a class-based approach for mapping the uncertainty of
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A class-based approach for mapping the
uncertainty of empirical chlorophyll
algorithms!
Timothy S. Moore!
University of New Hampshire!
NASA MODIS Meeting!
January 26, 2010!
…in collaboration with…!
Mark Dowell, JRC!
Janet Campbell, UNH!
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Updates since OCRT (May 2009)!
•! Fix to NOMAD screening (more oligotrophic points).!
•! Fix to membership function (increase in class
memberships).!
•! Generalized table for SeaWiFS, MODIS, MERIS.!
•! Migrated to a developmental l2gen.!
•! Updates to empirical chl uncertainties from v6
reprocessing.!
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What’s the problem?
•! Current single, bulk estimates of chlorophyll error (50-78%) for
the empirical algorithms exceed the desired goal of 35%.
•! This is misleading, as algorithms do not perform to the same
level of accuracy in different optical environments.
•! Product error is relevant to higher-order algorithms that use
OC products, and understanding changes in CDRs.
•! Question: How can we more accurately assess OC product
‘error’ and geographically map them?
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-2
-1
0
1
2
-0.6 0 0.6 1.2
log max Rrs/Rrs555
log C
HL
in situ data
SeaWiFS (OC4)
Range of
uncertainty
log Rrs(blue):Rrs(green)
OC3/OC4 Algorithms!
Average absolute error: 50% based on NOMAD V2!
Relative error!
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NOMAD V2!
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Approach
•! Previously, we have implemented a fuzzy logic methodology for
distinguishing different optical water types based on remote
sensing reflectance.
•! The same techniques can be adapted for characterizing
chlorophyll uncertainty (or more accurately called discrepency)
for empirical algorithms.
•! The advantage gained is that different regions of the empirical
algorithm can be 1) discretely characterized and 2) individually
mapped using satellite reflectance data.
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NOMAD V2
Aqua Validation Set
SeaWiFS Validation Set
•! Rrs!
•! In situ Chl!
•! Algorithm Chl!
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In-situ Database (NOMAD V2)
Rrs(!)
Cluster analysis
OC3/4 Rel. Error
station data
sorted by class
class-based
average relative error
8 classes
Class
Mi, !i"
Satellite Measurements
Individual class
error
Merged
Image Product
Calculate
membership
Rrs(!)
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NOMAD V2 Clustering Results
•! Cluster analysis on
SeaWiFS Rrs bands
•!8 clusters optimal
based on cluster
validity functions!N~2400!
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Class Means!
•! Rrs mean spectra behave
as endmembers !
•! Rrs class statistics form
the fuzzy membership
function.!
wavelength (nm)!
Rrs
(0-)!
Type!
1
2345678
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Aqua validation set!
N=541! N=1576!
Log10(max(Rrs443,Rrs488)/Rrs551)!
chlo
rophyll
m
g/m
3!
chlor a
uncertainty
Type!
12345678
SeaWiFS validation set!
NOMAD V2!
N=1543!
Characterizing class uncertainty
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Class
NOMAD
(OC3)
OC3
(v5)
OC3
(v6)
1 28 17 18
2 25 32 33
3 27 39 42
4 44 62 58
5 77 62 59
6 94 79 60
7 80 86 60
8 55 N/A N/A
Avg. 53 78 74
Relative Error - %!
Aqua validation set!
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Aqua GAC - May 2005!
0! 1!
Membership!
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Producing the Discrepency Map!
Relative
Error
18
33
42
58
59
60
60
N/A
" fi *!i = 1…8!
For each pixel,!
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May 2005!chlor a!
rel. error!
125!
100!
75!
0!
50!
25!
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Frequency of low membership sum!
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Conclusions!
•! Single, bulk estimates of algorithm performance do not realistically describe the spatial distribution of error.!
•! Basing OC3/OC4 error statistics with the Aqua and SeaWiFS validation data set is recommended because it reflects product discrepency.!
•! The class-based method is a way to characterize product discrepency
for different optical environments and to dynamically map them pixel by pixel.!
•! Class-based approach provides a common framework that can be
applied to different satellites and different algorithms at multiple spatial scales.!
•! We envision the error maps as separate, companion products to the
existing suite of NASA OC products (currently in developmental l2gen).!
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MERIS image - Aug. 22, 2008!
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MERIS/Seawifs/MODIS!
ME
RIS
M
OD
IS/A
qua
Sea
WiF
S
Class 1 Class 2 Class 3 Class 4 Class 5 Class 6 Class 7 Class 8
May 2004
Channel 1-5 Channel 1,2,3,5
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!! Designed to handle data imprecision and ambiguity
!! Allows for multiple outcomes using a fuzzy membership
0! 10! 20! 30!
Forest!
Wetland!
Water!
Reflectance Band 1!
Refl
ecta
nce
Ban
d 2!
Mean class vector!
Unknown measurement vector!
Traditional minimum-distance criteria!
Hard!
0! 10! 20! 30!
Forest!
Wetland!
Water!
Reflectance Band 1!
Refl
ecta
nce
Ban
d 2!
Fuzzy graded membership!
Water = 0.05!
Wetland = 0.65!
Forest = 0.30!
Fuzzy!
What is fuzzy logic?!
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Z2 = (Vrs - yj)t"
j -1(Vrs - yj
)
Vrs – satellite pixel vector
yj – jth class mean vector
"j – jth class covariance matrix
y2!
y1!Vrs
!
Z1
2
!
Z2
2
Chi-square PDF
The Membership Function
Result: A number between 0 and 1 that is a
measure of the vector’s membership to that class.!
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125!
100!
75!
0!
50!
25!
Relative Error (%)!
SeaWiFS OC4!
Aqua OC3!
May 2005!
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SeaWiFS!
OC4 Error!
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Jan 2005! Apr 2005!
Jul 2005! Oct 2005!
125!
100!
75!
0!
50!
25!
Relative Error (%)!Aqua OC3 Error!