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Merging Algorithm Sensitivity Analysis

Merging Algorithm Sensitivity Analysis. ACRI-ST/UoP. Content. Review of the merging procedure Averaging, weighted averaging procedure Subjective analysis Blended analysis GSM01 algorithm Optimal interpolation Example of merged images Method of the s ensitivity analysis Results

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Merging Algorithm Sensitivity Analysis

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  1. Merging Algorithm Sensitivity Analysis ACRI-ST/UoP GlobColour CDR Meeting ESRIN 10-11 July 2006

  2. Content • Review of the merging procedure • Averaging, weighted averaging procedure • Subjective analysis • Blended analysis • GSM01 algorithm • Optimal interpolation • Example of merged images • Method of the sensitivity analysis • Results • Conclusion GlobColour CDR Meeting ESRIN 10-11 July 2006

  3. Averaging, weight averaging procedure • Advantages • Simple to implement • No source is considered better than another • Disadvantage • Requires unbiased data sources • If error bars of the data source can be characterized, a weight average can be implemented GlobColour CDR Meeting ESRIN 10-11 July 2006

  4. Subjective analysis • Information relevant to the quality of the sensors is used to develop a system weighting function, used during the merging • Weighting functions represent variables that may determine the performance of a sensor: • Satellite zenith angle • Solar zenith angle • Sensor behaviour • Sun glint • Advantage • Relies on scientific and engineering information • Disadvantages • Difficult task that requires detailed information for each mission involved • Computationally demanding GlobColour CDR Meeting ESRIN 10-11 July 2006

  5. Blended analysis • Traditionally applied to merge satellite and in situ data • Principle: • Assumes that in situ data are valid and uses these data to correct the final product • Applied to merge multiple ocean colour data: • in situ data are replaced by data from one or more sensor established as superior (better characterisation, calibration, viewing conditions, …) • Advantage: • can provide a bias correction • effective at eliminating biases if a "truth field" can be identified • Disadvantage • the effectiveness of the bias-correction capability not well documented in satellite-satellite merging. • Can result in over correction GlobColour CDR Meeting ESRIN 10-11 July 2006

  6. GSM01 algorithm • A second order Gordon reflectance model (Gordon et. al., 1988) used with the optimized parameters (Maritorena et. al., 2002) • In this equation, the absorption coefficient a() can be written as • where aw(), aphyto(), acdom() are the spectral absorption coefficient of • pure water • phytoplankton cells • Colored dissolved organic material respectively • Similarly, bb() can be written as: • where bbsw (), bbp () are the • backscattering coefficient of pure seawater • backscattering coefficient of particulate matter GlobColour CDR Meeting ESRIN 10-11 July 2006

  7. GSM01 algorithm • Among these five components: • aw() and bbsw () are known and constant • aphyto(), acdom() and bbp () change as a function of • Phytoplankton • CDOM • particulate matter They are modeled as: • a*phyto is the chlorophyll a specific absorption coefficient • [Chl] is the chlorophyll a concentration • acdom(0) and bbp (0) are the CDOM absorption coefficient and particulate backscattering coefficient at the reference wavelength 0 • S is the spectral decay constant for CDOM absorption •  is the power law exponent for particulate backscattering coefficient GlobColour CDR Meeting ESRIN 10-11 July 2006

  8. GSM01 algorithm • Equation • is therefore a function of three variables: • Chl a, acdom (0), bbp (0). • These three variables are retrieved by minimizing the mean square difference MSD: • In this equation, Rrs_modelled refers to calculated remote sensing reflectance and Rrs_sat refers to the measured remote sensing reflectance. The MSD equation was solved using the nonlinear method. Chl acdom(0) bbp(0) GlobColour CDR Meeting ESRIN 10-11 July 2006

  9. GSM01 algorithm • Advantage: • algorithm based on optical theory and not empirical relationships • Generate several products regardless of the number of data sources: Chl, acdom(0), bbp(0) • Merging done implicitly during the inversion process • Completely different approach • When different sensors have the same set of spectral LwN(), data are used individually, without any averaging or other transformation • Disadvantage • Errors associated with the parameterization and design of the model influence the quality of the merged product • Computationally demanding GlobColour CDR Meeting ESRIN 10-11 July 2006

  10. Optimal interpolation • Principle: • weights are chosen to minimize the expected error variance of the analysed field • uses a statistical approach to define weights. • The weight matrix W represents the error correlations (error covariance matrix) • Advantage • widespread use in data assimilation problems • objectivity in selecting the weights • Good at bias-correction • Disadvantage • statistical interpretation of the merged data set, as opposed to a scientific evaluation. • computational complexity • very slow. • requires a good knowledge of data accuracy • shall be adapted from one region to the other (according to variogram that is the signature of the spatial correlation within each area) • dependent on a number of additional a priori information (e.g. as chlorophyll variability) GlobColour CDR Meeting ESRIN 10-11 July 2006

  11. Spatial characterisation of natural variability: Elementary inputs for optimal interpolation and objective analysis Characterisation of the variance through semi-variogram (to quantify co-variability of information separated by a distance « d ») i d j GlobColour CDR Meeting ESRIN 10-11 July 2006

  12. GlobColour CDR Meeting ESRIN 10-11 July 2006

  13. One orbit later GlobColour CDR Meeting ESRIN 10-11 July 2006

  14. High fluctuations / regionalisation : use of sensitive a priori information Large area – higher variability Small area – lower variability GlobColour CDR Meeting ESRIN 10-11 July 2006

  15. Other illustrations Indian ocean North sea Mediterranean North sea GlobColour CDR Meeting ESRIN 10-11 July 2006

  16. Global daily chlorophyll product from SeaWiFS, MODIS-A and MERIS % of sea pixels covered 11.20 % 8.97 % 4.82 % Results Initial daily images GlobColour CDR Meeting ESRIN 10-11 July 2006

  17. % of sea pixels covered 17.65% Merged chlorophyll GlobColour CDR Meeting ESRIN 10-11 July 2006

  18. GlobColour CDR Meeting ESRIN 10-11 July 2006

  19. GlobColour CDR Meeting ESRIN 10-11 July 2006

  20. Comparison between averaging and GSM01 algorithm GlobColour CDR Meeting ESRIN 10-11 July 2006

  21. Comparison between averaging and GSM01 algorithm GlobColour CDR Meeting ESRIN 10-11 July 2006

  22. Method of the sensitivity analysis • Sensitivity analysis on chlorophyll concentration retrieval for • GSM01 algorithm • averaging procedure • based on global SeaWifs, MODISA and MERIS 9km standard map images • results obtained on June 15th 2003 as an example • Adding noise to input parameters and evaluating the impact on the merged chlorophyll product • Gaussian errors are introduced on the input parameters • on the nLw for the procedure using the GSM01 algorithm • on global chlorophyll products of individual sensors for the averaging technique • Input products for the merging are used as available from each sensor: • no attempt was made to weight neither input chlorophyll nor input Normalized Water Leaving Radiances • 10% 30% error when merging chlorophyll products • 5 to 10% error with the GSM01algorithm + % error calculated by McClain + % error calculated in the characterisation section • Presentation of the result for • 30% error on Chl product • McClain and Characterisation error on nLw products GlobColour CDR Meeting ESRIN 10-11 July 2006

  23. Sensitivity analysis averaging procedure GlobColour CDR Meeting ESRIN 10-11 July 2006

  24. GSM01 algorithm McClain + Characterisation error GlobColour CDR Meeting ESRIN 10-11 July 2006

  25. Sensitivity analysis GSM01 algorithm SeaWiFS Error SeaWiFS Error MODISA Error MODISA Error MERIS Error MERIS Error All Errors All Errors GlobColour CDR Meeting ESRIN 10-11 July 2006

  26. GSM01 algorithm Characterisation error GlobColour CDR Meeting ESRIN 10-11 July 2006

  27. Sensitivity analysis GSM01 algorithm SeaWiFS Error SeaWiFS Error MODISA Error MODISA Error MERIS Error MERIS Error All Errors All Errors GlobColour CDR Meeting ESRIN 10-11 July 2006

  28. Conclusion • The averaging procedure showed little sensitivity with up to 30% error • The GSM01 algorithm showed little sensitivity to errors from McClain for SeaWiFS and MODIS-A. Despite the level of error introduced with the characterisation results, the chlorophyll output remained in good agreement with the initial calculations. GlobColour CDR Meeting ESRIN 10-11 July 2006

  29. GlobColour CDR Meeting ESRIN 10-11 July 2006

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