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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
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?
-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
NOMAD V2
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.
NOMAD V2
Aqua Validation SetSeaWiFS Validation Set
• Rrs
• In situ Chl
• Algorithm Chl
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()
NOMAD V2 Clustering Results
• Cluster analysis on SeaWiFS Rrs bands
•8 clusters optimal based on cluster validity functions
N=2372
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
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?
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.
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
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 - %
Aqua GAC - May 2005
0 1
Membership
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Producing the Uncertainty Map
AquaOC3 Error
27
52
55
72
63
123
57
83
= Uncertainty image fi *i = 1…8
For each pixel,
125
100
75
0
50
25
Relative Error (%)
SeaWiFS OC4
Aqua OC3
May 2005
Jan 2005 Apr 2005
Jul 2005 Oct 2005
125
100
75
0
50
25
Relative Error (%)Aqua OC3 Error
SeaWiFSOC4 Error
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
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.
MERIS image - Aug. 22, 2008