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Abstract Many data assimilation methods require knowledge of the first two moments of the background and observation errors to function optimally. To ensure the effective performance of such methods, it is often advantageous to estimate the second moment of the observation errors directly. We examine three different strategies for doing so, focusing specifically on the case of a single scalar observation error variance parameterr. The first method is the well-known Desroziers et al. “diagnostic check” iteration (DBCP). The second method, described in Karspeck, adapts the “spread–error” diagnostic—used for assessing ensemble reliability—to observations and generates a point estimate ofrby taking the expectation of various observation-space statistics and using an ensemble to model background error statistics explicitly. The third method is an approximate Bayesian scheme that uses an inverse-gamma prior and a modified Gaussian likelihood. All three methods can recover the correct observation error variance when both the background and observation errors are Gaussian and the background error variance is well specified. We also demonstrate that it is often possible to estimatereven when the observation error is not Gaussian or when the forward operator mapping model states into observation space is nonlinear. The DBCP method is found to be most robust to these complications; however, the other two methods perform similarly well in most cases and have the added benefit that they can be used to estimaterbefore data assimilation. We conclude that further investigation is warranted into the latter two methods, specifically into how they perform when extended to the multivariate case. Significance StatementObservations of the Earth system (e.g., from satellites, radiosondes, aircraft, etc.,) each have some associated uncertainty. To use observations to improve model forecasts, it is important to understand the size of that uncertainty. This study compares three statistical methods for estimating observation errors, all of which can be continuously implemented whenever new observations are used to correct a model. Our results suggest that all three methods can improve forecast outcomes, but that, if observations are believed to have highly biased or skewed errors, care should be taken in choosing which to use and interpreting its results. Future studies should investigate robust methods for estimating more complicated types of errors.
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Foundations for Universal Non‐Gaussian Data Assimilation
Abstract In many applications of data assimilation, especially when the size of the problem is large, a substantial assumption is made: all variables are well‐described by Gaussian error statistics. This assumption has the advantage of making calculations considerably simpler, but it is often not valid, leading to biases in forecasts or, even worse, unphysical predictions. We propose a simple, but effective, way of replacing this assumption, by making use of transforming functions, while remaining consistent with Bayes' theorem. This method allows the errors to have any value of the skewness and kurtosis, and permits physical bounds for the variables. As such, the error distribution can conform better to the underlying statistics, reducing biases introduced by the Gaussian assumption. We apply this framework to a 3D variational data assimilation method, and find improved performance in a simple atmospheric toy model (Lorenz‐63), compared to an all‐Gaussian technique.
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- Award ID(s):
- 2033405
- PAR ID:
- 10479350
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Geophysical Research Letters
- Volume:
- 50
- Issue:
- 23
- ISSN:
- 0094-8276
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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