# Estimating Underwater Light Regime under Spatially Heterogeneous Sea Ice in the Arctic
## 1 Introduction  
The vertical distribution of underwater light is an important driver of many aquatic processes such as primary production by phytoplankton, and photochemical reactions such as the photodegradation of organic matter. Hence, an adequate description of the underwater light regime is mandatory to understand energy fluxes in aquatic ecosystems. In open water, when assuming an optically homogeneous water column, downward irradiance at any given wavelength follows, as a first approximation, quite well a monotonically exponential decrease with depth, which can be modelled as follows [1] (Equation (1)):  
\[E_{d}(z)=E_{d}(0^{-})\ e^{-K_{d}(z)\ z} \tag{1}\]  
where \(E_{d}(z)\) is the downward plane irradiance (W m\({}^{-2}\)) at depth \(z\) (m), \(E_{d}(0^{-})\) is the downward plane irradiance (W m\({}^{-2}\)) just below the surface and \(K_{d}(z)\) is the diffuse vertical attenuation coefficient (m\({}^{-1}\)) describing the rate at which downward irradiance decreases with increasing depth. \(K_{d}\) is oneof the most commonly used apparent optical properties (AOP) of seawater, and a good estimation of this parameter is important for measuring or modelling primary production. \(K_{d}\) may vary with depth because of changes in seawater inherent optical properties (IOPs), the angular structure of the light field, and the effects of inelastic radiative processes such as Raman scattering by water molecules and fluorescence by phytoplankton pigments or dissolved organic matter. As [PERSON] (1964) pointed out, for practical considerations in oceanography and limnology, the \(K_{d}\) value, even when averaged within the euphotic zone, provides a useful proxy to represent the downward irradiance attenuation in the upper water column. For example, to determine primary production based on simulated on-deck incubations or photosynthetic parameters derived from photosynthesis-irradiance curves (P vs. E curves) requires measured or estimated values of \(K_{d}\) (e.g., [PERSON] (1964)). Nowadays, \(K_{d}\) is relatively easy to estimate using commercially available radiometers. The ice-infested regions of the Arctic ocean are characterized by a complex mosaic made of sea ice with snow, melt ponds, ridges, and leads ([PERSON], 1964; 1965; 1965). Phytoplankton are exposed to a highly variable light regime while drifting under these heterogeneous features (e.g., [PERSON] et al. (1996)). Estimating primary production of phytoplankton under sea ice requires an approach that is adequate to capture this large-area variability in the light field. In situ incubations at single locations of seawater samples inoculated with \({}^{14}\)C or \({}^{13}\)C are not appropriate because they reflect primary production under local light conditions, which is not representative of the range of irradiance experienced by drifting phytoplankton over a large area. One classical approach that is more adequate consists in conducting on-deck simulated 24-h incubations of seawater samples inoculated with \({}^{14}\)C or \({}^{13}\)C and applying the light attenuation at the depths of sample collections, using natural illumination and neutral filters. An alternative approach consists in calculating primary production using modelled or measured daily time series of incident irradiance, sea ice transmittance and in-water vertical attenuation coefficients, combined with photosynthetic parameters determined from P-E curves measured with short (under two hours) incubations of seawater samples inoculated with \({}^{14}\)C. The latter two methods require that the vertical profile of the irradiance experienced by drifting phytoplankton be appropriately determined, which is challenging due to surface heterogeneity. Traditionally, one or very few \(E_{d}(z)\) profiles are measured at discrete locations under sea ice (e.g., [PERSON] et al. (1996)). Such measurements, however, do not capture the variability induced by sea ice features.