observations of summer turbulent surface fluxes in a high arctic fjord

Quarterly Journal of the Royal Meteorological Society Q. J. R. Meteorol. Soc. 140: 666–675, January 2014 B DOI:10.1002/qj.2167

Observations of summer turbulent surface fluxes in aHigh Arctic fjord

Stephan T. Kral,a,b* Anna Sjoblom,a,c and Tiina Nygarda,b,d

aThe University Centre in Svalbard, Longyearbyen, NorwaybFinnish Meteorological Institute, Helsinki, Finland

cGeophysical Institute, University of Bergen, NorwaydUniversity of Helsinki, Finland

*Correspondence to: S. Kral, Finnish Meteorological Institute, PO Box 503, 00101 Helsinki, Finland.E-mail: [email protected]

The summer atmospheric boundary layer over a fjord in the High Arctic has beeninvestigated during three consecutive years (2008–2010). Measurements of turbulentsurface layer fluxes of momentum and sensible heat using a sonic anemometer and slow-response instruments were taken from a tower on the coast of Isfjorden, Svalbard, andanalysed for seasonal variability and differing fetch conditions. The results resembled theatmospheric boundary layer characteristics previously found for ice-free winter conditions.The momentum flux was usually directed downwards, but for low wind speeds there was apossible contribution of swell, giving an upward directed momentum flux. The cross-windcomponent of the momentum flux sometimes contributed significantly to the total flux. Thesensible heat flux was very dependent on the origin of air, whether it had a long over-waterfetch, or originated from land areas with or without glaciers. In addition to non-stationarityof the flow due to the influence of the fjord’s shape and its surrounding topography, lowwind speeds questioned the validity of the Monin–Obukhov similarity theory, whereas theover-water fetch and off-wind angle were of minor importance. Moreover, some results,especially the off-wind angle, were very sensitive to how the raw data were treated, inparticular which coordinate rotation method was employed, the double rotation or theplanar fit method.

Key Words: marine atmospheric boundary layer; surface layer; Svalbard; Monin–Obukhov similarity theory; sonicanemometer; topographic effects; coordinate rotation and tilt correction

Received 21 December 2012; Revised 12 March 2013; Accepted 2 April 2013; Published online in Wiley Online Library 19June 2013

1. Introduction

It is well known that the marine atmospheric boundary layerdiffers significantly from that over land. The presence of sea-surface waves might induce an additional cross-wind momentumflux or even result in an upward directed flux of momentum incases with swell (i.e. waves travelling faster than the wind) (e.g.Drennan et al., 1999; Grachev et al., 2003; Sjoblom and Smedman,2003; Hogstrom et al., 2008). However, meteorological conditionsover Arctic fjords, which can be considered as transition zonesbetween land and the open ocean, are not as well known, althoughobservations of local intensification of winds over Arctic fjordswere already made as early as 1935–36 by the British EastGreenland Expedition (Manley, 1938).

During recent years, meteorological conditions over Arcticfjords have received growing interest and several studies based onobservations and numerical models have contributed to increaseknowledge about the interactions of sea, land and atmosphere(e.g. Skeie and Grønas, 2000; Beine et al., 2001; Argentini et al.,

2003; Kilpelainen and Sjoblom, 2010; Kilpelainen et al., 2011,2012; Makiranta et al., 2011; Vihma et al., 2011). Several otherstudies have addressed the atmospheric boundary layer over openwater or ice-covered coastal regions in the Arctic (e.g. Andreasand Cash, 1999; Heinemann, 2003). Most of these studies havefocused on winter and spring, when the stratification of theatmospheric boundary layer is typically either convective overopen water or stable over sea ice. In addition, most studies haveonly covered relatively short time periods, i.e. from a few days tosome months. However, there are some exceptions, for examplethe surface heat budget of the Arctic Ocean experiment (SHEBA)(e.g. Uttal et al., 2002; Pinto et al., 2003; Grachev et al., 2005,2007, 2008; Mirocha et al., 2005), which was a year-long ice campon the Arctic pack ice.

The Monin–Obukhov (MO) similarity theory (e.g. Foken2006), which is commonly used to parametrize the turbulentfluxes in atmospheric models, assumes horizontal homogeneity,stationarity and that the surface stress vector is aligned withthe mean wind direction. These assumptions might, however,

c© 2013 Royal Meteorological Society

Observations of Summer Turbulent Surface Fluxes in a High Arctic Fjord 667

be violated in an Arctic fjord environment. The presence of landwith different surface characteristics might result in heterogeneity,while mesoscale variability, such as drainage flows, steering andchannelling by the fjord’s topography or gravity waves, mightcause significant non-stationarity of the flow within the surfacelayer (Mahrt et al., 1996). In addition, sea-surface waves maycause the surface stress vector to deviate from the mean winddirection (Geernaert et al., 1993). Therefore, it is questionablewhether the MO similarity theory is applicable in Arctic fjords.

The most direct way to measure turbulent fluxes in the surfacelayer is the eddy correlation method. This method is basedon fast-response measurements from a three-dimensional sonicanemometer which derives all components of the instantaneouswind vector and the sonic temperature at sampling frequencies ofup to 100 Hz, from which turbulent quantities can be calculated.For the analysis of such data, it is common practice to expressthe variables in a mean streamline coordinate system by applyinga coordinate transformation. This is also necessary to correcterrors in the alignment of the sonic anemometer, since even asmall tilt can result in considerable errors in the measurementsof the horizontal Reynolds stress (e.g. Dyer, 1981; McMillen,1988). In the marine surface layer, where both longitudinal andlateral stress components are of interest, the double rotationmethod (DR) has traditionally been used. However, this methoddoes not include a full correction for instrument tilt. Wilczaket al. (2001) showed that a tilt of even 1◦ in the uncorrectedy-z plane, which can also result from unavoidable flux samplingerrors, can cause a deviation of up to one order in the lateralstress component, leading to an overestimation of the total surfacestress. To overcome this weakness, Wilczak et al. (2001) presentedthe planar fit method (PF) as an alternative, which improves theestimate of the lateral stress significantly. Finnigan (2004), whocarried out a theoretical comparison of different coordinatetransformation methods, suggests that the DR can be used whenthe instrument is well levelled, but that the PF should be preferredwhen measurements are carried out in complex terrain. RecentlyOh et al. (2011) found higher cross-wind stresses resulting fromthe DR compared to the PF. This disagreement led to significantdifferences in the calculated off-wind angles.

Kilpelainen and Sjoblom (2010) described the exchange ofmomentum and sensible heat in an Arctic fjord system onSpitsbergen, Svalbard (Norway) during spring 2008 applying DR.During their study period, the stratification of the surface layerwas found to be mostly unstable due to ice-free conditions. Thecharacteristics of the surface layer differed from those observedover both land and the open ocean. They found that conventionalstability and scaling parameters were often questionable due tocross-wind and upward momentum transfer which were mostlikely related to topographic effects and swell. Nevertheless, theMO similarity theory was found to be applicable during moderateand high winds along the fjord. The present work is based ona continuation of these measurements, but with focus on thesummer period, and aims to enhance the picture of the turbulentexchange in an Arctic fjord. The data used in this study includesonic anemometer data and profile data of wind speed, direction,temperature and humidity derived from a 30 m high tower onthe coast of Isfjorden, Svalbard (Figure 1) from three consecutivesummers (2008–2010). The data were used to study turbulentexchange processes during summer and to test the validity of theMO similarity theory within a fjord. In addition, the extensivedataset allowed us to apply different coordinate transformationmethods and to address whether the choice of the rotation methodhas a significant impact on the turbulent quantities at a fjord site,where the cross-wind component of the Reynolds stress vectormight be significant.

Section 2 describes the measurements and section 3 sometheoretical considerations. How the data have been selected andprocessed is discussed in section 4, while section 5 presents theresults and discusses the findings. Conclusions are given in section6.

Figure 1. Upper panel: the Svalbard archipelago with its main island Spitsbergenand the Isfjorden system. Lower panel: the Isfjorden system with the threemain branches, the main fjord with the mouth located in the west (I), thenorthern branch Nordfjorden (II) and the northeastern branch, Sassenfjorden(III). The wind rose showing the distribution of the mean wind direction and thecorresponding mean velocities. The lengths of the sectors indicate the fraction ofsamples from this direction, while the shades indicate the wind speed. Maps areadapted from Kilpelainen and Sjoblom (2010). This figure is available in colouronline at wileyonlinelibrary.com/journal/qj

2. Measurements

The Arctic archipelago of Svalbard with its largest islandSpitsbergen (Figure 1) is located about midway between theNorwegian mainland and the North Pole. It borders the ArcticOcean to the north, the Barents Sea to the east and the FramStrait to the west. Isfjorden is the largest fjord system on thewest coast of Spitsbergen and covers an area of 3084 km2. Itis orientated in a southwest to northeast direction and has anapproximate 10 km wide mouth connecting it to the open ocean.The Isfjorden system has no distinct shallow sill at its entranceand is therefore directly linked to the shelf and slope area alongthe west of Spitsbergen, allowing relatively warm Atlantic Waterfrom the West Spitsbergen Current to enter the fjord.

It is convenient to divide the fjord system into three branchesin the same way as Kilpelainen and Sjoblom (2010): the mainfjord with the mouth to the west (branch I, defined from 245◦to 270◦), and two branches to the north (branch II, 330◦ –0◦)and west (branch III, 30◦ –45◦), as shown in Figure 1. Thetopography around the fjord is dominated by mountains, risingto 400–1100 m, several valleys and glaciers. Two glaciers onthe eastern side are connected to an extensive inland ice cap.These topographic features influence the boundary layer overthe fjord by channelling, drainage flows and mountain lee waves(Kilpelainen and Sjoblom, 2010; Kilpelainen et al., 2011, 2012).

c© 2013 Royal Meteorological Society Q. J. R. Meteorol. Soc. 140: 666–675 (2014)

668 S. T. Kral et al.

A 30 m high tower at Vestpynten (78◦15′N, 15◦24′E), whichis located a few tens of metres from the shoreline on thesouthern coast of Isfjorden, was used. This tower was equippedwith a three-dimensional sonic anemometer (CSAT3, CampbellScientific) at 15.3 m, from which the turbulent fluxes of sensibleheat and momentum were determined. Vertical profiles of windspeed and direction were measured from slow-response cupanemometers (A100LK, Vector Instruments) and wind vanes(W200P, Vector Instruments) at four levels (9.8, 13.8, 18.8 and24.8 m) and temperature and humidity profiles from combinedsensors (HMP45C, Campbell Scientific) at two levels (13.8 and24.8 m). A more detailed description of the measurement site andinstrumentation, as well as flux footprint estimates, can be foundin Kilpelainen and Sjoblom (2010).

Measurements have been running semi-continuously fromJanuary 2008 until October 2010 with some intermissions due totechnical problems. Only data from May until October are used. Atthe measurement site, the water level varied by maximum ±1 m,and a correction to the measurement height of the instruments wasapplied using water-level estimates provided by the NorwegianHydrological Service. The estimates were based on harmonicconstants for Longyearbyen. These estimates were corrected formeteorological effects, which were converted from observations inNy-Alesund (78◦54′N, 11◦53′E) which lies approximately 110 kmnorthwest of Longyearbyen.

3. Theory

3.1. Momentum and sensible heat fluxes

The eddy correlation method is the most direct way to derivethe turbulent fluxes of momentum and sensible heat using sonicanemometer measurements. From the kinematic momentumfluxes, u′w′ and v′w′, which are the correlations of the measuredvelocity fluctuations (u′, v′, w′), the two components of thehorizontal stress vector, τx and τy, and its total magnitude, |τ |,can be calculated as

τx = −ρu′w′, (1)

τy = −ρv′w′, (2)

|τ | = ρu2∗, (3)

with the density of dry air, ρ, and the friction velocity:

u∗ ={(−u′w′)2 + (−v′w′)2

}1/4. (4)

The magnitude of the horizontal stress vector may also beregarded as the vertical flux of horizontal momentum. Bydefinition, positive values of τx correspond to a downward-directed momentum transport, originating from the along-winddirection.

The relative off-wind angle, α, between the total horizontalstress vector, τ , and the mean wind vector, U, is defined as

α = arctan(−v′w′/ − u′w′) . (5)

Positive angles correspond to a deviation of the total stressvector to the left of the mean wind vector and vice versa fornegative angles. This is due to the right-handed coordinatesystem predetermined by the CSAT3 sonic anemometer andmight disagree with other authors’ definitions (e.g. Grachev et al.,2003). In cases with an upward-directed momentum flux (i.e.τx < 0), Eq. (5) has to be corrected by 180◦ to account for thefact that the directions of τx and U are opposite to each other,resulting in |α| > 90◦.

The sensible heat flux follows directly from the kinematictemperature flux, w′T′, as

Hs = ρcpw′T′, (6)

where cp is the specific heat capacity of dry air at constant pressure.Since the sonic anemometer measures the sonic temperature Ts,which is directly linked to the speed of sound and therefore alsoa function of humidity, w′T′ was determined by applying thefollowing humidity correction (in accordance with Schotanuset al., 1983):

w′T′ = w′T′s

(1 + 0.51T

�q

�θ

)−1

, (7)

where T is the mean air temperature at the height of the sonicanemometer, and �q and �θ are the vertical differences in meanspecific humidity and mean potential temperature.

3.2. Non-dimensional gradients

The MO similarity theory (e.g. Foken, 2006) connects surfacefluxes, such as momentum and sensible heat, to the verticalprofiles of meteorological variables, i.e. wind and potentialtemperature, by defining the non-dimensional wind andtemperature gradient as

φm

( z

L

)= kz

u∗∂U

∂z, (8)

φh

( z

L

)= kz

θ∗∂θ

∂z, (9)

where ∂U/∂z is the mean vertical gradient of the horizontalwind speed and ∂θ/∂z the mean vertical gradient of potentialtemperature. The Von Karman constant k is set to 0.40 inaccordance with Hogstrom (1996), z represents the measurementheight above the surface and

θ∗ = −w′T′/u∗ (10)

the scaling temperature. The MO stability parameter z/L isdefined as

z/L = − zgkw′T′s

T◦u3∗, (11)

with the buoyancy parameter, g/T◦.The shape of the similarity functions can be predicted from the

following empirically determined formulations:

φH96m = (

1 − 19 zL

)−1/4for − 2.0 ≤ z

L < 0,

φH96m = 1 + 5.3 z

L for 0 ≤ zL ≤ 0.5

(12)

and

φH96h = 0.95

(1 − 11.6 z

L

)−1/2for −2.0 ≤ z

L < 0,

φH96h = 0.95 + 8 z

L for 0 ≤ zL ≤ 0.5,

(13)

which are based on the review and comparison of several differentformulations of φm and φh by Hogstrom (1996, hereinafterindicated by superscript H96). Additional formulations can befound in, for example, Hogstrom (1988), Sorbjan (1989) andGarratt (1994).

The above-mentioned formulations are based on overlandobservations and can be questionable when applied to the marineboundary layer under certain conditions such as swell (Rutgerssonet al., 2001; Sjoblom and Smedman, 2002). They can also beaffected by the height of the boundary layer (Hogstrom et al.,2008) and the height of the wave boundary layer (Sjoblom andSmedman, 2003). When applying the MO similarity theory, oneshould also consider horizontal homogeneity and stationarity ofthe flow. In addition, the theory requires that gradients of thevertical fluxes are small and v′w′ is negligible, meaning α (Eq. (5))is close to zero. Furthermore, wind speeds should not be toolow, to assure u∗ does not approach zero and that the molecularexchange is small compared to the turbulent exchange.



3.3. Coordinate rotation and tilt correction

For the interpretation of turbulent flux data from eddy correlationmeasurements, it is common to rotate the sonic anemometer datafrom the instruments’ coordinate system into a stream-wisecoordinate system. This is necessary to express the turbulentquantities in a coordinate system that is aligned to the meanflow. Moreover, it applies a correction for a physical tilt of theinstrument relative to the surface.

A common method is the rotation into a right-handed naturalwind coordinate system, in which two rotation angles are usedto align the x-axis with the mean wind vector for each averaginginterval (McMillen, 1988). A third rotation forces v′w′ to zero.This method is frequently used in boundary layer observationsover flat land where a homogeneous surface can often be assumed.For observations of the atmospheric boundary layer over seasurfaces this method is not preferable, since the possible presenceof swell might cause v′w′ to deviate from zero significantly(Geernaert et al., 1993).

Two other methods that conserve the cross-wind momentumflux are the double rotation (DR) (e.g. Lee et al., 2004) and theplanar fit rotation (PF) (Paw et al., 2000; Wilczak et al., 2001).In the DR method the two first rotations mentioned aboveare applied to align the x-axis with the mean wind vector, i.e.u = |U| and v = w = 0. This might, however, imply that possibleinstrument tilt angles are not corrected sufficiently. More recentlythis method has been criticized because the missing lateral tiltcorrection can lead to a significant overestimation of the surfacestress (Wilczak et al., 2001). Moreover, single events that havenothing to do with the coordinate system (e.g. convection, gusts,coherent structures) may result in significant rotation angles forparticular averaging intervals (Foken et al., 2004).

In the PF (e.g. Wilczak et al., 2001), a mean streamline plane forthe measurement site is determined through two rotation angles,so that the long-term mean of the vertical velocity component,calculated from all data samples, becomes zero. A third rotationis applied for every averaging period so that the x-axis is parallelto the projection of the mean wind vector, U, to the mean plane.Hence the z-axis is perpendicular to this plane and fixed for thecomplete dataset, while the x and y-axes, which span the plane,vary from sample to sample (Foken et al., 2004).

The PF is generally considered to overcome the deficiencies ofthe DR, such as over-rotation, and should give more reasonablevalues of the lateral surface stress. In addition, the coordinateaxes are not prone to the effect of instrument offset in thevertical velocity component because the offset is eliminatedin the procedure for determining the mean plane (Lee et al.,2004). However, since the PF method requires an extensivedataset to determine a horizontal plane which is not sensitive torandom errors, its application is limited to longer measurementcampaigns. For the same reason it cannot be used to computereal-time fluxes (Wilczak et al., 2001).

The results presented in section 5.1 were produced by applyingthe PF method. In order to compare both methods, some resultswere reproduced applying the DR method in section 5.2.

4. Data

4.1. Data processing

The choice of averaging period determines which scales ofatmospheric motion are included in the computed flux (Mahrtet al., 1996). Kilpelainen and Sjoblom (2010) analysed thecontribution of eddies with different sizes (i.e. frequencies) tothe total fluxes of sensible heat and momentum by applying anogive analysis to data from the Vestpynten site. According to theirresults a 30 min averaging period is the most convenient choiceto capture a maximum of the turbulent eddies, while reducingthe contribution of mesoscale motions to the calculated fluxes, at

this site. Therefore the same averaging period was applied in thisstudy.

A thorough quality control was applied to the dataset.Unrealistic temperature and wind speed values and otherobviously erroneous data were discarded. Spikes in the sonicdata were detected and removed using an algorithm similar tothat of Vickers and Mahrt (1997). 30 min records were discardedwhen more than 1% of the data was affected by spikes.

The three velocity components of the wind speed data retrievedfrom the sonic anemometer were rotated into stream-wisecoordinates using the PF and DR method as described insection 3.3. Cross-wind contamination of the turbulence datawere corrected online, while a humidity correction (Schotanuset al., 1983) was applied to the kinematic temperature flux(Eq. (7)). The vertical gradients were calculated by applying athird-order polynomial fit to the wind profile data and a linearfit to temperature and humidity profile data in accordance withSjoblom and Smedman (2003). Due to a malfunctioning cupanemometer at 18.8 m during summer 2009 a second-orderpolynomial was applied for this period.

4.2. Data selection

Only measurements with a mean wind direction from the fjordsector (245◦ –360◦ and 0◦ –50◦, Figure 1) were used and datawith wind speeds below 1.5 m s−1 were discarded. For analyses ofthe non-dimensional temperature gradient, φh (Eq. (9)), recordswith very low heat fluxes |Hs| < 2 W m−2 (about 7% of the data)were excluded.

The data were tested for stationarity by applying the methodpresented by Foken and Wichura (1996). By calculating the rateof non-stationarity (RN) for each data record and comparing thenon-dimensional gradients of wind and potential temperatureas functions of the Monin–Obukhov stability parameter fordifferent categories of RN, we found that a value of RN < 0.3 isthe most suitable threshold. This is in accordance with the valuesuggested by Foken and Wichura (1996).

5. Results and discussion

In 30% of all the 30 min records, the flow originated from thefjord sector. This resulted in 4253 records of which 2205 couldbe regarded as stationary (section 4.2). Non-stationarity occurredmostly under conditions with weak winds or stable stratification.The 30 min mean wind speed had a maximum of 13 m s−1 in June2009. The mean temperature typically varied between −3 ◦C and5 ◦C with a minimum of −10 ◦C in the end of October 2008 and amaximum of 10 ◦C in August 2010. The relative humidity variedbetween 47% and 98%. The observed stratification was mostlyunstable, stable conditions were observed only in 9% of the data.

The distribution of the wind direction and the correspondingmean horizontal velocity is presented in Figure 1. Topographicsteering of the flow resulted in a dominating wind direction alongthe fjord’s main axis. In about 35% of all cases, the wind wasfrom west to westsouthwest, i.e. from the mouth of Isfjorden(branch I). In about 20% of the data, the mean flow originatedfrom the northeast, i.e. branch III. The influence of branch II isnot very distinct. However, in about 20% of the data the floworiginated from the land area between branch II and III. Thehighest wind speeds occurred when the flow was along one of thefjord’s main branches (50% of all samples), the directions withthe longest fetch. Compared to winter conditions reported byKilpelainen and Sjoblom (2010), the wind direction distributionin summer had a much larger contribution of winds from themouth (branch I) and smaller contribution of winds from branchII. These dissimilarities in the wind distributions are in accordancewith differences in summer and winter large-scale flow patterns.



240 270 300 330 0 30 60−180

−135

−90

−45

0

45

90

135

180

Wind direction (deg)

α (d

eg)

I II III

measurements

bin–averaged measurements

Figure 2. The off-wind angle α calculated using the PF method as a function ofmean wind direction. The shaded areas denote the branches of Isfjorden. Thisfigure is available in colour online at wileyonlinelibrary.com/journal/qj

5.1. Turbulent fluxes

The results from the PF method were used to investigate theturbulent fluxes of momentum and sensible heat with regardto spatial and temporal variability. They were also employed todetermine the validity of the MO similarity theory in this section.The summer results are compared with previous results for thewinter unstable boundary layer (Kilpelainen and Sjoblom, 2010).

Spatial variability of turbulent fluxes is occasionally extremewithin Arctic fjords due to different large-scale flow, topographyand surface type (Kilpelainen et al., 2011). Although our resultsdo not necessarily represent conditions everywhere in the fjord,some spatial variability has been captured since the different fjordbranches each have distinct physical characteristics.

5.1.1. Momentum flux

The magnitude of the horizontal stress vector, |τ | (Eq. (3))and its along wind component τx (Eq. (1)) were, as expected,strongly dependent on horizontal wind speed, U , increasingwith greater velocity (not shown). The flux of momentum wastypically downward directed; however, in 1.5% of the data, underconditions with U ≤ 5 m s−1, the direction of the momentumflux changed, most likely due to the effect of swell (e.g. Grachevand Fairall, 2001). The cross-wind stress, τy, was nearly evenlydistributed around zero, but occasionally the magnitudes were ofthe same order as τx.

Figure 2 shows the relative off-wind angle, α, between thehorizontal stress vector and mean wind vector (Eq. (5)) asa function of the mean wind direction. A downward-directedmomentum flux (τx > 0) corresponds to |α| < 90◦, while τx < 0results in |α| > 90◦. An influence of the different branches ofIsfjorden on α can be seen. In cases with flow from branch I,the mean value of α increases from about −12◦ to 0◦. α isnearly constant with −10◦ within branch II, while in branch III αincreases from 22◦ to 30◦. The largest deviations in the directionof the surface stress vector to the mean wind direction occurprimarily during light winds. In general, the measured off-windangles match observations over the open ocean, with DR (e.g.Drennan et al., 1999; Sjoblom and Smedman, 2002), althougheven higher values of α have been observed (e.g. Grachev et al.,2003). Berg et al. (2012), who also observed comparable values ofα, suggested that α = 0 is rarely the case in the real atmosphere.The magnitudes of these off-wind angles are comparable toprevious results for Isfjorden in winter (Kilpelainen and Sjoblom,2010), although the influences of the fjord branches differed

to some extent. As shown in section 5.2, this is mainly due todifferences in rotation methods used and partly due to seasonaldifferences. The results of Kilpelainen and Sjoblom (2010) for τy

tend to negative values with higher standard deviations as the DRmethod does not correct a possible tilt of the sonic anemometerin the y-z plane. Nevertheless, some of the difference at low windspeeds might be explained by the influence of sea-surface waves.Consequently, the differences in τy are reflected in α, showingeven opposite directions of τ relative to U. However, both of thetwo studies reveal a clear influence of the surrounding topographyon α.

According to (Geernaert et al., 1993), the direction of τ liesbetween the mean wind and the wave direction. Within thefjord topographic steering in combination with the impact ofsea-surface waves on the turbulent fluxes are most likely tocause the systematic deviation between the directions of U and τ(Kilpelainen and Sjoblom, 2010). Since no wave measurementshave been carried out during the measurement period, it is notpossible to study the effects of waves on τ and α in more detail.

Due to α �= 0, the requirements for applying the MO similaritytheory might be violated in the environment of an Arcticfjord system. Furthermore, the MO similarity theory might bequestioned under conditions with weak winds or varying fetchconditions. In Figure 3, φm is plotted against z/L for differentcategories (similar to those used by Kilpelainen and Sjoblom,2010): different wind speeds in Figure 3(a) and (b), differentwind directions (along and across the fjord) in Figure 3(c)and (d) and different off-wind angles in Figure 3(e) and (f).The measured values of φm (Eq. (8)) are compared to theempirically determined stability functions defined by Hogstrom(1996, Eq. (12)), hereinafter φH96

m . Values of the non-dimensionalgradients φm lying above φH96

m indicate a less efficient transportof momentum than expected from ∂U/∂z.

For higher wind speeds, the mean values of φm are muchcloser to φH96

m (Figure 3(a) and (b)) and show smaller standarddeviations, at least for −1.5 < z/L < 0. For z/L > 0 the standarddeviations increase but for high wind speeds φm still follows φH96

mto a high degree (Figure 3(b)). During light winds (Figure 3(a)),φm is generally smaller than φH96

m , indicating a higher-momentumflux than expected from the vertical wind shear. The dependencyon wind speed is in general agreement with the results fromwinter (Kilpelainen and Sjoblom, 2010). Since φm is stronglyinfluenced by the wind speed, only data with U > 3 m s−1 areused in Figure 3(c)–(f). The wind direction, i.e. along and acrossthe fjord, (Figure 3(c) and (d)) seems to have a small effect onφm, except for z/L > 0 in Figure 3(c), but here the quantity ofdata is too small to draw conclusions. The impact of α is alsosmall; for cases with |α| ≤ 20◦ (Figure 3(e)) φm follows φH96

mfairly well, while larger absolute values of α (Figure 3(f)) result inφm being slightly smaller, but still within one standard deviation,for z/L ≤ 0.

The condition U > 3 m s−1 appears to be the best compromisebetween a high yield of data and good agreement of φm with φH96

m .One reason for U being the most important factor is most likelyrelated to mesoscale motions which become more importantunder conditions with weak turbulence, i.e. low wind speeds.Therefore, neglecting data with U ≤ 3 m s−1 may be interpretedas an additional non-stationary filter. Due to the accuracy ofthe slow-response instruments, the relative error in the verticalwind gradient may be significant during weak winds. The effect ofdifferent wind directions and off-wind angles seems to be of minorimportance, possibly due to the relatively long fetch conditions,even for cross-fjord directions, and the primarily rather unstablestratification. Some of the scatter in Figure 3 might be causedartificially by self-correlation (e.g. Baas et al., 2006). However, it islikely that our results do not suffer from serious self-correlation,as Kilpelainen and Sjoblom (2010) found no self-correlation inφm in unstable conditions.



−2 −1.5 −1 −0.5 0 0.5−0.5

0

0.5

1

1.5

2

2.5

3

3.5

z/L

−2 −1.5 −1 −0.5 0 0.5

z/L

−2 −1.5 −1 −0.5 0 0.5

z/L

−2 −1.5 −1 −0.5 0 0.5

z/L

−2 −1.5 −1 −0.5 0 0.5

z/L

−2 −1.5 −1 −0.5 0 0.5

z/L

φ m(a)

−0.5

0

0.5

1

1.5

2

2.5

3

3.5

φ m

(b)

−0.5

0

0.5

1

1.5

2

2.5

3

3.5

φ m

(c)

−0.5

0

0.5

1

1.5

2

2.5

3

3.5

φ m

(d)

−0.5

0

0.5

1

1.5

2

2.5

3

3.5

φ m

(e)

−0.5

0

0.5

1

1.5

2

2.5

3

3.5

φ m

(f)

U ≤ 3.0 m s−1

measurementsbin–averaged measurements

φmH96

U > 3.0 m s−1

U > 3.0 m s−1

alongU > 3.0 m s−1

across

U > 3.0 m s−1

|α| ≤ 20°U > 3.0 m s−1

|α| > 20°

Figure 3. φm calculated using the PF method against z/L for different wind speeds, U ≤ 3 m s−1 and U > 3 m s−1 in (a) and (b); wind directions, along and acrossthe fjord in (c) and (d); different off-wind angles, |α| ≤ 20◦ and |α| > 20◦ in (e) and (f). This figure is available in colour online at wileyonlinelibrary.com/journal/qj

5.1.2. Sensible heat flux

The sensible heat flux, Hs, was determined using the eddycorrelation method (Eq. (6)) applying the moisture correction(Eq. (7)). A complex environment such as an Arctic fjord cancreate significant spatial variability (Kilpelainen et al., 2011).In order to address this, Hs is presented as a function of themean wind direction in Figure 4. The measurements from June toSeptember are indicated by dots; measurements from the transientperiods (April and October) are marked by crosses. More than90% of all samples exhibit a positive (upward-directed) flux ofsensible heat. The values of Hs are, as expected, significantly higher

during May and October than in the summer months and showa larger variability. During these transient periods there were justsome events with Hs < 0, but relatively strong positive fluxesup to 135 W m−2 were found in October. For June–September,Hs shows smaller variability with, on average, relatively weakupward-directed heat fluxes. Nearly all the events with Hs < 0were related to a mean wind direction from about 10◦ to 30◦,which is from the land area between branch II and branch III(Figure 1), while the highest mean value (Hs = 43 W m−2) isreached in the sector from 240◦ to 330◦.

During winter and early spring even stronger fluxes, exceeding250 W m−2, have been measured at the same site (Kilpelainen



240 270 300 330 0 30 60−50

−25

0

25

50

75

100

125

150


Hs

(W m

−2)

I II III

measurements (June – September)

measurements (April, October)

bin–averaged measurements

Figure 4. The sensible heat flux Hs calculated using the PF method as afunction of the mean wind. This figure is available in colour online atwileyonlinelibrary.com/journal/qj

and Sjoblom, 2010). This seasonal variability is due to the higherannual variability of the air temperature compared to the sea-surface temperature, which is relatively constant. The possibility ofrelatively warm water from the West Spitsbergen Current (outsideSvalbard) to enter the fjord, in combination with solar heatingduring the summer, often causes the sea surface to be warmerthan the overlying air, under conditions with low sea-ice coverage.The high number of events with Hs < 0, related to a mean winddirection from the sector 10◦ –30◦ might be explained by thespecific surface conditions of the land area between branch II andbranch III, which is not covered with large glaciers, in contrastto the northern coast of Isfjorden and, therefore it experiencesstronger diabatic heating during summer. This causes an increasein the air temperature of the surface layer and consequently adownward-directed flux of sensible heat when this air is advectedover the fjord. The opposite effect, i.e. relatively cold air, advectedoff glaciers around the fjord, results in the strong heat fluxes from270◦ to 330◦ (Figure 4).

The non-dimensional temperature gradient, φh (Figure 5), isinvestigated in the same manner as φm (Figure 3) and comparedto the empirical stability function, determined by Hogstrom(1996, Eq. (13)), hereinafter φH96

h . The dependence of φh on themean wind speed (Figure 5(a) and (b)) shows that φh is fairlyclose to φH96

h only for U > 3 m s−1, although generally slightlyhigher. However, for z/L > 0 the standard deviations increaseremarkably, which is also an effect of less data. An impact of thewind direction on φh was hardly detectable and the effect of theoff-wind angle α on φh also appeared to be relatively small (bothnot shown).

In general, the measured values of φh seem to be slightlyhigher than φH96

h , indicating that the measured flux is higherthan estimated from the vertical temperature gradient. Similarbehaviour was found during winter (Kilpelainen and Sjoblom,2010). Since temperature was measured at only two levels, ∂θ/∂zhad to be calculated assuming a linear temperature profile. Thismight lead to an underestimation of the actual temperaturegradient at the height of the sonic anemometer. The clear influenceof wind speed is similar to φm and most likely due to strongermesoscale variability and instrument uncertainties during lightwinds.

5.2. Sensitivity to different coordinate transformation methods

As described in section 3.3, the choice of coordinatetransformation method might influence the results of the surface

−2 −1.5 −1 −0.5 0 0.5−1

0

1

2

3

4

5

6

z/L

−2 −1.5 −1 −0.5 0 0.5

z/L

φ h

(a)U ≤ 3.0 m s−1

measurementsbin–averaged measurements

φhH96

−1

0

1

2

3

4

5

6

φ h

(b)U > 3.0 m s−1

Figure 5. φh calculated using the PF method against z/L for different wind speeds,U ≤ 3 m s−1 in (a) and U > 3 m s−1 in (b). This figure is available in colouronline at wileyonlinelibrary.com/journal/qj

layer measurements significantly. Therefore, the DR and the PFmethods are compared by investigating differences in turbulentquantities calculated with both methods. Figure 6 shows thefractional difference in the fluxes between the PF and the DRmethods in a similar manner to Wilczak et al. (2001), but asa function of the mean wind direction: (a) differences betweenthe PF and DR longitudinal stresses, τx, normalized by τ PF

x ; (b)differences between the PF and DR lateral stresses, τy, normalizedby τ PF

x ; (c) differences between PF and DR magnitudes of thetotal stress, |τ |, normalized by

∣∣τ PF∣∣; (d) differences between the

PF and DR sensible heat flux, Hs, normalized by the HPFs . In

addition, the mean of the absolute normalized differences, thestandard deviation and the correlation coefficient, R, between thetwo corresponding variables are shown in each plot. The p-values,indicating the statistical significance of R, are omitted, since p ≈ 0for all four cases.

All variables in Figure 6 exhibit the smallest deviation fromzero at a wind direction of about 295◦, indicating a dependenceof the tilt correction error on the mean wind direction. Whilethe differences for τx and Hs (Figure 6(a) and (d)) are relativelysmall, τy (Figure 6(b)) shows large differences, exceeding themean difference of τx by a factor of three. The change in signat 295◦ points out a systematic bias related to wind direction.The correlation coefficient of R = 0.11 indicates poor agreementbetween the two methods. Consequently, this causes relativelyhigh mean differences in |τ | (Figure 6(c)), even though thecorrelation (R = 0.75) is high.



240 270 300 330 0 30 60−4

−3

−2

−1

0

1

2

3

4


(τxP

F−

τ xDR)

/ τxP

F

(a)

I II III

mean = 0.32std = 1.00R = 0.81

240 270 300 330 0 30 60−4

−3

−2

−1

0

1

2

3

4


(τyP

F −

τ yDR)

/ τxP

F

(b)

I II III

mean = 0.92std = 2.20R = 0.11

240 270 300 330 0 30 60−4

−3

−2

−1

0

1

2

3

4


(|τP

F| −

|τD

R|)

/ |τ

PF|

(c)

I II III

mean = 0.44std = 1.47R = 0.75

240 270 300 330 0 30 60−4

−3

−2

−1

0

1

2

3

4


(HsP

F −

HsD

R)

/ HsP

F

I II III

(d)mean = 0.22std = 0.80R = 0.98

Figure 6. Normalized differences between PF and DR of (a) τx ; (b) τy ; (c) |τ |; (d) Hs; all as a function of mean wind direction. The mean, standard deviation and thecorrelation coefficient R of the normalized differences are shown in the plots. This figure is available in colour online at wileyonlinelibrary.com/journal/qj

240 270 300 330 0 30 60−180

−135

−90

−45

0

45

90

135

180


α (d

eg)

I II III

measurements DR

bin–averaged measurements DR

bin–averaged measurements PF

Figure 7. The off-wind angle α calculated using the DR method as a functionof the mean wind direction. Dots represent measurements, the thin solid linethe bin-averaged mean and standard deviation and the thick solid line the bin-averaged mean of α calculated with the PF method. For standard deviationswith the PF method, see Figure 2. This figure is available in colour online atwileyonlinelibrary.com/journal/qj

Because of the poor agreement in τy, the impact on the relativeoff-wind angle α might be quite large as well. For that reason α isrecalculated using the DR method and plotted as a function of themean wind direction in Figure 7. In order to compare αDR to thecorresponding results of αPF, the bin-averaged mean of αPF fromFigure 2 is also included (thick solid line). The resulting off-wind

angles differ considerably between the two rotation methods.The DR has generally larger magnitudes of α than the PF, αDR

frequently exceeding αPF by a factor of two or more. In thevicinity of branch II both methods give similar results, althoughthe magnitudes of αDR are generally higher, while for branches Iand III the two methods give results even contrary to each other.In a narrow range around 295◦ both methods seem to agree. Thestandard deviations are higher for αDR than for αPF, with thesmallest values at about 295◦, where also the differences betweenτx, τy, |τ | and Hs are smallest (Figure 6). The high agreement ofαDR (Figure 7) with the observations of Kilpelainen and Sjoblom(2010) confirms that differences in α are strongly related to theunderlying coordinate transformation method.

In previous studies it has been shown that the DR methodmay cause biased results; in particular, τy is very sensitive totilt errors (e.g. Wilczak et al., 2001). The minimum normalizeddifferences at about 295◦ (Figure 6) indicate a physical tilt ofthe instrument at this direction. This tilt causes partially largedifferences between τ PF

y and τDRy , which are the reason for

the considerable disagreement between αPF and αDR (Figures 2and 7). Foken et al. (2004) argue that the DR method does notadequately correct for instrument tilt and often causes unrealisticrotation angles. Hence results of αDR have to be interpreted withcaution. Nevertheless, the dependency of α on the mean winddirection can be seen with either of the two methods.

In Figure 8, the non-dimensional gradients, φm in (a) and φh

in (b), are reproduced using the DR method for U > 3 m s−1

(as in Figures 3(b) and 5(b)). The bin-averaged mean of φPFm and

φPFh from Figures 3(b) and 5(b) are also included (thick solid

line), while φH96m and φH96

h are indicated by different backgroundshadings. The influence of the different rotation methods on φm

and φh is relatively small. Even though DR causes higher standard



−2 −1.5 −1 −0.5 0 0.5−0.5

0

0.5

1

1.5

2

2.5

3

3.5

z/L

−2 −1.5 −1 −0.5 0 0.5

z/L

φ m(a)

U > 3.0 m s−1

measurements

bin–averaged measurements DR

bin–averaged measurements PF

−1

0

1

2

3

4

5

6

φ h

(b)U > 3.0 m s−1

Figure 8. The non-dimensional gradients, φm in (a) and φh in (b), calculatedusing the DR method compared to the PF method for wind speeds U > 3 m s−1.The borderline between the areas shaded in white and grey indicates φH96

m andφH96

h . This figure is available in colour online at wileyonlinelibrary.com/journal/qj

deviations (compare Figures 3(b) and 5(b)), both methods agreefairly well. Considerable differences only arise for z/L > 0 withsmaller values of φDR

m and φDRh . However, the limited quantity of

data for z/L > 0 prohibits more general conclusions.

6. Conclusions

Three summers of meteorological measurements on the coastof Isfjorden, Svalbard, provided an extensive dataset of theatmospheric surface layer over an Arctic fjord. From this theturbulent fluxes of momentum and sensible heat were calculatedand analysed in terms of seasonal variability and differing fetchconditions. Furthermore, the validity of the MO similarity theorywas examined, and two different coordinate rotation methodswere carefully compared.

The local wind field was found to be influenced bytopographic effects, especially during strong winds. However,surface heterogeneity in combination with radiative heating overland might also affect the flow inside Isfjorden under certainconditions. It is likely that during some events with weak windsthe influence of swell caused an upward-directed momentumflux. The combination of wave influence and topographic effectscaused significant mean off-wind angles between the surface stressvector and the mean wind direction, in some cases exceeding 30◦,which is comparable to typical values over the open ocean. Theturbulent flux of sensible heat during summer was considerablyweaker and sometimes negative compared to ice-free winterconditions. As well as this typical seasonal cycle, the sensible heat

flux showed a strong dependency on the origin of the mean flow,indicating strong spatial variability over the fjord, which mightbe due to differential solar heating of the surrounding land andadvection of the overlying air.

The MO similarity theory was found applicable to the surfacelayer of an Arctic fjord under certain conditions. The non-dimensional gradients of wind and potential temperature werefound to depend primarily on the mean wind speed, with abetter agreement with theory for moderate and high wind speeds.The complex terrain surrounding the fjord also had an influenceon the results. In cases with a mean flow across the fjord themomentum fluxes were higher than expected from the theory,resulting in φm < φH96

m . In addition, for flow along the fjord,topographic steering and the effect of swell occasionally led todifferences between the observed stress vector and the winddirection. The same effect of the topography could not be foundfor φh. Interestingly, the results were generally similar to previousresults for ice-free winter conditions.

Some turbulent quantities, especially the off-wind angle, werestrongly influenced by the underlying coordinate rotation method(planar fit or double rotation method), applied to the data. TheDR method resulted in much larger values of α and even differentsigns for certain wind directions compared to the PF method.This disagreement is most likely due to the DR method beingmore sensitive to the physical tilt of the sonic anemometer, whichresults in increased values of αDR. Errors due to instrument tiltare better treated in the PF method. Therefore, we recommendthe use of the PF method when possible and that turbulentquantities, such as the off-wind angle, should be treated carefullyif the DR method is used. Other quantities, such as the non-dimensional gradients, did not show a significant dependency onthe coordinate transformation method.

Acknowledgements

The authors want to thank the Norwegian Hydrological Servicefor providing the sea-level data. We also acknowledge the supportof technicians, Stefan Claes and Tor de Lange, in helping with theinstallation of the measurement systems. Dr Stephen J. Coulson isthanked for valuable comments on the manuscript. The work ofTiina Nygard was supported by the Academy of Finland throughthe CACSI project (contract 259537).

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