A Multiscale Local Gain Form Ensemble Transform Kalman Filter (MLGETKF)

Wang, Xuguang; Chipilski, Hristo G.; Bishop, Craig H.; Satterfield, Elizabeth; Baker, Nancy L.; Whitaker, Jeffrey S.

doi:10.1175/mwr-d-20-0290.1

Cited by 21 publications

(35 citation statements)

References 44 publications

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“…This result implies that increments in RADAR_H15_V1.1 were featured by larger contributions of all scales compared to REF1. These reduced contributions of all scales in REF1 are speculated to have been caused by the dampened correlation at small scales and then the weakened cross-correlations between small and large scales when applying tighter localization radii for radar DA, consistent with [76,77]. For the wind increments, similar tendencies for the spectral differences were displayed in the two experiments (not shown).…”

Section: Impact Of Localization Radii For Radar Damentioning

confidence: 54%

Rapid Update with EnVar Direct Radar Reflectivity Data Assimilation for the NOAA Regional Convection-Allowing NMMB Model over the CONUS: System Description and Initial Experiment Results

Wang

2021

Atmosphere

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This study first describes the extended Grid-Point Statistical Interpolation analysis system (GSI)-based ensemble-variational data assimilation (DA) system within the North American Mesoscale Rapid Refresh (NAMRR) system for the Nonhydrostatic Multiscale Model on the B grid (NMMB). Experiments were conducted to examine three critical aspects of data assimilation configuration in this system. Ten retrospective high-impact convective cases during the warm season of 2015–2016 were adopted for testing. A 10-member, 18 h ensemble forecast was launched for each experiment. Specifically, the experiment using horizontal (vertical) localization radii (Lr) of 300 km (0.55-scaled height measured in the nature log of pressure) overall had more skills than that of 500 km (1.1-scaled height) for conventional in-situ observation assimilation. Diagnostics suggest that the higher forecast skills could be attributed to applying smaller Lr in the boundary with large temperature and moisture gradients. For radar DA, the experiment was more skillful with horizontal (vertical) Lr of 15 km (1.1-scaled height) than that of 12 km (0.55-scaled height). Diagnostics suggest that the improved forecasts were achieved by using wider Lr to spread radar observations into unobserved areas more effectively. Slight forecast skill differences between the relaxation inflation factors of 95% and 65% are presented. The impact of varying inflation magnitudes primarily occurred in the upper-level spread.

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Section: Impact Of Localization Radii For Radar Damentioning

confidence: 54%

Rapid Update with EnVar Direct Radar Reflectivity Data Assimilation for the NOAA Regional Convection-Allowing NMMB Model over the CONUS: System Description and Initial Experiment Results

Wang

2021

Atmosphere

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“…This is consistent with the finding of Wang et al . (2021) that observation‐space localization results in a lower rank ensemble than modulated ensemble in the GETKF solver.…”

Section: Resultsmentioning

confidence: 99%

“…We suspect that it would be possible to model the static covariance as a separable process, with a separate set of eigenvectors for the vertical and horizontal correlation functions. Such implementation can be similar to: (a) Lei et al (2018), where the GETKF algorithm is used to assimilate satellite radiances that represent vertical integrals of atmospheric quantities; and (b) Wang et al (2021) who used eigenvectors to characterize horizontal multi-scale correlation functions. The Joint Effort for Data Assimilation Integration (JEDI) framework provides a unique opportunity for developing GETKF-OI algorithms because it provides the reference 3DVAR solutions, vertical balance operators, and variable transforms needed to capture horizontal balances.…”

Section: Discussionmentioning

confidence: 99%

“…In this paper, as well as in the multiscale localization paper of Wang et al (2021), one faces a problem of efficient computations of the observations for the modulated ensemble: can then be related to the global square root √ P static n eigSt by developing a linear mapping operator M (i) (see Figure B2). Then Equation (B2) can be re-written as: to the observation locations in the reference frame of the local volume.…”

Section: Appendix B: Fast Algorithm For Ensemble Modulation In a Loca...mentioning

confidence: 99%

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Including parameterized error covariance in local ensemble solvers: Experiments in a 1D model with balance constraints

Фролов

Whitaker

Draper

2022

Quart J Royal Meteoro Soc

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Lack of efficient ways to include parameterized error covariance in ensemble‐based local volume solvers (e.g. the local ensemble‐transform Kalman filter – the LETKF) remains an outstanding problem in data assimilation. Here, we describe two new algorithms: GETKF‐OI and LETKF‐OI. These algorithms are similar to the traditional optimal interpolation (OI) algorithm in that they use parameterized error covariance to update each of the local volume solutions. However, unlike the traditional OI that scales poorly as the number of observations increases, the new algorithms achieve linear scalability by using either the observational‐space localization strategy of the traditional LETKF algorithm or the modulated ensembles of the gain‐form (GETKF) algorithm. In our testing with a simple one‐dimensional univariate system, we find that the GETKF‐OI algorithm can recover the exact solution within the truncation bounds of the modulated ensemble and the LETKF‐OI algorithm achieves a close approximation to the exact solution. We also demonstrate how to extend GETKF‐OI algorithm to a toy multivariate system with balance constraints.

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“…(A15) is positive semidefinite. Wang et al (2021) discussed how to construct a similar matrix for multiscale localization using matrix square roots. The simplest case is to let α ij = 1 for all i, j .…”

Section: Xymentioning

confidence: 99%

Multivariate localization functions for strongly coupled data assimilation in the bivariate Lorenz 96 system

Stanley

Grooms

Kleiber

2021

Nonlin. Processes Geophys.

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Abstract. Localization is widely used in data assimilation schemes to mitigate the impact of sampling errors on ensemble-derived background error covariance matrices. Strongly coupled data assimilation allows observations in one component of a coupled model to directly impact another component through the inclusion of cross-domain terms in the background error covariance matrix. When different components have disparate dominant spatial scales, localization between model domains must properly account for the multiple length scales at play. In this work, we develop two new multivariate localization functions, one of which is a multivariate extension of the fifth-order piecewise rational Gaspari–Cohn localization function; the within-component localization functions are standard Gaspari–Cohn with different localization radii, while the cross-localization function is newly constructed. The functions produce positive semidefinite localization matrices which are suitable for use in both Kalman filters and variational data assimilation schemes. We compare the performance of our two new multivariate localization functions to two other multivariate localization functions and to the univariate and weakly coupled analogs of all four functions in a simple experiment with the bivariate Lorenz 96 system. In our experiments, the multivariate Gaspari–Cohn function leads to better performance than any of the other multivariate localization functions.

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A Multiscale Local Gain Form Ensemble Transform Kalman Filter (MLGETKF)

Cited by 21 publications

References 44 publications

Rapid Update with EnVar Direct Radar Reflectivity Data Assimilation for the NOAA Regional Convection-Allowing NMMB Model over the CONUS: System Description and Initial Experiment Results

Rapid Update with EnVar Direct Radar Reflectivity Data Assimilation for the NOAA Regional Convection-Allowing NMMB Model over the CONUS: System Description and Initial Experiment Results

Including parameterized error covariance in local ensemble solvers: Experiments in a 1D model with balance constraints

Multivariate localization functions for strongly coupled data assimilation in the bivariate Lorenz 96 system

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