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