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WATER RESOURCES RESEARCH, VOL. 45, W05429, doi:10.1029/2008WR007042, 2009
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Modeling snow accumulation and ablation processes
in forested environments
Konstantinos M. Andreadis,1 Pascal Storck,2 and Dennis P. Lettenmaier1
Received 28 March 2008; revised 18 February 2009; accepted 19 March 2009; published 30 May 2009.
[1] The effects of forest canopies on snow accumulation and ablation processes can be
very important for the hydrology of midlatitude and high-latitude areas. A mass and
energy balance model for snow accumulation and ablation processes in forested
environments was developed utilizing extensive measurements of snow interception and
release in a maritime mountainous site in Oregon. The model was evaluated using 2 years
of weighing lysimeter data and was able to reproduce the snow water equivalent
(SWE) evolution throughout winters both beneath the canopy and in the nearby clearing,
with correlations to observations ranging from 0.81 to 0.99. Additionally, the model
was evaluated using measurements from a Boreal Ecosystem-Atmosphere Study
(BOREAS) field site in Canada to test the robustness of the canopy snow interception
algorithm in a much different climate. Simulated SWE was relatively close to the
observations for the forested sites, with discrepancies evident in some cases. Although the
model formulation appeared robust for both types of climates, sensitivity to parameters
such as snow roughness length and maximum interception capacity suggested the
magnitude of improvements of SWE simulations that might be achieved by calibration.
Citation: Andreadis, K. M., P. Storck, and D. P. Lettenmaier (2009), Modeling snow accumulation and ablation processes in forested
environments, Water Resour. Res., 45, W05429, doi:10.1029/2008WR007042.
1. Introduction
[2] Snow is an important part of the hydrologic cycle,
especially in high-latitude and high-elevation river basins.
The contrast between snow presence and absence strongly
affects the surface energy (e.g., albedo) and water (e.g.,
storage and streamflow) balances. Where forest cover is
present, it alters snow accumulation and ablation processes,
mostly by intercepting snowfall and modifying the surface
micrometeorology (incoming radiation and wind speed),
respectively. Intercepted snow can account for as much as
60% of annual snowfall in both boreal and maritime forests
[Storck et al., 2002], while losses to sublimation can reach
30– 40% of annual snowfall in coniferous canopies [Pomeroy
and Schmidt, 1993].
[3] Although the importance of snow interception and
sublimation processes has been recognized, their incorporation in hydrologic models as well as their representation in
land surface schemes used in numerical weather and climate
prediction models has been limited [Pomeroy et al., 1998;
Essery, 1998]. While a number of studies have examined
snow interception processes in boreal forests [Claassen and
Downey, 1995; Harding and Pomeroy, 1996; Hedstrom and
Pomeroy, 1998; Nakai et al., 1999; Pomeroy et al., 2002;
Gusev and Nasonova, 2003], few of these studies are
applicable to maritime climates. Snow interception can be
quite different in maritime and continental climates, mostly
because of the dominance of micrometeorology over canopy
1
Wilson Ceramic Laboratory, Civil and Environmental Engineering,
University of Washington, Seattle, Washington, USA.
2
3TIER Environmental Forecast Group, Inc., Seattle, Washington, USA.
Copyright 2009 by the American Geophysical Union.
0043-1397/09/2008WR007042$09.00
morphology in controlling snow interception [Satterlund
and Haupt, 1970; Schmidt and Gluns, 1991].
[4] Miller [1964] hypothesized that three factors control
snow interception: canopy morphology, air temperature and
wind speed. Simple interception models were developed for
individual snow storms by Satterlund and Haupt [1967],
which demonstrated the different mechanisms controlling
rain and snow interception. Schmidt and Gluns [1991]
found low interception efficiency for light and heavy snow
loadings on the canopy, with an increase in interception
efficiency as snowfall increases because of cohesion of
snow particles to intercepted snow and increased effective
projected area of the canopy. In contrast, Calder [1990] and
Harestad and Bunnell [1981] found a decrease in interception efficiency as snowfall increased. The contrast in the
magnitude of observed snow interception between maritime
and continental climates suggests the importance of micrometeorological conditions [Bunnell et al., 1985]. Schmidt
and Gluns [1991] found that snow interception was relatively similar between three branch species at two sites,
while Satterlund and Haupt [1970] found that there was no
significant differences in the amount of snow intercepted by
two tree species which had considerable morphological
differences. The effects of air temperature on snow interception were found to be more pronounced as the canopy
collection area became narrower with minimum interception
at low air temperatures [Ohta et al., 1993].
[5] Intercepted snow can be removed from the canopy by
sublimation, mass release, or meltwater drip. Sublimation
from intercepted snow has been studied using tree weighing
[Schmidt, 1991; Lundberg, 1993; Montesi et al., 2004] and
eddy covariance [Molotch et al., 2007], or both [Suzuki
and Nakai, 2008] measurement techniques. Lundberg and
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Halldin [2001] found sublimation rates from intercepted
snow reaching 1.3– 3.9 mm/d. High rates of sublimation
from snow intercepted by forest canopies can be sustained by
both net radiation and sensible heat flux, and can be well
predicted by a simple energy balance model if the canopy
aerodynamic resistance is adjusted for the presence of snow
cover. Mass release of intercepted snow occurs because of
either mechanical wind effects or melt. Both of these mechanisms are governed by the adhesion of intercepted snow to
the tree branches. As the adhesion becomes stronger (i.e.,
during snowfall or at temperatures just below freezing)
removal of snow due to wind becomes rare. On the other
hand, as intercepted snowmelts it destroys the bonds between
the snow and the canopy facilitating mass release. Meltwater
drip was measured by Kittredge [1953] over a period of
5 years in the Sierra Nevada; during 57 snowfalls only 4
produced more than 2 mm of meltwater drip, with an average
of 0.8 mm out of an average total snowfall of 40 mm.
[6] In recent years some land surface models have
incorporated snow interception algorithms [Tribbeck et al.,
2004; Gusev and Nasonova, 2003] but most have focused
on either alpine or boreal forest environments. Verseghy et
al. [1993] and Bartlett et al. [2006] developed a new snow
interception algorithm for the Canadian Land Surface
Scheme which controlled the interception efficiency by
canopy morphology, with a maximum threshold. Hedstrom
and Pomeroy [1998] developed an interception/unloading
model by assuming an exponential decay with increasing
snowfall, with a similar approach taken by Koivusalo and
Kokkonen [2002], as well as Gelfan et al. [2004], who
evaluated their model in both Canadian and Russian sites
and suggested that atmospheric processes might be governing snow accumulation and ablation rather than canopy
characteristics. A model of canopy snow interception,
sublimation and melt was incorporated into a GCM land
scheme by Essery et al. [2003], which they found improved
its performance in off-line simulations. A similar model was
developed by Niu and Yang [2004] to represent the effects
of canopies on the surface snow mass and energy balance,
which they found improved the estimation of snow albedo.
A number of snow interception models describe the maximum interception capacity of the canopy as a function of
the leaf area index (LAI) [Stahli and Gustafsson, 2006;
Lehning et al., 2006; Strasser et al., 2007] and are based on
the approach taken by Pomeroy et al. [1998].
[7] In this paper our objective is to describe a model of
snowpack dynamics in forested environments based on
observations of snow accumulation and ablation at a mountain maritime site [Storck et al., 2002] and to demonstrate
its applicability to both maritime and boreal forested environments. The model is evaluated with observations of
snow water equivalent and depth from sites in both maritime and boreal climates. These observations are described
in section 2, while the model governing equations and
validation results are presented in sections 3 and 4, respectively. Finally, section 5 shows results from a sensitivity
analysis of simulated snow accumulation and ablation to
different model formulations and parameters.
2. Study Sites and Measurements
[8] The observations sites are in the Umpqua National
Forest, OR where observations were made by the second
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author during the winters of 1996 – 1997 and 1997 – 1998
[Storck et al., 2002], and three sites in the boreal forest of
Sasketchewan (first two sites) and Manitoba (second site),
respectively. Observations at the boreal forest sites were
taken as part of the Boreal Ecosystem-Atmosphere Study
(BOREAS) conducted from 1993 to 1996 [Sellers et al.,
1997].
2.1. Umpqua, Oregon
[9] During the winters of 1996 –1997 and 1997– 1998 a
field study was conducted in the Umpqua National Forest,
Oregon. The field campaign was part of the Demonstration
of Ecosystem Management Options (DEMO) experiment
[Aubry et al., 1999]. The objective of observations made at
the Umpqua National Forest field site was to observe the
processes governing snow interception by forest canopies
and beneath-canopy snow accumulation and ablation in a
mountainous maritime climate, with the ultimate aim of
understanding the role of rain-on-snowmelt processes on
flooding [Storck et al., 2002]. Annual precipitation at the
field site is about 2 m, most of it in winter, with an annual
maximum snow water equivalent (SWE) of about 350 mm
in clearings, with precipitation in the observation years
being about half (1 and 0.7 m, respectively) and peak snow
water equivalent (SWE) being 340 and 225 mm, respectively. Midwinter melt is common and final melt occurs in
late April or early May. Frequent rain-on-snow events occur
at this site throughout the winter, while spring melt is
radiation dominated.
[10] Four weighing lysimeters were used to measure
ground snowpack accumulation and melt, two of which
were beneath a mature canopy (mostly Douglas fir), and the
other two in clear-cut and shelterwood (partially harvested)
sites, respectively. The sites were all located within 3 km of
each other with no significant differences in topography.
Differences in SWE between lysimeters beneath the forest
canopy and the adjacent clearing were used to infer snow
interception. Additional measurements included precipitation (taken using two tipping bucket gauges), wind speed,
incoming shortwave and longwave radiation, air temperature, and relative humidity at 2 m above the soil surface.
The field observations are described in detail by Storck et al.
[2002].
2.2. BOREAS
[11] The objective of the BOREAS field program, conducted between 1994 and 1996, was to improve the understanding of the dynamics that govern mass and energy
transfer between the boreal forest and the lower atmosphere
[Sellers et al., 1995]. The BOREAS study region covered
most of Saskatchewan and Manitoba, with individual measurement sites located within the northern and southern
study areas (NSA and SSA, respectively) [Sellers et al.,
1997], each of which is of area roughly 104 km2, separated
by about 500 km. Topographic relief is small in both sites,
but land cover is nonuniform within each study area and
contains open areas and forests of different canopy types.
Meteorological measurements, including below and above
canopy air temperature, incoming shortwave and longwave
radiation, relative humidity, wind speed, precipitation were
taken by automated meteorological stations (AMS) [Osborne
et al., 1998] every 15 min. Additionally, the AMSs recorded
snow depth and canopy temperature at the same temporal
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ANDREADIS ET AL.: VIC SNOW MODEL
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Figure 1. Schematic of snow accumulation and ablation processes modeled by VIC.
resolution, while biweekly manual snow depth and water
equivalent measurements were taken beneath a range of
canopy types during the same period. Two sites in the SSA
and two in the NSA were selected for this study; these
sites were covered mostly with mature jack pine (SSA-OJP
and NSA-OJP), aspen (SSA-OA), and mixed spruce/poplar
(NSA-YTH) trees.
3. Model Formulation
[12] Model formulation of the canopy interception processes relies heavily on field measurements described by
Storck et al. [2002]. The main processes represented in the
model are shown schematically in Figure 1. The snow
processes model has been incorporated into the macroscale
Variable Infiltration Capacity (VIC) hydrologic model,
which essentially solves an energy and mass balance over
a gridded domain [Liang et al., 1994]. The spatial resolution
for macroscale models usually ranges from 10 to 100 km
(grid spacing), which are larger than characteristic scales of
the modeled processes. Therefore, subgrid variability in
topography, land cover and precipitation is modeled by a
mosaic-type representation, wherein each grid cell is partitioned into elevation bands each of which contain a number
of land cover tiles. The snow model is then applied to each
land cover/elevation tile separately, and the simulated energy and mass fluxes and state variables for each grid cell are
calculated as the area averages of the tiles. Downward
energy and moisture fluxes are required to drive the model,
these include precipitation, air temperature, wind speed,
downward shortwave and longwave radiation, and humidity. Alternatively, the last three terms can be estimated from
the maximum and minimum daily air temperature and
precipitation according to algorithms described by Thornton
and Running [1999] and Kimball et al. [1997], respectively.
snowpack similarly to other cold land processes models
[Anderson, 1976; Wigmosta et al., 1994; Tarboton et al.,
1995]. Energy exchange between the atmosphere, forest
canopy and snowpack occurs only with the surface layer.
The energy balance of the surface layer is
rw cs
dWTs
¼ Qr þ Qs þ Qe þ Qp þ Qm
dt
ð1Þ
where cs is the specific heat of ice, rw is the density of
water, W is the water equivalent and Ts is the temperature of
the surface layer, Qr is the net radiation flux, Qs is the
sensible heat flux, Qe is the latent heat flux, Qp is the energy
flux advected to the snowpack by rain or snow, and Qm
is the energy flux given to the pack because of liquid
water refreezing or removed from the pack during melt.
Equation (1) is solved via a forward finite difference scheme
over the model time step (Dt).
[14] Net radiation at the snow surface is either measured
or calculated given incoming shortwave and longwave
radiation as
Qr ¼ Li þ Si ð1 aÞ sTs4
ð2Þ
where Li and Si are incoming long and shortwave radiation,
and a is the snow surface albedo. The flux of sensible heat
to the snowpack is given by
Qs ¼
rcp ðTa Ts Þ
ra;s
ð3Þ
where r is the air density, cp is the specific heat of air, Ta is
the air temperature, and ra,s is the aerodynamic resistance
between the snow surface and the near-surface reference
height, given by
3.1. Ground Snowpack Accumulation and Ablation
[13] The model represents the snowpack as a two-layer
medium (a thin surface, and a thick deeper layer), and
solves an energy and mass balance for the ground surface
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ln
ra;s ¼
z ds
z0
k 2 Uz
2
ð4Þ
ANDREADIS ET AL.: VIC SNOW MODEL
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where k is von Karman’s constant, z0 is the snow surface
roughness, ds is the snow depth, and Uz is the wind speed at
the near-surface reference height z. Similarly, the flux of
latent heat to the snow surface is given by
Qe ¼ li r
0:622 eðTa Þ es ðTs Þ
Pa
ra;s
ð5Þ
where li is the latent heat of vaporization when liquid water
is present in the surface layer and the latent heat of
sublimation in the absence of it, Pa is the atmospheric
pressure, and e and es are the vapor and saturation vapor
pressure, respectively. Advected energy to the snowpack via
rain or snow is given by
Pr þ Ps
Qp ¼ rw cw Ta
Dt
temperature of the pack layer is below freezing then liquid
water transferred from the surface layer can refreeze. Liquid
water remaining in the pack above its holding capacity is
immediately routed to the soil as snowpack outflow. The
dynamics of liquid water routing through the snowpack are
not considered in this model because of the relatively coarse
temporal and spatial resolutions of the model (typically 1 to
3 h and 50 – 100 km2, respectively) [Lundquist and
Dettinger, 2005].
[15] Following a similar approach to Anderson [1976],
compaction (due to snow densification) is calculated as the
sum of two fractional compaction rates representing compaction due to metamorphism and overburden, respectively:
Drs
¼ ðCRm þ CRo Þrs
Dt
ð6Þ
where cw is the specific heat of water, Pr is the depth of
rainfall, and Ps is the water equivalent of snowfall.
Precipitation is partitioned into snowfall and rainfall on
the basis of a temperature threshold
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ð11Þ
where rs is the snow density, and CRm, CRo are the
compaction rates due to metamorphism and overburden,
respectively. Destructive metamorphism is important for
newer snow, and the following empirical function is used:
CRm ¼ 2:778 106 c3 c4 e0:04ð273:15Ts Þ
Ps ¼ P
Ta Tmin
Tmax Ta
Ps ¼
P
Tmax Tmin
Tmin < Ta < Tmax
Ps ¼ 0
c3 ¼ c4 ¼ 1
Qnet < 0
Qnet 0
ð9Þ
Qe
Qm
Dt
rw lv rw lf
Qe
Qm
Dt
þ
rw ls rw lf
ð10Þ
where Qe exchanges water with the liquid phase if liquid
water is present and Qe exchanges water with the ice phase
in the absence of liquid water. If Wice exceeds the maximum
thickness of the surface layer (typically taken as 0.10 m of
SWE), then the excess, along with its cold content, is
distributed to the deeper (pack) layer. Similarly, if Wliq
exceeds the liquid water holding capacity of the surface
layer, the excess is drained to the pack layer. If the
Ps c5 ð273:15Ts Þ c6 rs
e
e
h0
ð13Þ
where h0 = 3.6 106 N s/m2 is the viscosity coefficient at
0°C, c5 = 0.08 K1, c6 = 0.021 m3/kg, and Ps is the load
pressure. Snowpacks are naturally layered media, therefore
the load pressure is different for each layer of the pack
corresponding to different compaction rates. The model
represents that ‘‘internal’’ compaction as an effective load
pressure, i.e.,
Ps ¼
DWice ¼ Ps þ
rl > 0
CRo ¼
The mass balance of the surface layer is given by
DWliq ¼ Pr þ
ð12Þ
where Ts is the snowpack temperature, and rl is the bulk
density of the liquid water in the pack. After the initial
settling stage, the densification rate is controlled by the
overburden snow, and the corresponding compaction rate
can be estimated by
ð8Þ
If Qnet is negative, then energy is being lost by the pack, and
liquid water (if present) is refrozen. If Qnet is sufficiently
negative to refreeze all liquid water, then the pack may cool.
If Qnet is positive, then the excess energy available after the
cold content has been satisfied, produces snowmelt:
rs > 150 kg=m3
c4 ¼ 2
The total energy available for refreezing liquid water or
melting the snowpack over a given time step depends on the
net energy exchange at the snow surface
Qm Dt ¼ min Qnet ; rw lf Wliq
Qm Dt ¼ Qnet þ cs Wice Tst
c3 ¼ e0:046ðrs 150Þ
ð7Þ
Ta Tmax
Qnet ¼ Qr þ Qs þ Qe þ Qp Dt
rl ¼ 0; rs 150 km=m3
1
g rw ðWns þ f Ws Þ
2
ð14Þ
where g is the acceleration of gravity, Wns, Ws is the amount
of newly fallen snow and snow on the ground (in water
equivalent units), respectively, and f is the internal
compaction rate coefficient taken as 0.6 after calibration
to measurements from the Cold Land Processes Experiment
in Fraser Park, Colorado [Andreadis et al., 2008].
[16] Snow albedo is assumed to decay with age on the
basis of observations from the DEMO experiment:
0:58
aa ¼ 0:85 lta
0:46
am ¼ 0:85 ltm
ð15Þ
ð16Þ
where aa, am are the albedo during the accumulation and
melting seasons, t is the time since the last snowfall (in
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days), la = 0.92, and lm = 0.70. Accumulation and melt
seasons are defined on the basis of the absence and presence
of liquid water in the snow surface layer, respectively.
3.2. Atmospheric Stability
[ 17 ] The calculation of turbulent energy exchange
(equations (3), (4), (5)) is complicated by the stability of
the atmospheric boundary layer. During snowmelt, the atmosphere immediately above the snow surface is typically
warmer. As parcels of cooler air near the snow surface are
transported upward by turbulent eddies they tend to sink back
toward the surface and turbulent exchange is suppressed. In
the presence of a snow cover, aerodynamic resistance is
typically corrected for atmospheric stability according to
the bulk Richardson’s number (Rib). The latter is a dimensionless ratio relating the buoyant and mechanical forces (i.e.,
turbulent eddies) acting on a parcel of air [Anderson, 1976]:
Rib ¼
gzðTa Ts Þ
0:5ðTa þ Ts ÞU ð zÞ2
ð17Þ
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The Y functions are given for stable conditions (za/L > 0) as
z za
a
¼ 5 ;
Y
L
L
z a
¼ 5;
Y
L
ras
Rib
1
Ricr
0 Rib < Ricr
2
Riu ¼
ð18Þ
ras
ð1 16Rib Þ
0:5
Rib < 0
u3 r
* H
kg
Ta cp
1
ð20Þ
1
za
þ5
ln
z0
uk
z
z
Y
ln
z0
L
Rib
Ricr
2 ra
ð23Þ
ð24Þ
1
ras ¼ 1
Riu
Ricr
0 Rib Riu
ð25Þ
Rib > Riu
ð26Þ
2 ra
3.3. Snow Interception
[19] While many models characterize the effect of the
forest canopy on the micrometeorology above the forest
snowpack, almost none attempt to model explicitly the
combined canopy processes that govern snow interception,
sublimation, mass release, and melt from the forest canopy.
A simple snow interception algorithm is presented here that
represents canopy interception, snowmelt, and mass release
at the spatial scales of distributed hydrology models.
[20] During each time step, snowfall is intercepted by the
overstory up to the maximum interception storage capacity
according to
I ¼ fPs
The friction velocity (u*) and the sensible heat flux (H) are
given by
u* ¼
1
ras ¼ ð19Þ
where Ricr is the critical value of the Richardson’s number
(commonly taken as 0.2). While the bulk Richardson’s
number correction has the advantage of being straightforward to calculate on the basis of observations at only one
level above the snow surface, previous investigators have
noted that its use results in no turbulent exchange under
common melt conditions and leads to an underestimation of
the latent and sensible heat fluxes to the snowpack [e.g.,
Jordan, 1991; Tarboton et al., 1995].
[18] An alternative formulation for the stability correction
(adopted by Marks et al. [1998]) is based on flux profile
relationships in which the vertical near-surface profiles of
wind and potential temperature are assumed to be log linear
under stable conditions [Webb, 1970]. In this case, the effect
of atmospheric stability is described by the Monin-Obukhov
mixing length (L):
L¼
za
>1
L
where Riu is the upper limit on Rib. Consequently, the
stability correction with the bulk Richardson’s number
becomes
and in unstable conditions as
ras ¼
za
1
L
The stability correction (equations (20) – (23)) does not
force the sensible heat flux to zero. Unfortunately solution
of these equations requires an iterative procedure which is
computationally too burdensome for a large-scale, spatially
distributed model. Therefore, a Rib formulation that does not
entirely suppress turbulent exchange under stable conditions
was developed. Similar to the limit on Y imposed by
equation (23), an upper limit can be placed on Rib at which
z/L is equal to unity. Combining equations (20) – (22) into
one expression for L yields the following expression for the
bulk Richardson’s number when z/L is equal to 1:
with the correction for stable conditions given as
ras ¼ 0
ð21Þ
where I is the water equivalent of snow intercepted during a
time step, Ps is the snowfall over the time step, and f is the
efficiency of snow interception (taken as 0.6) [Storck et al.,
2002]. The maximum interception capacity is given by
B ¼ Lr mð LAI Þ
ðTa Ts Þku* rcp
H¼ z za
a
Y
ln
z0
L
ð22Þ
ð27Þ
ð28Þ
where LAI is the single-sided leaf area index of the canopy
and m (same units as B, in meters) is determined on the
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ANDREADIS ET AL.: VIC SNOW MODEL
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basis of observations of maximum snow interception
capacity. The leaf area ratio Lr is a step function of
temperature:
Lr ¼ 4:0
Ta > 1 C
Lr ¼ 1:5 Ta þ 5:5 1 C Ta < 3 C
Lr ¼ 1:0
Ta 3 C
ð29Þ
which is based on observations from previous studies of
intercepted snow as well as data collected during the field
campaign described [Storck et al., 2002]. Kobayashi [1987]
observed that maximum snow interception loads on narrow
surfaces decreased rapidly as air temperature decreases
below 3°C. Results from Kobayashi [1987] and Pfister and
Schneebeli [1999] suggest that interception efficiency
decreases abruptly for temperatures less than 1°C, and is
approximately constant for temperatures less than 3°C,
leading to a discontinuous relationship (equation (29)).
[21] Newly intercepted rain is calculated with respect to
the water holding capacity of the intercepted snow (Wc),
which is given by the sum of capacity of the snow and the
bare branches:
Wc ¼ hWice þ e4 ð LAI2 Þ
ð30Þ
where h is the water holding capacity of snow (taken
approximately as 3.5%) and LAI2 is the all sided leaf area
index of the canopy. Excess rain becomes throughfall.
[22] The intercepted snowpack can contain both ice and
liquid water. The mass balance for each phase is
DWice
Qe
Qm
Dt
¼I M þ
þ
rw ls rw lf
DWliq ¼ Pr Ptf þ
Qe
Qm
Dt
rw lv rw lf
ð31Þ
ð32Þ
where M is the snow mass release from the canopy, Ptf is
canopy throughfall, and ls, lv, lf are the latent heat of
sublimation, vaporization, and fusion, respectively. Snowmelt is calculated directly from a modified energy balance,
similar to that applied for the ground snowpack, with
canopy temperature being computed by iteratively solving
the intercepted snow energy balance (equation (1)). Given
the intercepted snow temperature and air temperature,
snowmelt is calculated directly from equations (8) and (9).
The individual terms of the energy balance are as described
for the ground snowpack model. However, the aerodynamic
resistance is calculated with respect to the sum of the
displacement and roughness lengths of the canopy. Incoming shortwave and longwave radiation are taken as the
values at the canopy reference height. The same formulation
is used for the albedo of the ground snowpack and the snow
on the canopy (equations (15) – (16)), the difference being in
the transmitted radiative fluxes.
[23] Snowmelt in excess of the liquid water holding
capacity of the snow results in meltwater drip (D). Mass
release of snow from the canopy occurs if sufficient snow is
available and is related linearly to the production of meltwater drip
M ¼0 Cn
ð33Þ
M ¼ 0:4D
C>n
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where n is the residual intercepted snow that can only be
melted (or sublimated) off the canopy (taken as 5 mm on the
basis of observations of residual intercepted load). The ratio
of 0.4 in equation (33) is derived from observations of the
ratio of mass release to meltwater drip [Storck et al., 2002].
4. Model Evaluation
[24] The measurements that were used for model evaluation spanned two winters at both the Oregon (1997 and
1998) and the BOREAS (1995 and 1996) sites. The model
was uncalibrated and used a set of default parameters
[Cherkauer et al., 2003]. This allowed testing of the
robustness of the model given the difference between the
climates at the two study areas (maritime versus boreal).
4.1. Umpqua, Oregon
4.1.1. Implementation
[25] Hourly micrometeorological observations from the
shelterwood site were used to force the model during its
evaluation. These included observations of precipitation, air
temperature, incoming shortwave and longwave radiation,
wind speed, relative humidity, and were taken to be representative of above-canopy conditions. Wind speed at the 2 m
height was corrected for snow accumulation beneath the
anemometer and then scaled to the 80 m canopy height
assuming a logarithmic profile and a surface roughness of
1 cm.
[26] The effective fractional canopy coverage was determined as 80% on the basis of observed longwave radiation
beneath the forest canopy. Air temperature and humidity
were assumed identical at the shelterwood and beneathcanopy sites. Canopy characteristics were taken from the
North American Land Data Assimilation System (N-LDAS)
data set [Gutman and Ignatov, 1998; Hansen et al., 2000],
for the forest type at the site (Douglas Fir), with canopy
heights taken as 11 m [Storck et al., 2002], vegetation
roughness length as 1.5 m, displacement height as 8.0 m,
and LAI ranging from 3.4 to 4.4.
4.1.2. Evaluation (1996 – 1998)
[27] The model was evaluated using the shelterwood and
beneath-canopy weighing lysimeter data for the 1996 – 1997
and 1997– 1998 winter seasons. A set of default model
parameters was used, including snow roughness length (set
here at 1 mm), and the value of m (equation (28)), which
controls the maximum snow interception capacity as a
function of LAI (set at 5 mm). These could have been used
for calibration purposes, in addition to the air temperature
thresholds when rain or snow can fall (minimum and
maximum, respectively), which were set to 0.5°C and
0.5°C, respectively, as default parameters. Figure 2a (gray
lines) shows the measured SWE from the two lysimeters at
the beneath-canopy site compared to the model predicted
SWE for 1996 – 1997. Although the model slightly underestimates accumulation during December 1996, and predicts
too little snowmelt during February and March 1997 leading
to an overestimation of SWE, it follows the SWE variability
fairly well, and predicts the complete melt of the snowpack
fairly accurately. The correlation between the observed and
modeled SWE (number of observations is 1770 with a 2 h
time step) was 0.90, while the relative mean squared error
(RMSE) was 28.3 mm (15.6%). Figure 2b shows the model
predicted snow interception (in mm of SWE), with a
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Figure 2. (a) Comparisons between observed (dashed
lines) and model-predicted (solid lines) SWE during the
1996 – 1997 period for the shelterwood (black) and beneathcanopy (gray) Oregon sites. (b) Model-predicted intercepted
snow water equivalent during the same period.
maximum of about 35 mm. According to Storck et al.
[2002] snow interception was observed to reach a maximum
of about 40 mm, which might explain the small discrepancy
between the modeled and observed accumulated SWE
during December 1996. Figure 2a (black lines) shows the
same comparisons, as above, for the shelterwood site (no
canopy). Model predictions show good agreement with the
observed SWE. The model underestimates snowmelt in
mid-April 1997, but otherwise follows the SWE variability
closely throughout the season. Correlation for this site was
0.86 (same number of observations as above), while the
RMSE was 54.3 mm (15.9%).
[28] Figure 3 is similar to Figure 2, showing SWE simulations during 1997 – 1998 and that the model underestimates snow accumulation during December 1997, but
predicts SWE reasonably well until mid-February 1998.
The model then underestimates snow accumulation during
an early spring snowfall event, possibly due to overestimating intercepted SWE (Figure 3b). Observations show that
the snowpack melts almost completely by early April 1998,
which the model captures relatively well. The RMSE for the
1997 – 1998 season was 8.6 mm (16.9%), while the correlation coefficient was 0.81. It is interesting to note the
difference in snow accumulation between the two winter
seasons for the beneath-canopy site (about 150 and less than
50 mm, respectively), while observed intercepted snow
loads exceeded 30 mm during the 1996– 1997 season but
remained below 20 mm during the 1997 – 1998 winter
[Storck et al., 2002]. Figure 3a also shows comparisons
between observed and model-predicted SWE at the shelterwood site; the model consistently underpredicts snow accumulation but follows the snow accumulation and ablation
pattern closely, and predicts the date of complete melt very
accurately, with RMSE and the correlation coefficient being
37.4 mm (15.6%) and 0.99, respectively.
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4.2. BOREAS
4.2.1. Implementation
[29] Simulations were performed for the period 1 September 1994 to 30 June 1996 at an hourly time step, with
meteorological data (precipitation, air temperature, wind
speed, incoming shortwave and longwave radiation, and
relative humidity) aggregated to the same temporal resolution. Whenever observations were missing, data from the
BOREAS Derived Surface Meteorological Data set [Knapp
and Newcomer, 1999] which contains interpolated data
from several surface observation sites over the NSA and
SSA were used. Precipitation and air temperature were
similar between the two winters, with relatively colder
temperatures in the NSA sites (as low as 40°C), but
somewhat higher precipitation in the SSA sites (peak annual
precipitation of 14.1 and 16.3 mm/h for SSA versus 11.4
and 7.4 mm/h for NSA). These simulations used the same
default parameters as in the Oregon simulations. Comparisons of the simulated snow depth and water equivalent
were made beneath the canopy using the snow course
measurements, and AMS-measured snow depth from small
open areas within different canopy types was also used to
evaluate the simulated snow depths. Canopy characteristics
were taken from the N-LDAS data set, as in the Oregon
case, for the forest type at each site (Jack Pine and Old
Aspen, considered as deciduous needleleaf trees), with
canopy heights taken as 17 m at SSA-OJP, 22 at SSA9OA, and 13 at NSA-OJP [Link and Marks, 1999], vegetation roughness length as 1.2 m, displacement height as
6.7 m, and LAI ranging from 1.5 to 5.0.
4.2.2. Evaluation (1994 – 1996)
[30] Figure 4 shows the continuous snow depth measurements (SWE continuous measurements were not available)
from the AMS towers compared with the model-simulated
snow depth at four different sites, OJP (Figure 4a) and OA
(Figure 4b) at the SSA, and OJP (Figure 4c) and YTH
(Figure 4d) at the NSA. The tower measurements have been
Figure 3. (a) Comparisons between observed (dashed
lines) and model-predicted (solid lines) SWE during the
1997 – 1998 period at the shelterwood (black) and beneathcanopy (gray) Oregon sites. (b) Model-predicted intercepted
snow water equivalent during the same period.
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Figure 4. Measured (gray) and VIC-simulated (black) snow depths at the BOREAS (a) SSA-OJP,
(b) SSA-OA, (c) NSA-OJP, and (d) NSA-YTH sites during 1 September 1994 to 30 June 1996.
aggregated to hourly to be directly comparable with the
model simulations. The model snow depth is very close to
the observations at SSA-OJP (Figure 4a), with a correlation
coefficient of 0.82 and an RMSE of 10.2 cm (19.2%), and
partially captures a large melt event in April 1996. The
model underestimates snow depth throughout the winter of
1995 – 1996 at the SSA-OA site (Figure 4b), but performs
well during 1994 – 1995. The overall correlation is 0.60 (n =
16,056) with an RMSE of 16.0 cm (23.2%). Despite the
differences during the second winter, the model appears to
follow the accumulation and melt events closely, which
suggests that it might be overestimating snow density
leading to an underestimation of snow depth. Results from
the NSA-OJP site (Figure 4c) show a relatively good
agreement between the model predictions and the observations, although the model overestimates snow depth both
during spring 1995 and winter 1996, and delaying the melt
onset in spring 1996. The correlation for this site is 0.83
(n = 16,056) and the RMSE is 16.4 cm (20.4%). Figure 4d
shows a similar comparison for the NSA-YTH site, where
the correlation coefficient was 0.78 (n = 16,056) and the
RMSE 21.4 cm (23.1%). The model predicts the dates of
melt onset and complete melt relatively well (differences of
less than 1 week), but consistently overestimates snow
depth over the 1994 – 1995 season and displays a slower
melt rate during spring 1996.
[31] In addition to the automatic snow depth measurements which were taken in clearings at each site, manual
snow depth and water equivalent measurements were taken
about every 15 days beneath the dominant canopy type
close to each study site, with the exception of NSA-YTH
(which is not included in these beneath-canopy comparisons). Figures 5 and 6 show comparisons between the
model simulations and snow course measurements for
SWE and snow depth, respectively, at selected dates for
three sites beneath the canopy. At the SSA-OJP site (jack
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Figure 5. Measured snow water equivalent (gray circles) from snow courses compared with VICsimulated SWE (black line) at the BOREAS (a) SSA-OJP, (b) SSA-OA, and (c) NSA-OJP sites for the
period 1 September 1994 to 30 June 1996.
pine), the model overestimates SWE over the entire 1994 –
1995 season with the exception of early to mid-December
1994 and April 1995. During the 1995 – 1996 season the
model captures snow accumulation quite well, but overpredicts peak SWE while capturing part of the snowmelt
pattern (Figures 5a and 6a) with an overall RMSE of
25.3 mm for SWE and 10.8 cm for depth (correlations of
0.85 and 0.82, respectively). At the SSA-OA site (old
aspen), model predictions of SWE follow the observations
very closely (Figure 5b) in both seasons (RMSE 9.1 mm
and correlation of 0.94), whereas simulated snow depth is
consistently smaller than the observed during the 1994 –
1995 season and very close to the observed depth during
the 1995– 1996 water year (Figure 6b) with an RMSE of
11.7 cm and correlation of 0.83, suggesting an overestimation of snow density during 1994– 1995. At the NSA-OJP
study site (jack pine), the model captures snow accumulation up to midwinter 1995 and the period near the end of
melt, but overestimates peak SWE. During 1995– 1996 it
overestimates SWE significantly (underestimating interception), although it seems to capture the complete melt of the
pack relatively well. This is evident in the RMSE, which is
52.7 mm (correlation of 0.81) for SWE and 11.9 cm (correlation of 0.72) for snow depth, with relatively improved
snow depth predictions being an artifact of the underprediction of snow density (Figures 5c and 6c).
[32] Observations of solar radiation were made beneath
the canopies at the SSA-OA site, with measurements lasting
for about 4 days. The radiative flux of shortwave energy
reaching the snow surface beneath a forest canopy is very
important for the ground snowpack energy balance. Figure 7
compares the model-predicted and observed shortwave
radiation reaching the ground surface at the SSA-OA site
(aspen) between 4 March 1996 2000 UT and 8 March 1996
1700 UT. Measurements were taken with a 1 min frequency,
and were aggregated to hourly for purposes of this comparison. Figure 7 shows the downward shortwave radiation
measured at the top of the canopy for reference. The model
is able to reproduce the time series of observed solar
radiation quite well, with an RMSE of 25.6 W/m2 (5.4%)
and a correlation of 0.97 with observations. Although the
duration of the measurements is relatively short, the comparison indicates that the model’s simplified approach for
predicting shortwave radiation transfer through forest canopies works well, which is also reflected in the SWE
comparisons for this study site (Figure 5b).
5. Model Sensitivity
[33] Although VIC performed reasonably well in both
maritime and boreal sites with default parameters, there were
nonetheless some persistent discrepancies in the comparisons of simulated SWE (Oregon) and depth (BOREAS) with
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Figure 6. Measured snow depth (gray circles) from snow courses compared with VIC-simulated depth
(black line) at the BOREAS (a) SSA-OJP, (b) SSA-OA, and (c) NSA-OJP sites for the period 1 September
1994 to 30 June 1996.
observations, as noted in section 4. Therefore, the question
of the sensitivity of simulated snow mass on model parameters arises. Despite the robustness of the model formulation
to capture snow processes in different climates, snow interception capacity as well as snow properties (such as roughness length) can vary. Therefore, a sensitivity analysis of
simulated SWE with snow roughness length, maximum
interception capacity (LAI multiplier in equation (28)), and
atmospheric stability correction was performed.
[34] Figure 8 shows observed and simulated beneath
canopy SWE for the Oregon (Figures 8a – 8c) and BOREAS
(Figures 8d– 8f) sites, with snow roughness length (Figure 8a
and 8d) being 0.1 mm, 10 mm and 1 mm (default value);
maximum interception capacity varying through the LAI
multiplier (Figure 8b and 8e) which was set to 0.005 mm
(default value), at 0.005 mm and 0.00005 mm; and using
atmospheric stability correction or not (Figure 8c and 8f).
Table 1 shows the correlation coefficients for the different
simulations at all sites.
[35] Snow roughness length has a significant effect at the
Oregon site after the initial accumulation of December
1996. The largest impact on the simulated SWE occurs
from changing the maximum interception capacity in the
model, which can be attributed to the relatively large snow
interception observed at the site (up to 40 mm) which was
about 10% of the peak SWE in the adjacent clearing. On the
other hand, application of the atmospheric stability correction scheme makes a substantial difference, especially after
the initial melt event in January 1997. Results for the 1997 –
1998 season are not as pronounced when varying snow
roughness length, probably because of the lower snowfall,
but high sensitivity to the maximum interception capacity is
apparent (Table 1).
[36] In contrast, changing snow roughness length had a
minimal impact in the colder BOREAS sites (Figure 8d and
Table 1), while simulated SWE showed somewhat higher
sensitivity to maximum interception capacity, especially for
the NSA-OJP site (Figure 8e). The SSA sites did not show
much sensitivity to either snow roughness length or maximum interception capacity (Table 1). Similarly, applying
Figure 7. Comparison of simulated (solid black line) and
observed (gray line) shortwave radiation beneath the
canopy, along with the incoming radiation (dashed black
line) at the SSA-OA BOREAS site during 4 March 1996
2000 UT and 8 March 1996 1700 UT.
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Figure 8. Observed and simulated SWE for different model parameterizations: (a) snow roughness
length (Oregon site), (b) maximum interception capacity (Oregon site), (c) atmospheric stability
correction (Oregon site), (d) snow roughness length (BOREAS NSA-OJP site), (e) maximum interception
capacity (BOREAS NSA-OJP site), and (f) atmospheric stability correction (BOREAS NSA-OJP site).
the atmospheric stability correction scheme resulted in relatively smaller differences in simulated snow mass (Figure 8f
and Table 1) as compared with the maritime Oregon site.
The atmospheric stability correction is primarily used for
calculating turbulent heat fluxes in the model, and its effect
can be assessed by comparing simulated sensible and latent
heat fluxes with measurements that were made in the SSAOA BOREAS site. These above-canopy measurements
were obtained from a tower using the eddy correlation
method, and also included measurements of carbon dioxide,
radiative fluxes as well as meteorological parameters. Measurements were taken between 20 April and 31 December
1996, so we can compare with the second half of the
winter 1996 simulations. Application of the stability
correction algorithms led to a modest improvement in
the RMSE of estimating latent (62.2 versus 67.4 W/m2
for the uncorrected) and sensible (75.8 versus 77.4 W/m2
for the uncorrected) heat fluxes, although these changes did
have an effect on the simulated SWE (Figure 8f).
6. Summary
[37] A mass and energy balance model for snow accumulation and ablation processes in forested environments
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Table 1. Correlation Coefficients of Simulated SWE for Different Model Parameterizations at the Forested Oregon and BOREAS Sites
Oregon, 1996 – 1997
Oregon, 1997 – 1998
SSA-OJP
SSA-OA
NSA-OJP
z = 10 mm
z = 0.1 mm
m = 0.05 mm
m = 0.0005 mm
No Stability Correction
0.93
0.79
0.85
0.94
0.80
0.84
0.73
0.86
0.94
0.83
0.86
0.72
0.87
0.92
0.66
0.71
0.85
0.85
0.94
0.81
0.86
0.88
0.74
0.40
0.85
was developed utilizing extensive measurements of snow
interception and release in a maritime climate mountainous
site in Oregon. The model was able to reproduce the SWE
evolution throughout two winters beneath the canopy as
well as the nearby clearing, with correlations ranging from
0.81 to 0.99 without any calibration. The model was also
evaluated using observations from the BOREAS field
campaign in Canada at sites with a much different continental climate with colder, thinner snowpacks. The model
was able to predict SWE and snow depth reasonably well at
both sites. Although the model formulation appeared suitable for both maritime and boreal climates, the high
sensitivity to model parameters such as snow roughness
length and maximum interception capacity at the Oregon
site suggests that improved simulations may be attained by
adjusting those parameters for different climatic conditions.
[38] The model is intended primarily for large-scale
applications. It has been incorporated as the standard snow
scheme within the Variable Infiltration Capacity model,
which represents subgrid spatial variability by simulating
state and fluxes in land cover/elevation tiles, and also
contains modeling components for wind redistribution of
snow [Bowling et al., 2004]. Within the VIC model, it is
used in a parameterization of partial snow cover and frozen
soil [Cherkauer and Lettenmaier, 2003]. It is also used in a
real-time hydrologic forecast system for the western U.S.
[Wood and Lettenmaier, 2006], and has been used in
numerous analyses, diagnoses, and predictions of climate
variability and change [e.g., Su et al., 2006; Christensen
and Lettenmaier, 2007].
[39] Acknowledgment. This work was primarily supported by the
National Aeronautics and Space Administration (grant NNG06GD79G).
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