Optical Properties Of Sea Ice Research Articles

The Characteristics of Different Apparent Optical Property Parameters in Non‐Destructively Estimating Absorptive Substances Within Sea Ice: A Case Study in Liaodong Bay

AbstractAbsorptive substances (AS) embedded in sea ice can alter irradiance transmission, exerting a significant influence on oceanic biogeochemical processes. Their quantification is thus essential, and a regression model based on the normalized difference index of transmittance (T(λ)) has been widely used for retrieving ice algal biomass. However, the potentials of albedo (α(λ)) and the diffuse attenuation coefficient (Kd(λ)) in AS estimation have not been explored. To fill this gap, sea ice optical properties observed in Liaodong Bay in 2009, 2010, 2013, and 2022 were used to investigate the characteristics of α(λ), T(λ), and Kd(λ) in non‐destructively estimating As through sensitivity analyses based on the Hydrolight radiative transfer model. The effects derived from AS vertical distribution, scattering coefficient and ice thickness were studied specifically. Ultimately, a significant relationship between α(λ) and the total absorption coefficient of AS was derived (R2 = 0.79) for Liaodong Bay sea ice. Sensitivity analyses revealed that it could only retrieve AS in the upper 15–20 cm, which was influenced by variations in ice thickness and scattering coefficient. In contrast, T(λ) could retrieve AS throughout the ice column and is less affected by scattering variation; but it is significantly affected by the vertical distribution of AS in the upper layer. Kd(λ) has the best potential in AS estimation, but for sea ice thinner than 30 cm, the effect of variation in ice thickness could not be neglected, similar to T(λ). Knowledge of this is helpful for the future development of AS estimation.

Seasonality of spectral radiative fluxes and optical properties of Arctic sea ice during the spring–summer transition

The reflection, absorption, and transmittance of shortwave solar radiation by sea ice play crucial roles in physical and biological processes in the ice-covered Arctic Ocean and atmosphere. These sea-ice optical properties, particularly during the melt season, significantly impact energy fluxes within and the total energy budget of the coupled atmosphere-ice-ocean system. We analyzed data from autonomous drifting stations to investigate the seasonal evolution of the spectral albedo, transmittance, and absorptivity for different sea-ice, snow, and surface conditions measured during the MOSAiC expedition in 2019–2020. The spatial variability of these properties was small during spring and increased strongly after melt onset on May 26, 2020, when liquid water content on the surface increased, largely accounting for the enhanced variability. The temporal evolution of surface albedo and sea-ice transmittance was mostly event-driven, thus containing episodic elements. Melt ponds reduced the local surface albedo by 31%–45%. Over the melting season, single ponding events increased the energy deposition of the sea ice by 35% compared to adjacent bare ice. Thus, single melt ponds may impact the summer energy budget as much as seasonal evolution over 1 month. Absorptivity and transmittance showed strong temporal and spatial variabilities independently of surface conditions, possibly due to the different internal sea-ice properties and under-ice biological processes. The differences in seasonal evolution shown for different sea-ice conditions strongly impacted the partitioning of shortwave solar radiation. This study shows that the formation and development of melt ponds, in reducing albedo by a third of bare ice sites, can notably increase the total summer heat deposition. The vastly different seasonal evolutions, different sea-ice conditions, and timing and duration of ponding events need to be considered when comparing local in-situ observations with large-scale satellite remote sensing datasets, which we suggest can help to improve numerical models.

Melt pond fractions on Arctic summer sea ice retrieved from Sentinel-3 satellite data with a constrained physical forward model

Abstract. The presence of melt ponds on Arctic summer sea ice significantly alters its albedo and thereby the surface energy budget and mass balance. Large-scale observations of melt pond coverage and sea ice albedo are crucial to investigate the role of sea ice for Arctic amplification and its representation in global climate models. We present the new Melt Pond Detection 2 (MPD2) algorithm, which retrieves melt pond, sea ice, and open-ocean fractions as well as surface albedo from Sentinel-3 visible and near-infrared reflectances. In contrast to most other algorithms, our method uses neither fixed values for the spectral albedo of the surface constituents nor an artificial neural network. Instead, it aims for a fully physical representation of the reflective properties of the surface constituents based on their optical characteristics. The state vector X, containing the optical properties of melt ponds and sea ice along with the area fractions of melt ponds and open ocean, is optimized in an iterative procedure to match the measured reflectances and describe the surface state. A major problem in unmixing a compound pixel is that a mixture of half open water and half bright ice cannot be distinguished from a homogeneous pixel of darker ice. In order to overcome this, we suggest constraining the retrieval with a priori information. Initial values and constraint of the surface fractions are derived with an empirical retrieval which uses the same spectral reflectances as implemented in the physical retrieval. The snow grain size and optical thickness change with time, and thus the ice surface albedo changes throughout the season. Therefore, field observations of spectral albedo are used to develop a parameterization of the sea ice optical properties as a function of the temperature history of the sea ice. With these a priori data, the iterative optimization is initialized and constrained, resulting in a retrieval uncertainty of below 8 % for melt pond and 9 % for open-ocean fractions compared to the reference dataset. As reference data for evaluation, a 10 m resolution product of melt pond and open-ocean fraction from Sentinel-2 optical imagery is used.

A significant change in sea ice diffuse attenuation coefficient with temperature and its implications for the Arctic Ocean

AbstractSea ice transparency is essential to the ecology of the ice‐covered sea. Research suggests that the diffuse attenuation coefficient of downwelling irradiance () varies with ice temperature (); however, the characteristics of its response are not well understood yet, particularly from a quantitative perspective. In an attempt to fill this gap, three independent laboratory experiments were performed between 2016 and 2022 to investigate the variations of with changing . Validation experiments were further performed in Liaodong Bay in 2018 and 2022. To explore the dominant factors controlling this phenomenon, corresponding changes in scattering properties were estimated through a two‐stream radiative transfer model. To examine its implications for local ice algal primary production and radiation transport, of Arctic sea ice was parameterized as a function of . Our results from the laboratory and field experiments showed that decreases (increases) with ice warming (cooling), and a 1°C change in results in a 0.29 m−1 average change in . The response of to between −9°C and −2°C is more notable than that observed between −24°C and −9°C. This is associated with the different variations in the scattering properties of sea ice. It reveals a significant effect on ice algal primary production under severe light‐limited conditions but a weaker effect on radiation transport. Knowledge of this ‐temperature dependence would further improve our understanding of the optical properties of sea ice and the parameterization of ice transparency in large‐scale climate models.

Seasonal Evolution of Light Transmission Distributions Through Arctic Sea Ice

AbstractLight transmission through sea ice is a critical process for energy partitioning at the polar atmosphere‐ice‐ocean boundary. Transmission of sunlight strongly impacts sea ice melting by absorption, as well as heat deposition, and primary productivity in the upper ocean. While earlier observations relied on a limited number of point observations, the recent years have seen an increase in spatially distributed light measurements underneath sea ice using remotely operated vehicles covering a wide range of ice conditions. These measurements allow us to reconstruct the seasonal evolution of the spatial variability in light transmission. Here we present measurements of sea ice light transmittance distributions from 6 years of Arctic under‐ice remotely operated vehicle operations. The data set covers the entire melt period of Central Arctic sea ice. Data are combined into a pseudo time series describing the seasonal evolution of the spatial variability of sea ice optical properties from spring to autumn freezeup. In spring, snowmelt increases light transmission continuously, until a secondary mode originating from translucent melt ponds appears in the histograms of light transmittance. This secondary mode persists long into autumn, before snowfall reduces overall light levels again. Comparison to several autonomous time series measurements from single locations confirms the detected general patterns of the seasonal evolution of light transmittance variability. This also includes characteristic spectral features caused by biological processes at the ice underside. The results allow for the evaluation of three different light transmittance parameterizations, implying that light transmission in current ice‐ocean models may not be accurately represented on large scales throughout all seasons while ice thickness alone is a poor predictor of light transmittance.

Reflective properties of melt ponds on sea ice

Abstract. Melt ponds occupy a large part of the Arctic sea ice in summer and strongly affect the radiative budget of the atmosphere–ice–ocean system. In this study, the melt pond reflectance is considered in the framework of radiative transfer theory. The melt pond is modeled as a plane-parallel layer of pure water upon a layer of sea ice (the pond bottom). We consider pond reflection as comprising Fresnel reflection by the water surface and multiple reflections between the pond surface and its bottom, which is assumed to be Lambertian. In order to give a description of how to find the pond bottom albedo, we investigate the inherent optical properties of sea ice. Using the Wentzel–Kramers–Brillouin approximation approach to light scattering by non-spherical particles (brine inclusions) and Mie solution for spherical particles (air bubbles), we conclude that the transport scattering coefficient in sea ice is a spectrally independent value. Then, within the two-stream approximation of the radiative transfer theory, we show that the under-pond ice spectral albedo is determined by two independent scalar values: the transport scattering coefficient and ice layer thickness. Given the pond depth and bottom albedo values, the bidirectional reflectance factor (BRF) and albedo of a pond can be calculated with analytical formulas. Thus, the main reflective properties of the melt pond, including their spectral dependence, are determined by only three independent parameters: pond depth z, ice layer thickness H, and transport scattering coefficient of ice σt.The effects of the incident conditions and the atmosphere state are examined. It is clearly shown that atmospheric correction is necessary even for in situ measurements. The atmospheric correction procedure has been used in the model verification. The optical model developed is verified with data from in situ measurements made during three field campaigns performed on landfast and pack ice in the Arctic. The measured pond albedo spectra were fitted with the modeled spectra by varying the pond parameters (z, H, and σt). The coincidence of the measured and fitted spectra demonstrates good performance of the model: it is able to reproduce the albedo spectrum in the visible range with RMSD that does not exceed 1.5 % for a wide variety of melt pond types observed in the Arctic.

Optical properties of sea ice doped with black carbon – an experimental and radiative-transfer modelling comparison

Abstract. Radiative-transfer calculations of the light reflectivity and extinction coefficient in laboratory-generated sea ice doped with and without black carbon demonstrate that the radiative-transfer model TUV-snow can be used to predict the light reflectance and extinction coefficient as a function of wavelength. The sea ice is representative of first-year sea ice containing typical amounts of black carbon and other light-absorbing impurities. The experiments give confidence in the application of the model to predict albedo of other sea ice fabrics. Sea ices, ∼ 30 cm thick, were generated in the Royal Holloway Sea Ice Simulator ( ∼ 2000 L tanks) with scattering cross sections measured between 0.012 and 0.032 m2 kg−1 for four ices. Sea ices were generated with and without ∼ 5 cm upper layers containing particulate black carbon. Nadir reflectances between 0.60 and 0.78 were measured along with extinction coefficients of 0.1 to 0.03 cm−1 (e-folding depths of 10–30 cm) at a wavelength of 500 nm. Values were measured between light wavelengths of 350 and 650 nm. The sea ices generated in the Royal Holloway Sea Ice Simulator were found to be representative of natural sea ices. Particulate black carbon at mass ratios of ∼ 75, ∼ 150 and ∼ 300 ng g−1 in a 5 cm ice layer lowers the albedo to 97, 90 and 79 % of the reflectivity of an undoped clean sea ice (at a wavelength of 500 nm).

Refinement of the ice absorption spectrum in the visible using radiance profile measurements in Antarctic snow

Abstract. Ice is a highly transparent material in the visible. According to the most widely used database (IA2008; Warren and Brandt, 2008), the ice absorption coefficient reaches values lower than 10−3 m−1 around 400 nm. These values were obtained from a vertical profile of spectral radiance measured in a single snow layer at Dome C in Antarctica. We reproduced this experiment using an optical fiber inserted in the snow to record 56 profiles from which 70 homogeneous layers were identified. Applying the same estimation method on every layer yields 70 ice absorption spectra. They present a significant variability but absorption coefficients are overall larger than IA2008 by 1 order of magnitude at 400–450 nm. We devised another estimation method based on Bayesian inference that treats all the profiles simultaneously. It reduces the statistical variability and confirms the higher absorption, around 2 × 10−2 m−1 near the minimum at 440 nm. We explore potential instrumental artifacts by developing a 3-D radiative transfer model able to explicitly account for the presence of the fiber in the snow. The simulation shows that the radiance profile is indeed perturbed by the fiber intrusion, but the error on the ice absorption estimate is not larger than a factor of 2. This is insufficient to explain the difference between our new estimate and IA2008. The same conclusion applies regarding the plausible contamination by black carbon or dust, concentrations reported in the literature are insufficient. Considering the large number of profiles acquired for this study and other estimates from the Antarctic Muon and Neutrino Detector Array (AMANDA), we nevertheless estimate that ice absorption values around 10−2 m−1 at the minimum are more likely than under 10−3 m−1. A new estimate in the range 400–600 nm is provided for future modeling of snow, cloud, and sea-ice optical properties. Most importantly, we recommend that modeling studies take into account the large uncertainty of the ice absorption coefficient in the visible and that future estimations of the ice absorption coefficient should also thoroughly account for the impact of the measurement method.

The impact of atmospheric mineral aerosol deposition on the albedo of snow & sea ice: are snow and sea ice optical properties more important than mineral aerosol optical properties?

Abstract. Knowledge of the albedo of polar regions is crucial for understanding a range of climatic processes that have an impact on a global scale. Light-absorbing impurities in atmospheric aerosols deposited on snow and sea ice by aeolian transport absorb solar radiation, reducing albedo. Here, the effects of five mineral aerosol deposits reducing the albedo of polar snow and sea ice are considered. Calculations employing a coupled atmospheric and snow/sea ice radiative-transfer model (TUV-snow) show that the effects of mineral aerosol deposits are strongly dependent on the snow or sea ice type rather than the differences between the aerosol optical characteristics. The change in albedo between five different mineral aerosol deposits with refractive indices varying by a factor of 2 reaches a maximum of 0.0788, whereas the difference between cold polar snow and melting sea ice is 0.8893 for the same mineral loading. Surprisingly, the thickness of a surface layer of snow or sea ice loaded with the same mass ratio of mineral dust has little effect on albedo. On the contrary, the surface albedo of two snowpacks of equal depth, containing the same mineral aerosol mass ratio, is similar, whether the loading is uniformly distributed or concentrated in multiple layers, regardless of their position or spacing. The impact of mineral aerosol deposits is much larger on melting sea ice than on other types of snow and sea ice. Therefore, the higher input of shortwave radiation during the summer melt cycle associated with melting sea ice accelerates the melt process.

Influence of melt-pond depth and ice thickness on Arctic sea-ice albedo and light transmittance

Solar radiation drives the melting of Arctic sea ice in summer, but its parameterization in thermodynamic modeling is difficult due to the large variability of the optical properties of sea ice in space and time. Here, a two-stream radiative transfer model was developed for the propagation of solar radiation in ponded sea ice to investigate the dependence of apparent optical properties (AOPs), particularly albedo and transmittance, on sky conditions, pond depth, ice thickness, and the inherent optical properties (IOPs) of ice and water. The results of numerical experiments revealed that decrease in melt-pond albedo during melting results not only from increase in pond depth but also from decrease in underlying ice thickness, and the latter is more important for thin ice with thickness less than 1.5m. Hence, a parameterized pond albedo as a function of both pond depth and ice thickness is more suitable for thinning Arctic sea ice than the previously used exponential function of pond depth, which is valid for thicker ice. The increase in broadband transmittance during melting can be explained by the decrease in underlying ice thickness, because its dependence on ice thickness is nearly three times stronger than on pond depth. The spectral dependence of the pond albedo on depth is significant only in the 600–900-nm band, while it depends clearly on ice thickness in the 350–600-nm band. The uncertainty resulting from the absorption coefficient of ice is limited, while the effect of scattering in ice is more important, as determined by a sensitivity study on the influence of the IOPs on the AOPs of sea ice. The two-stream model provides a time-efficient parameterization of the AOPs for ponded sea ice, accounting for both absorption and scattering, and has potential for implementation into sea-ice thermodynamic models to explain the role of melt ponds in the summer decay of Arctic sea ice.

Multi-angular thermal infrared emission characteristics of Bohai Sea ice based on in situ measurements

AbstractWe report on the radiative transfer process and optical properties of sea ice in the thermal infrared (TIR) band, presenting two new linear kernel driver models (Relative Emissivity Distribution Function, REDF) that describe TIR emission characteristics of smooth and rough ice. In order to test the models and determine the necessary coefficients, in situ measurements from the Bohai Sea were carried out during the 2011/12 and 2012/13 boreal winters. The results show that the relative emissivity of smooth sea ice decreases along with increasing viewing zenith angle, and the shape of the relative emissivity curve is similar to that of an ideal plane. Affected by parameters such as roughness and surface temperature distribution, the anisotropy of relative emissivity of sea ice with a high degree of roughness is stronger relative to the cosine emitter. The model coefficients were also obtained using a robust regression method based on the measured data. The presented models are more practical than the numerical radiative transfer model and can be used for multi-angular TIR remote sensing.

Removal of snow cover inhibits spring growth of Arctic ice algae through physiological and behavioral effects

The snow cover of Arctic sea ice has recently decreased, and climate models forecast that this will continue and even increase in future. We therefore tested the effect of snow cover on the optical properties of sea ice and the biomass, photobiology, and species composition of sea ice algae at Kangerlussuaq, West Greenland, during March 2011, using a snow-clearance experiment. Sea ice algae in areas cleared of snow was compared with control areas, using imaging variable fluorescence of photosystem II in intact, unthawed ice sections. The study coincided with the onset of spring growth of ice algae, mainly an increase in two pennate diatoms (Achnanthes taeniata and Navicula directa), as temperature increased and ice thickness and brine volume stabilized. The increase in biomass was accompanied by an increase in minimum variable fluorescence (F o) and the maximum quantum yield of PSII (F v /F m) and filling of brine channels with fluorescing cells. In contrast, in the minus snow area, PAR transmittance increased sixfold and there was an exponential decrease in chl-a and no increase in F o, and the area of fluorescing biomass declined to become undetectable. This study suggests that the onset of the spring bloom is predominantly due to temperature effects on brine channel volume, and that the algal decline after snow removal was primarily due to emigration rather than photodamage.

Optical properties of sea ice in Liaodong Bay, China

Many industrial, agricultural, and residential areas surrounding Liaodong Bay are responsible for much of the particulate matter (PM) and colored dissolved organic matter (CDOM) found in the sea ice in the bay. Understanding the optical properties of “dirty” sea ice is important for analyzing remote sensing data and calculating energy balances. We designed a hyperspectral radiation instrument to observe the optical properties of sea ice. The results show that albedo peaks ranged from 0.3 to 0.85 and that the peaks shifted to a longer wavelength for high PM and CDOM concentrations. The absorption and scattering coefficients for sea ice were obtained. The bulk absorption coefficient shows that bulk absorption is primarily determined by PM and CDOM at shorter wavelengths, while pure ice and brine pockets become more important at longer wavelengths. Scattering coefficients for sea ice ranged from 197 to 1072 m−1, and showed consistent variations with gas bubble and brine pocket concentrations. The effects of PM and CDOM on the bulk absorption coefficient of sea ice were studied. At 440 nm, particulates accounted for 55–98% and CDOM accounted for 2–37% of the bulk absorption. Ratios between particulate absorption and bulk absorption for sea ice were almost constant from 400 to 550 nm, and began to decrease sharply for wavelengths >550 nm. Ratios between CDOM and bulk absorption decreased almost linearly with increasing wavelength.

Sea ice properties in the Bohai Sea measured by MODIS-Aqua: 1. Satellite algorithm development

Based on the fact that sea ice reflectance drops significantly in the shortwave infrared (SWIR) wavelengths, black pixel assumption is assessed for three SWIR bands for the Moderate Resolution Imaging Spectroradiometer (MODIS)–at 1240, 1640, and 2130nm—over the sea ice in the Bohai Sea in order to carry out atmospheric correction for deriving sea ice reflectance spectra. For the SWIR 1240nm band, there is usually a small (but non-negligible) reflectance contribution over sea ice. Although there is a slight sea ice reflectance contribution at the MODIS 1640nm band over sporadic land-fast or hummock ice, the black pixel assumption is generally valid with the MODIS bands 1640 and 2130nm in the Bohai Sea. Thus, the SWIR-based atmospheric correction algorithm using MODIS bands at 1640 and 2130nm can be conducted to derive sea ice optical properties in the region. Based on spectral features of the sea ice reflectance, a regionally optimized ice-detection algorithm is proposed. This regional algorithm shows considerable improvements in detecting sea ice over the Bohai Sea region, compared with a previous MODIS global sea ice detection algorithm. The sea ice coverage as identified in the new algorithm matches very well with the sea ice coverage from both the MODIS true color image and the imagery from the Interactive Multisensor Snow and Ice Mapping System (IMS).

In situ measurement of the solar radiance distribution within sea ice in Liaodong Bay, China

Understanding the optical properties of polluted sea ice is important for analyzing remote sensing data, and studying energy balance. Liaodong Bay in China provides a kind of representative of dirty sea ice for there are many industrial and residential areas surrounding it. Optical properties of sea ice were observed. Albedos for different types of sea ice surface were obtained, and their peaks would tend to shift to longer wavelengths for the high concentrations of PM and CDOM in sea ice. Upwelling (K-u) and downwelling (K-d) irradiance extinction coefficients profiles were obtained in situ with a self-made instrument. At 586 nm, the maximum K-u reached 13.68 m(-1) in a layer close to ice bottom, while the maximum K-d reached 15.52 m(-1) in surface layer. Because understanding the energy distribution in sea ice is important to research mass budget in air-ice-sea, solar radiance distribution in sea ice was observed in a series of bored holes in situ. From 4 cm to ice bottom, the logarithms of radiance profiles almost decrease linearly with increasing the path length of light transfer. Because sea ice is a highly scattering medium and the effects of scattering become stronger with increasing depth, the dependence of scattering light on scattering angle (theta) becomes weaker with increasing depth. An optical model was brought forward to describe the solar radiance distribution at a random depth and theta. Crown Copyright (C) 2011 Published by Elsevier B.V. All rights reserved.

Contribution of mycosporine‐like amino acids and colored dissolved and particulate matter to sea ice optical properties and ultraviolet attenuation

In the Baltic Sea ice, the spectral absorption coefficients for particulate matter (PM) were about two times higher at ultraviolet wavelengths than at photosynthetically available radiation (PAR) wavelengths. PM absorption spectra included significant absorption by mycosporine‐like amino acids (MAAs) between 320 and 345 nm. In the surface ice layer, the concentration of MAAs (1.37 µg L−1) was similar to that of chlorophyll a, resulting in a MAAs‐to‐chlorophyll a ratio as high as 0.65. Ultraviolet radiation (UVR) intensity and the ratio of UVR to PAR had a strong relationship with MAAs concentration (R2 = 0.97, n = 3) in the ice. In the surface ice layer, PM and especially MAAs dominated the absorption (absorption coefficient at 325 nm: 0.73 m−1). In the columnar ice layers, colored dissolved organic matter was the most significant absorber in the UVR (< 380 nm) (absorption coefficient at 325 nm: 1.5 m−1). Our measurements and modeling of UVR and PAR in Baltic Sea ice show that organic matter, both particulate and dissolved, influences the optical properties of sea ice and strongly modifies the UVR exposure of biological communities in and under snow‐free sea ice.

Contribution of mycosporine-like amino acids and colored dissolved and particulate matter to sea ice optical properties and ultraviolet attenuation

In the Baltic Sea ice, the spectral absorption coefficients for particulate matter (PM) were about two times higher at ultraviolet wavelengths than at photosynthetically available radiation (PAR) wavelengths. PM absorption spectra included significant absorption by mycosporine-like amino acids (MAAs) between 320 and 345 nm. In the surface ice layer, the concentration of MAAs (1.37 μg L(-1)) was similar to that of chlorophyll a, resulting in a MAAs-to-chlorophyll a ratio as high as 0.65. Ultraviolet radiation (UVR) intensity and the ratio of UVR to PAR had a strong relationship with MAAs concentration (R(2) = 0.97, n = 3) in the ice. In the surface ice layer, PM and especially MAAs dominated the absorption (absorption coefficient at 325 nm: 0.73 m(-1)). In the columnar ice layers, colored dissolved organic matter was the most significant absorber in the UVR (< 380 nm) (absorption coefficient at 325 nm: 1.5 m(-1)). Our measurements and modeling of UVR and PAR in Baltic Sea ice show that organic matter, both particulate and dissolved, influences the optical properties of sea ice and strongly modifies the UVR exposure of biological communities in and under snow-free sea ice.

Snowball Earth: A thin‐ice solution with flowing sea glaciers

The late Neoproterozoic era, ∼600–800 Myr ago, was marked by at least two intervals of widespread cold that left glacial deposits at low paleolatitudes. Both “Snowball” solutions with global ice cover and “Slushball” solutions with ice‐free tropical oceans have been proposed to explain the paleomagnetic data. The Snowball model is best able to explain the auxiliary geological evidence, particularly the existence of cap carbonates, but it implies drastic survival pressure on the photosynthetic biota if the ice cover was everywhere thick enough to prevent sunlight from reaching the underlying ocean. A “thin ice” solution that avoids this problem has been proposed but is thought to be inconsistent with realistic optical properties of sea ice and with the equatorward flow of sea glaciers. Here we use a coupled energy‐balance climate/sea‐glacier model to argue that these apparent difficulties can be overcome and that thin tropical ice may have prevailed during these remarkable glacial episodes. We also suggest that (1) some processes beyond the scope of zonal mean energy‐balance models may significantly affect the solutions and (2) thin ice could have prevailed on low‐latitude seas (or large lakes) protected from large‐scale sea‐glacier flow by surrounding land even if most of the Earth was in a “hard Snowball” state.

Top‐of‐atmosphere shortwave broadband observed radiance and estimated irradiance over polar regions from Clouds and the Earth's Radiant Energy System (CERES) instruments on Terra

Empirical angular distribution models for estimating top‐of‐atmosphere shortwave irradiances from radiance measurements over permanent snow, fresh snow, and sea ice are developed using CERES measurements on Terra. Permanent snow angular distribution models depend on cloud fraction, cloud optical thickness, and snow brightness. Fresh snow and sea ice angular distribution models depend on snow and sea ice fraction, cloud fraction, cloud optical thickness, and snow and ice brightness. These classifications lead to 10 scene types for permanent snow and 25 scene types for fresh snow and sea ice. The average radiance over clear‐sky permanent snow is more isotropic with satellite viewing geometry than that over overcast permanent snow. On average, the albedo of clear‐sky permanent snow varies from 0.65 to 0.68 for solar zenith angles between 60° and 80°, while the corresponding albedo of overcast scenes varies from 0.70 to 0.73. Clear‐sky permanent snow albedos over Antarctica estimated from two independent angular distribution models are consistent to within 0.6%, on average. Despite significant variability in sea ice optical properties with season, the estimated mean relative albedo error is −1.0% for very dark sea ice and 0.1% for very bright sea ice when albedos derived from different viewing angles are averaged. The estimated regional root‐mean‐square (RMS) relative albedo error is 5.6% and 2.6% when the sea ice angular distribution models are applied to a region that contains very dark and very bright sea ice, respectively. Similarly, the estimated relative albedo bias error for fresh snow is −0.1% for very dark snow scenes and 0.1% for very bright snow scenes. The estimated regional RMS relative albedo error is 3.5% and 5.0% when angular distribution models are applied to a region that contains very dark and very bright fresh snow, respectively. These error estimates are only due to angular distribution model error and do not include the error caused by scene identification.

Complex yet translucent: the optical properties of sea ice

Sea ice is a naturally occurring material with an intricate and highly variable structure consisting of ice platelets, brine pockets, air bubbles, and precipitated salt crystals. The optical properties of sea ice are directly dependent on this ice structure. Because sea ice is a material that exists at its salinity determined freezing point, its structure and optical properties are significantly affected by small changes in temperature. Understanding the interaction of sunlight with sea ice is important to a diverse array of scientific problems, including those in polar climatology. A key optical parameter for climatological studies is the albedo, the fraction of the incident sunlight that is reflected. The albedo of sea ice is quite sensitive to surface conditions. The presence of a snow cover enhances the albedo, while surface meltwater reduces the albedo. Radiative transfer in sea ice is a combination of absorption and scattering. Differences in the magnitude of sea ice optical properties are ascribable primarily to differences in scattering, while spectral variations are mainly a result of absorption. Physical changes that enhance scattering, such as the formation of air bubbles due to brine drainage, result in more light reflection and less transmission.