merging algorithm sensitivity analysis

GlobColour CDR Meeting ESRIN 10-11 July 2006

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 sensitivity analysis• Results• Conclusion


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


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


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


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


• 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


• 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


• 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


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)


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


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)


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


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


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


Results

• Global daily chlorophyll product from SeaWiFS, MODIS-A and MERIS

• % of sea pixels covered– 11.20 %– 8.97 %– 4.82 %

Initial daily images


Merged chlorophyll

• % of sea pixels covered– 17.65%


Three sensors, MODIS & MERIS, SeaWiFS & MERIS,

SeaWiFS & MODIS, MERIS, MODIS, SeaWiFS


Comparison between averaging and GSM01 algorithm


Comparison between averaging and GSM01 algorithm

Regression between chlorophyll product of

GSM01 and averaging procedures, considering SeaWifs pixels only


GSM01 and averaging procedures, considering MODISA pixels only


GSM01 and averaging procedures, considering MERIS pixels only


GSM01 and averaging procedures, considering SeaWiFS & MODISA pixels


GSM01 and averaging procedures, considering MERIS pixels only


GSM01 and averaging procedures, considering SeaWiFS & MODISA pixels


GSM01 and averaging procedures, considering SeaWiFS & MERIS pixels


GSM01 and averaging procedures, considering MODIS & MERIS pixels


GSM01 and averaging procedures, considering SeaWiFS, MODISA & MERIS

pixels

0

200000

400000

600000

800000

1000000

1200000

Nu

mb

er o

f p

ixel

s


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


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


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




nLw555 16.64 Not available Not available

nLw650 Not available 48.824


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


by Mac Clain


by Mac Clain and characterisation

SeaWiFS Error SeaWiFS Error MODISA Error MODISA Error

MERIS Error MERIS Error All Errors All Errors


Mean % Difference

Product SeaWiFS MODIS-A MERIS

nLw412 -18.312 -14.806 77.419

nLw443 21.386 71.088 62.442




nLw531 Not available Insufficient match-ups Not available


nLw555 19.888 Not available Not available

nLw650 Not available 48.824

GSM01 algorithm Characterisation error


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


(c) Error on MERIS nLw as determined by


(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


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.

merging algorithm sensitivity analysis

Documents

cdom absorption coefficient

satellitesatellite merging

merge satellite

multiple ocean colour

bbp change

constant aphyto

situ dataprinciple

merging procedureaveraging