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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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Quantifying and Understanding Errors in Molecular Geometries
Electronic structure calculations are ubiquitous in most branches of chemistry, but all have errors in both energies and equilibrium geometries. Quantifying errors in possibly dozens of bond angles and bond lengths is a Herculean task. A single natural measure of geometric error is introduced, the geometry energy offset (GEO). GEO links many disparate aspects of geometry errors: a new ranking of different methods, quantitative insight into errors in specific geometric parameters, and insight into trends with different methods. GEO can also reduce the cost of high-level geometry optimizations and shows when geometric errors distort the overall error of a method. Results, including some surprises, are given for both covalent and weak interactions.
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- Award ID(s):
- 1856165
- PAR ID:
- 10220448
- Date Published:
- Journal Name:
- The journal of physical chemistry letters
- Issue:
- 0
- ISSN:
- 1948-7185
- Page Range / eLocation ID:
- 9957–9964
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1021/acs.jpclett.0c03034
