencies to simulate the effect of random errors in the physical parameterizations (ST-method). In this work an alternative method (XB-method) is proposed to simulate model uncertainties, based on adding to the model background field, perturbations with statistical characteristics defined by the model background error covariance matrix. EDAs with similar data uncertainties but different model error representations are compared and the proposed XB-method is found to lead to the largest spread both in amplitude and spatial scale. Normal-mode diagnosis not only has confirmed that XB-EDA methodology produces larger spread at all scales but also that the spread projects more than the other onto the unbalanced part of the motion. The different EDAs have been employed to define the background error covariance matrix to be used in a higher-resolution deterministic assimilation system. Specific diagnostics have been applied to estimate the quality of the modelled background error covariance matrix from the different ensembles presented. Results have shown that XB method produces a background error covariance matrix that allows the assimilated observations to be more influential. Consequently, despite the fact that all the other ensemble methodologies apply an artificial global inflation whereby background error variances are inflated by a certain factor, all the corresponding deterministic assimilation systems result having a considerably smaller degree of freedom for signal. XB-EDA based background error statistics can therefore be used in data-assimilation without any artificial inflation that is currently used in the operational ensemble analysis.

GMAO Head: Michele Rienecker Global Modeling and Assimilation Office NASA Goddard Space Flight Center

Curator: Nikki Privé Last Updated: May 27 2011