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Local polynomial fitting and cross over difference analysis

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. Local Polynomial Fitting. Smoothing radius is explicitly controlled (bandwidth B )

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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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