## 3 Results and Discussion
### CDOM, \(S_{g}\), and DOC Climatology  
Because the Aquarius mission (providing sea surface salinity) was limited to <4 year data record (~August 2011-June 2015), climatologies for retrieved DOC similar to those presented below for \(a_{g}\) and \(S_{g}\) are not possible. Instead, three years (2011-2013) of coincident MODIS Aqua and Aquarius data were used to generate a three-year mean 9 km global DOC product (Figure 11). An overlay of in situ surface DOC from GOCAD was examined, but not included here because with no temporal coincidence in this comparison, strong biases likely to occur in the field data (e.g., field sampling of high latitudes is proscribed during winter for obvious practical reasons) will not be reflected in the mean DOC satellite product. Nevertheless, the relatively large (\(\pm\)-50%--100%) disparities apparent in several regions--including high latitudes and the Atlantic subtropical gyre--indicate fundamental weaknesses in the global DOC algorithm. For instance, as mentioned in 3.2.1, the subtropical Atlantic gyre is characterized by an accumulation of DOM not reflected in the CDOM nor apparently traceable with changes in salinity, and is therefore overlooked by the DOC algorithm presented here (MLR2). Based on the tuning statistics, there appears to be merit in the approach, but more study will be required to establish when and where the algorithm works best, and what (if anything) can be done for remotely sensing DOC in regions where no robust optical proxies exist. As outlined in the introductory sections, a common assumption made in ocean color remote sensing on a global scale is that CDOM and other water-borne pigmented material covary with Chl. Figure 11: Retrieved three-year mean, 9 km nominal resolution DOC from Aquarius and MODIS Aqua using the MLR2 inversion. Validation statistics are reasonably good for the MLR2 (Figure 9, Table 8), but a larger number and wider geographic distribution of validation stations than are currently available is required to thoroughly evaluate the geographic and water-type limitations for MLR2, particularly in the mid-ocean gyres (see text Section 3.2.2). Overestimates of DOC (~41%) retrieved with the MLR2 were found in the southern oceans (S of 40° S)), but only for MODIS Aqua (i.e., not Terra, and no SeaWiFS stations were identified). Elsewhere (i.e., north of 40° S), retrievals tend to slightly underestimate DOC (<10%). Caution is therefore advised in interpreting MLR2 retrievals in mid-ocean gyres, and in the southern oceans using Aqua. A valid concern with empirical approaches to retrieve CDOM from ocean color--particularly for those that use some of the same spectral bands as Chl algorithms like OC3M--is that they are essentially tuning themselves to Chl, and not CDOM. While performance metrics for MLR are quite robust (e.g., Figure 5, Table 3), there remains the possibility that this is true in part because these spectral bands are sensitive to Chl, and CDOM is simply covarying with Chl as per Case 1 assumptions. In fact, this was not found to be the case generally from global CDOM and Chl field data in GOCAD (r\({}^{2}\) = 0.00, N = 19,446, \(\lambda\) = 412), nor in the investigation by [PERSON] et al. (2002), although there exist areas of open ocean outside of the strong influence of terrestrial run-off and upwelling zones where fluctuations in CDOM are clearly driven by local productivity. To quantify the distinction between retrievals of CDOM using MLR and Chl using OC3M, we calculate retrievals of each over the course of the entire MODIS Aqua mission, and then calculate a residual of the normalized properties, as defined by:  
\[\overline{Chl}-\overline{CDOM}=\frac{Chl_{i}}{median(Chl)}-\frac{a_{g_{i}}( \lambda)}{median\big{(}a_{g}(\lambda)\big{)}} \tag{10}\]  
where the median is taken over an entire composite image to scale each property by its magnitude. For example, MODIS imagery was separated into seasonal composites for the entire Aqua era, then processed to CDOM and Chl, and the residual calculated for each (Figure 12).