1. Introduction
Most evergreen forests around the world are disturbed by fire, wood product harvesting, energy developments, agricultural developments, roads and pipelines, or community development (Riitters et al. 2000). These same forests are often seasonally snow covered and provide the source areas for water runoff generation that supply vast areas and populations downstream (Bales et al. 2006). The accumulation of snow in forest clearings is of great interest in forest watershed management (e.g., Pomeroy and Gray 1995) as streamflow generation depends on the rate of melt, which can differ substantially between clearings and that in adjacent forests and open terrain (Golding and Swanson 1986; Troendle and Reuss 1997; Pomeroy et al. 2012; Broxton et al. 2015). The timing of snowmelt and transition to snow-free ground also plays a crucial role in terrestrial ecosystem dynamics (Cooper 2014; Cox et al. 2017).
To calculate the rate of snowmelt reliably requires the estimation of energy and mass fluxes to snowpacks in forest clearings, which is especially challenging in forest clearings. Large heterogeneities in solar and thermal radiation, snow accumulation, and snowpack thermal state produce radiation balances that are distinct from those under the forest canopy (Essery et al. 2008; Pomeroy et al. 2008; Seyednasrollah and Kumar 2014; Musselman et al. 2015; Webster et al. 2016; Musselman and Pomeroy 2017) or in open environments (Lawler and Link 2011; Ellis et al. 2013). How net radiation (Rnet) is then partitioned into other terms of the snowpack energy balance—specifically, the turbulent fluxes of sensible and latent heat and changes to snowpack internal energy—has a large influence on the energy available for melt. This partitioning is also important for atmospheric modeling as it determines the fluxes of sensible and latent heat at the atmosphere’s lower boundary. There has been little to no research on this topic in snow-covered forest clearings.
In the context of snowpack energy balance modeling, specification of turbulent heat fluxes is usually made through some variant of the Monin–Obukhov similarity theory (MOST). Bulk aerodynamic schemes are most commonly used, with atmospheric stability correction functions based on the bulk Richardson number (e.g., Martin and Lejeune 1998) or the Obukhov length scale (e.g., Jordan et al. 1999). However, in forest clearings, many of the assumptions inherent in MOST are violated: flat, homogenous surfaces that experience turbulence generated solely at the snow surface do not exist. For instance, at the edges of a clearing there is a transition in the surface boundary layer due to influences from the forest canopy. Therefore, depending on the size of the clearing, the boundary layer is likely to be poorly developed over all or part of the clearing (Oke 1987). As an internal boundary layer forms over the new surface, fluctuations in the vertical wind take longer to adjust to the new surface than horizontal wind, suggesting that assumed relationships between turbulence and mean flow should be used with care near transitions (Yang et al. 2006). In forest clearings only tens of meters in diameter, the assumption of a constant flux surface layer is likely invalid. In addition, the influence of low-frequency outer-layer perturbations on turbulent exchange has been often observed in mountain environments (Smeets et al. 1998; Helgason and Pomeroy 2012a; Litt et al. 2015). Hence, there is good reason to suspect that the magnitude of turbulent heat exchange at the snow surface within forest clearings may not be directly proportional to mean wind speed, temperature, and humidity gradients when stability correction functions developed under ideal conditions are used.
Given the violations of MOST in small (tens of meters in diameter) forest clearings and the large sampling area of standard-sized eddy covariance instruments (Foken 2008, p. 105), accurate direct measurements of turbulent heat fluxes to and from the snow surface using the eddy covariance technique are not currently possible in these environments. Alternative methods to estimate the turbulent heat fluxes, for example, by combining conceptual models and observations, are therefore required. One such method is to assess the magnitude of the turbulent fluxes through the ability of a physically based snowpack model to accurately simulate snowmelt (e.g., Brun et al. 1989; Klok and Oerlemans 2002). However, biases in other terms of the energy balance may confound the contribution of turbulent heat fluxes to melt, and so it has been recommended to use surface temperature as additional data to validate models (Lapo et al. 2015; Pomeroy et al. 2016). Indeed, the surface temperature of the snowpack is an important variable to simulate in both hydrological and atmospheric models as it represents the boundary condition for turbulent exchange and as such helps to determine the rate of sublimation, sensible heat exchange, and melt.
In many low wind speed situations, modeled snow surface temperature tends to “crash” during nocturnal cooling events, reducing to unrealistic values that are well below the observed snow surface temperature (Derbyshire 1999). This crash is due to strongly negative Rnet, which is not matched by turbulent energy supply to the surface (mainly through the sensible heat flux) nor from conduction from within the snowpack. The erroneously low snow surface temperature in the model creates a positive feedback mechanism that further enhances the calculated atmospheric stability and further reduces the sensible heat flux. The poor performance of snowpack models in modeling snow surface temperature during low-wind conditions is not restricted to clearing environments, implying issues with violations of MOST in low-wind conditions extend to snowpacks in open areas (e.g., Andreas et al. 2010). Over time, numerous schemes have been developed to prevent this numerical crash: modified stability corrections that permit turbulence above standard critical thresholds (Monteith 1957; Louis 1979; Holtslag and de Bruin 1988), the specification of a minimum wind speed (Martin and Lejeune 1998), artificial adjustment of observed wind speed (Andreas et al. 2010), limitation of stability correction functions at moderate or high stability (Martin and Lejeune 1998; Giesen et al. 2008), and the specification of a windless exchange coefficient (Jordan et al. 1999). The windless exchange coefficient is the most aggressive of these schemes and provides additional sensible heat exchange that is proportional only to the temperature difference between the air and snow surface. All these schemes allow for increased sensible heat exchange during low wind speed situations to maintain modeled surface temperature closer to the observed surface temperature.
However, schemes to enhance modeled turbulent heat exchange have not been assessed with respect to uncertainties in model input data in a forest clearing environment. Moreover, the effect of these schemes on modeled snowmelt has not been rigorously assessed. Given the violation of key assumptions in MOST and the need to correctly estimate both snow surface temperature and snowmelt within snowpack models, the key question of this paper is, How should turbulent heat fluxes over snow surfaces in forest clearings be represented?
This question is addressed using a physically based snowpack model driven with meteorological observations from two forest clearings in the Canadian Rockies. We test various formulations for modeling the turbulent fluxes of heat and moisture, accounting for uncertainties in both input data and model parameters. Observations of the evolution of snowpack mass and temperature are used to evaluate model performance and to provide recommendations for modeling turbulent heat fluxes in forest clearing environments, including those in mountains, which are considered the most challenging due to outer-layer turbulence generated by complex terrain.
2. Methods
a. Study sites and instrumentation
The sites used in this study are part of the Canadian Rockies Hydrological Observatory and are located in the Kananaskis Valley to the east of the continental divide in the Canadian Rocky Mountains (Fig. 1). The first site, Bonsai Clearing (FBC), is located in the Fortress Mountain Snow Laboratory and is situated 15 km south-southwest of the second site, Upper Clearing (UC), which is located in the Marmot Creek Research Basin. The two clearings are at similar elevations (2100 and 1860 m above sea level, respectively). FBC is approximately 30 m in diameter, while UC is roughly twice the diameter (56 m; Musselman et al. 2015).
(top) Site maps and (bottom) photos for (a),(c) UC and (b),(d) FBC.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
(top) Site maps and (bottom) photos for (a),(c) UC and (b),(d) FBC.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
(top) Site maps and (bottom) photos for (a),(c) UC and (b),(d) FBC.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Each clearing was instrumented with a standard automatic weather station in a central location (Table 1). This study used data from periods when additional measurements were made at each site (FBC: 2014; UC: 2012). At FBC, a three-dimensional sonic anemometer (CSAT3) was deployed during the late winter and spring of 2014 to assess the performance of cup and propeller anemometers in low wind speed situations. At UC, an array of thermocouples suspended in the snowpack (referred to as a “snowharp”; Helgason and Pomeroy 2012b) was used to determine the evolution of temperature within the snowpack during the spring of 2012. A narrow-view thermal infrared sensor also provided additional measurements of snow surface temperature that were independent from the surface temperature calculated from measurements of outgoing longwave radiation, which may sometimes include exposed small trees and bushes in the field of view.
Instrumentation at FBC and UC during the study periods.
A key difference between the two sites was the depth of snow that accumulated during the study periods (Fig. 2). Compared to FBC, the UC site had a shallower snowpack; this was due to lower precipitation at the more easterly site. The thermal conditions inside the snowpack, as revealed by measurements of internal snowpack temperatures (not shown here; see Table 1 for instruments), were dynamic at both sites. The snowpack internal energy deficit (with respect to an isothermal snowpack at 0°C) that developed at FBC during the early part of 2014 was effectively depleted by day of year (DOY) 98 (corresponding to 7 April). Rapid melt occurred throughout the months of May and June after the snowpack ripened. At UC, the snowpack internal energy deficit was highly variable through the winter period, and the snowmelt period in 2012 was shorter and earlier than at FBC in 2014.
Evolution of snow depth at (a) FBC and (b) UC during 2013–14 and 2011–12, respectively. Periods selected for SNTHERM runs during cold and melt periods are marked “cold” and “melt,” respectively.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Evolution of snow depth at (a) FBC and (b) UC during 2013–14 and 2011–12, respectively. Periods selected for SNTHERM runs during cold and melt periods are marked “cold” and “melt,” respectively.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Evolution of snow depth at (a) FBC and (b) UC during 2013–14 and 2011–12, respectively. Periods selected for SNTHERM runs during cold and melt periods are marked “cold” and “melt,” respectively.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Two time periods from each clearing were chosen to represent cold and melting snowpack conditions (FBC_cold, UC_cold, FBC_melt, and UC_melt), as shown by the gray shading in Fig. 2. The length of each period was determined by the length of record for which quality-controlled input data (particularly radiation data) were available during characteristic snowpack conditions. The snow water equivalent [SWE; mm water equivalent (mm w.e.)] contained in the snowpack at the beginning and end of each period was calculated from snow depth measured by the ultrasonic sensor, using snow pit data to determine the average density of the snowpack.
b. Data corrections
Accurate measurements of wind speed are challenging to make in environments with erratic and generally low wind speeds. While both cup and propeller anemometers give reliable temporal data coverage, these devices are liable to stalling during periods of low wind speed (Tables 2 and 3). Both types of anemometers can also overestimate the mean wind speed in gusty conditions to the extent that the distance constant is higher than dimensions of gusts. In addition, cup anemometers can overestimate mean wind speed when there are significant lateral and vertical fluctuations in the wind vector (Kristensen 1998).
Specifications of mechanical wind sensors used. The asterisk indicates that the accuracy listed for the CSAT3 was calculated at 1.5 m s−1 (details are given in Table 3).
Specifications of sonic wind sensors used.
Comparison of wind speed observed by cup and propeller anemometers to CSAT3 mean instantaneous wind speed at FBC for (a) uncorrected 30-min values and (b) values corrected using Eq. (1).
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Comparison of wind speed observed by cup and propeller anemometers to CSAT3 mean instantaneous wind speed at FBC for (a) uncorrected 30-min values and (b) values corrected using Eq. (1).
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Comparison of wind speed observed by cup and propeller anemometers to CSAT3 mean instantaneous wind speed at FBC for (a) uncorrected 30-min values and (b) values corrected using Eq. (1).
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
During periods of high incoming shortwave radiation (SWin) and low wind speed, warming of unventilated air temperature sensors can be significant. In this study, observed air temperature was corrected using the expression of Huwald et al. (2009). Local coefficients for the correction function were derived for each instrument and radiation shield pair using measurements of humidity-corrected sonic temperature from the CSAT3 at FBC. The local coefficients were found to produce a smaller correction than the original coefficients (local: a = 1.7, b = 0.6; original: a = 3.1, b = 0.5).
The snow surface at FBC is gently sloping (5°), and therefore SWin measurements were corrected for slope using the method of van As (2011). This method exploits the geometric relationships between the solar beam and plane of measurement of the instrument, scaling only the direct portion of SWin after excluding the diffuse radiation (increased during cloud cover). Since outgoing shortwave radiation (SWout), incoming longwave radiation (LWin), and outgoing longwave radiation (LWout) have more isotropic distributions, measurements of these components are not particularly sensitive to tilt, and data from these sensors were not corrected. To avoid errors due to snow covering the upward-facing radiation sensors, the data were carefully screened using a critical threshold for daily average albedo (>0.9). Daily average albedo was calculated as the ratio of the sum of SWin and the sum of SWout over a day. Only periods where no snow was detected on the sensors were used for UC_cold, FBC_melt, and UC_melt. For FBC_cold, SWin data were corrected; when the daily average albedo exceeded 0.90 (the approximate albedo of fresh snow), SWin was calculated as SWin = SWout/0.90.
c. SNTHERM
Two schemes were used to calculate turbulent heat fluxes within SNTHERM, each denoted by the parameter that was varied. These two schemes are listed and described below.
The first scheme, designated in this paper as z0, calculates exchange coefficients for H and LE using a strict application of MOST, with the roughness length for momentum z0 being the only parameter specified. The roughness lengths for temperature and humidity were calculated using the Andreas (1987) formulation, and the stability correction functions of Holtslag and de Bruin (1988) were used during stable atmospheric conditions. For baseline runs using the z0 scheme, z0 was set to 1 × 10−3 m. As is shown later, the magnitude of the turbulent heat fluxes is not especially sensitive to this choice because of the compensating effects of the Andreas (1987) formulation on the temperature and humidity roughness lengths.
The second scheme, designated in this paper as WE, adds a windless exchange coefficient WE (W m−2 K−1) into the calculation of H (Jordan et al. 1999). In very stable conditions where turbulent exchange under z0 would not be permitted, H becomes a function of air temperature only and is maintained regardless of wind speed. The physical mechanism hypothesized to be responsible for WE is gustiness caused by breaking internal gravity waves during periods when the mean wind is near zero (Jordan et al. 1999). LE is calculated as per z0 with a roughness length for momentum of 1 × 10−3 m. The values for WE in baseline runs at each site were determined by selected the values of WE that produced the best fit to the measured snow surface temperature during cold snowpack conditions. From test runs with WE varying between 0 and 6 W m−2 K−1 in steps of 0.5 W m−2 K−1, optimal values were found to be 3.5 and 4 W m−2 K−1 at FBC and UC, respectively. These values were adopted for the baseline runs with the WE scheme, though we note they are substantially larger than values suggested by Jordan et al. (1999).
In essence, z0 represents a scheme that allows turbulence in very stable conditions while maintaining a strict application of MOST, while WE represents the most aggressive scheme used to enhance turbulent sensible heat flux in stable conditions. Other intermediate schemes such as the Louis (1979) formulation for stable conditions lie somewhere in between these two schemes and are not investigated within this paper for brevity.
d. Treatment of uncertainty through Monte Carlo simulations
To assess the influence of input data uncertainty and turbulent heat flux parameter choice on the SNTHERM outputs, Monte Carlo simulations were performed for each combination of site, time period, and turbulent flux scheme. Errors were introduced to all model input data [SWin, SWout, LWin, air temperature Ta, relative humidity (RH), wind speed (WS), and precipitation] in a systematic fashion (i.e., held constant for a single run). Errors were specified by randomly selecting numbers from a normal distribution with a mean of 0 and standard deviation equal to the instrument uncertainty. This distribution ensures the input data represent the uncertainty, while not influencing the mean value. Instrument uncertainties used were 10% (precipitation), 0.3 K (Ta), 3% (RH), 0.3 m s−1 (WS), and 5% (all radiation components). Random errors at each time step were not introduced as they have much less effect on model output (Lapo et al. 2015). Nonphysical input variables were avoided by adjusting SWout so that albedo did not exceed 0.95, adjusting LWin so that atmospheric emissivity did not exceed 1, and limiting RH to between 0.5% and 100%. Wind speed was also given a lower limit of 0.1 m s−1, which was the lowest recorded wind speed at FBC during the period of CSAT3 measurement.
For each combination of site, time period, and turbulent heat flux scheme, simulations containing 2000 model runs were initially made. For runs using the z0 scheme, z0 was randomly chosen from a uniform distribution between 10−1 and 10−6 m, while for runs using the WE scheme, WE was randomly chosen from a uniform distribution between 0 and 6 W m−2 K−1. Because of model stability, 400 runs with WE > 6 W m−2 K−1 were discarded from simulations using WE for each site and time period.
Rather than undertake simulations over the full winter–spring period, separate simulations were made for cold and melt periods at each site. This was designed to investigate the effects of turbulent heat flux uncertainties on snow surface temperature (during the cold period) and total melt (during the melt period), while minimizing spurious feedbacks. In runs made over the full winter–spring period, an example of a spurious feedback would be when a positive bias in air temperature (during the cold period) results in less snowfall (more rainfall) and, therefore, maximum SWE that is less than the actual conditions at the start of the melt period. The lower initial spring SWE would then confound the impact of a positive bias in air temperature on the energy available for melt (through the magnitude of the turbulent heat fluxes). To enable direct comparison of model performance between cold and melt periods (Fig. 2), simulations at each site used the same set of perturbations for runs in cold and melt periods.
3. Results
a. Meteorological environment in the clearings
The meteorological environment of both forest clearings was characterized by low average wind speed and a predominantly stable atmosphere above the snow surface (Table 4). Despite low average wind speeds, calm conditions were surprisingly infrequent. Data from the sonic anemometer at FBC showed 30-min mean wind speed below 0.3 m s−1 occurred in only 1.4% of the study period, and mean wind speed below 0.1 m s−1 did not occur. To characterize variability in the wind direction at FBC, we calculated directional consistency from the ratio of scalar-averaged wind speed 
Mean meteorological variables and surface radiation fluxes for each site and period. Average instrument heights above snow surface are as follows: 2.2 m for Ta and RH and 3.2 m for WS (±0.3 m) in FBC_cold; 2.8 m for Ta and RH and 3.8 m for WS (±0.6 m) in FBC_melt; 1.5 m for Ta, RH, and WS (±0.1 m) in UC_cold; and 1.3 m for Ta, RH, and WS (±0.3 m) in UC_melt.
b. Modeled surface temperature during cold snowpack periods
During the cold period snowpack runs with the z0 scheme, the modeled snow surface temperature frequently dropped well below the observed snow surface temperature (Fig. 4); this commonly occurred during periods of strong Rnet deficit during the night. Despite making corrections to measured wind speed during light-wind periods, these corrections were unable to remove the negative bias in snow surface temperature when using a strict implementation of MOST in z0, and large biases occurred during a range of wind speeds less than 2 m s−1. For model runs with the WE scheme, modeled snow surface temperature showed an improved prediction of observed snow surface temperature at both sites. The root-mean-square error (RMSE) between the mean of Monte Carlo simulations and observed snow surface temperature at FBC decreased from 4.5 K for z0 to 2.1 K for WE. At UC, RMSE decreased from 4.0 K for z0 to 1.8 K for WE. The WE scheme provided the greatest improvement during periods when measurement uncertainty created larger variance between the runs (e.g., DOY 24 at the UC site). The improved prediction of snow surface temperature with the WE scheme is due to the additional turbulent heat fluxes allowed by the scheme. The net turbulent heat flux (H + LE) in WE runs was between 20 and 50 W m−2 larger than that in z0 runs during periods of strong Rnet deficit (not shown).
Observed and modeled snow surface temperature Ts during a subset of (a) FBC_cold and (b) UC_cold for the z0 (blue) and WE simulations (orange). Solid colored lines indicate the model ensemble mean and the colored shading the interquartile range of runs in the Monte Carlo simulation. Observed surface temperature is given in black.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Observed and modeled snow surface temperature Ts during a subset of (a) FBC_cold and (b) UC_cold for the z0 (blue) and WE simulations (orange). Solid colored lines indicate the model ensemble mean and the colored shading the interquartile range of runs in the Monte Carlo simulation. Observed surface temperature is given in black.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Observed and modeled snow surface temperature Ts during a subset of (a) FBC_cold and (b) UC_cold for the z0 (blue) and WE simulations (orange). Solid colored lines indicate the model ensemble mean and the colored shading the interquartile range of runs in the Monte Carlo simulation. Observed surface temperature is given in black.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
c. Modeled SWE during melt periods
The wide range of modeled SWE at the end of each melt period (Fig. 5) indicated modeled SWE was strongly affected by systematic errors over the short melt periods (29 and 16 days at FBC and UC, respectively). The range of modeled SWE was roughly equal in magnitude to the observed loss of SWE during each of the periods. This range implied that upper bounds on the uncertainty are on the order of ±100%. Notwithstanding this uncertainty, the distribution of modeled SWE for z0 runs (mean of 283 and 145 mm w.e. at FBC and UC, respectively) was more evenly spread around the observed SWE (265 and 158 mm w.e. at FBC and UC, respectively). The distribution for WE runs was shifted toward lower values (mean of 169 and 103 mm w.e. at FBC and UC, respectively), indicating melt was more often overestimated by the WE scheme.
Histograms of SWE at the end of model runs during (a) FBC_melt and (b) UC_melt. Data are split into 15 bins of equal width. Initial values of SWE at the beginning model runs were 736 and 266 mm w.e. at FBC and UC, respectively.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Histograms of SWE at the end of model runs during (a) FBC_melt and (b) UC_melt. Data are split into 15 bins of equal width. Initial values of SWE at the beginning model runs were 736 and 266 mm w.e. at FBC and UC, respectively.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Histograms of SWE at the end of model runs during (a) FBC_melt and (b) UC_melt. Data are split into 15 bins of equal width. Initial values of SWE at the beginning model runs were 736 and 266 mm w.e. at FBC and UC, respectively.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
d. Comparison of biases in snow surface temperature and SWE
Scatterplots of individual runs in the Monte Carlo simulations revealed a consistent trade-off in model performance between snow surface temperature and SWE (Fig. 6). Larger values of the z0 and WE parameters, which favor increased magnitudes of H, reduced the bias in snow surface temperature, while, at the same time, created negative biases in SWE (through increased ablation). The z0 and WE schemes produced a similar range of model fits at each site despite quite different formulations for H because of the effect of input data uncertainties and the wide parameter range tested for z0 and WE. The large spread in snow surface temperature bias was primarily due to uncertainty in the radiative input data. The larger apparent scatter in SWE bias at UC compared to FBC was due to the shorter melt period and the influence of precipitation phase uncertainties at UC. Baseline runs of the model (i.e., no input data errors and fixed values for z0 and WE) at FBC and UC showed moderate biases in snow surface temperature when using the z0 scheme and biases in SWE when using the WE scheme.
Scatterplots showing biases (model − observations) in average snow surface temperature Ts from cold period simulations and end-of-period SWE from melt period simulations for runs with the same parameter values and input data uncertainties. Separate simulations are made for (a),(c) FBC and (b),(d) UC, using the (left) z0 and (right) WE schemes. Colors denote the parameter values (warm = large z0 or WE, cold = small z0 or WE). Baseline runs (no input errors and set parameter values) are shown as solid black circles for reference. Note the different y-axis scales, which reflect the lower snow accumulation and shorter melt period at UC. The horizontal-line-like patterns at the lower-right end of the point clouds come from runs where the full snowpack has been melted, thus limiting the negative bias in SWE.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Scatterplots showing biases (model − observations) in average snow surface temperature Ts from cold period simulations and end-of-period SWE from melt period simulations for runs with the same parameter values and input data uncertainties. Separate simulations are made for (a),(c) FBC and (b),(d) UC, using the (left) z0 and (right) WE schemes. Colors denote the parameter values (warm = large z0 or WE, cold = small z0 or WE). Baseline runs (no input errors and set parameter values) are shown as solid black circles for reference. Note the different y-axis scales, which reflect the lower snow accumulation and shorter melt period at UC. The horizontal-line-like patterns at the lower-right end of the point clouds come from runs where the full snowpack has been melted, thus limiting the negative bias in SWE.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Scatterplots showing biases (model − observations) in average snow surface temperature Ts from cold period simulations and end-of-period SWE from melt period simulations for runs with the same parameter values and input data uncertainties. Separate simulations are made for (a),(c) FBC and (b),(d) UC, using the (left) z0 and (right) WE schemes. Colors denote the parameter values (warm = large z0 or WE, cold = small z0 or WE). Baseline runs (no input errors and set parameter values) are shown as solid black circles for reference. Note the different y-axis scales, which reflect the lower snow accumulation and shorter melt period at UC. The horizontal-line-like patterns at the lower-right end of the point clouds come from runs where the full snowpack has been melted, thus limiting the negative bias in SWE.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
At FBC, very few combinations of model parameters eliminated bias in both SWE and snow surface temperature, despite wide uncertainties introduced to the input data (Figs. 6a,c). At UC, a group of runs showed biases close to 0 for both SWE and surface temperature (Figs. 6b,d). However, the distribution of input data errors used for this group of runs was skewed from the original distribution (not shown), with, on average, much higher incoming longwave and lower net shortwave radiation fluxes. These errors help to explain the good fit to both metrics: the higher incoming longwave radiation reduced the nocturnal LWnet deficit and maintained a warmer snow surface temperature (closer to the observed snow surface temperature), while lower net shortwave radiation compensated for the additional melt energy from LWnet to produce more physically reasonable values of SWE. Such an observation supports the idea that incoming longwave radiation is a major control of snow surface temperature and a large source of uncertainty in snowpack models.
The lack of a realistic optimal parameter set for modeling turbulent heat fluxes in both cold and melt periods leads to a further question: Are there potential sources of energy deficit in the model that could account for the low bias in snow surface temperature while not biasing the calculated values of SWE? This question is explored further in the discussion.
4. Discussion
a. Possible reasons for modeling trade-off
A number of processes could account for the snow surface energy deficit that causes the modeled snow surface temperature to crash during periods of strongly negative Rnet. These include uncertainties in meteorological driving data, an imperfect representation of snowpack energetics, biases in incoming radiation, or an incorrect specification of turbulent heat fluxes to and from the snowpack. As shown above, systematic uncertainties in meteorological data could not account for the low bias in modeled snow surface temperature when the turbulent heat fluxes were calculated using a strict application of MOST. Further reasons for a snow surface energy deficit are examined in the following sections.
1) A bias in dU/dt
In most snowpack studies, dU/dt is not directly observed and is calculated by the model. During UC_cold, a snowharp gave detailed measurements of temperature distribution throughout the snowpack and allowed direct calculation of dU/dt. The penetration of nocturnal cooling through the snowpack was observed, as were periods of abrupt warming associated with cloud cover and precipitation around DOY 22, 25, and 29 (Fig. 7a). The general trends in snowpack temperature evolution were well represented by the baseline run of SNTHERM using the WE scheme (Figs. 7b–d). However, temperatures deeper in the snowpack were consistently underestimated. Given a physically correct simulation of snow surface temperature, the underestimation of internal snowpack temperature was perhaps associated with how the snowpack effective thermal conductivity is calculated within SNTHERM. However, snowpack thermal properties in SNTHERM are specified as a function of snow density, and we were therefore unable to assess the model sensitivity to this parameter without producing an unrealistic modification to the modeled snowpack mass.
Snowpack temperature during UC_cold (a) observed by the snowharp and snow temperature at the (b) surface, and (c),(d) different heights above ground level (AGL) compared to those modeled in the baseline run using the WE scheme (WE = 3.5 W m−2 K−1).
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Snowpack temperature during UC_cold (a) observed by the snowharp and snow temperature at the (b) surface, and (c),(d) different heights above ground level (AGL) compared to those modeled in the baseline run using the WE scheme (WE = 3.5 W m−2 K−1).
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Snowpack temperature during UC_cold (a) observed by the snowharp and snow temperature at the (b) surface, and (c),(d) different heights above ground level (AGL) compared to those modeled in the baseline run using the WE scheme (WE = 3.5 W m−2 K−1).
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
The snowpack internal temperature structure was also used to quantify observed and modeled dU/dt during UC_cold (Fig. 8). In general, modeled dU/dt followed the temporal evolution of observed dU/dt and was of a similar or larger magnitude than that observed. While there is some uncertainty in the bulk density and temperature in the top few centimeters of the snowpack, dU/dt is relatively insensitive to these uncertainties and is mostly controlled by fluctuations in average snowpack temperature. During cooling events, observed dU/dt peaked from around −6 to −12 W m−2, while modeled values were between −12 and −17 W m−2. As the negative numbers indicate a loss of energy from the snowpack, the larger magnitude of modeled dU/dt indicated that the model was supplying more energy to close the energy balance at the surface than that observed. When the z0 scheme was used, snow surface temperature was underestimated, and dU/dt was even larger in magnitude (not shown). Thus, it is unlikely that the dU/dt term was responsible for producing a surface energy deficit within the model.
Observed dU/dt during UC_cold compared to modeled dU/dt from the baseline run using the WE scheme. Both observed and modeled dU/dt have been smoothed with a 6-h moving average. The contribution of melt to dU/dt on day 29 was removed from the modeled values to ensure consistency with measurements made by the snowharp.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Observed dU/dt during UC_cold compared to modeled dU/dt from the baseline run using the WE scheme. Both observed and modeled dU/dt have been smoothed with a 6-h moving average. The contribution of melt to dU/dt on day 29 was removed from the modeled values to ensure consistency with measurements made by the snowharp.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Observed dU/dt during UC_cold compared to modeled dU/dt from the baseline run using the WE scheme. Both observed and modeled dU/dt have been smoothed with a 6-h moving average. The contribution of melt to dU/dt on day 29 was removed from the modeled values to ensure consistency with measurements made by the snowharp.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
2) Errors in incoming radiative fluxes
As discussed earlier, snow surface temperature is most sensitive to incoming longwave radiation (Lapo et al. 2015; Pomeroy et al. 2016), while snowmelt is sensitive to variations in both shortwave and longwave radiation. It is therefore useful to review possible sources of errors in measurements of incoming longwave radiation. These include the deposition of snow or rime ice on the sensor, sky view considerations, and the interference of solar radiation on measurements. The influence of snow and rime can be significant and hard to quantify. Here, the effect of rime or snow would be to reduce Rnet deficits and improve the estimations of surface temperature. To ensure this effect was minimized, here, the input data were screened for snow covering the radiation sensors using a critical threshold for albedo, and only periods with snow-free data were used (UC_cold, FBC_melt, UC_melt) or the data corrected (FBC_cold).
In small clearings, changes in the measurement height of incoming radiation will change the fraction of sky and trees within the view of the sensor. At lower measurement heights, the fraction of trees increases, so actual incoming longwave radiation at the surface could be larger than that measured at standard measuring heights (2 m). The effect of this is likely to be modest during periods of nocturnal cooling, but during the daytime, the effect of trees on incoming radiation can be much larger, with Musselman and Pomeroy (2017) showing that forest emissions of longwave radiation into clearings are significant within a few meters of the clearing edge.
Design limitations of radiation sensors mean that measurements of incoming longwave radiation are affected by incoming shortwave radiation. Small offsets occur because of absorption of solar radiation by the sensor window and subsequent enhanced emission toward the thermopile inside of the sensor enclosure. Published window heating offset correction factors for Kipp and Zonen radiation sensors vary from 0.012 to 0.025 (Obleitner and De Wolde 1999; Sicart et al. 2005). The manufacturer’s current suggestion is to not make the correction on the premise that incoming shortwave is the dominant input to Rnet during these periods (Kipp and Zonen 2002, 2014) and the effect on Rnet is only small. However, at FBC, a correction of 0.025 would reduce melt energy by 5.6 W m−2 or 42-mm snow ablation (9% of melt). At UC, the same correction would reduce melt energy by 4.7 W m−2 or 19-mm snow ablation (12% of melt). In addition, when two sensors are placed inside one enclosure case to measure incoming and outgoing radiation (e.g., the Kipp and Zonen CNR1), thermal gradients can occur between the inside of the upper and lower sensors. These gradients can cause an offset between the observed body temperature and the temperature of the thermopile and produce biases in radiation up to 5 W m−2 (Brotzge and Duchon 2000). As forest clearings are environments that can maintain a snowpack later into the snow ablation season when incoming solar radiation exceeds 1000 W m−2, window heating and thermal gradients have the potential to account for a significant fraction of the observed overestimation of snowmelt. Further work is needed to derive robust correct factors in these environments and increase our ability to model the spatial patterns of incoming longwave radiation within forest clearings (Musselman and Pomeroy 2017) if we are to robustly measure and model this key variable.
3) Windless exchange for latent heat fluxes
It is common practice to only include a windless exchange coefficient for H and not LE, as a windless exchange coefficient for LE has little effect on modeled snow surface temperature during nocturnal cooling events (Jordan et al. 1999; Lapo et al. 2015). However, the physical reasoning behind this choice is questionable, as one would expect the exchange processes that the windless exchange coefficient represents would affect both H and LE in a similar way (as both H and LE depend on the motion of the same parcels of air). Furthermore, during melting periods, applying a windless exchange coefficient to LE may reduce the energy available for melt as enhanced vapor loss from the snowpack will counteract increased H.
To test the effect of using a windless exchange coefficient for LE, new runs were made over the FBC_melt and UC_melt periods using the WE scheme. For these runs, the baseline runs (i.e., no input error and WE of 4 and 3.5 W m−2 K−1 at FBC and UC, respectively) were modified to include a windless exchange for LE. In these new runs, melt decreased by 35 and 18 mm w.e. at FBC and UC, respectively. These changes amount to 28% and 43% of the excess melt produced by baseline WE runs at FBC and UC, respectively. Despite a large increase in the magnitude of LE with respect to the baseline runs, mass loss by sublimation was still very small in the new runs. At FBC, sublimation increased from a mean of −0.0077 to −0.1872 mm w.e. day−1, while at UC, sublimation increased from a mean of −0.0517 to 0.2265 mm w.e. day−1. The sublimation rates in the new runs were similar to those observed in sheltered snow-covered environments (Reba et al. 2012) and open sites (Male and Granger 1981). Thus, a more realistic estimation of both melt and sublimation may be produced by using a windless exchange coefficient for LE.
4) Nonturbulent heat fluxes
There is a growing body of literature that shows nonturbulent processes can create large fluxes of scalars such as sensible heat and CO2. Vertical advective fluxes arise from nonzero mean vertical wind speed in the presence of vertical gradients in temperature, while horizontal advective fluxes are caused by spatial variation in the gradients of wind speed and temperature around a site. Detailed measurements at a sloping forested site show that during stable nighttime periods the vertical and horizontal advective fluxes of CO2 are of a similar magnitude to turbulent fluxes (Feigenwinter et al. 2008) and that these fluxes can be enhanced or dampened by large-scale wind systems (Feigenwinter et al. 2010). Fluxes of sensible heat at the same site show similar diurnal patterns, with the advective heat flux being much larger than the turbulent flux during the nighttime (Moderow et al. 2011). Large eddy simulations of an idealized forest slope show nighttime fluxes of CO2 during stable conditions are dominated by vertical advection driven by the interaction of slope-induced wind flows with landscape heterogeneities (Sun et al. 2006). On a wider scale, the lack of energy balance closure at eddy covariance measurement sites has been linked to landscape heterogeneity (Stoy et al. 2013), suggesting that the contribution of nonturbulent fluxes is important for sites with spatial variations in land cover and topography. Collectively, these studies suggest that it is likely that nonturbulent fluxes of sensible heat are an important contribution to the surface energy balance in forest clearing environments, especially in situations where turbulence is not well developed and large gradients in temperature develop. While the slopes of the clearings in this study are not large, their position in topographical drainages suggests that slope-induced flows may operate at each site. In the context of snowpack modeling, perhaps it is more appropriate to think of H and LE as representing the sum of turbulent and nonturbulent fluxes of sensible and latent heat, rather than introduce a separate term for nonturbulent heat fluxes. Further research should aim to quantify the contribution of advective fluxes to the surface energy balance in forest clearings.
b. What are reasonable values for turbulent heat flux parameters?
Snowharp measurements during UC_cold allow dU/dt to be quantified, so estimates of CH are made for this period. To avoid large errors associated with small absolute values of Q, CH was only calculated for 30-min periods when Q was less than −10 W m−2. Estimates were also limited to periods of net turbulent heat transport toward the snow surface, as our interest is primarily in stable atmospheric conditions. To compare the observed values of CH to the values of CH calculated using the z0 and WE schemes in SNTHERM, the sum of modeled values of H + LE were substituted for Q in Eq. (5).
The mean value of CH derived from the measured energy balance residual during UC_cold was 3.9 × 10−3 (standard deviation of 1.1 × 10−3; measurement height of 1.5 m). This equates to an effective roughness length of 2.7 × 10−3 m (standard deviation of 0.76 × 10−3 m)—similar to values used in other sheltered environments (Brun et al. 1989; Reba et al. 2012). A roughness length of 2.7 × 10−3 m is not exceptionally large for z0, but is larger than z0 commonly assumed for smooth snow surfaces (Pomeroy and Gray 1995). In a forest clearing, it is likely that the surrounding canopy and terrain elements generate the additional turbulence required for the transfer of warm air to the snow surface. In this way, the exchange coefficient or effective roughness length is a characteristic of the clearing environment and not solely a function of the snow surface roughness.
The values of CH derived from the measured energy balance residual exhibited little variation with respect to the measured temperature difference between the air–snow surface (
CH during UC_cold, back calculated from (a),(d) measured energy balance residual (Rnet + G − dU/dt) and modeled turbulent heat fluxes from baseline runs using (b),(e) z0 and (c),(f) WE. The blue line in (d) shows the best-fit line in Eq. (6).
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
CH during UC_cold, back calculated from (a),(d) measured energy balance residual (Rnet + G − dU/dt) and modeled turbulent heat fluxes from baseline runs using (b),(e) z0 and (c),(f) WE. The blue line in (d) shows the best-fit line in Eq. (6).
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
CH during UC_cold, back calculated from (a),(d) measured energy balance residual (Rnet + G − dU/dt) and modeled turbulent heat fluxes from baseline runs using (b),(e) z0 and (c),(f) WE. The blue line in (d) shows the best-fit line in Eq. (6).
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
To show the effect of a simple scheme for calculating H + LE (designated here as CH) with a dimensionless exchange coefficient that does not depend on atmospheric stability, further SNTHERM runs were made for 12 days at the start of FBC_cold and UC_cold. Baseline runs using the z0 and WE schemes were compared to using the CH scheme with CH = 0.004 (Fig. 10). The temporal evolution of snow surface temperature was very well captured when using the CH scheme, with RMSEs of 2.1 and 2.0 K at FBC and UC, respectively. In contrast, RMSEs for the z0 scheme were 4.6 and 4.7 K at FBC and at UC, respectively. RMSEs for the WE scheme were 2.1 and 2.3 K, respectively.
Snow surface temperature Ts during a subset of (a) FBC_cold and (b) UC_cold. Snow surface temperature measured (black) and modeled using the z0 (blue), WE (orange), and CH (magenta) schemes.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Snow surface temperature Ts during a subset of (a) FBC_cold and (b) UC_cold. Snow surface temperature measured (black) and modeled using the z0 (blue), WE (orange), and CH (magenta) schemes.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Snow surface temperature Ts during a subset of (a) FBC_cold and (b) UC_cold. Snow surface temperature measured (black) and modeled using the z0 (blue), WE (orange), and CH (magenta) schemes.
Citation: Journal of Hydrometeorology 19, 10; 10.1175/JHM-D-18-0050.1
Persistent errors in the simulation of snow surface temperature by SNTHERM are evident where all schemes converge around the same value (Fig. 10). Some of these errors are related to the reset of snow surface temperature to the ice-bulb air temperature when new precipitation is present (e.g., DOY 30 at UC). This is a feature of the SNTHERM model. Some of these errors are likely due to either measurement errors in the input data or model representation of snowpack conditions (e.g., DOY 81 at FBC). Because of these persistent errors, a reduction of the RMSE below 2 K was not possible at either site.
Despite the extreme atmospheric stability and low wind speed experienced in the two forest clearings studied here, a relatively simple bulk aerodynamic scheme appears to be sufficient to account for a deficit in the snowpack energy balance and successfully simulate snow surface temperature. This scheme uses only air and surface temperatures, wind speed at one height, and an exchange coefficient. The scheme requires that the incoming longwave radiation fluxes are accurately specified and that dU/dt and G are correctly modeled. The use of such a simple scheme is supported by the breakdown of universal scaling laws in the presence of landscape heterogeneities (e.g., surface cover and topography) that create additional turbulent structures (beyond those predicted by MOST) and encourage vertical and horizontal heterogeneities in wind and scalar fields that lead to advective fluxes. As vertical advective fluxes depend on vertical gradients in temperature (as does the turbulent flux predicted by MOST), it is likely that this nonturbulent flux contributes significantly to the total heat flux in conditions where turbulent processes are limited.
5. Conclusions
Meteorological observations from two forest clearings in the Canadian Rockies have been used to drive a physically based 1D snowpack model (SNTHERM) to test various formulations for modeling turbulent fluxes of heat and moisture above a snowpack in a forest clearing. Forest clearings are challenging environments to model turbulent heat fluxes, as many of the key assumptions of MOST are violated. Surface cover heterogeneity and the discontinuity created by the forest edge provides good reason to suspect that the universal scaling laws will not be valid in these environments. Here we find that, as in many low wind speed environments, using MOST to specify turbulent heat fluxes causes negative biases in modeled snow surface temperature during periods of net longwave deficit. Even complex formulations of MOST—with relaxed limits on the dampening of turbulence in stable conditions—were unable to permit sufficient turbulent sensible heat flux toward the snow surface to maintain modeled snow surface temperatures close to those observed during these periods. Monte Carlo simulations showed that uncertainties in meteorological and surface radiation observations could not account for the negative bias in modeled surface temperature. Corrections to wind speed measurements made by cup and propeller instruments removed spurious zero wind speed periods in the model input data but did not markedly improve the correspondence of modeled and observed snow surface temperature.
The introduction of a windless exchange coefficient for H improved the prediction of snow surface temperature, though only at very large values where such a correction has very little or no physical basis. The windless exchange coefficient also produced a trade-off that caused excessive melt during the primary melt period. Caution is warranted when optimizing snowpack models on observed surface temperature until the reasons for this trade-off are resolved. When a windless exchange coefficient for LE is included, some of the extra energy supplied by H during melting conditions is compensated, reducing the bias in modeled SWE.
Measurements of the evolution of snowpack internal temperature were used to assess if changes in internal snowpack energy could account for a snow surface energy deficit during periods when modeled snow surface temperature is underestimated. Modeled changes in internal snowpack energy were similar to or larger than those observed, suggesting that this term is not responsible for the surface energy deficit.
An independent estimate of the magnitude of turbulent fluxes was obtained from measurements of the surface energy balance residual during a midwinter period at one site (UC). This estimate was then used to calculate a bulk aerodynamic exchange coefficient. The results suggest a large exchange coefficient that is fairly constant with wind speed and temperature—equivalent to computing the turbulent heat fluxes in a bulk aerodynamic scheme that discounts atmospheric stability using an effective roughness length (common to momentum, temperature, and humidity) of 2.7 × 10−3 m. A large exchange coefficient is presumed to arise from surrounding canopy and terrain elements that produce sufficient turbulence to mix warm air toward the snow surface, despite the counteracting forces of the extreme atmospheric stability and the relatively smooth snow surface. Nonturbulent advective heat fluxes may also contribute significantly to the large exchange coefficient estimated during stable low-wind conditions.
Physical processes related to the temporal evolution of snowmelt should be correctly represented in both hydrological and meteorological models. While methods to enhance turbulent exchange in snowpack models produce more melt and, therefore, negative biases in modeled SWE, these results suggest that uncertainties in precipitation phase partitioning and incoming radiation tend to have a greater effect on modeled values of SWE. There is a possibility that calibrating turbulent heat fluxes to obtain reasonable ablation rates may hide persistent errors in the underlying physics of a snowpack evolution model. If the magnitudes of H and LE can be constrained using other methods (such as those presented here), it may be possible to correctly specify these fluxes during the snowmelt period, thereby allowing for a better understanding of how the physics of a snowpack evolution model can be optimized or modified. In particular, biases in longwave radiation have a fundamental control on both snow surface temperature and melt, and further effort is needed to resolve uncertainties in measurements and modeling of these radiation fluxes in forest clearings. One such opportunity is to use physically detailed models such as that proposed by Musselman and Pomeroy (2017) to quantify forest emissions of longwave radiation around clearing edges.
Acknowledgments
Financial contributions from Alberta Agriculture and Forestry, Alberta Environment and Parks, the NSERC Changing Cold Regions Network, the Canada Research Chairs Programme, the Canada Excellent Research Chair in Water Security, and the Canadian Foundation for Climate and Atmospheric Sciences made this study possible. The logistical support of Nakiska Ski Resort, Fortress Mountain Resort, and the University of Calgary Biogeosciences Institute and the field support from May Guan, Angus Duncan, and many others from the Coldwater Laboratory are gratefully appreciated. The datasets used in the manuscript are available on request from the corresponding author.
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