Improved snowmelt simulations with a canopy model forced with photo-derived direct beam canopy transmissivity


  • Keith N. Musselman,

    Corresponding author
    1. Department of Civil and Environmental Engineering, University of California,Los Angeles, California,USA
    2. Institute of Arctic and Alpine Research and Department of Geography, University of Colorado Boulder,Boulder, Colorado,USA
      Corresponding author: K. N. Musselman, Institute of Arctic and Alpine Research and Department of Geography, University of Colorado, 1560 30th St., 450 UCB, Boulder, CO 80309-0450, USA. (
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  • Noah P. Molotch,

    1. Institute of Arctic and Alpine Research and Department of Geography, University of Colorado Boulder,Boulder, Colorado,USA
    2. Jet Propulsion Laboratory, California Institute of Technology,Pasadena, California,USA
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  • Steven A. Margulis,

    1. Department of Civil and Environmental Engineering, University of California,Los Angeles, California,USA
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  • Michael Lehning,

    1. WSL Institute for Snow and Avalanche Research SLF,Davos Dorf,Switzerland
    2. School of Architecture, Civil and Environmental Engineering, École Polytechnique Fédérale de Lausanne,Lausanne,Switzerland
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  • David Gustafsson

    1. Department of Land and Water Resources Engineering, Royal Institute of Technology KTH,Stockholm,Sweden
    2. Swedish Meteorological and Hydrological Institute,Norrköping,Sweden
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Corresponding author: K. N. Musselman, Institute of Arctic and Alpine Research and Department of Geography, University of Colorado, 1560 30th St., 450 UCB, Boulder, CO 80309-0450, USA. (


[1] The predictive capacity of a physically based snow model to simulate point-scale, subcanopy snowmelt dynamics is evaluated in a mixed conifer forest, southern Sierra Nevada, California. Three model scenarios each providing varying levels of canopy structure detail were tested. Simulations of three water years initialized at locations of 24 ultrasonic snow depth sensors were evaluated against observations of snow water equivalent (SWE), snow disappearance date, and volumetric soil water content. When canopy model parameters canopy openness and effective leaf area index were obtained from satellite and literature-based sources, respectively, the model was unable to resolve the variable subcanopy snowmelt dynamics. When canopy parameters were obtained from hemispherical photos, the improvements were not statistically significant. However, when the model was modified to accept photo-derived time-varying direct beam canopy transmissivity, the error in the snow disappearance date was reduced by as much as one week and positive and negative biases in melt-season SWE and snow cover duration were significantly reduced. Errors in the timing of soil meltwater fluxes were reduced by 11 days on average. The optimum aggregated temporal model resolution of direct beam canopy transmissivity was determined to be 30 min; hourly averages performed no better than the bulk canopy scenarios and finer time steps did not increase overall model accuracy. The improvements illustrate the important contribution of direct shortwave radiation to subcanopy snowmelt and confirm the known nonlinear melt behavior of snow cover.

1. Introduction

[2] Forest cover affects a significant fraction of Earth's snow water resources. The importance of water for agriculture, hydroelectric power, and other societal needs [Kittredge, 1953] has motivated decades of research on snow processes in forested environments. The need for accurate predictions of these resources has prompted the development of numerous snow models, many of which account for the presence of forest vegetation cover and its effects on snow accumulation, redistribution, and melt. An intercomparison study of 33 snow models by Rutter et al. [2009] found that model errors were greater at forested sites than open sites. In addition, individual models showed inconsistent performance between different forested sites and particularly between paired forested and open sites in the same year. These model inconsistencies, observed under optimal point-scale conditions, are further compounded when models are distributed to the catchment scale.

[3] In midlatitude regions (e.g., the Sierra Nevada, California), solar radiation comprises more than 70% of the net snowpack energy balance [Aguado, 1985; Marks et al., 1992]. As a result, snowmelt patterns largely reflect the heterogeneous distribution of surface shortwave irradiance. Spatiotemporal patterns of solar irradiance are determined by solar elevation, local and regional terrain, cloud cover, and particularly, forest vegetation. In forested regions, spatial snowmelt patterns are dictated by canopy architecture and resulting subcanopy energy gradients. For example, Musselman et al. [2012] and Talbot et al. [2006] showed that patterns of subcanopy shortwave irradiance explain ∼60% of the variability in snowmelt rates. Pomeroy et al. [2009] documented a strong positive relationship between the attenuation of shortwave radiation by canopy elements and locally enhanced longwave irradiance at the snow surface. The results imply that spatial patterns of subcanopy long- and shortwave irradiance are not strictly independent.

[4] Vegetation canopy models vary in their representation of radiative transfer (RT) from simple bulk approximations to complex treatments of the effects of individual canopy elements on attenuation, reflection, and transmission of radiation. Many of the simpler models employ a one-dimensional “big-leaf” canopy representation, which is most applicable over flat, homogeneous terrain [Baldocchi et al., 1987]. In big-leaf models, canopy RT is treated with a two-stream approximation [Dickinson, 1983] and above-canopy radiation is attenuated by a two-parameter application of the Beer-Lambert law [Monsi and Saeki, 1953], which assumes the exponential reduction of radiation through a homogeneous medium [Shugart, 1984]. The application of the Beer-Lambert law to above-canopy radiation is generally inadequate to resolve subcanopy irradiance at subdaily time scales, largely as a result of discontinuous canopy gaps [Reifsnyder et al., 1971]. Exponential attenuation has, however, been shown to adequately estimate the net subcanopy irradiance over longer periods [e.g., Larsen and Kershaw, 1996; Reifsnyder et al., 1971] provided that the parameters are derived from field measurements [Bréda, 2003]. The use of separate exponential attenuation coefficients for diffuse and direct radiation has been shown to partially explain time-varying canopy transmission as a consequence of snow interception, cloud cover, and canopy gaps [Stähli et al., 2009]. In big-leaf models, canopy gaps are accounted for with a canopy openness fraction and the remaining fraction of vegetation is assumed to be randomly distributed [Nijssen and Lettenmaier, 1999]. The assumptions inherent to canopy RT models parameterized with bulk canopy metrics make them difficult to apply to point-scale locations beneath a discontinuous forest canopy.

[5] To account for the effect of canopy heterogeneity on RT, more complex methods using detailed canopy structure parameters have been used [e.g., Li et al., 1995; Ni et al., 1997]. In practice, however, models that are physically realistic but employ only those parameters that are routinely available may be preferable [Nijssen and Lettenmaier, 1999]. Semiempirical studies conducted with physically realistic snowmelt models have reported that canopy height and stand density, two common bulk forest metrics, exert first-order control on subcanopy cumulative shortwave irradiance and simulated snowmelt rates [e.g., Davis et al., 1997]. More recent studies have used airborne scanning light detection and ranging (LiDAR) to represent the spatial arrangement of forest canopies [e.g., Essery et al., 2008b; van Leeuwen and Nieuwenhuis, 2010; Varhola et al., 2010]. As high-resolution vegetation data become more available, the use of detailed canopy metrics to improve snowmelt model representation of snow-atmosphere interactions must be explored.

[6] Physically based snowmelt models are well suited to evaluate the complex linkages between meteorology, forest cover, snow accumulation and melt, and the basin-scale water balance [e.g., Lehning et al., 2006; Pomeroy et al., 2007]. The ability of a physically based snow-canopy model to simulate these processes is limited, in part, by the difficulty of obtaining detailed canopy structure information [Tribbeck et al., 2004]. Additionally, the error associated with validating simulated snowmelt rates under different canopy conditions is large [Nijssen and Lettenmaier, 1999]. For example, issues of scale arise when a canopy model commonly parameterized by bulk canopy metrics is used to estimate heterogeneities in subcanopy hydrometeorological processes as measured at a few point-scale locations. This study demonstrates many of these scale issues.

[7] Plot-scale variability in the timing of melt onset and snowmelt duration influences the distribution of soil moisture [Bales et al., 2011; Molotch et al., 2009], infiltration, groundwater recharge, and streamflow [Seyfried and Wilcox, 1995]. Detailed simulations of plot-scale variability could improve the representation of subgrid variability in modeled hydrometeorological states and fluxes [e.g., Claussen, 1991; Luce et al., 1999] and help to resolve related scaling issues [e.g., Blöschl, 1999]. Improved simulations of snow processes at the plot scale could also inform the representativeness of satellite-derived snow covered area (SCA) to actual subcanopy SCA [e.g., Hall et al., 1998; Klein et al., 1998; Molotch and Margulis, 2008].

[8] More detailed canopy representation in model structure and/or model parameterization may improve the accuracy of physical snowmelt models. For example, upward-looking hemispherical photography is an inexpensive method of estimating forest canopy structure and the likelihood that direct beam solar radiation is transmitted through the canopy [Hardy et al., 2004]. Hardy et al. [2004] improved simulated snowmelt rates using a photo-derived seasonal mean canopy transmissivity value compared to simulations with a bulk (i.e., Beer-Lambert type) reduction of above-canopy solar radiation. However, diurnal and seasonal variability in solar magnitude and the timing of the sun's track across discontinuous canopy gaps limit the utility of seasonal mean transmissivity estimates. A measure of direct beam canopy transmissivity at a temporal resolution that adequately captures the diurnal and seasonal variability of subcanopy shortwave irradiance may improve snowmelt simulations. To our knowledge, no study has applied direct beam canopy transmissivity as a time-variant input to a physically based snow model.

[9] This study evaluates snowmelt estimates from a big-leaf canopy model coupled to a finite element snowmelt model. Three years of subcanopy snow observations from 24 locations spanning a range of terrain and forest structure provide the basis for the evaluation. The methods examine whether model skill is gained from an increased level of detail in the canopy structure information provided to the canopy module, with a focus on the treatment of direct beam canopy transmissivity. The following questions are addressed: (1) How do various methods of obtaining bulk canopy metrics affect snowmelt model accuracy? and (2) Does an explicit treatment of direct beam canopy transmissivity improve snowmelt model accuracy?

[10] Section 2 describes the study area, instrumentation, canopy structure, and the regional hydrometeorological data. Section 3 presents the snow model details as well as the simulation methodology. Results, discussion, and conclusions are described in sections 4, 5, and 6, respectively. A summary of the SNOWPACK canopy model is provided in Appendix A.

2. Experimental Design and Methods

[11] The one-dimensional soil-snow-vegetation model SNOWPACK [Bartelt and Lehning, 2002; Lehning et al., 2002a, 2002b] was forced with observations of above-canopy meteorology to simulate subcanopy snowpack dynamics. The model was initialized at locations of 24 ultrasonic snow depth sensors for water years 2008, 2009 and 2010; a total of 72 sensor years. For each sensor year, three distinct scenarios were evaluated for their effect on model accuracy. The three scenarios specified different levels of canopy structure detail to the big-leaf canopy module: (1) Scenario N is the nominal scenario designed to represent a modeling case where no ground-based observations of canopy structure are available, necessitating the use of gridded satellite data or a land surface look-up table; this approach is commonly applied in distributed modeling studies [e.g., Wigmosta et al., 1994]. The SNOWPACK canopy model parameters canopy openness and effective leaf area index ( inline image) were derived from satellite data at 30 m resolution and estimated from literature-based sources, respectively, as described in section 2.2. The canopy parameters were chosen to be as representative as possible of the canopy conditions at snow depth sensor locations where models were initialized. (2) Scenario NP is the “nominal-photo” case in which upward-looking hemispherical canopy photos were taken at snow depth sensor locations where models were initialized. The photos were used to derive the SNOWPACK canopy model parameters canopy openness and inline image (see section 2.2); this approach is common in point-scale modeling studies [e.g., Rutter et al., 2009] and is expected to yield more accurate estimates of these bulk parameters compared to scenario N. (3) Scenario NPDBT builds upon the level of photo-derived canopy structure detail provided in the NP scenario with a modification to the structure of the canopy model that permits an explicit, time-variant treatment of solar direct beam canopy transmissivity (DBT) derived from the same photos (rather than a bulk representation) as described in section 2.3. Three years of data from repeated snow surveys and a network of subcanopy snow depth and soil moisture sensors were used to evaluate model performance.

2.1. Site Description, Instrumentation, and Hydrometeorology

[12] Work was conducted in the 7.22 km2 Wolverton basin of Sequoia National Park on the western slope of the southern Sierra Nevada, CA, USA (36.59°N, 118.717°W) (Figure 1). Musselman et al. [2012] provides a description of the basin and the four instrumented sites stratified across the basin's range of elevation, aspect, and canopy cover (Figure 1, and Tables 1 and 2). At each site, six ultrasonic snow depth sensors (Judd Communications) recorded hourly snow depth (Figure 2). The data were processed to remove outliers and fill gaps following Lehning et al. [2002a]. Volumetric soil water content (VWC; Campbell Scientific CS 616 sensors) and soil temperature sensors (T-107 sensors) were installed horizontally in the soil column beneath three of the six snow depth sensors at each site, for a total of 12 instrumented soil profiles. Only VWC data from −10 cm soil depths were used in this study as the primary interest was in meltwater leaving the base of the snowpack (Figure 2). The presented VWC data were uncalibrated and as such were only used to evaluate the timing of meltwater pulses in the soil. At each site, hourly soil temperature data were obtained at −10, −30, and −60 cm soil depths beneath three of the six snow depth sensors. Spatial averages of the three soil profiles provided hourly estimates of the site-specific soil temperature profile, which was assumed to be representative of the soil temperature beneath all six snow depth sensors at the respective sites.

Figure 1.

The Wolverton basin and its four instrumented research sites (red squares) in the southern Sierra Nevada, California (top). The location of two meteorological towers (black diamonds) and an upper elevation snow course (yellow asterisk) are indicated. Elevation contours and LiDAR-derived vegetation heights within 60 m × 60 m domains centered on each of the four sites are included. Red circles and reference numbers mark the locations of the six ultrasonic snow depth sensors at each site.

Figure 2.

Observations of snow depth (colored lines) from six ultrasonic depth sensors and volumetric soil water content (black line) measured at a soil depth of −10 cm at each of the four research sites for water years 2008, 2009, and 2010.

Table 1. Terrain Variables Provided to the Models Initialized at Locations of the Six Ultrasonic Snow Depth Sensors at Each of the Four Research Sites
SensorSite 1Site 2
Elevationa (m)22532300
Aspect (degrees from north)355355355355355355451201201208060
Slope (deg)222222222222101515151515
SensorSite 3Site 4
  • a

    Elevation of depth sensor locations at a given site varied by less than ∼5 m. Because elevation was only used to determine the precipitation lapse rate, the intrasite elevation variability specified to the model was negligible.

Elevationa (m)26202665
Aspect (degrees from north)4070959595NA101010101010
Slope (deg)10101086081010101217
Table 2. Canopy Variables Provided to the Models Initialized at Locations of the Six Ultrasonic Snow Depth Sensors at Each of the Four Research Sites
SensorSite 1Site 2
Canopy opennessa (%)242626262626343445454848
inline image (m2 m−2)3.92.872.912.
inline image (%)282726294342343937294139
SensorSite 3Site 4
  • a

    Canopy openness was determined from Landsat-derived NLCD, 2001 canopy density.

  • b

    Sky view factor (SVF) was determined from hemispherical canopy photos as the weighted average of all photo pixels from 65° zenith to nadir (0° zenith) (i.e., SVF65°).

Canopy opennessa (%)717163633636804233423334
inline image (m2 m−2)3.432.631.241.532.
inline imageb (%)645254493735424538393641

[13] Two 7 m meteorological towers, each located near sites 1 and 2 at 2232 m above sea level (asl) and sites 3 and 4 at 2642 m asl, provided hourly observations of air temperature (Figure 3a), relative humidity (Figure 3b), and wind speed (Figure 3c) at an average sensor height of 6 m. The towers are located in large canopy gaps and the collected data were assumed to be representative of above-canopy conditions (Figure 1).

Figure 3.

Meteorological variables representing conditions at the lower (red) and upper (blue) elevation research sites including: (a) daily mean (line) and range (shading) of air temperature, (b) daily mean relative humidity, (c) maximum daily wind velocity, (d) cumulative annual precipitation for each water year (1 October to 30 September), (e) hourly (gray) and daytime mean (points) shortwave radiation from the Topaz Lake meteorological station, and (f) daily mean (line) and range (shading) of longwave radiation.

[14] Snow density data were obtained from monthly snow pit measurements made at the instrument sites and approximately monthly California cooperative snow survey (CCSS) measurements (Table 3). Snow pit density measurements, made in duplicate profiles with 1000 cm3 cutters, were assumed representative of the site-average snow density. CCSS snow course density data represent the average of Federal snow tube measurements made along multiple transects near sites 3 and 4 (Figure 1). Observations from four (2008), six (2009), and four (2010) snow density surveys were used to estimate the SWE at individual snow depth sensors on each survey date (Table 3). The SWE at each sensor location was obtained using the site-average density and the sensor-specific depth. Surveys conducted before and after the date of maximum annual SWE were considered to represent the accumulation and melt seasons, respectively (see Table 3).

Table 3. Dates, Locations, and Results of Snow Density Surveys in the Wolverton Basin for Three Snow Seasonsa
Survey DateSurvey Location(s)Density (kg m−3)SWE: Site Mean ± SD (mm)
Lower ElevationsUpper ElevationsSite 1Site 2Site 3Site 4
  • a

    Average snow densities at lower (sites 1 and 2) and upper (sites 3 and 4) elevations are used with the snow depth sensor measurements on the day of each survey to estimate SWE (mean and SD) at each site. Shading indicates survey dates considered to represent the melt season.

  • b

    Number in parentheses denote number of operational snow depth sensors at a given site on the day of a snow density survey.

  • c

    CCS: California cooperative snow survey location (near sites 3 and 4).

  • d

    Density only measured at upper elevations and assumed representative of lower elevation sites.

12 Jan. 2008Sites 1,3,4336361319 ± 69b(6)320 ± 10(5)521 ± 45(3)523 ± 48(4)
17 Feb. 2008Sites 1,3349381469 ± 88(6)460 ± 15(5)744 ± 117(3)755 ± 52(4)
23 Mar. 2008Sites 1,3391441560 ± 129(6)470 ± 92(5)931 ± 142(4)988 ± 83(3)
27 Apr. 2008Sites 1,2,3443440(0)168 ± 208(5)674 ± 158(4)792 ± 83(3)
25 Jan. 2009CCSc330d330187 ± 75(4)161 ± 26(6)261 ± 110(4)286 ± 25(4)
14 Feb. 2009Sites 1,2,3254271334 ± 49(4)290 ± 31(6)405 ± 108(4)(0)
22 Feb. 2009CCS360d360553 ± 64(4)481 ± 58(6)651 ± 156(4)701 ± 20(4)
21 Mar. 2009Sites 1,3314354(0)263 ± 83(6)550 ± 173(3)592 ± 63(5)
2 Apr. 2009CCS440d440(0)395 ± 105(4)669 ± 159(4)747 ± 84(5)
25 Apr. 2009Sites 1,3425411291 ± 144(6)213 ± 158(4)509 ± 123(4)652 ± 50(5)
25 Jan. 2010CCS270d270462 ± 62(5)456 ± 43(5)572 ± 59(6)582 ± 34(5)
1 Mar. 2010CCS340d340672 ± 96(4)673 ± 94(5)873 ± 99(5)916 ± 48(5)
29 Mar. 2010CCS450d450832 ± 131(5)697 ± 134(5)969 ± 128(6)1092 ± 71(5)
2 May 2010CCS500d500948 ± 151(5)687 ± 257(5)1253 ± 156(5)1395 ± 108(6)

[15] Precipitation was recorded at two additional meteorological stations. The Lower Kaweah station (36.56611°N, 118.7778°W, 1890 m asl), operated by the National Park Service, includes a shielded, heated tipping bucket precipitation gauge. The station is located 5 km SW of the Wolverton basin and ∼340 m lower in elevation. The Giant Forest station (36.562°N, 118.765°W, 2027 m asl), operated by the US Army Corps of Engineers, includes a shielded storage precipitation gauge. The Giant Forest gauge is located 4.6 km SSW of the Wolverton basin and ∼205 m lower in elevation. Data from the two precipitation gauges were merged in an effort to fill data gaps. Catch efficiency of precipitation gauges depends on the gauge and shield design, the wind speed, and the precipitation type (rain or snow) [Groisman and Easterling, 1994]. The catch efficiency of the two gauges was assumed to be equal and was specified according to Groisman and Easterling [1994] as 0.95 for rain and 0.4 for snow, which is near the lower end of the reported efficiency range but higher than used in other studies [e.g., Pierce et al., 2008]. Air temperature is used as a simple proxy for precipitation type such that a catch efficiency of 0.4 is used at temperatures ≤1°C and 0.95 is specified at temperatures >1°C. The corrected gauge measurements are then scaled to the respective elevations of the four Wolverton basin research sites with seasonally dependent orographic precipitation adjustment factors derived by Thornton et al. [1997] as presented by Liston and Elder [2006]. Cumulative precipitation data for the three water years (i.e., 1 October 2008–30 September 2010) at the two meteorological stations are shown in Figure 3d.

[16] While the two Wolverton meteorological stations were located in forest clearings, measurements of incoming shortwave ( inline image) and longwave ( inline image) radiation were affected by tall vegetation on the periphery of the clearings. Instead, inline image data used in this study were measured at a station 8 km ENE of the Wolverton basin at Topaz Lake (3220 m asl), which is located above the timberline and is minimally shadowed by local terrain. In a previous study, the inline image data from Topaz Lake were found to adequately represent the regional above-canopy shortwave field [see Musselman et al., 2012] and were used without correction in the current study to represent inline image in the Wolverton basin (Figure 3e). The inline image data were obtained from the Emerald Lake meteorological station, located 5 km ENE of the Wolverton basin at elevation 2816 m asl. The temperature dependence of inline image and differences in temperature between the Wolverton study sites and Emerald Lake must be considered. Therefore, the incoming atmospheric longwave radiation expected under clear sky conditions ( inline image) was estimated for each of the Emerald Lake and the two Wolverton meteorological stations. The fluxes were estimated from local air temperature and relative humidity measurements as by Satterlund et al. [1979]. The enhancement of longwave radiation by cloud cover was accounted for by computing the maximum of the hourly measured and clear-sky estimated fluxes at Emerald Lake. The fractional increase between hourly inline image and inline image is represented as

display math

The time-variant fraction inline image was used to adjust the hourly clear-sky estimates computed from measurements made at the two meteorological stations in the Wolverton basin inline image as

display math

The hourly inline image data for the lower and upper elevation Wolverton meteorological stations were assumed to be representative of above-canopy longwave fluxes at sites 1 and 2, and sites 3 and 4, respectively (Figures 1 and 3f).

2.2. Canopy Structure Metrics

[17] Two levels of canopy structure detail are presented. The first, used in scenario N, is a coarse approximation of canopy openness and effective leaf area index ( inline image) obtained from remote sensing and literature, respectively, with no in-situ canopy structure knowledge. Remotely sensed bulk canopy openness, defined as (1 – canopy density), was obtained from the National Land Cover Database (NLCD, 2001), which is a 30 m resolution product of Landsat Enhanced Thematic Mapper (ETM +) satellite data [Homer et al., 2004]. The coarse approximation of inline image was specified as a constant value for all point locations in the basin and was estimated from direct measurements of one-sided leaf surface area made in the greater Wolverton region by Spanner et al. [1990]. However, direct LAI measurements are typically 25% to 50% higher than those obtained by indirect optical methods (see thorough review by Bréda [2003] and references therein) such as hemispherical photography or the LAI-2000 Plant Canopy Analyzer (Li-COR, Nebraska, USA). Strictly, optical methods measure the plant area index, which is a more accurate metric of how all canopy elements, including woody areas, combine to influence RT. The differences between the values provided by direct and indirect methods are a product of nonrandom clumping of canopy elements at a variety of scales as well as the ratio of woody area to leaf area; all metrics that vary significantly within a single stand and are typically estimated with a high degree of uncertainty [Bréda, 2003]. The average direct measurement of LAI reported by Spanner et al. [1990] of ∼7.5 m2 m−2 was simply reduced by 30% to 5.25 m2 m−2 to be consistent with the indirect hemispherical photo measurement technique described below (hereafter, the optical estimate of effective leaf area index is referred to as inline image to be consistent with the literature).

[18] The second and more detailed level of canopy structure, used in scenarios NP and NPDBT, was measured in situ by upward looking hemispherical photographs taken directly beneath each of the 24 snow depth sensors. Figure 4a provides an example of a hemispherical photo taken at site 3 beneath depth sensor 1. Readers are referred to Musselman et al. [2012] for a description of the photo acquisition and processing. inline image was estimated from photos following Norman and Campbell [1989] and accounting for a sloped surface as Schleppi et al. [2007] to range from 1.20 to 4.88 m2 m−2 with an average of 2.72 m2 m−2 (Table 2). An estimation of canopy openness in all azimuth directions as viewed by a hemispherical photo requires a zenith angle ( inline image) be specified to compute the sky view factor ( inline image) as the hemispherical weighted sum of the fraction of sky pixels to total pixels from the specified zenith angle to nadir (Figure 4c). As terrain tended to enter the images at inline image values greater than ∼70°, a zenith angle of 65° was chosen to compute inline image from all photos. It should be noted that when iteratively computed at 1 deg inline image angles from 1° to 90° for nearly 90 photos taken at the field site, in no case did inline imageincrease when computed with inline image angles greater than 65° (not shown). Canopy openness at 24 snow depth sensor locations was obtained by computing inline image from a zenith angle of 65° to nadir (see Table 2).

Figure 4.

Example of a hemispherical canopy photo taken beneath snow depth sensor 1 at site 3. The (a) raw, georeferenced color photo is (b) processed to produce a binary representation of sky and nonsky elements, and analyzed to evaluate canopy openness metrics (c) SVFθ across the full range of zenith angles at 1 deg increments and (d) directional SVF at 3° angular resolution, or a discretization of 120 azimuth and 30 zenith solid angles.

2.3. Direct Beam Canopy Transmissivity

[19] An explicit evaluation of the probability of solar beam transmission through the forest canopy at a given time and at the location of a hemispherical photograph required that photos be analyzed in discrete solid angles, or sky regions, specified by both azimuth and zenith angular increments. Hemispherical images taken at each of the 24 depth sensor locations were divided into 120 azimuth and 30 zenith regions and the directional inline image was computed for each sky region (see example in Figure 4d). Methods of Musselman et al. [2012] were used to estimate the direct beam canopy transmissivity by sampling the directional inline image in the sky region corresponding to the solar position. Direct beam canopy transmissivity for the three water years at each photo location was estimated at 1 min instantaneous steps and averaged to 10 min estimates. Figure 5a illustrates the 10 min canopy transmissivity at site 3, depth sensor 1, estimated during daylight hours between the winter and summer solstices of water year 2008. Examples of direct beam canopy transmissivity at the same location but averaged to 60, 30, and 1 min temporal resolutions are provided in Figures 5b–5d.

Figure 5.

Direct beam canopy transmissivity for daylight hours of all days (vertical axes) between the winter and summer solstices at the location of site 3, sensor 1 determined from hemispherical photo by sampling the directional SVF in the sky direction defined by the solar coordinates at (a) 10 min, (b) 60 min, and (c) 30 min temporal aggregation and (d) 1 min instantaneous values. Temporal resolution at the diurnal scale describes the resolution of the horizontal axes while daily values are plotted along the y axes.

3. Modeling Methods

3.1. Snow Model

[20] The SNOWPACK model was chosen for this study based on its documented performance in forested environments in the SnowMIP2 model intercomparison project [Rutter et al., 2009]. The model calculates the vertical exchange of mass and energy in multilayered snow and soil profiles. The upper and lower boundary conditions are determined by measured atmospheric forcing and (if available) soil layer thermodynamic properties, respectively. When vegetation cover is present, the upper boundary conditions of the snow or bare ground surface are calculated by a canopy module in terms of inline image, inline image, and turbulent heat exchange coefficients as outlined by Lehning et al. [2006]. The SNOWPACK canopy module includes treatment of interception and throughfall of precipitation, evaporation of intercepted snow or rain, transpiration, as well as the canopy influence on radiative and turbulent energy fluxes. The model treatment of shortwave radiation transmission is described in detail by Stähli et al. [2009]. However, most details of the canopy model have not been published to date and the reader is provided a short summary in Appendix A. Hydrometeorological data (Figure 3) used to force the model represented above-canopy fluxes. Hourly temperature data of a three-layer soil profile (i.e., 0 to −10 cm, −10 to −30 cm, and −30 to −60 cm) were provided as forcing to determine the temperature gradient at the snow-soil interface (i.e., Dirichlet boundary conditions). Required soil parameters such as albedo (0.2), porosity (0.21), density (2200 kg m−3), thermal conductivity (3.8 W m−1 K−1), and specific heat (900 J kg−1 K−1) were estimated based on in situ soil observations of the largely gravely loam.

3.2. Canopy Model Modification

[21] Scenario NPDBT required a modification to how the canopy model treats direct beam inline image transmission. Rather than treat both direct and diffuse inline image with a static canopy absorption factor (see equation (A1)), the photo-derived transmissivity of direct inline image was specified together with hydrometeorological measurements as time-variant input data valid at the snow surface. The treatment of above-canopy diffuse shortwave and longwave fluxes was unchanged. Feedback processes within the canopy layer between attenuated shortwave radiation and reemitted longwave radiation were considered via the canopy temperature balance. The modification was only applied in the case of the scenario NPDBT.

3.3. Simulations

[22] The three model scenarios were initialized at locations of the 24 snow depth sensors for three water years. In addition to the 72 sensor-year simulations for each of the three model scenarios, the influence of temporal averaging of direct beam canopy transmissivity on the accuracy of scenario NPDBT was explored. In this test, the scenario NPDBT framework was used but the model was forced with direct beam canopy transmissivity estimated at 1 min (instantaneous) time steps, and averaging periods of 10, 20, 30, and 60 min. The model forcing data were linearly interpolated accordingly and the five temporal test cases were run with the same inputs and structure. For all presented model scenarios, the third canopy structure parameter, canopy height, was specified as 40 m. The canopy extinction coefficient inline image, required by the canopy absorption factor (see equation (A1)) for all model scenarios was specified as 0.7, slightly lower than reported by Sicart et al. [2004] with similar inline image values, lower canopy heights, and higher canopy density. On the other hand, the value is larger than 0.6 reported by Stähli et al. [2009]. By design, model simulations were not calibrated to an objective function and the three canopy model parameters (i.e., canopy openness, inline image, and canopy height) were specified as detailed above. Simulations were initialized at the start of each water year (i.e., 1 October), rather than at maximum accumulation, to permit the model to most accurately represent snowpack properties such as the density profile.

3.4. Model Evaluation

[23] Model performance was evaluated against the following in situ observations: (1) manual SWE estimates, (2) continuous snow depth, (3) snow disappearance date, and (4) the timing of soil moisture increase at a soil depth of −10 cm. Automated snow depth measurements were used in conjunction with density observations from manual snow surveys (Table 3) to estimate location-specific SWE on survey dates. At each sensor location, simulated SWE values at times corresponding to the survey dates were evaluated against measurements as the square root of the variance of the residuals (i.e., root mean square error (RMSE)). Similarly, the model SWE bias was calculated as the average difference between modeled and measured SWE values. The bias was computed separately on SWE values obtained during accumulation and melt seasons, defined relative to the date of maximum accumulation (see section 4.1).

[24] An evaluation of simulated and measured hourly (normalized) snow depth during the melt season was used to infer the relative accuracy of simulated snowmelt rates. Simulated and measured snow depths were normalized by respective snow depths on specified melt-season dates. To focus on melt-driven ablation rather than post-accumulation compaction, the dates used to normalize the depth values were specified as six days after the last significant accumulation event for a given snow year. The 6 day period was deemed sufficiently long to permit the new snow to settle and beyond 6 days it was assumed that decreases in snow depth were caused by melt. These dates were 29 February 2008, 19 April 2009, and 1 May 2010. The average (normalized) melt-season snow depth error, in percent, for each simulation and sensor year was computed as the mean difference between modeled and measured values. The third model evaluation metric, error in the simulated snow disappearance date, was simply the difference, in days, between the simulated and measured snow disappearance dates.

[25] The final metric for model evaluation utilized the availability of soil moisture data from sensors at a soil depth of −10 cm at three depth sensor locations at each of the four sites. Hence, the simulated timing of seasonal meltwater fluxes exiting the snowpack base, in millimeter per time step, was compared to the measured timing of the seasonal increase in VWC (at −10 cm soil depths). The initial timing of simulated snowmelt infiltration was determined as the first peak in meltwater flux exceeding 6 mm d−1 for three consecutive days during which no liquid precipitation events occurred. The “first” peak was defined as that occurring after continuous snow cover was recorded for a minimum of 30 days. The above criteria excluded from consideration early season accumulation and subsequent complete melt events, rain-on-snow events, and the slow release of meltwater throughout the snow-covered period due to ground heat fluxes. The date of measured snowmelt infiltration at −10 cm soil depth was determined as the first pulse exhibiting a minimum of 3% volumetric increase in VWC over three days during which no liquid precipitation events occurred and after snow cover had persisted for a minimum of 30 days. The error was computed as the difference, in days, between the simulated and measured initial meltwater pulses. A slight time lag would be expected between the simulated meltwater exiting the snowpack and that being measured at −10 cm soil depth, such that a small degree of “error” on the order of a day or two would occur even under conditions of ideal model performance.

[26] The evaluation of sensor-year simulations against the metrics listed above (other than soil moisture) was limited by depth sensor functionality. Thus, not all sensor years could be evaluated with all metrics. For consistent intercomparison of different sensor years, SWE metrics were evaluated for those sensor years that included at least one survey measurement made during both the accumulation and melt season. An exception was made for water year 2010, in which the 2 May survey was the last of the season and corresponded to maximum accumulation in some sensor locations but the melt season in others. In this case, the 2 May 2010 survey was considered to represent the melt season and the other three surveys the accumulation season (Table 3). Of the 24 sensor locations, 12, 17, and 19 met this criterion in 2008, 2009, and 2010, respectively. Similar data limitations influenced the other three model evaluation metrics. The normalization of melt-season snow depth was only applied to sensor years in which snow depth was recorded for at least 50% of the melt season. This criterion was met at 16, 18, and 20 sensor locations in 2008, 2009, and 2010, respectively. The snow disappearance date was recorded at 17, 19, and 21 sensor locations in the three respective years. Of the 12 snow depth sensor locations with underlying soil moisture sensors, the timing of the seasonal increase in VWC was measured at 10, 8, and 8 locations in 2008, 2009, and 2010, respectively.

[27] Section 4 presents results from the suite of depth and density observations for three water years followed by an illustrative example of the three model scenarios at two different locations for the same season. Results are then summarized for the three model scenario runs conducted on all sensor years.

4. Results

4.1. Depth and SWE Measurements

[28] Compared to the 86 year historical record from CCSS measurements near sites 3 and 4 (Figure 1), maximum annual SWE was near the long-term average (∼950 mm) in 2008, was 48% below average in 2009, and was 43% above average in 2010. Seasonal maximum SWE was estimated to coincide with density surveys conducted on 23 March 2008, 21 March 2009, and 2 May 2010 [Musselman et al., 2012]. The average maximum SWE across all four sites was 737 mm in 2008, 420 mm in 2009, and 1074 mm in 2010. The seasonal timing and duration of the melt seasons are defined both by the date of maximum SWE and the date of snow disappearance. The date of snow disappearance varied markedly by year, site aspect and elevation, and between sensors at individual sites (Figure 6). The average snow disappearance dates across all sites were 25 May 2008, 17 May 2009, and 15 June 2010. The average annual melt-season duration was 64, 57, and 45 days corresponding to seasonal average melt rates of 11.5, 7.4, and 23.9 mm d−1 in 2008, 2009, and 2010, respectively. The standard deviation (σ) of the snow disappearance date determined at all sensor locations on an average per-site basis was 10.4 days in 2008, 5.8 days in 2009, and 7.8 days in 2010. Water year 2008 exhibited the most variability in the date of snow disappearance of all three years. This is attributed, in part, to the 2008 melt season having the longest duration, the fewest snow events (see Figure 4), and the least cloud cover [see Musselman et al., 2012] of the three years. These prolonged melt conditions could be a potential cause of the pronounced subcanopy snowpack variability observed in 2008. A similar explanation could be applied to water year 2010, which exhibited the second most variable snow disappearance date despite having the shortest melt season. However, rather than a prolonged melt season, enhanced energy fluxes coincident with a later melt season likely resulted in high variability in the date of snow disappearance. On average over all years, σ was greater (p < 0.05) at sites 2 and 3 (10.3 days) than at sites 1 and 4 (5.6 days). This is attributed to sites 1 and 4 being north facing with relatively homogeneous aspect relative to sites 2 and 3 (Table 1). The observations indicate that both seasonal meteorology and physiography (i.e., terrain and canopy configuration) interact to determine the date of snow disappearance and the timing and duration of meltwater inputs. The high variability of the observations and the dynamic nature of subcanopy snow processes provide the motivation for this modeling study.

Figure 6.

Date of snow disappearance measured by the six ultrasonic snow depth sensors at each of the four sites for water years 2008, 2009, and 2010. The average and standard deviation of the snow disappearance date computed for the operational sensors at each site for the three years are indicated by the filled circles and vertical bars.

4.2. Illustrative Example of Two Different Simulation Results

[29] Results from scenarios N, NP, and NPDBT run at two sensor locations (site 2, sensor 2; and site 3, sensor 4) for water year 2008 exhibited different trends in the magnitude and sign of the respective melt-season model errors (Figure 7, top). At both locations, minimal differences in snow depth or SWE were observed from initial accumulation until late February, after which melt began in earnest and the scenario simulations diverged. Compared to measurements, the N, NP and NPDBT scenarios run at site 2, sensor 2 (Figure 7, left) overestimated SWE on 23 March 2008 by 391.9, 429.5, and 211.6 mm, respectively. Snow had disappeared from the sensor location by the 27 April survey date, which was captured by NPDBT (i.e., 0 mm SWE) but scenarios N and NP exhibited high positive SWE biases (Figure 7, left). The normalized N and NP predictions of melt-season snow depth had an average error of +20.8% and +18.4% and an error in the predicted snow disappearance date of +32 days and +28 days, respectively (Figure 7, bottom left). The overestimation of normalized melt-season snow depth is analogous to an underestimation of snowmelt. The NPDBT model improved the predictions significantly for this sensor year with an average normalized snow depth error of −0.2% and an error in the date of simulated snow disappearance of +7.5 days. The cumulative subcanopy direct beam solar radiation from 29 February to 26 April (i.e., NPDBT snow disappearance date) was 470, 685, and 852 MJ m−2 for the N, NP, and NPDBT scenarios, respectively (Figure 7, bottom left). Note that the NP and NPDBT scenarios simulated 45.7% and 81.3% greater direct beam radiation than the nominal scenario N over this time period.

Figure 7.

Simulations and measurements of (top) snow depth and (middle) SWE at (left) site 2, sensor 2 and (right) site 3, sensor 4 for water year 2008. (bottom) The simulated and measured melt-season snow depth normalized by the respective depth on 29 February 2008, six days after the last appreciable accumulation event are plotted with the cumulative subcanopy direct beam solar radiation (horizontal) simulated by the three scenarios (bottom panels, top axes). Error bars on the reported SWE measurements represent a 5% uncertainty in both snow density and depth observations.

[30] All 2008 simulations run at site 3, sensor 4 also accurately estimated SWE and depth in early winter and errors were more pronounced in the spring (Figure 7, right). Unlike simulations shown in the left-center panel of Figure 7 in which the nominal N and NP scenarios overestimated measured SWE, the same 2008 scenario runs at site 3, sensor 4 underestimated SWE by 95 and 43 mm, respectively (Figure 7, middle right). Scenario NPDBT slightly overestimated SWE by 24 mm. The normalized N and NP melt-season snow depth predictions had an average error of −18.5% and −16.0% and an error in the predicted snow disappearance date of −16 and −10 days, respectively (Figure 7, bottom right). The underestimation of normalized melt-season snow depth is analogous to an overestimation of snowmelt. The NPDBT model improved the predictions for this sensor year with an average normalized snow depth error of −12.5% and a −7 day snow disappearance date error. The cumulative subcanopy direct beam solar radiation from 29 February to 26 April was 836, 807, and 616 MJ m−2 for the N, NP, and NPDBT scenarios, respectively (Figure 7, bottom right). Note that the NPDBT scenarios at both sensor locations in Figure 7 outperformed the nominal scenarios while simulating 81.3% more (site 2, sensor 2) and 26% less (site 3, sensor 4) cumulative direct beam solar radiation over the same time period (29 February to 26 April) (Figure 7, bottom). The results suggest that the dynamic treatment of direct beam canopy transmissivity by the NPDBT scenario is able to correct for both positive and negative cumulative energy biases resulting from the use of static, bulk canopy transmissivity estimates.

[31] The model differences seen during the melt season at site 2, sensor 2 location in 2008 are also reflected in the simulated meltwater fluxes from the snowpack base compared to measured soil moisture at −10 cm depth at the same location (Figure 8). Timing differences in the initiation of the melt fluxes from the snowpack base simulated by the N and NP models were +9 and +7 days, respectively (Figure 8). The NPDBT model improved these estimates with simulated initial meltwater flux from the snowpack base preceding the measured soil moisture increase by two days (Figure 8); note that the snowmelt flux would be expected to precede soil moisture response.

Figure 8.

Measured volumetric soil water content at −10 cm soil depth (left axes, bold line) and simulated meltwater flux from the snowpack base (right axes, thin line) from water year 2008 at the same site 2, sensor 2 location and three model runs (N, top; NP, middle; NPDBT, bottom) shown in Figure 7 (left). Red arrows indicate model-simulated timing of the initial spring meltwater pulse from the snowpack base. Black arrows indicate the timing of the initial spring meltwater pulse as measured by a soil moisture sensor at −10 cm.

4.3. Results From All Sensor-Year Simulations

4.3.1. SWE Simulations

[32] On average across 62 operational sensor years the N, NP, and NPDBT scenarios yielded relatively high SWE RMSE values of 151, 146, and 127 mm, respectively. During the three accumulation seasons, no single scenario consistently reduced the SWE biases (Figure 9). During the melt seasons, lower (upper) elevation SWE biases were positive (negative) for all scenarios (Figure 9). At lower elevations during the 2008 melt season, the high positive biases in the N (316.6 mm) and NP (341.8 mm) scenarios were reduced by approximately 66% with the NPDBT scenario (106.4 mm) (Figure 9). Similar reductions in positive melt season SWE biases obtained with the NPDBT scenario relative to the mean SWE biases of the two nominal scenarios were obtained at lower elevations in 2009 (74% reduction) and 2010 (45% reduction) (Figure 9). The NP model scenarios reduced the average SWE RMSE and biases of the N scenarios by <5%.

Figure 9.

Biases in simulated SWE from the three model scenarios run at lower (sites 1 and 2) and upper (sites 3 and 4) elevation sensor locations during the 2008, 2009, and 2010 accumulation and melt seasons, respectively, computed on measured and modeled SWE values (left) before and (right) after maximum accumulation. The error bars represent the mean bias ± the standard deviation of the bias.

4.3.2. Snow Disappearance Date

[33] Across the 57 sensor years in which measurements were available, the average error in the date of simulated snow disappearance was positively biased toward later snow cover by 7.7, 7.4, and 1.7 days for the N, NP, and NPDBT scenarios, respectively. Relative to the N and NP scenarios, the NPDBT scenario reduced the mean bias in the snow disappearance date from 7.9 and 7.6 to 0.6 days in 2008 and from 15.1 and 15.0 to 6.9 days in 2010 for the three respective scenarios (see Figure 10). In 2009 a mean bias reduction was not observed; the N, NP, and NPDBT scenarios had an average bias of −0.7, −1.2, and −3.1 days, respectively.

Figure 10.

Simulated date of snow disappearance compared to depth sensor observation provided as model error (model – measurement) in number of days (y axis) for each of the three model cases and for simulations conducted at locations of operational sensors (x axis) at the four sites (rows) for water years 2008, 2009, and 2010 (columns). Site-average errors and site mean absolute errors and standard deviations are indicated by the filled circles and vertical lines, respectively.

[34] The mean absolute error (MAE) values of the simulated snow disappearance date from all N scenarios (13.8 days) and NP scenarios (13.5 days) were reduced by ∼37% to 8.7 days with the NPDBT scenario; 40%, 19%, and 43% average error reductions in 2008–2010, respectively. The relative improvement between the N and NP model scenarios as indicated by the MAE in simulated snow disappearance date was noticeable in 21 of the 57 sensor years, but the average improvement was less than two days and the difference was not statistically significant (Figure 10). The NPDBT scenario reduced the average of the N and NP snow disappearance date errors in 40 of the 57 sensor years (Figure 10). When evaluated on the basis of individual years, on average, the NPDBT model simulations for water years 2008 and 2010 showed significant improvements over the NP scenario in the predicted snow disappearance date of 6.0 (p < 0.05) and 9.2 (p inline image 0.01) days, respectively. In 2009, the mean reduction in snow disappearance date error between the NP and NPDBT runs was 2 days and the difference was not statistically significant. Model error and relative improvement also showed trends with elevation. When simulations from all years were evaluated, compared to the NP simulations, the lower (i.e., sites 1 and 2) and upper (i.e., sites 3 and 4) elevation NPDBT runs reduced the MAE in the predicted date of snow disappearance by 7 and 3 days (p < 0.01), respectively.

4.3.3. Normalized Melt-Season Snow Depth

[35] Based on the 54 sensor years evaluated for error in the normalized melt-season snow depth, the N and NP scenarios had a slight positive bias of 3.8% and 3.3%, respectively, while the NPDBT scenario had a slight negative bias of −1.1% (Figure 11). In 2008 and 2009 scenarios N and NP had positive biases and NPDBT exhibited negative biases; the average biases were less than 2%. In 2010 large positive melt-season snow depth biases of 8.4% and 8.3% from the N and NP scenarios were reduced to 0.2% for the NPDBT scenarios (Figure 11). The absolute errors of the normalized melt-season snow depth for the three scenarios in 2010 were 11.2%, 10.6%, and 7.8%, respectively. The results indicate snowmelt simulations were generally improved with an explicit treatment of direct beam canopy transmissivity and improvements were greatest in the year with the latest melt season.

Figure 11.

Normalized melt-season snow depth error, in percent, for each scenario run for sensor years that recorded a minimum of half the time steps over a period between 6 days after each year's last appreciable accumulation event and the date of snow disappearance. Missing values represent either sensor years in which the depth sensor did not record at least 50% of the melt season or sensor years in which depth data were missing on the specified normalization date.

4.3.4. Timing of Meltwater Soil Infiltration

[36] In general, large differences were found between the simulated timing of meltwater exiting the snowpack base and the timing of initial seasonal increase in soil water content measured at −10 cm (Table 4). Overall, the NPDBT scenario reduced snowmelt infiltration timing errors by 50% in nearly half of the sensor years compared to the N and NP model scenarios. At lower elevations, modeled meltwater flux timing occurred later than the measured snowmelt infiltration by 22, 20, and 10 days for scenarios N, NP, and NPDBT, respectively. At upper elevations, the modeled meltwater flux occurred 18 days earlier than observed for all three scenarios in 2008 and 2009; but occurred 15, 8, and 6 days later than observed in 2010 for the three respective scenarios. Improvements (greater than 3 days) in the predicted timing of initial melt flux between scenarios N and NP were only recorded in three sensor years during which an average improvement of 13 days was observed (Table 4). Improvements gained over the N and NP model scenarios with the NPDBT scenario were observed in 11 sensor years with an average improvement of 11 days. Interestingly, in no case did the NPDBT scenario increase the mean absolute melt flux timing error by more than 1 day compared to the N or NP scenarios (Table 4).

Table 4. Lag/Error, in Number of Days, Between Modeled Date of Initial Spring Meltwater Flux From the Snowpack Base and the Date of Seasonal Volumetric Soil Moisture Increase Measured at −10 cm Beneath the Soil Surface at Three Snow Depth Sensor Locations at Each of the Four Sites for Water Years 2008, 2009, and 2010a
Model Snow Depth Sensor200820092010
  • a

    Results from the three model scenarios at each sensor location and the mean absolute error (MAE) for each site for the three years are included. Missing values (–) reflect an incomplete soil moisture data record.

  • b

    The soil moisture sensors at site 3 are positioned beneath snow depth sensors 3, 4 and 5.

Site 1N17292524303099
Site 2N141014132728282814174826
Site 3bN−5−21139−131114510
Site 4N−39−4040−20−262339020

[37] Despite the improvements with the explicit treatment of direct beam canopy transmissivity, the high MAE values in Table 4 (23 sensor-year MAE of 18 days with the NPDBT scenario) indicate substantial unresolved issues related to predicting the timing of melt fluxes into the soil system. This finding was surprising as maximum SWE and the date of snow disappearance were often simulated with a high degree of accuracy (see section 5). The results highlight challenges with both the simulation and measurement of snowmelt runoff. Distinct melt-freeze layers on the order of 2 to 5 cm were commonly observed in the snowpack. These icy melt-freeze layers were a result of surface melting between snow events and subsequent refreezing. The layers may have acted as barriers to capillary flow and could have impeded preferential “finger” flow formation by lateral dispersion [Waldner et al., 2004]. Most models are not designed to simulate these nonlinear meltwater dynamics. Similar heterogeneous flow patterns are known to exist in the soil matrix. In the case of pronounced lateral dispersion and heterogeneous preferential flow patterns, a single point measurement of near-surface soil water content may be inadequate to capture the snowpack runoff dynamics occurring over a larger spatial footprint. It should also be noted that any model misspecification of rain/snow input will influence the timing of melt fluxes as discussed in more detail below.

4.4. Sensitivity to Temporal Averaging of Direct Beam Canopy Transmissivity

[38] The effect of averaging the direct beam canopy transmissivity over time periods of 60, 30, 20, and 10 min as well as forcing the model with 1 min instantaneous values was first examined at a single location (Figure 12). Relative to automated measurements, the mean error in the normalized depth simulated by models N, NP, and the direct beam model run at 60 min temporal resolution (i.e., NPDBT(60)) were +17.2%, +14.8%, and +13.7%, respectively (Figure 12, bottom), and errors in snow disappearance date for this sensor year were +21, +19, and +20 days, respectively. Running the NPDBT model at a time step of 30 min reduced the normalized melt error by 50% and the snow disappearance date error by 33%. The error was further reduced at finer temporal resolution; the normalized melt errors of the model forced at 20, 10, and 1 min resolution were +4.4%, +0.4%, and −5.5%, respectively, and the simulated snow disappearance date errors for the three models were +12, +7, and +1 days, respectively (Figure 12, bottom).

Figure 12.

(top) Snow depth simulations and measurements during the 2010 water year at site 3, sensor 1; the location of photos shown in Figures 4 and 5. The effect of averaging the direct beam canopy transmissivity used to force the NPDBT models is examined at 60, 30, 20, and 10 min averaging and 1 min instantaneous steps. (bottom) Melt-season snow depth was normalized by the respective simulated or measured (black line) depth on 1 May 2010 to compare simulated melt rates to measured values.

[39] When all sensor years were evaluated, improved results from running NPDBT at higher temporal resolution were not as ubiquitous as the sensor year in Figure 12 illustrates. Compared to the simulated error in snow disappearance date predicted by scenario NP, the NPDBT(60) scenario reduced errors by 4 days in 2008 (p < 0.05) and 1 day each in 2009 and 2010. The NPDBT(30) simulations further reduced error by 2 days in 2008, 1 day in 2009, and by 7 days in 2010 (p < 0.05). Reducing the time step from 30 to 20 min showed no mean absolute error reduction in 2008 and 2009, and an error reduction of 1 day in 2010. Further reducing the time step from 20 to 10 min showed no mean improvement for any year (not shown). Interestingly, increasing the time step from 10 to 1 min increased the average model error of the 57 sensor years in which snow disappearance was recorded by 4 days in 2008 and 3 days on average in 2009 and 2010 (not shown). Note that the error reductions reported above that were not statistically significant (i.e., p > 0.05) were not provided with p values.

5. Discussion

[40] Of the three SNOWPACK model scenarios tested, the bulk scenario N exhibited the greatest overall error when evaluated against point metrics of SWE, snow disappearance date, and the relative timing of snowmelt soil infiltration. In scenario N, canopy openness values for depth sensor/simulation locations were sampled from the 30 m gridded canopy product. The short spacing (8 to 55 m) between sensor locations relative to the coarser grid scale of the satellite product caused three to four sensors at a given site to fall within the same grid element. In these instances, multiple neighboring sensor/simulation locations were assigned the same canopy openness value corresponding to the common NLCD grid cell. In these cases, because inline image was also held constant for scenario N, the only location-specific differences provided to the model at a given site were slope and aspect. The results highlight challenges associated with the evaluation of snowmelt models that use gridded vegetation data against ground-based (often point-scale) observation systems. This scale mismatch was implicit in the experimental design. A common source of uncertainty is faced by studies that evaluate gridded model output against point-scale automated station measurements without explicit consideration of the subgrid representativeness of the station [Meromy et al., 2012]. While it is possible that scenario N would have been better evaluated against gridded measurements of snowpack processes, scenario NP was designed to test whether model skill was improved when parameterized with point-scale canopy measurements. Any improvement with scenario NP over scenario N would implicitly be a result of (1) removing this scale mismatch and (2) improving point-specific canopy model parameterization.

[41] Systematic model biases were not observed across all sites and years, but errors of similar direction and magnitude were observed at lower and upper elevation sites for particular years. These model errors were likely a combined effect of errors in the meteorological forcing data, the challenge of simulating mixed rain-snow precipitation events, and the lack of consideration of subgrid scale canopy variability. For example, the high positive SWE bias at lower elevations in 2008 (Figure 9) were the result of a significant rain-on-snow event in early January as indicated by the increased soil moisture at sites 1 and 2 (see Figure 2). During this event, significantly more rain fell at lower elevations where air temperatures were above freezing but below the 1°C rain-snow temperature threshold specified to the model, resulting in a model misallocation of SWE to the snowpack that persisted as a positive bias through the season. In contrast, negative SWE biases were observed at upper elevations (Figure 9), possibly as a result of errors in the seasonal lapse rates used to estimate upper elevation precipitation.

[42] The minimal improvement over the bulk scenario N with the added photo-derived canopy structure detail provided to scenario NP was surprising. On average the photo-derived inline image specified to scenario NP was 2.53 m2 m−2 less than that specified to the bulk model; a fact that should have significantly reduced the positive bias in snow cover persistence seen in scenario N by permitting more radiation to pass through the canopy. In addition, hemispherical SVF (used in scenario NP) has been found to exceed satellite-derived “viewable gap fraction” (used in scenario N) as a result of off-nadir satellite view geometry, slope, and aspect [Liu et al., 2004]. However, the use of SVF65° rather than SVF90° would be expected to reduce the bias reported by Liu et al. [2004]. Compared to the bulk scenario N, the two photo-derived metrics would effectively reduce the model representation of canopy effects and theoretically should have reduced the bias in scenario N snow cover persistence. Simulations of subcanopy solar radiation are known to be highly sensitive to the value of the canopy extinction parameter kLAI [e.g., Jost et al., 2009]. It is possible that the constant kLAI coefficient of 0.7 used in all scenarios was too high and could partially explain the minimal improvement between the N and NP scenarios. Potential radiative feedbacks in the canopy model could also explain the limited model improvement. For example, a reduction in simulated vegetation coverage would increase the canopy transmission of shortwave but reduce the canopy absorption and emission of longwave radiation. In a natural forest canopy, these radiative feedbacks are nonlinear three-dimensional processes, a thorough analysis of which is beyond the scope of this study.

[43] The limited accuracy of the N and NP scenarios points to challenges associated with the use of a big-leaf canopy module at the point scale. Aside from parameter uncertainty, a Beer's-type exponential reduction of above-canopy shortwave radiation may be too coarse of a scaling method to approximate the in situ radiation dynamics beneath a heterogeneous forest [Ni et al., 1997]. Of particular concern is the treatment of direct beam solar radiation because bulk canopy structure parameters are measured over an inordinately larger canopy area than impacts the direct beam. In addition, the nonuniform (and nonrandom) distribution of vegetation structure causes a many-to-one problem when using a bulk canopy openness metric (i.e., derived from photos or satellite). Many different canopy gap configurations can result in the same canopy openness value. These different canopy configurations will influence mass and energy exchange differently, yet the differences would not be resolved with the single canopy openness metric. Rather than treat all fluxes with a bulk canopy treatment, an explicit consideration of detailed canopy structure may be more accurate; the NPDBT model was designed to test this hypothesis.

[44] In general, significant improvements were gained from a modification of SNOWPACK to accept a time-variant input of direct beam canopy transmissivity derived from hemispherical photos. The benefit of the NPDBT scenario was particularly reflected in melt-season model results. Both positive and negative biases in melt-season SWE and snow disappearance date predicted by the N and NP scenarios were greatly reduced with the NPDBT scenario. The reductions of both positive and negative biases indicate the effectiveness of the direct beam modification; NPDBT is not simply globally increasing or decreasing the canopy transmission. The positive melt-season biases and subsequent improvements with the explicit treatment of direct beam canopy transmissivity suggest that the big-leaf model tends to underestimate shortwave canopy transmission during the melt season when solar radiation is relatively high and the sun tracks across a higher and much larger sky area (see Figure 5b).

[45] The interannual differences in relative model improvement gained from the explicit treatment of the direct beam may be attributable to interannual differences in melt-season meteorology. Musselman et al. [2012] computed a clearness index from the same above-canopy shortwave radiation data used in this study for melt seasons 2008–2010. The index identified 4, 23, and 8 cloudy days for the three respective melt seasons. The results indicate that the cloudiest year (i.e., 2009) showed the lowest degree of model improvement with the NPDBT scenario. Of the three years, 2009 also exhibited the least SWE and lowest variability in measured snow disappearance date. Conversely, the melt-season errors in the bulk, nominal models were generally greater in magnitude and positive (indicating an underestimation of melt) in 2010 when snowmelt occurred later in the year, under conditions of enhanced energy fluxes. Of the three years evaluated, improvements gained by the direct beam modification were greatest under these conditions of enhanced energy, higher solar elevations, and reduced cloud cover.

[46] Positive and negative errors in the simulated timing of snowmelt soil infiltration (Table 4) indicate substantial issues related to predicting the timing of melt fluxes into the soil system despite accurate representation of peak SWE and snow disappearance date. It is possible that a model misspecification of snow instead of rain at upper elevations during a 4–7 January 2008 rain-on-snow event underestimated the liquid water absorbed by the snowpack; the soil moisture record (see Figure 2) indicates all liquid precipitation from this event at upper elevations was stored in the pack. As the liquid water content in a snowpack affects the thermodynamic properties as well as the melt dynamics and runoff production, particularly in areas of deep snow cover [Livneh et al., 2010], precipitation-type classification errors could significantly impact the simulated timing of snowmelt soil infiltration in addition to model weaknesses in representing water transport as discussed above.

[47] The improvement offered by NPDBT run at 10 min resolution compared to the N and NP scenarios run at 60 min time steps raises two main questions regarding (i) limitations of the Beer's law treatment of shortwave radiation through a discontinuous canopy; and (ii) the time step required of direct beam canopy transmissivity to capture the mean subcanopy shortwave irradiance over a given time period. While numerous studies have confirmed the former [e.g., Li et al., 1995; Ni et al., 1997; Nijssen and Lettenmaier, 1999; Yang et al., 2001], fewer studies have conducted explicit sensitivity tests of the latter [e.g., Baldocchi et al., 1986; Reifsnyder et al., 1971]. Subcanopy shortwave irradiance in forests with numerous canopy gaps exhibits a general bimodal distribution as a result of sunflecks (i.e., higher mode) and shadows (i.e., lower mode) [Essery et al., 2008a] similar to what has been observed in the upper portions of continuous canopies [e.g., Norman and Jarvis, 1974; Ovington and Madgwick, 1955]. Consequently, representing subcanopy shortwave irradiance with a mean value is complicated, particularly when the median of the direct beam canopy transmissivity distribution is close to zero and the mean is sensitive to sunflecks [seeMusselman et al., 2012]. Hardy et al. [2004] suggest that choosing an optimum temporal resolution requires careful consideration of the data application. The 10 min averages of 1 min instantaneous estimates (Figure 5a) were used in this study because this resolution was deemed adequate to capture the temporal dynamics of sunflecks on the forest floor relative to coarser time steps. Pearcy [1990] found that cumulative subcanopy irradiance from sunflecks longer than 10 min could account for more than two-thirds of the daily shortwave irradiance. In addition, this approach was less computationally intensive and was more typical of meteorological measurement intervals than the 1 min scenario.

[48] The presence of canopy coverage is known to decrease snow model predictive accuracy, largely as a result of errors in simulating individual surface energy flux terms [Ellis et al., 2010; Rutter et al., 2009; Sicart et al., 2004] such as shortwave [Hardy et al., 2004] and longwave radiation and their associated feedbacks with canopy elements [Pomeroy et al., 2009]. There are numerous uncertainties associated with atmospheric forcing (e.g., catchment-scale cloud cover patterns), individual model equations (e.g., the empirical disaggregation of shortwave into direct and diffuse components), and parameters (e.g., the canopy extinction coefficient). Hemispherical photography represents a method of estimating high-resolution direct beam canopy transmissivity, thus minimizing a significant source of model uncertainty. The presented methods are simple and inexpensive compared to the requirements needed to maintain long-term subcanopy radiation monitoring stations in forested regions. In addition, transmissivity values derived from photos taken in healthy conifer forests are generally valid over long time scales. The methods could be used to improve estimates of snowmelt dynamics at individual research sites for hydrological and ecological applications.

[49] The physical basis of the SNOWPACK model made it well suited for this study. Future work should evaluate the utility and potential differences of introducing direct beam canopy transmissivity measurements to other process-based models. Additionally, many questions remain regarding scale issues related to canopy parameters and the assumptions inherent to Beer's-type canopy radiation models, particularly when applied to areas of steep terrain and heterogeneous canopy coverage. For example, research is needed that bridges observations made at forested catchment and plot scales to quantify hydrometeorological variability (e.g., variance) in representations of mean states and fluxes at larger scales relevant to hydrologic and climate models. Future efforts will address some of these scale issues by applying the presented methods to airborne LiDAR data [e.g., Essery et al., 2008b] with an explicit treatment of longwave radiation [e.g., Pomeroy et al., 2009] within the distributed land surface model Alpine3D [Lehning et al., 2006] and snowpack reconstruction techniques [e.g., Durand et al., 2008a, 2008b; Molotch, 2009; Molotch and Margulis, 2008]. Toward this goal, preliminary tests conducted in the Wolverton basin of voxel aggregation of multiple-return discrete LiDAR data [e.g., Hagstrom et al., 2010] combined with an efficient ray tracing algorithm [e.g., Hagstrom and Messinger, 2011] and look-up table shows promise for producing high-resolution, spatially distributed estimates of direct beam canopy transmissivity.

6. Conclusions

[50] When canopy model parameters canopy openness and inline image were obtained from satellite data at 30 m resolution and literature-based sources, respectively, the nominal model (scenario N) was unable to resolve the highly variable subcanopy snowpack dynamics. When the same two canopy model parameters were obtained from hemispherical photos (scenario NP), consistently improved results were not obtained. When the nominal model was modified to accept a time series of photo-derived direct beam canopy transmissivity (scenario NPDBT), the average error in the date of snow disappearance was improved by 6 days. The positive biases in melt-season SWE obtained at lower elevations with scenario N were reduced by no less than 45% (2010) and as much as 74% (2009). The MAE of the simulated snow disappearance date was reduced by 40% in 2008, 19% in 2009, and 43% in 2010. Compared to soil moisture measurements, average improvements in the timing of snowmelt soil infiltration of 11 days were observed with the explicit consideration of direct beam canopy transmissivity. The optimum temporal resolution of the direct beam canopy transmissivity was determined to be 30 min averages of 1 min instantaneous values; hourly averages performed no better than the N or NP scenarios and time steps finer than 30 min did not result in overall improvement. The model improvements gained by including time-variant photo-derived direct beam canopy transmissivity were greatest in 2010; a year with high SWE, a late melt season, and low spring cloud cover. The results illustrate the important contribution of direct beam shortwave radiation to the subcanopy melt-season snowpack dynamics. The estimation of time-variant direct beam canopy transmissivity thus minimizes a significant source of snowmelt model uncertainty at the point scale in forested regions.

Appendix A:: Snowpack Canopy Model Description

[51] The SNOWPACK model treats the canopy as a single big leaf with a temperature Tc (K) and storage of intercepted water I (mm) characterized by three common input parameters: canopy height, LAI′, and canopy openness. The canopy temperature is calculated by solving an energy balance equation for the canopy layer, including shortwave and longwave radiation and the turbulent energy fluxes. Heat storage in the canopy is assumed to be zero, thus the energy needed for phase change between frozen and liquid interception is neglected.

[52] The model uses a two-layer RT model for a single canopy layer adopted from Taconet et al. [1986], which takes into account multiple reflections between the canopy layer and the surface layer below (snow or bare soil). Absorption of inline image and inline image by the canopy layer is determined by the dimensionless absorption factor inline image:

display math

where inline image (–) is an extinction parameter that is a function of needle orientation and stand structure, and is typically between 0.4 and 0.8. The reflectance or absorption of incident inline image and inline image on the canopy elements is determined by the canopy layer albedo and emissivity, respectively. The canopy emissivity is assumed to be equal to unity, while the canopy albedo is treated as a dynamic function of intercepted rain or snow:

display math

where fwet (–) is the fraction of the canopy covered by intercepted water calculated as the ratio of the interception storage and the interception capacity Imax:

display math

and αwet (–) and αdry (–) are parameters for the albedo of wet and dry canopy, respectively. The albedo for the wet part of the canopy can be set differently for liquid and frozen interception. Typical values for needleleaf canopies are αdry = αwet,rain = 0.1 and αwet,snow = 0.3–0.4. The radiation fluxes for the two-layer canopy module are only applied to the fraction of the surface covered by the canopy as defined by the canopy openness parameter and otherwise above-canopy inline image and inline image fluxes are permitted to pass to the ground surface unimpeded by the canopy layer. Model improvements have been made to enable a more dynamic treatment of canopy transmissivity than the static representation evaluated in this study. In the most recent model version, the canopy openness is assumed to be constant for inline image and the diffuse fraction of inline image (as in this study), whereas it is adjusted as a function of solar elevation angle and an assumed canopy geometry defined by the height and diameter of the trees following Gryning et al. [2001]. The adsorption factor for direct solar radiation can now either be calculated using equation (3) or optionally modified as a function of solar angle Ω following Chen et al. [1997]. The combined transmission of direct and diffuse shortwave radiation is then given by

display math

where inline image (–) is the diffuse fraction of above-canopy global shortwave radiation. Future efforts will evaluate this dynamic, bulk treatment of canopy transmissivity against the results of the explicit, photo-derived methods presented here.

[53] The maximum canopy interception rate ΔI (mm h−1) of above-canopy precipitation inline image (mm h−1) is calculated as a function of canopy storage saturation with an equation originally proposed by Merriam [1960], in the form given by Pomeroy et al. [1998]:

display math

where cΔt is a time step dependent parameter called the unloading coefficient, with a suggested value of 0.7 for hourly time steps [Pomeroy et al., 1998], fthrough is the fraction of direct throughfall set equal to the canopy openness parameter, and Imax (mm) is the maximum interception capacity. The latter is calculated as a linear function of LAI:

display math

where the parameter iLAI (mm) is assumed to be a constant for intercepted rain, and a function of the density of intercepted snow ρs,int (kg m−3) following Pomeroy et al. [1998]:

display math

Schmidt and Gluns [1991] reported estimates of the parameter imax (mm m−2) for spruce (5.9) and pine (6.6). The density of the intercepted snow ρs,int (kg m−3) is estimated as a function of air temperature [Lehning et al., 2002a]. The interception is further assumed to be liquid above and frozen below the air temperature threshold for frozen precipitation (1°C) specified to the SNOWPACK model and used to determine precipitation gauge catch efficiency, described in section 2.1. Thus, unloading of snow as a consequence of increased air temperature and reduced storage capacity is calculated whenever I exceeds Imax.

[54] The aerodynamic resistances for sensible and latent heat fluxes are calculated using a two-layer model that assumes logarithmic wind profiles above, within, and below the canopy adopted from [Blyth et al., 1999]. The aerodynamic resistances from the canopy level to the reference level of the meteorological forcing data is calculated with the usual bulk formulation based on displacement height and surface roughness lengths of momentum and heat including a Monin-Obukhov stability correction following Högström [1996] and Beljaars and Holtslag [1991]. An additional within-canopy resistance radd (s m−1) is added for the fluxes from the canopy surface and the snow surface to the canopy layer on the general form:

display math

where z0m and z0h are the surface roughness lengths of either the canopy or the snow surface, inline image is the friction velocity estimated above the canopy, and k is the Von Kármán constant (0.4). The final term in equation (A8), fLAI, is an exponential function of LAI:

display math

where the parameter ra,LAI is the maximum multiplicative increase.


[55] The authors gratefully acknowledge P. Kirchner and R. Bales for their contribution to field data acquisition. Sequoia National Park supported field access and research efforts. Financial support was provided by the National Science Foundation grants EAR-071160, EAR-1032295, EAR-1032308, EAR-1141764, the Southern Sierra Critical Zone Observatory (EAR-0725097), a Major Research Instrumentation grant (EAR-0619947), the Mountain Research Initiative, NASA grant NNX11AK35G and a National Aeronautics and Space Administration (NASA) Earth System Science Fellowship. Radiation data from the Tokopah basin were provided by J. Melack and J. Sickman. Assistance in the field was provided by S. Roberts, B. Forman, D. Perrot, E. Trujillo, D. Berisford, L. Meromy, M. Girotto, A. Kahl, and M. Cooper, among many others. The authors thank three anonymous reviewers for their comments and support of the paper.