Title: Errors of representativity

Authors: J. A. Pocock (University of Reading)
A. S. Lawless (University of Reading)
S. L. Dance (University of Reading)
N. K. Nichols (University of Reading)

The observation error covariance matrix is an important component of any data assimilation scheme. This error matrix consists of two parts; one contains the information on the instrument error, the other contains information on the errors of representativity. Errors of representativity are errors that arise when observations can resolve spatial scales that the model cannot or when the observation operator does not correctly model the observations. Currently these errors of representativity are not modelled correctly in data assimilation schemes. In this study we seek to understand the general structure of errors of representativity. We generate solutions of the Kuramoto Sivashinsky equation at high resolution and use this as our truth. We then create pseudo-observations of this state using different integral weighting functions and calculate the errors of representativity for observations calculated at a lower spectral resolution. We also consider observation operators that both correctly and incorrectly represent these observations. As expected we find that the errors of representativity are reduced when the observation operator correctly models the observations. We also see that the structure of the error of representativity changes when the observation weighting is altered. Finally we see that the calculated errors of representativity are sensitive to the assumed covariance of the true state.

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

Curator: Nikki Privé Last Updated: May 27 2011