Preprints
https://doi.org/10.5194/npg-2021-8
https://doi.org/10.5194/npg-2021-8

  03 Mar 2021

03 Mar 2021

Review status: a revised version of this preprint was accepted for the journal NPG and is expected to appear here in due course.

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

Zofia Stanley, Ian Grooms, and William Kleiber Zofia Stanley et al.
  • Department of Applied Mathematics, University of Colorado, Boulder, Colorado

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 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 non-negative definite localization matrices, which are suitable for use in 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 analogs of all four functions in a simple experiment with the bivariate Lorenz '96 system. In our experiment the multivariate Gaspari-Cohn function leads to better performance than any of the other localization functions.

Zofia Stanley et al.

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on npg-2021-8', S.G. Penny, 27 Mar 2021
    • AC1: 'Reply on RC1', Zofia Stanley, 10 Jun 2021
  • RC2: 'Comment on npg-2021-8', Anonymous Referee #2, 30 Mar 2021
    • AC2: 'Reply on RC2', Zofia Stanley, 10 Jun 2021
  • RC3: 'Comment on npg-2021-8', Anonymous Referee #3, 19 Apr 2021
    • AC3: 'Reply on RC3', Zofia Stanley, 10 Jun 2021

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on npg-2021-8', S.G. Penny, 27 Mar 2021
    • AC1: 'Reply on RC1', Zofia Stanley, 10 Jun 2021
  • RC2: 'Comment on npg-2021-8', Anonymous Referee #2, 30 Mar 2021
    • AC2: 'Reply on RC2', Zofia Stanley, 10 Jun 2021
  • RC3: 'Comment on npg-2021-8', Anonymous Referee #3, 19 Apr 2021
    • AC3: 'Reply on RC3', Zofia Stanley, 10 Jun 2021

Zofia Stanley et al.

Model code and software

Multivariate Localization Functions Zofia Stanley and Ian Grooms https://doi.org/10.5281/zenodo.4574612

Zofia Stanley et al.

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Short summary
In weather forecasting, observations are incorporated into a model of the atmosphere through a process called data assimilation. Sometimes observations in one location may impact the weather forecast in another faraway location in undesirable ways. The impact of distant observations on the forecast is mitigated through a process called localization. We propose a new method for localization when a model has multiple length scales, as in a model spanning both the ocean and the atmosphere.