Model Error Variance Estimation for Weak Constraint Data Assimilation
Published in (submitted to SIAM/ASA Journal on Uncertainty Quantification), 2024
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Abstract: State estimates from weak constraint four-dimensional variational (4D-Var) data assimilation can vary significantly depending on the data and model error variance. As a result, the accuracy of these estimates heavily depends on the correct specification of both model and observational data error variances. In this work, we assume that the data error is specified and frame weak constraint 4D-Var as a regularization inverse problem, with the scalar model error variance as the regularization parameter. We employ the representer method to reduce the 4D-Var solution search space from the state space to the data space, which provides an analytical expression for the optimal state estimates. This method allows us to derive matrix expressions for three regularization parameter selection methods: the L-curve, generalized cross-validation (GCV), and the χ2 method, used to estimate the model error variance. We validate our approach by assimilating simulated data into a 1D transport equation modeling wildfire smoke transport under various observational noise and first guess perturbations. The results show that the estimated model error variances accurately the balance between the influence of observational data and model predictions on assimilated estimates.
Bibtex:
@article{4dvar_reg,
year = 2024,
publisher = {},
volume = {},
number = {},
pages = {},
author = {S. Babyale, J. Mead, D. Calhoun, P. Azike},
title = {Model Error Variance Estimation for Weak Constraint Data Assimilation},
journal = {}
}