The observations analyzed in this study were performed during PASCAL , which took place in the sea-ice-covered area north of Svalbard in summer 2017. The RV Polarstern carried a suite of remote sensing and in situ instrumentation. Additionally, an ice floe camp was erected in the vicinity of the ship . describe the synoptic situation during the operation of the ice floe camp as climatologically warm with prevailing warm and moist maritime air masses advected from the south and east. The meteorological conditions were influenced by a high-pressure ridge east of Svalbard. The present study is based on measurements with instruments carried by the tethered balloon system BELUGA Balloon-bornE moduLar Utility for profilinG the lower Atmosphere; . BELUGA was launched from the sea ice floe at around 82∘ N, 10∘ E in the period of 5–14 June 2017. The balloon measurements are complemented by radiosoundings launched every 6 h and by ship-based remote sensing observations from a vertical-pointing, motion-stabilized cloud radar , a lidar , and a microwave radiometer of the OCEANET platform , which were processed with the synergistic instrument algorithm Cloudnet .

The observational basis for this study is a persistent layer of increased specific humidity above a single-layer stratocumulus deck during the period between 5 and 7 June 2017. Figure  illustrates the temporal development of the vertical specific humidity profile derived from radiosonde measurements. Cloud top and bottom and the time–height curves of the corresponding BELUGA flights are added for the investigated period. The BELUGA flights were conducted around noon on each of the three consecutive days. A local maximum of specific humidity is observed above the cloud top throughout almost the entire period, with a slight diurnal cycle peaking at noon and a maximum specific humidity on 6 June. It is worth noting that the observations show a well-defined layer of increased specific humidity, hereafter referred to as the humidity layer, rather than a distinct and sharp SHI with only a slight decrease above.

The cloud top and base height in Fig.  are estimated from the cloud radar and lidar (near-field channel) data, averaged over 30 s and with a vertical resolution of 30 m. Throughout the 3 d period, cloud height and thickness decrease to a minimum at noon of 6 June and thereafter increase again. The cloud is almost permanently of mixed-phase type with a maximum liquid water content (LWC) between 0.15 and 0.6 gm-3 and an estimated ice water content (IWC) of about 0.03 gm-3 derived from Cloudnet data (not shown here).

Figure  depicts the high variability in cloud top and bottom heights. To illustrate the cloud situation around the BELUGA flights in more detail, Fig.  shows the radar reflectivity and cloud boundaries for the particular three balloon flights. On 5 June, the cloud top height is approximately constant, whereas on 6 June the cloud top fluctuates between 350 and 230 m in the course of the flight. During the 7 June flight, the cloud layer thins by 110 m starting from the cloud top.

The BELUGA system consists of a 90 m3 helium-filled tethered balloon with a modular setup of different instrument packages to explore the ABL between the surface and 1500 m altitude. BELUGA can operate under cloudy and light icing conditions in the Arctic. Fixed to the balloon tether, a fast (50 Hz resolution) ultrasonic anemometer, supported by an inertial navigation system, measures the wind velocity vector in an Earth-fixed coordinate system together with the sonic temperature. Especially at low specific humidity, the sonic temperature is close to the virtual temperature, which will be used in the following. Furthermore, barometric pressure, relative humidity, and the static air temperature are measured with lower resolution (1 Hz). Relative humidity (RH) is measured with a capacitive humidity sensor. The housing of the RH sensor, which has a high diffusivity for water vapor, also accommodates a temperature sensor for the sensor-internal temperature. The air temperature is measured with a PT100 for reference and a thermocouple for temperature fluctuations (at 50 Hz). A second instrument payload is fixed simultaneously to the tether, measuring broadband terrestrial and solar net irradiances. Technical details on BELUGA, its instrumentation, and operation during PASCAL as well as data processing methods are given by .

Several studies address the associated systematic errors of radiosonde RH and T measurements and identify three main sources, (i) wet-bulbing, (ii) solar heating, and (iii) time response errors: i.

Wet-bulbing occurs when a water film develops on the sensor during cloud penetration, with subsequent evaporative cooling under sub-saturated conditions above the cloud. This effect leads to an overestimation of RH and underestimation of T in the sub-saturated environment until the water film has completely evaporated. show that wet-bulbing is an issue for the radiosonde type used during PASCAL. However, the error induced by wet-bulbing is difficult to quantify .

Although radiosonde data processing routines consider the time response error, fast humidity changes in cold conditions are still affected . The time constants for the BELUGA RH sensor were estimated in a laboratory study (see Appendix ) and are τRH≈50 s for RH and τTs≈70 s for the internal temperature. The time constant for the T measurements based on the thermocouple on BELUGA was found to be below 1 s and, thus, has a minor influence on the vertical temperature profile compared to the humidity observations.

We perform sensitivity studies to analyze how the three error sources (cf. Sect. ) for T and RH measurements combine and influence the derivation of q. The errors are simulated as T and RH deviations from a synthetic reference case (grey line in Fig. ), which represents a simulated measurement of a temperature inversion combined with a decrease in RH. The temperature linearly increases by 6 K in the 200 m thick inversion layer, whereas RH linearly decreases from 100 % to 40 % in the same height range, resulting in monotonically decreasing specific humidity without a SHI.

First, we consider the influence of possible measurement errors in the temperature inversion region for the T and RH sensor separately. That is, only one sensor will be influenced by an increased or decreased signal while keeping the other sensor reading at the reference value.

The magnitude of the simulated deviations (Fig. a and b) is arbitrary, but the qualitative profile of the affected signal is according to the error sources, as discussed in Sect. .

The effect of the four errors (T or RH too high or too low in the temperature inversion region) on the specific humidity profile is shown in Fig. c. An artificial humidity layer above the cloud can emerge when the RH sensor overestimates the moisture due to wet-bulbing (but keeping the temperature sensor unaffected), or when the temperature sensor is heated in the inversion region but the humidity sensor is unaffected. Vice versa, q shows a deficit compared to the reference when one of the sensors indicates underestimated values compared to the reference scenario. If a single phenomenon affects both the temperature and RH sensor (e.g., solar heating results in underestimated RH and overestimated temperature), the errors in the determination of q have an opposite effect and, therefore, the overall error in q is reduced.

As a second step, we simulate the influence of different time constants τRH and τT for the RH and temperature measurements. If both time constants have similar values, the resulting q does not change significantly in magnitude, but the vertical structure shifts upwards or downwards for an ascent or descent. With a slow-response RH sensor (τRH≫τT), the measured RH in the SHI region is overestimated on the ascent and underestimated on the descent with the effects on q as shown in Fig. c and with an artificial SHI on the ascent.

As a result of these sensitivity studies, the error in q is reduced when both the temperature and humidity sensors are affected by the same error source (e.g., solar heating on both sensors), and when both sensors have comparable time constants. Under these conditions, a detected SHI can be considered as most likely real and does not need to be interpreted as an artifact.

A simple and convincing test of the possible influence of the error sources on the SHI observations is profiling in opposite direction, that is a descent from the free troposphere through the SHI into the cloud layer. This is commonly impossible in case of standard radiosoundings, but feasible for the BELUGA observations. Figure  shows vertical profiles of RH, T, and q as measured by radiosounding and BELUGA on 5 June 2017. Qualitatively, the measurements of both platforms show a similar vertical structure with a sharp temperature inversion capping the cloud layer. The cloud top (estimated from the observed downward terrestrial irradiance) is situated close to the temperature inversion base. However, the cloud top height derived from radiation observations should be treated with caution due to the vertical separation of the radiation and thermodynamic sensors by about 20 m, corresponding to a temporal shift between the observations of about 20 s during profiling. In the course of the measurement period of almost 2 h, the temperature inversion base and the cloud top remain at almost constant altitude. The radiosonde observation shows a layer of increased q between 400 and 550 m altitude just above the temperature inversion base. The increased specific humidity emerges from RH remaining high within the temperature inversion, before decreasing to the free troposphere level well above the inversion base.

Before comparing the q measurements from the radiosonde to BELUGA observations, we illustrate the effect of the applied RH correction and the consequences for the q profile. Figure a shows the uncorrected and time-response-corrected RH for an ascent and descent. The uncorrected RH ascent profile deviates strongly from the descent in the cloud top region. While descending through the cloud, the sensor requires a 150 m height difference for rising from 55 % to 95 % RH. The RH hysteresis around the cloud top is visible as a systematic deviation in all observed flight data (not shown). A comparison to Fig.  (orange lines) suggests that the major part of the error is due to a slow RH sensor. Furthermore, the sensor underestimates RH in the cloud on the descent, which might indicate solar heating. After applying the time lag correction, the RH profile shows a significantly reduced difference between ascent and descent. The remaining difference is qualitatively consistent with the temperature observations as shown in Fig. b. The temperature profiles show a warming of the cloud top and inversion region between 300 and 500 m during the descent leading to a reduced RH.

The “uncorrected” specific humidity in Fig. c is calculated from the uncorrected RH and the temperature measured with the fast-response thermocouple. The resulting q profiles show a SHI on the ascent and the descent of the BELUGA flight with a similar structure and location compared to the radiosonde data. The q profile as observed during the descent is shifted to lower q values in the region of the hysteresis of the uncorrected RH.

The corrected q results from the RH and the sensor-internal temperature Ts after correcting both signals for the time lag error according to Eq. (). We argue that using Ts should be preferred instead of the thermocouple readings because RH and Ts have similar time constants, and RH is measured at Ts instead of the temperature of the atmospheric environment. The ambient temperature and Ts differ slightly due to the thermal inertia of the sensor housing.

After applying the corrections, the maximum value of the SHI, as observed during the BELUGA ascent, is reduced by about 0.6 gkg-1 compared to the uncorrected q maximum. After correction, all BELUGA profiles and the radiosonde data exhibit the SHI with similar structure and amplitude. This consistency suggests that the observed SHI is a natural feature instead of an instrumental artifact. We can exclude wet-bulbing as the main reason for the observed SHIs because the SHI is also present during the descent. The influence of solar heating and time-lag errors is minimized. Our conclusion also strengthens the confidence in SHIs as frequently observed by radiosondes.

Throughout the observation period, we observe a persistent layer of increased specific humidity above the cloud layer. One of the governing questions of this analysis is to understand how observed SHIs relate to the general ABL structure and, in particular, to the temperature inversion. Figure a and b shows vertical profiles of potential temperature θ and specific humidity q recorded in the period of 5–7 June 2017. Both parameters are normalized to their near-surface values and plotted in relation to the base height of the temperature inversion zi. The cloud boundaries are shown in Fig. c for reference.

All measurements show a similar vertical structure of θ within the ABL. Below the temperature inversion base zi, the stratification is near-neutral to weakly stable. Above the inversion, the thermodynamic stability is higher and exhibits more variability compared to below the inversion. No systematic difference between ascents and descents is visible. The ABL is thermodynamically coupled to the surface, which makes normalizing to surface values meaningful.

Within the mixed layer below zi, specific humidity decreases slightly with height but increases when reaching zi. Above zi, the normalized specific humidity exhibits more variability compared to the normalized temperature. The descent of 7 June 09 h shows a temperature inversion with some internal structure in the form of two smaller “steps” in θ. We define zi at the lower step, with the SHI base being located clearly above at the upper step at z≈1.2⋅zi. For this case, a deficit in q is observed below the SHI, which is plausible because between ascent and descent cloud top had decreased to about 0.95⋅zi.

For most profiles, the cloud top coincides with zi, and the increased humidity is observed above the cloud layer. Only for two profiles (both descents on 5 June), the lower bound of the SHI is already located below the cloud top. We do not find clouds penetrating into the temperature inversion, although such situations have been frequently observed in previous studies e.g., . However, two of the descent profiles (6 June 09 h and 7 June 09 h) show situations where the cloud top had decreased between ascent and descent, and the SHI is vertically separated from the cloud top.

The cloud top variability, here defined as the cloud top height difference between ascent and subsequent descent for each profile, is related to zi and the lower boundary of the SHI. For all 3 d, a descending cloud top is observed between the ascent and subsequent descent with a cloud top height difference of 50 to 100 m. This cloud top variability is indicated by in situ irradiance and thermodynamic measurements and also confirmed by radar reflectivity (cf. Fig. ). In order to illustrate the relation of cloud top height, SHI, and other ABL parameters, Figs. – show profiles of mean θ, RH, q, downward terrestrial irradiance Fterr↓, horizontal wind velocity U, and Richardson number Ri as measured during ascents and descents on 5, 6, and 7 June, respectively. We analyze only continuous profile data without longer breaks at certain heights for the first profile of each day. The cloud top height is defined by the discontinuity of the Fterr↓ profile and marked with horizontal lines, whereas zi is indicated with triangles. The Richardson number is the ratio between thermodynamic stability and wind shear and, therefore, a measure for the ability of turbulence generation (Ri ≲ 1) or dissipation (Ri ≳ 1).

On 5 June (Fig. ), zi lowers from 430 to 380 m in the course of the BELUGA flight. The temperature difference across the inversion of Δθ≈9 K, which is also the strongest observed during our flights, stays constant during ascent and descent. The RH decreases within the temperature inversion, accompanied by an increase in q above zi of about 0.25 gkg-1 (ascent) and 0.5 gkg-1 (descent). The radiosonde, launched around 2 h prior to the BELUGA flight, shows a higher zi but qualitatively a similar vertical structure of θ, RH, and q. The cloud top agrees well with zi for the ascent and descent. The horizontal wind velocity U is around 2 ms-1 inside the cloud layer and decreases to 1 ms-1 in the free troposphere, resulting in horizontal wind shear. During the ascent, the wind shear zone is clearly located below zi with a sudden increase in Ri to values greater than 1 above zi and cloud top. During the descent, the strongest wind shear is observed around zi, and the resulting increase in Ri is slightly above zi. This vertical shift suggests a slightly stronger turbulent coupling between cloud top and the SHI above, as compared to the ascent.

The general ABL structure observed on 6 June (Fig. ) in terms of the profiles of θ, RH, and q is quite similar to the 5 June observations, showing a decreasing cloud top height during the balloon operation. Here, zi decreases from 290 m during the ascent to about 230 m during the descent. The radiosonde, launched 1.5 h after the BELUGA flight, shows a similar zi to the balloon ascent, indicating that zi and cloud top recover between BELUGA descent and radiosounding. This is in agreement with the radar observations in Fig. . The lower bound of the SHI with Δq≈0.3gkg-1 on the ascent and 0.7 gkg-1 on the descent is coupled to zi in both cases. On the ascent, zi coincides with the cloud top. During the descent, the cloud top is almost 20 m below zi, which could possibly result from cloud top heterogeneity. However, the temperature gradient is smoother compared to the ascent, which leads to a less clear determination of zi. The humidity structure above the cloud layer observed by the radiosonde exhibits a distinct SHI with a lower bound coupled to the temperature inversion. Peak values of q are comparable with BELUGA observations made during the descent. The horizontal wind velocity is about 5 ms-1 and almost height-constant for the entire ascent but increases by about 2 ms-1 inside the cloud layer during the descent. The radiosonde provides a similar picture to the balloon descent. For the ascent, the sharp increase in Ri is connected to zi, whereas for the descent this increase in Ri is – similar to the previous day – about 20 m above cloud top, allowing for some turbulent exchange between the cloud and the SHI above.

On 7 June, a clear SHI develops with a lower boundary at around 580 m, which is similar in the two BELUGA and the radiosonde profiles (Fig. ). For the BELUGA ascent and the radiosonde profile, this boundary agrees well with zi and cloud top (for the radiosonde data cloud top can be roughly estimated from the RH profile). The radiosonde profile and BELUGA ascent are shifted in time by about 70 min and the remarkable match in zi should not be over-interpreted. For the BELUGA descent, the thermal stratification changes again (similar to the previous days). The temperature inversion weakens and zi is shifted downward by about 110 to 480 m, together with the cloud top. Thus, the cloud top and the SHI base are separated by 110 m on the descent. The terrestrial irradiance inside the cloud layer fluctuates strongly, especially on the descent, which suggests a patchy cloud with cloud holes. The horizontal wind velocity agrees qualitatively for all three profiles. Inside the ABL, a higher wind velocity of around 6 ms-1 is observed with the BELUGA observations, showing a local maximum of 8 ms-1 slightly below zi. Above this maximum, U gradually decreases to 2 ms-1 in the free troposphere. According to the Richardson number, wind shear limits turbulence above the cloud top for both ascent and descent.

To resume, we observed mean profiles of several cases where cloud tops coincide with zi and the SHI base. Although some cloud tops show more or less strong horizontal wind shear, the stabilizing effect of the temperature inversion leads to a sudden increase in Ri just above the cloud layer, which suggests a rather low turbulent exchange with the humidity layers above. However, for one case a special situation provides a new aspect of this phenomenon: zi and cloud top height had decreased while the humidity layer remained at its vertical position, leading to a humidity gap between cloud top and SHI.

To get an insight into the transition from cloud top to the humidity layer above, measurements were taken at a constant height in the temperature inversion region. Figure  shows a 500 s time series measured on 6 June at a constant altitude around zi≈300 m (second last constant altitude segment in Fig.  for 6 June). The local dissipation rate ε is evaluated in 2 s segments to illustrate the evolving turbulence intensity.

Within the first third of the record, the virtual potential temperature θv (as approximately measured by the ultrasonic anemometer) shows strong variations on a typical timescale of 30–50 s with amplitudes up to 3 K. Based on the temperature gradient (Fig. ), the changes in θv would correspond to a height variation of ∼10m. More likely, parts of the height-constant measurements (Δz≈1 m) are taken in potentially colder, drier, and more turbulent air masses at the inversion base, interrupted by measurements in potentially warmer, more humid, and less turbulent air masses at higher altitudes well within the T inversion. This variability is also visible in the wind direction (not shown here). Depending on the relative location of zi to the measurement height, the co-variance w′θv′ is highly intermittent and no mean flux is derived from these observations.

The center part of the record is characterized by a comparably low variability leading to the conclusion that this part of the observations is performed entirely inside the descending temperature inversion. Finally, observations are performed well above zi inside the stably stratified T inversion layer, characterized by values of ε 1 order of magnitude lower compared to at the inversion base. Here, variations in θv and q are again correlated and caused by changes in relative height.

The observations do not allow for drawing quantitative conclusions, such as time and area-averaged turbulent heat fluxes, from this record. However, these measurements vividly illustrate the difficulties in estimating turbulent fluxes based on covariance methods in the vicinity of the temperature inversion, although the measurement height is kept at a remarkably constant height level. Therefore, the methods for estimating turbulent fluxes based on mean vertical gradients and slant profiles are more suitable for this study and are used below.

The vertical distribution of turbulence parameters, such as local dissipation rate ε and the turbulent kinetic energy TKE, provide an insight into the coupling between the cloud layer and the SHI. The local ε values are derived from second-order structure functions by applying inertial subrange scaling as described by . Different from that study, here ε is calculated from non-overlapping, 2 s sub-records yielding a vertical resolution of about 2 m. Regions without inertial sub-range scaling are excluded. Turbulent kinetic energy (=0.5⋅ui2) is calculated in a moving 50 s window. The observed TKE noise level is about 0.005 m2s-2 and is usually reached at z/zi ≳ 1.1.

Figure  shows ε and TKE for each first profile of 5, 6, and 7 June as a function of normalized height (the descent of 5 June is excluded due to data issues). The cloud and humidity layers are shaded for reference. For the presented cases, turbulence is most pronounced in the upper cloud layer and around cloud top with typical values of ε∼10-3 m2s-3 and TKE ∼ 0.02 m2s-2. For 5 and 6 June, the turbulence intensity is rather constant in the cloud. For 7 June, with increased wind velocity, a maximum of ε is evident just below cloud top.

Figure  also illustrates how the SHI and cloud layer are either separated or overlap, and how they are connected by turbulent motion. At a certain height level, ε decreases to the low-turbulence free-troposphere level. The transition is gradual, indicating turbulent mixing in this region. On 5 June and the ascents of 6 and 7 June, the SHI and the cloud are directly coupled by turbulent mixing. For the descents of 6 and 7 June, most of the mixing takes place at the interface of the cloud top with the humidity gap between cloud and SHI. In this case, inside the SHI the turbulence intensity is reduced almost to the free-troposphere level and the SHI seems to be decoupled from the cloud layer via the humidity gap in between.

We can only speculate about the reason for the development of this humidity gap, which is most pronounced for the descent of 7 June. One explanation could be long-range advection of increased moisture in the free troposphere combined with a temporary collapse of the well-mixed cloud layer leading to a vertical separation of cloud top and SHI. However, this interesting feature leads to new research questions that require further observations and a more detailed LES analysis.

The turbulent exchange of moisture can be quantified by the latent heat flux 4L=ρ‾⋅Lv⋅w′q′‾, whereas the virtual sensible heat flux is given by 5H=ρ‾⋅cp⋅w′θv′‾, with an overline describing an average of the sub-record. Here, ρ‾ is the mean air density, Lv=2.5×106Jkg-1 is the latent heat of evaporation, and cp=1005 Jkg-1K-1 is the specific heat capacity of air. This direct calculation of H and L requires sufficient long, stationary, and homogeneous records in a certain height to provide time-averaged estimates of the covariances with statistical significance . Our observations focus mainly on vertical profiling, and only a limited number of height-constant records around the cloud top and inversion region are available. As shown in Sect. , the conditions around the temperature inversion are highly instationary and, thus, we use the vertical profiles to study the fluxes in this region. We apply two approaches for estimating fluxes from vertical profiles: (i) describing the flux profile by applying the so-called “slant profile method” and (ii) relating the turbulent flux to mean gradients (flux gradient method).

The slant profile method is based on the assumption that for a certain height range the profile data are considered as a homogeneous record and Eq. () can be applied. For this method, instantaneous values of H are estimated for a defined height range, defining also the length scales contributing to the flux. For our observations, this method provides only results for H due to the lack of fast-response humidity measurements. Alternatively, L can be estimated with the flux gradient method. This method is based on the relation between the covariances and the mean gradients of θv and q: 6w′θv′‾=-KH⋅∂θ‾v∂z, and 7w′q′‾=-KQ⋅∂q‾∂z, with KH and KQ being the turbulent exchange coefficients for sensible and latent heat, respectively. The coefficients are defined as positive, which means that the flux is directed against the mean gradient. Values of K can be derived from parameterizations based on turbulence observations such as proposed by or by directly applying Eq. () with the measured H, yielding KH. With KQ≈KH for a wide range of stratification and the mean humidity gradient ∂q‾/∂z, we estimate L by combining Eqs. () and ().

Before estimating H from the slant profiles by applying Eq. (), the turbulent fluctuations must be determined. This is done by applying a high-pass filter of Bessel type with a filter window of 10 s, corresponding to a horizontal length scale of about 10 to 70 m (depending on the horizontal wind velocity) and a vertical length scale of about 10 m. After filtering, the fluxes are averaged over a moving 50 s window by applying Eq. (). The filter and averaging windows are similar to the values proposed by and , who estimated turbulent fluxes from aircraft-based slant profiles.

Figure  shows five selected cases (cf. Fig. ) with profiles of H based on the slant profile method and L based on the flux gradient method. The upper part of the cloud layer is mainly characterized by an upward-oriented heat flux (H>0), most pronounced for the last two profiles with a local maximum between 0.8<z/zi<1. Only for the first ascent of 5 June is the H flux almost height-constant with much lower values compared to the other days. For this day, θv exhibits larger variability around and slightly above zi, which differs from the typical structure of a turbulent flow. This variability mainly causes the positive values of H around zi, which, therefore, should not be misinterpreted. This is a similar effect to that discussed in Sect. . A negative peak of H around or slightly above zi is visible for the descent of 6 June and both profiles of 7 June. On 7 June, a secondary, weaker negative peak in H is located at the lower part of the SHI.

Although it is known that in general K=K(z), we estimate a constant KH for each ascent and descent in the lower region of the SHI, which is the focus area of our study. In that region, we observe negative H fluxes and positive θv gradients. Applying Eq. () leads to mean values of KH between 0.001 and 0.004 m2s-1 for the five profiles. The KH(=KQ) values for each profile are used for calculating the L profile based on the flux gradient method.

A negative peak in L is observed for all days in the lower SHI region. The downward energy flux at cloud top is common for the entrainment region, where potentially warmer and usually drier air from the free troposphere is mixed downward into the (cloudy) ABL. However, for our observations, this downward flux in the lower SHI region means a downward transport of potentially warmer but more humid air into the region below. The situation is different for the descent profile of 7 June, with the vertical humidity gap between cloud top and SHI. Here, the negative peak in L at the lower SHI is accompanied by a positive L at cloud top. This profile does not suggest a significant transport of humidity into the cloud top. Instead, for the special case where the cloud and the SHI are separated, the gap in between receives moisture from both the SHI above and from the cloud layer below.