a class-based approach for mapping the uncertainty of empirical chlorophyll algorithms timothy s....
DESCRIPTION
Range of uncertainty log Rrs(blue):Rrs(green) OC3/OC4 Algorithms Average absolute error: 50% based on NOMAD V2 Relative errorTRANSCRIPT
![Page 1: A class-based approach for mapping the uncertainty of empirical chlorophyll algorithms Timothy S. Moore University of New Hampshire NASA OCRT Meeting May](https://reader035.vdocuments.us/reader035/viewer/2022062401/5a4d1b7e7f8b9ab0599b9fd4/html5/thumbnails/1.jpg)
A class-based approach for mapping the uncertainty of empirical chlorophyll
algorithms
Timothy S. MooreUniversity of New Hampshire
NASA OCRT MeetingMay 3-5, 2009 NYC
…in collaboration with…
Mark Dowell, JRCJanet Campbell, UNH
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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 1.2log max Rrs/Rrs555
log CHL
in situ dataSeaWiFS (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 error (uncertainty) for empirical algorithms.
• The advantage gained is that different parts of the empirical algorithm can be 1) discretely characterized for error and 2) individually mapped using satellite reflectance data.
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NOMAD V2
Aqua Validation SetSeaWiFS 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 classerror
Merged Image Product
Calculatemembership
Rrs()
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NOMAD V2 Clustering Results
• Cluster analysis on SeaWiFS Rrs bands
•8 clusters optimal based on cluster validity functions
N=2372
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Class Mean Reflectance SpectraClass Mean Reflectance Spectra
Class Means
• Rrs mean spectra behave as endmembers
• Rrs class statistics form the fuzzy membership function.
wavelength (nm)
Rrs
(0-)
Type12345678
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Designed to handle data imprecision and ambiguity Allows for multiple outcomes using a fuzzy membership
0 10 20 30
ForestWetland
Water
Reflectance Band 1
Ref
lect
ance
Ban
d 2
Mean class vectorUnknown measurement vector
Traditional minimum-distance criteria
Hard
0 10 20 30
ForestWetland
Water
Reflectance Band 1R
efle
ctan
ce B
and
2
Fuzzy graded membership
Water = 0.05Wetland = 0.65Forest = 0.30
Fuzzy
What is fuzzy logic?
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Z2 = (Vrs - yj)tj -1(Vrs - yj)
Vrs – satellite pixel vector yj – jth class mean vector j
– jth class covariance matrix
y2
y1
Vrs
€
Z12
€
Z22
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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Aqua validation set
N=464 N=1576
Log10(max(Rrs443,Rrs488)/Rrs551)
chlo
roph
yll
mg/
m3
chlor auncertainty
Type12345678
SeaWiFS validation set
NOMAD V2
N=1543
Characterizing class uncertainty
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ClassNOMAD(OC3)
SeaWiFSOC4
AquaOC3
1 29 35 27
2 27 53 52
3 30 35 55
4 42 73 72
5 73 77 63
6 82 93 123
7 60 95 57
8 36 110 83
Avg. 49 78 74
Relative Error - %
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Aqua GAC - May 2005
0 1
Membership
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QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
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Producing the Uncertainty Map
AquaOC3 Error
27
52
55
72
63
123
57
83
= Uncertainty image fi *i = 1…8
For each pixel,
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125
100
75
0
50
25
Relative Error (%)
SeaWiFS OC4
Aqua OC3
May 2005
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Jan 2005 Apr 2005
Jul 2005 Oct 2005
125
100
75
0
50
25
Relative Error (%)Aqua OC3 Error
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SeaWiFSOC4 Error
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MERIS/Seawifs/MODISM
ER
ISM
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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Conclusions
• Single, bulk estimates of algorithm performance do not realistically describe the spatial distribution of error.
• The class-based method is a way to characterize product uncertainty for different optical environments and to dynamically map them.
• Basing OC3/OC4 error statistics with the Aqua and SeaWiFS validation data set is recommended because it reflects product error.
• 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.
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MERIS image - Aug. 22, 2008