Introduction
One-dimensional multi-layer physics-based snowpack models, for example SNTHERM89 , CROCUS and
SNOWPACK , are widely used to assess various aspects of the snow
cover. Recently, the SNOWPACK model has been extended with a solver
for Richards equation (RE) in the snowpack and soil, which
improved the simulation of liquid water flow in snow from
the perspective of snowpack runoff compared to
a conventional bucket-type approach . In
that study, a comparison of snowpack runoff measured by
a snow lysimeter with modeled snowpack runoff showed
a higher agreement when simulating liquid water flow with
RE, especially on the sub-daily timescale. Additionally,
the arrival of meltwater at the base of the snowpack in
spring was found to be better predicted. However, these
results were solely based on an analysis of liquid water
outflow. The study raised questions to what extent the two
water transport schemes differ in the simulation of the
internal snowpack structure and whether the improvements in
snowpack runoff estimations with RE are also consistent with
simulations of the internal snowpack.
For many applications, especially in hydrological studies,
the primary variables of interest are snow water equivalent
(SWE) and snowpack runoff, as the first provides possible
future meltwater and the latter provides the liquid water
that directly participates in hydrological processes. In
spite of its importance, direct measurements of SWE are
relatively sparse. In contrast, snow height measurements are
relatively easy to obtain either manually or automatically,
and long climatological records of snow height are
available. Methods have been developed to relate snow height
to SWE . Snow density is another
parameter that is variable in time and
space and rather cumbersome to measure
in the field. Although it is seldom of primary interest, it
may serve wide applications as an intermediate parameter
between a property that is observed and a property that one
is interested in. For example, proper estimates of snow
density will increase the accuracy of translating snow
height to SWE. Snow density is also required for the
conversion of measured two-way travel time (TWT) from radar
applications to snow depth in dry-snow
conditions or translating
dielectric measurements to liquid water content, as for
example with the Snow Fork or the
Denoth meter .
Apart from bulk snowpack properties, there is also a demand
for detailed snowpack models to assess the layering and
microstructural properties of the snowpack, for example with
the purpose of avalanche forecasting. Layer transitions
within the snow cover with pronounced contrasts in for
example density, grain shape or grain size can act as zones
in which fractures can be initialized and slab avalanches
release . The presence of liquid water
can reduce the strength of a snowpack
considerably . showed that this reduction of strength depends also on the grain shape in the snow layers.
When snowpack models are used to understand wet
snow avalanche formation, it is important that the model can
reproduce capillary barriers, at which liquid water may
pond . Also
the arrival of meltwater at the bottom of the snowpack is
considered to be a good indicator for the onset of wet snow
avalanche activity. However, reliable liquid water content
(LWC) measurements for the snowpack are difficult to
obtain. Some attempts for continuous monitoring are
promising but are
not yet operational. Recently,
and demonstrated the potential of
upward-looking ground-penetrating radar (upGPR) to monitor
the progress of the meltwater front and
present data for quasi-continuous observations of bulk
liquid water content over several years and for three
different test sites. Here, their results concerning the
position of the meltwater front will be compared with
snowpack simulations. We also consider temperature
measurements taken during manual snow profiling as
a reliable and precise way to determine which part of the
snowpack is at the melting point (often termed
isothermal) and likely contains a fraction of liquid water
due to infiltration (i.e., the movement of liquid water in
snow) or local snowmelt.
As with snow density, snow temperatures are rarely of
primary interest in snow studies. However, a correct
representation of the temperature profile of the snowpack is
required, as it has a large influence on the snow
metamorphism (grain shape and size) and settling
rates . Temperature gradients drive
moisture transport and have a strong influence on the grain
growth . Furthermore, temperature profiles are an
indicator of whether the combination of the surface energy
balance, the ground heat flux and the internal heat
conductivity of the snowpack is adequately approximated.
In this study, the SNOWPACK model is driven by measurements
from an automated weather station at Weissfluhjoch (WFJ)
near Davos, Switzerland. Simulations are extensively
verified for several bulk properties of the snowpack and
against snow profiles made at WFJ, with the aim to verify
the representation of the internal snowpack structure. Time
series of soil and snow temperatures, snow lysimeter
measurements and upGPR data from WFJ are used to validate
snowpack temperature profiles, snowpack runoff and the
progress of the meltwater front within the snowpack in the
simulations. This study focusses on snowpack variables that
are influenced by liquid water flow with the aim of a more
in-depth comparison of differences between RE and the
conventional bucket scheme. The comparison is limited to
snow height, SWE, liquid water runoff from the snow cover,
snow density, snow temperature and grain size and shape, as
for these variables validation data are
available. Internally, the SNOWPACK model also uses
additional state variables, like sphericity, dendricity and
bond size .
Theory
The theoretical basis of the SNOWPACK model regarding the
heat transport equation and snow settling has been discussed
in . The treatment of the snow
microstructure and several parameterizations, as for example
for snow viscosity, snow metamorphism and thermal
conductivity, are presented in . Some of
those parameterizations have been refined in later versions
of SNOWPACK. The treatment of the meteorological forcing for
determining the energy balance at the snow surface is
discussed in . Finally, the liquid water
transport schemes are presented and verified
in . Here, we will outline theoretical
aspects not discussed in the aforementioned literature.
Water retention curves
Richards equation in mixed form reads
∂θ∂t-∂∂zK(θ)∂h∂z+cosγ+s=0,
where θ is the volumetric liquid water content (m3 m-3),
K is the hydraulic conductivity (m s-1), h is the pressure head
(m), z is the vertical coordinate (m, positive upwards and perpendicular to
the slope), γ is the slope angle and s is a source/sink term
(m3 m-3 s-1).
To solve this equation, the water retention curve and the saturated
hydraulic conductivity Ksat (ms-1)
need to be specified. For the water retention curve, the van
Genuchten model is used :
θ=θr+θs-θr1+α|h|n-mSc.
The water retention curve is then described by several parameters: residual water content
θr (m3m-3), saturated
water content θs (m3m-3)
and parameters α (m-1), n (-) and m
(-). Sc corrects the water retention curve using the approach by
to take into account the air entry pressure. As
in , an air entry pressure of 0.0058 m was
used, corresponding to a largest pore size of 5 mm.
Note that the residual water content in the water retention curve, which is
the dry limit, is not comparable to the water holding capacity or irreducible
water content in the bucket scheme, which refers to wet conditions. For the
soil part, the ROSETTA class average
parameters are implemented to provide
these parameters for various soil types.
For snow, the parameterization for α in the van
Genuchten model as proposed by reads
α=7.3(2000rg)+1.9,
where 2rg is the classical grain size (m),
which is defined as the average maximum extent of the snow
grains . For n, the original
parameterization by was modified
by to be able to extend the
parameterization beyond grain radii of 2 mm:
n=15.68e(-0.46(2000rg))+1.
Here, we will abbreviate this parameterization of the water
retention curve as Y2010. This parameterization has been used
in .
The Y2010 parameterization was determined for snow samples
with similar densities. In , an updated
set of experiments was described for a wider range of snow
density and grain size, leading to the following
parameterization of the van Genuchten parameters:
α=4.4×106ρ2rg-0.98
and
n=1+2.7×10-3ρ2rg0.61,
where ρ is the dry density of the snowpack
(kgm-3). This parameterization will be referred
to as Y2012. Both parameterizations will be compared
here. θr and θs are
defined as described in and
Ksat is parameterized
following :
Ksat=ρwgμ3.0res2exp-0.013θiρice,
where ρw and ρice are the
density of water (1000 kgm-3) and ice
(917 kgm-3), respectively, g is the
gravitational acceleration (taken as 9.8 ms-2),
μ is the dynamic viscosity (taken as
0.001792 kg(ms)-1), θi is the
volumetric ice content (m3m-3) and
res is the equivalent sphere radius (m),
approximated by the optical radius, which in turn can be
parameterized using grain size, sphericity and
dendricity .
In both parameterizations and for soil layers, the van
Genuchten parameter m is chosen as
m=1-(1/n),
such that the Mualem model for the hydraulic conductivity in
unsaturated conditions has an analytical
solution .
The method to solve RE requires the calculation of the
hydraulic conductivity at the interface nodes. It is common
to take the arithmetic mean (denoted AM) of the hydraulic
conductivity of the adjacent elements, although other
calculation methods have been proposed (e.g.,
see ). Here, we compare the default
choice of AM with the geometric mean (denoted GM), as
proposed by , to investigate the
possible influence of the choice on averaging method on the
simulations of liquid water flow.
Soil freezing and thawing
Due to the isolating effects of thick snow covers and the
generally upward-directed soil heat flux, soil freezing at
WFJ is mostly limited to autumn and the beginning of the
winter, when the snow cover is still shallow. To solve phase
changes in soil, we follow the approach proposed
by . They express the freezing point
depression in soil as a function of pressure head as
T∗=Tmelt+gTmeltLh,
where T∗ is the melting point of the soil water (K),
Tmelt is the melting temperature of water
(273.15 K), L is the latent heat associated with the
phase transition from ice to water (334 kJkg-1)
and h is the pressure head (m).
When the soil temperature T (K) is at or below T∗,
the soil is in freezing or thawing state and a mixture of ice and liquid water is present. Then, the pressure
head associated with the liquid water part (hw, m) can
be expressed as
hw=h+LgT∗T-T∗,
where h is the total pressure head of the soil (m). The
van Genuchten model provides the relationship between
pressure head and LWC:
θ=θr+θs-θr1+α|hw|n-mSc,
where θ is the volumetric LWC
(m3m-3). Consequently, the ice part can be
expressed as
θi=θr+θs-θr1+α|h|n-mSc-θ.
In , a splitting method is introduced
to solve both the heat transport equation and RE for liquid
water flow in a semi-coupled manner. We approach the problem
by finding the steady-state solution for T, θ and
θi in Eqs. (),
() and
(). This steady-state solution is
found numerically by using the Bisect–Secant
method , where the starting points for the
method are taken as all ice melting and all liquid water
freezing, respectively. In soil, liquid water flow can
advect heat when a temperature gradient is present. In the
soil module of SNOWPACK, heat advection associated with the
liquid water flow is calculated after every time step of the
RE solver, before assessing soil freezing and thawing.
Data and methods
Data (1): meteorological time series
The SNOWPACK model is forced with a meteorological data set
from the experimental site WFJ at an
altitude of 2540 m in the Swiss Alps near Davos . This
measurement site is located in an almost flat part of
a southeasterly oriented slope. During the winter months,
a continuous seasonal snow cover builds up at this
altitude. The snow season is defined here as the main
consecutive period with a snow cover of at least 5 cm on
the ground during the winter months and is denoted by the
year in which they end. The snow season at WFJ generally
starts in October or November and lasts until June or July.
The data set contains air temperature, relative humidity,
wind speed and direction, incoming and outgoing longwave and
shortwave radiation, surface temperature, soil temperature
at the interface between the snowpack and the soil, snow
height and precipitation from a heated rain
gauge . An undercatch
correction is applied for the measured
precipitation . Snow temperatures are
measured at 50, 100 and 150 cm above the ground surface,
using vertical rods placed approximately 30 cm apart. From
September 2013 onwards, soil temperatures are measured at
50, 30 and 10 cm depth. The experimental site is also
equipped with a snow lysimeter with a surface area of
5 m2, as described in . The rain
gauge and snow lysimeter measure at an interval of
10 min, whereas most other measurements are done at
30 min intervals.
In the area surrounding WFJ, field data to validate soil
freezing and thawing are lacking. For modeling the
snowpack, the most important influence of the soil is the
heat flux that is provided at the lower boundary of the
snowpack. For this purpose, we will use the temperature
measured at the interface between the soil and the snowpack
to validate the soil module. This temperature measurement is
influenced by soil freezing and thawing. Our primary
interest here is to investigate to what degree the
previously described soil module of SNOWPACK is capable of
providing a realistic lower boundary for the snowpack in the
simulations.
SNOWPACK can be forced with either measured precipitation
amounts or with measured snow height. In
precipitation-driven simulations (Precip driven), measured
precipitation is assumed to be snowfall when the air
temperature is below 1.2 ∘C and rain otherwise. For
these types of simulations, the study period is from
1 October 1996 to 1 July 2014 (1 week after melt-out date),
consisting of 18 full snow seasons. In case of snow-height-driven simulations (HS driven), an additional
threshold for relative humidity (≥70 %) and a maximum value for the
temperature difference between the air and the snow surface (≤3 ∘C)
is used to determine whether snowfall is possible. The latter condition tests
for cloudy conditions, when the increase in incoming longwave radiation will
warm the snowpack surface close to air temperature. Then,
snowfall is assumed to occur when measured snow height exceeds
the modeled snow height and, consequently, new snow
layers are added to the model domain in order to match the measured snow
height again. These layers are initialized with a new snow density dependent
on meteorological conditions . In both modes, new snow
layers
are added for each 2 cm of new snow. An uninterrupted,
consistent data set for this type of simulations is available
from 1 October 1999 to 1 July 2014, consisting of 15 full
snow seasons. The last snow season (2014) of the studied
period has the most data available and will be used as the
example snow season to explain how SNOWPACK simulates the
snow cover. Results for the other snow seasons are included
in the online Supplement.
Many processes in SNOWPACK are based on physical
descriptions that require calibration, for example for wet
and dry snow settling, thermal conductivity and new snow
density. For this purpose, dedicated data sets with some
additional detailed snowpack measurements from snow seasons
1993, 1996, 1999 and 2006 have been used when constructing
the model. Snow metamorphism processes were mainly
calibrated against laboratory
experiments .
Data (2): manual snow profiles
Every 2 weeks, around the 1st and 15th of each month (depending on weather conditions), a manual
full depth snow profile is taken at WFJ , following the
guidelines from . The snow profiling is carried out in the morning
hours, starting around 09:00 LT. Measurements include snow
temperature at a resolution of 10 cm and snow density in
steps of approximately 30 cm. Snow density and SWE are determined by
taking snow cores using a 60 cm high aluminium cylinder
with a cross-sectional area of 70 cm2 inserted vertically into the snowpack. The snow core is then weighted
using a calibrated spring. For comparison
with the simulations, SWE values are corrected for
differences in snow height at the snow pit and at the
automatic weather station to eliminate the effect of
spatial variability. Grain size (following the classical
definition of average maximum extent of the snow grains) and
grain shape are evaluated by the observer using a magnifying
glass. Also snow wetness is reported in five wetness classes as well as hand
hardness in six classes . Because judging snow wetness has a
subjective component and estimating the actual LWC is generally considered
rather difficult, we consider here only three categories: dry (class 1;
0 % LWC), moist (class 2; 0–3 % LWC) and wet (class 3 or higher; ≥3 % LWC).
Data (3): upward-looking ground-penetrating
radar
An upGPR is located within the test site at a distance of
approximately 20 m from the meteorological
station . The upGPR is
buried in the ground with the top edge level to the ground
surface and points skyward. The radar instrument and data
processing is described in . Measurement
intervals for all observed melt seasons were set to 30 min
during daytime. The only difference in the processing scheme
applied for this study in comparison to
is that for an optimized retrieval of the dry–wet transition
within the snow cover, we reduced the length of the
moving-window time filter to a few days (1–3) instead of
6 weeks. Since percolating water results in strong
amplitude increases at the respective depth of percolation
and a decrease in wave speed for electromagnetic waves
traveling through wet layers, we searched for occurrences
of sharp amplitude contrasts together with diurnal
variations in the location of signal responses of the
overlying layers. For snow layers in which liquid water is
appearing during the day and refreezing during the night, or
when LWC reduces through outflow, a clear diurnal cycle in
TWT of the respective signal
reflections can be observed. describe
first attempts to determine percolation depths
automatically within the recorded radargrams. For this
study, we manually determined all observations of the
dry–wet transition in the snowpack and converted TWT in
height above the radar by assuming a constant wave speed in
dry snow of 0.23 mns-1 . Data on liquid water percolation measured
with upGPR have been presented in for the
snow seasons 2011 and 2012. Here, we present data of two
more snow seasons (2013, 2014) and compare all measured
depths of the dry–wet transition with simulation results. In
snow seasons 2011, 2013 and 2014, additional snow profiles
were made in close proximity of the upGPR, with a higher
frequency during the melt season than the regular snow
profiles discussed in the previous section.
Methods (1): model setup
For the simulations in this study, the SNOWPACK model solves
the energy balance at the snow surface. The
turbulent fluxes are calculated using the stability
correction functions as in . This is an
adequate approximation for most of the snow season, when the
snow surface cooling due to net outgoing longwave radiation
causes a stable stratification of the atmospheric
boundary layer. The surface albedo is calculated from the
ratio of measured incoming and reflected shortwave
radiation. The net longwave radiation budget is determined from the difference in measured incoming and calculated
outgoing longwave radiation. The aerodynamic roughness
length (z0) of the snow is fixed to 0.002 m.
The soil at WFJ consists of coarse material with some loam
content, as was observed when installing the soil
temperature sensors. The ROSETTA class average parameters
for the loamy sand class are taken for the van Genuchten
parameterization of the water retention curve for the soil
(θr=0.049 m3m-3,
θs=0.39 m3m-3,
α=3.475 m-1, n=1.746,
Ksat=1.2176⋅10-5 ms-1). For the thermodynamic
properties, the specific heat for the soil constituents was
set to 1.0 kJkg-1K-1 and the heat
conductivity to 0.9 Wm-1K-1. The total
soil depth in the model is taken as 3 m, with a variable
layer spacing of 1 cm in the top layers and 40 cm for the
lowest layer. The dense layer spacing in the top of the soil
is necessary to describe the large gradients in soil
moisture and temperature occurring here. At the lower
boundary, a water table is prescribed, together with
a Neumann boundary condition for the heat transport
equation, simulating a constant geothermal heat flow of
0.06 Wm-2.
All simulations are run on the same desktop computer as
a single-core process, using a model time step of
15 min. In the solver for RE, the SNOWPACK time step may
be subdivided in smaller time steps when slow convergence is
encountered . The computation time is in
the order of a few minutes per year, where RE takes about
twice as much time as the bucket
scheme . Checks of the overall mass and
energy balance reveal that the mass balance for all
simulations is satisfied well within 1 mm w.e. and the
energy balance error is generally around
0.05 Wm-2 (see
Table ). We consider these errors
to be well acceptable for our purpose.
Average and standard deviation (in brackets) of bulk snowpack statistics over all snow seasons for various simulation
setups (bucket or Richards equation (RE) water transport scheme,
snow-height-driven (HS) or precipitation-driven (Precip) simulations,
Y2010 or Y2012 water
retention curves and arithmetic or geometric mean for hydraulic
conductivity) for all simulated snow seasons. Differences are
calculated as modeled value minus measured value; ratios are
calculated as modeled value divided by measured value. The
isothermal part is only considered during the melt phase (from
March to the end of the snow season).
Variable
Bucket
RE-Y2010AM
RE-Y2012AM
RE-Y2012GM
Bucket
RE-Y2012AM
HS driven (2000–2014)
Precip driven (1997–2014)
RMSE HS (cm)
4.16 (1.73)
4.00 (1.56)
4.11 (1.64)
4.12 (1.71)
20.86 (12.31)
23.12 (11.38)
Difference HS (cm)
1.33 (2.24)
0.87 (2.09)
0.88 (2.17)
0.89 (2.21)
-1.23 (12.31)
-5.24 (11.38)
Difference melt out (days)
-0.67 (1.45)
-0.73 (1.44)
-0.73 (1.44)
-0.73 (1.44)
-3.94 (6.08)
-7.00 (6.83)
RMSE SWE (mm w.e.)
39.28 (15.51)
39.62 (14.71)
39.78 (15.50)
39.39 (15.45)
84.96 (36.34)
99.03 (36.23)
Difference SWE (mm w.e.)
-5.67 (27.20)
-7.08 (27.04)
-9.29 (27.05)
-8.06 (27.14)
-16.14 (67.61)
-36.00 (66.91)
Ratio SWE (mm w.e.)
1.01 (0.09)
0.99 (0.08)
0.99 (0.08)
0.99 (0.08)
0.97 (0.19)
0.91 (0.17)
Ratio runoff sum (–)
1.08 (0.28)
1.14 (0.28)
1.13 (0.28)
1.13 (0.28)
0.98 (0.31)
0.98 (0.31)
NSE 24 h (–)
0.72 (0.32)
0.73 (0.32)
0.73 (0.32)
0.73 (0.32)
0.66 (0.32)
0.67 (0.31)
NSE 1 h (–)
0.13 (0.37)
0.57 (0.35)
0.59 (0.34)
0.58 (0.34)
0.02 (0.39)
0.39 (0.34)
r2 24 h runoff sum (–)
0.85 (0.11)
0.87 (0.10)
0.87 (0.10)
0.87 (0.10)
0.84 (0.12)
0.85 (0.13)
r2 1 h runoff sum (–)
0.52 (0.06)
0.78 (0.08)
0.78 (0.08)
0.78 (0.08)
0.48 (0.07)
0.68 (0.11)
Lag correlation for runoff (h)
-1.47 (0.79)
-0.20 (0.37)
-0.17 (0.31)
-0.13 (0.30)
-1.72 (0.79)
-0.44 (0.48)
RMSE cold contents (kJ m-2)
627 (274)
529 (244)
554 (285)
551 (277)
786 (556)
742 (509)
Difference cold contents (kJ m-2)
-129.0 (312.9)
11.1 (326.2)
-30.5 (336.2)
-36.7 (322.9)
-46.0 (604.0)
62.4 (565.0)
r2 cold contents (–)
0.76 (0.36)
0.78 (0.36)
0.79 (0.36)
0.78 (0.36)
0.77 (0.36)
0.78 (0.36)
r2 isothermal part (–)
0.64 (0.33)
0.74 (0.36)
0.74 (0.36)
0.73 (0.35)
0.65 (0.32)
0.74 (0.36)
r2 avg. grain size (–)
0.47 (0.31)
0.45 (0.30)
0.45 (0.30)
0.45 (0.30)
0.39 (0.29)
0.37 (0.28)
Mass balance error (mm w.e.)
0.01 (0.00)
0.01 (0.00)
0.01 (0.00)
0.01 (0.00)
0.09 (0.25)
0.02 (0.03)
Energy balance error (W m-2)
0.03 (0.08)
0.06 (0.08)
0.06 (0.08)
0.05 (0.08)
-0.05 (0.07)
0.05 (0.08)
CPU time (min)
0.57 (0.07)
1.39 (0.26)
1.44 (0.36)
1.45 (0.37)
0.61 (0.11)
1.55 (0.45)
Methods (2): analysis
The analysis of the simulations is done per snow season,
ignoring summer snowfalls. The snow season at WFJ is
characterized by an early phase at the end of autumn or
beginning of winter, when the snow cover is still relatively
shallow and occasionally melt or rain-on-snow events are
occurring. End of November to mid-March can be defined as
the accumulation period, in which snowpack runoff is
virtually absent and the snowpack temperature is below
freezing. This implies that in this period, all
precipitation is added to the snow cover as solid mass
either by rain refreezing inside the snowpack or by
snowfall. Small amounts of snowmelt occurring near the
surface refreeze during night or, after infiltration, inside
the snowpack. Therefore, the increase in SWE between the
biweekly profiles can be used to verify the undercatch
correction in case the SNOWPACK model is driven with
measured precipitation from the heated rain gauge or to
verify the combined effect of parameterized new snow density
and snow settling in case snow height is used to derive snowfall amounts. The final phase is the melting phase, starting
in April in most snow seasons, when the snowpack is
isothermal and wet and produces snowpack runoff.
The snow temperature sensors may be influenced by
penetrating shortwave radiation in the snowpack. Therefore,
snow temperature measurements are only analyzed when the
measured snow height is at least 20 cm above the height of
the sensor. Comparing snow temperatures between snow seasons
was done by first standardizing the measurement time of the
temperature series between 0 and 1 for the start and end of
the snow season, respectively. Then the data were binned in
steps of 0.01 and bin averages were calculated. These series
were then used for calculating the average and SD of
differences between snow seasons. The same procedure was
followed for snow height.
To compare manual snow profiles with the model simulations,
several processing steps are
required . The snow height at the snow
pit is generally different from the simulated snow
height. This is not only due to the model not depicting the
snowpack development perfectly but also because the snow pit
is made at some distance from the snow height sensor which
is used to drive the simulations. Therefore, we scale the
simulated profile to the observed profile by adjusting each
layer thickness, without adjusting the density. This implies
that mass may be added or removed from the modeled
domain. Then, the model layers are aggregated to match the
number and thickness of the layers in the
observations. Model layers are assigned to observed layers
based on the center height of the model layer. The typical
thickness of a model layer is around 2 cm, so possible
round-off errors are expected to be small. For temperature,
the matching with modeled layer temperatures is achieved by
linear interpolation from the measured temperature profile
to the center point of the modeled layer.
The cold content of the snowpack is the amount of energy
necessary to bring the snowpack to 0 ∘C, after
which an additional energy surplus will result in net
snowmelt. The total cold content Qcc
(Jm-2) of the snowpack is defined in discrete
form as the sum of the cold content of each layer:
Qcc=∑i=1nρiciΔziTi-Tmelt,
where i is an index to a snow layer, n is the number of
snow layers in the domain, ρi is the density of the
layer (kgm-3), ci is the specific heat of
the layer (Jkg-1K-1), Δzi is the
layer thickness (m) and Ti is the temperature of the
layer (K). The cold content is calculated for both the
observed and modeled profiles, where the modeled profile
is first aggregated onto the observed layer spacing with the
procedure described above.
Results and discussion
Snow height and snow water equivalent
Measured and modeled snow height for different model
setups (bucket or Richards equation (RE) water transport scheme,
snow-height-driven (HS) or precipitation-driven (Precip) simulations,
Y2010 or Y2012 water
retention curves, and arithmetic (AM) or geometric mean (GM) for
hydraulic conductivity) for the example snow season 2014, from
October 2013 to July 2014. Note that apart from forcing with either snow
height or precipitation measurements, differences between simulation setups
cause only small differences in snow height simulations, resulting in
overlapping lines in the figure.
Figure shows the snow height
for several simulation setups. Per construction, the snow-height-driven simulations provide a high degree of agreement
between measured and modeled snow height. The general
tendency of the precipitation-driven simulations is to
follow the measured snow height, although it can be clearly
seen that some precipitation events are overestimated,
whereas others are underestimated. These differences are
caused by inaccuracies when measuring solid precipitation
with a rain gauge , imperfections in the
undercatch correction or the effect of aeolian wind
transport causing either erosion or accumulation of snow at
the measurement site. As drifting snow mainly occurs
close to the surface, the rain gauge is rather insensitive
to these effects as its installation height is higher than
the typical depth of a saltation layer. However, at WFJ, drifting snow is expected to play a relatively
small role.
As listed in Table , the RMSE of
snow height for all simulated snow seasons is significantly
larger for precipitation-driven simulations than for snow-height-driven ones. As snow-height-driven simulations are forced to closely
follow the measured snow height, it can compensate for deviations in measured
and modeled snow height due to over- or underestimated snow settling or snowmelt and occasional erosion or deposition of snow by wind. This is not
possible with precipitation-driven simulations, which solely take
precipitation amounts to determine snowfall.
This contrast is additionally illustrated in
Figs. S1 and S2 in the Supplement, where snow height for the various
model setups is shown for each snow season. Typical
year-to-year variability of inconsistencies in the
precipitation-driven simulations are present, whereas the
snow-height-driven simulations follow the measured snow
height more closely. Consequently, the snow-height-driven simulations exhibit
a better agreement on the melt-out date, typically within 1 day from the
observed melt-out date, than the precipitation-driven ones (see
Table ).
In Fig. ,
the average snow height difference is shown for all
simulated snow seasons, relative to the standardized date in the snow season.
Snow-height-driven simulations generally have almost no bias to measured snow
height for most of the snow season. A slight positive bias in mid-winter for
precipitation-driven simulations is caused by a few overestimated snowfall
events, for which the bias persists throughout the snow season (see for
example snow season 2011–2012 in Fig. S2e in the Supplement). Contrastingly,
in the end of the snow season (i.e., the melt season), an underestimation of
the
snow height occurs in precipitation-driven simulations, which is also expressed by a negative overall snow height bias in Table .
This does not
necessarily imply that the melt rates are overestimated, as
snow height is the combined result of snow accumulation,
settling and melt.
Difference in modeled and measured snow height relative to
the snow season for both snow-height-driven (HS) and precipitation-driven (Precip) simulations determined over 15 and 18 years,
respectively, using the bucket scheme or Richards equation
with water retention curve and arithmetic
mean for hydraulic conductivity (RE-Y2012AM). For every snow
season, the first day with a snow cover is set at 0 and the last day
at 1.
Comparison of measured and modeled SWE (mm w.e.)
(a) and increase in SWE in the biweekly profiles and the
simulations during the accumulation phase (b) for both
snow-height-driven (HS) and precipitation-driven (Precip) simulations,
using the bucket scheme or Richards equation
with water retention curve and arithmetic
mean for hydraulic conductivity (RE-Y2012AM). Colored lines
denote the linear fits to the corresponding data; the black line
indicates the line y=x. The blue and cyan dots in (b)
perfectly overlap.
SWE is generally a better indicator of snow accumulation and
snowmelt than snow height. A comparison between observed SWE
in manual profiles and modeled SWE
(Fig. a) shows that the agreement
between both is high. The linear fits to the data points
show that on average, the prediction of SWE in the model is
accurate for both snow-height-driven and precipitation-driven
simulations. The scatter is larger for precipitation-driven
simulations and there seems to be an underestimation of low
SWE values and an overestimation of high ones.
The modeled SWE is a result of several effects: (i) snowfall amounts, which rely on an accurate estimation of
new snow density in case of snow-height-driven simulations
or an adequate undercatch correction in the case of
precipitation-driven simulations; (ii) snow settling in the
case of snow-height-driven simulations; (iii) snowmelt; and
(iv) liquid water flow in snow and subsequent snowpack
runoff. To separate the effects of liquid water flow and
snowpack runoff from the other effects,
Fig. b shows the increase in SWE in
biweekly profiles during the accumulation phase of the snow
season at WFJ, when only factors (i), (ii) and (iii)
play a role. The snow-height-driven simulations on average
provide a high degree of agreement with the
measured increase in SWE during the accumulation phase, with
only a marginal difference between the bucket scheme and
RE. Here, it needs to be mentioned that in snow-height-driven simulations, the snow settling formulation is
able to compensate for errors in the estimation of new snow
density and vice versa. For example, when new snow is
initialized with a too high density, and thus too much mass
is added, the snow settling will be underestimated, and
consequently, the next snowfall amount is also
underestimated. Because the snowfall amounts in
precipitation-driven simulations are independent of the
settling of the snow cover, the increases in SWE are
independent of the predicted settling. From the linear least squared fit to the observed and simulated changes in SWE, it can be concluded that
in the accumulation phase, the combined effect of new snow
density and snow settling provides a slightly
underestimated SWE increase in snow-height-driven simulations, whereas the opposite is found
for precipitation-driven simulations. In the latter case, particularly a few overestimated large snowfall events can be identified to have influenced the fit.
Difference in modeled and observed SWE
in the biweekly profiles for both snow-height-driven (HS) and
precipitation-driven (Precip) simulations, using the bucket scheme
or Richards equation with water retention
curve and arithmetic mean for hydraulic conductivity
(RE-Y2012AM).
Figure shows the difference in SWE between model
simulations and the snow profiles for all simulated snow
seasons. The difference in snow-height-driven simulations is
rather small, compared to precipitation-driven
simulations. All simulations show that in the melt phase,
the model underestimates SWE. This points towards either an
overestimation of melt rates, a too early release of
meltwater at the base of the snowpack or a combination of
both. The fact that the discrepancies for the
precipitation-driven simulations are larger than for the
snow-height-driven ones is related to the underestimation
of snow height during the melt phase. In the snow-height-driven mode, an overestimated decrease in snow height
during snowmelt is compensated for by a continuous adding of
fresh snow when the snowfall conditions are met.
Liquid water content and snowpack runoff
Snow LWC (%) for the snow-height-driven simulation with
the bucket scheme (a) and with Richards equation using
the water retention curve and arithmetic
mean for hydraulic conductivity (RE-Y2012AM, b) for the
example snow season 2014.
Dots denote layers that have been reported as dry (0% LWC, white
with black center dot), moist (0–3 % LWC, light blue) or wet, very
wet or soaked (≥ 3 % LWC, dark blue) from the biweekly snow
profiles. When layers are reported as “1–2” (dry–moist), it is
considered moist. In the zoom insert, major and minor x axis ticks
denote midnight and noon, respectively.
Figure a and b show the distribution of liquid
water within the snowpack for the example snow season 2014
for the bucket scheme and RE, respectively. Here, liquid
water is present during the beginning of the snow season and
during the melt season, which is a typical pattern for
WFJ. The simulations with RE show a quicker downward routing
of meltwater from the surface, where the meltwater is
produced, than the simulations with the bucket
scheme. Furthermore, the latter provides a rather
homogeneous LWC distribution throughout the snowpack, except
for the lighter surface elements, where LWC is significantly
higher. A diurnal cycle is not visible in the simulations,
except for layers close to the surface. With RE, there is
both a strong variation in the vertical direction as well as
in time. Marked accumulations of liquid water can be seen at
transitions between layers with different
characteristics. These accumulations peak at around 10 % LWC
and occur during the first wetting of the snowpack
and above capillary barriers inside the snowpack. The apparent slow downward
movement of liquid water accumulations during the melt season results from
snowpack settling moving the specific layers with water accumulations closer
to the ground.
The formation of water accumulations on capillary barriers was also observed in natural
snow covers (e.g., Techel and Pielmeier, 2011), and this process is considered to
contribute to wet snow avalanche
formation . The effect is
particularly present during the first wetting, as later in
the melt season, wet snow metamorphism reduces the contrast
between microstructural properties, and this is at least qualitatively reproduced by the model. Furthermore, the
increase in hydraulic conductivity when the snowpack below
the capillary barrier gets wet, reduces its function as
a barrier. RE also introduces a strong diurnal cycle in LWC
in the simulations. The results for other snow seasons can
be found in the Supplement Figs. S3–S5, and they illustrate
that the differences occurring between both water transport
schemes in the example snow season are similar for the
other snow seasons as well.
Direct comparison of these model results with measurements
is difficult, as continuous, non-destructive observations of
the vertical distribution of LWC are not available. However,
snowpack runoff is strongly coupled to the LWC
distribution. Snowpack runoff at the measurement site WFJ
typically occurs in the melt season and in some snow
seasons during autumn when early snowfalls may be
alternated by short melt episodes or rain-on-snow
events. This is illustrated by the cumulative runoff curves
in the Supplement Figs. S6
and S7. Table shows the ratio of
modeled to measured snowpack runoff. Snowpack runoff from
precipitation-driven simulations is on average 2 % less than
observed, whereas snow-height-driven simulations show about
8–14 % more runoff than is observed. From the snow-height-driven simulations, simulations with RE again have
higher runoff sums than the simulations with the bucket
scheme. This behavior is found in most simulated snow
seasons, as shown by Fig. . The overestimation of total runoff in snow-height-driven simulations is caused by the previously
described mechanism where the snow-height-driven simulations
add snow layers in spring when the snow height decrease is
overestimated. The approach is inadequate during the melt
season, as these new snow layers have low densities compared
to the rest of the snowpack and snow settling will quickly
reduce the modeled snow height again below the measured
one. As the wet snow settling is a little stronger when
using RE, this effect is slightly larger for those
simulations.
Seasonal runoff sums (mm) from the perspective of the snowpack mass balance (negative values denote snowpack outflow).
A common measure to quantify the agreement between measured
and modeled snowpack runoff is the Nash–Sutcliffe model
efficiency (NSE; ), which is shown in Table
and Figs. S8 and S9 in the
Supplement for completeness. Further discussion can be found
in . NSE coefficients increase for
simulations with RE, especially on the 1 h timescale, as
well as the r2 value. The decrease of performance in terms of NSE
coefficient, in particular for the bucket scheme, can be mainly attributed to
poor timing of meltwater release during the day. For example, the bucket
scheme does not take percolation time into account, resulting in rather low
NSE coefficients. The NSE coefficients and r2
values tend to be lower for precipitation-driven simulations
than for snow-height-driven ones, especially in the
simulations with RE. This likely is a result of a more
accurate prediction of percolation time of liquid water
through the snowpack in snow-height-driven simulations. This
is also indicated by the difference in time lag correlation
(see Table ) between
precipitation-driven simulations and snow-height-driven
ones. The best timing of snowpack runoff on the hourly timescale is achieved with snow-height-driven simulations with
RE.
The NSE coefficients and r2 values reported here were calculated over
the snow-covered period from the simulations. However, this is an arbitrary
choice, given the discrepancies in melt-out date from simulations and
measurements, particularly for precipitation-driven simulations (see
Table ). When considering both possible
definitions for snow-covered period (either determined from simulations or
from measurements), differences in NSE coefficients up to 0.16 are found for
individual years. This is particularly the case for precipitation-driven
simulations, where the prediction of melt-out date is less accurate (see
Table ). However, for the average NSE
coefficients, the differences are less than 0.02 for both precipitation and
snow-height-driven simulations, as the year-to-year differences cancel out.
The choice of calculation period has a larger influence on r2 values,
since the late melt season is associated with the highest snowpack runoff
and consequently has a large effect on the r2 values. Nevertheless, the
differences between simulation setups within either snow-height-driven
simulations or precipitation-driven ones are smaller than the differences
between both simulation types. This implies that the same conclusions about
simulation setups can be drawn regardless of the choice of calculation
period.
Soil temperatures
Measured and modeled soil temperatures at 10, 30 and
50 cm below the surface for the example snow season 2014
(a) and measured and modeled snow–soil interface
temperature for snow seasons 2000–2014 (b). Only the
snow-height-driven (HS-driven) simulations with the bucket scheme
and Richards equation using the water
retention curve and arithmetic mean for hydraulic conductivity
(RE-Y2012AM) are shown. Note that in (a), the x axes for 30 and 50 cm depth are staggered by 3 ∘C to prevent overlap.
At WFJ, soil temperatures are available at three depths but
only for the last snow season in this study (see
Fig. a). The simulated
soil temperatures are satisfactorily simulated, although the
soil never showed temperatures well below
0 ∘C. This indicates that no significant soil
freezing occurred, limiting the usefulness of these data to
validate the new soil module. However, it is primarily
important for this study that the soil as modeled by
SNOWPACK serves as an adequate lower boundary condition for
the snowpack simulations. For this purpose, we examine the
soil temperature in the topmost soil part at the snow–soil
interface, which is available for the snow seasons
2000–2014 (see
Fig. b). For most of
the time when a snow cover is present, the interface
temperature at the snow–soil interface is close to
0 ∘C, except in the beginning of the snow season
when the snow cover is still shallow. This is common for
deep alpine snowpacks due to the isolating effect of thick
snow covers and the generally upward-directed soil heat
flux. Figure b shows
that the simulations capture the variability in early season
soil–snow interface temperature to a high degree in most
years and that the soil module in SNOWPACK is providing an accurate lower
boundary for the snow cover in simulations.
Snow temperature (∘C) for the snow-height-driven
simulation with the bucket scheme (a) and with Richards
equation using the water retention curve and
arithmetic mean for hydraulic conductivity (RE-Y2012AM,
(b) for example snow season 2014. Snow at exactly
0 ∘C is colored black to mark areas of the snowpack that
are melting or freezing.
Snow temperatures
Figure a and b show the simulated temperature
distribution within the snowpack for the example snow season
2014 for the bucket scheme and RE, respectively. The other
snow seasons are shown in the Supplement Figs. S10–S12. For
each snow season, the snowpack temperature at WFJ is below
freezing for an extended period of time and for these
periods no noticeable differences are found between
simulations with the bucket scheme or RE. As a result of the
differences in liquid water flow depicted in
Fig. a and b, the parts of the snowpack
that are isothermal differ significantly. Table shows that the r2 value
between the relative part of the snowpack that is
isothermal, as determined from measurements in the observed
snow profiles and from the simulated ones, increases from
0.74 to 0.87 when solving liquid water flow with RE.
The temperature distribution of the snowpack is strongly
related to the combination of the net energy balance of the
snowpack and snow density. The latter influences the snow
temperature through the thermal inertia of dense snow layers
and through the strong density dependence of thermal
conductivity (e.g., ). Errors in either
the energy balance or snow density may result in errors in
snow temperatures. The cold content of the snowpack may be
considered a more robust method to verify the simulated
energy balance of the snow cover. Table shows that the RMSE in cold
content in the snow-height-driven simulations is larger for
the bucket scheme than RE, with a RMSE of around
630 kJm-2, which is equivalent to
2 mm w.e. snowmelt. This shows that the estimation of cold
content in the simulations is adequate when, for example,
estimating the onset of snowmelt and refreezing capacity
inside the snowpack. Larger RMSE for precipitation-driven
simulations can be associated with the larger discrepancy
between measured and modeled snow height. The bias in the
cold content is small compared to the RMSE, denoting that
the average simulated energy input in the snowpack is
accurate compared to its temporal variation. This conclusion
is only valid for the period when the snowpack temperature
is below freezing, as in the melt season the cold content
is by definition 0 kJm-2.
Measured and modeled snow temperatures at 50, 100 and
150 cm above the ground for snow-height-driven (HS-driven)
simulations using the bucket scheme or Richards equation using
the water retention curve and arithmetic
mean for hydraulic conductivity (RE-Y2012AM) for the example snow
season 2014. Values are only plotted when the snow height was at
least 20 cm more than the height of the temperature
sensor. Note that the x axes for 100 and 150 cm depth are staggered by 3 ∘C to prevent overlap.
Figure shows the
measured and modeled snow temperature time series at three
heights for the example snow season. The change of snow
temperature over the snow season is adequately
captured. There is almost no difference between simulations
with the bucket scheme and RE except for the timing when the
snowpack gets isothermal, associated with the meltwater
front moving through the snowpack. For this example snow
season, simulations with RE seem to better capture when the
snowpack becomes 0 ∘C, suggesting a better
prediction of the movement of the meltwater front through
the snowpack. In the Supplement Figs. S13 and S14, results
for each snow season are shown. In most snow seasons,
simulations with the RE provide a better agreement with
measured temperatures in spring than the bucket
scheme. However, in some snow seasons (e.g., 2001 and 2011),
simulations with RE show an increase in snow temperature
before the measured temperature increases, which suggests
a simulated progress of the meltwater front that is too fast.
Average (a) and SD (b) of the difference
between modeled and measured snow temperatures, surface
temperature and ground temperature (∘C) relative to the
snow season. For every snow season, the first day with a snow
cover is set at 0 and the last day at 1. The statistics are
determined over the 15 snow seasons of the snow-height-driven
simulations using the bucket scheme or Richards equation using
the water retention curve and arithmetic
mean for hydraulic conductivity (RE-Y2012AM).
In Fig. a and b,
the average and SD, respectively, of the
difference between modeled and measured temperatures are
shown, including snow surface and snow–soil interface
temperatures, determined over all 15 snow seasons of the
snow-height-driven simulations and plotted as a function of
the relative date in the snow season. During the main winter
season, the temperatures at 50 and 100 cm height are on
average up to 0.5 ∘C lower in the model than in the
measurements, whereas the temperature at 150 cm is on
average up to 1.0 ∘C too high in the
simulations. Interestingly the snow surface temperature is
generally underestimated, whereas the temperature at the highest snow
temperature sensor is overestimated in the simulations. The contrasting result
suggests that the snow layers near the top of the snowpack
have a too low density in the simulations, impacting both thermal
conductivity and heat capacity of those layers, or the thermal conductivity
is underestimated for typical snow densities found close to the surface.
These effects provide
a stronger isolation of the snowpack, causing heat from
inside to escape at a slower rate and allowing the surface
to cool more. This offers an explanation why the underestimation of the snow
surface temperature particularly occurs at night (not shown). In contrast,
errors in diagnosing the snowpack energy
balance (i.e., in net shortwave or longwave radiation or in turbulent fluxes) would be expected to influence all temperature
sensors in the same direction.
The SD of the difference between modeled and measured
temperatures shows an increase with height above the
ground. This can be attributed to higher temporal variations
in temperature in the upper snowpack due to highly variable
surface energy fluxes. The SD for the snow and snow–soil
interface temperature typically is less than
1.0 ∘C and decreases towards the melt season. For
the surface temperature, the SD is typically
high in the beginning and the end of the snow season. In the
beginning of the snow season, lower snow densities, low air
temperatures and reduced incoming shortwave radiation allow
for a strong radiative cooling of the snow surface, which is
delicate to simulate correctly and may result in errors in
simulated snow temperatures up to 10 ∘C. In the
melt season, discrepancies in the duration the snow surface
needs to refreeze at night may contribute to the increase in
SD between modeled and measured surface
temperatures.
Figure a also shows that in the
beginning of the melt season, the difference between snow
temperatures simulated with RE and measurements is on
average smaller than with the bucket scheme at 0, 50 and
100 cm depth. Although this suggests a better timing of the movement of
the meltwater front through the snowpack and the associated
temperature increase to 0 ∘C, heat advection through the ice
matrix and preferential flow and subsequent refreezing inside the snowpack
may also increase the local snowpack temperature to 0 ∘C. The reason why
the results from the temperature series at 150 cm contrast those at 0, 50
and 100 cm depth
remains unclear.
Snow density
Snow density (kgm-3) for the snow-height-driven
simulation with the bucket scheme (a) and with Richards
equation using the water retention curve and
arithmetic mean for hydraulic conductivity (RE-Y2012AM,
b) for example snow season
2014. Dots with a black center point indicate measured snow density reported
from the biweekly snow profiles, where the black center point is located in
the middle of the observed layer and the white bars denote the extent of the
layer of the respective density measurement.
Figure a and b show simulated snow density
profiles for the bucket scheme and RE, respectively, for the
example snow season 2014. In Supplement Figs. S15–S17, the
other snow seasons are shown. Differences in density mainly
arise when liquid water is involved. The accumulation and
subsequent partial refreeze of meltwater at some layers form
denser parts, whereas other layers remain less dense because
less meltwater is retained. This type of stratification is
known to happen, although verification is difficult, because
density is sampled at a low spatial resolution in the manual
snow profiles.
Average simulated and measured snow density
(kgm-3) (a) and average and SD of the
difference between simulated and measured snow density
(kgm-3) (b), for
the lower, middle and upper part of the snowpack. The statistics are determined over the 15 snow seasons of
the snow-height-driven simulations using the bucket scheme or
Richards equation using the water retention
curve and arithmetic mean for hydraulic conductivity
(RE-Y2012AM).
In Fig. a, average snow density as
observed in the manual profiles is compared with the
modeled snow densities for the snow-height-driven
simulations for the period 1999–2013. Generally, the
seasonal trend in snow density is captured well in the
model. Discrepancies between modeled and observed profiles
are larger than the differences arising from the different
water transport schemes. In general, SNOWPACK overestimates
the density near the base of the snow cover, while it
underestimates the density of the upper part of the
snowpack. The bucket scheme, which was used to calibrate the wet snow settling,
keeps higher densities near the surface than RE, which is in closer agreement with observed snow density.
These observations are consistent for all simulated snow seasons,
as illustrated in Supplement Fig. S18. It supports the
argument in the previous section. These over- and
underestimations are larger than the differences between
water transport schemes. In Fig. b,
the average and SD of the difference between
simulated and observed density is shown, determined over the
15 snow seasons of the snow-height-driven
simulations. Average discrepancies in snow densities are
less than 25 kgm-3, increasing to
50–100 kgm-3 shortly before melt out. The
SD of the discrepancies is less than
50 kgm-3, increasing to
100–150 kgm-3 near the end of the melt
season. This illustrates that the new snow density
parameterization and the snow settling formulation are able
to provide accurate predictions of snow density. During the
snowmelt season, the deviations between observed and
simulated snow density increase as a result of new snowfall
events that are simulated to compensate for the
overestimated SWE depletion.
The depletion rate is the result of many interacting
processes. First of all, it is strongly coupled to snowmelt,
and thus dependent on the surface energy fluxes. Given the
high agreement in cold content in the main winter season,
errors in diagnosing the surface energy balance due to
uncertainties in atmospheric stability and measurement
errors in radiation, wind speed or air temperature seem to
be small on average. However, a consistent or incidental
overestimation of the energy input in the snow cover during
the snowmelt period may result in overestimated snowmelt. Once the meltwater leaves the snowpack, the mass
associated with it is definitely lost. Additionally, we
would argue that an insufficient simulation of the
densification during spring, under the influence of liquid
water flow, may also be important here. A too low snow
density will result in a deeper penetration of shortwave
radiation, effectively providing heat transport into the
snowpack. Furthermore, heat conductivity will be
underestimated, with the consequence that the simulated
snowpack in spring is too isolated to be able to release
heat during night.
Grain size
Grain size (mm) for the snow-height-driven simulation with
the bucket scheme (a) and with Richards equation using
the water retention curve and arithmetic
mean for hydraulic conductivity (RE-Y2012AM, b) for the
example snow season 2014. Dots with a black center point indicate observed
grain sizes reported from the biweekly snow profiles, where the black center
point is located in the middle of the observed layer.
Grain size plays an important role in liquid water flow, as
it has a strong influence on the water retention curves
(Eqs. –). Figure a
and b show modeled grain size
profiles for the example snow season 2014 for the bucket
scheme and RE, respectively. Differences between the schemes
are mainly found in the melt season where the bucket scheme
produces slightly larger grains. This is associated with the
typically higher liquid water content using that scheme
(Fig. a) compared to RE
(Fig. b). This results in
a stronger wet snow grain growth rate. Figure
b also illustrates the cause of the
liquid water accumulation found near a height of 120 cm in
the beginning of April in
Fig. b. The layer below the ponding
water consisted of significantly larger grains and was
creating a capillary barrier for the liquid water. In the
Supplement Figs. S19–S21, results are shown for each snow
season and a comparison with the LWC distribution (see
Supplement Figs. S3–S5) shows that capillary barriers are
a typical occurrence in simulations with RE for the deep,
non-isothermal, stratified snow cover as found at WFJ. For completeness, Figs. S23–S25 in the Supplement show simulated grain shapes for each snow season.
Average (a) and SD (b) of observed and
modeled grain size (mm) from snow-height-driven (HS) simulations
using both the Bucket scheme and Richards equation using
the water retention curve and arithmetic
mean for hydraulic conductivity (RE-Y2012AM).
Figure a and b show the
average and SD of the grain sizes from the
manual profiles and the simulations for the snow seasons
2000–2014. Most distinguishable is the steady increase in
grain size towards and during the melt season. Both
simulations show an increase in grain size towards the end
of the snow season, although the average observed grain size
is often underestimated. The underestimation of grain size
in simulations with RE compared to the bucket scheme is consistent for most snow seasons. It results from generally
lower LWC values in the snowpack in simulations with RE and,
consequently, lower wet snow grain growth rates. This
contributes to a reduced r2 value for grain size (see
Table ). Most of the variation in
grain size that exists before the initial wetting of the
snow remains present throughout the snow season in the
simulations. However, the vertical variation of grain size
typically decreases during the melt season, as shown in
Fig. b. However, opposite trends can be
found, mainly caused by snowfalls during the melt
season. The simulations tend to provide a decrease of the
SD in the melt season and the agreement with
the observations varies from year to year. Especially large
variations in grain size in the profiles are not captured in
the simulations.
Comparison of simulated dry–wet transition with
upGPR
Snow height (dashed line), manual snow profiles (colored
bars, legend provided in e) and the position of the
meltwater front as detected from the upGPR data (cyan dots),
modeled with the bucket scheme (black dots), Richards equation
with water retention curve and arithmetic
mean for hydraulic conductivity (RE-Y2012AM, green dots) and
similar but with geometric mean (RE-Y2012GM, brown dots) for snow
season 2011 (a), 2012 (b), 2013 (c) and
2014 (d). Measured snowpack runoff is denoted by blue
bars. The simulations were snow height driven.
Detailed comparisons of radar-determined dry–wet transitions
with simulations of the water transport schemes for the snow
seasons 2011 through 2014 are presented in
Fig. . Measured snowpack runoff (by the snow
lysimeter) is included in this presentation together with
grain shapes observed in snow pits, both of which are
indicative of water flow processes in snow. The dry–wet
transition is only plotted when the upGPR signal indicated
that parts of the snowpack were wet (see Sect. 3.3) or,
for the simulations, when the modeled snowpack was partly
wet. Due to beam divergence, a preferential flow path that
forms in the vicinity above the upGPR could potentially be
detected, although generally the upGPR would be particularly
sensitive to matrix flow. However, liquid water
accumulations above ponding layers are clearly visible in
radargrams independent of matrix or preferential flow that
formed such accumulations. It is impossible to discriminate
from the radar data which flow regime caused the respective
liquid water accumulations. In addition, layer transitions
within the resolution limit of the radar (≈0.07 m
for dry-snow conditions; ) are impossible
to discriminate as well and as a consequence, percolation
depths of the wetting front close to the ground surface
(<10 cm above the ground) cannot be accurately allocated
anymore. Interferences with the reflection signal from the
cover box of the radar prevent an accurate location of such
signals.
From the four snow seasons presented in
Fig. , the following observations can be
made: (i) snowpack runoff measured by the snow lysimeter
consistently starts earliest in the snow season; (ii) the
progress of the meltwater front is always faster in the
simulations with RE compared to the bucket scheme; (iii) the
radar-derived meltwater front progresses generally slower
through the snowpack than in both water transport schemes in
the model; (iv) the manual snow profiles mostly show melt forms
in parts of the snowpack that have been wet according to the
radar data, whereas the simulations often show larger parts
of the snowpack becoming wet earlier than indicated by the
profiles. These observations will now be discussed in more
detail.
(i) Since preferential flow can route liquid water efficiently
through the snowpack , upGPR-determined depths of dry–wet
transitions are not necessarily linked to the onset of
measured snowpack runoff . Studies
by and found
that ponding plays a crucial role in forming preferential
flow in both laboratory experiments as well as model
simulations. The ponding of liquid water in the simulations
for WFJ (see Fig. b) suggests that
preferential flow may have developed. The amount of snowpack
runoff measured before the arrival of the meltwater front is
highly variable. From 1 to 8 April in snow season
2011, large amounts of snowpack runoff were observed, most
likely due to lateral flow processes, whereas in snow season
2014 only marginal amounts were observed. In the latter
snow season, there is a strong increase in observed snowpack
runoff close to the time of the arrival of the radar-derived
meltwater front at the snowpack base. This variability
between years is not necessarily caused by different
preferential flow path structures but may also result from
the limited capturing area of the snow
lysimeter . (iii, iv) The vertical distribution of the melt forms in the observed
snow profiles may be considered particularly representative
for matrix flow and for the 4 presented years it
generally corresponds well with the parts of the snowpack
that may be considered wet from the upGPR signal. (ii) As the
bucket scheme shows a higher correspondence with the upGPR
data than RE, the convenient improvement in the accuracy of
simulated snowpack runoff with RE, as found
in , seems to be partly caused by
(unintentionally) mimicking some preferential flow
effects. To what extent this is caused by parameterizations
of the water retention curve or hydraulic conductivity, or
by the specifics of the implementation of RE in SNOWPACK,
remains unclear. (ii, iii) Although the bucket scheme may seem to
better coincide with the meltwater front in the upGPR data,
it may as well be argued that the differences between both
water transport schemes are smaller than the discrepancies
with the upGPR data. It is likely that the limits of
one-dimensional models with a single water transport
mechanism will prevent a correct simulation of both snowpack
runoff as well as the internal snowpack structure at the
same time.
In the beginning of the melt season, observations contrasting to the main melt phase discussed above can be made. The initial melt phase is characterized by a regularly disappearing meltwater
front at night. During this period, the depth to
which the liquid water infiltrates the snowpack is
underestimated in the simulations. Here, the RE scheme shows
larger infiltration depths, which are in better agreement
with the upGPR data, although again differences between both
simulations are smaller than the discrepancies with the
upGPR data. This result is contradictory with the main melt
phase, where the speed with which the meltwater front
progresses through the snowpack is largely overestimated in
the simulations. Furthermore, the distribution of melt forms
in the snow profiles does not always coincide with the
deeper infiltration depths detected by the upGPR.
An exception to the discussion above is snow season 2012,
for which the results are consistent to a high degree. The
progress of the meltwater front through the snowpack is
accurately modeled by RE and only slightly less accurately
by the bucket scheme for this snow season when comparing
with the upGPR signal. The snow lysimeter measurements show
runoff almost directly at the time the meltwater front as
detected from the upGPR reaches the soil. In the first snow
profile made afterwards, melt forms were found for most
parts of the snow cover. However, it is important to note
that the progress of the meltwater front is much quicker
than in the other snow seasons. Firstly, due to large snowfalls in that snow season, the snow stratification was
rather homogeneous, limiting the amount of possible
capillary barriers or impermeable layers in the snowpack
that could hinder the liquid water flow. The relatively
homogeneous stratification can be found in snow density
(Supplement Fig. S17e, f) as well as in grain size (Supplement
Fig. S21e, f) and grain type (Supplement Fig. S25e, f). Secondly, the onset of the snowmelt was initiated
by a very warm period, leading to sufficient snowmelt to
infiltrate the complete snowpack in a short amount of
time. These factors all provide fewer challenges for the
model.
Figure also illustrates the effects of the
choice of averaging method for the hydraulic conductivity at
the interface nodes. The progress of the meltwater front
follows a stepwise pattern. The arithmetic mean
reduces the contrast in hydraulic conductivity, causing
a smearing of liquid water between layers as well as over
microstructural transitions inside the snowpack. The
geometric mean puts more weight on the lowest
hydraulic conductivity, which is found in dry snow. This
results in a strengthened capillary barrier, indicated by
the flatter temporal position of the meltwater front
compared to the arithmetic mean.
Outlook
The extensive validation of the SNOWPACK model presented here has indicated
several areas for future research and development. When focussing on
processes directly impacted by liquid water flow, we can identify grain size
and snow density as important properties, since they also influence hydraulic
properties. It was found that during the spring melt season, both water
transport schemes underestimated grain growth. Furthermore, indications were
found that snow density in the melt season, which depends on the wet snow
settling, is underestimated. This could be a result of either not fully
representative parameterizations of these process in SNOWPACK or an
underestimation of LWC in the snowpack. The latter hypothesis is supported by
the comparison of bulk LWC from simulations and upGPR measurements, which has
revealed an underestimation of bulk LWC in both water transport schemes on
the flat site WFJ . Interestingly, this underestimation was
not found on slopes, which leads to the proposed hypothesis that on a flat
field, capillary barriers and ice lenses may introduce stronger ponding of
liquid water inside the snowpack than on slopes, where water can flow
laterally.
It was also identified here that SWE depletion rates in the SNOWPACK model
for the measurement site WFJ are overestimated. The SWE depletion in spring
is dependent on many factors, such as snow density and wet snow settling,
influencing the heat capacity, internal heat fluxes and penetration of
shortwave radiation, as well as the surface energy balance and liquid water
flow. These processes are difficult to investigate separately and errors
could also be introduced by errors in the meteorological measurements that
are used to force the model. For verifying the surface energy balance,
ideally, repeated cold content measurements could be performed using the
calorimetric method. However, this type of measurement is rather cumbersome
to perform in the field. Accurate turbulent flux measurements would allow us
to verify the parameterizations for latent and sensible heat. Snow compaction
(settling) could be assessed with in situ snow harps or snow profiles at a
higher temporal resolution than only biweekly. In addition, recent advances
in snow micro-penetrometry (SMP) are
also highly promising, allowing us to achieve density measurements at high
temporal and spatial resolution with relatively little effort
. A drawback of that method is that SMP
measurements are not suitable for wet snow conditions.
The simulation of liquid water flow in snow currently only considers a one-dimensional component, assuming homogeneity in the horizontal dimension.
However, this is a very strong simplification. In reality, liquid water flow
exhibits strong variation in three dimensions due to preferential flow paths
or flow fingering . The comparison of
modeled liquid water flow with upGPR data and snowpack runoff measurements
has identified that this simplification is indeed introducing representation
errors. Numerical experiments and laboratory
observations have provided promising indications that
these processes could be described using Richards equation in three
dimensions. At the same time, several processes that do appear in one-dimensional simulations, as for example the ponding of liquid water on
capillary barriers, seem to be essential in forming preferential flow paths.
This possibly allows for a parameterization of preferential flow in the
SNOWPACK model that is closely linked to physical processes. Validation
could be achieved by more detailed snow lysimeter studies, for example from
measurement sites with multiple neighboring lysimeter, improved laboratory
experiments or further exploiting the upGPR data.
Conclusions
The one-dimensional physics-based multi-layer SNOWPACK model
has been evaluated against measured time series and manual
snow profiles for the measurement site WFJ in the Swiss Alps
near Davos. Two water transport schemes, the bucket scheme
and RE, were taken into consideration as well as two modes
to provide the precipitation forcing for the simulations:
snow height driven (15 snow seasons) and
precipitation driven (18 snow seasons). Along with the
implementation of the solver for RE, the soil module of
SNOWPACK has also been updated. Comparing simulated and
measured temperatures at the snow–soil interface confirmed
that the updated soil module can provide a correct lower
boundary for the snowpack in the model.
The snow-height-driven simulations provide good agreement
with measured snow height (RMSE around 4 cm) and, during
the accumulation phase of the snow cover, with SWE. This
indicates that the model adequately simulates the
combination of snow settling and new snow density. In
precipitation-driven simulations, the SWE in the
accumulation phase exhibits a slightly larger error than in
snow-height-driven simulations, which is mainly caused by
deficiencies in the precipitation undercatch correction and
possibly snow drift effects. This results in a lower RMSE
for snow height (20–23 cm). For the simulations at WFJ,
SNOWPACK consistently overestimates the depletion rate of
SWE during the spring melt season, resulting in an
underestimation of SWE of typically 200 mm w.e. near the
end of the snow season, accompanied by an underestimation of
snow height up to 30–40 cm. In snow-height-driven
simulations, this is compensated for by simulating regular
snowfalls in order to match measured snow height. This
procedure has as a drawback that too much mass is added to
the snowpack in spring, resulting in an about 8–14 %
overestimation of cumulative runoff over the snow season,
whereas precipitation-driven simulations provide on average
2 % less snowpack runoff than measured.
The comparison of simulated snow density with snow density
measurements made in snow profiles has shown that both the
average snow density and the seasonal trend is well
simulated in SNOWPACK during the main winter season. Average
bias is around 25 kgm-3 and the density of deep
snow layers is slightly overestimated, whereas the density
of upper layers is slightly underestimated. In snow-height-driven simulations, the
discrepancies grow in the melt season, when SNOWPACK
underestimates snow density on average by up to
100 kgm-3 as a result of new snowfall events
that are simulated to compensate for overestimated SWE
depletion. The model
provides simulations of grain size which are consistent with
observations in manual snow profiles. Although RE causes
a slight underestimation of grain size compared to the
bucket scheme, snow density and grain size are adequately
simulated for the parameterization of the water retention
curves.
Modeled and measured snow temperatures showed a satisfying
agreement with average discrepancies of around
0.5 ∘C. The discrepancies in the surface
temperature were found to be larger, likely associated with
the above mentioned underestimation of snow density in the
upper layers and consequently the effect on thermal
conductivity. The discrepancy in the cold content of the
snow cover from simulations and field measurements was found
to be small, suggesting that the surface energy balance and
the soil heat flux are on average satisfactorily
estimated. However, this conclusion only holds for the main
winter period, as the defined cold content can only be used
to assess energy budgets of snow that is below freezing.
The temporal evolution and the vertical distribution of the
LWC in the snowpack differ significantly between the bucket
scheme and RE. The latter provides a faster downward
propagation of the meltwater front. This is accompanied by
a higher r2 value and NSE coefficient between simulated
and measured snowpack runoff for the simulations with RE
compared to the bucket scheme. RE also provides a higher
r2 value for the isothermal part of the snowpack
compared to the manual snow profiles as well as a closer
agreement with snow temperatures during the melt
season. These results suggest a more accurate simulation of
the progress of the meltwater front through the snowpack
with RE. Although the data from the upGPR support the
deeper meltwater infiltration in the snowpack in the early
melt phase as simulated with RE, the opposite is found for
the main wetting phase. Additionally, the distribution of
melt forms in the observed snow profiles shows a higher
agreement with the upGPR signal than with the
simulations. Both type of observations may be considered
particularly representative of matrix flow processes. The
high agreement between simulations with RE and snowpack
runoff therefore suggests that the use or implementation of
RE is unintentionally mimicking preferential flow
effects. However, the differences between both water
transport schemes are relatively small compared to the
differences between simulations and the observed meltwater
front in the upGPR data. The results suggest that the
ability of a one-dimensional approach to correctly estimate
both snowpack runoff as well as the internal snowpack
structure in wet snow conditions is rather limited. As the
simulation of ponding of liquid water on capillary barriers
and crusts is only captured with RE and not with the bucket
scheme, RE seems promising however for the ability of
SNOWPACK to assess wet snow avalanche risks. Future studies
may also focus on the possibilities to assimilate radar-derived vertical snowpack structure (e.g., density, ice
layers, liquid water) into the SNOWPACK model. This would
allow us to better understand to what extent discrepancies
between simulations and radar data are caused by deviations
in the simulated snowpack state at the onset of snowmelt or
by an insufficient process representation in the model.
The validation has shown that SNOWPACK has sufficient
agreement with measurements for snow temperatures, snow
density and grain size in the main winter season for a wide
range of applications. When using RE, we found that the
Y2012 water retention curve provides better results than the
Y2010 parameterization, whereas different averaging methods
to determine the hydraulic conductivity at the nodes between
layers seem to have little influence. In general, several
aspects of the simulations related to liquid water flow
improve with RE, although often the differences between
simulations tend to be smaller than differences between the
simulations and the observations and the improvements are
often inconsistent with the representation of the internal
snowpack structure as indicated by the upGPR data.