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GlobColour CDR Meeting ESRIN 10-11 July 2006
Merging Algorithm Sensitivity Analysis
ACRI-ST/UoP
GlobColour CDR Meeting ESRIN 10-11 July 2006
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
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
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
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
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
i
b
b
iirs ba
blR
2
1
cdomphytow aaaa
bp bsw bb b b
GlobColour CDR Meeting ESRIN 10-11 July 2006
• 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
00
00
*
exp*
*)(
bpbp
cdomcdom
phytophyto
bb
Saa
Chlaa
GSM01 algorithm
GlobColour CDR Meeting ESRIN 10-11 July 2006
• 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.
i
b
b
iirs ba
blR
2
1
2
1
00 )(,,,1
1modelled
N
i
irsbpcdomirs SatRbaChlaRN
MSD
Chl
acdom(0)
bbp(0)400 450 500 550 600
Wavelength (nm)
Rrs
SeaWiFS
MODIS-A
MERISBest fit
GSM01 algorithm
GlobColour CDR Meeting ESRIN 10-11 July 2006
• 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
GSM01 algorithm
GlobColour CDR Meeting ESRIN 10-11 July 2006
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
i
j
d
)d(N
2))j(Chla(Log))i(Chla(Log2
1)d(
Characterisation of the variance through semi-variogram (to quantify co-variability of information separated by a distance « d »)
Spatial characterisation of natural variability:Elementary inputs for optimal interpolation and objective analysis
GlobColour CDR Meeting ESRIN 10-11 July 2006
0.00 50.00 100.00 150.00 200.00 250.00distance (km )
0.00
0.01
0.02
0.03
0.04
varia
nce
of L
og(C
hla)
GlobColour CDR Meeting ESRIN 10-11 July 2006
0.00 50.00 100.00 150.00 200.00 250.00D istance (km )
0.00
0.02
0.04
0.06
0.08
0.10
Var
ianc
e of
Log
(C
hla)
One orbit later
GlobColour CDR Meeting ESRIN 10-11 July 2006
0.00 50.00 100.00 150.00 200.00 250.00D istance (km )
0.00
0.02
0.04
0.06
0.08
0.10
Var
ianc
e of
Log
(C
hla)
Large area – higher variability
Small area – lower variability
High fluctuations / regionalisation :use of sensitive a priori information
GlobColour CDR Meeting ESRIN 10-11 July 2006
0.00 50.00 100.00 150.00 200.00 250.00D istance (km )
0.00
0.10
0.20
0.30
0.40
0.50V
aria
nce
of L
og (
Chl
a)
Indian ocean
North sea
North seaMediterranean
Other illustrations
GlobColour CDR Meeting ESRIN 10-11 July 2006
Results
• Global daily chlorophyll product from SeaWiFS, MODIS-A and MERIS
• % of sea pixels covered– 11.20 %– 8.97 %– 4.82 %
Initial daily images
GlobColour CDR Meeting ESRIN 10-11 July 2006
Merged chlorophyll
• % of sea pixels covered– 17.65%
GlobColour CDR Meeting ESRIN 10-11 July 2006
Three sensors, MODIS & MERIS, SeaWiFS & MERIS,
SeaWiFS & MODIS, MERIS, MODIS, SeaWiFS
GlobColour CDR Meeting ESRIN 10-11 July 2006
Three sensors, MODIS & MERIS, SeaWiFS & MERIS,
SeaWiFS & MODIS, MERIS, MODIS, SeaWiFS
GlobColour CDR Meeting ESRIN 10-11 July 2006
Comparison between averaging and GSM01 algorithm
GlobColour CDR Meeting ESRIN 10-11 July 2006
Comparison between averaging and GSM01 algorithm
Regression between chlorophyll product of
GSM01 and averaging procedures, considering SeaWifs pixels only
Regression between chlorophyll product of
GSM01 and averaging procedures, considering MODISA pixels only
Regression between chlorophyll product of
GSM01 and averaging procedures, considering MERIS pixels only
Regression between chlorophyll product of
GSM01 and averaging procedures, considering SeaWiFS & MODISA pixels
Regression between chlorophyll product of
GSM01 and averaging procedures, considering MERIS pixels only
Regression between chlorophyll product of
GSM01 and averaging procedures, considering SeaWiFS & MODISA pixels
Regression between chlorophyll product of
GSM01 and averaging procedures, considering SeaWiFS & MERIS pixels
Regression between chlorophyll product of
GSM01 and averaging procedures, considering MODIS & MERIS pixels
Regression between chlorophyll product of
GSM01 and averaging procedures, considering SeaWiFS, MODISA & MERIS
pixels
0
200000
400000
600000
800000
1000000
1200000
Nu
mb
er o
f p
ixel
s
GlobColour CDR Meeting ESRIN 10-11 July 2006
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
Sensitivity analysis averaging procedure
30% error on SeaWifs Chl
30% error on MODISA Chl
30% error on MERIS Chl
30% error on all Chl inputs
30% error on SeaWifs Chl
30% error on MODISA Chl
30% error on MERIS Chl
30% error on all Chl inputs
GlobColour CDR Meeting ESRIN 10-11 July 2006
GSM01 algorithm McClain + Characterisation error
Mean % Difference
Product SeaWiFS MODIS-A MERIS
nLw412 10.78 5.62 77.419
nLw443 13.35 10.86 62.442
nLw488 Not available 5.97 Not available
nLw490 12.13 Not available 52.954
nLw510 11.08 Not available 49.182
nLw531 Not available 6.96 Not available
nLw551 Not available 14.02 Not available
nLw555 16.64 Not available Not available
nLw650 Not available 48.824
GlobColour CDR Meeting ESRIN 10-11 July 2006
Sensitivity analysis GSM01 algorithm
Error on SeaWifs nLw as determined
by Mac Clain
(c) Error on MERIS nLw as determined
by the characterisation
(b) Error on MODISA nLw as determined
by Mac Clain
(d) Error on all sensors nLw as determined
by Mac Clain and the characterisation
(a) Error on SeaWifs nLw as determined by
Mac Clain
(c) Error on MERIS nLw as determined by
the characterisation
(b) Error on MODISA nLw as determined
by Mac Clain
(d) Error on all sensors nLw as determined
by Mac Clain and characterisation
SeaWiFS Error SeaWiFS Error MODISA Error MODISA Error
MERIS Error MERIS Error All Errors All Errors
GlobColour CDR Meeting ESRIN 10-11 July 2006
Mean % Difference
Product SeaWiFS MODIS-A MERIS
nLw412 -18.312 -14.806 77.419
nLw443 21.386 71.088 62.442
nLw488 Not available 154.075 Not available
nLw490 22.995 Not available 52.954
nLw510 8.140 Not available 49.182
nLw531 Not available Insufficient match-ups Not available
nLw551 Not available 451.181 Not available
nLw555 19.888 Not available Not available
nLw650 Not available 48.824
GSM01 algorithm Characterisation error
GlobColour CDR Meeting ESRIN 10-11 July 2006
Sensitivity analysis GSM01 algorithm
(a) Error on SeaWifs nLw as determined by the
characterisation
(c) Error on MERIS nLw as determined by the
characterisation
(a) Error on SeaWifs nLw as determined by
the characterisation
(c) Error on MERIS nLw as determined by
the characterisation
(b) Error on MODISA nLw as determined by the
characterisation
(d) Error on all sensors nLw as determined by the
characterisation
(b) Error on MODISA nLw as determined
by the characterisation
(d) Error on all sensors nLw as determined
by the characterisation
(b) Error on MODISA nLw as determined
by the characterisation
(d) Error on all sensors nLw as determined
by the characterisation
SeaWiFS Error SeaWiFS Error MODISA Error MODISA Error
MERIS Error MERIS Error All Errors All Errors
GlobColour CDR Meeting ESRIN 10-11 July 2006
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