## 3 Results
### In-Water Irradiance
#### 3.2.3. OMI Retrievals  
In this section, OMI retrievals are shown for OMI orbit 2573 on 7 January 2005. All the retrievals are limited to SZA \(<80^{\circ}\). The retrievals include the surface erytal dose rates and penetration depths for the DNA damage dose rates. The DNA damage dose rate at a given depth is defined as the integral of the DNA-weighted irradiance over the UV spectral range:  
\[D(z)=\int_{290}^{400}E(\lambda,z,SZA)\,A(\lambda)\,d\lambda, \tag{7}\]  
where \(E(\lambda,z)\) is either the planar or scalar irradiance, \(A(\lambda)\) is the DNA damage action spectrum [48] and SZA is defined for each OMI pixel at the time of the satellite overpass. The penetration depth is calculated from the following equation: \(D(z_{p})=\epsilon D(0)\), where \(\epsilon=0.1\). Figure 6 shows maps of the main input parameters of orbit 2573 used for the OMI retrievals. The chlorophyll concentrations shown in Figure 6 were obtained from the MODIS/Aqua chlorophyll-a product [52]. We use the monthly averaged Level 3 MODIS chlorophyll product, which is reported at a spatial resolution of 4 km [53]. All available monthly MODIS chlorophyll data within the OMI field-of-view (FOV) were averaged. In the case where MODIS data were not available from the monthly product for an OMI FOV, gap filling was performed using monthly climatology. If monthly data were unavailable, an annual mean was used. Figure 7 shows maps of the OMI-derived surface erytal dose rates. The dose rates were calculated using the planar and scalar irradiances convolved with the erytal action spectrum [54] (see also, [[https://www.temis.nl/uvradiation/product/action.html](https://www.temis.nl/uvradiation/product/action.html)]([https://www.temis.nl/uvradiation/product/action.html](https://www.temis.nl/uvradiation/product/action.html)), accessed on 30 March 2022). As expected, the scalar erytal dose rates were noticeably higher than the planar erytal dose rates. Both planar-based and scalar-based erytal dose rates depend on SZA and cloud cover. The erytal dose rates exhibit a strong spatial correlation with the effective cloud optical depth shown in Figure 6d. The ratio of the scalar dose rates to the planar dose rates (Figure 7c) was highly correlated with SZA (Figure 6a) and increased with SZA except for very high SZA \(>70^{\circ}\) in the northern part of the orbital swath. For those high SZAs, the ratio decreased with increasing SZA (see Figure 2b of Appendix B). This dependence of the ratio on SZA for high values of SZA was similar to the so-called Umkehr effect that is related to ozone absorption in the atmosphere. In general, the ratio  
Figure 6: Maps of the main input parameters: (**a**) solar zenith angle; (**b**) chlorophyll concentration in mg/m\({}^{3}\); (**c**) ozone amounts in DU; and (**d**) effective cloud optical depth at 360 nm. of the scalar erytomal dose rates to the planar erytomal dose rates varied from 1.5 to about 3.0. Figure 8 shows maps of the penetration depths of the DNA damage dose rates calculated using the planar and scalar irradiance and their difference. The maps of the penetration depths show that a governing parameter that mostly defines the penetration depth is chlorophyll concentration. There is a strong spatial correlation between the chlorophyll concentration (Figure 6b) and the penetration depths (Figure 8a,b). Other input parameters play an insignificant role in the spatial distribution of the penetration depths. The penetration depths vary from a few meters in areas of productive waters of the Southern Ocean to about 30-35 m in the clearest waters of the South Pacific Gyre. Differences between the planar penetration and scalar penetration depths are small. They do not exceed a couple of meters (Figure 8c). This fact follows from Hydrolight computations that show a small difference between \(K\) functions for the planar and scalar irradiances for a wide range of input parameters (Figure 5).