Preprints
https://doi.org/10.5194/egusphere-2022-996
https://doi.org/10.5194/egusphere-2022-996
 
10 Oct 2022
10 Oct 2022

How far can the error estimation problem in data assimilation be closed by collocated data?

Annika Vogel1,2 and Richard Ménard1 Annika Vogel and Richard Ménard
  • 1Air Quality Research Division, Environment and Climate Change Canada (ECCC), Dorval - QC, Canada
  • 2Rhenish Institute for Environmental Research (RIU) at the University of Cologne, Cologne, Germany

Abstract. Accurate specification of error statistics required for data assimilation remains an ongoing challenge, partly because their estimation is an ill-posed problem that requires statistical assumptions. Even with the common assumption that background and observation errors are uncorrelated, the problem remains underdetermined. One natural question that could arise is: Can the increasing amount of overlapping observations or other datasets help to reduce the total number of statistical assumptions, or do they introduce more statistical unknowns? In order to answer this question, this paper provides a conceptual view on the statistical error estimation problem for multiple collocated datasets, including a generalized mathematical formulation, an exemplary demonstration with synthetic data as well as a formulation of the minimal and optimal conditions to solve the problem. It is demonstrated that the required number of statistical assumptions increases linearly with the number of datasets. However the number of error statistics that can be estimated increases quadratically, allowing for an estimation of an increasing number of error cross-statistics between datasets for more than three datasets. The presented optimal estimation of full error covariance and cross-covariance matrices between dataset does not accumulate uncertainties of assumptions among estimations of subsequent error statistics.

Annika Vogel and Richard Ménard

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Annika Vogel and Richard Ménard

Annika Vogel and Richard Ménard

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Short summary
Accurate estimation of error statistics required for data assimilation remains an ongoing challenge, as statistical assumptions are required to solve the estimation problem. This paper provides a conceptual view on the statistical error estimation problem in the light of increasing amount of available datasets. It is found that the total number of required assumptions increases with the number of overlapping datasets, but the relative amount of error statistics which can be estimated increases.