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

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

7. 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( )

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

10.  Designed to handle data imprecision and ambiguity  Allows for multiple outcomes using a fuzzy membership 0102030 Forest Wetland Water Reflectance Band 1 Reflectance Band 2 Mean class vector Unknown measurement vector Traditional minimum-distance criteria Hard 0102030 Forest Wetland Water Reflectance Band 1 Reflectance Band 2 Fuzzy graded membership Water = 0.05 Wetland = 0.65 Forest = 0.30 Fuzzy What is fuzzy logic?

11. Z 2 = (V rs - y j ) t  j -1 (V rs - y j ) V rs – satellite pixel vector y j – jth class mean vector  j – jth class covariance matrix y2y2 y1y1 V rs 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.

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

13. Class NOMAD (OC3) SeaWiFS OC4 Aqua OC3 1293527 2 5352 3303555 4427372 5737763 68293123 7609557 83611083 Avg.497874 Relative Error - %

14. Aqua GAC - May 2005 01 Membership

16. Producing the Uncertainty Map Aqua OC3 Error 27 52 55 72 63 123 57 83 = Uncertainty image   f i * i = 1…8 For each pixel,

17. 125 100 75 0 50 25 Relative Error (%) SeaWiFS OC4 Aqua OC3 May 2005

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

20. SeaWiFS OC4 Error

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

22. 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.

23. MERIS image - Aug. 22, 2008