Observation-Informed Generalized Hybrid Error Covariance ModelsSource: Monthly Weather Review:;2018:;volume 146:;issue 011::page 3605DOI: 10.1175/MWR-D-18-0016.1Publisher: American Meteorological Society
Abstract: AbstractBecause of imperfections in ensemble data assimilation schemes, one cannot assume that the ensemble-derived covariance matrix is equal to the true error covariance matrix. Here, we describe a simple and intuitively compelling method to fit calibration functions of the ensemble sample variance to the mean of the distribution of true error variances, given an ensemble estimate. We demonstrate that the use of such calibration functions is consistent with theory showing that, when sampling error in the prior variance estimate is considered, the gain that minimizes the posterior error variance uses the expected true prior variance, given an ensemble sample variance. Once the calibration function has been fitted, it can be combined with ensemble-based and climatologically based error correlation information to obtain a generalized hybrid error covariance model. When the calibration function is chosen to be a linear function of the ensemble variance, the generalized hybrid error covariance model is the widely used linear hybrid consisting of a weighted sum of a climatological and an ensemble-based forecast error covariance matrix. However, when the calibration function is chosen to be, say, a cubic function of the ensemble sample variance, the generalized hybrid error covariance model is a nonlinear function of the ensemble estimate. We consider idealized univariate data assimilation and multivariate cycling ensemble data assimilation to demonstrate that the generalized hybrid error covariance model closely approximates the optimal weights found through computationally expensive tuning in the linear case and, in the nonlinear case, outperforms any plausible linear model.
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contributor author | Satterfield, Elizabeth A. | |
contributor author | Hodyss, Daniel | |
contributor author | Kuhl, David D. | |
contributor author | Bishop, Craig H. | |
date accessioned | 2019-09-19T10:04:51Z | |
date available | 2019-09-19T10:04:51Z | |
date copyright | 8/3/2018 12:00:00 AM | |
date issued | 2018 | |
identifier other | mwr-d-18-0016.1.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl1/handle/yetl/4261305 | |
description abstract | AbstractBecause of imperfections in ensemble data assimilation schemes, one cannot assume that the ensemble-derived covariance matrix is equal to the true error covariance matrix. Here, we describe a simple and intuitively compelling method to fit calibration functions of the ensemble sample variance to the mean of the distribution of true error variances, given an ensemble estimate. We demonstrate that the use of such calibration functions is consistent with theory showing that, when sampling error in the prior variance estimate is considered, the gain that minimizes the posterior error variance uses the expected true prior variance, given an ensemble sample variance. Once the calibration function has been fitted, it can be combined with ensemble-based and climatologically based error correlation information to obtain a generalized hybrid error covariance model. When the calibration function is chosen to be a linear function of the ensemble variance, the generalized hybrid error covariance model is the widely used linear hybrid consisting of a weighted sum of a climatological and an ensemble-based forecast error covariance matrix. However, when the calibration function is chosen to be, say, a cubic function of the ensemble sample variance, the generalized hybrid error covariance model is a nonlinear function of the ensemble estimate. We consider idealized univariate data assimilation and multivariate cycling ensemble data assimilation to demonstrate that the generalized hybrid error covariance model closely approximates the optimal weights found through computationally expensive tuning in the linear case and, in the nonlinear case, outperforms any plausible linear model. | |
publisher | American Meteorological Society | |
title | Observation-Informed Generalized Hybrid Error Covariance Models | |
type | Journal Paper | |
journal volume | 146 | |
journal issue | 11 | |
journal title | Monthly Weather Review | |
identifier doi | 10.1175/MWR-D-18-0016.1 | |
journal fristpage | 3605 | |
journal lastpage | 3622 | |
tree | Monthly Weather Review:;2018:;volume 146:;issue 011 | |
contenttype | Fulltext |