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Comparison of 2D fields of GENIE data

Comparison of 2D fields of GENIE data. V.Livina, T.Lenton, S.Goswami. Method. Singular value decomposition of 2D matrix M ( ): where & are unitary matrices ( & ), is diagonal matrix of singular values. Efficiency criterion for time series:

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Comparison of 2D fields of GENIE data

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  1. Comparison of 2D fields of GENIE data V.Livina, T.Lenton, S.Goswami

  2. Method • Singular value decomposition of 2D matrix M ( ): where & are unitary matrices ( & ), is diagonal matrix of singular values. • Efficiency criterion for time series: Here and are series of singular values (in non-increasing order) • If E=1, two series are identical (point-wise comparison)

  3. Experiment I • GENIE-2, EMBM & C-Goldstein, ‘eb_go_gs’ air temperature over land, 36 x 36 grid • GENIE-1, EMBM & ENTS-land, land temperature, 36 x 36 grid

  4. EMBM temperature over land ENTS land temperature

  5. Singular values and coefficients all SVs: E=0.95 first 10 SVs: E=0.92 first 5 SVs: E=0.85

  6. Experiment II • GENIE-land, ‘ig_fi_fi’, land temperature, 64 x 32 grid (averaged to 32x32) • GENIE-1, EMBM & ENTS-land, land temperature, 36 x 36 grid (cut to 32x32)

  7. GENIE-land, ig_fi_fi land temperature ENTS land temperature

  8. Singular values and coefficients all SVs: E=0.48 first 10 SVs: E=0.26 first 5 SVs: E=-0.08

  9. Comparison of model & real data • If one to compare two model fields, the generalised criterion is applicable • If one to compare model field with the real one, the asymmetric criterion is preferable (real data prioritised)

  10. Generalization to 3D Given 3D field (for instance, (x,y,t) time-evolution of the stream function), one can • apply the method to 2D slices (x,y,i), i=1..N • compile a time series of consequent sets of singular values • then apply the efficiency criterion

  11. Applications • Automated comparison (to check whether E close to 1 without visualisation) • Further detailed analysis of possible discrepancies (which singular values deviate) • Possible generalisations for higher dimensions

  12. Discussion • Introducing weights for singular values? Different distributions have very different sets of singular values! • Ways to compare fields with different grids: truncation, averaging?

  13. Thank you!

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