## 4 Discussion  
### IOP Model Limitations  
The largest source of uncertainty in the estimation of UV penetration into the ocean is related to the IOP model used in RT computations with Hydrolight. HydroLight is a radiative transfer numerical model that computes radiance distributions and derived quantities for natural water bodies. This model solves the unpolarized RT equation to obtain the radiance distribution within a plane-parallel water body. We neglect the errors of solving the RT equation with Hydrolight because a main source of the errors in the Hydrolight output is related to uncertainties in the Hydrolight input. In general, the Hydrolight inputs consist of the absorbing and scattering properties of water, the properties of the wind-blown ocean surface, the reflectance of the bottom in the case of shallow waters and the angular distribution of radiance incident on the ocean surface. Here, we assume the Case I model of IOPs that allows us to minimize the number of input parameters and, therefore, to use the standard satellite ocean color product as input for Hydrolight. Within the Case I model, the IOPs of ocean water are assumed to be fully correlated and can be parameterized through chlorophyll concentration. The Case I ocean water model is supposed to work well for open ocean waters where the influence of terrigenic matter is negligible. The Case I model is not applicable for coastal zones of the world ocean where suspended particulate matter and CDOM may not be fully correlated with chlorophyll concentration. Our parameterization of the particulate-matter absorption coefficient, \(a_{ph}\), Ref. [10] is based on in situ data collected on the California Cooperative Oceanic Fisheries Investigations (CalCOFI) cruises in different areas and seasons. The CalCOFI region encompasses a large dynamic range of coastal and open ocean trophic structures. The optics data have been collected for Chl-a concentrations at the surface, ranging four orders of magnitude, from \(0.05\,\mathrm{mg}\,\mathrm{m}^{-3}\) for offshore stations to about \(20\,\mathrm{mg}\,\mathrm{m}^{-3}\) and higher. The taxonomic composition across the onshore-offshore gradient ranges from a dinoflagellate/diatom-dominated coastal community to a pico-plankton-dominated community offshore. The offshore region of CalCOFI is typical of the open ocean oligotrophic subtropical gyres with low surface Chl-a and a deep Chl-a maximum between \(100\)-\(130\,\mathrm{m}\). Unfortunately, there are few measurements of particulate-matter absorption below \(350\,\mathrm{nm}\). That is why a direct comparison of our parameterization with other data is limited. The lack of the \(a_{ph}(\lambda)\) data compels us to assume an arbitrary spectral dependence of \(a_{ph}\) in the UV. For instance, [PERSON] et al. [57] assume that \(a_{ph}\) is spectrally flat for \(\lambda<412\,\mathrm{nm}\), which is rather unrealistic. However, this model is currently embedded in NASA's SeADAS software. A classification of \(a_{ph}(\lambda)\) measured down to the \(350\,\mathrm{nm}\) at \(5\,\mathrm{nm}\) step was proposed in [58]. The \(a_{ph}\) spectra were divided into twelve groups based on a value of \(a_{ph}(440)\), covering oligotrophic oceanic waters to waters with phytoplankton blooms. However, a parameterization of \(a_{ph}\) in UV that would be suitable for a global application was not proposed. [PERSON] et al. [59] show two normalized phytoplankton absorption spectra from \(300\) to \(750\,\mathrm{nm}\) taken at the Bermuda Atlantic Time Series (BATS) site. Their spectra are highly variable with seasons and depths between \(300\) and \(365\,\mathrm{nm}\). This variability is likely due to mycosporine-like amino acids (MAAs), which strongly absorb near \(320\,\mathrm{nm}\). The shape of the summer spectrum [59] is quite different from our paramterization. This is explained by averaging many spectra collected in different seasons in our parameterization, while [PERSON] et al. [59] show examples of the phytoplankton absorption spectra.