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Outline. Dynamic ocean topography using geodetic approach Characteristics of the data sets used for assimilation into global finite element ocean model (FEOM) Details of data assimilation scheme Results. Geodetic DOT. DOT=H= h-N h = sea surface height (from altimetric measurements)

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  1. Outline • Dynamic ocean topography using geodetic approach • Characteristics of the data sets used for assimilation into global finite element ocean model (FEOM) • Details of data assimilation scheme • Results

  2. Geodetic DOT DOT=H= h-N h = sea surface height (from altimetric measurements) N = geoid height (from recent geoid models)

  3. Geodetic DOT • Spectral consistency is achieved by applying a Gauss-type filter (Jekeli/Wahr) on sea surface and geoid. • The filter length is driven by the spectral resolution of the gravity field.

  4. Profile approach filtering (Bosch and Savcenko, 2010) • The filtering by means of Jekeli-Wahr filter with the half-width of 241.7 km, 121 km, 97 km and 81 km was applied to geoid and sea surface. • Information from high resolution geoid EGM2008 was used. • GOCO01S (Pail et al. 2010) combines GRACE and two months of GOCE data Launched March 17, 2009

  5. South Atlantic half-width of 241.7 km half-width of 121 km half-width of 81 km half-width of 97 km On the mean DOT superimposed are location of the fronts from Orsi et al. (1995)

  6. Geostrophic velocities GRACE/GOCE GRACE Albertella et al.

  7. Data assimilation scheme for assimilation of geodetic DOT into finite element ocean model (FEOM) • SEIK filter algorithm • Localization technique • Localization covariance • Changes in algorithm due to different spectral content of the data

  8. SEIK filter algorithm • DOT satellite observation available at tk (every 10 days) • forecast error covariance matrix is time evolving error covariance matrix derived from ensemble of model states, multivariate, nonstationary, nonisotropic. • observational error covariance matrix • analysis error covariance matrix Pham et al. 2001 Analysis error covariance is used together with second order exact resampling technique to generate new ensemble members that are evolved with full model in time.

  9. Janjic et al. submitted to MWR

  10. Janjic et al. submitted to MWR

  11. Janjic et al. submitted to MWR

  12. Janjic et al. submitted to MWR

  13. Janjic et al. submitted to MWR

  14. DOT filtered up to half width of 241 km is used first only

  15. Choice of localization function • Assimilation is performed with domain localized SEIK filter. • Different correlation function are used for the method SD+ObsLoc. • The observational error standard deviation is 5 cm. • Observations within radius of 900 km are used. Goal: To study the filtering behavior when different correlation functions for the weighting of observations are applied. Janjic et al. submitted to MWR

  16. For different spectral content of data DOT 121 km 5TH 900 km cutoff It was shown that the optimal infuence region is a circle with a radius of 900 km (cutoff length) for observations that are filtered to half width 241 km and that optimal covariance for localization of ensemble Kalman filter algorithm approximates well a Gaussian with length scale of 246 km. For the data filtered up to 121 km experiments were performed using same specification, as well as a localization function with length scale of 123 km (450 km cutoff). DOT 121 km 5TH 450 km cutoff

  17. Comparison of analysis • Assimilation of DOTs filtered up to degree 241,121 and 97 km. • Cutoff is optimized for each spectral content to be 900,450 and 360 km Difference between geodetic DOTs as a result of assimilation. Left: for assimilation of data with the half width of 241 and 121 km. Right: and the difference in results for assimilation of data with 121 km and 97 km.

  18. Conclusion • DOT with much finer space scales, that were previously poorly resolved, is obtained by combining GRACE and GOCE gravity field data. • Fine space scale structures are particularly visible in the areas of strong currents. Here we show South Atlantic and Southern Ocean example only. • Results of assimilation into the global finite element ocean model, shows similar increase in the resolution of DOT obtained as seen in the data.

  19. Conclusion • The algorithms that use the full rank covariance show superior performance for both Lorenz 40 and the example of assimilation of DOT. • Localization function determents spectral properties and accuracy of the solution as seen for both L40 model as for the realistic global assimilation of DOT. • Cutoff of localization functions need to be modified to appropriately take care of the spectral properties of the data • Further comparison of the results with independent ARGO data set shows positive impact of increased resolution in Weddell Sea area.

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