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Local polynomial fitting and cross over difference analysis

This workshop, held from March 9-11, 2010, focused on local polynomial fitting techniques and crossover difference analysis, particularly using data from the Aquarius satellite. Participants learned to control smoothing radius and modify the order of fits through Taylor series approximations. Key applications included analysis of simulated Aquarius products in the North Atlantic, emphasizing the examination and removal of orbit errors in surface salinity from the inner and outer beams. The workshop culminated in discussions on the effects of harmonic errors on adjusted data and on generating residual error histograms.

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Local polynomial fitting and cross over difference analysis

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  1. Hsun-Ying Kao, Gary Lagerloef and Johnathan Lilly Earth and Space Research Local polynomial fitting and cross over difference analysis Aquarius Algorithm Workshop March9-11 2010

  2. Local Polynomial Fitting • Smoothing radius is explicitly controlled (bandwidth B) • The order of the fit can be modified (p) The approximation of the surface z(x,y) by a Taylor series expansion: Decaying parabola r is the distance between two points

  3. In Matrix form

  4. Example 1 Bandwidth = 1

  5. Application on simulated Aquarius product for 2007 in north Atlantic B = 150km P1 - P0 P = 0 P2 - P0 P = 1 P2 - P1 P = 2

  6. Crossover Differences Analysisorbit error removal

  7. Crossover points at western equatorial Atlantic Crossover points between the inner and middle beams

  8. 21-Days Average SSS from the Three Beams November 2004 Middle(34.1332 psu) Outer(34.0282 psu) Inner (34.0999 psu)

  9. Crossover differences among the three beams middle-outer inner-middle inner-outer

  10. Cross over difference between Beam a and Beam b

  11. Remove orbit errors Beam 1 SSS (assume error free) Beam 2 SSS (with constant and harmonic errors added) Adjusted SSS (with constant and harmonic errors removed) Residual errors

  12. Histogram of the crossover differences

  13. Remove orbit errors Beam 1 SSS (with harmonic errors added) Beam 2 SSS (with constant and harmonic errors added) Adjusted Beam 1 SSS (with harmonic errors removed) Adjusted Beam 2 SSS (with constant and harmonic errors removed)

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