## 2 Data and Methods
### Atmospheric RT Model  
RT solutions in the atmosphere and ocean are coupled through the contribution of photons backscattered by the ocean and then scattered back to the ocean by the atmosphere, see, e.g., Ref. [34] and the references therein. However, if the ocean reflectance is small enough, the atmospheric and oceanic RT problems can be treated separately. [PERSON] and [PERSON] [8] estimated that the separation of the atmospheric and oceanic RT models produces less than 10% resulting error in UV underwater irradiance. This RT scheme allows us to significantly reduce the computational burden and calculate spectral UV penetration into the ocean using global satellite measurements with reasonable computational resources. RT calculations of hyperspectral surface planar irradiance, \(E(\lambda)\), are needed to create a boundary condition for Hydrolight calculations of underwater downwelling irradiance. \(E(\lambda)\) is determined in the presence of Rayleigh scattering from the molecular atmosphere, the absorption of ozone, scattering by clouds, both scattering and absorption by aerosols and reflection from the surface. To accommodate variable BWF spectra, we extended the OMI surface UV algorithm [22] from 4 to 110 wavelengths producing \(E(\lambda)\) at every 1 nm from 290 to 399 nm at the OCI spectral resolution of 5 nm. The algorithm is based on interpolation of lookup tables of clear sky irradiance, \(E_{clr}(\lambda)\), and cloud/aerosol transmittance factor, \(C_{T}\), given by:  
\[E(\lambda)=E_{clr}(\lambda)\;C_{T}(\lambda). \tag{2}\]  
Calculation of \(E_{clr}\) from satellite measurements of total column ozone, \(\Omega\) and Lambertian equivalent surface reflectivity, \(R_{s}\), is described in [PERSON] et al. [35; 36]. We use climatological ozone absorption profiles. Each standard profile represents a multi-year average for a given total ozone bin for all profiles within a latitude band. These profiles cover a range of 225-475 DU for low latitudes and 125-575 DU for middle and high latitudes, in steps of 50 DU. \(R_{s}\) is estimated from a monthly climatology of the minimum LER at 380 nm, which is small over the ocean (\(R_{s}<0.1\)). We screen OMI pixels affected by sun glint, which is highly non-Lambertian. In practice, we calculate \(C_{T}(\lambda)\) using full radiative transfer calculations for a model of a homogeneous, plane-parallel C1 cloud model [37] embedded in a Rayleigh scattering molecular atmosphere with climatological ozone absorption profiles. The C1 cloud model represents a water cloud model having the modified gamma size distribution of water droplets with the mode radius of 4 microns. The cloud effective optical thickness, \(\tau_{c}\)assumed spectrally independent, is derived by matching pre-calculated and measured OMI TOA reflectances at 360 nm corrected for non-elastic (Raman) scattering and collision-induced O\({}_{2}\)-O\({}_{2}\) absorption [38]. The C\({}_{T}(\lambda,\Omega,\tau_{c},R_{s},\mathrm{SZA})\) lookup table is calculated at multiple wavelengths for a fixed climatological ozone profile (\(\Omega=300\) DU), \(\tau_{c}\) (0-100), surface albedo, \(R_{s}\) (0-1) and solar zenith angles (SZA = 0-88\({}^{\circ}\)). The cloud height and geometrical thickness are fixed (3-5.5 km). We use the DIScrete ORdinate Radiation Transfer (DISORT) code [39] for large \(\tau_{c}\), where polarization can be neglected, and the Gauss-Seidel RT code [40] for \(\tau_{c}<10\), where polarization may have an effect on backscattered radiances. The effective \(\tau_{c}\) corresponds to the actual cloud optical thickness only in an idealized case of a homogeneous plane-parallel cloud layer with complete coverage of the satellite field of view (pixel). For inhomogeneous cloud fields, the \(\tau_{c}\) and C\({}_{T}\) are spatially averaged quantities that depend on the sub-pixel 3D cloud structure and satellite observational geometry in more complex ways [41]. The spectral independence of \(\tau_{c}\) is a good approximation in the UV region and was confirmed by Mie calculations.