Merging Algorithm Sensitivity Analysis

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Merging Algorithm Sensitivity Analysis

• ACRI-ST/UoP

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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

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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

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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

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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

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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

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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
• aphyto 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

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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)
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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

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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)

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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
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One orbit later
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High fluctuations / regionalisation use of
sensitive a priori information
Large area higher variability
Small area lower variability
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Other illustrations
Indian ocean
North sea
Mediterranean
North sea
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Results
Initial daily images

• Global daily chlorophyll product from SeaWiFS,
  MODIS-A and MERIS
• of sea pixels covered
• 11.20
• 8.97
• 4.82

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Merged chlorophyll

• of sea pixels covered
• 17.65

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Comparison between averaging and GSM01 algorithm
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Comparison between averaging and GSM01 algorithm
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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

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Sensitivity analysis averaging procedure
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GSM01 algorithm McClain Characterisation error
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Sensitivity analysis GSM01 algorithm
SeaWiFS Error
SeaWiFS Error
MODISA Error
MODISA Error
MERIS Error
MERIS Error
All Errors
All Errors
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GSM01 algorithm Characterisation error
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Sensitivity analysis GSM01 algorithm
SeaWiFS Error
SeaWiFS Error
MODISA Error
MODISA Error
MERIS Error
MERIS Error
All Errors
All Errors
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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.

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