Radiative fluxes in the High Arctic region derived from ground-based lidar measurements onboard drifting buoys

The Arctic is facing drastic climate changes that are not correctly represented by state-of-the-art models because of complex feedbacks between radiation, clouds and sea-ice surfaces. A better understanding of the surface energy budget requires radiative measurements that are limited in time and space in the High Arctic (>80◦N) and mostly obtained through specific expeditions. Six years of lidar observations onboard buoys drifting in the Arctic Ocean above 83◦N have been carried out as part of the 5 IAOOS (Ice Atmosphere arctic Ocean Operating System) project. The objective of this study is to investigate the possibility to extent the IAOOS dataset to provide estimates of the shortwave (SW) and longwave (LW) surface irradiances from lidar measurements on drifting buoys. Our approach relies on the use of the STREAMER radiative transfer model to estimate the downwelling SW scattered radiances from the background noise measured by lidar. Those radiances are then used to derive estimates of the cloud optical depths. In turn, the knowledge of the cloud optical depth enables to estimate the SW and 10 LW (using additional IAOOS measured information) downwelling irradiances at the surface. The method was applied to the IAOOS buoy measurements in spring 2015, and retrieved cloud optical depths were compared to those derived from radiative irradiances measured during the N-ICE (Norwegian Young Sea Ice Experiment) campaign at the meteorological station, in the vicinity of the drifting buoys. Retrieved and measured SW and LW irradiances were then compared. Results showed overall good agreement. Cloud optical depths were estimated with a rather large dispersion of about 47 %. LW irradiances showed 15 a fairly small dispersion (within 5 W m−2), with a corrigible residual bias (3 W m−2). The estimated uncertainty of the SW irradiances was 4%. But, as for the cloud optical depth, the SW irradiances showed the occurrence of a few outliers, that may be due to a short lidar sequence acquisition time (no more than four times 10 mn per day), possibly not long enough to smooth out cloud heterogeneity. The net SW and LW irradiances are retrieved within 13 W m−2.

IAOOS (Ice Atmosphere arctic Ocean Operating System) project. The objective of this study is to investigate the possibility to extent the IAOOS dataset to provide estimates of the shortwave (SW) and longwave (LW) surface irradiances from lidar measurements on drifting buoys. Our approach relies on the use of the STREAMER radiative transfer model to estimate the downwelling SW scattered radiances from the background noise measured by lidar. Those radiances are then used to derive estimates of the cloud optical depths. In turn, the knowledge of the cloud optical depth enables to estimate the SW and 10 LW (using additional IAOOS measured information) downwelling irradiances at the surface. The method was applied to the IAOOS buoy measurements in spring 2015, and retrieved cloud optical depths were compared to those derived from radiative irradiances measured during the N-ICE (Norwegian Young Sea Ice Experiment) campaign at the meteorological station, in the vicinity of the drifting buoys. Retrieved and measured SW and LW irradiances were then compared. Results showed overall good agreement. Cloud optical depths were estimated with a rather large dispersion of about 47 %. LW irradiances showed 15 a fairly small dispersion (within 5 W m −2 ), with a corrigible residual bias (3 W m −2 ). The estimated uncertainty of the SW irradiances was 4%. But, as for the cloud optical depth, the SW irradiances showed the occurrence of a few outliers, that may be due to a short lidar sequence acquisition time (no more than four times 10 mn per day), possibly not long enough to smooth out cloud heterogeneity. The net SW and LW irradiances are retrieved within 13 W m −2 .

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The Arctic is facing rapid climate changes with surface temperatures increasing twice as fast then the rest of the world (Serreze and Barry, 2011). One of the most notable changes in the Arctic region over the recent decades is the reduced sea ice coverage and thickness (Meier et al., 2014). This thinner ice breaks more easily to form open water leads, increasing the heat flux and surface properties, but such expeditions are limited in time and cover only a limited part of the Arctic region. Satellitebased remote sensing instruments documenting clouds, such as CALIOP aboard CALIPSO (Lacour et al., 2017) or CloudSat (Stephens et al., 2018) are limited to latitudes below 82 • N because of the satellite flight path (Winker et al., 2009). To respond to the need for more observations in the Arctic and compensate the lack of satellite observations at the highest latitudes, multiple buoys have been deployed in the Arctic Ocean between 2014 and 2019 as part of the IAOOS (Ice Atmosphere arctic Ocean 70 Operating System) project (Mariage et al., 2017;Maillard et al., 2021). Buoys have also limitations, e.g. their limited available space and the capacity of their batteries, but spread across the Arctic Ocean allows a wider spatial coverage and longer periods of observations, where other remote sensing instruments (for example onboard satellites) are blind.
This study investigates the possibility to provide a more complete dataset from the IAOOS observations, including estimated radiative fluxes from buoys lidar data that do not have such measurements. The paper presents a method to estimate the 75 cloud optical depths and the SW and LW irradiances using a combination of zenith-pointing backscatter lidar measurements and radiative transfer model outputs. A similar approach has already been used by Chiu et al. (2014) on warm mid-latitude continental low-level clouds. They retrieved the cloud optical depth from ground-based lidar solar background measurements, located in ARM Oklahoma, from 2005 to 2007. Here, a similar methodology is used on cold low-level mixed-phase clouds in the Arctic Ocean to derive both optical depths and radiative irradiances. Our approach is applied to observations sampled 80 from buoys as part of the IAOOS project, and its limits and associated uncertainties are discussed. The results are compared to SW and LW irradiances measurements at the vicinity of the buoy from the N-ICE expedition. Section 2 details the dataset used in this study. The radiative transfer model and the approach developed in this study are described in Sect. 3. In Sect. 4, the methodology is applied to lidar data aboard buoys from the IAOOS campaigns, uncertainties and limitations of the approach are discussed and results are compared to standard measurements of radiative fluxes. Conclusions are finally drawn (Sect. 5). 85 2 Observational dataset

IAOOS lidar data aboard buoys
The main objective of the IAOOS project, led by Sorbonne University, was to collect real time observations of the ocean, ice, snow and atmosphere of the Arctic simultaneously. The project allowed several field experiments between 2014 and 2019 using autonomous buoys equipped with atmospheric and oceanic profiling instruments and distributed over the Central Arctic 90 region (Provost et al., 2015). Each floating plaform was locked into the pack ice during several months, left to drift with it and tacked by GPS every day. The buoys were equipped with a micro backscatter lidar shooting in the zenith direction in the near infrared, designed for cloud and aerosol profiling in the lower troposphere (Mariage et al., 2017), surface meteorological sensors on a 502 luft weather station at 2 m, snow and ice temperature profiler (Koenig et al., 2016) and ocean profilers (Provost et al., 2015). Figure 1 presents the tracks of those autonomous platforms and the N-ICE expedition camp site during the field 95 campaign. Lance during the N-ICE field experiment (gray and black symbols) in the North of Svalbard in 2015. In this study, the data from the IAOOS7 buoy (red dotted line) and the leg 3 of N-ICE (triangles) in the springtime period are used.
This study will mostly focus on the lidar measurements acquired from January to June 2015 onboard three buoys during the N-ICE field experiment. They have already been used to investigate the occurrence and distribution of winter to summertime clouds and aerosols in the high Arctic Ocean (Di Biagio et al., 2018Biagio et al., , 2020Maillard et al., 2021). The lidar emits a laser at a wavelength of 808 nm and the field of view of the receiver is ∼ 1.4×10 −6 sr. Measurements were performed 2 to 4 times a day 100 with a 10-minute averaging sequence for each profile. During that interval, the window topping the lidar emitter and receiver was heated to avoid frost deposition. Unfortunately, in wintertime (from mid-December to early March), when temperatures could reach down to 230K, the window heating system was not sufficient, leading to a layer of frost on the top of it that strongly attenuated the lidar signal or even blinded it. As a consequence, data discussed in this study only cover the spring period from April to June 2015 and profiles with attenuated signal by frost (frost index lower than 0.7 as defined by Mariage (2015)) were 105 removed. This corresponds to 20 profiles out of 65 for the 2015 spring period. The approach proposed in this paper relies on the measured solar background B that is calculated as the average raw lidar signal above 20 km, where photons are assumed to be emitted by the sun only, as will be explained in Sect. 3.

N-ICE2015 radiative measurements
As part of the N-ICE campaign that took place from January to June 2015, the research vessel Lance drifted with several floes 110 Cohen et al., 2017), two in wintertime (from January to March) and two from late spring to early summer (April to June) (Fig. 1). Three IAOOS buoys were deployed during this campaign in the northern part of the Nansen basin and drifted in the first three ice floes close to the research vessel. No buoy was deployed during the last floe as it drifted closer to the ice edge (Granskog et al., 2018). Atmospheric observations were mostly performed at a ice camp about 300 m away from the Lance vessel Granskog et al., 2018). Vertical profiles of temperature, relative humidity, and winds were 115 reported twice a day from radiosondes from 16 January to 26 March, and from 17 April to 22 June . In particular, the temperature at two meters, measured with a ventilated and shielded Vaisala HMP-155A sensor, had an accuracy of 0.3 • C (2.4%) Cohen et al., 2017).
Radiative (up and down) fluxes at the surface (∼ 1 m above snow) were measured on all four floes .
and upwelling (F ↑ SW , F ↑ LW ) SW and LW irradiances were measured at 1 min resolution with Kipp & 120 Zonen CMP22 and CGR4 radiometers (having a 200 to 3600 nm and a 4.5 to 42 µm bandwidths, respectively). Their accuracy was 5 W m −2 (∼ 3%) for the SW and 3 W m −2 (∼ 2%) for the LW Hudson et al., 2016). According to the quality flags (QF) classification introduced by Walden et al. (2017), we only considered observations defined as "good data" (QF=0) and selected only days having more than 70% of data with QF=0. Finally, we also eliminated 41 days when the IAOOS buoy (IAOOS7) was too far from the ice camp. This removed a total of 63 days of measurements. The radiative fluxes 125 observed in the spring period (April to June) and used as a reference in this study are presented in Fig. 2.
During the drift, the solar zenith angle θ decreases from 66 • in April to 58 • in June at noon, with a diurnal variation of ∼ 20 • . The SW irradiances F ↓ SW and F ↑ SW present a clear diurnal cycle with minimal absolute values reaching ∼ 80 W m −2 and ∼ 67 W m −2 , respectively (Fig. 2). In springtime, Walden et al. (2017); Cohen et al. (2017) indicated that the meteorological conditions were quite stable and that the surface temperature did not significantly vary. The resulting F ↑ LW was very stable

ERA5 reanalyses
The temperature T c of the cloud at the effective altitude z c of its emission (Sect. 3.3) is determined from the temperature profile obtained from the European Centre for Medium-Range Weather Forecasts Reanalyses v5 (ERA5) (Hersbach et al., 2018). The ERA5 data have a resolution of 0.25 • × 0.25 • and are interpolated at the buoy location. Figure 3 shows a good agreement between the temperature T c obtained from ERA5 reanalyses and measured by radiosoundings during the N-ICE expedition, 140 with Pearson correlation coefficient of 0.95. The ERA5 temperature therefore tends to be a good estimate of T c , even though the simulated values are slightly colder than the N-ICE measurements, a cold bias of −0.3 K and a root mean square error (RMSE) of 1.6 K. In this study, the SW (direct and scattered) radiances and irradiances were calculated with the STREAMER-Version 3 radiative transfer model (Key and Schweiger, 1998) for a wide variety of atmospheric and surface conditions. Calculations are based on the plane-parallel theory of radiative transfer with a discrete ordinate (DISORT) solver. The source code was modified to output the scattered radiance simultaneously with the SW irradiance at the surface. The model was set to have a field of view similar to that of the receiver of the IAOOS lidar. Upwelling and downwelling irradiances were computed over 24 SW 150 bands in the same bandwidth as the one of the pyranometer used during the N-ICE experiment (200 to 3600 nm). We chose snow-covered surface conditions with a visible spectral albedo varying from 0.73 to 0.87. It is in agreement with the values reported by Merkouriadi et al. (2017); Granskog et al. (2018) during the N-ICE campaign, suggesting that the field of view of the upwelling instruments always encompassed a snow-covered sea-ice surface. The vertical profiles of pressure, temperature and humidity were interpolated from the profiles measured by radiosoundings  during the N-ICE field 155 experiment and averaged over spring 2015. Because the Arctic region is typically covered by mixed-phase clouds, representing 80% of the cloud coverage (McFarquhar et al., 2007;Shupe et al., 2011;Morrison et al., 2011), we assumed the presence of mixed-phase clouds in our STREAMER simulations with a cloud optical depth (τ ) varying from 0 (clear sky conditions) to 200 (opaque cloud). Clouds were assumed to have a fixed geometrical depth with base and top at 200 and 800 m above mean sea level, respectively, and to be composed of two cloud layers: a 100 m-width cloud layer composed of 6.9 ± 1.8 µm-diameter 160 water droplets overcoming a 500 m-width cloud layer composed of 25.2±3.9 µm-diameter hexagonal ice crystals, as described by McFarquhar et al. (2007).  level and to be composed of two cloud layers: a 100 m-width cloud layer composed of 6.9 ± 1.8 µm-diameter water droplets overcoming a 500 m-width cloud layer composed of 25.2 ± 3.9 µm-diameter hexagonal ice crystals, as described by McFarquhar et al. (2007). The surface is supposed covered by snow with a albedo of 0.82 in the visible.
values of θ as the sun position is lower over the horizon, and increasing values of τ as the cloud becomes more opaque. L ↓ s also becomes weaker when the sun goes down above the horizon. In contrast, L ↓ s increases with τ as long as τ remains lower than a threshold value τ max (θ), between 1 and 4, depending on the solar zenith angle, and decreases afterwards.

Estimation of the SW irradiance from lidar measurements 170
The total downwelling SW irradiance F ↓ SW can be written as the sum of its direct F ↓ SW,d and scattered F ↓ SW,s components, as a function of the cloud optical depth τ : The direct component is calculated as : where S 0 = 1354.2 W m −2 , C and τ r are the solar constant, the Sun-Earth distance correction factor, and the Rayleigh optical depth of the atmosphere, respectively. τ r is calculated using the vertical profiles of temperature and pressure measured during the N-ICE campaign according to Bucholtz (1995). Similarly, the upwelling SW irradiance is calculated as the reflected SW irradiance by the surface : with α the surface albedo. When the values of τ and θ are known, the scattered downwelling SW irradiance F ↓ SW,s is calculated from STREAMER by integrating the downwelling scattered SW radiance L ↓ s over the solid angle of the upwelling hemisphere ( fig.5). Platt et al. (1998) showed that the measured solar background B obtained from a lidar backscatter signal is proportional to L ↓ s integrated over the solid angle described the field of view of the lidar receptor : The constant K L in W −1 m 2 sr only depends on the instrumental characteristics of the lidar system (Zhang et al., 2018;Mariage et al., 2017;Platt et al., 1998).

Figure 5 presents a comparison between the downwelling scattered SW irradiance and radiance derived from STREAMER
for 6 values of τ . For each value of τ (0, 0.5, 1, 5, 10, 50), a quasi-linear relationship between the F ↓ SW,s and L ↓ s is observed. As a result, the knowledge of the measured solar background B derived from the lidar helps to determine the downwelling scattered SW radiance using Eq. 4 and the corresponding downwelling scattered SW irradiance from the STREAMER simulation (Fig. 5).
This leads in turn to a determination of the total SW irradiances F ↓ SW and F ↑ SW for each value of the solar zenith angle (Eq. 1 and Eq. 3). This approach therefore relies on the knowledge of the cloud optical depth τ and the K L constant.

Estimation of the LW irradiance from lidar measurements
The estimation of the downwelling LW irradiance F ↓ LW is simply obtained from the equation detailed by Minnis et al. (1993): (5) s = 0.98 and a = 0.7 are typical emissivities of the surface and the atmosphere, respectively, representative of the Arctic region (Mariage et al., 2017). T s is the skin temperature of the surface, T 2m the temperature at 2 m and T c the effective temperature of the cloud. Because the approach used here must be independent of N-ICE measurements and as T s and T 2m were not measured in spring 2015 on the IAOOS platforms, values of T s and T 2m are then obtained from ERA5 reanalyses.

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In the absence of cloud (cloud mask c = 0), the downwelling LW irradiance F ↓ LW is simply calculated as the downwelling emission flux from the lowest atmospheric layer. In the presence of a cloud (cloud mask c = 1), F ↓ LW is the sum of two terms: the LW emission of the cloud toward the surface and the reflection by the cloud of the upwelling LW irradiance from the surface F ↑ LW , given by : The cloud emissivity c is assessed as in Minnis et al. (1993): with β 1 = 0.4734 and β 2 = 1.0216. When the cloud optical depth τ is above 3, the cloud is considered to act as a black body, and c = 1. The vertical profiles of temperature obtained from ERA5 reanalyses help to interpolate T c at z c , the effective altitude of the contributed radiation of the cloud. That latter is estimated from the attenuated scattering ratio profiles in the 210 infrared (SR att,IR ). The attenuated scattering ratio SR att derived from the lidar in the visible (808 nm) at range z from the lidar emitter can be expressed as : with β mol the molecular backscatter coefficient and β att the attenuated total backscatter coefficient, linked to the backscatter coefficient β(z) : Previous analyses during the IAOOS campaign used a lidar ratio (extinction-to-backscatter ratio) of S c = 18 sr and a multiple scattering factor η = 0.8 (Mariage et al., 2017). Garnier et al. (2012) estimated the ratio between the cloud optical depths in the visible and infrared domains to be roughly 2. SR att,IR can be therefore be calculated as follows: β is obtained from Eq.9 using a forward inversion (Klett, 1985). In our study, clouds are observed at low altitudes, below 2 km (Fig. 6) and could be co-localized with aerosol layers (Di Biagio et al., 2018).

Results and Discussion
In this section, we present the results of the determination of the cloud optical depth τ and the K L constant required to assess the radiative fluxes from the lidar measurements. The estimation of the SW and LW irradiances is then given and compared to 230 values measured during the N-ICE experiment. The limits of the approach are finally discussed.
4.1 Determination of the cloud optical depth from the radiometers during N-ICE : τ NICE Figure 4 summarizes the values of F ↓ SW and L ↓ s for various values of θ and τ at α = 0.82. Determining the cloud optical depth from the radiative fluxes measured by the radiometers during the N-ICE campaign is relatively straightforward. Since the relationship between F ↓ SW and τ is bijective at a fixed value of θ, τ can be obtained at any instant (or any solar zenith 235 angle value) in springtime by minimizing the absolute differences between the observed and the simulated values of F ↓ SW . This determination is referred to as τ NICE in the following. For each day, the simulated values of F ↓ SW derived from STREAMER have been corrected of the Earth-Sun distance. Figure 6 shows the time series of τ NICE in spring 2015. The temporal evolution of τ NICE confirms that low-level clouds with a large optical depth are very frequent north of Svalbard in spring, as it was discussed by Di Biagio et al. (2020). Their average optical depth is found to be 16 ± 10 and is in agreement with values derived from the 240 ERA5 reanalyses and CERES (Clouds and the Earth's Radiant Energy System) satellite (Di Biagio et al., 2020). On 23 May, clear sky conditions were observed during the whole day . The fact that the optical depth τ NICE is weak (< 0.2) can be explained by the presence of aerosols.
4.2 Relation between the solar background B and the downwelling scattered SW radiance L ↓ s Assessing the cloud optical depth from the IAOOS lidar measurements is more tricky as it requires a series of steps. The first 245 of them is the calculation of the K L constant. This coefficient is the theoretical slope of the linear dependency of the solar background B on L ↓ s (Sect. 3.2), and is a sole function of instrumental and optical properties of the lidar system. An accurate knowledge of the instrumental properties of an autonomous lidar in the Arctic Ocean is however a challenge, not only because there is a limited number of clear-sky days enabling to check the lidar calibration, but also as a frost layer is often deposited on the window of the lidar, disturbing the received signal (Sect. 2.1). We propose here an alternative method to determine the 250 slope K L . The downwelling scattered SW radiance L ↓ s has been calculating using STREAMER with the optical depth τ NICE determined in Sect. 4.1. This method is applied for each measured value of B, giving a total of 20 points. Results are shown in To ensure that the cloud cover is homogeneous in the area observed by the lidar and the radiometers (with different fields of view), a linear regression between B and L ↓ s has been computed only for opaque clouds (Fig. 7). The Pearson correlation coef-255 ficient is found to be 0.97. Since the intercept b is not zero (b = 3143.53), the relation between the measured solar background B and the downwelling scattered SW radiance L ↓ s can be written as : with K L = 118.54 W −1 m 2 sr retrieved from the fitting procedure. The vast majority of the cases with opaque clouds can be correctly represented by this linear relationship. Since semi-transparent and opaque clouds represent about 83% of the cloudy 260 situations met during the drift (Sect 4.1), and because we did not observe any dependency on the solar zenith angle θ to build the  Figure 4 highlights that for a given value of L ↓ s and a known value of θ, there are two possible solutions for the cloud optical depth τ , delimited by the threshold value τ max (L ↓ s ) (Sect. 3.1). Those two solutions correspond a transparent cloud (τ < τ max ) and a semi-transparent to opaque cloud (τ > τ max ). In a similar approach applied on warm mid-latitude continental low-level clouds in ARM Oklahoma, Chiu et al. (2014) proposed a threshold value of τ max = 5. This threshold value is not appropriate here on cold low-level mixed-phase clouds in the Arctic Ocean, as L ↓ s peaks at lower values 270 of τ max between 0.4 and 4 (Fig. 4). To remove this ambiguity, a first guess of the cloud optical depth (τ 0 ) is needed. This latter is inferred from the maximum backscatter coefficient retrieved from the lidar range-corrected vertical profile, as in Di Biagio et al. (2020). In each cloud layer detected between the base z b and the top z t in the visible (similar to the base and top infrared in Sect. 3.3), the first guess of the cloud optical depth τ 0 is simply obtained as : where S c is the lidar ratio in the cloud layer and β max is the maximal value of the backscatter coefficient β within a vertical profile. The limit of that approach is that it permits the determination of τ only when z t can be identified, which generally occurs as long as the cloud optical depth does not reach τ ≈ 3 (Maillard et al., 2021). This approach is therefore not suitable to provide an accurate estimate of τ for opaque clouds, but it offers the opportunity to provide a rough information on the optical properties of the cloud and to determine whether τ IAOOS is larger or lower than the threshold value τ max (θ) seen in Fig. 4.

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Hence, this first guess helps to decide which of the two possible solutions is actually observed, permitting a determination of τ IAOOS from the knowledge of L ↓ s . Figure 6 presents the time series of τ IAOOS and z c in spring 2015. Frequent low-level clouds (below 500 m altitude) with a strong optical depth between 10 and 50 are observed by the IAOOS lidar in spring. The average value of τ IAOOS is 17 ± 8, which is slightly higher than that found using the radiometers as part of the N-ICE field experiment. Clouds are detected in the

Comparison of the values of the cloud optical depth from the two methods
The frequencies of τ NICE and τ IAOOS determined from N-ICE and IAOOS measurements co-localized in time, corresponding to 290 three classes are presented in Table 1. The three categories (transparent, semi-transparent and opaque clouds) are defined from the values of the SW irradiance at θ = 74 • (shown on Fig. 4). Transparent clouds with τ < 0.4 are characterized by a stronger direct SW irradiance then scattered SW irradiance. When τ is comprised between 0.4 and 4, clouds are called semi-transparent.
In this regime, the direct SW beam is reduced and as a consequence the total SW downwelling irradiance is mostly controlled by its scattered component, which is close to its maximum. When τ is above 4 (opaque clouds), the direct SW beam is negligible 295 with a value less then 0.5 W m −2 and F ↓ SW is much less sensitive to changes in the value of τ (Appendix B1). Transparent clouds were not reported in spring 2015, using the observations from the lidar systems as part of the IAOOS campaigns or the observations from the radiometers during N-ICE at the same time as the IAOOS measurements. In contrast, 17% of the cases are classified as transparent clouds using all N-ICE measurements (Sect. 4.1). The whole set N-ICE radiometric data in spring (Sect. 4.1) presents a distribution shifted towards semi-transparent and opaque clouds : 59% of the clouds are classified 300 as opaque clouds and 24% as semi-transparent clouds. The frequency of opaque clouds obtained from N-ICE measurements is similar to the value (60%) estimated by Zuidema et al. (2005) over a period of 10 days in May during SHEBA. Conversely, table 1 shows similar frequencies from the observed clouds for IAOOS and N-ICE taken at the same time, with opaque clouds ∼ 90% of the time and semi-transparent clouds ∼ 10% of the time. Both datasets lead to very similar results with a discrepancy of only 4% (Table 1). Using a direct inversion of the lidar backscatter signals obtained from the IAOOS buoys during all drifts,  is estimated to be 16 ± 10 when N-ICE data are used and 17 ± 8 from the IAOOS lidar observations. The largest differences between the optical depths estimated from the two datasets lead to misclassified cloud types (semi-transparent versus opaque clouds).
The discrepancies between τ NICE and τ IAOOS may be ascribed to two main reasons : a difference in the field of view of the two instruments and the role played by frost deposition on the lidar window. Chiu et al. (2014) also reported a correct representation 315 of the optical depth, but they underlined discrepancies when compared to a radiometer that they attributed to the low field of view of a lidar. The radiometers (pyranometer and pyrgeometer instruments) measure the downwelling irradiances over a full hemisphere (2π sr) whereas the downwelling scattered radiance L ↓ s used to calculate τ IAOOS is derived from the backgound noise observed by the lidar with a narrow field of view of 0.67 mrad (∼ 3.5 × 10 −7 sr) (Mariage et al., 2017). The instruments are close to each other (distance lower than < 300 m). Hence, heterogeneous structures of a cloud may lead to differences in the 320 observed irradiances by the various instruments. Because of its very narrow field of view and since clouds are often detected in the lowest layers of the troposphere, the lidar can only detect an homogeneous portion of a single cloud. Radiometers used during the N-ICE campaign however sample a very broad area of the sky that may encompass clear sky zones and multiple inhomogeneous clouds. Notwithstanding, visual inspection during the campaign mostly revealed homogeneous cloud conditions observed during the spring period , as as a consequence this hypothesis is likely insufficient 325 to explain all differences between τ NICE and τ IAOOS . The observed discrepancy may also be due to the formation of frost on the window of the receptor system. Signals obtained whit a frost index lower than 0.7 have been discarded, but frost may cover a smaller fraction of the receptor window and strongly attenuate the intensity of the signal, underestimating the solar background. In turn, L ↓ s derived from Eq. 11 may also be underestimated. According to Fig. 4, this underestimation of the downwelling radiances caused by the deposition of frost on the lidar window would be compensated (at a constant solar zenith 330 angle) leading to an overestimation of the cloud optical depth.

Estimation of F ↓ SW and F ↓ LW irradiances
The determination of the cloud optical depth from the measured solar background of the lidar (Sect. 4.3) enables to calculate F ↓ SW,s (τ IAOOS , θ) using STREAMER and finally F ↓ SW (τ IAOOS , θ) from Eq. 1. This downwelling SW irradiance F ↓

SW, IAOOS
is further compared to that directly measured by the radiometers as part of the N-ICE 2015 campaign (F ↓ SW, NICE ). The esti-335 mated uncertainty on F ↓ SW, IAOOS is ±4% (Appendix A). The comparison and differences between those two downwelling SW irradiances are reported in Fig. 8a and b. Figure 8a generally highlights a good agreement between the estimated F ↓ SW, IAOOS and the measured F ↓ SW, NICE irradiances, with a Pearson correlation coefficient of 0.96. The methodology introduced here to estimate the SW irradiances from the measured solar background of the IAOOS lidar therefore reproduces the SW irradiances directly measured by radiometers with 340 an uncertainty close to 9 W m −2 (Appendix A). The absolute differences between F ↓ SW, IAOOS and F ↓ SW, NICE are represented in Fig. 8b. These results highlight a small mean bias of −3.7 W m −2 , even though strong discrepancies are observed for a few outlier showing an absolute differences of 50 W m −2 . The downwelling LW irradiance is estimated using the methodology described in Sect. 3.3. In particular the IAOOS lidar measurements help to determine the cloud mask c, the effective altitude of the cloud z c (Sect. 3.3) and the optical depth of 345 the cloud τ IAOOS (Sect. 4.3). That latter is used to determine c through Eq. 7 and finally the downwelling LW irradiance F ↓ LW,IAOOS thanks to Eq. 5. This radiative flux is then compared to the downwelling LW irradiance F ↓ LW,NICE directly measured by the pyrgeometer during the N-ICE campaign. The results are shown in Fig. 9a. The estimated uncertainty on F ↓ LW, IAOOS is 9 W m −2 (Appendix A).
A fairly good correlation is obtained between the estimated F ↓ LW,IAOOS and the measured F ↓ LW,NICE LW irradiances, with a 350 Pearson correlation coefficient of 0.98. The differences, shown in Fig. 9b, are always lower than 12 W m −2 , with a corrigible residual bias of 3 W m −2 . The approach relying on IAOOS lidar observations to derive LW downwelling irradiances, provides a good estimation of the fluxes within an uncertainty range of 9 W m −2 .

Discrepancies of F ↓ SW and F ↓ LW irradiances
The absolute differences between the estimated and measured SW irradiances ∆F ↓ SW as a function of the absolute difference 355 between τ IAOOS and τ NICE are shown in Fig. 10a. ∆τ decreases monotonically with ∆F ↓ SW : when the optical depth is over-estimated (resp. underestimated), the downwelling SW irradiance is underestimated (resp. overestimated). A decrease in the downwelling scattered SW irradiance associated to a larger optical depth indeed leads to an underestimated total downwelling SW irradiance. In our study, as cloud optical depths are always large (τ IAOOS > 3), F ↓ SW,s therefore depends linearly on L ↓ s (Fig. 5). The values of L ↓ s used in Fig. 7 to obtain Eq. 11 were retrieved from STREAMER assuming that clouds have an optical 360 depth equal to τ NICE (Sect. 4.2). The absolute difference ∆τ is thus directly linked to the differences between the regression line and the L ↓ s values obtained from STREAMER at τ NICE on Fig. 7, confirming the decreasing trend observed in Fig. 10a. Actually, according to Fig. B1, F ↓ SW varies linearly with the logarithm of the cloud optical depth ; hence the relationship between the relative error on τ and the absolute error on F ↓ SW is quasi-linear. Frost deposition on the lidar window and the difference in the field of view of the two instruments are the two main reasons explaining the discrepancies between τ IAOOS and τ NICE (sect. 4.4), 365 which in turn are responsible of the differences between F ↓ SW, IAOOS and F ↓ SW, NICE . The cloud properties (type and size of particle, geometrical height, etc) do not participate in the observed discrepancies since both τ IAOOS and τ NICE are estimated from the same modeled mixed-phase cloud. Some of the outliers, represented on Fig. 8b and Fig. 10a are characterized by strong differences between F ↓ SW, IAOOS and F ↓ SW, NICE that can reach ±50 W m −2 . They cannot be explained by frost deposition on the window, as solar background signals significantly attenuated by frost have been removed (frost index lower than 0.7). On the 370 contrary, the fact that the two instruments (lidar and radiometer) with different fields of view see distinct atmospheric scenes, as suggested in Fig. 7, leads to differences between τ IAOOS and τ NICE (Fig. 10a). As a result, an underestimation (resp. overestimation) of F ↓ SW, IAOOS is observed as soon as ∆τ > 0 (∆τ < 0). Outliers are represented by strong absolute differences of ∆τ = 11 and ∆τ = −22. When those outliers are excluded from the analysis, our methodology based on IAOOS lidar measurements provides good estimations of the SW irradiances with a mean bias of −1.5 W m −2 . However, due to the difference 375 in the observed atmospheric scenes, the RMSE ≈ 24 W m −2 is larger than the uncertainty of the determination of F ↓ SW, IAOOS (9 W m −2 , Appendix A). A longer lidar sequence acquisition time could possibly smooth out cloud heterogeneity and improve the determination of F ↓ SW . Maximum discrepancies between the estimated and the measured LW irradiances can reach 12 W m −2 (Fig. 9b). The fact that all LW irradiance values reported on Fig. 9a are larger than 230 W m −2 suggests that the lidar system detected 380 clouds (c = 1) for the entirety of the spring period (Table 1). Equation 5 shows that T s has therefore a very limited role on the determination of F ↓ LW,IAOOS . Hence the differences between the estimated and measured fluxes can be explained by two possible factors : either by errors in the optical properties of the clouds detected by the lidar (τ IAOOS ) or by an incorrect estimation of the cloud temperature T c . The cloud optical depth drives the emissivity of the cloud c . Since, the lidar detected almost exclusively opaque clouds (Table 1), clouds are considered as black bodies on 93% of the cases and c = 1. The error that would be caused 385 by an incorrect determination of the cloud optical depth is very weak: the distribution of τ IAOOS in Table 1 reveals that 7% of the clouds have an optical depth lower than 4. Even when τ IAOOS ∈ [0.4, 4], remains close to 1 and the LW irradiance is not terribly modified. Figure 10b confirms that the discrepancy on the optical depth ∆τ does not significantly modify the downwelling LW irradiance. Only small differences in the temperature at cloud height between ERA5 and the N-ICE radiosoundings at cloud height were noticed (Fig. 3). Those discrepancies are characterized by a mean bias of −0.3 K and a RMSE of 1.6 K. The 390 only significant cause of the discrepancies between F ↓ LW,IAOOS and F ↓ LW,NICE is thus the effective altitude of the cloud z c that drives the effective temperature of the cloud T c . During the spring period, we estimated an average value of T c 261 ± 5 K.
The effective temperature of the cloud T c is however very sensitive to the altitude of the cloud z c , which may present spatial heterogeneities. A difference of ∆z c = 200 m leads to ∆T c = 2 • C and, in turn, to a variation of ∆F ↓ LW = 4 c σT 3 c ∆T c ≈ 8.7 W m −2 on the downwelling LW irradiance. The net SW F net SW and net LW F net LW irradiances are calculated as the difference between the downwelling and the upwelling irradiances. Using Eq 3 and Eq 6, F ↑ SW,IAOOS and F ↑ LW,IAOOS are both estimated with uncertainties of 9 W m −2 (Appendix A). The absolute difference ∆F net SW between the estimated net SW irradiance and its counterpart observed during the N-ICE experiment are represented in Fig. 10c. ∆F net SW presents a mean bias of −1 W m −2 and a RMSE of 5 W m −2 , within the 400 uncertainty range of the method developed here to estimate the SW irradiances. The relationship between ∆F net SW and ∆τ follows the same tendency than that previously discussed for ∆F ↓ SW in Sect. 4.5. ∆τ decreases monotonically with ∆F net SW . An underestimation of F net SW,IAOOS is observed when ∆τ > 0 and, in contrast, an overestimation is seen when ∆τ < 0. The discrepancy between the estimated and measured net irradiances is systematically lower than ∆F ↓ SW discussed in Fig. 10a, even for the outliers. It suggests that the differences between the estimated and measured upwelling components ∆F ↑ SW partly 405 compensate the differences on the downwelling irradiances ∆F ↓ SW . An overestimation (resp. underestimation) of F ↓ SW, IAOOS over F ↓ SW, NICE leads to a quasi-proportional overestimation (resp. underestimation) of F ↑ SW,IAOOS over F ↑ SW,NICE . The surface albedo is supposed to be very similar on the locations of the two instruments and, consequently, the difference on ∆F ↓ SW is partly canceled out by a proportional difference on ∆F ↑ SW . This approach enables to estimate the net SW irradiance from solar background measurement by a lidar with an uncertainty lower than 13 W m −2 , in good agreement with the net SW irradiance 410 observations from the N-ICE experiment, with a Pearson correlation coefficient of 0.95.
Conversely, the absolute differences on the net LW irradiances ∆F net LW (Fig. 10d) are higher than the absolute differences on the downwelling irradiances ∆F ↓ LW discussed in Sect. 4.5. The mean bias on ∆F net LW is 2 W m −2 and the associated RMSE is 5 W m −2 . The absolute differences are mostly positive and may reach 11 W m −2 , indicating that F ↑ LW,IAOOS ≤ F ↑ LW,NICE , which partly compensate ∆F ↓ LW . The discrepancies on the cloud optical depth ∆τ do not affect the net LW irradiance, since all 415 clouds are opaque or semi-transparent with τ IAOOS above 3, acting as black bodies. In addition, the 2-m air temperature does not either play any role on F net LW,IAOOS given that episodes of clear sky were never observed by the lidar (Eq. 5). The surface emissivity is not sufficient to explain the underprediction of F ↑ LW,IAOOS . The only possible explanation is due to errors on the skin temperature. The skin temperature taken from the ERA5 reanalysis may be colder than the actual skin temperature. A difference of ∆T s = 2 • C leads to a difference on the upwelling LW irradiance of 9 W m −2 . The uncertainty on F net LW caused 420 by the use of the ERA5 reanalysis does not exceed the uncertainly range of 13 W m −2 (Appendix A). This approach provides a reasonable estimate of the net LW irradiance from temperature and lidar measurements with a Pearson correlation coefficient of 0.7.
Both the net SW and LW irradiances are well reproduced when using the IAOOS lidar measurements. The total net irradiance (F net SW + F net LW ) can be similarly determined from lidar measurements. A fairly good agreement (not shown) with the total net 425 irradiance (SW+LW) measured during the N-ICE campaign is found, with a mean bias of −0.5 W m −2 and a RMSE of 8 W m −2 .

Conclusions
To complete the need for more data on the Arctic atmosphere beyond 80 is even more shifted toward opaque clouds: τ NICE and τ IAOOS present very similar frequencies of 89% and 93% for opaque clouds and 11% and 7% for semi-transparent clouds. The small differences between τ NICE and τ IAOOS can be ascribed either to frost formed on the window of the receptor or to differences in the atmospheric scenes seen by the two instruments (lidar and radiometer) having different fields of view.
The downwelling SW irradiance is assessed from the solar background measured by the IAOOS lidar with an uncertainty of 9 445 W m −2 . Discrepancies noted between the two instruments are linked to their different fields of view so that distinct atmospheric scenes are observed or to frost forming on the window of the lidar. An overestimation (resp. underestimation) of τ will lead to an underprediction (resp. overprediction) of the downwelling SW irradiance. The net SW and LW irradiances are finally estimated with an uncertainty lower than 13 W m −2 . The net SW irradiance assessed from the lidar measurements is reproduced with a lower bias (−1 W m −2 ) and lower RMSE (5 W m −2 ) than its downwelling component (mean bias of −1.5 W m −2 and RMSE of 24 W m −2 ). Indeed discrepancies on the downwelling SW irradiance are partly compensated by proportional differences on its upwelling counterpart (due to the surface albedo). The upwelling LW irradiance is assessed from the skin temperature of ERA5, which may be colder than the actual skin temperature.

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The resulting net LW irradiance is partly overestimated, with a mean bias of 2 W m −2 and a RMSE of 5 W m −2 . Measuring the skin temperature on the IAOOS buoy (not available in spring 2015) could improve the upward LW irradiance, as well as the net LW irradiance. The net SW and LW irradiances retrieved from the IAOOS lidar observations are in agreement with the measured values during the N-ICE field campaign in spring 2015.
This promising approach to estimate the downwelling, upwelling and net SW and LW irradiances from lidar measurements 465 on drifting buoys together with radiative model calculations will be further applied to 6 years of measurements in the High Arctic region. This will provide the key components of the radiative budget on ice surfaces. Efforts are nevertheless needed to better correct the solar background measured by the lidar when frost is deposited on the receptor window in order to increase the number of observations.
Code and data availability.  Hudson et al. (2016) and Walden et al. (2017) estimated a measurement error on the downwelling SW irradiance of ∆F ↓ SW = 5 W m −2 on the radiometer observations. The uncertainty on the downwelling SW scattered radiance can be calculated as ∆L ↓ s = ∆B K L using Eq. 11, where ∆B = 810 is the uncertainty on the solar background noise. We therefore estimated ∆L ↓ s = 6.75 W m −2 sr −1 . According to Fig. 4, the resulting uncertainties on the optical depth were assessed to ∆τ m NICE = 0.14 and ∆τ m IAOOS = 0.35.

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To assess the influence of the surface and cloud parameters used in our reference simulation (Fig. 4), we performed sensitivity tests of the dependence of F ↓ SW and L ↓ s on the surface albedo, the cloud phase, and the size of the hydrometeors (cloud droplets and ice crystals). A total of 54 simulations were run : the solar zenith angle was set to a constant value of 74 • , with different values for the surface albedo (0.78, 0.82, 0.86), the type of hydrometeors inside the first layer (plate-like or column-like ice crystals), the diameter of ice crystals (21.3 µm, 25.2 µm and 29.1 µm) and the diameter of water droplets (5.1 µm, 6.9 µm and 490 8.7 µm). In each sensitivity test, the minimization of the absolute differences between the observed and modeled values of the irradiances or radiances lead to an estimation of τ . The Root Mean Squared Error (RMSE) of the optical depth between those 54 sensitivity tests and the reference simulation (presented in Fig. 4)  Applying the variance formula on Eq. 5 enables to compute the uncertainty on the downwelling LW irradiance ∆F ↓ LW,IAOOS . In cloudy situations, representing all cases during the drifts of the IAOOS buoys during spring 2015, it can be written as : The global uncertainty on the downwelling LW irradiance is therefore ∆F ↓ LW,IAOOS = 9 W m −2 . Finally, using Eq. 6, the 515 uncertainty on the upwelling LW irradiance can be simply written as ∆F ↑ LW,IAOOS = 4 s σT 3 s ∆T s = 9 W m −2 .
Appendix B: Definition of cloud types Figure B1 shows the direct and scattered downwelling SW irradiance computed using the STREAMER radiative transfer model at a solar zenith angle θ = 74 • for different values of τ . Three categories of clouds (transparent, semi-transparent and opaque clouds) are defined according to the values of the downwelling SW irradiance. Transparent clouds with τ < 0.4 are character-520 ized by a larger direct SW irradiance than its scattered counterpart. When τ is comprised between 0.4 and 4, clouds are called semi-transparent. In this regime, the direct SW beam is reduced and as a consequence the total SW downwelling irradiance is mostly controlled by its scattered component, which is close to its maximum. When τ is above 4 (opaque clouds), the direct SW beam is negligible with a value less then 0.5 W m −2 and F ↓ SW is much less sensitive to changes in the value of τ .  Competing interests. The authors declare that they have no conflict of interest.