Broadband albedo of sea ice, including snow-covered sea ice, is a key parameter in Arctic climate studies. It is defined as the ratio of reflected to incident irradiance in the waveband 200–5000 nm . The broadband albedo of sea ice determines the energy budget of the surface and controls the heat and mass balance of sea-ice cover . Even small changes in the broadband albedo at the surface can strongly influence the Arctic climate via the albedo feedback mechanism. As broadband albedo of sea ice decreases, more radiation is absorbed at the surface, resulting in an increase in surface temperature and a loss of sea ice, which amplifies the albedo reduction .

For a better understanding of the strong sensitivity of the Arctic climate to surface broadband albedo variations, climate studies need surface broadband albedo values that meet two criteria. Firstly, the surface broadband albedo has to be comprehensive in space and time to capture its strong variability, with low albedo over melt ponds and high albedo over snow-covered sea ice. Many surface broadband albedo data products from different satellite missions are available for this purpose. Table  provides an overview of the major ones and their specifications. The albedo data from the MODerate resolution Imaging Spectroradiometer (MODIS) onboard Terra and Aqua have been widely used as a reference for evaluating other albedo products. The Polar Pathfinder-Extended (APP-x) climate data record from Advanced Very High Resolution Radiometer (AVHRR) measurements onboard various NOAA POES (U.S. National Oceanic and Atmospheric Administration Polar Operational Environmental Satellites) includes the first long time series of consistent surface broadband albedo, starting from 1982 . MERIS (MEdium Resolution Imaging Spectrometer) onboard ENVISAT (ENVIronmental SATellite) provides the surface albedo of Arctic sea ice on a daily basis . VIIRS (Visible Infrared Imaging Radiometer Suite) onboard S-NPP (Suomi National Polar-orbiting Partnership) belongs to the newest moderate spatial resolution imaging radiometers generating the surface albedo . High spatial resolution surface albedo (30 m) at the expense of reduced temporal resolution (16 d) are generated by Operational Land Imager (OLI), Thematic Mapper (TM), and Enhanced Thematic Mapper Plus (ETM+) onboard the Landsat satellites . A 34-year time series of black-sky surface albedo (SAL), as part of the second edition of the CLoud, Albedo, and surface RAdiation data set (CLARA-A2), has been derived from AVHRR measurements onboard NOAA and Metop (Meteorological Operational) satellites . Furthermore, surface albedo can be retrieved from collaborative observations of multiple platforms, e.g., GlobAlbedo and Global LAnd Surface Satellite GLASS,, or from radiation budget data sets, e.g., Clouds and the Earth's Radiant Energy System – Energy Balanced And Filled and the International Satellite Cloud Climatology Project ISCCP,.

Secondly, the surface broadband albedo included in climate models has to fulfill an absolute accuracy of 0.02–0.05 as shown in sensitivity analyses . However, the satellite-retrieved albedo products underlie uncertainties, depending on the number and spectral distribution of satellite channels (i.e., narrowbands) available, the temporal and spatial resolution of the measurement (Table ), and the approach to retrieve the broadband albedo (kernel-driven, bidirectional reflectance distribution function, BRDF, methods or anisotropy reflectance correction, ARC, methods, both combined with a narrow-to-broadband conversion, NTBC, direct estimation methods, and methods using radiative transfer theory, RTT) . The latter dependency is caused by pre-assumed surface and atmospheric conditions in most retrieval methods. Their representativeness of the actual conditions determines the accuracy of the retrieved albedo product. Only the algorithm for MERIS data by utilizes a physical model of sea ice that considers its melting stage and therefore does not depend on a priori assumptions of the surface and atmospheric conditions, which can introduce an error in the retrieved albedo product.

However, the retrieval algorithm by calculates the broadband albedo from MERIS data by linearly averaging the MERIS-derived spectral albedo at wavelengths of 400, 500, 600, 700, 800, and 900 nm. Therefore, the MERIS-derived broadband albedo only covers the waveband 400–900 nm. It cannot be used directly in climate studies, which usually need surface albedo values in the waveband 300–5000 nm , and is not comparable with other satellite-derived broadband albedo products with wavebands larger than 300–3000 nm (Table ). A comparison of surface broadband albedo products in different wavebands reveals significant discrepancies, which can exceed the required albedo accuracy in climate simulations . The validation of MERIS-derived broadband albedo against airborne measurements showed that over landfast ice the MERIS broadband albedo is higher by 0.06 on average than respective airborne measurements in the waveband 285–2800 nm because of its lack of radiative information in the near infrared spectral region .

In this paper, we introduce a spectral-to-broadband conversion (STBC), which replaces the conversion method proposed by for calculating broadband albedo in the waveband 300–3000 nm from spectral albedo retrieved from MERIS swath observations via the Melt Pond Detector (MPD) algorithm . With these new broadband albedo values, we improve the validation results of the MPD algorithm from . The new MERIS broadband albedo can be used to evaluate and validate other albedo products from different satellite observations and to test albedo parameterizations in climate models and atmospheric reanalyses. As the MPD algorithm additionally retrieves the melt pond fraction from MERIS observations, it is possible for the first time to include simultaneously derived broadband albedo values and melt pond fractions into climate models and atmospheric reanalyses.

After a short description of the MPD algorithm, the empirically derived spectral-to-broadband conversion of the albedo is presented (Sect. ). It is tested against the conversion techniques by and in Sect. . Section  discusses its uncertainty. The new broadband albedo of Arctic sea ice retrieved from MERIS observations is validated in Sect. . In Sect. , it is compared with respective values derived from the fifth generation of climate atmospheric reanalysis data set ERA5 produced by the European Centre for Medium-Range Weather Forecasts (ECMWF) to investigate the consistency of the sea-ice albedo used in a state-of-the-art atmospheric reanalysis with satellite observations. Section  concludes our findings.

In order to maintain short expressions, the following sections always refer to albedo products at the surface even if they are not explicitly declared as such.

Daily averages of broadband albedo over Arctic sea ice are derived from MERIS observations in three steps: MERIS swath Level 1b data over Arctic sea ice are used by the Melt Pond Detector (MPD) algorithm to derive time-synchronous spectral albedo values which are averaged daily afterwards (Sect. ). The output is converted into broadband albedo values (Sect. ).

We investigate the performance of the empirically derived STBC (Sect. ) and compare this new conversion to those methods proposed in and (Sect. ). For the evaluation, we used the root-mean-square deviation (RMSD), as an estimator for the statistical deviation; the mean difference of retrieved and measured albedo (bias), as an estimator for the systematic deviation; and the coefficient of determination (R2), which allows conclusions about the quality of correlation. Measurement uncertainties in the considered data sets are neglected as they are small compared to influences due to time offsets or different spatial resolutions of the measurements.

Along the path of converting the spectral albedo to broadband albedo, inconsistencies of physical (state of the sea-ice surface, solar zenith angle, waveband, and contrast between black- and blue-sky albedo) and meteorological variables (sky and atmospheric condition) may influence the accuracy of the derived broadband albedo product. Their presence and impact on the albedo is discussed in the following.

The STBC is based on various sea-ice surface types in the early season (April–June) mentioned at the end of Sect. . Nevertheless, it can be applied to later seasonal (July–September) Arctic surface types as well, as those surface types, like snow-covered sea-ice, white ice, and refrozen surface types, are similar to the surface types included in the training data set (snow layers and frozen melt ponds). Therefore, the STBC can be used for all Arctic sea-ice surface types.

Moreover, we have tested the performance of a STBC, when it is derived for each surface type separately. To that end, we classified the albedo measurements by into “snow surface”, “bare ice”, and “melt pond”. Measurements from 2009 (1194 samples) were used as a training data set to derive the coefficients ki in Eq. () for each surface class. The surface-specific STBCs were tested with the respective classified albedo measurements from 2008 (526 samples). The RMSD, bias, and R2 between measured and retrieved broadband albedo are 0.05, 0.02, and 0.96, respectively. Using the albedo measurements from 2009, independent of the surface type, as the training data set to derive the coefficients ki in Eq. () and applying those to all albedo data from 2008, leads to the same RMSD, bias, and R2. Therefore, the STBC can be derived independently of the Arctic surface type without deterioration of their accuracy.

A substantial uncertainty in the derivation of the broadband albedo is the sky condition. Most of the albedo measurements used for the empirical development of the STBC were influenced by clouds. Those can slightly increase the broadband albedo of snow by up to 0.06 and therefore influence the empirical derivation of the STBC. This cloud-influenced STBC is applied in Sect.  to albedo measurements under clear-sky conditions, which can contribute to the discrepancies shown in Fig. a. However, deriving the coefficients in Eq. () using only albedo measurements under clear-sky conditions (113 albedo spectra and broadband albedo values) by and an application of those to the cloud-free albedo measurements during ACLOUD enlarges the RMSD and bias given in Fig. a by 0.02 and 0.03, respectively (not shown).

According to , a wide range of atmospheric conditions and solar zenith angles are required to develop the STBC generally applicable to any spectral albedo measurement in the Arctic. We can confirm a high variability of the former via available aerosol optical depth from AERONET (Aerosol Robotic Network) data measured in Utqiaġvik, AK, USA, for the days of albedo measurements by when the sun disk was visible. However, due to the lack of the exact times of albedo measurements, we cannot determine the actual variability in the solar zenith angle. Since variations in the atmospheric visibility and the solar zenith angle influence the broadband albedo only marginally, they play a minor role in the uncertainties of the empirically derived STBC. Additionally, those effects are overlaid by the cloud effects mentioned above.

Different wavebands of broadband albedo products may affect their comparison. Applying the STBC, the derived broadband albedo covers the wavelength range 300–3000 nm. In contrast, the broadband albedo at ACLOUD was measured in a broader waveband (200–3600 nm). Resulting discrepancies between both albedo products are estimated by the radiative transfer model libRadtran and are lower than 0.01. Those systematic errors are negligible when comparing both broadband albedo products.

Although the STBC has been derived for blue-sky albedo (bihemispherical reflectance, ) in Sect. , it shall be applied to the MERIS-derived spectral albedo, which is referred to as black-sky albedo (directional hemispherical reflectance). estimated the discrepancy between black- and blue-sky broadband albedo for 87 individual surface reflectance spectra from USGS (U. S. Geological Survey) Spectroscopy Lab data, which includes, among others, snow, ice and water spectra. It is typically lower than 0.05 at solar zenith angles around 60∘ and at aerosol optical depths up to 1 at 440 nm. We expect that the aerosol optical depth is considerably lower in the Arctic such that the difference between black- and blue-sky albedo decreases and seems to be negligible against the cloud effect. Hence, we decide not to adjust any albedo measurement for the blue-sky to black-sky discrepancy.

The MPD algorithm by is combined with the empirically derived STBC to retrieve more accurate broadband albedo values of Arctic sea ice from MERIS observations compared to the procedure described in . With these new values, we will improve the validation of the MPD algorithm performed in .

The new MERIS broadband albedo data product is validated with measured broadband albedo during the aircraft campaign MELTEX (impact of melt ponds on energy and momentum fluxes between atmosphere and sea ice) performed by the Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research (AWI), over the southern Beaufort Sea between May and June 2008. The goal of the campaign was to improve the quantitative understanding of the impact of melt ponds on radiation, heat, and momentum fluxes over Arctic sea ice .

To determine the broadband albedo, two Eppley Precision Spectral Pyranometers were mounted on the Polar 5 aircraft in a fixed position measuring simultaneously the hemispheric down- and upwelling radiation integrated over the waveband from 285 to 2800 nm. Analogous to the broadband measurements during ACLOUD, the measurements of downwelling radiation at clear-sky conditions were corrected for deviations from horizontal attitude due to misalignment of the instrument based on the method given by .

On 5 individual days (26 May and 3, 4, 6, and 7 June 2008), airborne broadband albedo was measured under almost clear-sky conditions. Measurement times are given in Table . Maps of flight tracks are shown in . The flight altitude was between 50 and 400 m. On 6 June, broadband albedo was measured over landfast ice, on the other selected days measurements were performed over drifting ice with ice floes of different sizes.

Due to two warming events between 23–24 May and 1–7 June, broadband albedo was measured over sea ice at different melting stages. On 26 May and 3 June, melt ponds at early stages were overflown. On 4 June, the snow was either melted away or was very wet and the number and size of melt ponds rose. On 6 and 7 June, the observed sea ice was homogeneously covered by well-developed melt ponds.

Airborne-measured broadband albedo is colocated with MERIS broadband albedo derived for each grid cell from MERIS swath data at a reduced resolution of 1.2 km. The MERIS overflight times that correspond to the airborne flights are also given in Table . The time difference between the airborne and satellite measurements stays below 2 h except for 3 and 7 June, with a maximum difference of 3 and 4 h, respectively.

For the colocation of airborne and MERIS broadband albedo, the orthodromic distance between each MERIS grid cell center and the location of a given airborne measurement is calculated. Each airborne measurement is allocated to the satellite grid cell with the smallest orthodromic distance. Depending on the orientation and location of the flight track, as well as MERIS grid cell availability, up to 14 airborne broadband albedo measurements are colocated to one MERIS-derived broadband albedo value. The airborne broadband albedo values are averaged for each satellite grid cell.

The scatterplots in Fig.  show the correlation of the MERIS-derived and colocated airborne broadband albedo for measurements over landfast ice (Fig. 3a) and over drift ice (Fig. 3c), respectively. Colocated airborne and MERIS broadband albedo values are used for validation only if more than five airborne broadband albedo values are available for one MERIS grid cell. Time differences between airborne and MERIS measurements up to 1.5 h were allowed.

For the landfast ice case (Fig. a), MERIS broadband albedo is slightly higher at low albedo values than the corresponding airborne broadband albedo. For drift ice cases (Fig. c), the respective overestimation is higher but at high albedo values an underestimation occurs (slope=0.53, intercept=0.25).

The highest correlation and lowest RMSD value is found for broadband albedo values over landfast ice on 6 June 2008 (R2=0.93, RMSD=0.04, Fig. a). Compared to landfast ice, the RMSD=0.07 for the drifting ice cases (Fig. c) is nearly twice as high and the correlation is lower (R2=0.78). Correlation and RMSD values depend on weather conditions, ice concentration, surface inhomogeneity, time differences between satellite overflight and airborne measurements, and spatial resolution of the observation. As landfast ice is stationary over long periods of time, airborne measurements are not displaced relative to satellite measurements during the time lag between both observations. Over drifting ice floes at lower sea-ice concentrations, a higher sea-ice drift can be expected (free drift conditions). Therefore, the surface conditions observed by the aircraft and satellite can become more different (see the three outliers at low measured albedo values in Fig. c). The discrepancies between MERIS-derived and airborne broadband albedo values are increased by their different spatial resolution, which depends on observation heights and instrument optics. As clearly seen in the histogram in Fig. d, the coarser spatial resolution of MERIS observations leads to a lower albedo variability compared to the respective airborne measurements. Moreover, the bimodal albedo distribution shown in the latter is smeared out in the respective satellite retrievals. For the landfast ice case, the surface conditions are more homogeneous, and thus the difference in spatial resolution has less influence on the comparison (see Fig. b).

In contrast, the validation of MERIS broadband albedo values derived via the procedure described in , i.e., the combination of the MPD algorithm and the spectral averaging method using coefficients given in Table , results in similar correlation values of R2=0.94 for the landfast ice case and R2=0.78 for the drift ice cases. The RMSDs are 0.06 (landfast ice) and 0.09 (drift ice) and thus exceed the values found above. This again illustrates the better performance of the empirically developed STBC compared to the spectral averaging method proposed in .

During the melt season in Arctic summer, the Arctic sea ice experiences rapid changes in the albedo mainly caused by the melt pond development . As the melt pond fraction on sea ice evolves according to the sequence of melt stages , the melt pond fraction and the melt evolution are beneficial information in the representation of the summer energy balance in atmospheric reanalyses, especially in above-mentioned situations where accurate albedo representation is challenging.

Although a vast amount of satellite and in situ observations are assimilated into every atmospheric reanalysis, there is no published reference about assimilation of melt ponds in those models at the time of writing. Instead, the sea-ice surface is characterized by a parameterized surface albedo. We test the albedo parameterization used for the atmospheric reanalysis data set ERA5 by comparing ERA5 and MERIS broadband albedo values.

ERA5 is the fifth generation of climate reanalysis data set produced by ECMWF. It provides hourly values of atmospheric and land variables from 1950 onwards, with a spatial resolution of 31 km, obtained by an ensemble 4D-Var data assimilation system . The sea-ice albedo is simply prescribed as constants following the albedo values given in and considers the spectral variation. It is representative for dry snow during the months September to May, representative for melting snow in June, and representative for bare sea ice in July and August. Melt ponds are not represented at any time. The Ebert and Curry values are taken to be valid on the 15th day of the month, and the values for all other days are obtained by linear interpolation. The grid cell albedo for ERA5 is then a linear combination between the sea-ice albedo and the open-water albedo: 2αERA5=c⋅αseaice+(1-c)⋅αwater, with c representing the sea-ice concentration from ERA5 generated by . It has been developed under the Ocean and Sea Ice Satellite Application Facilities (OSI-SAF) using passive microwave satellite data from SSMIS (Special Sensor Microwave Imager Sounder) at 10 km resolution . The open-water albedo αwater is calculated in dependence of the solar zenith angle according to for the clear-sky case and is equal to αwater=0.06 for diffuse irradiation .

The effective grid cell broadband albedo of ERA5 can be calculated from hourly averaged ERA5 net and downward irradiances, Fnet(h) and Fdn(h), at surface in the waveband 200–4000 nm. Thus, daily averaged ERA5 grid cell broadband albedo is given by 3αERA5=1-Fnet(h)‾Fdn(h)‾. The bars illustrate the averaging of the hourly (h) irradiances per day at which the sun is above the horizon. Fnet and Fdn were generated by using .

Analogously, the MERIS grid cell broadband albedo for sea-ice grid cells can be expressed as follows: 4αMERIS=(1-s)⋅αice+s⋅αpond, since the STBC is linear. The parameters αice and αpond represent the broadband albedo of ice and melt pond, and s represents the melt pond fraction.

Although the structure of Eqs. () and () is identical, the single variables cannot be compared directly. According to the MPD algorithm, MERIS-derived albedo αMERIS is only available at 100 % sea-ice concentration (Sect. ) and is simultaneously derived by the melt pond fraction s and albedo portions αice and αpond. Consequently, all three components are influenced by the reflection properties of undetected small cracks and leads (oceanic water). In contrast, the ERA5 albedo αERA5 does not consider melt ponds, and its components c, αseaice, and αwater are determined independently. Thus, unconsidered melt ponds influence the sea-ice concentration c only, via a nonlinear relationship. However, both equations can explain variations and differences between the ERA5 and MERIS grid cell broadband albedo that are considered below.

In this study, a spectral-to-broadband conversion (STBC) has been developed empirically, which can be used in combination with the Melt Pond Detector (MPD) algorithm to derive broadband albedo (300–3000 nm) of Arctic sea ice from MERIS swath data. The empirically derived STBC has been developed with spectral and broadband albedo measured over landfast ice close to Utqiaġvik, AK, USA, between April and June of 2008 and 2009 . It has been validated with airborne-measured spectral and broadband albedo of drifting sea ice north of Svalbard on 25 June 2017 (Fig. a). Compared to the measured broadband albedo, the empirically derived STBC calculates broadband albedo with a low root-mean-square deviation (RMSD) of 0.02 and a high correlation of 0.98. However, low broadband albedo values are slightly underestimated. It performs more accurately than conversions proposed by and which results in RMSDs of 0.09 and 0.05, respectively (Fig. b and c).

The empirically derived STBC replaces the spectral averaging method proposed by in the derivation of broadband albedo from MERIS swath data. The new broadband albedo values improve the validation of the MPD algorithm with respective airborne measurements over the southern Beaufort Sea between May and June 2008 (Fig. ). The RMSD varies between 0.04 for landfast ice and 0.07 for drift ice. Both RMSDs are 0.02 lower than those when using the conversion method by . The higher RMSD for drift ice can result from the sea-ice drift, which displaces the airborne measurements relative to satellite observations during the time lag between both measurements. Another cause of uncertainty is the different spatial resolution of airborne and satellite measurements in combination with the more inhomogeneous surface condition of drift ice relative to landfast ice.

The new MERIS-derived broadband albedo of sea ice has been compared with respective albedo values retrieved from the atmospheric reanalysis data set ERA5 to test the albedo parameterization used in ERA5. Both albedo products agree in the large scale and the seasonal pattern, but differences occur spatiotemporally with RMSDs of around 0.10 (Fig. ), exceeding the required absolute accuracy of 0.02–0.05 in climate models . The monthly interpolation of constant sea-ice albedo values in ERA5 based on literature values of dry snow (May, September), melting snow (June), and bare sea ice (July, August) is not suited to simulating the observed spatiotemporal variability and change in sea-ice albedo. Thus, the ERA5 broadband albedo is underestimated over multiyear ice between June and August by up to 0.1 and overestimated over first-year ice from mid-August to mid-September by up to 0.2 compared to the MERIS broadband albedo (Fig. ). Due to unconsidered melt ponds in ERA5, its broadband albedo over first-year ice is up to 0.1 lower than MERIS broadband albedo in June to mid-August.

As an interim solution, prognostic modeling schemes of sea-ice albedo should be developed for ERA5, which can be validated against observational products like the MERIS-derived broadband albedo presented here. In order to obtain more individual values, it might be desirable to assimilate satellite-derived sea-ice albedo when producing an atmospheric reanalysis. MERIS-derived broadband albedo can be useful in this context because it is not based on a priori values and is available daily even though only at daylight and under cloud-free conditions.

The empirically derived STBC has been developed based on an albedo data set measured under clear-sky, cloudy, and overcast conditions. However, clouds increase the broadband albedo of snow up to 0.06 . Thus, clouds affect the accuracy of the empirically derived STBC, which may contribute to the uncertainty in converting spectral-to-broadband albedo under clear-sky conditions, i.e., the only conditions when satellite data are available. The influence of this uncertainty on the satellite albedo retrieval needs further investigation. Radiative transfer simulations can be a beneficial approach in this context because they offer more flexible and specific setups of surface, atmosphere, and cloud types than are available in short-term campaigns. Another advantage of radiative transfer simulations is the calculation of different radiometric parameters for the same meteorological situation, whereas measurements are done within a certain time frame in which the meteorological situation can rigorously change.

The combination of the MPD algorithm and the empirically derived STBC allows us to derive broadband albedo for the complete Arctic sea ice cover under cloud-free conditions between March 2002 and April 2012 from MERIS swath data. This 10 year data set (available at https://www.seaice.uni-bremen.de/, last access: 14 November 2019) can be used with the additional melt pond fraction data in Arctic climate investigation for evaluation, validation, and data assimilation purposes, as well as in comparative studies. As a next step, swath data from OLCI (Ocean and Land Color Instrument) onboard Sentinel-3 will be implemented in the MPD algorithm to extend the broadband albedo time series of Arctic sea ice from 2016 to the present.