Inversion Methods
Analysis Definition
To address
Question #2 for the IOP Workshop. i.e.:
(2) What is the optimization or inversion method used?
* How critical is the choice of inversion method (can others be used)?
* What are the sensitivities of the available inversion methods?
* Does the reliability of the methods vary based on location or trophic level?
in situ and SeaWiFS data have been processed using a fixed algorithm (GSM) with 4 different inversion methods:
- Levenberg-Marquart non-linear least squares (LM)
- Downhill Simplex method (amoeba, AMB)
- Singular-Valued Decomposition (SVD)
- Lower-Upper Deconvolution (LUD)
The first two are iterative minimization schemes, while the latter two are direct matrix inversion methods. The model inversion was performed using each of these 4 inversion methods and varying sets of input Rrs wavelengths from 412 to 670nm. i.e.:
- 3-Band input: 412-490-555
- 4-Band input: 412-443-490-555
- 5-Band input: 412-443-490-510-555
- 6-Band input: 412-443-490-510-555-670
Note that LUD is only valid for a square matrix (equal number of bands and model parameters), so for standard GSM, only the 3-Band case was inverted using LUD.
Satellite processing was performed with l2gen->l2bin->l3bin (the OBPG operational data processing stream). The in situ processing for NOMAD was performed using IDL-based code, independently implemented and analyzed. Global satellite data was processed to 9.2-km monthly means for March, June, September, and December of 2005, and common bins were evaluated over several water classification subsets. i.e.:
- global: all bins
- deep: bins where water depth exceeds 1000 meters
- olig: oligotrophic bins (where chl < 0.1 mg m^3 on average, based on SeaWiFS mission mean)
- meso: mesotrophic bins (where 1 < chl < 0.1 mg/m^3 on average, based on SeaWiFS mission mean)
- eutr: eutrophic bins (where 10 < chl < 1 mg/m^3 on average, based on SeaWiFS mission mean)
Analysis Results
Observations and conclusions:
- All methods give identical results for the 3-Band case (equal number of equations to unknowns).
- AMB and LM give identical results for all cases (AMB is just slower).
- For the over-determined cases, the matrix method (SVD) does not agree with the iterative minimization schemes (AMB,LM).
- SVD shows much higher sensitivity to the specific wavelength set (both satellite and in situ confirm).
- SVD shows high sensitivity to low-signal noise (noisey SeaWiFS 670 band in blue water).
- SVD does not retrieve well at high and low end of absorption and backscatter range in many cases (see NOMAD results).
Discussion and Revision
A
lively group discussion ensued. Additional analysis suggested that the sensitivity differences between SVD and (LM,AMB) in the over-determined case were due in part to the way the problem was formulated. The linearization scheme was revised as per the group discussion and the analyses were re-evaluated.
