Spectral characteristics of background error covariance and multiscale data assimilation
Abstract
The steady increase of the spatial resolutions of numerical atmospheric and oceanic circulation models has occurred over the past decades. Horizontal grid spacing down to the order of 1 km is now often used to resolve cloud systems in the atmosphere and submesoscale circulation systems in the ocean. These fine resolution models encompass a wide range of temporal and spatial scales, across which dynamical and statistical properties vary. In particular, dynamic flow systems at small scales can be spatially localized and temporarily intermittent. Difficulties of current data assimilation algorithms for such fine resolution models are numerically and theoretically examined. Our analysis shows that the background error correlation length scale is larger than 75 km for streamfunctions and is larger than 25 km for water vapor mixing ratios, even for a 2km resolution model. A theoretical analysis suggests that such correlation length scales prevent the currently used data assimilation schemes from constraining spatial scales smaller than 150 km for streamfunctions and 50 km for water vapor mixing ratios. Moreover, our results highlight the need to fundamentally modify currently used data assimilation algorithms for assimilating highresolution observations into the aforementioned fine resolution models. Lastly, within the framework of fourdimensional variational data assimilation,more »
 Authors:

 California Inst. of Technology (CalTech), Pasadena, CA (United States)
 Univ. of California, Los Angeles, CA (United States)
 Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Publication Date:
 Research Org.:
 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC23)
 OSTI Identifier:
 1260165
 Report Number(s):
 BNL1123232016JA
Journal ID: ISSN 02712091; R&D Project: 2016BNLEE630EECABudg; KP1701000
 Grant/Contract Number:
 SC00112704
 Resource Type:
 Accepted Manuscript
 Journal Name:
 International Journal for Numerical Methods in Fluids
 Additional Journal Information:
 Journal Name: International Journal for Numerical Methods in Fluids; Journal ID: ISSN 02712091
 Publisher:
 Wiley
 Country of Publication:
 United States
 Language:
 English
 Subject:
 54 ENVIRONMENTAL SCIENCES; variational data as similation; Kalman Filter; atmospheric and oceanic models; multiscale algorithm; background error covariance; spectral power density
Citation Formats
Li, Zhijin, Cheng, Xiaoping, Gustafson, Jr., William I., and Vogelmann, Andrew M. Spectral characteristics of background error covariance and multiscale data assimilation. United States: N. p., 2016.
Web. doi:10.1002/fld.4253.
Li, Zhijin, Cheng, Xiaoping, Gustafson, Jr., William I., & Vogelmann, Andrew M. Spectral characteristics of background error covariance and multiscale data assimilation. United States. doi:10.1002/fld.4253.
Li, Zhijin, Cheng, Xiaoping, Gustafson, Jr., William I., and Vogelmann, Andrew M. Tue .
"Spectral characteristics of background error covariance and multiscale data assimilation". United States. doi:10.1002/fld.4253. https://www.osti.gov/servlets/purl/1260165.
@article{osti_1260165,
title = {Spectral characteristics of background error covariance and multiscale data assimilation},
author = {Li, Zhijin and Cheng, Xiaoping and Gustafson, Jr., William I. and Vogelmann, Andrew M.},
abstractNote = {The steady increase of the spatial resolutions of numerical atmospheric and oceanic circulation models has occurred over the past decades. Horizontal grid spacing down to the order of 1 km is now often used to resolve cloud systems in the atmosphere and submesoscale circulation systems in the ocean. These fine resolution models encompass a wide range of temporal and spatial scales, across which dynamical and statistical properties vary. In particular, dynamic flow systems at small scales can be spatially localized and temporarily intermittent. Difficulties of current data assimilation algorithms for such fine resolution models are numerically and theoretically examined. Our analysis shows that the background error correlation length scale is larger than 75 km for streamfunctions and is larger than 25 km for water vapor mixing ratios, even for a 2km resolution model. A theoretical analysis suggests that such correlation length scales prevent the currently used data assimilation schemes from constraining spatial scales smaller than 150 km for streamfunctions and 50 km for water vapor mixing ratios. Moreover, our results highlight the need to fundamentally modify currently used data assimilation algorithms for assimilating highresolution observations into the aforementioned fine resolution models. Lastly, within the framework of fourdimensional variational data assimilation, a multiscale methodology based on scale decomposition is suggested and challenges are discussed.},
doi = {10.1002/fld.4253},
journal = {International Journal for Numerical Methods in Fluids},
number = ,
volume = ,
place = {United States},
year = {2016},
month = {5}
}