# Measuring and Modeling the Polarized Upwelling Radiance Distribution in Clear and Coastal Waters
## 4 Conclusions  
We have compared measurements of the polarization properties of the upwelling light field in the marine environment to radiative transfer models based on the measured inherent optical properties (IOPs) and an average normalized Mueller matrix for the scattering. For the Ligurian Sea and New York Bight data sets, the base RT model used the same volume scattering phase function (Petzold) and Mueller matrix (V-F) for the standard model, with the scattering and absorption coefficients as measured coincidently on location. For Hawaii, the IOPs were not measured, but were estimated based on an average _Chl_ value of 0.1 mg/m\({}^{3}\) at the measurement location. Even with the fixed scattering matrix parameters, on average, the \(DOLP_{diff}\) was less than 5%, and in almost every case was within one standard deviation of zero. Thus, to get more information, or discrimination, from the \(DOLP\) measurements, the uncertainty of the measured \(DOLP\) must be smaller than 5%, and the other parameters (scattering phase function, Mueller matrix, and absorption coefficient) need to be known well enough to constrain the \(DOLP\) model to this accuracy.  
Some of the variability in our data was due to instrument noise (on the order of 2%); however, other noise was due to the variability in the environment resulting from the incident light field interacting with the wavy air-sea interface. This was more of a problem for the downwelling light field but was still evident in the upwelling light field. For remote sensing, this radiance (Stokes vector) would have been propagated through the (wavy) air-sea interface, which would introduce more noise.  
The 5% agreement of the model with the data shows that the model will provide sufficient accuracy for correcting residual polarization effects in ocean color instruments. However, more work must be done at improving the measurement accuracy of the instrumentation if the goal is to be able to use polarization effects to characterize (and differentiate with respect to) the physical properties of the suspended particles other than \(c/a\).  
Data curation, K.J.V., M.S.T., and J.-F.B.; Formal analysis, A.C.R.G. and H.R.G.; Funding acquisition, K.J.V.; Methodology, A.C.R.G., K.J.V., and H.R.G.; Software, A.C.R.G. and H.R.G.; Supervision, K.J.V.; Writing--original draft, A.C.R.G., K.J.V., and H.R.G.; Writing--review and editing, A.C.R.G., K.J.V., H.R.G., and M.S.T.  
This work was supported by NASA under grants NNX08 AH93A and NNX14 AP63G ([PERSON]), and the NASA PACE Science Team ([PERSON]), and by NOAA under grant NA150 AR4320064. The BP'09 cruise (Ligurian Sea) was funded by the NATO Undersea Research Centre.  
Figure 10: Scatter plots of \(Q/I\) (**a**) and \(U/I\) (**b**) for model versus data for the Ligurian Sea data set. Also shown is the best fit line between the model and data for each parameter (black line). The 1:1 line is shown in red.  
**Acknowledgments:** [PERSON], [PERSON], [PERSON], and [PERSON] are thanked for their technical assistance in the field and with the instrumentation and data reduction.  
**Conflicts of Interest:** The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.