Five flight campaigns were conducted within the collaborative research project “Arctic Amplification: Climate Relevant Atmospheric and Surface Processes, and Feedback Mechanisms” (AC)3 between 2017 and 2022 . The airborne activities were carried out with the research aircraft Polar 5 (P5) and Polar 6 (P6) and focused on observations of Arctic clouds and of the Arctic atmospheric boundary layer as well as surface properties in the European Arctic in different seasons between 2017 and 2022. Table 1 gives an overview of the campaigns considered in this study. Apart from the “Polar Airborne Measurements and Arctic Regional Climate Model Simulation Project” (PAMARCMiP) campaign, which was based at the Danish Villum research station (Station Nord), Greenland (81°36′ N, 16°40′ W), all campaigns were based in Longyearbyen (78°13′ N, 15°38′ E), Svalbard. The “Arctic CLoud Observations Using airborne measurements during polar Day” (ACLOUD) took place in early summer 2017 and used both P5 and P6. Spring Arctic conditions were observed with P5 only during PAMARCMiP and during the “Airborne measurements of radiative and turbulent FLUXes of energy and momentum in the Arctic boundary layer” (AFLUX) campaign. Within the most recent spring observations in 2022, HALO-(AC)3, both aircraft, P5 and P6, were used with a similar instrumental setup to that during ACLOUD. The set of airborne observations during polar day was completed by the “MOSAiC Airborne observations in the Central Arctic” (MOSAiC-ACA) campaign, which took place in autumn 2020, as an airborne component of the MOSAiC expedition.

For this study, only low-level (flight altitude below 300 m) flight sections were considered, which were performed above sea ice and open water without clouds between the aircraft and surface. This selection was made to minimize atmospheric masking effects in the albedo observations . Further, the data were filtered with respect to aircraft pitch and roll angles within a range of ±4° to reduce the uncertainties of radiation measurements due to horizontal misalignment . Figure  shows the coverage of all selected flight sections for the five aircraft campaigns, together with the sea ice edge as defined from the satellite observation of the sea ice concentration (SIC) derived from the Advanced Microwave Scanning Radiometer 2 (AMSR2) instrument using the method from . Here, the ice edge is based on 80 % SIC. The strong variations in the sea ice edge position are linked to not only the period of observations but also interannual changes. While the northernmost retreat of sea ice was observed during MOSAiC-ACA in autumn, the southern sea ice edge in the measurement area during ACLOUD in early summer and during the two spring campaigns HALO-(AC)3 and AFLUX does not differ so much. A relatively far northern location of the ice edge for spring conditions was observed during PAMARCMiP in 2018. However, due to the more northern starting point of the aircraft at Station Nord, Greenland, mostly surfaces with more than 80 % of SIC could be overflown. For MOSAiC-ACA, a significant fraction of measurements were carried out in the marginal sea ice zone (MIZ), while for the other campaigns mainly flight sections with SIC larger than 80 % remained after application of the selection criteria. The total numbers of data points and flight days are listed in Table . Most flights over sea ice were performed during ACLOUD. However, the largest number of selected measurements was determined for MOSAiC-ACA, where the instrumental setup of the P6 differed from the configuration of the P5, resulting in different time resolutions of the data products.

The surface albedo scheme of the coupled regional climate model HIRHAM–NAOSIM was recently revised based on surface broadband albedo measurements performed during the ACLOUD campaign . The original parametrization of the snow albedo, as described in , was adapted with respect to illumination dependence and snow property changes in terms of threshold temperatures describing the transition between dry and melting snow.

In general, the surface broadband albedo in an inhomogeneous model grid cell is composed of the sum of the surface subtype albedo values weighted by the areal fractions (c) of the respective surface subtypes of open water (subscript ow) and sea ice (subscript i), where sea ice is further divided into snow-covered ice (subscript s), bare ice (subscript bi), and melt ponds (subscript mp): 4α=cow⋅αow+ci⋅αiαi=cs⋅αs+cmp⋅αmp+cbi⋅αbi. Note that the surface type “white ice”, which is a highly reflective scattering layer on top of melting bare ice , is not explicitly considered in HIRHAM–NAOSIM. Due to its higher albedo compared to bare ice, white ice is added to the class of snow-covered ice in this work and classified accordingly based on camera observations during the measurement flights. The open-water fraction is not parameterized within this surface albedo scheme and is calculated with a separate prognostic equation. The surface albedo of open water is set to a fixed value of 0.1, while the individual subtype albedo of the ice types is assumed to be variable within a given range of the surface skin temperatures (Tsurf) in units of degrees Celsius . A temperature range with temperature thresholds Td was defined within which the surface albedo varies linearly from maximum (dry ice or snow) to minimum values (melting ice or melting snow). The parameterized surface albedo of the snow-covered ice, for example, is then determined by 5αs=αmin+(αmax-αmin)⋅f(Tsurf), with f(Tsurf) representing the surface-skin-temperature-dependent function: 6f(Tsurf)=min(1,max(0,Tsurf/Td)).

The same holds for the two other surface types bare ice and melt ponds. Table  summarizes the surface albedo ranges of the individual subtypes and threshold temperatures.

The areal fractions of the sea ice subtypes used in Eq. () are estimated by the snow thickness (hs). For snow-covered sea ice, the fraction is calculated as 7cs=cs,max⋅tanhhsh0.75, where cs,max is the maximum snow cover fraction of 1.00, and h0.75=0.03 m giving, the snow thickness at which approximately 75 % of the sea ice is covered by snow . The melt pond fraction is subject to the restriction that it is not allowed to exceed the fraction of the sea ice surface not covered with snow (1-cs). It is parameterized by 8cmp=min(1-cs,cmp,max⋅(1-f(Tsurf))), with cmp,max being the maximum melt pond fraction of 0.22 as derived from observational data during SHEBA , which agrees with observations made during MOSAiC . Locally, however, higher melt pond percentages may occur, e.g., on level first-year ice . Finally, the bare-ice fraction is calculated as the residual (cbi=1-cs-cmp). Note that if the actual ice thickness is lower than 0.25 m, then a linear transition between water and bare-ice albedo is applied to account for the transparent behavior of thin ice .

The model output was given with spatial resolution of about 27 km distributed over 200 × 218 grid points on a circum-Arctic domain. For the prognostic variables of the atmospherical model component HIRHAM, a 1 % nudging to reanalysis data of the ERA5 data set was applied. The HIRHAM–NAOSIM model was run for 2018, covering the time frame of the PAMARCMiP campaign (temporal resolution of 1 h) and for the entire MOSAiC period (temporal resolution of 3 h), including the time frame of the ground-based measurements from spring to autumn 2020 and the period of the aircraft observations during MOSAiC-ACA.

The outline of the comparison of measured and modeled surface albedo is illustrated in Fig. . In the first step the albedo scheme was run offline (i.e., without HIRHAM–NAOSIM), decoupling the two parametrizations of the subtype surface albedo and subtype surface fraction. Because the subtype surface fraction is parameterized as a function of the snow depth, which was not a measured parameter, we used only the parametrization of the subtype surface albedo along with measured values of the prognostic variable Tsurf and the measured surface type fractions. The offline evaluation was applied to perform a seasonal comparison between observed and parameterized surface albedo considering data of all aircraft campaigns. In the second step, for an online evaluation, the HIRHAM–NAOSIM output was compared to airborne and ground-based observations. The satellite-based surface albedo derived from Sentinel-3 OLCI was used to characterize the spatial variation on an intermediate grid size scale between local ground-based or aircraft observations and the model output. To match the satellite and model data, all data points of the satellite product that fall into one single grid point of the model were area-averaged accordingly. However, since the satellite product can only be derived for cloudless conditions, the comparison is limited to a few cases.

An overview of the proportions of classified subtypes along the flight tracks of the five campaigns is shown in Fig.  as a stacked area plot. The temporal evolution of the surface broadband albedo and surface skin temperature is given in the corresponding lower panels. Flight sections in spring (Fig. a–f) were mostly carried out over snow or white ice (ice with a highly scattering layer on top) with surface skin temperatures below -15 °C. As expected, the variability in the surface albedo depends on the variability in the surface types within the FOV of the downward-looking pyranometer. However, flight sections over snow or white ice also revealed a spatial albedo variability in the range of up to ±0.1 as an effect of surface roughness and variations in snow grain size. In particular for high SZAs, surface roughness tends to reduce the surface albedo compared to a flat surface depending on the feature orientation with respect to the sun . Note that longer distances were overflown during PAMARCMiP compared to the other two spring campaigns, which explains the strong variation in Tsurf (Fig. b). The occurrence of open water, caused by either sea ice dynamics or flight sections close to the sea ice edge, leads to a significant increase in surface albedo variability and a decrease in the surface albedo itself down to 0.2. A small percentage of melt ponds was found only in areas with a high fraction of open water (flight on 4 April 2019 during AFLUX) when Tsurf is close to 0 °C. The onset of melt pond development on sea ice usually starts in summer, as observed at the end of the ACLOUD campaign (26 June) with melt pond fractions of up to 8 % (Fig. g). In general, the surface albedo decreases over time as a consequence of an increase in surface grain size and melt pond fraction, which are both related to the increase in skin temperature during ACLOUD (Fig. h). In September the overflown surface showed the most variable conditions (Fig. i, j). Surface sections during the first flight were dominated by open water, with surface skin temperatures being in a similar range to that for sea ice (most southern flight track in Fig. ). Camera images showed that most of the melt ponds were already refrozen and therefore classified as bare ice.

Typically, an increase in sea ice fraction is correlated with an increase in the surface albedo. This relation is influenced by the spectral and directional distribution of the incident solar radiation. Compared to cloudless conditions, clouds may cause an increase in surface broadband albedo due to a spectral shift in the incident radiation. The shift is caused by absorption of solar radiation in the near-infrared spectral range. Figure k shows the relationship of the sea ice fraction (white ice plus bare ice) and the surface albedo for all campaigns separated into cloudless and cloudy cases. The surface albedo was averaged within each bin of sea ice fraction (bin size of 10 %). In general, we observed a higher albedo for the same amount of sea ice under cloudy conditions than under cloudless conditions. This effect was more pronounced when a high proportion of sea ice was present. For sea ice fractions around 100 % mean surface albedo, values of 0.76 ± 0.08 (cloudless cases) and 0.81 ± 0.08 (cloudy cases) were calculated. The variability in the surface albedo at 100 % sea ice cover was further examined with respect to a potential dependence on the SZA. For cloudless conditions the correlation coefficient of R=0.37 indicates a low correlation between both quantities. In a cloudy atmosphere the incoming radiation is dominated by the diffuse component, which is independent of the SZA as confirmed by a R value of -0.02. Since the majority of measurements were carried out for surface skin temperatures below -15 °C, melting processes can be ruled out as the cause of the surface albedo variability. Only during the summer campaign (ACLOUD) was a temperature effect on the magnitude of snow albedo observed .

The surface albedo scheme of the coupled HIRHAM–NAOSIM model was applied to the measurement data of the different aircraft campaigns to evaluate the performance of the surface albedo parametrization for spring, summer, and autumn conditions. Taking the measured subtype fractions into account, the surface albedo α was parameterized following Eq. () using surface-type-specific albedo values defined by Eq. (). The results separated into cloudy and cloudless cases for spring, summer, and autumn are presented in Fig. . The plots show the distributions of the measured and parameterized surface albedo, together with the median value. The parametrization was initially optimized based on the ACLOUD summer campaign data set, leading to reasonable agreement between measurements and parametrization with a root mean square error (RMSE) of 0.05 .

For cloudless conditions, the median values of the measured surface albedo are well represented by the parametrization. A different picture is revealed for cases where clouds are present. While in summer the modeled median surface albedo deviates from the measured value by only 0.01, we observe an overestimation of the modeled median surface albedo of 0.06 in spring. The increase in the surface albedo caused by clouds in summer is much less pronounced in the spring measurements. As this cloud effect depends on the cloud absorption of the downward irradiance in the NIR spectral range, it is assumed that the generally optically thinner clouds in spring do not alter the spectral surface albedo to the same extent as the optically thicker clouds in summer. Therefore, we argue that the cloud parameter in the surface albedo scheme that was defined for summer conditions leads to the overestimation of modeled surface albedo in spring. The distributions shown for autumn (MOSAiC-ACA) are primarily affected by the surface sampled. While measurements under cloudless conditions mostly coincided with flight sections over areas with a high fraction of open water, most of the cloudy cases were sampled over compact ice (see Fig. i), which justifies the large difference between the two median values of the cloudless and cloudy distributions. The modes representing the measurements over sea ice indicate a higher parameterized surface albedo than that derived from the measurements. That is possibly caused by the presence of refrozen melt ponds, which were classified as bare ice. Compared to bare ice of considerable thickness that occurs after snowmelt, refrozen melt ponds have little ice thickness on top, resulting in a dark appearance and a lower surface albedo. The model parameters of bare ice may not properly represent such thin ice layers, leading to an overestimation of parameterized surface albedo. In general, however, the distributions were reproduced by the parametrizations for all seasons using the measured sea ice fractions.

The net solar irradiance at the surface is defined as the difference between downward and upward irradiance: 9Fnet=F↓-F↑. The difference between the modeled and measured net irradiances is calculated to estimate the impact of the model bias for the solar radiative energy budget: 10ΔFnet=Fnet,model-Fnet,meas. Based on the model results introduced in Sect. , we compared the measured and modeled net irradiance for all model grid points that covered the selected flight tracks during the PAMARCMiP and MOSAiC-ACA campaign. Figure  shows the scatterplot of both net irradiances. The corresponding standard deviation illustrates the variability in Fnet with a maximum of about 60 W m-2. The correlation R between the measured and modeled net irradiances is 0.80, and the RMSE of the model is 30.2 W m-2, with deviations increasing accordingly for larger differences between measured and modeled surface albedo.

Not only do the Fnet differences between measurements and the model depend on Δα, but we must also take into account the difference in the downward irradiance (ΔF↓). A negative ΔF↓ (smaller symbols in Fig. ) may occur when the modeled extinction of F↓ caused by modeled clouds is higher than an observation would show. This is especially the case when cloudless situations were observed but not modeled. It would lead to an underestimation of the modeled net irradiance, assuming the same surface albedo. In fact, a mean negative bias of the modeled F↓ (mean ΔF↓=-31 W m-2) was found, which can be related to an overestimation of the modeled cloud cover. However, the downward irradiance itself also depends on the surface albedo. In particular, F↓ under cloudy conditions is enhanced for brighter surfaces due to multiple-scattering between the surface and cloud base. A positive surface albedo bias would lead to a positive bias in F↓, assuming a similar cloud representation. On average Δα was 0, indicating a small effect of surface albedo on the modeled F↓.

Overall, both cloud properties and surface albedo must be well represented for modeling net irradiance correctly. To estimate whether the representation of clouds or the surface albedo potentially contributes more to the uncertainty in Fnet, we calculated the standardized regression coefficients. Such standardization is useful as the parameters are expressed in different units. HIRHAM–NAOSIM provides the total cloud water path (CWP) as a measure of the cloud microphysics. To account for the available incident radiation we also consider the SZA as a third parameter. The standardized regression coefficients βj with j being either α, CWP, or SZA are calculated directly from the unstandardized regression coefficient bj between Fnet and the variables and the standard deviations (σ) of the variables: 11βj=bj⋅σjσFnet. This means that a change of 1 standard deviation in one of the parameters is associated with a change of β standard deviations in Fnet so that the more important variable will have the maximum absolute value of βj. For the analyzed cases during MOSAiC-ACA and PAMARCMiP we found the strongest impact of the surface albedo (βα=-0.80) and less impact of the CWP (βCWP=-0.38) and SZA (βSZA=-0.23). This highlights the importance of a reliable surface albedo parametrization for modeling a realistic surface energy balance. However, we expect a seasonal dependence of the standardized regression coefficients. According to Eq. (), a stronger variability in the individual parameters contributes to a higher magnitude of βj. In summer, for example, clouds tend to have a higher cloud water path with greater variability, while the surface albedo reaches its minimum. Therefore, it is assumed that the contribution of the surface albedo bias to the Fnet uncertainty is reduced, while the model representation of cloud properties becomes more important compared to the two periods shown in this study.

In contrast to the study of the HIRHAM–NAOSIM results, the application of the offline evaluation allows dependencies of the Fnet bias to be considered for the comparison of the parametrization with the airborne measurements. The measured subtype fractions were used to identify only the influence of the bias of the parameterized surface albedo on Fnet without having to consider the uncertainties in the subtype fraction parametrization. The net irradiance was determined along the flight path for 7 selected days during all five flight campaigns, covering cloudy and cloudless conditions. Radiative transfer simulations (Appendix A) were performed for these cases using the measured and parameterized surface albedo. In this way, the sensitivity of net irradiance to surface albedo was quantified under the same predefined atmospheric conditions. These conditions matched the measurements made during the selected flights (see Appendix A). For cloudless conditions broadband upward and downward irradiances were simulated so that the direct impact of surface albedo can be derived from the difference in the resulting net irradiance, according to Eq. (). For cloudy conditions the setup of the radiative transfer model required information of the cloud microphysical properties. We estimated these profiles along the flight path as follows: where appropriate, we used profile in situ measurements of the liquid or ice water content and particle size to define a standard cloud profile. In a second step this standard profile was adjusted by scaling the water content of the profile so that the measured and the simulated downward irradiances matched at each measurement point along the flight track. This provides an estimate of the cloud optical depth (COD). Radiative transfer simulations were then performed using this scaled cloud profile and the parameterized surface albedo to derive Fnet,model. A table summarizing the corresponding microphysical profiles can be found in Appendix A.

Figure a shows a scatterplot of the net irradiances that were derived from the measured and parameterized surface albedo. A significantly smaller spread between measured and parameterized Fnet with R=0.97 and RMSE = 13.5 W m-2 is obtained. We identify two clusters. The first one represents all spring and autumn cases and data derived for cloudy conditions in summer (Fnet<100 W m-2). As an effect of a low downward irradiance and a high surface albedo, the lowest Fnet values were derived for spring cases under cloudy conditions that are dominated by a high fraction of dry snow surfaces. The second cluster (Fnet: 150–350 W m-2) indicates the cloudless cases in summer that are obtained at a lower SZA (56–66°) and low surface albedo due to wet snow. Figure b illustrates the dependence of ΔFnet on Δα and SZA. The linear relationship between ΔFnet and Δα for similar atmospheric conditions results directly from the correlation of surface albedo and upward irradiance. A positive bias of the parameterized surface albedo leads to a higher upward irradiance and consequently results in a lower Fnet compared to the measurements. The maximum impact of the albedo bias on ΔFnet is derived for cloudless summer conditions (ΔFnet=±80 W m-2). For the same range of Δα in spring, ΔFnet is found to be less than half of its magnitude in summer (ΔFnet=±35 W m-2). This means that the bias of modeled surface albedo can have greater effects on the simulated net solar irradiance at the surface in summer compared to spring. In spring, however, we observed from the flight measurements an increased albedo bias with a wider distribution (Δα=0.02±0.07) than in summer (Δα=0.00±0.04). The deviation from the linear relationship between ΔFnet and Δα at a similar SZA can be attributed to different cloud conditions. We used the estimated cloud optical depth to illustrate the cloud impact on ΔFnet. Figure c shows the frequency distribution of ΔFnet of all analyzed cases separated into three cloud classes. Accordingly, the cloudless cases comprise the largest range of values with a low mean positive bias (median: 2.5 W m-2). The Fnet bias for cases with optically thicker clouds (COD >5) is distributed around its median value of 0.1 W m-2, showing the narrowest distribution (interquartile range: 10.4 W m-2). A clear negative Fnet bias (median: -6.4 W m-2) is observed for optically thin clouds (COD <5), which results from the systematic overestimation of the cloud enhancement effect for αmodel in the case of optically thin clouds. A better description of the surface albedo dependence on the cloud property is required to overcome this systematic effect.