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A class-based approach for mapping the uncertainty of empirical chlorophyll algorithms

This study proposes a class-based methodology to accurately assess and map the uncertainty of empirical chlorophyll algorithms, overcoming the limitations of current single estimates. By implementing fuzzy logic techniques, different parts of the algorithm can be discretely characterized for error and individually mapped using satellite reflectance data. The approach allows for a dynamic mapping of errors across different optical environments, providing a common framework applicable to various satellites and algorithms at multiple spatial scales.

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A class-based approach for mapping the uncertainty of empirical chlorophyll algorithms

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  1. A class-based approach for mapping the uncertainty of empirical chlorophyll algorithms Timothy S. Moore University of New Hampshire NASA OCRT Meeting May 3-5, 2009 NYC …in collaboration with… Mark Dowell, JRC Janet Campbell, UNH

  2. 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?

  3. OC3/OC4 Algorithms Relative error Range of uncertainty log Rrs(blue):Rrs(green) Average absolute error: 50% based on NOMAD V2

  4. NOMAD V2

  5. 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.

  6. Rrs • In situ Chl • Algorithm Chl NOMAD V2 SeaWiFS Validation Set Aqua Validation Set

  7. In-situ Database (NOMAD V2) Rrs() OC3/4 Rel. Error 8 classes Cluster analysis station data sorted by class class-based average relative error Class Mi, Si Satellite Measurements Rrs() Individual class error Calculate membership Merged Image Product

  8. NOMAD V2 Clustering Results • Cluster analysis on SeaWiFS Rrs bands • 8 clusters optimal based on cluster validity functions N=2372

  9. Class Mean Reflectance Spectra Type 1 • Rrs mean spectra behave as endmembers • Rrs class statistics form the fuzzy membership function. 2 3 4 5 6 7 Rrs(0-) 8 wavelength (nm) Class Means

  10. What is fuzzy logic? Fuzzy Hard Fuzzy graded membership Traditional minimum-distance criteria Water Water Reflectance Band 2 Reflectance Band 2 Wetland Wetland Forest Forest Water = 0.05 Wetland = 0.65 Forest = 0.30 Unknown measurement vector Mean class vector 0 10 20 30 0 10 20 30 Reflectance Band 1 Reflectance Band 1 • Designed to handle data imprecision and ambiguity • Allows for multiple outcomes using a fuzzy membership

  11. Chi-square PDF The Membership Function Vrs y1 y2 Z2 = (Vrs - yj)tj -1(Vrs - yj) Vrs – satellite pixel vector yj – jth class mean vector j– jth class covariance matrix Result: A number between 0 and 1 that is a measure of the vector’s membership to that class.

  12. Characterizing class uncertainty chlor a uncertainty chlorophyll mg/m3 Type 1 2 3 4 5 6 7 8 Log10(max(Rrs443,Rrs488)/Rrs551) NOMAD V2 N=1543 Aqua validation set SeaWiFS validation set N=464 N=1576

  13. Relative Error - %

  14. Aqua GAC - May 2005 Membership 0 1

  15. Producing the Uncertainty Map For each pixel, Sfi* = Uncertainty image i = 1…8

  16. May 2005 Relative Error (%) 125 100 75 SeaWiFS OC4 50 25 0 Aqua OC3

  17. Aqua OC3 Error Relative Error (%) 125 100 Jan 2005 Apr 2005 75 50 25 0 Jul 2005 Oct 2005

  18. SeaWiFS OC4 Error

  19. Channel 1-5 Channel 1,2,3,5 MERIS/Seawifs/MODIS MERIS MODIS/Aqua May 2004 SeaWiFS Class 1 Class 2 Class 3 Class 4 Class 5 Class 6 Class 7 Class 8

  20. 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.

  21. MERIS image - Aug. 22, 2008

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