Title: Allowing for model error in strong constraint 4DVAR

Author: Katherine Howes (University of Reading)
Amos Lawless (University of Reading)
Alison Fowler (University of Reading)

Four dimensional variational data assimilation (4DVAR) can be used to obtain the best estimate of the initial conditions of a weather or ocean forecast model, namely the analysis. Our work is focused on improving theanalysis by allowing for the fact that the model contains error, without requiring prior knowledge about the model error statistics.

The 4DVAR method developed acknowledges the presence of random error in the model at each time step, by replacing the observation error covariance matrix with an error covariance matrix that includes both observation error statistics and model error statistics. A method for estimating this matrix is presented which allows for the model error to increase over the assimilation window. ‘Dezrosiers-type diagnostics’are derived and used to verify the consistency of the background errorcovariance matrix with thecombined observation error and model error covariance matrix to be used in 4DVAR.

We present analytical results for an erroneous scalar model which show a decrease in the variance of the error in the analysis when using our new method. We show that the improvement the method can make to the accuracy of the analysis is dependent on both the size of the model error and on the ratio between the observation error variance and background error variance. We then further demonstrate numerically that the new method also works to reduce the analysis error covariance when using a non-linear chaotic system with erroneous parameter values. We discuss the fact that an improved analysis will not necessarily provide a better forecast.

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

Curator: Nikki Privé Last Updated: Feb 9 2015