# Estimating Underwater Light Regime under Spatially Heterogeneous Sea Ice in the Arctic
## 1 Introduction
In recent studies, to better document the spatial variability of \(E_{d}(z)\), radiometers were attached to either remotely operated vehicles (ROV) (1965) or a surface and under-ice trawl (SUIT), a net developed for deployment in ice-covered waters, typically behind an icebreaker (1965). Both a ROV and a SUIT allow a better description of the light field right under sea ice, which is more appropriate for determining average irradiance experienced by drifting phytoplankton. Such under-ice measurements can then be combined with averaged \(K_{d}\) values to propagate light at depth. Estimating irradiance at depth for primary production measurement or calculation using \(K_{d}\) values derived from only a few discrete vertical profiles of \(E_{d}(z)\) under heterogeneous sea ice is problematic whatever the platform for radiometer deployment. Let us consider that phytoplankton, by continuously drifting horizontally relative to sea ice, are exposed to fluctuations in irradiance due to surface heterogeneity, and that the relevant light metrics for primary production in such conditions is irradiance at any depth averaged over some horizontal area. When measuring an irradiance profile at one given location under sea ice, as the depth of the upward-looking detector increases, light from a larger area on the underside of the ice enters the detector field of view. In other words, the detector \"sees\" different things at different depths. One consequence is that \(E_{d}(z)\) measured that way may not follow the usual monotonically exponential decrease with increasing depth (Equation (1)). For example, irradiance profiles measured beneath low-transmission sea ice (e.g., white ice) relative to surrounding areas showing melt ponds, show subsurface light maxima. The literature reports subsurface maxima varying between 5 m and 15 m in depth (1965; 1965; 1965). Conversely, it is also important to note that \(K_{d}\) estimations are biased when profiles are measured beneath an area of high transmission (e.g., a melt pond) relative to surrounding areas (1965). Indeed, with depth, light decreases more quickly than what would be expected from the IOPs of the water column. In the field, this situation is more difficult to identify compared to profiles showing subsurface maxima because the former measurements may appear to follow a single exponential decrease but would not produce a diffuse attenuation coefficient that adequately describes the water mass. So, two vertical light profiles measured a few meters apart under sea ice are often very different. More importantly, local measurements of light under heterogeneous sea ice do not provide an adequate description of the average light field as it would be seen by drifting phytoplankton cells at different depths. This makes estimations of primary production and the interpretation of biogeochemical data challenging in the presence of sea ice. To fit vertical profiles of \(E_{d}(z)\) under bare ice that do not follow an exponential decay under sea ice covered with melt ponds, [PERSON] et al. [8] proposes a simple geometric model (Equation (2)). \[E_{d}(z)=\pi E_{d}(0^{-})(1+P(N-1)\cos^{2}\phi)e^{-K_{d}(z)\ z} \tag{2}\]  
where \(E_{d}(0^{-})\) is the irradiance directly below the ice/snow, \(P\) the areal fraction of the ice cover, \(N\) the ratio between ice and melt ponds transmittance and \(\phi\) a fitting parameter defined as \(\arctan(R/z)\) with \(R\) the radius of the ice patch and \(z\) the depth. A major drawback of this method is that additional field observations of \(N\) and \(P\) are required to adequately parametrise the model, which makes its use more difficult. To address this concern (among others), [PERSON] et al.