Flow over a snow-water-snow surface in the high Arctic, Svalbard: Turbulent fluxes and comparison of observation techniques

From observations in a High Arctic valley and ice-free fjord in Svalbard during March and April 2013 we show that, while some caution needs to be applied, ordinary slow-response instruments placed over a snow-water-snow surface can be effectively used as a proxy for more sophisticated measuring techniques at complex sites such as leads or a polynyas. The turbulent fluxes of momentum, sensible and latent heat were measured at three locations with a snow-water-snow fetch. At the snow site upwind of the water, the stability was generally stable, the momentum flux small, and the sensible heat flux positive. Over the water however, the internal boundary layer that was formed gave on average an increased vertical gradient in wind speed, temperature, and humidity and turbulent heat fluxes exceeding 400 W m (cid:0) 2 . At the snow surface downwind of the water, the conditions were highly variable and all the fluxes were, on average, of very small magnitude. That the behaviour of the internal boundary layers can be highly variable is demonstrated through four case studies. This phenomenon is likely to increase in occurrence with a changing climate.


Introduction
The sea ice cover in the Arctic is generally highly variable in terms of amount, size, and thickness.Openings, such as leads and polynyas can give rise to very large heat fluxes from the water to the atmosphere.Despite covering only a few percent of the Arctic Ocean, leads are thought to contribute with approximately 50% of this regions sensible heat flux to the atmosphere (e.g., Ruffieux et al., 1995).Moreover, polar regions are one of the most affected areas of the ongoing climate change with consequences for physical processes as well as biological systems (e.g., AMAP, 2011;Førland et al., 2011;Walsh et al., 2011).As Taylor et al. (2018) point out, air-sea exchanges are becoming increasingly important in a thawing Arctic.
Regardless of their importance, direct observations in the Arctic are generally rare and observation campaigns short due to the challenging environmental conditions (e.g.severe weather conditions, logistical problems, or the lack of a power supply).Measurements over leads and polynyas possesses particular challenges since the size of the open water can change rapidly (e.g., Cottier et al., 2010) making the deployment of instrumentation somewhat demanding.Even if numerical models have increased in reliability (e.g., Renfrew and King, 2000;Esau, 2007), the need for more in-situ measurements still exists by which to populate and validate the models.Therefore, simple measuring techniques and cheap instrumentation that can be left unattended for long periods are required for better understanding of the processes.
Several of the first reports of successful measurements over leads and polynyas came in the 1970s-1980s (e.g., Andreas et al., 1979;Smith et al., 1983;den Hartog et al., 1983).Since then, both measuring techniques and a deeper understanding of the physical processes have been developed and Morales Maqueda et al. (2004) and Vihma et al. (2014) presented thorough reviews of the current state of knowledge.The increased use of aircraft (e.g., Tetzlaff et al., 2015) and icebreakers (e.g., Brooks et al., 2017) have made it possible to take observations from large ice-covered areas.In addition, the use of remote sensing observations is also growing (e.g., Cristóbal et al., 2017) as a method to attain longer measurement time series.There are also examples of longer surface based observation campaigns on sea-ice, for example the one month period in 1992 where instruments were deployed over a lead in the Arctic during the LEADEX project.Or, the SHEBA experiment in the Canadian Arctic 1997-1998(e.g., Persson et al., 1997;Pinto et al., 2003;Andreas et al., 2010a;Andreas et al., 2010b) that is still considered to be one of the finest datasets available.
Observations in High Arctic fjords, i.e., the transition between the open ocean and land, is an alternative way to understand air-ice-sea interaction processes since the meteorological instruments can be deployed on land with a fetch over snow, ice, or open water depending on the specific focus.In addition, monitoring of the instruments will be simpler, which makes this an attractive choice of method especially for gathering long-term measurements (e.g., Kilpeläinen and Sjöblom, 2010;Mäkiranta et al., 2011;Kral et al., 2014;Fortuniak et al., 2017).However, these High Arctic fjords are usually surrounded by high mountains that introduce other phenomena such as the channelling of wind, pressure driven circulations, or other topographical effects.Despite this, and with some caution, the Monin-Obukhov similarity theory (e.g., Obukhov, 1971) can be applied in High Arctic fjords, both for air-sea interaction (Kilpeläinen and Sjöblom, 2010;Kral et al., 2014) and air-ice interaction (Mäkiranta et al., 2011).
We here investigate flow over a High Arctic valley and ice-free fjord in Svalbard during two winter months.Three stations were deployed along a transect, one upwind of the water with a snow fetch, the next with an ice-free water fetch, and the final one downwind of the water and again with a snow fetch (Fig. 1).This snow-water-snow fetch can in some aspects be considered as a proxy for a lead or a polynya, while taking into consideration that the observations are in a valley and a fjord.Emphasis is given to how the turbulent fluxes change with respect to changing surface conditions, both in general during a two-month campaign in spring 2013 but also in more detail in four case studies representing "typical" spring cases.
The eddy-covariance method (ECM) could only be used at the station over water, so in order to obtain comparable results from all three stations the gradient method (GM), which uses slow-response measurements at two arbitrary levels, was instead selected to calculate the fluxes.This method has previously been shown by Sjöblom (2014) to work satisfactory over a tundra surface in Svalbard, especially for the momentum flux.Sjöblom (2014) therefore concluded that the GM can be used to estimate turbulent fluxes when the ECM is not available.The ECM can be quite challenging to apply in polar regions due to the requirements of a stable platform and power supply, homogeneous conditions, and that the instrumentation itself is delicate.Hence, the GM might be an appropriate alternative for long term measurements at remote locations in the Arctic.Since Sjöblom (2014) only had measurements over land, the ECM and GM were here first compared over water before applying to all three stations.
The analysis is based on the same set of observations as Andersson et al. (2017) and Andersson et al. (2019) who focused on the flux of CO 2 and sensible heat in the unstable very close to neutral conditions (UVCN).Section 2 defines some of the theory and is followed by a description of the observations and data handling given in Section 3. The results from the comparison of methods, the flow over snow-water-snow, and four case studies are then presented in Section 4 and finally a discussion with conclusions in Section 5.

Theory
Two methods have been used to determine the turbulent fluxes: the ECM and the GM.The ECM use fast-response instruments to measure turbulent heat fluxes and the momentum flux (or stress), τ (N m − 2 ).τ is calculated as: where ρ is the density of air (kg m − 3 ), u, v, and w the velocity in the along, across, and vertical directions (m s − 1 ), u'w' and v ' w ' the kinematic momentum fluxes (m 2 s − 2 ), and u * the friction velocity (m s − 1 ).The vertical fluxes of sensible (H S ) and latent (H L ) heat (positive upwards) are given by: where c p is the heat capacity of air (J kg − 1 K − 1 ) and L e the latent heat of evaporation (J kg − 1 ).w'θ' (m K s − 1 ) and w'q' (m kg s − 1 kg − 1 ) are the kinematic heat and moisture flux respectively.The GM, by contrast, only requires slow-response measurements of the gradients of wind speed, U (m s − 1 ), potential temperature, θ (K), and specific humidity q (kg kg − 1 ): z 1 and z 2 are arbitrary measuring heights, k the von Karman constant, equal to 0.40 (Högström, 1996), and φ m , φ h , and φ q the non-dimensional gradients of wind speed, temperature, and humidity A. Sjöblom et al.
θ * and q * are characteristic temperature and humidity scales.The non-dimensional gradients are dependent on the atmospheric stability (or stratification) L is the Obukhov length (m), w'θ ' v is the virtual kinematic heat flux (m K s − 1 ), closely connected to the heat flux measured by a sonic anemometer (Sjöblom and Smedman, 2002), g the acceleration due to gravity (m s − 2 ), and T 0 a reference temperature for the surface layer (K).φ m (z/L), φ h (z/L), and φ q (z/L) can be determined experimentally and, in the GM, the φ-functions from Högström (1996) were used: For z/L < 0 and for z/L > 0 z/L is connected to the Richardson number, Ri, another measure of stability, where the bulk Richardson number Ri B , can be used as an approximation of Ri (Arya, 2001): with Δ-values determined directly between two arbitrary levels and valid at the geometric mean height z m = (z 1 z 2 ) 1/2 .For stable conditions (0 ≤ Ri ≤ 0.2), Arya (2001) suggested while for unstable conditions (-z/L < 0.5), Högström (1996) suggested

Observation and data handling
The observation campaign took place outside Longyearbyen in the Svalbard archipelago (78 • 13 ′ 3.79 ′′ N 15 • 38 ′ 49.11 ′′ E, Fig. 1) between early March and late April 2013.Situated in the High Arctic, about 60% of Svalbard is covered with permanent snow or ice and permafrost occurs throughout the archipelago, Longyearbyen has a long period of polar night but also midnight sun between 19 April and 23 August.However, from 2 April the sun is never far under the horizon and there is technically no night period.The observation campaign therefore covers the transition period from a normal day and night cycle to when the sun is permanently above the horizon.The fjords around Longyearbyen have a seasonal ice cover, but the amount of ice varies from year to year and Isfjorden is often considered to be a large-scale polynya (Nilsen et al., 2008).In 2013, both Adventfjorden and Isfjorden were mainly ice-free.Three sites were employed and designated: Adventdalen, Adventpynten, and Vestpynten (Fig. 1).The three stations are located along a south-east to north-west transect along the Advent valley and to the fjords, Adventfjorden adjacent to the larger fjord, Isfjorden.The area is surrounded by mountains with maximum heights varying between 600 and 900 m above sea level resulting in the wind being usually channelled and giving local wind directions that are either north-westerly or south-easterly.The main focus is on winds from the south-east, i.e., that the air will travel through the Advent valley over snow covered land, then passing over mostly ice-free water for approximately 4.5 km before approaching land again.The situation is hence somewhat analogous to a large lead in sea ice.
The measurements at Adventpynten are thoroughly described in Andersson et al. (2017) and Andersson et al. (2019) and consisted of one tower with slow-response instruments measuring wind (R.M. Young Windmonitor JR.R.M. Young Co., Traverse, MI, USA), temperature and relative humidity (HygroClip, Rotronic Instrument Corp., Hauppauge, NY, USA) at 0.5 m and 4 m heights with 1 Hz.A second tower was established with an eddy-covariance system installed at 3 m height measuring the three wind components, sonic temperature (Sonic anemometer CSAT3, Campbell Scientific North Logan, UT, USA), humidity, and CO 2 (LICOR-7500A, LI-COR Inc., Lincon, NE, USA) with 20Hz.The measurement heights were corrected for sea level variations in the fjord with tidal variations of approximately 1 m in amplitude.A temporary station at Vestpynten was deployed with an identical setup of slow-response instrumentation with a land fetch of approximately 3.5 km from Adventpynten for south-easterly winds.Adventdalen is a permanent station over land in the Advent valley measuring at two heights (1 Hz): wind speed and wind direction at 2 and 10 m (Alpine Wind Monitor model 05103-45, R.M. Young Co., Traverse, MI, USA), and temperature (naturally ventilated model 41342 Platinum Temperature Probe, R.M. Young Co., Traverse, MI, USA) and relative humidity (HygroClip, Rotronic Instrument Corp., Hauppauge, NY, USA) at 2 and 9 m.For more details on the instruments at Adventdalen, see Sjöblom (2014).
The data was averaged into 30-min means and, to avoid instrument uncertainties at low wind speeds, only measurements with U > 2 m s − 1 have been analysed.Further, threshold differences between the measuring levels (slow-response instruments) were applied: 0.1 m s − 1 for U, 0.1 • C for θ, and 1% for relative humidity (RH).It should, however, be noted that these values are still close to the accuracies of the instrumentation which might affect situations with small gradients.A double rotation procedure (Lee et al., 2004) was performed on the sonic anemometer data and spikes were removed according to Vickers and Mahrt (1997).The gas analyser data was screened for periods with icing (Andersson et al., 2017) and obvious periods with icing on the other instruments have also been removed.The vapour pressure used to determine q from the slow-response instruments was calculated from RH with respect to water at Adventpynten and to ice at Adventdalen and Vestpynten following Andreas et al. (2002).Since Eq. ( 7a) is not valid for very stable cases, cases with Ri B > 0.2 had to be disregarded.

General weather
The observation campaign was characterised by typical Svalbard weather as seen in Fig. 2 where the time series of standard meteorological parameters and Ri B at the three stations are presented.In Table 1, the average values for March and April are shown for all wind directions as well as wind directions only with the snow-water-snow fetch.Note that the values for Adventdalen in March are only based on a few measurements mainly due to technical problems.Further, to have a more representative value of Ri B , and avoiding spikes, the median was calculated instead of the mean.The difference between the median and the mean for the other variables was very small.In some periods, especially in the beginning of the campaign, ice floes came drifting into Adventfjorden.The fjord was completely ice covered on 9 March but the ice disappeared again on 11 March (Andersson et al., 2017).A second period with drift ice occurred from the 18 March to 20 April.Except for these days, the fjord can be assumed to be mainly ice free.However, there were some periods with new frazil ice forming in the water creating a mushy surface layer that was not visible to the eye but which may have affected the observations.
The temperature varied between day and night (Fig. 2a), especially at Adventdalen and the temperatures at all stations were normally well below zero with a minimum of approximately − 25 • C.Although these low temperatures are not considered to be unusual for Svalbard weather this time of the year, March and April 2013 were overall colder than average.This can be seen by comparing the monthly averages at Vestpynten, − 16.9 and − 11.  (1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000) at the nearby Svalbard airport (Førland et al., 2011).The wind speed (Fig. 2b) was relatively high despite the temperature being low.Wind speeds (30-min average) of up to 15 m s − 1 occurred on a couple of occasions and the wind was generally following the contours of the valley and fjord, with the wind coming from the valley towards the fjord (south-easterly winds) (Fig. 2c).The wind speed was higher in March than in April with the greatest average values at Adventpynten, especially over the snow-water-snow fetch (6.7 and 5.2 m s − 1 for March and April).The relative humidity (Fig. 2d) usually varied between 50 and 100% due to the cold conditions and was quite similar at all three stations.The specific humidity however was greater at Adventpynten due to the upwind water fetch (Fig. 2e).The Ri B (Fig. 2f) was largely on the stable side at Adventdalen, close to neutral at Adventpynten, and fluctuating with both stable and unstable stratification at Vestpynten.
The difference between data from all wind directions and data with only the snow-water-snow fetch was generally small (Table 1).The greatest differences are that the wind speed was slightly higher and the temperature a couple of degrees lower for the snow-water-snow fetch.At the end of the measuring campaign, a very warm air mass arrived bringing temperatures above zero, high wind speeds, and a great increase in specific humidity (Fig. 2).This resulted in that the station at Adventpynten lost its anchoring, blew down, and that the measurements had to be terminated.

Comparison of observation techniques
Since both fast and slow response instruments were deployed at Adventpynten, the completely independent observation techniques ECM (Eq.( 1)) and GM (Eq.( 2)) could both be applied and compared using the two different sets of instruments.Only measurements with an upward water fetch of more than two km were used in order to avoid the influence of land and/or flow distortion, corresponding to wind from the sector 90 • -130 • (Andersson et al., 2017).Further, negative H L,ECM have been removed since they can most likely be attributed to icing on the sonic anemometer and the gas analysers sensors and not a physical reality (e.g., Fortuniak et al., 2017).However, there may still be some values remaining that are affected by icing, especially early in the campaign (Andersson et al., 2019).
In Fig. 3, the time series of τ, H S , and H L for both the ECM and GM are shown.The two methods are directly compared in Fig. 4, and in Fig. 5 where the differences between the two methods are presented as functions of Ri B , wind speed and temperature.In both figures the data are displayed as March and April.The ECM and GM follow each other for all fluxes, but as seen in Figs. 4 and 5, there are some systematic differences.τ (Fig. 3a) follows the wind speed (Fig. 2b) clearly but τ GM has a magnitude of 64% (median) greater than τ ECM and a correlation between τ GM and τ ECM of 0.71 (p < 0.001).The difference between the two methods increases with increasing τ and, as shown in Figs.4a, 5a and 5b, the greatest differences therefore occur at close to neutral stability and high wind speeds.The dependence on the temperature (Fig. 5c) is much smaller.This difference is greater than that which Sjöblom (2014) reported over land in summer at Adventdalen and where τ GM was on average only 5% greater than τ ECM .Since the fetch over water is limited to a couple of km, the discrepancy might partly be explained by a reduction in the wind speed closest to the surface when the air is passing from the smooth snow-covered land to the rough water surface.This transition into an internal boundary layer will then reduce the wind

Table 1
Mean values of wind speed (U), wind direction (WD), temperature (T), relative humidity (RH), specific humidity (q), and the median bulk Richardson number (Ri B ) at Adventdalen (AD), Adventpynten (AP), and Vestpynten (VP) for March and April.All is all data and SWS data with the snow-water-snow fetch.Values in parenthesis are the number of 30-min periods that were used for the calculation.speed at the lowest level thereby causing an increase in the wind speed gradient and hence an increase in τ GM .Andreas et al. (1979) found a similar decrease in wind speed over an Arctic lead.Further, they also concluded that increased turbulence over water will lead to an acceleration of the wind at greater altitudes which will give rise to an even larger wind speed gradient.Since the wind speed gradient is directly employed in the GM it is likely to have an impact on the results.H S (Figs. 3b and 4b) was mostly positive (i.e.upward flux) for both methods with some values well over 400 W m − 2 .There were a few occasions where H S,GM went above 500 W m − 2 and even up to almost 600 W m − 2 , but H S,ECM were smaller at the same time.H S,GM and H S,ECM follow each other with a correlation coefficient of 0.67 (p < 0.001).
Contrary to τ, H S,GM is instead smaller than H S,ECM with a median of 58 W m − 2 .As seen in Fig. 5d, e, and 5f, this offset is almost constant, although there are some major differences for very low temperatures and neutral conditions.An offset of 58 W m − 2 is much greater than Sjöblom (2014) found over snow-free tundra (approximately 20 W m − 2 ).Andersson et al. (2019) showed enhanced heat fluxes when conditions were close to neutral but remained slightly unstable, using the same data.These enhanced heat fluxes were explained by eddies originating from the top of the boundary layer bringing colder and drier air downwards.Hence, the heat fluxes cannot be explained by classical surface layer theory, and are therefore not captured by the GM.There are also some cases (12%), and particularly in March, where the two methods gave different signs of H S which is likely to happen when the temperature gradient is very small and close to the accuracy of the instrument.H S,ECM is almost − 200 W m − 2 on a few occasions and, since it is unlikely to observe such great negative values over open water, it is probable this could have been caused by icing on the sonic anemometer that was not captured by the initial screening and which adds to further uncertainty.
H L (Figs. 3c and 4c) was of the same order of magnitude as H S on average, but only went above 200 W m − 2 on a few occasions for both methods.However, there are some cases where H L,ECM is well above 200 W m − 2 , especially in March.As Andersson et al. (2019) pointed out, icing on the gas analyser was frequent during the early periods of the campaign and can have been present more frequently than the initial screening captured and thereby affecting H L,ECM .Although the data is scattered (correlation 0.51, p < 0.001), H L,GM is only approximately 3 W m − 2 greater than H L,ECM as a median value.As seen in Fig. 5g, the scatter is again greatest at close to neutral conditions, but, as for τ, it also has as a dependency on the wind speed with H L,ECM > H L,GM for low wind speeds and H L,GM > H L,ECM for high wind speeds (Fig. 5h).Furthermore, the scatter increases for temperatures below − 15 • C (Fig. 5i), and hence also the icing, indicating the difficulty to measure H L with great accuracy at low temperatures.
The difference between the ECM and the GM is also visible when examining the φ-functions.In the GM (Eq.( 2)) the φ-functions suggested by Högström (1996) are used (Eq.( 5)), but since both fast-response and slow-response instruments are available here, the φ-values can also be directly determined from Eq. (3) using u * , θ * , and q * from the fast-response instruments and the gradients of U, θ, and q from the slow-response instruments.Fig. 6 shows the φ-values divided into March and April as a function of z/L calculated in two ways.In Fig. 6a, c, and 6e z/L is determined directly from the fast-response instruments (Eq.( 4)), while in Fig. 6b, d, and 6f, z/L is indirectly determined from Ri B (i.e. the slow-response instruments, Eqs. ( 6) and ( 7)) in the same manner as it is calculated in the GM.Högströms φ-function curves are also shown as gradient and therefore that τ GM is greater than τ ECM .For φ h (Fig. 6c and   d), the directly measured values are instead too low compared to Högström, while for φ q (Fig. 6e and f), they are scattered above and under the curve which corresponds to the behaviour of H S and H L in Fig. 4.That the two ways of determining z/L give slightly different results reflects the differences seen in the turbulent fluxes (Figs. 3 and 4).Further, the z/L GM have some negative values that are not seen in z/L ECM .
Nevertheless, Kilpeläinen and Sjöblom (2010) reported the opposite behaviour of φ m and φ h from a large ice-free High Arctic fjord, i.e. that observed values of φ m were lower than Högströms curve and φ h were greater.They also concluded that the scatter in the φ-values was great and a dependence on the shape and the size of the fjord could be seen.This can explain why the φ-values seen at Adventpynten with its much narrower fjord and shorter water fetch are different from a larger fjord.This of course will add to the uncertainties of using the GM under these conditions.
To conclude, the difference between the ECM and the GM was greater over this ice-free water surface than that which has been found over land.Although the ECM is often considered to be the most accurate method, the fast-response instruments are also the most sensitive and uncertainties due to, for example, icing on the instruments, can have contributed to the differences.However, despite these differences, the two methods follow each other and it is therefore suggested that the GM can be used to, at least generally, determine the turbulent fluxes, while remembering that there are uncertainties involved in the GM as discussed above.

Flow over the snow-water-snow surface
Since ECM was only conducted at Adventpynten, the GM was the only option to determine turbulent fluxes from all three stations.In order to investigate the flow over the snow-water-snow surface, only measurements when the stations were parallel with the air flow were used, i.e. when the wind was coming from south-east.Table 2 shows the mean values for Ri B , τ, H S , and H L for the two months and Fig. 7 the time series of τ, H S , and H L .Note that the scales for Adventpynten and Adventdalen/Vestpynten are different.The time series of Ri B can be seen in Fig. 2f.Further, in Fig. 8, the Ri B and the fluxes from the different stations are plotted against each other.As discussed previously, there were limitations in the calculations for the most stably stratified values  3) as a function of z/L determined directly from the fast-response instruments (a), (c), and (e) (Eq.( 5)), and from the bulk Richardson number (Ri B , Eqs. ( 6) and ( 7)) (b), (d), and (e).(a) and (b) φ m , (c) and (d) φ h , and (e) and (f) φ q .The black lines are the φ-functions suggested by Högström (1996), which are used in the GM (Eq.( 5)).(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Table 2
Mean values of the bulk Richardson number (Ri B ), momentum flux (τ), sensible heat flux (H S ), and latent heat flux (H L ) at Adventdalen (AD), Adventpynten (AP), and Vestpynten (VP) for March and April (GM).Values in parenthesis are the number of 30-min averages used for the calculation.Only data with Ri B < 0.2 are included (see Eq. ( 7)).(Eq.( 7)).This means that the values in Table 2 are only based on Ri B < 0.2 which, of course, makes the average values biased, particularly for Adventdalen which had the most stable stratification.
Over the first snow surface upwind of the water, Adventdalen, stable conditions prevailed with Ri B well above zero both in March and April.τ was small on average and it was only during the high wind speeds 16-17 April that it went above 0.25 N m − 2 peaking at approximately 0.40 N m − 2 (Fig. 7b).The low τ is consistent with the smooth snow surface at Adventdalen and similar values have been found over snow covered sea ice (e.g.Andreas et al., 2010a).H S was always negative (i.e.directed downwards) and usually varied between − 50 and 0 W m − 2 , but had a greater magnitude during 16-17 April (Fig. 7d).Unfortunately, only one humidity sensor functioned at Adventdalen so no humidity gradients could be determined and, hence, no H L calculated.Moreover, there were some technical problems in March thereby limiting the amount of data collected.
Both the temperature and the wind speed increased on average as the air from Adventdalen passed over the water and reached Adventpynten (Fig. 2, Table 1).As discussed earlier, an internal boundary layer formed when the air left the snow-covered land surface and, on average, the stability went from stable to unstable (although very close to neutral) as indicated by Ri B (Table 2, Fig. 8a).Even so, there were some cases where the stability remained on the stable side also at Adventpynten although the magnitude was greatly reduced.Even though it was previously shown that τ GM was greater than τ ECM at Adventpynten, it is still clear that τ is almost 10 fold greater than at Adventdalen (Fig. 8c).This can partly be explained by the higher wind speed but also the increased wind speed gradient due to the rougher water surface as discussed earlier.
Since the stability changes sign, H S also changes direction from downwards to upwards (Figs.7c and 8e) due to the relatively warm water surface enhancing the turbulence and a large heat transfer from the water to the cold air (Andersson et al., 2019) leading to some values well over 400 W m − 2 .The greater turbulence over the water can also be seen from H L (Fig. 7e) which was of the same magnitude as H S (Table 2).The difference between H S and H L is smaller than Andreas et al. (1979) who reported that H S was two to four times larger than H L over an Arctic lead.
After the air passed Adventpynten, the surface returns to snowcovered land and a new internal boundary layer was formed before the air reached Vestpynten.The temperature and wind speed decreased again, although not to as low values as upwind of the water at Adventdalen (Fig. 2a and b).This also means that the stability was, on average, very close to neutral (Table 2) with both negative and positive, sometimes great, values of Ri B (Fig. 8b).τ was again small and comparable to that of Adventdalen (Figs. 7b and 8d) and H S (Figs. 7d and 8f) decreased to values close to zero (Table 2).Nevertheless, the small values of H S show that the distance between Adventpynten and Vestpynten (about 3.5 km) was not enough to transform the convective internal boundary layer seen at Adventpynten into a fully stable boundary layer as observed at Adventdalen.H L also decreased from Adventpynten to Vestpynten (Fig. 8g) and, although there are no values from Adventdalen to compare with, the magnitudes are consistent with what can be expected for a snow surface (e.g., Westermann et al., 2009;Grachev et al., 2017).It should also be noted that there were some technical problems also at Vestpynten, especially in the second half of March, where no data was received.

Four case studies
To further emphasise the transition snow-water-snow, four "typical" 6-h examples (i-iv) of the gradients of U, θ, and q are shown in Fig. 9 and the corresponding mean meteorological variables and turbulent heat fluxes for the three stations are presented in Table 3.
Case (i): 5 March 18.00 to 24.00 was a period early in the campaign (Fig. 9a, e, 9i), characterised by strong easterly large-scale winds.This was caused by a high pressure north-west of Svalbard and a low pressure to the south-east, bringing cold air to the archipelago.The wind was channelled in Adventdalen making the local wind direction between south and south-east and with wind speeds between 5 and 10 m s − 1 .This was also one of the colder periods in the campaign with temperatures between − 30 • C and − 20 • C. Starting with a relatively high wind speed of approximately 9 m s − 1 at Adventdalen, the wind speed decreased to approximately 8 m s − 1 over the water before reaching Adventpynten.The wind speed gradient was, however, greater at Adventpynten than at Adventdalen which is consistent with the rougher water surface as A. Sjöblom et al. discussed earlier and is further evident from the increase in τ (from 0.13 to 0.43 N m − 2 ).The air is also warmed and the moisture increased as it passes over the relatively warm water, and θ increased by about 2 • C and q by ca 0.25 g kg − 1 .This also influenced the stability which went from stable (Ri B = 0.09) at Adventdalen to slightly unstable (Ri B = − 0.04) at Adventpynten and H S changed from a strong downward flux (− 47 W m − 2 ) to a very strong upward flux (215 W m − 2 ).H L was much smaller than H S at Adventpynten which can also be seen in the small gradient of q.When the air reached land again after Adventpynten, the wind speed increased due to the smooth snow surface and at Vestpynten θ and q had decreased to similar values as at Adventdalen.However, the stability did not go back to a stable stratification but remained on the unstable side close to neutral (Ri B = − 0.01).The unstable stratification is also seen in both H S and H L which decreased to 44 and 14 W m − 2 respectively over the snow.It should, however, be noted that the average wind direction at Vestpynten was not in a perfect line from Adventpynten and may therefore also contain some flux from the nearby water surface.Nevertheless, the fetch over land seems to be long enough to influence the absolute values of U, θ, and q, but insufficiently great to revert the gradients back to their snow equivalent at Adventdalen during this cold period.
Case (ii): the second selected period, 9 April 00.00 to 06.00 (Fig. 9b, f, 9j), was also a cold period but a month later than (i), meaning that the sun was higher above the horizon during the day and twilight was the darkest period during the night.Svalbard was again situated between a high and a low pressure which produced cold large-scale winds from the north a few days before (ii), although the wind speeds were lower than in (i).During period (ii), the wind had just turned and stabilized to a south-easterly direction.The wind speed at Adventdalen was approximately 3 m s − 1 .The windspeed at the lowest level over water at Adventpynten remains very similar to the windspeed at the lowest level at Adventdalen (snow fetch).This indicates that the water surface was not as rough as in (i), but rather that its roughness was similar to that of snow.The wind speed at the highest level at Adventpynten, however, increased, resulting in a steep wind speed gradient and therefore producing some of the greatest values of τ of the campaign (0.86 N m − 2 on average).This larger increase in wind speed with height probably comes from the increased turbulence following the great difference in temperature between the water and the air (around 25 • C) making the air at higher altitudes accelerate.The air was also warmed by about 5 • C during this process and the stability changed from stable to slightly unstable.Both H S and H L at Adventpynten were very high (289 W m − 2 and 78 W m − 2 ) compared to case (i).As a comparison, H S,ECM during case (ii) was 203 W m − 2 .Unfortunately, no H L,ECM could be determined at the exact same time, but is in the order of 50-100 W m − 2 just before and afterwards.When returning to snow after Adventpynten, the flow adjusted back to slightly stable stratification at Vestpynten with a small downward H S (− 8 W m − 2 ).H L also decreased compared to Adventpynten, and was only 2 W m − 2 on average at Vestpynten.Further, since the temperature differences between air and land were greater and the wind speed lower than in (i), the internal boundary layer over land after Adventpynten had sufficient time to adjust back to the stable side before reaching Vestpynten but the stable boundary layer was not as fully developed as at Adventdalen.
Case (iii): 17 April 00.00 to 06.00 (Fig. 9c, g, 9k) was one of the windiest periods of the campaign.This originated from a low pressure situated south-east of Svalbard giving a relatively high large-scale wind speed from the east.At Adventdalen, wind speeds of up to 15 m s − 1 (30min average) were observed.The wind speed gradient was also large, resulting in a greater τ than earlier (0.34 N m − 2 ).Despite the windy conditions, the temperature was still fairly low at approximately − 13 • C. The high wind speeds also resulted in a stability closer to neutral than in the previous cases, but on average it was still on the stable side (Ri B = 0.03) at Adventdalen.Passing over the water, the wind speed stayed

Table 3
Mean values of wind direction (WD), wind speed (U), temperature (T), relative humidity (RH), specific humidity (q), bulk Richardson number (Ri B ), momentum flux (τ), sensible heat flux (H S ), and latent heat flux (H L ) at Adventdalen (AD), Adventpynten (AP), and Vestpynten (VP) for four typical cases (i-iv).approximately the same and the air had warmed to around − 9 • C when reaching Adventpynten.The stability was practically neutral, but H S was still great (119 W m − 2 ) due to the high wind speed.What is notable is that the H L was much larger than H S with an H L of 173 W m − 2 .This can also be seen in the large specific humidity gradient compared to (i) and (ii).The wind speed continued to decrease by a couple of m s − 1 by the time the air passed Adventpynten.However, the temperature was approximately the same at Vestpynten as it was at Adventpynten, although H S at Vestpynten was now very close to zero and H L has decreased to 20 W m − 2 .So, for this really windy case, it can be concluded that the wind was progressively decelerating independent of the surface, while the temperature was affected by the change to water but not by the new snow surface.The steep gradient in specific humidity seen over water disappeared over the new snow fetch and the absolute value was similar to that observed at Adventdalen.Case (iv) The last reliable measurements before the mast blew down at Adventpynten were on 21 April between 16.00 and 22.00 (Fig. 9d, h,  9l).As discussed earlier, these high wind speeds and temperatures were caused by an approaching low pressure.The temperatures that had been well below zero for the whole measuring campaign started to increase and went above zero later on 22 April.Unfortunately, the wind flow was not in a perfect alignment with the three stations in this case as the wind turned from 95 • at Adventdalen to 140 • and 135 • respectively at Adventpynten and Vestpynten.So (iv) should not be seen as a perfect snow-water-snow fetch case, but rather an example of independent observations during a transition to, for the High Arctic, very warm conditions.The wind speed was between 9 and 11 m s − 1 and the temperature just below zero at all three stations.The stability was stable (Ri B = 0.06) at Adventdalen as in the previous cases and H S was directed downwards with − 74 W m − 2 .At Adventpynten, the conditions were neutral and τ was again greatest at Adventpynten compared to the other stations.Regarding the heat fluxes at Adventpynten, there is a clear difference from the previous cases in that H S was directed downwards (− 16 W m − 2 ) indicating that the flux footprint has changed and characteristics of the land surface (or possible near shore ice in the fetch area) are seen at Adventpynten instead of the water fetch, a situation which was also discussed by Andersson et al. (2017).Despite this, H L at Adventpynten was still great at 113 W m − 2 suggesting that the specific humidity is less influenced by the land at the highest measurement (4.0 m) than at the lowest (0.5 m) thereby enhancing the gradient.At Vestpynten, the stability was also neutral, but the magnitude of both H S and H L were smaller than at Adventpynten, with − 2 and 29 W m − 2 , respectively.

Discussion and conclusions
Flow over a snow-water-snow surface has been analysed with observations from three stations located outside Longyearbyen, Svalbard, in the High Arctic during March and April 2013.The GM and the ECM were first tested and compared at Adventpynten and the GM was thereafter applied to observations from all three stations.The ECM and the GM tracked each other, but while τ GM was significantly greater than τ ECM , H S,GM was smaller than H S,ECM .Furthermore, although the scatter was considerable, there was only a 3 W m − 2 median difference between H L,ECM and H L,GM .These differences are much greater than Sjöblom (2014) found over land so it is difficult to say whether it was the open water fetch, possibly with the influence of some broken ice in this water, icing on instruments, and/or the time of the year that lead to this increased uncertainty in the results.It is, however, clear that the φ-functions used in the GM (Eq.( 5)) were not well suited for the conditions (Fig. 6) since the measured values did not coincide with the theoretical values used in the GM.Further, the difference between the methods were greater at close to neutral conditions (Fig. 5).This increased difference in H s can likely be explained by the appearance of the UVCN regime (Andersson et al., 2019).During UVCN conditions, detached eddies originating from the upper part of the boundary layer bring colder and dryer air down towards the surface, potentially enhancing H S,ECM .For the GM, however, which relies on Monin-Obukhov theory, this contribution to the total H s cannot be detected resulting in an underestimation of H s .Moreover, small gradients in U, T and q are difficult to capture with slow-response instruments, especially when the differences between the measuring levels are close to the accuracy of the instruments.In addition, icing on particularly the gas analyser in March may have contributed to the large differences observed between the methods on some occasions.
Although there are differences between the methods, it should still be possible to use the GM as an alternative when no fast-response instruments are available.Apart from being a cheaper and more robust alternative, the slow-response instruments are more robust than the fastresponse instruments, which is an advantage in a harsh Arctic environment.Moreover, if the temperature gradient can be measured in the lowest atmospheric boundary layer, then the actual surface temperature is not required, contrary to the classical bulk method (e.g., Andreas and Murphy, 1986;Andreas and Cash, 1999).The GM also has the advantage compared to the bulk method in that the exchange coefficient and roughness lengths do not need to be parameterised, which has proven to be difficult in Arctic regions (e.g., Lüers and Bareiss, 2010).Nevertheless, it must be remembered that the GM is not a direct method and still relies on several assumptions, including the Monin-Obukhov similarity theory.
Adventdalen upwind of the water resembles a typical smooth snowcovered surface in the Arctic and the Ri B was highly variable between zero and large positive values (Figs.2f and 8a).As Lüers and Bareiss (2010) pointed out, the existence of a very low inversion only seen in the lowest meter or so, or a strong surface warming especially in the Arctic spring, can influence the Ri B thereby contributing to the large value spread.Moreover, typical phenomena for the strong stable boundary layer, such as intermittent turbulence and drainage flows which are of particular importance since the measurements were conducted in a valley, might have influenced the observations.The low τ (0.07 and 0.10 N m − 2 for March and April) at Adventdalen (Figs. 7 and 8, Table 2) correspond to the early values from Hicks and Martin (1972) who also measured the turbulent fluxes over snow with averages of τ = 0.01 N m − 2 .H S (− 29 and − 41 W m − 2 ) had a greater average magnitude than that Grachev et al. (2017) observed at two Arctic terrestrial sites in Canada and Russia during wintertime, but they also concluded that the variation in the heat fluxes was irregular.Since no H L was measured at Adventdalen due to only one functioning humidity sensor, this cannot be directly compared, but the low q (Table 1) suggests that H L should also be small.
The open water over the fjord induced very high heat fluxes (Figs. 7 and 8) which were also seen visually as sea smoke on many days.Values over 400 W m − 2 were observed for H S , while H L was smaller than H s on average but still large.Even if such high values of H s are not uncommon over open water in otherwise ice-covered areas in the Arctic (e.g., den Hartog et al., 1983), they are much greater than compared to typical summer values over land in the Arctic.For example, Sjöblom (2014) described values up to 200 W m − 2 at Adventdalen for convective conditions and Westermann et al. (2009) had a summer average of 22.5 W m − 2 at Ny-Ålesund further north in Svalbard.
The second snow site downwind of the water, Vestpynten, showed a much more variable boundary layer with Ri B , H S , and H L on both the positive and negative sides (Figs.2f, 7 and 8) but generally both the H S and the H L were on the positive side.Since Vestpynten has a much shorter snow fetch than Adventdalen, the conditions more resembled an internal boundary layer where the development depends on the initial meteorological conditions at the change of surface and did not affect the whole boundary layer.This could clearly be seen in the four case studies presented (Fig. 9, Table 3) where the different parameters investigated were affected in a variety of ways depending on the situation.In case (ii), the snow fetch was long enough to return the characteristics of a stable boundary layer such as at Adventdalen although not as strong, while in case (i) only the absolute values were affected and not the gradients.
As Taylor et al. (2018) point out, with future climate change the understanding of the irregular and episodic behaviour of turbulent fluxes in the Arctic is essential to improve the climate predictions.For example, during the high wind speeds in case (iii), it was only the temperature that was affected by the water, while the wind was instead decelerating.So, depending on the up-wind conditions, the behaviour of the internal boundary layer that forms over the water and further on above the new snow can be quite different.In addition, case (iv) illustrated what can happen with the turbulent fluxes during the arrival of a very warm, windy, and moist air mass.This example of a quick change in temperature is something which is more likely to happen in the future (e. g., Førland et al., 2011;Walsh et al., 2011) and resulted in very close to neutral stability.Meanwhile, the temperature differences between the air and both the water and the snow were reduced, and H S also reduced in magnitude.Since the new airmass was very moist, H L also became much greater than H S .
To conclude, it has been shown that the flow over snow-water-snow in many ways resembles the flow over a lead or polynya.For example, the reduction in wind speed close to the surface over the water going from smooth snow to rough water and thereby giving rise to a greater wind speed gradient and partially hindering the heat flux which could be seen in case (i) and also from the average values in Table 2.This was the same effect as Andreas et al. (1979) found over an open lead.Although many of the results presented here are similar to that which may be expected over an open water surface in an otherwise ice-covered ocean, it still needs to be remembered that the observations took place in a fjord which may introduce influences from topography, drainage flows etc. that may influence the results.However, it has been shown above that an otherwise complex measuring situation close to leads and polynyas on an otherwise ice-covered ocean can be simplified both with measuring techniques and locations and yet still be able to estimate the turbulent fluxes with sufficient accuracy.

Fig. 1 .
Fig. 1.Map of Svalbard and location of the stations.Copyright © Norwegian Polar Institute.Used with courtesy of the Norwegian Polar Institute.
1 • C, to the average spring temperature − 8.3 • C

Fig. 2 .
Fig. 2. Time series of (a) temperature (T), (b) wind speed (U), (c) wind direction (WD), (d) relative humidity (RH), (e) specific humidity (q), and (f) the bulk Richardson number (Ri B ) for Adventdalen (red ), Adventpynten (black X), and Vestpynten (cyan ).Grey areas indicate the case studies (i-iv).(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 3 .Fig. 4 .
Fig. 3. Time series from Adventpynten of (a) momentum flux (τ), (b) sensible heat flux (H S ), and (c) latent heat flux (H L ), with ECM (green ) and GM (black X). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 5 .Fig. 6 .
Fig. 5. Fluxes from ECM -fluxes from GM at Adventpynten in March (magenta ) and April (blue ) of (a) momentum flux (τ) as a function of the bulk Richardson number (Ri B ), (b) τ as a function of the wind speed (U), (c) τ as a function of the temperature (T), (d) sensible heat flux (H S ) as a function of Ri B , (e) H S (U), (f) H S (T), (g) latent heat flux (H L ) as a function of Ri B , (h) H L (U), and (i) H L (T). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 7 .
Fig. 7. Time series from GM of (a-b) momentum flux (τ), (c-d) sensible heat flux (H S ), and (e-f) latent heat flux (H L ), with Adventdalen (red ), Adventpynten (black X), and Vestpynten (cyan ).Grey areas indicate the case studies (i-iv).(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 9 .
Fig. 9. Gradients of: (a-d) wind speed (U), (e-h) potential temperature (θ), and (i-l) specific humidity (q), at Adventdalen (red ), Adventpynten (black -), and Vestpynten (cyan ) for the four case studies (i-iv).Red circle ( ) in the lower panel indicate the only humidity measurement at Adventdalen.(For interpretation of the references to colour in this figure legend, the reader is referred to Web version of this article.)