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  • View in gallery
    Fig. 1.

    Photograph of study site showing tripod with eddy-covariance instrumentation. Surface conditions shown in the photograph were typical of the study period.

  • View in gallery
    Fig. 2.

    Time series of (a) air temperature and (b) wind speed, both measured at 1.75 m above the snow surface.

  • View in gallery
    Fig. 3.

    Time series of (a) incoming and outgoing longwave radiation fluxes and (b) net longwave radiation fluxes. Note negative outgoing fluxes are shown as positive for comparison to the incoming fluxes.

  • View in gallery
    Fig. 4.

    Frequency histogram of the measured turbulent heat fluxes.

  • View in gallery
    Fig. 5.

    Time series of selected snow temperatures that were used to calculate the rate of internal energy changes. Noted depths are provided with respect to the snow–atmosphere interface. Snow depth remained steady at 42.5 cm throughout the month.

  • View in gallery
    Fig. 6.

    Comparison of the sum of the turbulent heat fluxes (QH + QE) to the sum of the nonturbulent heat fluxes [dU/dt – (QG + Q*)]. Presented data are from 30-min periods when wind speeds were >3.0 m s−1.

  • View in gallery
    Fig. 7.

    Mean daily energy fluxes. The sum of the turbulent heat fluxes (QH + QE) have been calculated as the residual of the nonturbulent energy terms. The error bars denote the uncertainty associated with the estimate due to random measurement errors.

  • View in gallery
    Fig. 8.

    Time series comparison of the longwave radiation fluxes (left vertical axis), and the sonic air temperature measured (right vertical axis) for 7–8 Feb. Dashed–dotted vertical lines indicate the local times of sunrise and sunset.

  • View in gallery
    Fig. 9.

    Comparison of the air temperature and the mean near-surface snow temperature. Circled data highlight data measured between 0530 LT 14 Feb and 1730 LT 15 Feb.

  • View in gallery
    Fig. 10.

    Friction velocity directly measured by the sonic anemometer (× symbols) and estimated with two-level gradient method (dots) when (a) sensible heat flux was directed toward the snow and (b) when sensible heat flux was directed toward the atmosphere. Data shown are from near-neutral conditions only, where |z/L| < 0.1.

  • View in gallery
    Fig. 11.

    (a) Measured snow temperatures, (b) snow temperatures as modeled by SNTHERM, (c) comparison of the measured rate of internal energy change vs simulated rate of change, and (d) comparison of the measured and simulated sensible heat flux. Note: the legend shown in (b) also represent the lines in (a). The values refer to depth above the soil–snow interface.

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Problems Closing the Energy Balance over a Homogeneous Snow Cover during Midwinter

Warren HelgasonChemical and Biological Engineering, University of Saskatchewan, Saskatoon, Saskatchewan, Canada

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John PomeroyCentre for Hydrology, University of Saskatchewan, Saskatoon, Saskatchewan, Canada

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Abstract

Application of the energy balance approach to estimate snowmelt inherently presumes that the external energy fluxes can be measured or modeled with sufficient accuracy to reliably estimate the internal energy changes and melt rate. However, owing to difficulties in directly measuring the internal energy content of the snow during melt periods, the ability to close the energy balance is rarely quantified. To address this, all of the external energy balance terms (sensible and latent heat fluxes, shortwave and longwave radiation fluxes, and the ground heat flux) were directly measured and compared to changes of the energy content within an extensive, homogeneous, snowpack of a level field near Saskatoon, Saskatchewan, Canada. The snow was observed to lose significant amounts of energy because of a persistent longwave radiation imbalance caused by low incoming fluxes during cold, clear-sky periods, while solar heating of the snow surface caused an increase in the outgoing fluxes. The sum of the measured turbulent heat fluxes, ground heat flux, and solar radiation fluxes were insufficient to offset these losses, however the snowpack temperatures were not observed to cool. It was concluded that an unmeasured exchange of sensible heat was occurring from the atmosphere to the snowpack. The exchange mechanism for this is not known but would appear to be consistent with the concept of a windless exchange as employed to close the energy balance in various snow models. The results suggest that caution should be exercised when using the energy balance method to determine changes in internal energy in cold snowpacks.

Corresponding author address: Warren Helgason, Chemical and Biological Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon SK S7N 5A9, Canada. E-mail: warren.helgason@usask.ca

Abstract

Application of the energy balance approach to estimate snowmelt inherently presumes that the external energy fluxes can be measured or modeled with sufficient accuracy to reliably estimate the internal energy changes and melt rate. However, owing to difficulties in directly measuring the internal energy content of the snow during melt periods, the ability to close the energy balance is rarely quantified. To address this, all of the external energy balance terms (sensible and latent heat fluxes, shortwave and longwave radiation fluxes, and the ground heat flux) were directly measured and compared to changes of the energy content within an extensive, homogeneous, snowpack of a level field near Saskatoon, Saskatchewan, Canada. The snow was observed to lose significant amounts of energy because of a persistent longwave radiation imbalance caused by low incoming fluxes during cold, clear-sky periods, while solar heating of the snow surface caused an increase in the outgoing fluxes. The sum of the measured turbulent heat fluxes, ground heat flux, and solar radiation fluxes were insufficient to offset these losses, however the snowpack temperatures were not observed to cool. It was concluded that an unmeasured exchange of sensible heat was occurring from the atmosphere to the snowpack. The exchange mechanism for this is not known but would appear to be consistent with the concept of a windless exchange as employed to close the energy balance in various snow models. The results suggest that caution should be exercised when using the energy balance method to determine changes in internal energy in cold snowpacks.

Corresponding author address: Warren Helgason, Chemical and Biological Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon SK S7N 5A9, Canada. E-mail: warren.helgason@usask.ca

1. Introduction

There is considerable interest in modeling the interactions between snow and the atmosphere—primarily concerning the flow of energy between the two media. Some of the main applications for this knowledge are prediction of snowmelt rates for hydrological purposes, determination of land surface–atmosphere interactions for climate modeling and weather forecasting, and prediction of avalanche hazard for the transportation and recreation industries. Many of the snow physics models developed for these applications have been based upon the energy balance approach (e.g., Anderson 1968; Gray and Landine 1988; Brun et al. 1989; Jordan 1991; Marks and Dozier 1992; Bartelt and Lehning 2002). This technique can be summarized by considering a simple energy balance [Eq. (1)], presented in one-dimensional form for a horizontally homogeneous snowpack:
e1

The rate of change of internal energy, U, is equal to the sum of all of the vertical energy fluxes at the air–snow interface and the soil–snow interface: the turbulent fluxes of sensible heat, QH, and latent heat, QE ; the net radiation, Q*; the ground heat flux, QG; and the flux of advected energy, QA, such as that contained in rain falling on snow. Equation (1) is then coupled with the mass balance of the snowpack to determine the amount of melting (through the latent heat of fusion).

This seemingly straightforward approach becomes more complicated when one considers the complex structure of snow. Snowpacks are porous structures, deposited in permeable and highly heterogeneous layers, and are subject to further changes in structure due to wind redistribution and metamorphism. Thus, accurate accounting of snow mass and energy changes requires a sophisticated knowledge of how these processes evolve, both temporally and spatially. Snow physics models have been greatly improved by advances in our understanding of the physical processes, leading to the introduction of many new parameterizations such as radiative transfer (e.g., Dozier 1980; Warren and Wiscombe 1980; Wiscombe and Warren 1980), snow metamorphism (Lehning et al. 2002), turbulent transfer (Andreas et al. 2005), blowing snow (Pomeroy et al. 1993), etc. However, despite these advances, even sophisticated snowmelt models do not consistently produce acceptable results in all environments, as demonstrated in recent snowmelt model intercomparison projects (Etchevers et al. 2004; Rutter et al. 2009). This disparity can be partly attributed to an inability to robustly simulate the processes of the snowpack and the associated interactions with the atmosphere and soil boundary conditions. These problems were identified over 35 years ago (Male and Gray 1975) but have not been fully resolved.

Not only are the aforementioned physical processes imperfectly understood and difficult to represent within a model, but they are also very difficult to measure. Owing to this, rarely are all of the terms in Eq. (1) actually measured together in the same experiment. Measurement of internal energy is notoriously difficult because of the occurrence of phase changes within a melting snowpack. Thus, it is usually calculated as the residual of the other measured terms. Of the remaining terms, measurement of the turbulent heat fluxes has proven to be difficult. However, the use of the eddy correlation technique to measure the turbulent fluxes has become increasingly common in hydrological investigations (e.g., Shook and Gray 1997; Sauer et al. 1998; Pomeroy and Essery 1999; Hayashi et al. 2005; Pomeroy et al. 2006; Marks et al. 2008; Reba et al. 2009). Unfortunately, since the internal energy is rarely measured directly, there are no published measurements of the energy balance closure over snow-covered land; the degree of which can be a good indicator of the uncertainty in the measurements, and should be considered relative to the expectations of certain parameterizations that were derived from these measurements.

To calculate the rate of snowmelt, sublimation, or internal energy change, energy balance closure must be assumed. The underlying problem is that energy balance nonclosure is almost a ubiquitous observation reported by investigators of summertime land surface energy and gas fluxes (e.g., Aubinet et al. 2000; Wilson et al. 2002; Barr et al. 2006). In practically all cases, the energy balance does not close, and the available energy (Q*QG) exceeds the sum of the other terms (QH + QE) by about 10%–30% (Massman and Lee 2002; Wilson et al. 2002). Potential reasons have been discussed extensively (see Massman and Lee 2002 and Loescher et al. 2006 for comprehensive reviews). Undermeasurement of the turbulent heat fluxes can be related to systematic biases due to high-frequency flux attenuation that are caused by physical limitations of the sampling instrument (van Dijk 2002; Cuerva et al. 2003), lack of correlation between variables sampled by instruments that are physically separated (Kristensen et al. 1997), flow distortions introduced by sampling instruments (Högström and Smedman 2004) and towers (Dyer 1981), as well as data processing artifacts such as low-frequency losses due to inadequate averaging periods, detrending, or coordinate rotation (Finnigan et al. 2003; Moncrieff et al. 2004). Fortunately, corrective techniques have been developed to compensate for many of these limitations (e.g., Moore 1986; Laubach and McNaughton 1999; Massman 2000; Massman and Clement 2004), and have been recently evaluated over snow surfaces (Reba et al. 2009). Other causes that are more meteorological in nature include random errors introduced by atmospheric motions occurring on nonturbulent time scales, nonstationarity, and poorly developed turbulence in weak winds and stable conditions (Mahrt 1998; Aubinet 2008). Many of these latter conditions are regular features of the atmosphere that develop over snow; thus the ability to close the surface energy balance for snow surfaces warrants special consideration. The primary issue is that, because snow is a very effective emitter of thermal radiation, the snow surface temperature is predominantly colder than the overlying air, which creates a stable atmosphere in which the density stratification can effectively dampen or extinguish turbulent mixing. Furthermore, snow surfaces have very small roughness elements from which to generate turbulent mixing of the overlying air. As a result of these inherently low-turbulence levels, the measured heat fluxes are often very small and may be difficult to resolve. In essence, the boundary layer over snow is comparable to the nocturnal boundary layer over other land surface types, where the density stratification is well documented to present numerous challenges to the interpretation of surface fluxes measured using the eddy-covariance technique (e.g., Mahrt et al. 1998; Aubinet 2008; Acevedo et al. 2009).

This paper presents direct measurements of all of the energy balance components in a homogeneous prairie snowpack during a midwinter period. The purpose is to report the degree of energy balance closure observed and to investigate causes of nonclosure during midwinter periods.

2. Methods

a. Description of study site

The data were collected from Kernen Farm (52.16°N, 106.53°W), which is an agricultural research site located approximately 2.5 km east of the city of Saskatoon, Saskatchewan, Canada. The site is located on a gently undulating lacustrine plain that is immediately surrounded by agricultural fields with similar topography. To the south and east at distances greater than 4 km there is a range of low hills that are partly covered in deciduous trees and brush. This site is well suited for evaluation of the snow energy balance: it is relatively flat, and has a very homogeneous land cover for distances of 1–4 km, depending on direction. Within this fetch, there are no major obstacles (houses, trees, etc.) that would be expected to interfere with boundary layer development.

The experiment was conducted during the winter of 2006/07, with instrumentation installed in late November 2006 and data collected through March 2007. This paper specifically presents data that were collected during 1–28 February 2007.

Throughout February, the depth of snow at the instrument site was consistently around 42.5 cm. Deposition of fresh snow measured at the Saskatchewan Research Council climate reference station in Saskatoon amounted to 19 cm. However, this amount was contributed by five small precipitation events, which were subsequently eroded by blowing snow processes, resulting in a negligible increase in snow depth. Because of snow drifting, the snow surface exhibited gentle undulations at scales on the order of 10–20 m with sastrugi occasionally developing at shorter scales (1–2 m).

b. Measurements

Details regarding the instrumentation used in this experiment are presented in Table 1. A photograph of the site and main instruments is shown in Fig. 1. The setup consisted of a main tripod—which the two eddy-covariance systems (each consisting of a sonic anemometer and krypton hygrometer), reference temperature and relative humidity, and dataloggers were mounted on—and an auxiliary mast (not visible in Fig. 1), which supported the radiometers and a three-cup anemometer. This mast was essentially a 50-mm diameter pole anchored in the ground and tethered with guy lines. The slim profile of this mast created minimal obstruction to the radiometer field of view. The snow thermocouples, soil interface temperature, and heat flux plates were installed at a nearby location (approximately 2 m from main mast). A blowing snow particle detector (Brown and Pomeroy 1989) was installed approximately 10 cm above the ground, and was used to identify blowing snow conditions.

Table 1.

Instrumentation details.

Table 1.
Fig. 1.
Fig. 1.

Photograph of study site showing tripod with eddy-covariance instrumentation. Surface conditions shown in the photograph were typical of the study period.

Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-0135.1

All of the relevant terms in Eq. (1) were directly measured in this experiment and average values were calculated at 30-min intervals. The advection term QA was not included in the energy balance since there was neither rain falling on the snowpack nor meltwater leaving the snowpack during the selected data periods. Furthermore, the amount of snowfall received in any 30-min period was minimal, and could not be expected to contribute significant energy at these short time scales. A similar rationale was applied to blowing snow where it was generally observed that the amount of blowing snow entering the control volume was equal to the amount leaving, and did not affect the energy status of the wind hardened snowpack. Because of the extensive, uniform snow cover, the assumption of horizontal homogeneity was made and horizontal energy fluxes were not considered. Fluxes directed toward the snowpack were assigned a positive sign, and those directed away from the snowpack were considered to be negative.

1) Internal energy

The rate of internal energy change [Eq. (2)] depends on the rate that energy is required or liberated during melting RM and refreezing RF and the internal energy change associated with each snow constituent: ice (subscript i), liquid water (subscript w), and air (subscript a) as the temperature of the snowpack varies from a reference state (usually taken as 0°C). The constituents are considered on a fractional volumetric basis, and θi + θw + θa = 1. The formulation presented here assumes that the porous medium is at thermal equilibrium—that is, Ts = Ti = Tw = Ta, where the subscript s denotes snow (encompassing all of the aforementioned constituents). In Eq. (2) λFUS is the latent heat of fusion, ρ is the density, and cp is the heat capacity:
e2
During cold midwinter periods where the liquid water content of the snowpack is negligible, measurement of the internal energy change can represented as Eq. (3) since melting and refreezing are not occurring. Knowledge of the depth profiles of temperature, T(z), and snow density, ρ(z), can then permit the volumetric heat content to be integrated between the soil–snow interface (z = 0) and the upper boundary of the snowpack (z = H):
e3

As the data selected for this paper were only from periods where the air and snow temperatures were well below freezing, the internal energy was determined from the depth and density of the snowpack and the measured internal temperature changes.

Snow densities were obtained from samples collected using a triangular scoop of known volume from a snow pit nearby the snow thermocouple array on 21 January 2007 in which the average density was 310 kg m−3 but ranged from 265 kg m−3 for a depth hoar layer to 390 kg m−3 for a refrozen melt layer. To minimize disturbance around the measurement site, no further snow pit surveys were conducted. Instead, bulk snow densities along a nearby transect were sampled using an ESC-30 snow tube (30-cm diameter) on 6 February (305 ±70 kg m−3) and again on 22 February (265 ±35 kg m−3). To account for changes in density that would affect the calculation of internal energy, the Snow Thermal Model (SNTHERM; Jordan 1991) was used to model the snow metamorphism and associated density changes throughout the remaining winter period.

Internal snow temperature measurements were made using 30 gauge (0.25-mm diameter) type-E thermocouples that were attached to thin support wires, strung between a frame made from copper tubing painted white. The thermocouple wires were routed from the datalogger along the ground to the bottom of the frame (at the snow–soil interface) and then up the appropriate support wire to the measurement height. Each support wire contained only five thermocouple wires in an effort to reduce the mass that could absorb solar radiation and warm the snow. The thermocouple array was installed at the beginning of December 2006, when there was approximately 10 cm of snow on the ground. Natural snowfall and redistribution processes then formed the snowpack around the thermocouples, providing an in situ undisturbed measurement of the snow temperature profile.

The snow surface temperature Tsurf was measured using the outgoing longwave radiation measurement, and rearranging the longwave radiation balance Eq. (4) where the emissivity εv is taken as 0.99 (Warren 1982) and σ is the Stefan–Boltzmann constant:
e4

To calculate the rate of internal energy change, the snowpack was discretized into 11 vertical segments with a thickness of 2 cm near the surface, increasing to 10 cm near the ground.

The uncertainty of the internal energy measurement is primarily affected by the errors in the snow temperature and density measurements. With respect to temperature, the accuracy of the snow thermocouple array depends on the errors introduced by the reference temperature measurement, the manufacturing tolerances of thermocouple wire, the measurement errors of the datalogger, and the linearization errors associated with converting the measured voltage to temperature. In this case, the largest uncertainty is introduced by the reference temperature measurement of the dataloggers (Campbell Scientific CR23x and CR5000), which both use a thermistor, with an expected accuracy in the field of ±0.2°C, if temperature gradients at the terminal block are minimal. To ensure this, additional insulation was placed within the datalogger enclosure to ensure that the junction temperature measured was representative of the entire terminal block. The type-E thermocouple wire used in this study is specified to have a 1% slope error, implying that the typical error should be ±0.15°C. To minimize the effect of this error all of the thermocouples were made from the same spool of wire. Relative to the aforementioned error sources, the voltage measurement and temperature conversion errors are expected to be less than 0.002°C. If all of these errors were random, the temperature measurement would have a combined uncertainty of approximately ±0.25°C. However, it is more likely that the larger error terms are systematic, which will have minimal influence upon the calculation of relative changes (both temporally and spatially). Furthermore, the scatter associated with random error is reduced substantially by making measurements at 5-s intervals and calculating a 30-min average, which for slowly changing conditions will reduce the uncertainty of ΔT over a 30-min period to less than ±0.1°C. With respect to the snow density, an uncertainty of ±50 kg m−3 was assumed. It was also assumed that the thickness of the layer of snow (which was determined by the thermocouple spacing) was known to within 0.002 m. For the range of values observed in this study, based on consideration of the propagation of the individual errors (Figliola and Beasley 2006, 148–190), the changes in internal energy of the snow can be calculated with an uncertainty of approximately 10%–15%.

2) Ground heat flux

Two Hukseflux HFP01 ground heat flux plates (Hukseflux Thermal Sensors, Delft, The Netherlands) were installed near the base of the snow temperature array by inserting the plate directly between the snowpack and the soil. The ground heat flux term QG was obtained directly from the average of the two heat flux plates. The manufacturer-stated accuracy for uncalibrated use in soils was −5% to +15% (for 12-h totals). Based on the measured snow densities, the thermal conductivity of the bottom layer of the snowpack was likely on the order of 0.15–0.30 W m−1 K−1, while the frozen soil was likely between 0.5 and 1.5 W m−1 K−1, depending on antecedent moisture conditions. Since the range of thermal conductivities for the soil compares favorably to the thermal conductivity for the heat flux plate (0.8 W m−2 K−1), the technique should provide a reasonable measurement of the soil heat flux. However, considering the uncertainty in these estimates, it is possible that the systematic errors may be greater than the manufacturer-stated accuracy.

3) Radiation flux

The radiation fluxes were measured with a Kipp & Zonen CNR1 net radiometer composed of two pyranometers and two pyrgeometers, which provide separate downwelling and upwelling measurements of the shortwave (0.3–3.0 μm) radiation flux QSW and the longwave (5.0–50.0 μm) radiation flux QLW. The net radiation flux Q* was obtained from the sum of all four radiometers. To prevent rime growth on the sensors, the CRN1 body was conditionally heated using the onboard 12-V heater whenever the battery had sufficient charge and the relative humidity of the air was greater than 95% with respect to ice. An error similar to riming can occur when snow blocks the upward-facing sensors. To identify erroneous readings when the incoming shortwave dome was covered with snow, the outgoing radiation was used to provide an estimate of the incoming radiation by dividing QSWout by the albedo α, which was calculated from measurements during snow-free conditions for all solar zenith angles greater than 80°. To detect any periods where the longwave radiation may have been affected by snow or rime, an inspection similar to that described in van den Broeke et al. (2004) was used. Overall, these errors were infrequently observed, and are not believed to have affected this dataset to a significant extent.

The manufacturers state the accuracy of both the pyrgeometer and the pyranometer to be ±10% for daily totals. Known errors of this sensor occur because of heating, and also under conditions of strong insolation, where a differential temperature can develop between the sensor and the aluminum body containing the platinum resistance thermometer to which the radiation flux is referenced. In any case, this effect would cancel out when calculating the net longwave radiation.

4) Turbulent heat flux

The eddy-covariance technique used in this experiment employed a fast-response sonic anemometer (CSAT3; Campbell Scientific) to measure the wind velocity components—u, υ, and w—and the sonic air temperature Ts, as well as a krypton hygrometer (KH20; Campbell Scientific), which measures water vapor density ρυ. The two eddy-covariance systems were mounted on arms extending from the tripod with the sonic anemometers oriented to the southwest (220°) such that the two prevailing wind directions of NW and SE would not be obstructed by the sensor arms. The krypton hygrometers were mounted at the same height and were offset 15 cm behind the center of the sonic anemometer sampling volume. The effective measurement heights of the two eddy-covariance systems, after considering the snow depth, were 1.58 and 3.24 m, respectively. The data from both eddy-covariance systems were sampled and recorded at 20 Hz.

Prior to calculating fluxes, the raw data were despiked following a similar routine to that described by Vickers and Mahrt (1997). Additionally, the internal flag system of the CSAT3 was used to indicate measurement errors.

Following despiking, the data were separated into 30-min blocks, and the required moments were calculated and then rotated into a new coordinate system using the planar fit method (Wilczak et al. 2001). The upper sonic anemometer data were rotated into the coordinate system defined by the lower anemometer, thus ensuring that the output from both anemometers were in the same coordinate system.

The sensible heat flux was calculated as the covariance between the vertical velocity and sonic temperature, both of which were obtained from the sonic anemometer. Because of the effect of humidity on the speed of sound, the true sensible heat flux, , can differ from the heat flux calculated using the sonic temperature, . However, given the cold temperatures and very low specific humidities typical of midwinter periods, the difference was found to be negligible; therefore,
eq1

The latent heat flux was corrected for attenuation of the krypton radiation source due to O2 in the measurement volume following van Dijk et al. (2003). Under the cold and dry measurement conditions reported in this paper, the effects of the density variation due to the vapor flux [i.e., Webb–Pearman–Leuning (WPL) corrections (Webb et al. 1980)] were negligible and were not applied.

The analytical method of Massman (2000, 2001) was used to correct the measured fluxes for the effects of attenuation due to pathlength averaging, high pass filtering due to block averaging, and lateral separation of the KH20 sensor.

The calculated fluxes were removed from analysis if 1) the period contained excessive data spikes, 2) the wind directions were from the 60° sector centered on the tower, or 3) the signal from the KH20 was degraded, indicating moisture or frost buildup on the lens. Additionally, periods with low turbulence were excluded from the analysis of the energy balance closure based on a wind speed threshold determined using the nonstationarity metric suggested by Foken and Wichura (1996), which compares the mean value of the fluxes calculated over six nonoverlapping 5-min periods to the flux value calculated over a 30-min averaging period. When the absolute difference was less than 30%, the fluxes were considered to be approximately stationary. The threshold wind speed identified by this procedure was approximately 3 m s−1, which typically corresponded to a friction velocity of 0.1 m s−1. For wind speeds below this threshold, the calculated fluxes were influenced by low-frequency motions that were poorly sampled by the 30-min averaging period. This was confirmed by examining individual cospectra (data not shown) and by applying the multiresolution flux decomposition procedure (Howell and Mahrt 1997).

c. Modeling

The one-dimensional snow heat and mass balance model SNTHERM.89.rev4 (Jordan 1991) was used to model the snow energetics. The modeling domain was discretized into 11 thin control volumes for the snow, which were made as small as could be adequately represented by the available thermocouples. These were the same layers as used to calculate the internal energy content, as previously described. The snow layers ranged from 0.10 m at the bottom of the snowpack to 0.02 m near the top of the snowpack, and the surface layer was specified as a 0.005-m layer. The soil zone consisted of a single 0.10-m layer.

The model was driven with measurements of incoming longwave radiation and incoming and outgoing shortwave radiation as well as wind speed (three-cup anemometer), air temperature, and relative humidity all measured at 1.75 m above the snow surface. SNTHERM models the turbulent fluxes using the bulk transfer method, for which the adopted parameterizations are described in Jordan et al. (1999). For the modeling presented, the momentum roughness length z0m was fixed at 1 × 104 m (as measured by the sonic anemometers at this site). The ratio of the sensible and latent heat transfer coefficients relative to the drag coefficient were both set to 1.0.

3. Results and discussion

a. Relevant meteorological conditions

Air temperatures were cold for the first half of February (Fig. 2a), ranging from daily highs of −15°C to evening lows near −35°C; this period was followed by more moderate −5° to −15°C temperatures during the second half of the month. Because of the cold temperatures, the air was quite dry and the monthly mean water vapor pressure was approximately 170 Pa. Near-surface winds (Fig. 2b) were often calm, but were disrupted by five short events with wind speeds greater than 8 m s−1. This pattern is characteristic of a persistent arctic high-pressure ridge that often forms over the Canadian Prairies, which is interrupted by the passage of a low-pressure system. The frontal systems associated with the breakup of such high-pressure events often produce higher wind speeds and small amounts of snowfall, which are frequently associated with blowing snow.

Fig. 2.
Fig. 2.

Time series of (a) air temperature and (b) wind speed, both measured at 1.75 m above the snow surface.

Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-0135.1

b. Energy balance

The net longwave radiation flux (Fig. 3)—which, averaged over the month, was equal to −30.8 W m−2—was the dominant term in the measured surface energy budget. During the colder, initial part of the month, cloudy periods were less frequent, and short periods with losses of longwave radiant energy of up to 80 W m−2 were common. During the latter half of the month, warmer conditions were associated with more frequent cloud cover, which resulted in smaller net longwave radiation fluxes. The negative longwave radiation was not adequately compensated by net shortwave radiation. Because of the high northern latitude of the site, the days were relatively short and the incoming solar radiation flux was relatively small (peak values were less than 500 W m−2). Owing to the frequency of small snowfall events, and the nonmelting conditions, the measured albedo was consistently around 0.9, which resulted in a relatively minor contribution to the energy balance from QSW (averaging 7.6 W m−2 over the month).

Fig. 3.
Fig. 3.

Time series of (a) incoming and outgoing longwave radiation fluxes and (b) net longwave radiation fluxes. Note negative outgoing fluxes are shown as positive for comparison to the incoming fluxes.

Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-0135.1

Throughout February, soil temperatures were slightly warmer than the overlying snow, which resulted in a heat flux from the soil toward the snow of 15 W m−2 during the colder part of the month, decreasing to 2 W m−2 as air temperatures warmed. Average ground heat fluxes over the month were 8.3 W m−2.

Owing to the calm winds, the relatively smooth snow surface, and the often stable atmospheric conditions, measured turbulent heat fluxes were often small (Fig. 4). In fact, 51% of the sensible heat fluxes and 66% of the latent heat fluxes were between ±5 W m−2, and had a negligible impact on the energy budget. Of the sensible heat flux values that had an absolute magnitude greater than ±5 W m−2, about 15% were directed toward the atmosphere, and 34% directed toward the snowpack. Only 4% of the QH fluxes were greater than 30 W m−2. The average measured sensible heat flux over the month was 3.9 W m−2. The latent heat flux values were similarly small, with 31% of them indicating minor rates of sublimation and only 3% indicating condensation. The average measured latent heat flux was −2.9 W m−2. Worth noting is that latent heat during condensation is expected to be undermeasured because of the possibility of frost forming on the lens of the krypton hygrometer and causing rejection of the observation.

Fig. 4.
Fig. 4.

Frequency histogram of the measured turbulent heat fluxes.

Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-0135.1

Samples of the internal snow temperatures that were used to calculate dU/dt are shown in Fig. 5. A diurnal pattern was observed at depths down to 20 cm beneath the snow surface. This was caused by warming of the surface from solar radiation during the day, followed by radiative cooling from the surface at night. The transition from cold to warm weather that occurred around 14–15 February affected the temperatures at all depths. The near-surface snow temperatures exhibited a temporal response that was very similar to the measured air temperature (as indicated by the similarity between Figs. 2a and 5). The maximum rate of change of the internal energy ranged between ±60 W m−2, while the average rate of change over the month was coincidentally exactly equal to zero.

Fig. 5.
Fig. 5.

Time series of selected snow temperatures that were used to calculate the rate of internal energy changes. Noted depths are provided with respect to the snow–atmosphere interface. Snow depth remained steady at 42.5 cm throughout the month.

Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-0135.1

c. Energy balance closure

The measured energy balance closure can be evaluated from Fig. 6, where the turbulent heat fluxes are plotted against the sum of the remaining energy balance terms, , for 30-min averaging periods. These data have been filtered to include only those periods where the mean wind speed was greater than 3.0 m s−1 so as to avoid periods with weakly developed turbulence. The data are additionally separated into daytime periods, where QSWin > 200 W m−2, and nocturnal periods when QSWin = 0 W m−2. Surprisingly, the energy balance closure ratio (defined as the sum of the turbulent heat terms divided by the sum of the nonturbulent terms) was noticeably better during the night than during the day. During the nocturnal periods, for cases where there was a sufficiently large turbulent flux signal (i.e., QH + QE > 10 W m−2) the mean energy balance closure ratio was 0.55 ±0.14 (n = 83), with a mean energy balance residual of 18.7 ±9.4 W m−2. During the daytime, the measured turbulent heat fluxes were observed to be unusually small, resulting in an energy balance closure ratio near zero with a mean energy balance residual of 42.6 ±29.7 W m−2 (for all daytime data shown in Fig. 6). In all cases, the measured sensible heat was much too small to offset the longwave radiation losses, resulting in poor energy balance closure.

Fig. 6.
Fig. 6.

Comparison of the sum of the turbulent heat fluxes (QH + QE) to the sum of the nonturbulent heat fluxes [dU/dt – (QG + Q*)]. Presented data are from 30-min periods when wind speeds were >3.0 m s−1.

Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-0135.1

The exclusion of fluxes measured during low wind speeds was necessary to obtain a meaningful quantification of the energy balance closure. However, a significant bias was introduced by the filtering process—particularly at this site where 56% of the 30-min periods during the month had wind speeds below 3 m s−1. Moreover, without a complete time series of the turbulent heat fluxes, it is difficult to relate the energy balance closure to the governing meteorological characteristics. To partially address these issues, the turbulent heat fluxes have been calculated as the sum of the nonturbulent energy terms—that is, (QH + QE)residual = dU/dt − 1 – Q*QG, where they represent the residual that would be required to close the energy balance. These have been calculated on a daily time step, and are presented as average values in Fig. 7. The uncertainty in the estimate of (QH + QE)residual, which is due to the propagation of the random error in the nonturbulent terms, was calculated to be a maximum of ±8 W m−2. The turbulent heat fluxes calculated in this manner were much larger than the measured fluxes (as supported by Fig. 6). During the colder first half of the month, (QH + QE)residual was quite large, which, because of the residual nature of the technique, is in response to the large longwave losses. Interestingly, (QH + QE)residual was particularly large during the very calm period of 6–14 February (Figs. 1a and 1b), where the turbulent fluxes would be expected to be restricted by boundary layer stratification. Despite the large radiation losses, the measured internal energy changes were relatively small, except for days where there were large changes in the air temperature (which can be identified by cross referencing Fig. 2a with Fig. 7). For example, increases in the internal energy content were observed on 5 and 13 February where increases in air temperature were accompanied by increased wind speeds. Similarly, the largest negative changes were recorded when air temperatures dropped significantly during a 1–2 day period—for example, 2–3 and 26 February.

Fig. 7.
Fig. 7.

Mean daily energy fluxes. The sum of the turbulent heat fluxes (QH + QE) have been calculated as the residual of the nonturbulent energy terms. The error bars denote the uncertainty associated with the estimate due to random measurement errors.

Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-0135.1

d. Characteristics of the observed energy imbalance

Considerable longwave radiation losses occurred from the snowpack during the first half of the month where temperatures were cold and skies were mainly clear. The sum of all of the measured surface energy fluxes was consistently negative, predicting that the internal energy of the snow should be decreasing throughout the month. However, no significant cooling of the snowpack was observed during this period, thus an unmeasured heat transfer mechanism was compensating for the radiation losses.

To better understand the observed energy imbalance, it is useful to examine detailed examples that illustrate the meteorological forcing contributing to the energy residual. The first example illustrates the longwave radiation balance contribution to the overall energy balance. In Fig. 8 the longwave radiation fluxes are compared to the air temperature for 7–8 February. During this period, the wind was very calm (mean daily wind speeds were 1.0 and 1.8 m s−1 for the two days, respectively), and the atmosphere was stably stratified. An increase in QLWout was caused by the periodic presence of clouds, which can be noted by the sharp increases in QLWin, causing an increase in the surface temperature and thereby increasing QLWout. During cloudy periods, the longwave radiation balance tended toward zero, and the overall energy balance was more fully closed. A more detrimental increase in QLWout was caused by solar heating of the snow surface during the day. For example, on 7 February, the absorption of solar radiation within the upper snowpack caused an increase in the surface temperature that was not accompanied by a change in QLWin. Consequently, the net radiation balance became increasingly negative concomitant with increased internal energy of the snow (due to the heating of the snow). It is believed that this occurrence is partially responsible for the poor energy balance closure observed during the day, particularly during calm periods, where there was little means for turbulent mixing, and QH was very small.

Fig. 8.
Fig. 8.

Time series comparison of the longwave radiation fluxes (left vertical axis), and the sonic air temperature measured (right vertical axis) for 7–8 Feb. Dashed–dotted vertical lines indicate the local times of sunrise and sunset.

Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-0135.1

Another unique characteristic of the energy balance closure problem is that the internal energy content of the snow was much more responsive to changes in the air temperature than to the measured surface energy fluxes. Figure 9 compares the sonic temperature at 1.58 m to the calculated mean temperature of the uppermost 10 cm of snow (excluding the radiometric surface temperature). The snow energy content was observed to be well correlated with the air temperature, particularly for individual warming or cooling events, which appear as an approximately linear set of points. As an example, the significant warming event that occurred between 0530 local time (LT) 14 February and 1730 LT 15 February is highlighted by the circled data points, clearly suggesting a relationship between the thermodynamic states of the snow and near-surface atmosphere.

Fig. 9.
Fig. 9.

Comparison of the air temperature and the mean near-surface snow temperature. Circled data highlight data measured between 0530 LT 14 Feb and 1730 LT 15 Feb.

Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-0135.1

e. Causes of the energy imbalance

Before attributing the energy imbalance to the absence of any particular energy term, the uncertainty in the measurements were considered. The energy residual was much too large to be explained by random errors (as noted in Fig. 7); therefore, systematic errors that could contribute to the imbalance are described below.

Biases in the radiation terms have been minimized by subjecting the data to previously mentioned quality control procedures. The incoming longwave fluxes were within the expected range and QLWout was verified through the observation that the surface temperature derived from this flux closely resembled the near-surface snow temperatures measured by thermocouples. The incoming shortwave radiation fluxes were compared to the predicted clear-sky values calculated using the procedures outlined in Pomeroy et al. (2007), which verified that the magnitude of the solar radiation flux was appropriate. The measured snow albedo derived from the incoming and reflected shortwave radiation fluxes was typically around 0.90. This high albedo value is representative of a fresh dry snow cover that is free of impurities and was associated with the five snowfall events interspersed through the month. The day versus night difference in the energy balance closure noted in Fig. 6 could be suggestive of a systematic error, such as a bias in the measured shortwave radiation budget. However, even if relatively large errors in the shortwave radiation terms are considered, such as a 10% reduction in the noted albedo, this would result in the daytime values of the nonturbulent energy terms in Fig. 6 lying closer to the origin. However, a bias in the solar radiation of that nature does not satisfactorily explain the daytime energy imbalance, which is characterized by much smaller turbulent heat fluxes than during the evening periods. A source of error not attributable to the instrumentation is due to atmospheric divergence of radiation, which can be significant during stable nocturnal periods (Garratt and Brost 1981). This would result in cooling of the air above the snow surface, and result in measurements of the upwelling radiation that are not representative of the snow surface. However, given that the radiometer was installed within 2 m of the surface, and air at temperatures colder than −20°C can hold very little water vapor (less than 1 g of water per kg of moist air), this does not seem like a plausible mechanism.

Unavoidably, a bias in the ground heat flux measurement could be expected, as the heat flux plates were installed at the snow soil interface and could be expected to have a different thermal conductivity than either the basal snow or the frozen soil. However, QG does not change rapidly, and does not fit the temporal distribution of the energy balance residual, which is more pronounced during the day than during the night.

Since the internal energy was measured with thermocouples, heating due to solar radiation was a possible source of error. However, the best indication that the near-surface thermocouples were not affected to a significant degree is that during sunny conditions, the infrared surface temperature responds to solar heating at a similar rate as the near-surface thermocouple. Furthermore, any errors due to solar heating will not be accumulated when daily totals are considered, such as in Fig. 7. The snow thermocouple array was regularly inspected for possible disturbances around the support wires that would prevent adequate contact between the snow and the thermocouple junctions. No problems were identified until later in the winter when higher incoming solar radiation caused melting around the wires (this occurred after the reported period). Overall, the internal energy changes of the snowpack are believed to be accurately determined for the specific location of the measurement array, however little information as to the spatial distribution of energy within the snow is known. Forced convection within the snowpack, or “wind pumping” (Colbeck 1989) has been observed to influence thermal field within the snow (e.g., Albert and McGilvary 1992; Albert and Hardy 1995; Sokratov and Sato 2001; Albert and Schultz 2002). This has been commonly attributed to pressure gradients caused by small-surface topographical features (Colbeck 1989; Waddington et al. 1996; Albert 2002). Sastrugi were formed on the snow surface during the present experiment so it is possible that forced convection could have influenced the snow temperatures. Thermal convection within the snow could also have played a role in modifying the temperature profile, as noted by Sturm (1991), who observed convective circulations within the snowpack caused by spatial variations in temperature at the snow–soil interface. The footprint of the snow temperature measurements (<1-m horizontal extent) was smaller than that of the radiation terms (within a circle of approximately 10-m diameter), and much smaller than that of the turbulent heat fluxes (on the order of 100–200 m upwind). Thus, spatial heterogeneity of snowpack and the associated heat transfer processes would not be adequately captured by a single measurement of the rate of the internal energy change, and may have contributed to the poor energy balance closure.

With respect to the turbulent heat fluxes, the observed imbalance might be explained if there was a systematic undermeasurement of the sensible heat flux to the snow or of the latent heat flux representing the condensation rate. As previously remarked, measurement of the water vapor flux under condensing conditions is normally not possible because of the presence of frost forming on the window of the krypton hygrometer, which degrades the signal. Nonetheless, because of the cold temperatures the latent heat flux could be expected to be minimal when both the sensible heat flux and the latent heat flux were directed toward the snowpack, as the Bowen ratio is predicted to be much larger than 1 (Andreas 1989). Thus, there is good reason to suspect that the sensible heat fluxes were systematically undermeasured. The two key issues related to this were 1) it was difficult to resolve the flux magnitude under calm conditions and 2) the sensible heat fluxes were very small (even during strong wind conditions), particularly during the day. These issues are expanded upon in the subsequent paragraphs.

The failure of the eddy covariance technique during calm winds was not a surprise, as this is a well-documented limitation of the technique. In the present study, the fluxes that were measured when wind speeds were below 2 m s−1 often exhibited excessively large scatter because of the inclusion of nonturbulent motions within the 30-min averaging period (as also noted in Vickers and Mahrt 2006). However, the interesting observation from these data is that, even during calm winds, a significant amount of energy is required to be extracted from the atmosphere in order to offset the radiation losses (e.g., Fig. 7). Similar conclusions have been documented in a number of modeling studies (e.g., Brun et al. 1989; Jordan 1991; Brown et al. 2006) in which the authors found that a “windless exchange coefficient” was required to increase the rate of sensible heat transfer to the snow during low wind speeds in order to prevent the snow temperatures from dropping to unrealistic levels. This result, along with the excellent coupling between the near-surface air temperature and the near-surface snow temperature (Fig. 11), highlights the need to consider nonturbulent exchanges of sensible heat between the air and the snowpack.

The second, and perhaps more troubling, observation regarding the sensible heat fluxes measured in this study is that, even when turbulence was well developed, the fluxes were still relatively small and the energy balance residual was unacceptably large (Fig. 6). At wind speeds greater than 3 m s−1, most of the characteristics of the turbulent flux were quite normal, as would be expected for a homogeneous and level site. The z0m value measured by the sonic anemometers was around 0.1 mm, which is typical of snow sites in open environments. Although small sastrugi were observed, they were generally aligned parallel to the predominant wind, and had little effect upon the observed roughness length (Jackson and Carroll 1978). Very similar fluxes were noted between both measurement heights (suggesting that flux attenuation due to the low measurement height was not a significant concern) and the cospectra of momentum, heat, and vapor flux were very similar to modeled curves for homogenous areas (Helgason 2009). All of these factors increased our confidence in the measured turbulent fluxes. However, an indication that the boundary layer was perhaps not as ideal as anticipated was revealed by comparing the friction velocity measured by the sonic anemometers with that calculated from the wind speed gradient (Fig. 10). Marked differences in the near-neutral flux–gradient relationships were observed depending on the direction of the heat flux. When the sensible heat flux was directed toward the atmosphere, the friction velocity measured by the sonic anemometers were quite similar to those estimated using the two levels of wind speed data. However, when heat fluxes were directed toward the snow, the gradient method predicted greater momentum flux than was measured by the sonic anemometers. This suggests that, even during slightly stable periods, the height of the surface boundary layer did not always extend to the flux measurement height and may indicate boundary layer decoupling. It would be necessary to have knowledge of the boundary layer structure within a few meters of the snow surface to more fully understand this observation. Anomalies in the near-surface temperature profile have been noted to form near the snow surface in similar environments (e.g., Sodemann and Foken 2005; Lüers and Bareiss 2011). In the latter example, a persistent temperature inversion was observed in the lowest 3 m of the boundary layer, ultimately rendering the measured eddy-covariance fluxes unrepresentative of the true surface heat flux. The discrepancy observed in Fig. 10 rouses some suspicion that there is an underlying meteorological issue that is confounding the sensible heat flux measurements. A similar finding was recorded by Stössel et al. 2010, who observed that eddy-covariance measurements of the water vapor flux over snow were consistently smaller than the mass changes observed in small snow lysimeters installed within the flux footprint. The authors suggested that this could partly be due to a latent heat flux divergence that was observed near the surface. Although the flux divergence associated with near-surface heat storage is not likely to account for all of the missing energy in the present study, it does warrant a more detailed investigation of the near-surface boundary layer over snow in future campaigns.

Fig. 10.
Fig. 10.

Friction velocity directly measured by the sonic anemometer (× symbols) and estimated with two-level gradient method (dots) when (a) sensible heat flux was directed toward the snow and (b) when sensible heat flux was directed toward the atmosphere. Data shown are from near-neutral conditions only, where |z/L| < 0.1.

Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-0135.1

The one-dimensional snow energy balance model SNTHERM was used to confirm the adequacy of the measurements in terms of the conceptual understanding of the snow energy balance. Sample results from 13–15 February are provided in Fig. 11. Without any optimization of the model parameters, the simulated snow temperatures were adequately simulated relative to the measured values (Figs. 11a,b), and the internal energy of the snowpack (Fig. 11c) was predicted with sufficient accuracy to lend confidence to the ability of the model. There were some small differences observed between the measured and simulated snow temperatures, particularly during midday, that are likely due to a combination of measurement errors (involving solar radiation and snow temperature) and model process uncertainty (involving penetration of shortwave radiation and heat conduction through the snow matrix). The fact that the internal energy of the snow was reasonably well predicted suggests that these differences, although important, are not likely the critical cause of the snowpack energy imbalance. Overall, the most significant discrepancy concerned the sensible heat flux, which was consistently predicted to be much higher than the measured flux (Fig. 11d is a typical example). This is consistent with the hypothesis that the sensible heat was undermeasured by the experimental setup.

Fig. 11.
Fig. 11.

(a) Measured snow temperatures, (b) snow temperatures as modeled by SNTHERM, (c) comparison of the measured rate of internal energy change vs simulated rate of change, and (d) comparison of the measured and simulated sensible heat flux. Note: the legend shown in (b) also represent the lines in (a). The values refer to depth above the soil–snow interface.

Citation: Journal of Hydrometeorology 13, 2; 10.1175/JHM-D-11-0135.1

Although the measured energy balance closure was unacceptably low during most periods reported in this study, it is worth noting that the magnitudes of all of the energy fluxes are small during midwinter. The average energy residual of 20 W m−2, while significant in terms of the winter energy balance, is not large compared to the magnitude of summertime measurements, where a residual of 20%–30% of the sum of the nonturbulent energy terms could be as high as 200 W m−2, as found by Foken et al. (2010).

4. Summary and conclusions

The energy available for snowmelt is normally estimated by presuming accurate measurement or modeling of all external energy fluxes to the snowpack and then resolving the melt rate or internal energy change as the net residual of the external fluxes. A field study measuring all external and internal components of the energy balance of a cold snowpack on a level extensive field showed large and consistent imbalances in measured energy (which was 20 W m−2 on average, but was occasionally as high as 100 W m−2). The energy imbalance was caused by large longwave radiation losses that were not balanced by downward turbulent fluxes, solar radiation, or conductive heat from the ground. The imbalance was largest during daytime solar heating of the snowpack, which resulted in larger longwave losses than at night. In both high and low wind speed cases, the measured downward sensible turbulent heat flux was insufficient to overcome the longwave energy losses; however, the expected collapse in surface temperature from such small sensible fluxes did not occur, suggesting that the energy flux to the surface was underestimated.

Based upon careful consideration of uncertainty in all of the energy balance terms, it was hypothesized that it was the sensible heat exchange that was undermeasured in this experiment. This was supported by the following observations: 1) the air temperature and the snowpack temperatures were well correlated, suggesting that sensible heat from the air was efficiently transferred to the snowpack; and 2) the sensible heat fluxes predicted using SNTHERM were much larger than the measured fluxes, while other simulated fluxes (including the internal energy changes of the snowpack) were reasonably similar to the measured values. Considering that the site conditions were near ideal, and the data carefully collected and analyzed, it was not obvious why the eddy-covariance system measured much smaller sensible heat fluxes than expected, particularly during the midday period, which led to very poor energy balance closure. There were marked differences observed between the near-neutral friction velocity directly measured by the sonic anemometers and that estimated using the flux–gradient approach, which suggests that the boundary layer may not have been fully developed to the measurement height or that some other boundary layer anomaly is present. In the absence of fine-resolution temperature and wind speed measurements within 2 m from the snow surface, the exact mechanism of heat transfer to the snow could not be identified.

Estimation of the turbulent heat fluxes as a residual of the nonturbulent energy terms suggested that a considerable amount of heat was exchanged from the atmosphere to the snow in order to limit thermal radiation losses during cold, stable periods. This provides observational support for the phenomenon of “windless exchange” that has been implemented in energy balance models to improve their performance during low wind conditions.

The results of this study illustrate the challenges associated with measuring energy fluxes over snow where the signal-to-noise ratio is small, and subtle changes in meteorological forcing can have a large effect upon the energy balance. It is also pointed out that there is considerable uncertainty associated with applying the energy residual method for calculating snow energetics in the premelt period, and suggests a need for an expanded conceptual model beyond that of vertical energy fluxes at point scales. The magnitude of the observed imbalance warrants further investigation, particularly to determine whether this is a unique problem associated with snow-covered surfaces.

Acknowledgments

The authors thank the Department of Plant Sciences, University of Saskatchewan for allowing this study to be conducted on their research land. Instrumentation was graciously loaned by Richard Essery (University of Wales, Aberystwyth) and Alan Barr and Newell Hedstrom (Environment Canada). This work was funded in part by the National Sciences and Engineering Research Council, Canadian Foundation for Climate and Atmospheric Sciences (IP3, DRI Networks) and the Canada Research Chairs Program. Field assistance was provided by Mike Solohub.

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