1. Introduction
Sea-ice algae generate 10% of total marine-produced carbon and can cause sea ice to host the highest algal cell and chlorophyll concentrations of any marine environment (Tedesco and Vichi, Reference Tedesco and Vichi2014; Arrigo, Reference Arrigo and Thomas2017; Lund-Hansen and others, Reference Lund-Hansen, Bjerg-Nielsen, Stratmann, Hawes and Sorrell2021). The presence of contaminants such as black carbon (e.g. Marks and King, Reference Marks and King2013), sediment (e.g. Light and others, Reference Light, Eicken, Maykut and Grenfell1998; Gradinger and others, Reference Gradinger, Kaufman and Bluhm2009), crude oil (e.g. Redmond Roche and King, Reference Redmond Roche and King2022) or organisms (e.g. Fritsen and others, Reference Fritsen, Iturriaga and Sullivan1992, Reference Fritsen, Wirthlin, Momberg, Lewis and Ackley2011) can affect the apparent optical properties of sea ice, including albedo, transmittance, absorption and extinction of light. Photosynthetically active radiation (PAR, wavelength range 400–700 nm) is utilised by autotrophs for photosynthesis and is a critical component of the polar ecosystems, with ice algae being light-limited during the winter and later nutrient-limited once there is sufficient PAR (e.g. Cota and others, Reference Cota, Legendre, Gosselin and Ingram1991; Duarte and others, Reference Duarte2015; Leu and others, Reference Leu2015; Weckström and others, Reference Weckström2020); other factors such as temperature, salinity and iron can also limit production. PAR at the ice-ocean interface is primarily controlled by snow thickness and, to a lesser extent, by sea-ice thickness (e.g. Mundy and others, Reference Mundy, Ehn, Barber and Michel2007). The transmittance of PAR (the fraction of incident light which is transmitted) to the ice-ocean interface can also be considerably affected by the presence of sea-ice algae, with microalgae frequently being the principal absorbing material in sea ice and responsible for up to 25–90% of attenuation between 400 and 550 nm in first-year sea ice (Fritsen and others, Reference Fritsen, Iturriaga and Sullivan1992, Reference Fritsen, Wirthlin, Momberg, Lewis and Ackley2011; Light and others, Reference Light, Perovich, Webster, Polashenski and Dadic2015). The presence of ice algae may also affect the physical properties of sea ice and heat the sea ice through increased light absorption (Zeebe and others, Reference Zeebe1996). PAR availability at the ice-ocean interface is a fundamental constraint on marine primary production in the water column in the polar regions (Popova, Reference Popova2010) and potentially even on celestial bodies (e.g. Reynolds and others, Reference Reynolds, Squyres, Colburn and McKay1983; Hand and others, Reference Hand, Chyba, Priscu, Carlson, Nealson, Pappalardo, McKinnon and Khurana2009; France and others, Reference France, King and MacArthur2010). Therefore, parameterising the effect sea-ice algae have on PAR transmittance may be important to understand how sea-ice algae can affect the light availability for primary production beneath the ice (e.g. Petrich and others, Reference Petrich, Nicolaus and Gradinger2012; Ehn and Mundy, Reference Ehn and Mundy2013; Katlein and others, Reference Katlein, Nicolaus and Petrich2014; Hill and others, Reference Hill, Light, Steele and Sybrandy2022).
Columnar sea ice has a lamellar crystal structure to which inclusions (e.g. brine pockets, gas bubbles, contaminants) are usually aligned, resulting in sea ice scattering light anisotropically and predominantly downwards (Trodahl and others, Reference Trodahl, Buckley and Brown1987; Petrich and others, Reference Petrich, Nicolaus and Gradinger2012; Katlein and others, Reference Katlein, Nicolaus and Petrich2014). Previous studies have utilised simple Beer–Lambert exponential decay to predict the propagation of PAR in sea ice and snow (e.g. Grenfell and Maykut, Reference Grenfell and Maykut1977; Tedesco and others, Reference Tedesco and Vichi2014; Stroeve and others, Reference Stroeve2021; Lim and others, Reference Lim, Payne, van Dijken and Arrigo2022); however, measurements (e.g. King and others, Reference King, France, Fisher and Beine2005; Light and others, Reference Light, Perovich, Webster, Polashenski and Dadic2015) have shown that this can provide an inaccurate attenuation profile for non-optically thick sea ice (see Warren, Reference Warren2019 for a detailed description). Other studies (e.g. King and others, Reference King, France, Fisher and Beine2005; Redmond Roche and King, Reference Redmond Roche and King2024) have shown that dark layers in the base of the ice or present below the ice can affect the intensity of PAR throughout sea ice. Concentrations of sea-ice algae exhibit substantial geo-temporal variance, with column-integrated biomass concentrations from the bottom of ice-core sections ranging in chlorophyll a (chl-a, a proxy for ice algae biomass) between <2 mg chl-a m−2 in Greenlandic fjords, 7 mg chl-a m−2 in the Central Arctic, 53.8 mg chl-a m−2 in the European Arctic and 340 mg chl-a m−2 in the Canadian Arctic during maximum bloom conditions (Søgaard and others, Reference Søgaard2010, Reference Søgaard, Deming, Meire and Rysgaard2019; Leu and others, Reference Leu2015, and references therein). In the Antarctic, up to 500 mg chl-a m−2 has been recorded in sea ice (Riaux-Gobin and others, Reference Riaux-Gobin, Treguer, Poulin and Vetion2000) and up to 1090 mg chl-a m−2 has been recorded in the sub-ice platelet layer (Arrigo, Reference Arrigo and Thomas2017). Sea-ice algae can grow at extremely low light fluxes (0.17 μmol m−2 s−1) (Hancke and others, Reference Hancke2018) under thick snow cover and may begin growing as early as February in the Arctic Ocean (Stroeve and others, Reference Stroeve2021). Sea-ice algal blooms coincide with increasing PAR (~5 μmol m−2 s−1) between the end of winter and the beginning of sea-ice melt when basal ice layers begin to slough off (Cota and Smith, Reference Cota and Smith1991; Perovich and others, Reference Perovich, Cota, Maykut and Grenfell1993; Hill and others, Reference Hill, Light, Steele and Sybrandy2022). Blooms in the Arctic Ocean may also experience bimodal chl-a peaks in March and July (Melnikov and others, Reference Melnikov, Kolosova, Welch and Zhitina2002). The highest chl-a concentrations are found in the basal layers of sea ice, from the skeletal layer extending vertically up to ~0.2 m. Typically, ~95% of algal biomass is located near the ice-ocean interface in the bottom 0.02 m (e.g. Welch and Bergmann, Reference Welch and Bergmann1989; Perovich and others, Reference Perovich, Cota, Maykut and Grenfell1993; Lavoie and others, Reference Lavoie, Denman and Michel2005); however, different vertical distributions in biomass can occur in the base (0.2 m) and interior of sea ice. The effects of these varying distributions on PAR transmittance are poorly quantified in optical modelling studies (e.g. Lange and others, Reference Lange2015; Cimoli and others, Reference Cimoli, Meiners, Lund-Hansen and Lucieer2017).
Therefore, while many studies have considered how specific measured concentrations of chl-a affect PAR transmittance (e.g. Arrigo and others, Reference Arrigo, Sullivan and Kremer1991; Perovich and others, Reference Perovich, Cota, Maykut and Grenfell1993, Reference Perovich, Roesler and Pegau1998; Mundy and others, Reference Mundy, Ehn, Barber and Michel2007), the work presented here aims to use a coupled atmosphere-sea ice/snow radiative-transfer model to parameterise how the variance in column-integrated concentration (0–500 mg chl-a m−2) in measured ice algal biomass can affect PAR transmittance to the ice-ocean interface during winter, spring and summer sea ice and snow conditions. The study also aims to assess how different vertical distributions of sea-ice algae in the base of sea ice (0.01–0.08 m thick layers) and in the middle of sea ice (0.02–0.04 m thick layers) affect PAR transmittance throughout sea ice while keeping the volumetric concentration of algae constant. A visual description of the structure will be shown later in Figure 4.
2. Methods
The radiative-transfer modelling was undertaken using the Tropospheric Ultraviolet-Visible Radiation Model (TUV-snow) (Madronich and Flocke, Reference Madronich, Flocke and Boule1998; Lee-Taylor and Madronich, Reference Lee-Taylor and Madronich2002), an eight-stream DISORT algorithm (Stamnes and others, Reference Stamnes, Tsay, Wiscombe and Jayaweera1988) that calculates irradiance and photon flux parameters from the top of the atmosphere to the ice-ocean interface, similar to other publically available models (e.g. Flanner and others, Reference Flanner2021). The model is separated into 201 layers, comprising a 62-layer atmosphere (90 km thick), 20-layer snowpack (0.2 m thick) and 119-layer ice pack (2 m thick). The layers are assumed to be horizontally homogeneous with a wavelength-dependent absorption cross section, σ abs, wavelength-independent scattering cross section, σ scatt, asymmetry factor, g, for snow (0.89) and sea ice (0.98) (Mobley and others, Reference Mobley1998), and snow and sea-ice densities, ρ, listed in Table 1. The sea ice and snow matrix control light scattering while the ice, a typical Arctic black carbon mass ratio for snow (10 ng g−1) and sea ice (5.5 ng g−1) (Jiao and others, Reference Jiao2014; Warren, Reference Warren2019), and the varying concentrations of chl-a control the absorption in the PAR wavelength range. Scattering from black carbon particles and algae is not considered here as they are very minor compared to the scattering from the snow and sea-ice matrix (Perovich, Reference Perovich1996; Mobley and others, Reference Mobley1998). The TUV-snow model calculates the downwelling PAR for all layers in the model, and these are presented in this study as an integrated ‘flat plate’ PAR equal to an irradiance summed over 400–700 nm. The transmittance of PAR, T, is the value of downwelling PAR at that ice-ocean interface, PARice–ocean, relative to the value of downwelling PAR at the snow surface, PARsurf, (T = PARice−ocean/PARsurf). The TUV-snow model has previously been shown to reproduce light transmittance and reflectance in control laboratory-grown sea ice (e.g. Marks and others, Reference Marks, Lamare and King2017), and all modelling has been kept consistent with previous studies (Redmond Roche and King, Reference Redmond Roche and King2022, Reference Redmond Roche and King2024), where a comprehensive description is provided.
Table 1. Scattering cross-section (σ scatt) and density (ρ) values for all modelled sea ice and snow layers
Grenfell and Maykut (Reference Grenfell and Maykut1977); Perovich (Reference Perovich1990, Reference Perovich1996); Grenfell and others (Reference Grenfell, Light and Sturm2002); King and others (Reference King, France, Fisher and Beine2005); Light and others (Reference Light, Grenfell and Perovich2008, Reference Light, Perovich, Webster, Polashenski and Dadic2015, Reference Light2022); France and others (Reference France2011); Marks and King (Reference Marks and King2014); Lamare and others (Reference Lamare, Lee-Taylor and King2016); Warren (Reference Warren2019); Stroeve and others (Reference Stroeve2021); Vérin and others (Reference Vérin, Domine, Babin, Picard and Arnaud2022).
The sea ice and snow are separated into three layers: an interior ice layer below freeboard, a drained ice layer above freeboard and a homogeneous overlying snowpack. The freeboard is calculated assuming the sea ice is in hydrostatic equilibrium with a sea-ice density of 920 kg m−3, a snow density of 320 kg m−3 and a seawater density of 1027 kg m−3, consistent with previous studies (e.g. Alexandrov and others, Reference Alexandrov, Sandven, Wahlin and Johannessen2010; Zhang and others, Reference Zhang2020; Redmond Roche and King, Reference Redmond Roche and King2024). The sea ice and snow are modelled under three scenarios: winter (≪0°C), spring (<0°C) and summer (⩾0°C), consistent with Redmond Roche and King (Reference Redmond Roche and King2024) and comparable with phases 1, 2 and 3 described by Vérin and others (Reference Vérin, Domine, Babin, Picard and Arnaud2022). The density of sea ice can vary (700–950 kg m−3) (e.g. Perovich, Reference Perovich1990, Reference Perovich1996); however, here, it is 920 kg m−3 for all scenarios to be consistent with the freeboard approximation (Alexandrov and others, Reference Alexandrov, Sandven, Wahlin and Johannessen2010; Zhang and others, Reference Zhang2020) and to allow for a direct comparison of the optical effects of the algae in different sea-ice thicknesses. While the value of σ scatt of sea ice can be variable (Grenfell and Maykut, Reference Grenfell and Maykut1977; Perovich, Reference Perovich1990, Reference Perovich1996; King and others, Reference King, France, Fisher and Beine2005; Light and others, Reference Light, Grenfell and Perovich2008, Reference Light2022; Stroeve and others, Reference Stroeve2021), the three scenarios have been modelled in accordance with the average vertical scattering profiles presented in Figure 8 of Light and others (Reference Light, Perovich, Webster, Polashenski and Dadic2015). Bare sea-ice conditions are also considered in this study, however, melt ponds are not considered (e.g. Light and others, Reference Light, Grenfell and Perovich2008, Reference Light, Perovich, Webster, Polashenski and Dadic2015, Reference Light2022; Lamare and others, Reference Lamare, Hedley and King2023). The snow density and value of σ scatt differ between the three scenarios, with the winter, spring and summer scenarios being characterised by cold polar/fresh (0.1–0.5 mm grains), coastal windpack/windslab (0.5–2 mm grains) and melting/melt form snow types (2–5 mm grains), respectively (e.g. Grenfell and others, Reference Grenfell, Light and Sturm2002; France and others, Reference France2011; Marks and King, Reference Marks and King2014; Lamare and others, Reference Lamare, Lee-Taylor and King2016; Warren, Reference Warren2019; Vérin and others, Reference Vérin, Domine, Babin, Picard and Arnaud2022).
The absorption spectrum of sea ice and snow (Warren and Brandt, Reference Warren and Brandt2008) is small at shorter wavelengths (~300–500 nm) and small inclusions of contaminants can considerably modify light absorption (e.g. Warren, Reference Warren1982; Light and others, Reference Light, Eicken, Maykut and Grenfell1998; Doherty and others, Reference Doherty, Warren, Grenfell, Clarke and Brandt2010; Réveillet and others, Reference Réveillet2022). Indeed, it is often necessary to include small concentrations of black carbon, which has a relatively wavelength-independent absorption cross section when using radiative-transfer models to increase attenuation coefficients to match natural measurements of sea ice and snow (e.g. Warren, Reference Warren1982; Mundy and others, Reference Mundy, Ehn, Barber and Michel2007). The absorption spectrum of sea-ice algae is dominated by the pigment chl-a, which has a strong wavelength dependence, with a broad peak typically centred at 440 nm and a narrow peak centred at 680 nm (Arrigo and others, Reference Arrigo, Sullivan and Kremer1991). Figure 1 shows the typical chl-a absorption cross sections for sea-ice algae from both the Arctic and Antarctic (Perovich, Reference Perovich1991; Arrigo and others, Reference Arrigo, Sullivan and Kremer1991; Mundy and others, Reference Mundy, Ehn, Barber and Michel2007, Reference Mundy2011; Fritsen and others, Reference Fritsen, Wirthlin, Momberg, Lewis and Ackley2011; Arrigo, Reference Arrigo and Thomas2017; Wongpan and others, Reference Wongpan2018), in addition to phytoplankton chl-a (Bricaud and others, Reference Bricaud, Babin, Morel and Claustre1995), and phytoplankton photoprotectant and photosynthetic carotenoid pigment (Bidigare and others, Reference Bidigare, Ondrusek, Morrow and Kiefer1990). The absorption cross section of sea-ice algae is dependent on the ratio of pigments, which can lead to a packaging effect where the absorption may be flattened (e.g. Morel and Bricaud, Reference Morel and Bricaud1981; Wang and others, Reference Wang, Jiang, Xing, Chen and Meng2020). Sea-ice algae can increase or decrease their photosynthetic efficiency in response to changing PAR availability, which can lead to a packaging effect around 450–550 nm as the ratio of accessory pigments increases (Arrigo and others, Reference Arrigo, Sullivan and Kremer1991); however, chl-a is the dominant pigment present in sea-ice algae (Wang and others, Reference Wang, Jiang, Xing, Chen and Meng2020). Consequently, it is complex to accurately quantify the absorption cross section of sea-ice algae (e.g. SooHoo, Reference SooHoo1987; Light and others, Reference Light, Perovich, Webster, Polashenski and Dadic2015) as it is dependent on the concentration of pigments, so this study utilises the chl-a cross section presented in Mundy and others (Reference Mundy, Ehn, Barber and Michel2007) as a representative spectrum and wavelength-integrated PAR transmittance (T) is considered. Therefore, the study presented here will examine (i) the response of T to increasing chl-a column-integrated concentrations (0–500 mg chl-a m−2) in the bottom 0.02 m of sea ice and (ii) the response of T through sea ice under a fixed volumetric chl-a concentration vertically distributed in the basal 0.01, 0.02, 0.04 and 0.08 m of the sea ice, in addition to 0.02 and 0.04 m thick internal layers at 1 m.
Figure 1. Ice algal chlorophyll-a biomass (Arrigo and others, Reference Arrigo, Sullivan and Kremer1991, Reference Arrigo, Brown and Mills2014; Perovich, Reference Perovich1991; Mundy and others, Reference Mundy, Ehn, Barber and Michel2007, Reference Mundy2011; Fritsen and others, Reference Fritsen, Wirthlin, Momberg, Lewis and Ackley2011; Wongpan and others, Reference Wongpan2018), phytoplankton chlorophyll-a biomass (Bricaud and others, Reference Bricaud, Babin, Morel and Claustre1995) and phytoplankton photoprotectant and photosynthetic carotenoid (Bidigare and others, Reference Bidigare, Ondrusek, Morrow and Kiefer1990) mass absorption cross sections, taken from the literature. The spectral absorption cross section from Mundy and others (Reference Mundy, Ehn, Barber and Michel2007) (thick black line) has been utilised in this study. Congel. = congelation ice, Platel. = platelet ice, MS = McMurdo Sound, Antarctica, DS = Davis Station, Antarctica, Slush = surface slush, Top = top of the ice core, Bottom = bottom of the ice core, Photop. = photoprotectant carotenoid, Photosyn. = photosynthetic carotenoid.
3. Results and discussion
3.1. The response PAR transmittance to varying column-integrated concentrations of Chl-a
The transmittance of PAR through a 0.2 m thick snowpack and a 2 m thick sea ice is shown as an exemplar for the summer (a), spring (b) and winter (c) scenarios in Figure 2. The interior layer of the sea ice is 1.85 m thick, and the drained layer is 0.15 m thick, assuming that the sea ice is in hydrostatic equilibrium (Alexandrov and others, Reference Alexandrov, Sandven, Wahlin and Johannessen2010; Zhang and others, Reference Zhang2020). When no algae is present, the PAR decreases with depth in the snow and sea-ice layers, with maximum modelled values of 908, 866 and 708 μmol m2 s−1 at the snow surface for the winter, spring and summer scenarios, respectively. The values of PAR decrease to 3, 6 and 26 μmol m2 s−1 at the ice-ocean interface, respectively. Note, that the differences in surface values of PAR between the scenarios are due to the increased value of σ scatt in colder snow packs where the snow grain size is small. The values of T are 0.0033, 0.0069 and 0.037 for the winter, spring and summer scenarios, respectively; as the snow layers are highly scattering relative to the sea ice, they are responsible for 99, 98 and 90% of the attenuation of surface radiation, respectively.
Figure 2. Modelled values of PAR through snow (0.2 m) and sea ice (2 m) layers for the summer (a), spring (b) and winter (c) scenarios. The column-integrated concentrations of sea ice algae in the basal 0.02 m of the ice increase from 0.2 to 500 mg chl-a m−2. The change in T Rel as column-integrated concentrations of chl-a increase relative to the algae-free sea ice (T Rel = T chl=x/T chl=0) is shown for each seasonal scenario in the boxes. At the smallest column-integrated concentrations of chl-a, the effect on T Rel is negligible; however, as column-integrated concentrations increase (>20 mg chl-a m−2), the value of T Rel is significantly reduced. The effect on T Rel for the same column-integrated concentrations of chl-a is approximately invariant for the different seasonal scenarios (±1.2%).
As chl-a concentrations increase in the bottom 0.02 m layer of the sea ice, the attenuation of PAR significantly increases, and the value of T decreases. Figure 2 shows that as basal concentrations of chl-a increase, the transmittance value relative to the algae-free sea ice, T Rel, decreases to between ~99.4% at 0.2 mg and ~0.5% at 500 mg (T Rel = T chl=x/T chl=0), where x is the column-integrated concentration of chl-a. The effect on T Rel for the same chl-a relative to the algae-free sea ice is approximately invariant for the different seasonal scenarios (±1.2%). The values 1–10 mg chl-a m−2 have additionally been modelled and are presented in the supplementary material (Fig. S1); each additional mg of chl-a appears to decrease T Rel by 2–3% when columnar concentrations are ⩾10 mg chl-a m−2. The effect that different thicknesses of sea ice (0.5–3.5 m) and snow (0.05–1 m) representative for the Arctic Ocean (Kurtz and Harbeck, Reference Kurtz and Harbeck2017) may have on T Rel under typical Arctic Ocean peak basal column-integrated concentrations of chl-a (20 mg chl-a m−2) (Leu and others, Reference Leu2015; Lange and others, Reference Lange2015) are also considered in Figure 3; all data discussed in this manuscript are available in the online repository. The change in sea ice and snow thickness causes a minor variance in T Rel: ~57–63% and ~52–61%, respectively. Therefore, typical column-integrated concentrations of sea-ice algae (⩽500 mg chl-a m−2) in the basal 0.02 m of the sea ice can significantly affect the value of T Rel, with a minor variance due to changes in sea ice (±3.2%) and snow (±4.5%) thickness but general invariance (±1.2%) to seasonality. Bare ice was additionally modelled under cloudy conditions and clear sky conditions at a solar zenith angle of 60°; in general, there is a minor difference in the value of T Rel ± 0.06–3.7%. The values of T Rel are presented in the supplementary material (Table S1 and Fig. S2). Although it is improbable that the maximum chl-a values will occur during the winter scenario, they have been modelled for completeness, owing to the possibility that bimodal peaks occur in March and July (Duarte and others, Reference Duarte2015) in the Arctic and because of the wide range in the day of year for maximum sea-ice algae chl-a concentrations (Leu and others, Reference Leu2015). Similarly, the maximum considered column-integrated concentrations (340 and 500 mg chl-a m−2) have only been recorded in Resolute, Canadian Arctic, and in the Antarctic, respectively, whereas all other column-integrated concentrations are more relevant for the Arctic Ocean, Greenland and Labrador Seas. However, the fundamental aim of this study is to estimate the potential effects that sea-ice algae can have on PAR transmittance in sea ice, so they have been included in this study. Ultimately, the PAR available at the ice-ocean interface is dependent on the concentration of sea-ice algae in the basal layers. When the column-integrated concentration of chl-a is low (~<10 mg chl-a m−2) (e.g. the central Arctic Ocean and Greenlandic fjords), the effect on T Rel is small (T Rel > 75%). However, as chl-a column-integrated concentrations increase (~>10 mg chl-a m−2) (e.g. the ‘interior’ shelves of the Arctic Ocean (Williams and Carmack, Reference Williams and Carmack2015)), the effect on T Rel becomes more significant (T Rel < 75%), with the value of T Rel decreasing considerably (T Rel < 10%) when column-integrated concentrations exceed 150 mg chl-a m−2 (e.g. the Canadian Arctic and Antarctica) (see supplementary material Fig. S3). Consequently, when column-integrated concentrations of chl-a in sea ice exceed 10 mg chl-a m−2, they should be taken into account when calculating PAR transmittance at the ice-ocean interface using existing methodologies (e.g. Redmond Roche and King, Reference Redmond Roche and King2024); the values of T Rel presented in Figure 2 can be considered as empirical reduction factors for typical algal layers of typical thickness (~0.02 m), if the light transmittance through snow and sea ice and the algal concentration is known. The authors wish to stress that although the value of T Rel is mostly invariant to snow and sea-ice thickness and seasonality, the value of T is not; therefore, they must be accounted for when calculating T.
Figure 3. Changes in T Rel when 20 mg chl-a m−2 are present at different (a) sea ice (0.5–3.5 m) and (b) snow (0.05–1 m) thickness for the winter, spring and summer scenarios. The change in sea ice and snow thickness causes a minor variance in T Rel: ~57–63 and ~52–61%, respectively.
3.2. Vertical variance in algal layers
The effect that an algal layer of variable thickness can have on the value of T Rel for a 0.2 m thick snowpack and 2 m thick sea ice is shown in Figure 4 for the spring scenario. Note, that having the same vertically integrated (columnar) algal concentration for a small change in depth will not have a large effect on the value of T. However, increasing the thickness of the algal layer and the vertically integrated chl-a concentration but maintaining the volumetric concentration will affect the value of T, which is explored in this section. Therefore, the modelled vertically integrated algae concentration varies between 10 mg chl-a m−2 when 0.01 m thick and 80 mg chl-a m−2 when 0.08 m thick, consistent with typical Arctic Ocean peak basal chl-a concentrations examined in Section 3.1 (Leu and others, Reference Leu2015; Lange and others, Reference Lange2015). Basal ice communities extend vertically as high as 0.2 m (e.g. Arrigo and Sullivan, Reference Arrigo and Sullivan1992; Arrigo, Reference Arrigo and Thomas2017); however, brine salinity increases and nutrient availability decreases with distance from the ice-ocean interface, whereas the ‘rule of five’ (i.e. brine volume ⩾ 5%, ice temperature ⩾ −5°C, bulk salinity ⩾ 5) is permanently fulfilled in the basal ~0.01 m (Golden and others, Reference Golden, Ackley and Lytle1998; Leu and others, Reference Leu2015). Consequently, the bottom ~0.02 m of sea-ice hosts ~95% of algal biomass, and higher basal ice communities will typically have an order of magnitude lower biomass (e.g. Perovich and others, Reference Perovich, Cota, Maykut and Grenfell1993; Duarte and others, Reference Duarte2015), although there are exceptions to this (e.g. Meiners and others, Reference Meiners2012). Previous literature has shown that neglecting algae throughout the ice column can lead to substantial underestimations in net primary production (e.g. Duarte and others, Reference Duarte2015); however, aside from a study focusing on algal absorption heating sea ice (Zeebe and others, Reference Zeebe1996), the effect on PAR transmittance remains poorly constrained. Therefore, as Figure 2 considered 0.02 m thick algal layers, the aim is to assess the sensitivity of PAR transmittance to varying algal layer thicknesses in a 1-D vertically resolved model representative of typical basal sea-ice algal communities (0.01–0.08 m), comparable to the biologically active layer used in previous studies (e.g. Tedesco and others, Reference Tedesco, Vichi, Haapala and Stipa2010, Reference Tedesco, Vichi and Thomas2012; Tedesco and Vichi, Reference Tedesco and Vichi2014; Duarte and others, Reference Duarte2015; Lange and others, Reference Lange2015; Leu and others, Reference Leu2015; Lund-Hansen and others, Reference Lund-Hansen, Søgaard, Sorrell, Gradinger and Meiners2020).
Figure 4. Modelled values of PAR transmittance through snow (0.2 m) and sea ice (2 m) layers for the spring scenario with fixed volumetric chl-a concentrations and increasing vertically integrated chl-a concentrations. The vertical extent of the basal algal thickness varies between 0.01, 0.02, 0.04 and 0.08 m; two scenarios have a 0.02 m thick basal layer and a 0.02 and 0.04 m thick middle algal layer at 0.98–1 and 0.96–1 m, respectively. A schematic of the different sea ice and snow layers is presented on the right. As the algal layer doubles in thickness, there is an approximately linear decrease in the value of PAR at the ice-ocean interface.
As the basal algal layer increases in thickness, the value of T decreases to 0.0054, 0.0042, 0.0028 and 0.0014 when 0.01, 0.02, 0.04 and 0.08 m thick, respectively (Fig. 4). The value of T Rel decreases approximately linearly to 75.2, 59, 38.5 and 18.9% of the algae-free sea ice, respectively. While the varying thickness of the basal algae layer can affect the value of T at the base of the sea ice, it appears inconsequential on the light field near the top of the sea ice and the reflectivity of the sea ice and snow surfaces. Consequently, it may be challenging to remotely sense basal chl-a from wavelength-integrated reflectivity measurements of sea ice or snow. There can also be relatively high abundances of chl-a of varying thickness in the middle of sea-ice cores, particularly in multiyear ice where annual layers (i.e. bottom and melt pond communities) have been preserved (Lange and others, Reference Lange2015) or in areas where thick snow has caused negative freeboards and surface flooding has occurred (Arrigo, Reference Arrigo and Thomas2017). While surface flooding from negative freeboards is unusual in the Arctic, it occurs in up to 30% of Antarctic sea ice (Wadhams and others, Reference Wadhams, Lange and Ackley1987; Leu and others, Reference Leu2015). Thus, a 0.02 m thick basal algae layer is modelled with a 0.02 and 0.04 m thick internal algae layer at 0.98–1 and 0.96–1 m in the sea ice, respectively (Fig. 4). The presence of the middle algae layer causes the value of T Rel to decrease to 62.3 and 41.8% from the top to the bottom of the 0.02 and 0.040 m layers, respectively. The decrease in the value of T Rel in the mid-ice algal layers is analogous to the decrease from the top to bottom with basal algal layers of the same thickness: 60.7 and 39.7%, respectively. The value of T also appears to be largely unaffected by the vertical position of the algae layers in the ice, with the 0.04 m thick basal layer yielding a very similar value of T (0.0028) to the combined 0.02 m basal and 0.02 m middle layers combined (0.0024).
4. Conclusions
Sea-ice algae can considerably affect the transmittance of PAR, T, from the snow surface to the ice-ocean interface. The value of T will decrease as the column-integrated concentration of sea-ice algae within the ice increases: when a 0.02 m thick sea-ice algae layer is modelled in the base of the ice, the transmittance value relative to the algae-free sea ice, T Rel, decreases to between 99.4% (0.2 mg chl-a m−2) and 0.5% (500 mg chl-a m−2). The basal concentration of algae does not affect the wavelength-integrated reflectivity of sea ice or snow above it, leading to potential challenges in remotely sensing chl-a from top of the ice or snow. The decrease in T is also dependent on the thickness of the ice algae layer. When the volumetric chl-a concentration in the ice algae layer is fixed and the layer thickness is doubled, the decrease in T Rel is approximately linear: e.g. 59, 38.5 and 18.9%, at 0.02, 0.04 and 0.08 m thickness, respectively. However, the bottom ~0.01 m of sea ice permanently fulfils the ‘rule of five’; consequently, 95% of ice algae biomass is usually present in the basal ~0.02 m. Therefore, when a typical 0.02 m thick algae layer has a low column-integrated concentration of chl-a (~<10 mg chl-a m−2) (e.g. the central Arctic Ocean and Greenlandic fjords), the effect on the value of T Rel is small (T Rel > 75%). At higher column-integrated concentrations (~>10 mg chl-a m−2) (e.g. the ‘interior’ shelves of the Arctic Ocean, the Canadian Arctic and Antarctica), the effect can be significant (T Rel < 75%), and chl-a should be taken into account when predicting T.
Supplementary material
The supplementary material for this article can be found at https://doi.org/10.1017/jog.2024.72.
Data
All modelled data are available at https://doi.org/10.5281/zenodo.10680681.
Acknowledgements
This paper contains work conducted during a PhD study undertaken as part of the Centre for Doctoral Training (CDT) in Geoscience and the Low Carbon Energy Transition. It is sponsored by Royal Holloway, University of London, via their GeoNetZero CDT Studentship, whose support is gratefully acknowledged. The authors thank the technical staff in the Department of Earth Sciences at Royal Holloway, University of London, who supported this computational project. The authors also thank the reviewers and editors for their helpful comments.
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