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Advances in LAM 3D-VAR formulation

Advances in LAM 3D-VAR formulation. Vincent GUIDARD Claude FISCHER Météo-France, CNRM/GMAP. Introduction. Through various experiments, a drawback of biperiodic increments has arisen : « wrapping around » analysis increments. Introduction. Introduction.

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Advances in LAM 3D-VAR formulation

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  1. Advances in LAM 3D-VAR formulation Vincent GUIDARD Claude FISCHER Météo-France, CNRM/GMAP

  2. Introduction • Through various experiments, a drawback of biperiodic increments has arisen : « wrapping around » analysis increments

  3. Introduction

  4. Introduction • Through various experiments, a drawback of biperiodic increments has arisen: « wrapping around » analysis increments Controlling the lengthscale of the correlation functions is necessary: compact support • Introduction of a large-scale information in the LAM analysis to let the increments due to the observations be of mesoscale

  5. 1.1 Compact support - definition • Aim : Reducing the lengthscale of structure functions • The COmpactly SUpported (COSU) correlation functions are obtained through a gridpoint multiplication by a cosine-shape mask function.The mask should be applied to the square root of the gridpoint correlations (Gaspari and Cohn, 1999)

  6. 1.1 Compact support - definition Steps to modify the power spectrum: • Power spectrum modal variances • Fill a 2D spectral array from the 1D square root of the modal variances • Inverse bi-Fourier transform – mask the gridpoint structure – direct bi-Fourier transform • Collect isotropically and square to obtain modified modal variances • Modal variances power spectrum

  7. 1.2 Compact support – 1D model Gridpoint Auto- Correlations T 22

  8. 1.2 Compact support – 1D model Power Spectrum T 22

  9. 1.2 Compact support – 1D model Analysis

  10. 1.3 Compact support – ALADIN Horizontal covariances COSU 100km-300km Original B Univariate approach:

  11. 1.3 Compact support – ALADIN Multivariate approach: The multivariate formulation (Berre, 2000):*u is the umbalanced part of the * errorH is the horizontal balance operator

  12. 1.3 Compact support – ALADIN • COSU Horizontal autocorrelations; Vertical cross-correlations and horizontal balance operator not modified Whatever the distance of zeroing, results are « worse » than with the original B. Explanation : the main part of the (temperature) increment is balanced, while only the horizontal correlations for z are COSU, but not for Hz.

  13. 1.3 Compact support – ALADIN • Cure 1: a modification of the z power spectrum in order to have COSU correlations for Hz same results as the original B. • Cure 2: another solution is to compactly support the horizontal balance operator

  14. All COSU 300km-500km Original B 1.3 Compact support – ALADIN

  15. 1.3 Compact support – conclusion • Single observation: • Very efficient technique in univariate case • Needs drastic measures (COSU horizontal balance) to be efficient in multivariate case • Full observation set: • No impact, even with drastic measures • Further research is necessary • Problems possibly due to a large scale error which this mesoscale analysis tries to reduce  use of another source of information for large scales

  16. 2.1 « Large scale » cost-function • Aim : input a large scale information in the LAM 3D-VAR. • The large scale information is the analysis of the global model (ARPEGE) put to a LAM low resolution geometry • Thanks to classical hypotheses, plus assuming that the global analysis error and the LAM background error are NOT correlated, we simply add a new term to the cost function

  17. 2.1 « Large scale » cost-function • J(x) = Jb(x) + Jo(x) + Jk(x), where H1 : global  LAM low resolutionH2 : LAM high resolution  LAM low res.V : « large scale » error covariancesxAA : global analysis

  18. 2.2 Large scale update - evaluation • 1D Shallow Water « global » model (I. Gospodinov) LAM version with Davies coupling (P. Termonia)Both spectral models • 1D gridpoint analyses implemented: • Using LAM background and observation (Jb+Jo) BO • Using LAM background and global analysis (Jb+Jk)  BK • Using all information (Jb +Jo+Jk)  BOKPlus dynamical adaptation  DA • Aim: comparing DA and BK comparing BO and BOK

  19. 2.2 Large scale update - evaluation • Dynamical Adaptation versus BK Statistically (Fisher and Student tests on bias and RMS): No difference between DA and BK LAM background BK analysis DA global analysis truth

  20. 2.2 Large scale update - evaluation • BO versus BOK: observation over all the domain Statistically: No difference between BO and BOK LAM background BOK analysis BO analysis global analysis truth observation +

  21. 2.2 Large scale update - evaluation • BO versus BOK: obs. over a part of the domain Statistically: BOK better than BO LAM background BOK analysis BO analysis global analysis truth observation +

  22. 2.3 Large scale update - conclusion • The large scale information seems useful only in border-line cases, in the Shallow Water model • Next steps : • Evaluation in a Burger model • Ensemble evaluation of the statistics in ARPEGE-ALADIN (based on the work of Loïk Berre, Margarida Belo-Pereira and Simona Stefanescu) • Implementation in ALADIN

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