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    Schematic diagram of sensible heat flux computations in the land surface representation used in the TSEB model.

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    Location of the sagebrush and aspen study sites within the Reynolds Mountain East catchment in southwestern Idaho.

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    Photographs of the aspen site during the field survey in winter 2007.

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    Photographs of the sagebrush site during the field survey in winter 2007.

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    Measured snow depth at the aspen and sagebrush sites during the study period in 2007.

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    Scatterplot comparing snow depth at the aspen and the sagebrush sites, along with the linear relationship used to estimate missing snow depth values at the sagebrush site.

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    Scatterplots between modeled and measured half-hourly fluxes of (top) net radiation, (middle) sensible heat, and (bottom) latent heat at the aspen site.

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    Modeled and measured daily fluxes of (top) net radiation, (middle) sensible heat, and (bottom) latent heat fluxes at the aspen site as a function of DOY.

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    Time series of (top) modeled and measured half-hourly sensible heat flux, (middle) measured air temperature and modeled canopy and snow temperature, and (bottom) modeled scene and component sensible heat fluxes at the aspen site using the measured SAI of 0.45.

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    Sensitivity of agreement between modeled and measured half-hourly latent heat flux at the aspen site to the value specified for KSN in Eq. (18).

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    Time series of modeled half-hourly sensible heat flux of the total (H), canopy (HC) and snow surface (HS) at the aspen site using (top) SAI = 0.45 (observed value), (middle) SAI = 0.30, and (bottom) SAI = 0.75.

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    Modeled latent heat flux over the snow surface (λESN) at the aspen site using SAI = 0.45, SAI = 0.3, and SAI = 0.75.

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    Scatterplots between modeled and measured half-hourly fluxes of (top) net radiation, (middle) sensible heat, and (bottom) latent heat at sagebrush site.

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    Modeled and measured daily flux of (top) net radiation, sensible heat (middle), and latent heat (bottom) at the sagebrush site as a function of DOY.

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    Time series of (top) modeled and measured half-hourly sensible heat flux; (middle) modeled in-canopy air (TAC), canopy (TC), and snow (TS) surface temperatures; and (bottom) modeled scene (H), snow (HS), and canopy (HC) sensible heat fluxes at the sagebrush site.

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Evaluation of a Two-Source Snow–Vegetation Energy Balance Model for Estimating Surface Energy Fluxes in a Rangeland Ecosystem

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  • 1 Earth System Science Interdisciplinary Center, University of Maryland College Park, and NOAA/National Environmental Satellite, Data, and Information Service, College Park, Maryland
  • | 2 Hydrology and Remote Sensing Laboratory, Agricultural Research Service, USDA, Beltsville, Maryland
  • | 3 Department of Soil Science, University of Wisconsin—Madison, Madison, Wisconsin
  • | 4 Hydrology and Remote Sensing Laboratory, Agricultural Research Service, USDA, Beltsville, Maryland
  • | 5 Northwest Watershed Research Center, Agricultural Research Service, USDA, Boise, Idaho
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Abstract

The utility of a snow–vegetation energy balance model for estimating surface energy fluxes is evaluated with field measurements at two sites in a rangeland ecosystem in southwestern Idaho during the winter of 2007: one site dominated by aspen vegetation and the other by sagebrush. Model parameterizations are adopted from the two-source energy balance (TSEB) modeling scheme, which estimates fluxes from the vegetation and surface substrate separately using remotely sensed measurements of land surface temperature. Modifications include development of routines to account for surface snowmelt energy flux and snow masking of vegetation. Comparisons between modeled and measured surface energy fluxes of net radiation and turbulent heat showed reasonable agreement when considering measurement uncertainties in snow environments and the simplified algorithm used for the snow surface heat flux, particularly on a daily basis. There was generally better performance over the aspen field site, likely due to more reliable input data of snow depth/snow cover. The model was robust in capturing the evolution of surface energy fluxes during melt periods. The model behavior was also consistent with previous studies that indicate the occurrence of upward sensible heat fluxes during daytime owing to solar heating of vegetation limbs and branches, which often exceeds the downward sensible heat flux driving the snowmelt. However, model simulations over aspen trees showed that the upward sensible heat flux could be reversed for a lower canopy fraction owing to the dominance of downward sensible heat flux over snow. This indicates that reliable vegetation or snow cover fraction inputs to the model are needed for estimating fluxes over snow-covered landscapes.

Corresponding author address: Dr. Cezar Kongoli, NOAA/NESDIS, NOAA Center for Weather and Climate Prediction (NCWCP), 5830 University Research Ct. 2804, College Park, MD 20740. E-mail: cezar.kongoli@noaa.gov

Abstract

The utility of a snow–vegetation energy balance model for estimating surface energy fluxes is evaluated with field measurements at two sites in a rangeland ecosystem in southwestern Idaho during the winter of 2007: one site dominated by aspen vegetation and the other by sagebrush. Model parameterizations are adopted from the two-source energy balance (TSEB) modeling scheme, which estimates fluxes from the vegetation and surface substrate separately using remotely sensed measurements of land surface temperature. Modifications include development of routines to account for surface snowmelt energy flux and snow masking of vegetation. Comparisons between modeled and measured surface energy fluxes of net radiation and turbulent heat showed reasonable agreement when considering measurement uncertainties in snow environments and the simplified algorithm used for the snow surface heat flux, particularly on a daily basis. There was generally better performance over the aspen field site, likely due to more reliable input data of snow depth/snow cover. The model was robust in capturing the evolution of surface energy fluxes during melt periods. The model behavior was also consistent with previous studies that indicate the occurrence of upward sensible heat fluxes during daytime owing to solar heating of vegetation limbs and branches, which often exceeds the downward sensible heat flux driving the snowmelt. However, model simulations over aspen trees showed that the upward sensible heat flux could be reversed for a lower canopy fraction owing to the dominance of downward sensible heat flux over snow. This indicates that reliable vegetation or snow cover fraction inputs to the model are needed for estimating fluxes over snow-covered landscapes.

Corresponding author address: Dr. Cezar Kongoli, NOAA/NESDIS, NOAA Center for Weather and Climate Prediction (NCWCP), 5830 University Research Ct. 2804, College Park, MD 20740. E-mail: cezar.kongoli@noaa.gov

1. Introduction

Snow cover is an important earth surface characteristic because it influences partitioning of the surface radiation, energy, and hydrologic budgets. Snow is also an important source of soil moisture for agricultural crops and surface runoff, driving streamflow and replenishing water supplies in higher-latitude or mountainous areas. For instance, snowmelt provides approximately 50%–80% of the annual runoff in the western United States (Pagano and Garen 2006) and Canadian prairies (Gray et al. 1989; Fang and Pomeroy 2007).

In many snow-covered landscapes, the land surface is a composite of snow and vegetation, which can significantly affect the local surface energy balance with potential implications for regional climate and snow hydrology. For instance, when tall vegetation such as shrubs or trees protrude through the snowpack, they absorb more solar radiation and warm relative to the surrounding snow, thus providing an additional heat source (Strack et al. 2004). Strack et al. (2003) report that changing the land-cover specification in the Regional Atmospheric Modeling System (RAMS) from one that was masked by the snow (crop stubble) to one that had protruding vegetation (shrubs) produced sensible heat flux increases as large as 80 W m−2 during the day. The increased sensible heat flux produced a 6°C increase in afternoon air temperatures and a 200–300-m increase in the afternoon boundary layer height. Flerchinger et al. (2012) collected surface energy flux measurements at a sagebrush site and both above and below the canopy of an aspen site during snowmelt using the eddy covariance (EC) technique and compared these measurements to simulations from the Simultaneous Heat and Water (SHAW) model (Flerchinger et al. 2009)—a detailed model of energy and mass balance. They found upward sensible heat fluxes despite the presence of above-freezing air temperatures over the snow surface. Above-freezing air temperatures during snowmelt would indicate downward temperature gradients and sensible heat fluxes into the snow, indicative of a very stable air layer closer to the snow surface. Bewley et al. (2010) found similar upward sensible heat fluxes over shrub-dominated vegetation in a tundra environment through field measurements and simulations with a dual-source soil–vegetation model adopted from Blyth et al. (1999) and modified for snow. Heating of exposed shrubs led to upward sensible heat fluxes approaching 200 W m−2 while snow remained on the ground. Sturm et al. (2005) found that an increase in the abundance and size of shrub vegetation in tundra ecosystems causes a decrease in local surface albedo that could potentially boost winter heating by 70%. McCartney et al. (2006) showed that tall shrub canopies affect the timing and magnitude of streamflow discharge in tundra basins because of their enhancement of snow accumulation and rapid meltwater production, which overwhelms the infiltration capacity of soils. This suggests that an increase in the abundance of shrub vegetation in tundra regions resulting from climate warming could impact the timing and magnitude of freshwater runoff to the major drainage basins.

Given the importance of snow in the global energy and water balance, it is imperative that process-based models using remote sensing be developed and tested for large area assessments. While remote-sensing-based energy balance models for monitoring evapotranspiration from local to regional scales have matured (see review by Kalma et al. 2008), to the authors’ knowledge such methods are virtually nonexistent for applications over snow. In this study, a diagnostic snow–vegetation energy balance model based on remote measurements of land surface temperature is developed and evaluated in comparison with flux measurements made at two snow-covered sites. This approach is very different from, yet complementary to, existing prognostic snow modeling systems based on mass balance. An advantage of the diagnostic approach is that the surface fluxes are estimated without the need for continuous measurements of frozen precipitation, which are difficult to obtain and subject to large uncertainty due to inadequate sampling at landscape and regional scales. In combination, diagnostic and prognostic snow flux models provide independent assessments of snow energy dynamics that should be useful for improving both types of modeling systems.

The snow model parameterizations described here are adapted from the physically based two-source energy balance (TSEB) modeling scheme (Norman et al. 1995), which estimates fluxes from the vegetation and surface substrate separately using remotely sensed measurements of land surface temperature. The TSEB model is being applied routinely for monitoring of evapotranspiration and drought over snow-free surfaces within the continental United States. (Anderson et al. 2007c, 2011a,b, 2013). For such regional applications, the TSEB is applied in time-differential mode using measurements of morning surface temperature rise collected by geostationary weather satellites in a modeling framework called the Atmosphere–Land Exchange Inverse (ALEXI) (Anderson et al. 1997, 2007b). The associated disaggregated ALEXI (DisALEXI) algorithm uses the TSEB as applied to higher-resolution surface temperature data from polar orbiting systems like Landsat, Terra, or Aqua to spatially disaggregate ALEXI flux estimates down to multifield or subfield scales over sites of specific interest (Norman et al. 2003; Anderson et al. 2003, 2004, 2007a, 2012; Cammalleri et al. 2013). With the addition of a snow module, the application of ALEXI/DisALEXI can be extended to snow covered areas, which are currently masked out in routine analyses.

The focus of this study is the assessment of TSEB modified for snow (TSEBS) applied at local scales, using in situ measurements of surface temperature, radiation, and turbulent fluxes. Assessment of remote sensing applications of TSEBS at landscape and regional scales using ALEXI, and at field scales using DisALEXI, will be conducted in future studies. Snow modeling and measurement studies indicate that radiation and turbulent fluxes dominate the snow surface energy balance and that modeled turbulent fluxes over snow-covered surfaces are difficult to validate (Anderson 1976; Male and Granger 1981; Marks and Dozier 1992; Pomeroy et al. 1998; Kongoli and Bland 2002; Marks et al. 2008). In this study, TSEBS flux estimates are evaluated against field measurements at two sites in a mountainous rangeland ecosystem in southwestern Idaho during winter 2007: one site dominated by aspen trees and the other by sagebrush vegetation. Turbulent fluxes at both sites were measured with EC systems, which currently are the most direct way to measure sensible and latent heat over snow-covered fields. The current generation of EC systems has been shown to provide fairly reliable flux measurements over a wide variety of surfaces, including those that exhibit complex terrain and canopy structure, although the EC technique continues to be plagued by energy balance closure issues, typically underestimating the available energy by 10%–30% (Marks et al. 2008; Wilson et al. 2002; Foken 2008).

The paper contains seven sections. Section 2 presents an overview of the TSEB modeling framework, while section 3 details modifications to the TSEB to account for snow surface energy exchange. Section 4 describes field measurements at the aspen and sagebrush sites. Section 5 describes the application of TSEBS for estimating surface energy fluxes above canopy at the aspen and sagebrush sites during the winter. Section 6 discusses the results of the model simulations and comparisons with field measurements of surface fluxes. Finally, section 7 provides the summary and main conclusions of the study.

2. Overview of the TSEBS model

a. Original TSEB formulation for vegetated surfaces

Figure 1 depicts the atmosphere–soil–canopy system representation in the two-source energy balance model of Norman et al. (1995). The series resistance formulation in TSEB allows both soil and vegetation to influence the microclimate within the canopy air space. The resistances considered include RA, the aerodynamic resistance for momentum between the canopy and the upper boundary of the model (including diabatic corrections); RX, the bulk boundary layer resistance over all leaves in the canopy; and RS, the resistance through the boundary layer immediately above the soil surface. Mathematical expressions for these resistance terms are given by Norman et al. (1995) with modifications described in Kustas and Norman (1999).

Fig. 1.
Fig. 1.

Schematic diagram of sensible heat flux computations in the land surface representation used in the TSEB model.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-12-0153.1

The standard version of the TSEB partitions the composite surface radiometric temperature, TRAD, into characteristic soil and canopy temperatures, TS and TC, based on the local vegetation cover fraction apparent at the thermal sensor view angle, fC(θ):
e1
where fc(θ) is the fractional cover
e2
in which F is the leaf area index, Ω(θ) is the vegetation clumping factor apparent at sensor view angle θ (Anderson et al. 2005), and k is the light extinction coefficient.
Equations (1) and (2) are solved simultaneously with a set of equations describing the surface energy budget for the soil, canopy, and composite land surface system as system, soil, and canopy energy budgets:
e3
e4
e5
net radiation:
e6
e7
e8
sensible heat:
e9
e10
e11
latent heat:
e12
e13
and soil conduction heat:
e14
In the above equations RN is net radiation, H is sensible heat, λE is latent heat (λ is the latent heat of vaporization and E is the evaporation/condensation rate), G is the soil (conduction) heat flux, T is temperature, R is a transport resistance, ρ is air density, cp is the heat capacity of air at constant pressure, γ is the psychometric constant, and Δ is the slope of the saturation vapor pressure versus temperature curve. Subscripts A, AC, and X signify properties of the air above and within the canopy, and within the leaf boundary layer, respectively, while subscripts S and C refer to fluxes and states associated with the soil and canopy components of the system. The soil heat flux is computed as a fraction of the net radiation below the canopy, at the soil surface [Eq. (14)] (Choudhury et al. 1987), with αg = 0.31 derived from midmorning flux observations (Kustas et al. 1998). In Eq. (13), transpiration is tied to the net radiation divergence in the canopy (RNC) through a modified Priestley–Taylor relationship (Priestley and Taylor 1972), where αC is a coefficient with a nominal value of 1.3 that is downward adjusted if signs of vegetative stress are detected and fg is the fraction of green vegetation in the scene. Justification for this parameterization of λEC is provided by Norman et al. (1995) and more recently supported by Agam et al. (2010) under a wide range of vegetation types (both natural vegetation and agricultural crops). The longwave components of RN and RNS are a function of the thermal radiation from the sky (Ld), the canopy (LC), and the soil (LS) and the coefficient of diffuse radiation transmission through the canopy (τc). The shortwave components depend on insolation values above the canopy (Sd) and above the soil surface (Sd,s), and the reflectivity of the soil–canopy system (A) and the soil surface itself (ρs). Based on the work of Goudriaan (1977), Campbell and Norman (1998) provide analytical approximations for τc and A for sparse to deep canopies, depending on leaf absorptivity in the visible, near-infrared, and thermal bands; ρs; and F.

b. Model modifications for snow

When full snow cover is present, the scene is composed of snow and vegetation components. Snow on the ground will mask vegetation in proportion to its depth. Therefore, the exposed vegetation fraction (fe) varies with snow depth (SD) and is computed from the following expression (Strack et al. 2004):
e15
where hc is vegetation height (m) and fc is the fractional vegetation coverage that would be observed from nadir if there were no snow. When SD reaches or exceeds vegetation height, vegetation is “buried” under the snow, and thus the scene is composed of only snow cover. The fe fraction can also be estimated from snow cover fraction parameter (fsn), which can be obtained from remote sensing:
e16
Under patchy snow cover conditions, this equation may not always hold, with some fraction of the scene covered by bare soil. This transient “three source” situation will be explored in future studies. In addition, the effects of canopy interception of snow on masking of vegetation and on surface energy exchange are not currently considered.
The snow–vegetation surface energy balance scheme follows that of the two-source soil–vegetation framework in TSEB, with modifications made only to its soil component—replacing soil with a snow substrate and accounting for snow surface energy exchange. A simplified treatment is desired, such that these modifications can be easily implemented within existing TSEB applications (ALEXI and DisALEXI). As for a soil substrate [Eq. (3)], the snow surface energy balance is expressed as
e17
where RNSN, HSN, λESN, and GSN are net radiation, sensible heat, latent heat (λ is the latent heat of evaporation/sublimation and ESN is the evaporation/sublimation rate), and snowpack heat fluxes, respectively (W m−2). Upward fluxes toward the atmosphere are positive and downward fluxes are negative. Surface snow heat flux GSN is computed as a linear function of RNSN [as in Eq. (14)]:
e18
where KSN is an empirically defined constant (see discussion below). Parameterizations for computing RNSN and HSN are the same as in TSEB, with surface albedo and roughness parameter inputs being those associated with snow surfaces. As in TSEB, λESN is computed as a residual using Eq. (17). Note that the advected heat flux is not considered in the surface energy balance. Equations (17) and (18) are solved simultaneously with those representing the canopy energy balance to estimate snow and vegetation surface temperatures TSN and TC, along with component surface energy fluxes.

If the estimated TSN is greater than freezing, it means that the energy input to the snow surface cannot be balanced by thermal conduction into the snow. Surface melt will occur and TSN is then set to 0°C. Canopy surface temperature TC is recomputed from Eq. (1) and net radiation components over snow and canopy are recomputed from Eqs. (6) to (8). Melt energy Qm is recomputed from Eq. (18) (i.e., Qm = GSN). Additionally, turbulent fluxes are recomputed iteratively from Eqs. (3) to (5) and (9) to (11). This additional iteration routine is needed since changing surface temperatures over snow and canopy affects the resistances and the within-canopy air temperature TAC, which in turn affects sensible and latent heat fluxes. Given Qm and λESN fluxes estimated from the model, melt and sublimation rates can be easily computed as Qm/hf and λESN/λ, respectively, where hf and λ are the latent heat of fusion and vaporization, respectively (J kg−1).

3. Site description and in situ measurements

Data used in this study were collected during the 2007 winter season at two field sites located in the Reynolds Mountain East (RME) catchment in Idaho (Fig. 2): one site is dominated by aspen vegetation (Fig. 3) and the other by sagebrush vegetation (Fig. 4). The RME is a 39.0 ha headwater catchment that ranges in elevation from 2024 to 2139 m MSL (Fig. 2). The catchment is located in the southwestern portion of the Reynolds Creek Experimental Watershed (RCEW) operated by the U.S. Department of Agriculture Agricultural Research Service Northwest Watershed Research Center. The catchment is dominated by low and mountain big sagebrush (Artemesia arbuscula and Artemesia tridentada vaseyana) and rocky ground covering 69% of the catchment; patches of aspen (Populus tremuloides) and willow (Salix spp.) cover 26% and fir (Abies spp.) occupies the remaining 5% of the catchment area.

Fig. 2.
Fig. 2.

Location of the sagebrush and aspen study sites within the Reynolds Mountain East catchment in southwestern Idaho.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-12-0153.1

Fig. 3.
Fig. 3.

Photographs of the aspen site during the field survey in winter 2007.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-12-0153.1

Fig. 4.
Fig. 4.

Photographs of the sagebrush site during the field survey in winter 2007.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-12-0153.1

The data collected include measurements of standard meteorological variables, such as air temperature, wind speed, humidity, and air pressure, and nonroutine measurements of energy fluxes. Turbulent flux was measured by EC systems established to monitor fluxes across the RME catchment as part of a long-term study to characterize the hydrology of this mountainous watershed (Flerchinger et al. 2010, 2012). One system was located over a wind-exposed sagebrush site, another within the understory of the aspen grove, and a third situated above the aspen canopy. Vegetation at the sagebrush site consists of about half sagebrush, with the remainder consisting of equal amounts of native grasses and forbs. Sagebrush at the site is approximately 60 cm in height, with a leaf area index (LAI) of 0.77 based on point frame measurements. The site is a gently rolling ridge top with slope varying from 1% to 3%. The aspen site consists of an aspen grove with an understory of grasses and forbs. Average tree height was 9.5 m and the maximum tree height was 15 m. Using a LI-COR -2000 LAI instrument (LI-COR, Inc., Lincoln, Nebraska), the stem area index (SAI) of the trunks and limbs prior to the growing season was estimated to be ~0.45, while maximum LAI of the aspen measured during the growing season was 1.35 in August.

The EC systems deployed at these sites consisted of a three-dimensional sonic anemometer (Model CSAT3, Campbell Scientific, Inc., Logan, Utah) and an open path infrared gas analyzer (IRGA; Model LI-7500, LI-COR, Inc., Lincoln, Nebraska) sampled at 10 Hz. The EC systems were located at 5 m above the ground surface at the sagebrush site and 4.5 m (understory) and 19.25 m (above canopy) at the aspen site. Shortwave and longwave radiation, air temperature, and humidity were collected every 30 min using a four-component net radiometer (CNR-1, Kipp & Zonen, Delft, Netherlands) and a temperature/humidity probe (HMP45C, Viasala, Helsinki, Finland). Wind speed, humidity, and air temperature were measured using two-dimensional sonic anemometers at heights of 5 m above the ground surface at the sagebrush site and 4.5 m (understory) and 19.25 m (above canopy) at the aspen site. Temperature and humidity were also measured at heights of 3, 9, and 15 m within the aspen canopy. Dual-gauge precipitation systems especially designed for the windy and snow-dominated conditions prevalent in the area were used to measure precipitation. The dual-gauge system consisted of two Belfort-type weighing gauges, one shielded and one not. The corrected precipitation is computed from a ratio of the two gauges (Hanson et al. 2004). In addition, snow depth measurements at half-hourly intervals were also made with automatic sonic ranging sensors.

Processing of the eddy covariance data is described in Flerchinger et al. (2010). The EC system was powered by five 55-A-h batteries and two 40-W solar panels. Post processing of the 30-min EC data consisted of sonic temperature correction (Schotanus et al. 1983), density correction (Webb et al. 1980), and coordinate rotation (Kaimal and Finnigan 1994). Soil heat flux measured at 0.08 m below the soil surface was corrected for heat storage above the heat flux plates. Heat stored within the canopy was computed from the empirical equation of Blanken et al. (1997) based on the change in temperature over the 30-min averaging period. Quality control of the eddy covariance data, assessed by energy balance closure, was limited to periods without snow cover because measurements of snow temperatures and energy stored within the snowpack were not available.

The study period was restricted to 30 days from mid-February to mid-March [day of year (DOYs) 51 to 80]. This period was selected because the EC and meteorological datasets were generally complete, and it captured the period of snow ablation and melt. Even so, a considerable number of half-hourly measurements were screened out owing to poor data quality or unfavorable wind direction by removing periods when winds came from behind the instrument system and tower, whichgenerated wakes not associated with turbulence from the upwind land surface. Comparisons between simulated and measured fluxes were made for quality-controlled half-hourly and daily average fluxes over a 24-h interval. For daily flux comparisons, only those days with more than 50% of half-hourly measurements were included in the analysis to retain a reasonable sample of daily data in the analysis. Model performance was also assessed using a higher threshold (75%), but this difference in threshold had little effect on the statistical results.

4. Application of the snow–vegetation energy balance model

Comparisons were conducted between modeled net radiation and turbulent fluxes and field measurements collected above canopy at the aspen and sagebrush-dominated sites. The measurements of fluxes under the aspen canopy taken at 4.5-m reference height were not used in the analysis to assess modeled fluxes above the understory snow substrate. Flerchinger et al. (2012) noted that the measured understory fluxes were impacted by solar heating of aspen branches during melt periods, and as a result they did not provide reliable measurements of fluxes at the snow surface. The authors also note that the occurrence of the above-freezing air temperatures during melt was indicative of downward sensible heat flux that must have occurred close to the snow surface (correctly captured by model simulations), whereas the sensible heat flux measured by the eddy covariance system in the canopy air space was directed upward.

Table 1 lists TSEBS model inputs required to run the model along with fixed values used for the aspen and sagebrush sites. Key output variables estimated by TSEBS are also tabulated. Scene surface skin temperature inputs to the model were estimated offline from in situ measurements of upwelling and downwelling longwave radiation using the following equation:
e19
where Tskin is skin temperature of the composite surface, Lu (Ld) are the upwelling (downwelling) longwave fluxes, ε is the surface emissivity assumed at 0.98, and is σ is the Stefan–Boltzmann constant, which has a value of 5.670 51 × 10−8 W m−2 K−4. The measured downwelling shortwave and longwave radiation components were used as model inputs, while upwelling shortwave radiation was computed using the model-derived system albedo. In regional applications, the model includes parameterizations for computing downwelling longwave radiation using only meteorological data. The inputs for the snow substrate included snow depth and surface albedo.
Table 1.

TSEBS model inputs/outputs, along with input values used at the aspen and sagebrush sites.

Table 1.

For the period modeled (mid-February to mid-March), snow was present on the ground at both sites, although snow depth measurements at the sagebrush site were not available during most of the snow ablation period (Fig. 5). Snow depth for missing days at the sagebrush site was estimated from a linear relationship derived from least squares regression between available snow depth values at the aspen and sagebrush sites (Fig. 6). Note that the vegetation at the sagebrush site, with canopy height 60 cm, was essentially buried under snow between DOY 57 and 68. Given the short study period of simulation, visible/near-infrared snow albedo values were held constant at 0.70/0.45 at the aspen site and at 0.80/0.55 at the sagebrush site. High midwinter snow albedo values for the low-height sagebrush are consistent with values found in similar shrub vegetation environments (e.g., Bewley et al. 2010; Sturm et al. 2005), and lower midwinter snow albedo values for the aspen trees are also consistent with lower values found in forested environments (e.g., Melloh et al. 2002).

Fig. 5.
Fig. 5.

Measured snow depth at the aspen and sagebrush sites during the study period in 2007.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-12-0153.1

Fig. 6.
Fig. 6.

Scatterplot comparing snow depth at the aspen and the sagebrush sites, along with the linear relationship used to estimate missing snow depth values at the sagebrush site.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-12-0153.1

The green vegetation fraction fg was set to zero, thereby shutting down plant transpiration [λEC in Eq. (13)] during the simulation period. The fraction of dormant vegetation cover, fc(θ), consisting of stems and branches was computed from Eq. (2), with SAI replacing LAI (F) of snow-free ground measured at 0.45 (0.77) for the aspen (sagebrush) sites, and clumping factor Ω(θ) set at 1. The light extinction coefficient k was computed using the equation given by Campbell and Norman (1998) as a function of the mean leaf inclination or tip angle parameter x. The mean tip angle for the aspen and sagebrush sites was estimated from LAI-2000 measurements using the one-dimensional inversion model of Campbell and Norman (1989) and Norman and Campbell (1989), with values at 50° and 57°, respectively. The mean tip angle value of 50° for the aspen and 57° for the sagebrush canopy would correspond to values of x equal to 1.0 and 1.5 and computed extinction coefficients k at 0.65 and 0.5, respectively. The exposed vegetation fraction fe was computed from the snow depth using Eq. (15), with vegetation fraction for snow-free soil fc set equal to fc(θ).

An important model parameter is KSN in Eq. (18), which parameterizes the snow surface heat flux as the fraction of net radiation at the snow surface. Note that for melting snow, the heat flux into the snowpack equals the heat flux for melting snow (i.e., QM = GSN). The empirical form of Eq. (18) greatly simplifies computation of the surface energy balance for the snowpack. A more rigorous treatment of the surface snow heat conduction process would require knowledge of snow thermal properties and average temperature of the snowpack (e.g., Tarboton and Luce 1996) and other properties that are not easily retrievable over large areas. The simple parameterization adopted and tested here is particularly useful in regional application of the model using ALEXI and is consistent with the soil heat flux equation used in TSEB for snow-free areas. Energy balance studies over snow suggest that KSN values vary with snow season, with values during snow ablation estimated from measurements of net radiation and turbulent heat fluxes over only snow cover of between 0.6 (Anderson 1976) and 1.0 (Marks et al. 2008). For this study, in the absence of measured net radiation and turbulent fluxes over snow only, a nominal KSN value of 0.85 was determined by optimizing agreement between modeled and measured above-canopy turbulent fluxes at the aspen site, and then kept constant during model runs at both sites. This value lies within the range suggested by Anderson (1976) and Marks et al. (2008). Sensitivity of model–measurement agreement to the value of KSN is explored in section 5.

5. Results and discussion

a. Model comparisons of energy fluxes above the aspen canopy

Summary statistics describing model comparisons with measurements of net radiation and turbulent fluxes over the aspen canopy are listed in Table 2, including sample size (N), mean observed flux (O), mean bias error (MBE), and rms error (RMSE). Statistics shown are for quality-controlled half-hourly and daily average fluxes. Comparisons between modeled and measured half-hourly fluxes are also shown in scatterplots (Fig. 7), whereas Fig. 8 depicts the time evolution of modeled and measured daily fluxes.

Table 2.

Quantitative measures of snow–vegetation model performance in estimating half-hourly and daily fluxes above the canopy at the aspen and sagebrush sites.

Table 2.
Fig. 7.
Fig. 7.

Scatterplots between modeled and measured half-hourly fluxes of (top) net radiation, (middle) sensible heat, and (bottom) latent heat at the aspen site.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-12-0153.1

Fig. 8.
Fig. 8.

Modeled and measured daily fluxes of (top) net radiation, (middle) sensible heat, and (bottom) latent heat fluxes at the aspen site as a function of DOY.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-12-0153.1

Discrepancies between modeled and measured net radiation can be mainly attributed to use of a fixed albedo throughout the simulation period, given that downwelling shortwave and incoming longwave inputs to the model were derived from observations. This resulted in a relatively small mean bias (1 W m−2 for half-hourly and 0 W m−2 for daily fluxes) and RMSE (36 W m−2 for half-hourly and 18 W m−2 for daily fluxes) in model net radiation. Turbulent flux comparisons show overall reasonable agreement, given the small magnitude of these fluxes and the likely uncertainty in the eddy covariance measurements over the winter months (Flerchinger et al. 2010). For sensible heat flux mean bias is fairly low (10 W m−2 for half-hourly and for daily fluxes), and RMSE ranges between 53 and 35 W m−2 for half-hourly and daily fluxes, respectively. Half-hourly latent heat flux comparisons yield reasonably small bias (14 W m−2 for half-hourly and 17 W m−2 for daily fluxes) and RMSE values (31 W m−2 for half-hourly and 20 W m−2 for daily fluxes). These errors are comparable to those observed in TSEB evaluations over snow-free surfaces (e.g., Anderson et al. 2012), although the relative errors are larger in this case given the generally smaller magnitudes in the observed fluxes. The errors in turbulent fluxes are particularly exacerbated for daily values where both nighttime measurements and model computations under strongly stable conditions can have significant uncertainty or errors.

The quantitative assessment described above pertains to model comparisons of above-canopy surface fluxes for the entire simulation period. A more detailed analysis of model output at half-hourly time steps, focused on the melt periods, suggests that the model is reasonably robust in capturing evolution of surface energy fluxes during snowmelt. Figure 9 presents an example, showing modeled and measured half-hourly sensible heat fluxes during possible snowmelt between DOY 70 and 73, as inferred by estimated snow surface temperatures of 0°C and above-freezing modeled in-canopy air temperatures. Evolution of sensible heat fluxes over the composite (snow plus vegetation) surface is well captured, as shown by the close agreement with measurements (top panel of Fig. 9). Note the modeled above-freezing in-canopy air (TAC) and canopy (TC) temperatures (middle panel), whereas modeled snow surface temperatures (TS) are predominantly at 0°C. During the daytime, TC exceeds TAC because of solar heating of limbs and branches, leading to upward canopy sensible heat flux, which dominates composite sensible heat fluxes during the daytime despite the presence of a downward (negative) sensible heat flux over snow (bottom panel).

Fig. 9.
Fig. 9.

Time series of (top) modeled and measured half-hourly sensible heat flux, (middle) measured air temperature and modeled canopy and snow temperature, and (bottom) modeled scene and component sensible heat fluxes at the aspen site using the measured SAI of 0.45.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-12-0153.1

Model–measurement agreement in turbulent fluxes at the aspen site is to some extent influenced by the optimization of the KSN value in Eq. (18). Figure 10 presents an analysis of sensitivity of the agreement in half-hourly latent heat to the value of the KSN parameter, with values between 0.3 and 1.3. As shown, MBE is reduced with increasing KSN, whereas RMSE reaches a minimum of ~31 W m−2 using KSN ~ 0.85, the value adopted at both the aspen and sagebrush sites.

Fig. 10.
Fig. 10.

Sensitivity of agreement between modeled and measured half-hourly latent heat flux at the aspen site to the value specified for KSN in Eq. (18).

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-12-0153.1

Another model parameter having significant affect on radiation balance and melt is the snow albedo in the visible (VIS) wave band. A study of sensitivity of modeled surface fluxes to VIS snow albedo showed that a value of 0.5 gave better agreement with surface flux observations at the aspen site during melt periods, while a value of 0.80 resulted in better agreement with the measurements during nonmelt periods (Table 3).

Table 3.

Sensitivity of modeled surface fluxes (W m−2) to visible snow albedo input at the aspen site.

Table 3.

At present, remotely sensed estimates of fractional snow cover can be retrieved with an absolute accuracy of ~0.1 over the full range in cover, from 0 to 1.0 (Romanov et al. 2003; Salomonson and Appel 2004; Rittger et al. 2013). Sensitivity of modeled sensible heat flux to uncertainties in fsn was evaluated indirectly by comparing model output using SAI values that result in a ±0.1 deviation in cover fraction via Eq. (2), which in the case of the aspen site directly impacts more or less fe [see Eq. (16)]. Along with the observed SAI = 0.45, the model was also run using SAI = 0.30 and SAI = 0.75. Figure 11 shows model output of sensible heat flux computed using this range in SAI from the measured value of 0.45. Note the consistency in the deviations in modeled sensible heat flux for the lower and higher SAI values during daytime conditions compared to the output using the measured SAI = 0.45 (Fig. 11, top panel). For SAI = 0.30, the HSN component dominates such that the composite (snow plus canopy) flux remains negative on DOY 71 even during daytime warming of canopy limbs and branches (Fig. 11, middle panel), while using a SAI = 0.75 canopy HC causes even a higher positive H owing to the dominating effect of sensible heat flux from the canopy (Fig. 11, bottom panel). As a result, model-predicted λESN decreases with greater vegetation cover fraction/SAI (Fig. 12). This suggests that estimates of SAI/canopy and fractional snow cover need to be fairly reliable, particularly under low SAI/cover conditions, for the model to provide satisfactory half-hourly estimates under such conditions.

Fig. 11.
Fig. 11.

Time series of modeled half-hourly sensible heat flux of the total (H), canopy (HC) and snow surface (HS) at the aspen site using (top) SAI = 0.45 (observed value), (middle) SAI = 0.30, and (bottom) SAI = 0.75.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-12-0153.1

Fig. 12.
Fig. 12.

Modeled latent heat flux over the snow surface (λESN) at the aspen site using SAI = 0.45, SAI = 0.3, and SAI = 0.75.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-12-0153.1

b. Model comparisons of energy fluxes above the sagebrush canopy

Summary statistics comparing modeled estimates and measurements of net radiation and turbulent heat fluxes over the sagebrush canopy are presented in Table 2. In Fig. 13, scatterplots compare measured and modeled half-hourly fluxes, and in Fig. 14 daily modeled and measured fluxes are shown as a function of DOY.

Fig. 13.
Fig. 13.

Scatterplots between modeled and measured half-hourly fluxes of (top) net radiation, (middle) sensible heat, and (bottom) latent heat at sagebrush site.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-12-0153.1

Fig. 14.
Fig. 14.

Modeled and measured daily flux of (top) net radiation, sensible heat (middle), and latent heat (bottom) at the sagebrush site as a function of DOY.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-12-0153.1

The error statistics for the modeled fluxes above the sagebrush canopy (Table 2) are similar to those for the aspen site (Table 1), except for larger biases in all fluxes. The MBE values are substantially larger for sagebrush latent heat fluxes, whereas RMSE values are similar between the two sites. Poorer agreement with measurements for the sagebrush site could be due in part to less reliable estimates of sagebrush canopy fraction and snow depth, which had to be inferred from the aspen site measurements during the period of rapid melt (cf. Figs. 5 and 6). This is exacerbated by the low height of the sagebrush, which causes rapid changes in the exposed vegetation fraction fe computed by Eqs. (15) and (16) as the snow height varies, especially during snow ablation and melt.

In Fig. 15, an example of modeled sensible heat flux is shown with possible episodes of melt on DOY 78 followed by refreezing on DOY 79, as suggested by near- and below-freezing snow surface temperatures computed by the model. Evolution of sensible heat flux is reasonably well captured, as shown by the relatively close agreement between measured and simulated values of H (top panel). In examining surface energy balance over snow, below freezing surface snow temperatures are driven by negative RNSN despite the presence of above freezing in-canopy air temperatures and the HSN gains. Note that the above-freezing daytime canopy temperatures are lower than those for the aspen canopy depicted in Fig. 9. The predominance of higher daytime canopy surface temperatures at the aspen site during the melt period explains the occurrence of much higher simulated upward sensible fluxes at the aspen site.

Fig. 15.
Fig. 15.

Time series of (top) modeled and measured half-hourly sensible heat flux; (middle) modeled in-canopy air (TAC), canopy (TC), and snow (TS) surface temperatures; and (bottom) modeled scene (H), snow (HS), and canopy (HC) sensible heat fluxes at the sagebrush site.

Citation: Journal of Hydrometeorology 15, 1; 10.1175/JHM-D-12-0153.1

In these comparisons between modeled and measured surface energy fluxes, the impact of energy balance closure in the EC data has not been discussed because measurements of GSN are not available. Since the unclosed EC measurements were used to determine a reasonable magnitude of KSN, this coefficient has incorporated the likely effect of closure. Since the degree of closure at the sage brush and aspen site may differ, this may be an additional factor affecting model performance for the sagebrush versus aspen site.

6. Conclusions

In this study, the two-source (soil and vegetation) energy balance (TSEB) model parameterizations have been adapted for snow-dominated surfaces and evaluated with field measurements of surface energy fluxes at two sites in a rangeland ecosystem during the winter: one dominated by aspen trees and the other by sagebrush vegetation. Measurements of turbulent fluxes were collected using the eddy correlation method, which currently represents the most direct way to measure these fluxes over snow-covered landscapes. The modified TSEB for snow (TSEBS) treats the land surface as a composite of snow and vegetation elements with different temperatures, fluxes, and atmospheric coupling. This results in a single model formulation that can be applied to a wide range of snow canopy conditions, including partially vegetated surfaces. A significant advantage of the TSEB/TSEBS parameterizations is that the available thermal remote sensing data—the directional composite radiometric temperature and fractional vegetation cover—are diagnostic model inputs, which allow inverse application of this energy balance modeling scheme for interpretation of remote sensing measurements. These features have allowed TSEB application across a wide range of spatial scales.

The TSEBS modeling scheme includes routines to account for masking of vegetation by snow and snow surface energy exchange. Given surface melt and latent heat fluxes estimated from the model, snowmelt and sublimation rates can be easily computed, thus allowing application of the model in snowmelt and ablation studies. A key model parameterization for snow that was adopted from TSEB is the simple linear relationship for computing snow surface heat conduction from net radiation at the snow surface [Eq. (18)]. This is a major simplification that is desired in operational applications. The coefficient of this linear relationship, KSN, was estimated by model comparisons with measurements at the aspen site and kept constant during the melt period at both sites. Future research will investigate indirect methods for estimating nominal values of KSN that can be determined from remote sensing. Masking of vegetation by snow was accounted for by a linear relationship between visible vegetation fraction and snow depth.

The TSEBS model was applied to field measurements at both sites during the winter of 2007. Model comparisons for net radiation and turbulent fluxes above canopy showed reasonable agreement given the likely uncertainty in the measurements over the winter months and simplifications used by the TSEBS model parameterization of the snow surface heat flux (i.e., snowpack energy balance), particularly on a daily basis incorporating nighttime fluxes. Better agreement with measurements was found at the aspen compared to the sagebrush site. This may have been due to less reliable estimates of sagebrush canopy fraction and surface albedo, which for the low-height sagebrush can change rapidly and drastically, especially during snow ablation and melt. The TSEBS model reasonably captured the evolution of sensible heat fluxes during periods of melt at both sites. Additionally, the model captured the occurrence of upward sensible heat fluxes above canopy, which frequently exceeded the downward (negative) sensible heat flux estimated for the snow surface during the melt period. Upward (positive) sensible heat fluxes were larger in magnitude and frequency at the aspen site than at the sagebrush site. Model sensitivity to canopy fraction at the aspen site showed that sensible heat fluxes were sensitive to ±0.1 variation in cover fraction, particularly under low canopy cover conditions, and thus reliable vegetation and snow cover fraction inputs to the model become important for estimating fluxes over snow-dominated landscapes. Currently, remotely sensed estimates of fractional snow cover can be retrieved with an absolute accuracy of 0.1 over the full range in fractional snow cover, namely, 0 to 1. Further testing of the model for other snow covered landscapes is planned, as well as implementation of TSEBS with the Atmosphere–Land Exchange Inverse (ALEXI) regional model (Anderson et al. 2011b).

Acknowledgments

This study would not have been possible without the field measurements provided by the USDA–ARS Northwest Watershed Research Center and financial support from the USDA–ARS Hydrology and Remote Sensing Laboratory, the NOAA Climate Program Office (Agreement 60-1265-1-051), and the NASA Applied Sciences Program (Agreement 60-1245-3-053). USDA is an equal opportunity provider and employer.

REFERENCES

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