Arctic sea ice signatures: L-band brightness temperature sensitivity comparison using two radiation transfer models

Sea ice is a crucial component for short-, mediumand long-term numerical weather predictions. Most importantly, changes of sea ice coverage and areas covered by thin sea ice have a large impact on heat fluxes between the ocean and the atmosphere. L-band brightness temperatures from ESA’s Earth Explorer SMOS (Soil Moisture and Ocean Salinity) have been proven to be a valuable tool to derive thin sea ice thickness. These retrieved estimates were already successfully assimilated in forecasting models to constrain the ice analysis, leading to more accurate initial conditions and subsequently more accurate forecasts. However, the brightness temperature measurements can potentially be assimilated directly in forecasting systems, reducing the data latency and providing a more consistent first guess. As a first step towards such a data assimilation system we studied the forward operator that translates geophysical parameters provided by a model into brightness temperatures. We use two different radiative transfer models to generate top of atmosphere brightness temperatures based on ORAP5 model output for the 2012/2013 winter season. The simulations are then compared against actual SMOS measurements. The results indicate that both models are able to capture the general variability of measured brightness temperatures over sea ice. The simulated brightness temperatures are dominated by sea ice coverage and thickness changes are most pronounced in the marginal ice zone where new sea ice is formed. There we observe the largest differences of more than 20 K over sea ice between simulated and observed brightness temperatures. We conclude that the assimilation of SMOS brightness temperatures yields high potential for forecasting models to correct for uncertainties in thin sea ice areas and suggest that information on sea ice fractional coverage from higherfrequency brightness temperatures should be used simultaneously.

brightness temperatures have been validated for idealized typical Arctic conditions (e.g. Maaß et al. (2013), Tian-Kunze et al. (2014)), but have never been compared to L-Band remote sensing observations on a large scale.
In this study, we investigate the Arctic-wide performance of the radiative transfer models of Kaleschke et al. (2010) and Maaß et al. (2013) to account for diverse atmospheric and oceanic conditions and to identify the most important input parameters for a sea ice thickness application. In preparation for a brightness temperature assimilation, we concentrate on the input data of the 5 global ocean reanalysis product ORAP5 (Ocean ReAnalysis Pilot 5) produced by the ECMWF. We evaluate which radiative transfer model to use for assimilating sea ice thickness into the ORAP5 reanalyses by comparing simulated and observed brightness temperatures from the radiative transfer models with ORAP5 input data and SMOS observations, respectively.

Data and Methods
Both radiative transfer models provide brightness temperatures as a function of temperature, snow-and sea ice thickness, 10 incidence angle and the permittivity (Fig. 1). The latter is calculated with the snow, sea ice and sea water temperatures (as well as the snow/sea ice interface temperature), the bulk sea ice and water salinities and the snow and sea ice thicknesses.
The sea ice salinity is estimated with the empirical approach of Ryvlin (1974) making the ice salinity a function of the sea surface salinity, the sea ice thickness, the salinity ration of the bulk ice salinity at the end of the sea ice growing season and the growth rate coefficient. The latter two are taken from Kovacs (1996) who derived a value of 0.175 for the ice salinity ration 15 from observational data in the Arctic and 0.5 for the growth rate coefficient, as also suggested by Ryvlin (1974). To obtain the ice/snow interface we calculate the thermal conductivity of ice with the snow surface temperature and ice salinity (Untersteiner, 1964). Using this, we are able to determine the bulk sea ice temperature for our sea ice slab by assuming the heat fluxes are in equilibrium (Maykut and Untersteiner, 1971). We calculate the brine salinity with a polynomial approximation that uses bulk sea ice temperature (Vant et al., 1978;Leppäranta and Manninen, 1988) and the pure ice density as a function of bulk ice 20 temperature (Pounder, 1965). As the polynomial coefficients for the brine salinity calculation are only provided for 1 and 2 GHz, we linearly interpolate between these two frequencies to determine the coefficients for 1.4 GHz. By taking the ice and brine density, as well as the bulk ice temperature, we are able to calculate brine volume fraction using equations valid for ice temperatures below -2 • C from Cox and Weeks (1983) and above -2 • C from Leppäranta and Manninen (1988). Finally, the permittivity of sea ice is derived by an empirical relationship to the brine volume fraction (Vant et al., 1978) (for a summary of 25 references see table 1).
In order to represent sea ice brightness temperature measurements in partially covered data points over the open ocean, the models linearly include sea ice fractional coverage in the calculations for each grid cell. Additionally, both models consider the subpixel-scale heterogeneity of sea ice thicknesses with a statistical ice thickness distribution. We calculate the brightness temperatures for ten linearly divided sea ice thickness bins with a maximum of 2 meter thickness. Then, we translate the mean 30 sea ice thickness from the input data to a sea ice thickness distribution derived by observational data (As used in Algorithm II* by Tian-Kunze et al. (2014)). The final brightness temperature is the average of the ten respective bins weighted by the sea ice thickness distribution.

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The Cryosphere Discuss., doi:10.5194/tc-2016-273, 2016 Manuscript under review for journal The Cryosphere Published: 5 December 2016 c Author(s) 2016. CC-BY 3.0 License. Figure 1. Simplified schematic illustration for the determination of auxiliary parameters provided to the radiative transfer models utilized in this study. The studies for the methods are listed in Table 1. A listing of all input data and the most important parameters is given in Table 2.
Boxes with white background indicate input data from OPAP5 reanalyses. Table 1. Applied methods to obtain auxiliary parameters for brightness temperatures calculations above sea ice and snow. The numbers in the first row refer to the numbers in Fig.1.
Sea water emissivity calculations are based on Fresnel equations with the descriptions of sea water after Ulaby et al. (1981) with permittivities obtained by Klein and Swift (1977). Wind induced sea surface roughness influences are assumed to be small and will be neglected (Dinnat et al., 2003). To account for corrections of the galactic background radiation and atmospheric deviations a simplified atmospheric model (Peng et al., 2013) is taken forced by climatological data from 65 years of NCEP data (Kalnay and Kanamitsu, 1996). The cosmic contribution to the overall brightness temperatures is set to 2.7 Kelvin. In 5 these simulations, we restrict the brightness temperature calculation to nadir incidence angle. The freezing temperature of sea water is set to -1.8 • C.
The single-layer model conductivity set to climatological value of k snow = 0.31 (Yu and Rothrock, 1996)). In that setup, snow influences the brightness temperatures by a temperature insulation of sea ice from the atmosphere. As snow covers the ice it dampens the influence of atmospheric temperature changes to the ice. The effect appears to be significant and can be considered within the sea ice/snow  The multi-layer model The incoherent model used in Maaß et al. (2013) is based on radiative transfer equations and describes the emitted radiation from a stratified bare soil (referred as MA2013). The core equations are taken from Burke et al. (1979), but it has been substantially modified to suit the needs for sea ice. In our simulations the MA2013 model consists of three layers of sea ice and one layer of snow on top of the ice. All ice layers have the same properties except for the sea ice thickness that is simply divided 25 by the number of layers considered and the ice temperature that linearly changes between the lowest layer bordering the ocean and the upper layer facing the atmosphere. The snow is assumed to be dry and has a snow density of ρ snow = 330 [kg/m 3 ].
In contrast to the previous model, the snow layer does not only affect the temperature of the underlying sea ice, but also the radiation incidence angle, potentially leading to propagation effects. Snow changes the refraction index and thus the reflectivity between the air-snow and snow-ice boundaries. By changing the optical properties of the air-ice boundary and the temperature 30 of sea ice, snow has a passive effect on the brightness temperature (Schwank Mike et al., 2015).
As an addition to the model described in Maaß et al. (2013) we added the ability to take multiple reflections and refractions within the sea ice into account. Thus, the radiative beams are followed on their way through the layers of snow and ice and  added up when they leave the medium in upper direction towards the atmosphere. Reflected beams are removed after 15 interface passings when they are not able to leave the ice-snow medium on the short term. At this point, the intensity of the radiative beams are negligible and we are able to cap the computational effort for the calculation.

The ORAP5 reanalyses
The radiative transfer models are forced using data from the Ocean ReAnalysis Pilot 5 (ORAP5) project, which is provided by 5 the European Centre of Medium range Weather Forecast (ECMWF) (Tietsche et al., 2014). The sea ice and snow thicknesses, the surface and sea water temperatures, the sea ice fractional coverage and the sea surface salinity are taken from ORAP5 data ( Table 2). The NEMO global ocean model version 3.4 has been utilized to run on the DRAKKER ORCA025.L75 configuration for 34 years, covering the years from 1979 to 2013. The configuration uses a tripolar mesh grid with poles located in Greenland and Central Asia in the northern hemisphere, as well as a pole in the Antarctic in the southern hemisphere. The spatial resolution 10 ranges from 1/4 degree at the equator to a couple of kilometers in the polar regions with 75 vertical levels in the ocean.
The dynamic-thermodynamic Louvain-la-Neuve Sea Ice Model second generation (LIM2) has been coupled to the NEMO ocean model (Bouillon et al., 2009). Sea ice is represented with a two-dimensional viscous-plastic rheology that interacts with the atmosphere and the ocean. A simple three-layer model (one for snow and two layers for ice) is used at which sensible heat storage and vertical heat conduction are determined. Vertical heat fluxes are calculated based on the thermodynamic energy 15 balance according to Semtner (1976). The albedo is a function of the snow and ice thicknesses, the state of the surface and the cloudiness. Sea ice coverage is taken from the Operational SST and Sea Ice Analysis (OSTIA) system, which assimilates sea with the goal to deliver ocean reanalyses with highest quality standards the dataset is not yet operational and therefore further processed. The second limiting factor is a reasonable time-frame to describe brightness temperature changes with varying sea ice thicknesses. In the melting season, when melt ponds form on sea ice and temperatures begin to rise, SMOS brightness temperatures over sea ice are impossible to connect to a specific sea ice property (Kaleschke et al., 2010). Thus, November and March are the first and the last month, respectively, with full monthly data coverage from SMOS and therefore chosen. SMOS snapshots are influenced by Radio frequency interference (RFI) rooting from radar, TV and radio transmission (Mecklenburg et al., 2012). To account for the most critical disturbances, a RFI filter has been utilized. Brightness temperatures above 300 K identify a snapshot to be RFI-contaminated and be further ignored for the brightness temperature product. The threshold of 300 K is chosen as values higher than that are not expected to be seen in the Arctic or Antarctic.

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The brightness temperature product consists of vertical and horizontal polarization, which are averaged up to 40 • incidence angle when they are taken within 2.5 seconds time-interval (Kaleschke et al., 2012). These brightness temperatures are said to represent L-Band measurements at nadir as brightness temperature changes that are connected to the varying incidence angles are expected to cancel out each other when both polarisations are considered. The averaged product is available on a daily basis up to 85 • latitude. The data is collected for an entire day and is averaged for each grid point to provide a L3B daily mean 20 brightness temperature product. Finally, the data is geolocated on a NSIDC polar-stereographic projection that provides grid cells with the same areal extent of 12.5 km horizontal resolution.

Sea water correction
To investigate the quality of the radiative transfer models for partially covered sea ice areas in the ORAP5 setup, we first check the representation of emissivities over open ocean of the models. As mentioned before, both models use the same equations to 25 calculate the emissivity of water areas based on Klein and Swift (1977) and will thus produce the same brightness temperatures using same input data. Therefore we here only show the correction for MA2013. In any case, L-Band brightness temperature variations in open Arctic waters are low compared to sea ice and should fairly match between observed SMOS and simulated brightness temperatures from the radiative transfer models (Berger et al., 2002).
We simulate brightness temperatures in all open water areas north of 50 • latitude. As a first step, we project the ORAP5 30 reanalyses on the polar-stereographic grid SMOS is using. Afterwards, we obtain a monthly average by calculating brightness temperatures for each day of the month using daily input data. Then, we average all brightness temperatures corresponding to Kelvins and a second, weaker one beginning at 105, each one with a tail towards higher brightness temperatures of SMOS.
The first tail at 100 Kelvin can be explained by the gradual transition between land and water areas. As the SMOS land product only distinguishes between fully covered land and water points, it does not represent partially covered measurements of pixels 10 containing land and water. The region of higher TBs are located in the Baltic Sea. In that area, lower sea surface salinities and higher water temperatures compared to the rest of the Arctic waters leads to higher brightness temperatures. The water bias correction is used in all following simulations using the radiative transfer models.

Radiative transfer model sensitivity study
In order to identify the most important input variables for the radiative transfer models, we evaluate the sensitivity of the models to certain changes of sea ice, snow and sea water parameters. We keep all but one parameter fixed at a monthly value 5 and calculate the brightness temperatures for the minimum and the maximum simulated value within the month for one physical parameter. That will give us two different brightness temperatures, one for the minimum, one for the maximum, of which the  difference is the range of brightness temperature change related to one of the parameters that can be expected. Varying all input parameters provided by the ORAP5 reanalyses we quantify the impact of certain physical parameters on our brightness temperatures at a specific place over the time span of one month.
The most important input parameters for brightness temperature calculations with the radiative transfer models are the sea ice fractional coverage, sea ice thickness and sea ice temperature (Fig. 7, accounting for 92% grid points in March and the sea ice growth season in November, the leading impact of sea ice fraction extends all the way to the coastal areas in the East Siberian Sea, whereas the Canadian Basin is dominated by sea ice thickness growth. In any case, the sea ice thickness is most important in a large area close to the sea ice edge (25% of the area in November). This is partially true when sea ice thicknesses are predominantly thicker than half a meter and exceed SMOS sensitivity (5% in March). However, the effect of sea ice concentration and thickness is similar in both models. In the very outer marginal sea ice zone it appears that sea surface   Spreen et al., 2008) shows a rapid freeze-up to 80% sea ice coverage in just a few days. The brightness temperatures of SMOS measurements and the KA2010 and MA2013 models properly agree with some exceptions on the first days of the freezing period that starts around the 25. October. The simulated brightness temperatures appear to be underestimated at the beginning of the season which leads to a more linear brightness temperature increase rather than a logarithmic shape as observed from the SMOS measurements. However, the simulated sea ice concentration of ORAP5 appears to be lower than the 10 the observed ASI sea ice concentration and needs almost two weeks to catch up to the same coverage as ASI. The sea ice thickness on the other hand shows a fast thickening to more than half a meter even before the main freeze-up event takes place. The sea ice growth model of Lebedev (1938) accumulates sea ice as a function of the temperature difference between the surface air temperatures and freezing point of water, as well as the number of freezing days below zero degrees. In contrast to the sea ice thickness of ORAP5, Lebedevs' parameterization shows a gradual increase of ice thickness throughout the freeze-up event.

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Following, we observe an underestimation of sea ice concentration and an overestimation of sea ice thicknesses, although the brightness temperatures between observational and simulated data fits decently well.

Discussion
The simulated brightness temperatures from two incoherent radiative transfer models with ORAP5 input data generally match the SMOS observations in an overall Arctic-wide comparison. The analysis shows spatial differences throughout the Arctic for brightness temperature simulations are found to be the same throughout the Arctic (Fig. 7). Over thick sea ice in the central Arctic we find the sea ice/snow surface temperature to be the most influential parameter. Since sea ice concentration is close to 100% and sea ice thicknesses are above L-Band sensitivies, brightness temperature changes are due to the impact of snow 10 and sea ice/snow temperature changes that comes with it. Our results also show a significant influence of sea ice/snow and sea surface temperatures in areas of thin sea ice close to the ice edge. This is explained by a fractional sea ice coverage of less than 10%, where brightness temperature variations are dominated by changing open water emissivities. We point out that sea surface temperature and salinities get more important in regions with lower sea ice coverage. Therefore, in case partially covered sea ice concentrations are taken into account we caution that a climatology of sea ice/snow surface temperatures or 15 sea surface salinities might not be sufficient enough to picture the transition between open water towards the sea ice edge. This is especially true for the declining sea ice observed in the recent years as the sea ice edge is likely to be located at a different location than in the previous years.
Our results indicate that brightness temperature differences up to around 15 Kelvin can be due to the usage of different radiative transfer models (Fig. 3). Even though both models tend to have the same signatures, KA2010 shows lower brightness 20 temperatures than the MA2013 in the whole Arctic. This was expected as the MA2013 model is able to take multiple sea ice layers into account, as well as the radiometric effect of snow on top of sea ice, whereas KA2010 only indirectly includes the effect of snow with the representation of the thermodynamic insulation effect. Compared with SMOS brightness temperatures, it appears that MA2013 overestimates brightness temperatures in many parts of the Arctic, most pronouncedly in March in the central Arctic region. For a brightness temperature assimilation this would be rather detrimental, as we only expect benefits 25 from SMOS-based ice thickness assimilation thin sea ice regions because microwave radiation is not able to distinguish between thicker sea ice. In contrast, KA2010 shows good agreement in the central Arctic area. For brightness temperature assimilation purposes that would be clearly beneficial as the main assimilation should take place in regions with thin sea ice rather than in the The results of this study indicate that both models are able to simulate Arctic-wide monthly brightness temperatures. We are able to observe a similar increase of simulated and observed brightness temperatures from thin to thicker sea ice areas. Although both models show a decent fit in November, the model of Maaß et al. (2013)  The most important parameters for the brightness temperature calculations over thin sea ice are identified to be the sea ice 10 thickness and sea ice coverage. This result supports the findings of other studies (e.g. Kaleschke et al. (2012)). In thicker sea ice areas the dominant parameter is the sea surface temperature since the sea ice fractional coverage is close to 100% and sea ice thickness changes do not affect the measurements at 1.4 GHz. However, the smaller the sea ice fractional coverage, the more important are the sea surface temperature and salinity. This becomes relevant at sea ice concentrations below 15%, usually in small regions at the very outer sea ice edge.

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The brightness temperature assimilation is expected to result in more accurate sea ice thicknesses analysis than a direct assimilation of the physical parameter as the climate model provides a series of input variables to the forward operator. These variables do not need to be replaced by climatologies, parameterizations or assumptions that may inflict the results of our sea ice thickness retrieval. However, even though the sea ice thickness and concentration in ORAP5 are well constrained by observations (Tietsche et al., 2015), both show difficulties to represent a rapid freeze-up event with an underestimation of sea 20 ice concentration and an overestimation of sea ice thickness. That reveals the challenge to use brightness temperatures to correct for the right physical parameter and magnitude. We recommend to combine the brightness temperature assimilation for sea ice thickness with the assimilation of an independent auxiliary observational sea ice concentration product or the simultaneous assimilation of measurements taken at higher microwave frequencies, e.g. up to 37 GHz.
The assimilation of SMOS brightness temperatures appears to be a great chance for a better representation of sea ice thick- 25 nesses in the ORAP5 reanalyses. Substantial differences between observational and simulated brightness temperatures are found to be largest in regions with thin sea ice, in which SMOS uncertainties of the sea ice thickness retrievals are lowest (Kaleschke et al., 2010). That reveals the possibility to retrieve and correct sea ice thicknesses in future investigations. However, to what magnitude these results translate to other reanalyses products or climate forecasts has to be investigated. de/1/daten/cryosphere/l3b-smos-tb.html (Tian-Kunze et al., 2012). The reanalyses data of ORAP5 was kindly provided by