Using Singular Value Decomposition to Parameterize State-Dependent Model Errors

Christopher M. Danforth, Eugenia Kalnay
2008 Journal of the Atmospheric Sciences  
The purpose of the present study is to use a new method of empirical model error correction, developed by Danforth et al. (2007) , based on estimating the systematic component of the non-periodic errors linearly dependent on the anomalous state. The method uses Singular Value Decomposition (SVD) to generate a basis of model errors and states. It requires only a time series of errors to estimate covariances and uses negligible additional computation during a forecast integration. As a result, it
more » ... on. As a result, it should be suitable for operational use at relatively small computational expense. We test the method with the Lorenz '96 coupled system as the truth, and an uncoupled version of the same system as a model. We demonstrate that the SVD method represents a significant component of the effects of the model's unresolved state on the resolved state and show that the results are better than those obtained with the empirical correction operator of Leith (1978) . The improvement is attributed to the fact that the SVD truncation effectively reduces sampling errors. Forecast improvements of up to 1000% are seen when compared with the original model. The improvements come at the expense of weakening ensemble spread.
doi:10.1175/2007jas2419.1 fatcat:gh3ijnzwizgjleuzdhdo4theoa