# Presentation: 626446

## Quantify IOP quality derived from QAA

**ZhongPing Lee****1****, Robert Arnone****2**
**1****Northern Gulf Institute, Mississippi State University, Stennis Space Center, MS 39529; **_[zplee@ngi.msstate.edu](mailto:zplee@ngi.msstate.edu)_
**2****Naval Research Laboratory, Stennis Space Center, MS 39529**

## Q: How big is the error (or confidence) of inverted IOPs at each pixel?

**Q****: ****How big is the error (or confidence) of inverted IOPs at each pixel?**

- “Average error of an algorithm is insufficient to describe the error of specific locations.”

- -- Boss et al

- We should not expect the same error bars for the three pixels.

## The Quasi-analytical algorithm (QAA)

*R*rs()* *

*Y*

**The Quasi-analytical algorithm (QAA)**

- (Lee et al. 2002)

**The three stating points:**

## If Rrs is error free, and the relationship between Rrs and {bb,a} is accurate, quality of inverted a&bb by QAA depends on the estimation of a(λ0) and Y.

## A “Hydrolight” data set

- a440 distribution

- a550 distribution

- bbp440 distribution

- Y distribution

## QAA inverted a440&bbp440 vs known a440&bbp440

- QAA inverted *a*440&bbp440 vs known *a*440&bbp440

- -- when *a*550 and Y are known exactly.

*a*440known  [m-1]

*a*440inv  [m-1]

- _Indication__:  the formulation and scheme can get a closure!_

*b**bp*440known  [m-1]

*b**bp*440inv  [m-1]

## QAA inverted a440 vs known a440

- -- impact of imprecise *a*550; Y is known exactly

*a*440known  [m-1]

*a*440inv  [m-1]

- QAA inverted *a*440 vs known *a*440

*a*550 is 10% higher

*a*550 is 10% lower

- _Indication:__ nearly the same impact to all __*a*__440 values._

## QAA inverted a440 vs known a440

- -- impact of imprecise Y; *a*550 is known exactly

*a*440known  [m-1]

*a*440inv  [m-1]

- QAA inverted *a*440 vs known *a*440

*Y* is 0.4 higher

*Y* is 0.4 lower

- _Indication:__ nearly the same impact to all __*a*__440 values._

## QAA inverted a440 vs known a440

- -- _**compounding**_ effects of imprecise Y and imprecise *a*550

*a*440known  [m-1]

*a*440inv  [m-1]

- QAA inverted *a*440 vs known *a*440

*Y* is 0.4 _higher_ and a550 is 10% _higher_

*Y* is known; a550 is 10% _higher_

- _Indication:__ more errors!_

## QAA inverted a440 vs known a440

- -- _**compensation**_ between imprecise Y and imprecise *a*550

*a*440known  [m-1]

*a*440inv  [m-1]

- QAA inverted *a*440 vs known *a*440

*Y* is 0.4 _lower_; a550 is 10% _higher_

- Both* Y* and a550 known

- _Indication:__ nearly compensating each other._

## Error at a550 (εa550) vs estimated a550

- Error at *a*550 (εa550) vs estimated *a*550

- εa550

*a*550inv  [m-1]

- Q: 1. How big is the a550 error for different a550?
-      2. How this error propagates to other IOPs?

- Global ocean

## Slide 12

## Error at a440 vs compound error of a550 and Y (±0.2, ±0.4)

- Error at *a*440 vs compound error of *a*550 and Y (±0.2, ±0.4)

- Error at *a*550 (εa550)

- Error at *a*440

- εa440

- δa440

- δ: percentage error at 84th percentile or ***likelihood range ***

## Error at a410 vs compound error of a550 and Y (±0.2, ±0.4)

- Error at *a*550 (εa550)

- Error at *a*410

- εa440

- δa440

- δ: percentage error at 84th percentile

- Error at *a*410 vs compound error of *a*550 and Y (±0.2, ±0.4)

## Rrs  aλ0  ελ0  εIOP & δIOP

- Data flow to **quantify** quality of inverted IOP :

- Note: No Rrs error considered yet;
-      but can be added when quality measure of Rrs is known.

## Conclusion:

- Qualities of IOPs derived by QAA, in addition to quality of Rrs, rely on the estimation of *a*(λ0) and Y.
- The qualities at _*each pixel*_, measured by projected average error and projected likelihood range, can be quantified by evaluating the error propagation in the QAA process.
- Higher qualities for IOPs of oceanic waters, as both *a*(λ0) and Rrs possess higher reliability.

## Slide 17

## aw values dominate the longer wavelengths, so a(λ0) can be estimated reasonably well.