Introduction
In the Northern Hemisphere, around 19 % of the annually snow-covered
areas are forested (Rutter et al., 2009). As this type of ecosystem has
considerable implications for the mass and energy balance of the surface
snowpack (e.g., Harding and Pomeroy, 1996; Otterman et al., 1988), the proper
understanding and representation of the snow–canopy interactions is crucial
whenever realistic estimates of snow cover and melt dynamics in forested
environments are needed. This is specifically of concern for hydrological
modeling at all scales, runoff estimates from poorly gauged catchments,
flood and drought forecasting, global water budget assessment, and in support
of local water resources management including irrigation, provision of
drinking water,as well as industrial, touristic, or hydropower applications.
Also, the snowpack insulates the underlying soil from winter cold air
temperature, with implications for the ecosystem in terms of vegetation
cover and dynamics (Rasmus et al., 2011; Grippa et al., 2005), litter
decomposition (e.g., Saccone et al., 2013), or carbon cycling (e.g., Kelley et
al., 1968). The representation of this insulation is one of the critical
uncertainties of the modeling of the global soil carbon cycle and its
evolution in permafrost environments (Lawrence and Slater, 2010; Gouttevin
et al., 2012). The northwards migration of shrubs observed in the last
decades at high latitudes (e.g., ACIA, 2005) also indicates that snow–forest
interactions are to become more and more a concern for climate modeling in
the context of global warming.
The insulation properties of snow depend on snow depth and snow thermal
conductivity, which in the end relates to the type, characteristics, and
spatial arrangement of snow crystals within the snowpack. The realistic
description of these parameters can hence be a prerequisite for a reliable
representation of soil thermal regime and microbiological processes. Snow
stratigraphy is also of concern for specific local activities like reindeer
grazing in northern countries (Tyler et al., 2010; Vikhamar-Schuler et al.,
2013). At present, to the authors' knowledge, such a description is rarely
provided by modeling tools for sub-canopy snowpacks (Rasmus et al., 2007;
Tribbeck et al., 2006).
Several processes affect the snow cover in sub-canopy environments when
compared to open sites. Snow interception by dense canopies and subsequent
sublimation or melt of intercepted snow can reduce sub-canopy snow
accumulation by up to 60 % (Hardy et al., 1997). Conversely, canopy
shading from solar shortwave (SW) radiation can lead to longer lasting snow
cover in forested environments, while enhanced long-wave (LW) emission from
sunlit trees with low albedo can have the reverse effect (Sicart et al.,
2004; Strasser et al., 2011; Lundquist et al., 2013). In such an environment,
effects by topographical shading, solar angle, canopy structure, and
understory further complicate matters. Sub-canopy snow is additionally
sheltered from wind, thereby experiencing reduced turbulent fluxes. Finally,
canopy debris tends to accumulate over the snow and modify its optic
properties on the course of the season.
This complexity makes the understanding and prediction of the sub-canopy snow
cover evolution a challenging task. As a result, generations of modelers
have worked to capture how canopies affect the micro-meteorological
conditions above snow, and predict the resulting evolution of sub-canopy snow
(e.g., Essery, 1998; Pomeroy et al., 1998; Durot 1999; Liston and Elder, 2006;
Rutter et al., 2009; Strasser et al., 2011). The first focus of this
modeling was usually on snow interception, interception evaporation, and
(lack of) snow redistribution, as major features shaping the amount of snow
beneath canopies (Essery, 1998; Pomeroy et al., 1998). Later, the sub-canopy
or within-canopy micro-meteorology was increasingly refined to include a
representation of temperature, radiation, and turbulent fluxes: Durot (1999)
initiated a treatment of the meteorological fields provided by the French
analysis SAFRAN (Vidal et al., 2010) to translate them into sub-canopy fields. This involved an
homothetic transformation of the air temperature, an increase in air
humidity, a formulation for turbulent fluxes in canopy-dampened wind
conditions, and the shading from solar radiation through a Beer–Lambert or a
linear law. Later, Jansson and Karlberg (2001), Yamazaki (2001), Tribbeck et
al. (2004, 2006), Liston and Elder (2006), and Strasser et al. (2011) set up
dedicated snow models designed for forest environments, featuring different
strengths and weaknesses. For instance, the COUP model (Jansson and Karlberg,
2001) features an advanced representation of snow–canopy processes but lacks
a detailed, layered snowpack and the associated physical processes.
Oppositely, the SNOWCAN model (Tribbeck et al., 2004, 2006) couples a robust
radiative transfer model for canopies to the detailed snowpack model SNTHERM,
but their treatment of interception is coarse and experimental.
In 2004 and 2009, two significant international intercomparison exercises
were compiled to compare the skills of a broad scope of snow models, ranging
from land surface model snow schemes, to very sophisticated models designed
for local catchments or point-scale applications (SnowMIP: Etchevers et al.,
2004; SnowMIP2: Essery et al., 2008; Rutter et al., 2009). They demonstrated
the
increasing skill of the snow models to capture the dynamics of the sub-canopy
snow cover, but highlighted some remaining challenges: misrepresentation of
mid-winter melt events, lack of time-transferability of calibration at
forested sites, and difficulty in capturing the maximum snow accumulation in warm
environments, sometimes due to unreliable precipitation data. According to
Rutter et al. (2009), the former and the latter could be in part due not only to a
coarse representation of mixed-precipitation events and rain-on-snow, but
also to the misrepresentation of ablation events driven by air temperature
rising above 0 ∘C, when models diverge from observations due to
their treatment of sub-canopy long-wave radiation. In a recent publication,
Lundquist et al. (2013) pointed to long-wave canopy emissions as the main
cause of an early sub-canopy snow melt in snow regions where mean winter
temperature exceeds -1 ∘C and mid-winter melt events are frequent.
This effect, and the importance of accounting for the thermal structure of
different canopy elements, has been pinpointed before by other
observation-based studies (Ellis et al., 2013; Pomeroy et al., 2009; Sicart
et al., 2004). However, most snow models of the current generation fail to
capture it due to an inappropriate treatment of the canopy thermal regime:
most of them, like the COUP model or the SNOWPACK model before our work
(Bartelt and Lehning, 2002; Lehning et al., 2002a, b, 2006), use the
above-canopy air temperature as a substitute for canopy temperature. There
are though a few exceptions: in their design of a land surface model dedicated
to intensively cold regions, Yamazaki et al. (1992) and
Yamazaki (2001) resolve a separate energy balance
for two canopy layers (crown and trunks). However, they neither compare their
results to canopy temperature or radiation data, nor do they assess the added
value of this specific model design for the sub-canopy snow surface energy
balance. In the aforementioned SNOWCAN and in SnowModel (Liston and Elder,
2006), an observed or hypothesized canopy temperature can be used as a model
input to compute the thermal emission of the canopy and its impact on
sub-canopy snowmelt. However, this is not a comprehensive modeling approach,
which would compute the canopy temperature by itself. In ADMUNSEN, Strasser
et al. (2011) used the heuristic formulation by Durot (1999) which accounts
for thermal dampening by the canopy, but does not propose a physical
formulation of the canopy temperature. This approach may show some
limitations in specific meteorological conditions or in discontinuous forest
where trunks are exposed to direct solar radiation.
Our work here builds on the hypothesis by Rutter et al. (2009). We aim to
test how the sub-canopy energy balance is improved by a physically consistent
formulation of the canopy thermal structure and the distinction between woody
and leafy elements. Focus is mostly on snow-covered environments, but not
exclusively. For our purpose, we develop a two-layer canopy representation
(leaves and wood) in the aforementioned SNOWPACK model, which proposes a very
detailed physical and microphysical representation of the snowpack. Before
our work, it included a simple, one-layer canopy module where radiation and
precipitation interception by forest elements were represented (e.g.,
Musselman et al., 2012), but the equivalence between air and canopy
temperature was assumed. Because SNOWPACK was initially developed for alpine
environment and is still mostly used in alpine or boreal context where
conifers are dominant, our new canopy module is for now only suited for
needleleaf, evergreen forest.
Micro-meteorological and sub-canopy, stand-scale radiation data collected
during the SnowMIP2 experiment provide a proper data set for the evaluation
of our developments. We complement them with tree trunk temperature and
biomass flux measurements collected in a summer boreal environment, which is
an interesting test case for model transferability and robustness.
Our contribution is hence structured in the following way:
An exhaustive documentation of the new model and the canopy module is
included for the sake of clarity and knowledge dissemination. Earlier
versions of the canopy module had been only partially described in Stähli
et al. (2006) and in Appendix A of Musselman et al. (2012).
Existing simultaneous observations of sub-canopy radiation, snow
evolution,
and meteorological conditions from Alptal (Switzerland) are used to validate
the new model and demonstrate its robustness and improvement over simpler
canopy formulations and with respect to observations.
Model validity and transferability is finally tested against observations
of components of the canopy energy balance taken from a different coniferous
environment (Norunda, Sweden).
Model description
The SNOWPACK/Alpine3D snow model
SNOWPACK is a one-dimensional, physics-based snow-cover model originally
dedicated to avalanche risk assessment. Driven by standard meteorological
observations, the model describes the stratigraphy, snow microstructure, snow
metamorphism, temperature distribution, and settlement as well as surface
energy exchange and mass balance of a seasonal snow cover. It has been
extensively described in Bartelt and Lehning (2002) and Lehning et
al. (2002a, b). Since 2005, it has also included the effect of vegetation above
and within or below the snowpack.
Snowpack can be wrapped into an open-source, spatially distributed,
three-dimensional model for analyzing and predicting the dynamics of
snow-dominated surface processes in complex alpine topographies: Alpine3D
(Lehning et al., 2006). In addition to SNOWPACK, Alpine3D includes a
preprocessing and interpolation module for meteorological fields (Bavay and
Egger, 2014), a module computing the spatially distributed radiations as
affected by topography (Helbig et al., 2009), an optional snow transport
model (Groot Zwaaftink et al., 2011), and an optional runoff model (Zappa et al., 2003;
Comola et al., 2015). The interpolated or provided spatial meteorological
fields drive the energy and mass balance of the surface snowpack, computed by
SNOWPACK. The canopy module and its new features described hereafter can run
within Alpine3D. They are included in the SNOWPACK model version 3.2.1
(revisions from 741) which is available under GPL license and upon creation
of an account at https://models.slf.ch/.
The canopy model structure
The canopy module of SNOWPACK calculates the upper boundary conditions for
the snowpack or bare soil surface below the canopy. It is based on an energy
balance approach in order to be consistent with the distributed radiation
scheme used in Alpine3D. Interception and throughfall of precipitation,
transpiration, and evaporation of intercepted snow or rain, as well as the
influence of the canopy on radiative and turbulent heat fluxes at the snow
or soil surface, are included in the model.
In its one-layer version, the model represents the vegetation canopy as a single
big leaf with state variables (i) canopy temperature Tcan (K) and
(ii) storage of intercepted water or snow I (mm). All canopy processes are
then computed based on three basic input parameters: canopy height
zcan (m), leaf area index (LAI) or plant area index (PAI)
(m2 m-2), and direct throughfall fraction cf (–). PAI
has more of a physical sense as non-leafy canopy elements play a role in
radiative extinction and turbulent fluxes, but PAI and LAI can usually be
derived from each other via a factor depending on stand characteristics;
thus,
the switch between both just affects parameter values in our formulations.
The description here uses LAI; the direct throughfall fraction can be set to
zero if LAI is provided as a stand-scale average including canopy gaps of
moderate size (up to ∼ 1 m). These three model parameters intend to
describe differences between forest stands without further tuning.
Parameters used by the SNOWPACK canopy module.
Parameter (unit)
Description
Value
Model internal
imax (mm m-2)
Coefficient for the maximum interception capacity
Spruce: 5.9; pine: 6.6
parameters
iLAI (mm m-2)
Maximum interception of water by canopy per unit of LAI
Rain: 0.25; snow: imax0.27+46/ρs,int
kLAI (–)
Extinction coefficient for SW and LW radiations
[0.4–0.8] default: 0.75
fLAI (–)
Fraction of LAI in the uppermost canopy layer. For 2LHM only.
Default: 0.5
Dcan (m)
Average canopy diameter
1
αwet,snow (–)
Snow-covered canopy albedo
0.3
αdry=αwet,rain (–)
Dry and wet canopy albedo
0.11
αtrunk (–)
Lower canopy-layer albedo
0.09
fd (–)
Ratio d/zcan
2/3
fz0m (–)
Ratio z0m/zcan
0.1
fz0h/z0m (–)
Ratio z0h/z0m
0.999
ra,LAI (–)
Parameter for the excess resistance introduces by canopy between surface and reference level.
3
fra,snow
Factor for increased aerodynamic resistance for evaporation of intercepted snow
10
ρbiomass (kg m-3)
Bulk biomass density
900
Cp,biomass (J kg-1 K-1)
Bulk biomass heat capacity
2800
eleaf (m)
Mean leaf (or needle) thickness. For 2LHM only.
0.001
User provided
zcan (m)
Mean canopy height
parameters
LAI (m2 m-2)
One-sided mean stand leaf area index
cf (–)
Direct throughfall fraction
B (m2 m-2)
Stand basal area. For 2LHM only.
The consideration of the thermal inertia of the forest stand in the one-layer
version with heat mass (1LHM) and the two-layer version (2LHM) imposes the use
of an additional input parameter, the mean stand basal area B
(m2 m-2). The different parameters used by the SNOWPACK canopy
module are listed in Table 1, distinguishing between the ones to be provided
by users according to forest specificities, and the ones internal to the
model.
The idea behind the two-layer version of the canopy module is to capture the
thermal contrast between two distinct compartments of the canopy:
the upper (or outer) canopy compartment (leaves or needles) which is most
directly exposed to the atmosphere;
the lower (or inner) canopy compartment (twigs, branches, trunks, some
leaves), for which energy and mass fluxes have already been altered by the
upper canopy compartment.
This modeling choice relies on observational data highlighting this contrast
and its relevance for the sub-canopy energy balance (Pomeroy et al., 2009).
With respect to the one-layer version, one state variable is added, namely, the
temperature of the trunk or lower canopy compartment Ttrunk (K).
Tcan is then replaced by Tleaves, the temperature of the
upper canopy.
The coupled water and heat balances of the canopy layer are calculated in
three steps:
First, a preliminary mass balance is calculated including interception
and throughfall of precipitation.
Second, the canopy temperature Tcan is calculated by solving the
energy balance of the canopy. For this purpose, all the non-linear energy
fluxes to the canopy have been linearized in terms of canopy temperature via
the Taylor series. The radiation transfer and turbulent exchange of sensible and
latent heat are then deduced. For the two-layer version, the energy balance of
the upper canopy also includes thermal emission from the lower canopy which
is similarly linearized in terms of Tcan via the explicit
formulation of an energy balance for the lower canopy.
Third, the mass balance of the canopy is updated by the evaporation
(or condensation) calculated in step two.
The two-layer version affects the canopy energy balance and computation of net
radiation in each layer. For the sake of simplicity the one-layer canopy
module is first fully described. The specificities implied by the
consideration of two layers are then dealt with in the last part of this
section.
Interception parameterization
The mass balance of the canopy layer includes three fluxes of water:
interception of precipitation ΔI (mm day-1), interception
evaporation Eint (mm d-1), and water unloading from the canopy
U (mm d-1):
dI/dt=ΔI-Eint-U,
where I (mm) is the interception storage.
A fraction (1-cf) of the precipitation P (mm day-1) is
available for interception at each time step. The interception rate is
calculated as a function of canopy storage saturation with an equation
originally proposed by Merriam (1960), in the form given by Pomeroy et
al. (1998):
ΔI=c(Imax-I)1-exp-(1-cf)PImax,
where the parameter c (–) is a model time-step dependent parameter known
as the unloading coefficient. Pomeroy et al. (1998) suggested a value of c=0.7 appropriate for hourly time steps. Canopy interception capacity
Imax (mm) is assumed to be proportional to leaf area index:
Imax=iLAILAI,
where the parameter iLAI (mm) is either set to a constant
corresponding to the interception capacity for liquid precipitation when
these occur, or parameterized as a function of snow density during snowfall
events, following Pomeroy et al. (1998):
iLAI=imax(0.27+46/ρs,int).
Schmidt and Gluns (1991) reported estimates of the parameter imax (mm)
for spruce (5.9) and pine (6.6). The density of the intercepted snow ρs,int (kg m-3) is estimated as a function of air temperature
(Lehning et al., 2002b). Different values have been reported for the
interception capacity of snow, depending on forest type and climate (e.g.,
Koivusalo and Kokkonen, 2002; Essery et al., 2003). Most important is to recognize
the large difference between solid and liquid precipitation. The phase of the
intercepted water is assumed to be equal to the phase of precipitation at
each time step. A mixture of liquid water and snow can therefore form the
interception storage, and unloading proceeds as the interception capacity of
the needles decreases with the enhanced density of the intercepted mixture or
with a shift towards positive temperatures.
The partition of precipitation into snowfall and rainfall in SNOWPACK depends
on available data. Usually precipitation with undistinguished phase is used,
and a temperature threshold disentangles the phases with linear or logistic
smoothing around the threshold (Kavetski and Kuczera, 2007). When phase
information is available and mixed events occur, the interception capacity is
calculated according to Eq. (4), but using the weighed sum of liquid water
and new snow density instead of the density of snow. For rain-only or
snow-only events, Eqs. (3) and (4) are respectively used without change.
Different approaches have been proposed for calculations of snow unload from
the canopy: Essery et al. (2003) set the unload rate equal to a fraction
(40 %) of calculated melt of intercepted snow. Koivusalo and
Kokkonen (2002) assumed that all intercepted snow unloads as soon as the air
temperature rises above 0 ∘C. We have chosen to calculate snow
unload U (mm day-1) only when the interception storage exceeds the
actual interception capacity:
U=max[0,I-Imax]/Δt,
which happens when the interception capacity is reduced due to the
precipitation of heavy, wet snow or due to an increase in air temperature.
Sudden release of a large amount of snow is thus avoided since the intercepted
snow density is increased gradually towards the threshold air temperature
for snowfall. This is favorable for the numerical stability of the snowpack
simulation. This simple parameterization also respects the fact that
individual branches usually release snow at a time and total unloading of a
whole tree is not very frequent.
Throughfall T (mm day-1) to the forest floor is thus equal to
T=P-ΔI+U.
Evaporation of intercepted water is calculated as part of the canopy energy
balance (cf. below) and added to the water balance at the end of the model
time step.
Canopy energy balance
The canopy temperature is directly derived from the canopy energy balance.
The one-layer canopy module with no heat mass (1LnoHM, e.g., the version used in
previous modeling studies; Rutter et al., 2009; Musselman et al., 2012)
relies on an assumption of stationarity, whereby net radiation of the canopy
Rnet,can (W m-2) is assumed to equal the sum of sensible
Hcan (W m-2) and latent LEcan (W m-2) heat
fluxes neglecting any storage or sources/sinks of heat within the canopy:
Rnet,can=Hcan+LEcan.
In the new canopy module, one-layer version with heat mass (1LHM), the thermal
inertia of trees is accounted for via a biomass storage flux BMcan
(W m-1), modifying the canopy energy balance:
Rnet,can=Hcan+LEcan+BMcan.
Radiation transfer
A radiation transfer model for a single canopy layer above a snow or bare
soil surface has been adopted from Taconet et al. (1986) by Stähli et
al. (2009). The model assumes a fractional absorption of radiation in the
canopy layer given by the absorption factor σf (–). A
fraction of the absorbed radiation is reflected, as defined by the reflection
factors for shortwave (albedo) and long-wave radiation.
Radiation transmitted to the surface below is absorbed and reflected
according to the corresponding reflection factors for the surface.
Following these basic assumptions, and integrating n multiple reflections
between the canopy layer and the underlying surface, the net shortwave
radiation absorbed by the canopy layer SWnet,can (W m-2) is
given by
SWnet,can=SW↓-σfαcanSW↓-(1-σf)SW↓+∑n=1∞(αsurf)n(σfαcan)n-1(1-σf)SW↓-∑n=1∞(αsurf)n(σfαcan)n(1-σf)SW↓-∑n=1∞(αsurf)n(σfαcan)n-1(1-σf)2SW↓,
where SW↓ (W m-2) is the incoming shortwave radiation
above the canopy layer, and αcan (–) and αsurf
(–) are the albedo of the canopy and the snow/soil surface below,
respectively. The first three terms on the right hand side are the incident,
reflected, and transmitted downward radiation with regard to the canopy
layer. The remaining three terms are the sums of incident, reflected, and
transmitted upward radiation, as a result of multiple reflections between the
canopy and the surface below. Equation (9) can be simplified to
SWnet,can=SW↓(1-αcan)σf1+αsurf(1-σf)1-σfαsurfαcan
by mathematical relationships for geometric series. The same procedure can be
applied for net shortwave radiation absorbed by the ground surface
SWnet,surf (W m-2) which thus can be written as
SWnet,surf=SW↓(1-αsurf)(1-σf)1-σfαsurfαcan.
The calculation of the long-wave radiation is further simplified by assuming
an emissivity equal to 1, giving the following equations for net long-wave
radiation absorbed by the canopy LWnet,can (W m-2) and the
ground surface LWnet,surf (W m-2):
LWnet,can=σf(LW↓+σTsurf4-2σTcan4),LWnet,surf=(1-σf)LW↓+σfσTcan4-σTsurf4,
where σ is the Stefan–Boltzmann constant
5.67 × 10-8 W m-2 K-4 and LW↓ is the
thermal radiation from the sky. Neglecting the emissivity might overestimate
the loss and gain of thermal radiation from the canopy. On the other hand,
the absorption factor σf (–) has a similar effect on the net
adsorption/emittance, and it may be difficult to separate these two
properties.
The net radiation to the canopy is then the sum of the LW and SW net
contributions:
Rnet,can=SWnet,can+LWnet,can.
The albedo of the canopy αcan (–) is equal to
αcan=fwetαwet+(1-fwet)αdry,
where fwet (–) is the fraction of the canopy covered by
intercepted water calculated as
fwet=(I/Imax)2/3,
and αwet (–) and αdry (–) are the albedo of
wet and dry canopy, respectively. The albedo for the wet part of the canopy
can be set differently for liquid and solid interception (Table 1).
The canopy absorption factor σf (–) is assumed to be equal
for long-wave and diffuse shortwave radiation, independent of interception
storage and phase, and is calculated as a function of LAI:
σf=1-exp-kLAILAI,
where kLAI (–) is an extinction parameter with values normally
between 0.4 and 0.8.
For direct shortwave radiation, it can optionally be a function of solar
elevation angle θelev, following Chen et al. (1997):
σf,dir=1-exp-kLAILAIsin(θelev),
where θelev is limited to the range [0.001-π/2] to ensure
a positive value of σf,dir.
Direct and diffuse SW radiations are in this case disentangled by the model
after Erbs et al. (1982).
For the sake of completeness, the effective surface albedo, αtotal (–), and radiative surface temperature, Teff (K),
above the canopy layer are given as
αtotal=αcanσf+αsurf(1-σf)21-αcanαsurfσf
and
Teff=LW↓-LWnet,can-LWnet,surfσ0.25,
respectively. These variables have no influence on the one-dimensional simulations
presented here, but are used to estimate the contribution of long-wave and
shortwave radiation from surrounding terrain when the SNOWPACK model is used
within the distributed Alpine3D model.
Finally, the radiation fluxes calculated by the canopy module are only
applied to the fraction of the surface covered by the canopy, assumed to be
the complement of the direct throughfall parameter: (1-cf). An
exception to that occurs for direct shortwave radiation which is collimated
in the solar direction: when sun is not at the zenith, the sun beams are not
parallel to the tree trunks and the projected surface occupied by the canopy
along their trajectory is higher than (1-cf). This higher fraction
of canopy shading (1-cf,dir) is derived following Gryning et
al. (2001) from the mean canopy height zcan (m) and an average
canopy diameter Dcan (1 m by default):
1-cf,dir=Min1,(1-cf)⋅1+4×zcanπ⋅Dcan⋅tan(θelev).
In the remaining fraction of the surface, the exchange of long-wave and
shortwave radiation between the atmosphere and the ground surface is
calculated without influence of the canopy.
Turbulent fluxes
The turbulent fluxes of sensible and latent heat from the canopy to the
reference level of the meteorological input (above the canopy) are
calculated using the bulk formulation:
Hcan=ρcprHTcan-Tair,LEcan=0.622LRaTair1rEesat[Tcan]-eair,
where ρ (kg m-3) and cp (J kg-1 K-1) are
the density and heat capacity of air, Tcan (K) is the canopy-layer
temperature, Tair (K) and eair (Pa) are the air
temperature and the actual vapor pressure in the air at a reference level
zref (m) above the ground surface, L (J kg-1) is the latent
heat of vaporization of water (or sublimation when
Tair < 273.15 K), Ra is the specific gas constant
for air (J kg -1 K-1), and esat[Tcan]
(Pa) is the saturated vapor pressure corresponding to the canopy
temperature. Furthermore, the turbulent transfer coefficients for heat and
vapor are expressed in terms of the aerodynamic resistances rH
(s m-1) and rE (s m-1) (further described below).
Latent heat flux is the sum of transpiration Etr (mm s-1) and
evaporation of intercepted water Eint (mm s-1). The
partitioning of the components from partly wet canopies can be a delicate
problem. To simplify the numerical solution of the energy balance, we have
chosen to formulate an effective aerodynamic resistance rE for
latent heat calculated as an average of the corresponding values for
transpiration rEtr and interception evaporation rEint,
weighted by the fraction of wet canopy fwet:
1rE=1rEintfwet+1rEtr(1-fwet).
The total evaporation Ecan (m day-1) is calculated directly
(Eq. 23), and its components are derived as secondary results:
Eint=EcanrErEintfwet,Etr=EcanrErEtr(1-fwet).
The derivation of the aerodynamic resistances for transpiration and
interception evaporation is given in the next section. Transpiration is not
allowed if the achieved Ecan is negative (condensation). In such
cases, the solution of the energy balance has to be re-calculated using
fwet=1.
At temperatures below the freezing point the modeled canopies do not
transpire anymore. If the canopy energy balance forces, through Eq. (24), an
evaporation that cannot be sustained by the interception storage, the latter
limits the possible evaporation and the canopy energy balance is re-calculated
accordingly.
Aerodynamic resistances
The aerodynamic resistances for sensible and latent heat fluxes are
calculated using a two-layer model adapted from Blyth et al. (1999) which for
simplicity assumes logarithmic or log-linear wind profiles both above,
within, and below the canopy. More elaborate models have been suggested by
for instance Shuttleworth and Wallace (1985); however, the remaining
uncertainties in the representation of the within-canopy turbulent exchange
call for a simple approach. The aerodynamic resistance for scalars from the
canopy level, defined by the displacement height d (m), to the reference
level of the wind and temperature measurements zref above the
canopy, is calculated as
1/rair=u∗k/lnzref-dz0m+ψh+ch0/ρcp,
where u∗ (m s-1) is the friction velocity:
u∗=urefk/lnzref-dz0m+ψm,
k is the Kármán constant (0.4), z0h (m) and z0m (m) are
the canopy roughness lengths for heat and momentum, ψm (–) and
ψh (–) are functions correcting for atmospheric stability
following Högström (1996) and Beljaars and Holtslag (1991). In addition
to Blyth et al. (1999), and following, e.g., Koivusalo and Kokkonen (2002), we
introduce an additional parameter ch0 (W m-2 K-1)
representing a minimum heat exchange coefficient for windless conditions.
Displacement height, and canopy surface roughness length of momentum and heat
are related to the canopy height through the parameters fd (–),
fz0m (–), and fz0h/z0m (–) with values given
in Table 1:
d=fdzcan,z0m=fz0mzcan,z0h=fz0h/z0mz0m.
In addition to the resistance between the canopy air (canopy reference level)
and the reference level for meteorological measurements (above the canopy),
excess resistances from the canopy surface, and from the soil/snow surface
(beneath the canopy), to the canopy level are defined as
rcan=lnz0mz0h1u∗k,rsurf=lnz0mz0h,surf1u∗kfsurf.
There, a multiplicative increase of the resistance below the canopy
fsurf (–) is introduced as a function of the leaf area index:
fsurf=1+ra,LAI1-exp-LAI,
with a maximum value of 1+ra,LAI (–). The excess surface
resistance below the canopy, rsurf, affects the heat and latent
fluxes computed from the ground to the reference level. This resistance is
corrected for atmospheric stability by applying the same stability functions
as in Eqs. (27) and (28), but in this case using the temperature difference
between the canopy and the snow or bare soil surface instead of the
temperature difference between the canopy and the air. With the current
choice of parameter values, the excess resistance for the canopy surface is
almost zero, but the theoretical framework for a later use/optimization of
this parameter based on observational data is set.
In the end, the total aerodynamic resistances for heat from the reference
level to the canopy and the ground surface, respectively, are given by
rH,can=rair+rcan,rH,surf=rair+rsurf.
The aerodynamic resistances for sensible and latent heat from the ground
surface are assumed to be equal. For evaporation from intercepted snow, the
resistance from the canopy to the canopy layer can be increased with a factor
fra,snow (–) compared to rain following Lundberg et al. (1998) and
Koivusalo and Kokkonen (2002):
rEint=rair+rcan×fra,snow,Tair<0∘C1,Tair≥0∘C.
The total resistance for transpiration also takes the stomatal control into
account:
rEtr=rair+rcan+rstomata,
where the stomata resistance rstomata (–) is calculated as a
function of a minimum resistance rsmin (–), incoming solar
shortwave radiation, vapor pressure deficit and soil water content
Θsoil as suggested by Jarvis (1976), and soil temperature
Tsoil following Mellander et al. (2006) and Axelsson and
Ågren (1976):
rstomata=rsminf1[SW↓]f2[esat-eair]f3[θsoil]f4[Tsoil]LAI.
The functions f1–f4 in Eq. (39) all take values between 0 and 1,
specifying optimal conditions for root water uptake corresponding to the
response of the leaf stomata to conditions in the atmosphere and the root
zone.
Biomass heat flux
Due to their thermal inertia, trees can store energy over periods of high
exposure to solar radiation, and release it at night. This biomass heat flux
is accounted for in the 1LHM version of the canopy module via the areal heat
mass of trees HMcan (J K-1 m-2):
BMcan=HMcan⋅Tcant-Tcant-1Δt,
where Tcant (K) and Tcant-1 are the canopy
temperature at the model t and t-1 time steps, and Δt (s) is the
model time step. HMcan is here derived from parameters commonly
observed by foresters: LAI, mean stand basal area B (m2 m-2) and
mean canopy height (zcan).
HMcan=HMleaves+HMtrunkHMleaves=LAIeleafρbiomassCpbiomassHMtrunk=0.5BzcanρbiomassCpbiomass
The leaf thickness eleaf (m), biomass density ρbiomass
(kg m-3) and biomass specific heat mass Cpbiomass
(J kg-1 K-1) are fixed parameters with values 10-3, 900 and
2800, respectively (Lindroth et al., 2010). In Eq. (43), the volume of woody
biomass (referred to as “trunk” but comprising trunks and branches
assimilated to the lower canopy layer) is calculated from mean tree basal
area and height assuming a conical profile for trunks. In this study, areal
heat masses will be expressed as “water equivalent areal heat masses”
HMeq (kg m-2), e.g., as the areal mass of water yielding the
same heat mass than HM (J K-1 m-2):
HMeq=HMCpwater,
where Cpwater=4181 J kg-1 K-1 is the liquid water
specific heat mass.
Two-layer canopy version
With respect to the one-layer canopy module, the two-layer formulation induces
changes in the formulation of radiative transfer, turbulent and biomass
fluxes, and in the end the energy balance of the canopy. These differences
are the focus of the present section, whereby the upper canopy layer is
equivalently referred to as “leaves” while the lower canopy layer
is labeled “trunk”. The formulation of the radiative and
turbulent components of the two-layer module is illustrated in Fig. 1.
Radiative and turbulent fluxes in the two-layer canopy
module. Ellipses feature radiation sources, dotted lines indicate radiation
absorption within the layer with the indicated absorption factor; albedos at
the border between layers are underlined. For turbulent fluxes, arrows
denote aerodynamic resistance.
![]()
Radiative transfer
In a real forest the trunk-layer intercepts parts of the shortwave and
long-wave radiation transmitted, reflected, and emitted by the uppermost
canopy layer and upwelling from the soil surface.
Our model features a simplified representation of the following:
For SW radiation, only the transmitted radiation from the upper canopy (with absorption
factor σfleaves and albedo αleaves) are
intercepted or reflected by the trunk layer (with the respective factors
σftrunk and αtrunk). Radiation undergoing multiple
reflections between ground surface and upper canopy are unaffected by the
trunk layer (Fig. 1). The SW flux reaching the ground and both canopy
layers are expressed accordingly:
SWnet,trunk=SW↓(1-σfleaves)(1-αtrunk)σftrunk,SWnet,leaves=SW↓(1-αleaves)σfleaves1+αsurf(1-σfleaves)(1-σftrunk)1-σfleavesαsurfαtrunk,SWnet,surf,2L=SW↓(1-σfleaves)(1-σftrunk)(1-αsurf)1-σfleavesαsurfαleaves.
Obviously, the biomass responsible for SW and LW extinction now has to be
split into the two canopy layers so that the total extinction for SW is
similar in both versions. Equating the first-order radiation from Eqs. (11)
and (47) yields(1-σf)=(1-σfleaves)⋅(1-σftrunk),or equivalently, based on Eq. (17):LAI=LAIleaves+LAItrunk,where LAIleaves and LAItrunk are the respective portions
of the total LAI attributable to the upper and lower canopies. We denote
hereafterfLAI=LAIleavesLAIand express the leaf-layer and trunk-layer absorption factors as functions
of LAI and fLAI:σfleaves=1-exp{-kLAIfLAI⋅LAI},σftrunk=1-exp{-kLAI(1-fLAI)⋅LAI}.
Similarly to the one-layer version (Eq. 18), these factors can be adapted to
enhance absorption of direct SW radiation based on solar elevation angle.
fLAI is an a priori undetermined parameter of our model due to the
difficulty of deriving it from existing data sets for different forest
types and structures. In Sect. 4, we show that the calibration of the model
at Alptal against this parameter yields fLAI=0.5, which means
equal contribution from the woody and leafy parts of the forest to shortwave
extinctions. This value is adopted as default value in the model (see Sect. 5
for discussion).
For LW radiation, the choice of an emissivity of 1.0 for ground and
canopy suppresses multiple reflections. Thermal emission from the upper
canopy layer and from the ground is attenuated by the trunk layer with the
same absorption factor as for SW radiation σftrunk. The trunk
layer then radiates thermally towards the ground and the upper canopy layer
and sky.LWnet,trunk=σftrunk(LW↓(1-σfleaves)+σTsurf4+σfleavesσTleaves4-2σTtrunk4)LWnet,leaves=σfleavesLW↓+σTsurf4(1-σftrunk)+σftrunkσTtrunk4-2σTleaves4LWnet,surf,2L=(1-σfleaves)(1-σftrunk)LW↓+σfleaves(1-σftrunk)σTleaves4+σftrunkσTtrunk4-σTsurf4
As for the one-layer version, this radiation balance is only valid on the
canopy-covered fraction of the model grid cell, which is (1-cf) for diffuse
SW radiation and LW radiation, and (1-cf,dir) for direct SW.
Turbulent fluxes
Sensible heat exchange between the lower or upper canopy layer and the
atmosphere is parameterized the same way as in the one-layer model version,
e.g., via the resistance rH,can. We consider that latent heat
exchange between canopy and atmosphere only occurs through interception
evaporation and transpiration at the leaf level, e.g., via the upper canopy
layer only.
Biomass heat flux
The upper and lower canopy layers are respectively attributed the
HMleaves and HMtrunk heat masses from Eqs. (42) and (43)
which are used in the biomass heat flux parameterization
Eq. (40) in the place of
HMcan.
Energy balance
An energy balance is formulated separately for each layer according to the
energy balance equation with heat mass (Eq. 8), where all terms are
linearized as functions of Tleaves and Ttrunk. The
coupled system is then iteratively solved for both temperatures.
The values of all the model parameters as used in the SNOWPACK canopy module
are listed in Table 1.
Results
Alptal
Model calibration
Table 3 summarizes the results of the calibration of the five model versions
(1LnoHM, 1LHM, 2LHM, 1LHM*, 2LHM*) against LW↓BC
and SW↓BC data from the snow season 2003–2004.
For all versions, the calibrated extinction coefficient kLAI is
within the [0.4–0.8] range of expected values (Stähli et al., 2009).
Both LW↓BC and SW↓BC are affected
by kLAI but LW↓BC is less sensitive to
radiation extinction (as atmospheric LW extinction by canopy is partly
compensated by canopy thermal emission in the same range of magnitudes).
kLAI is therefore mostly determined by calibration against
SW↓BC and is the same for most versions, which differ
only in their modeling of LW↓BC.
The calibration of the fLAI parameter yields the value of 0.5.
fLAI partitions the forest LAI between the uppermost and lowermost
canopy layers in the 2LHM version. The value of 0.5 would have been a
reasonable first choice for that partition.
The successive addition of heat mass (1LHM) and a two-layer partition of the
canopy (2LHM) to the default 1LnoHM simulation improves the general model
performance, as reflected in the decrease of the CC error function and its
components (MB, RMSE).
In the two versions where canopy heat mass is optimized (1LHM*, 2LHM*),
optimization yields unrealistically high heat mass values
(HM = 90 kg m-2 and HM = 60 kg m-2, respectively,
whereby field data indicate 30 kg m-2). However, while optimizing heat
mass quite significantly improves the performance of the one-layer versions
(from CC = 23.6 W m-2 for 1LHM to CC = 19.3 W m-2 for
1LHM*), it only marginally affects the performance of the two-layer version
(from CC = 18.4 W m-2 for 2LHM to CC = 17.5 W m-2 for
2LnoHM). These are encouraging results for the two-layer canopy formulation: on
the one hand, this model version shows a better performance than the
one-layered canopy model, even with the physically estimated heat mass. With
the one-layered version, such a performance can only be approached with an
unrealistic canopy heat mass. On the other hand, the performance of 2LHM
shows a considerably reduced sensitivity to the prescribed areal heat mass of
the canopy, a physical parameter which can be spatially variable and hard to
retrieve with precision in non-instrumented forests.
For the two snow seasons when all model versions simulate a reasonable
dynamics for the Alptal snowpack (2004–2005 and 2006–2007; see
Sect. 4.1.3), the sensitivity of the modeled SWE to the calibration
parameters kLAI and fLAI was determined (not shown). The
modeled SWE is sensitive to kLAI and fLAI, but the
calibrated (kLAI, fLAI) values lead to RMSE to observed
SWE close to the absolute minimum obtained when varying kLAI and
fLAI over their full range (13 mm vs. 10 mm at minimum for
2006–2007). In the surrounding of the calibrated (kLAI,
fLAI) values, the modeled SWE has furthermore a reduced
sensitivity to variations in kLAI and fLAI. This result
enhances our confidence in the model robustness.
Model performance after calibration over 2003–2007.
Calibration over 2003–2007
Model
Best-fit
Results over
Results over
version
parameter
2003–2004
2003–2007
RMSE LW
MB LW
RMSE SW
MB SW
CC
RMSE LW
MB LW
RMSE SW
MB SW
CC
1LnoHM
kLAI=0.75
13.4
-2.4
9.4
-0.9
26.2
17.2
-9.1
9.0
0.2
27.3
1LHM
kLAI=0.85
11.4
-1.7
9.8
-1.8
24.8
14.2
-9.8
9.2
-0.5
33.8
2LHM
kLAI=0.85
8.2
0.3
9.8
-1.8
18.7
9.1
-5.8
9.2
-0.6
24.8
fLAI=0.5
The performance of all model versions after calibration over 2003–2004
slightly degrades over the longer 2003–2007 time period when observations
are available. Especially the MB in LW↓BC, and (to a
smaller degree) in SW↓BC, are increased over 2003–2007,
questioning the transferability of our 2003–2004 calibration. We therefore
calibrate the 1LnoHM, 1LHM, and 2LHM versions over the 2003–2007 period and
analyze the changes in best-fit parameters and performance (Table 4).
The calibration over 2003–2007 yields a slightly different best-fit
parameter value for the extinction coefficient in the 1LHM and 2LHM versions
(kLAI=0.85 vs. kLAI=0.75 when calibrated over
2003–2004): this enhanced radiation extinction improves the MB for
SW↓BC over the 2003–2007 period, but slightly degrades
the results over 2003–2004. The overall picture is however not changed after
this new calibration:
Over both periods, 2LHM performs better than 1LHM which also performs
better than 1LnoHM: this is an indication of the added value of our new
parameterizations.
For all model versions, performance is better over 2003–2004 than over
the full 2003–2007 period, especially for LW↓BC. This
may indicate that our model is still too simple to capture the full range of
snow–forest processes.
Over both periods, the two, slightly different calibrations yield
thoroughly comparable model performances. This gives confidence in the
validity of our calibration and in the possibility of calibrating the model
over only 1 year of data.
In the simulations discussed in the rest of the paper, calibration over
2003–2007 is used.
Model evaluation against thermal radiation
In Fig. 3 are compared observed and modeled LW↓BC as
computed by the different model versions without heat mass optimization
(1LnoHM, 1LHM, 2LHM) over 2003–2004. Similarly to the performance metrics of
Table 3, this figure illustrates gradually increasing model performances from
the 1LnoHM to the 2LHM model versions.
LW↓BC and SWE as represented by the
different model versions over the calibration period; (a, b) subsets of
daily cycles; (c) 24 h running means over the calibration period; (d) SWE.
![]()
With respect to 1LnoHM, the consideration of tree heat mass in 1LHM slightly
delays and reduces the canopy cooling at night and warming up in the morning:
this translates into a slight delay and smoothing of the diurnal cycle of
LW↓BC, part of which originates from canopy thermal
emission.
More striking, however, is the attenuation of the daily amplitude of
LW↓BC induced by 2LHM, which brings the modeling
results in closer agreement to observations: especially, the nighttime
(18:00–06:00 LT) mean bias in LW↓BC is considerably
reduced in 2LHM with respect to other model versions, amounting to -10.8,
-7.8, and -2.8 W m-2 in 1LnoHM, 1LHm and 2LHM respectively.
When only one bulk layer of canopy is considered, this layer is exposed at
night to intense radiative cooling towards the sky, whose thermal emissivity
is low. With two layers of canopy, only the uppermost layer experiences this
uncompensated cooling. The lower layer receives thermal radiation from the
upper layer which has a higher emissivity than the sky. This thermal
sheltering yields higher temperature and LW emission at night from the lower
canopy towards the ground surface. This mechanism proves to efficiently
reproduce the daily cycles (Fig. 3a, b) and daily averages (Fig. 3c) of the
thermal radiation affecting the snowpack.
Impact on the underlying snowpack
Over the four winters of interest here, a similar ranking of sub-canopy SWE
modeled by 1LnoHM, 1LHM, and 2LHM is observed, with 1LHM accumulating more
snow and 2LHM generally featuring the smallest SWE (except for the 2005–2006
winter; Figs. 3c and 4). With respect to the thermal behaviors of the
different model versions, such a result is somehow counterintuitive as 1LHM
and 2LHM generally deliver greater amounts of LW radiation to the snowpack
than does 1LnoHM (Fig. 3c.), hence contributing more energy to mid-winter
ablation events (e.g., Fig. 3d, December to January). In 1LHM, this increased
ablation is, however, compensated by a side effect of the thermal canopy
mass: as a result of the high thermal mass of the bulk canopy in 1LHM, the
canopy temperature and hence interception evaporation is reduced, and more
snow unloads than in the two other versions, resulting in higher sub-canopy
snow accumulation. In 2LHM, the high diurnal temperature variations of the
upper canopy temperature combine with stronger LW radiation to the snowpack,
resulting in a thinner snowpack.
Sub-canopy SWE at Alptal over 2004–2007.
![]()
Noteworthy, the model ability to represent SWE (as typically assessed by the
RMSE to observations) is degraded in 1LHM and improved in 2LHM with respect
to the original canopy module 1LnoHM. Hence, the LW-enhanced ablation in 2LHM (and
small associated changes in interception evaporation) does not
deteriorate the overall model skills.
In some specific ablation periods, 2LHM also proves to reproduce the observed
snowpack dynamics better: one such event is the early February 2004 severe
ablation, when high thermal exposure of the snowpack is better reproduced by
2LHM (Fig. 3c) while the concomitant ablation is also stronger in 2LHM, which
matches the observations better (Fig. 3d). Similarly, the LW-enhanced
ablation in 2LHM leads to a sub-canopy SWE dynamics in closer agreement with
observations in the 2005 ablation phase and in early 2007 (mid-winter
complete snow disappearance).
As mentioned in the methods, we do not trust the modeling of the
accumulation phases, where high uncertainties in precipitation phase and
interception (enhanced by the warm temperatures at Alptal) can initiate a
permanent bias in the modeled snow cover. Therefore, we do not use observed
SWE records to validate or evaluate our model. However, the capability of a
model to better reproduce observed, relative ablation events when
precipitations are absent (like in the 2005 main ablation phase) reliably
means enhanced performances: our results are therefore encouraging for the
overall consistency of the 2LHM canopy module.
Comparison between observed pine trunk
temperature at 1.5 m height, 1 cm deep into the trunk, and modeled canopy
temperatures: bulk canopy temperature for 1LnoHM and 1LHM, lowermost
canopy-layer temperature for 2LHM.
![]()
Norunda: tree temperature and biomass<?xmltex \hack{\break}?> storage flux
At the Norunda site, SNOWPACK is run using the Alptal calibration from
2003 to 2007, and a canopy basal area and areal heat mass derived from local
data (Sect. 3). The difference in latitudes (hence in solar angle), tree
species (mostly Scots Pine at Norunda), and context (Alpine winter vs. boreal
summer) between both sites constitutes a huge challenge and an excellent
benchmark to test one desired feature of a physically based model, e.g., its
transferability to different climate and ecosystem types. We here specify
that SNOWPACK includes all the necessary features to be used as a
soil–vegetation–atmosphere transfer (SVAT) model in the absence of a snow
cover: a soil water balance, a surface and canopy energy balance, and a
temperature diffusion scheme in the soil. The model has also been used as
such in continuous multi-year simulations in previous studies (e.g., Bavay et
al., 2013).
We compare observed tree trunk temperature to modeled temperature of the
bulk canopy (for 1LnoHM and 1LHM) or of the lower trunk layer (for 2LHM) over
summer 1995 at Norunda (Fig. 5; Table 5). The modeled trunk-layer
temperature of 2LHM shows an improved ability to reproduce the observed tree
trunk temperature signal: similar to the improvements seen at Alptal,
radiative loss of energy from the lower layer at night is considerably
reduced with 2LHM, bringing nighttime modeled temperature in closer
agreement to observed data at Norunda. Also, the reduced SW insolation
received by the lower canopy layer during daytime in 2LHM prevents too high
midday temperature of the trunks, an observation that 1LHM and 1LnoHM cannot
reproduce. Finally, the combination of thermal sheltering of the lowermost
canopy layer and its thermal inertia delays the tree trunk cooling (warming) at evening (morning) times, improving the temporal correlation
with observations.
Statistics of model evaluation at
Norunda; “corr” is the correlation coefficient. The mean
modeled and observed biomass (and biomass + air) heat fluxes are null over
a period between two equal thermal states.
Biomass + air
Field
Trunk temperature
Biomass heat
heat storage
data
at 1.5 m (K)
flux (W m-2)
flux (W m-2)
Model
version
MB
RMSE
corr
RMSE
corr
RMSE
corr
1LnoHM
-0.41
1.7
0.88
16.3
0.
24.2
0.
1LHM
-0.05
1.6
0.92
24.5
0.79
18.9
0.86
2LHM
0.05
1.1
0.96
15.7
0.88
11.3
0.92
Heat fluxes to canopy elements are a substantial, though not dominant,
component of the canopy energy balance (Lindroth et al., 2010, their Fig. 6):
they can amount to ∼ 7 % of the daily net radiation received by the
canopy. To assess the consistency of the SNOWPACK canopy module, we compare
the modeled canopy heat fluxes to the ones derived by Lindroth et al. (2010)
from field measurements and extrapolated at the stand scale. Note that
1LnoHM, having no heat mass, does not consider any such fluxes.
Both the 1LHM and 2LHM versions overestimate the daily amplitude of biomass
heat fluxes with respect to observations, with an increased bias for 1LHM
(Fig. 6; Table 5). This is in line with an overestimation of the daily
amplitude of canopy temperature (or of the temperature of the lower canopy
layer for 2LHM) which is stronger with 1LHM (Fig. 5). Also, the model biomass
heat fluxes peak ∼ 2 h earlier than the observed ones. We interpret
this as an artifact of modeling the canopy with only one or two thermally
homogeneous layers, whereas it is in reality a continuous medium experiencing
thermal diffusion at scales smaller than our layers. In reality, the low
thermal inertia of a bark surface layer provokes quick surface heating as a
result of solar energy input (e.g., in the morning). This temporarily limits
further heating from turbulent and radiative fluxes, until the surface heat
has diffused into the trunk. In other words, heat uptake by trunks is
diffusion limited. Contrarily, the bulk, thermally inert trunk layer of our
model heats up to a smaller temperature because the heat flux is accommodated
by the whole layer and not only by its uppermost surface: further heating by
turbulent and radiative fluxes is then still possible and the heat flux
towards the biomass keeps being sustained. As a result, our modeled canopy
accommodates incoming energy more rapidly than a real one during the first
part of the diurnal cycle. The aforementioned mechanism can also cause the
accommodation of more heat energy by the modeled trunk layer than in
reality: in reality, the capacity of the canopy to accommodate heat is
limited by thermal diffusion within the wood. Heat uptake stops when
available solar energy starts going down. At that time, the wooden medium may
not have reached an homogeneous, high temperature yet (e.g., Fig. 1 from
Lindroth et al., 2010).
Comparison between biomass (and biomass + air) storage
fluxes inferred from observations (obs) and biomass fluxes modeled by the
different SNOWPACK versions (model) at Norunda.
![]()
As such, the representation of the biomass storage fluxes by 1LHM and 2LHM
yield only a moderate improvement to the model: they feature a reasonable
(though slightly shifted) diurnal cycle (cf. the correlation coefficients in
Table 5) but their RMSE to observations is on the order of magnitude of the
standard deviation of the observed biomass fluxes (Table 5, first row).
However, model performance, especially for 2LHM, is improved if the total
heat-storage flux towards the biomass and canopy air space is considered
(thick black line in Fig. 6; Table 5). The air heat-storage flux corresponds
to the changes in latent and sensible heat stored in the within-canopy air
space. Lindroth et al. (2010) provided estimates of these heat storage terms
based on air temperature and humidity measurements at seven heights within the
canopy air space. On a daily basis, the air heat-storage term reacts more
rapidly to solar heating than the biomass heat-storage flux. The air heat-storage flux is not specifically accounted for in SNOWPACK. However, the
increased correlation coefficient and reduced RMSE, obtained when the SNOWPACK
canopy heat flux is compared to the sum of estimated air and biomass heat
fluxes, indicate that the canopy module produces a bulk representation of the
observed fluxes. Such a result should be confirmed against further
observational data sets.
Discussion
Our results show that the new features implemented in the SNOWPACK canopy
module, especially the two-layer scheme, improve the representation of the
radiation budget at the sub-canopy level. The importance of accounting for
the canopy temperature and for contrasts between different canopy elements
has often been underlined (Sicart et al., 2004; Pomeroy et al., 2009).
Pomeroy et al. (2009) compared three sub-canopy thermal irradiance models
based on measurements of (i) air temperature only; (ii) air, trunk and
needles temperatures; and (iii) air temperature and empirical
shortwave–long-wave conversion function by the canopy. The two latter
formulations exhibited distinctively better performances than the first one
in terms of mean bias and RMSE in both the uniform and discontinuous stands
investigated. Our present work confirms these findings also propose a
seamless physics-based canopy model to account for this effect. This has to
our knowledge never been brought to the scientific literature.
Radiation can be an important driver of the springtime sub-canopy snow
energy balance and subsequent melt. Garvelmann et al. (2014) reported a
contribution of about 50 % from the net long-wave radiation to the
sub-canopy energy balance during two cloudy-sky rain-on-snow events closely
monitored in the Black Forest, Germany. In open environments the long-wave
contribution to the surface energy balance does not exceed 20 % for the
same meteorological conditions, and is at times negative. According to
Lundquist et al. (2013), forest regions with average
December–January–February (DJF) temperatures greater than -1 ∘C
experience 1 to 2 weeks reduction in snow-cover duration compared to adjacent
open areas because of increasing long-wave radiation from the canopies. There,
the sub-canopy snowpack is mostly impacted during mid-winter warm events,
when the long-wave enhancement by the canopy dominates over the shadowing from
shortwave radiations. This is precisely the situation observed at Alptal,
where mean DJF temperature is about 1.5 ∘C (1975–2005), and our
improved canopy module with more realistic thermal heating from the canopy
yields a better reproduction of the two mid-winter ablation events from
2004 to 2005 and 2006 to 2007. In that sense our work contributes an enhanced
capability to model sub-canopy melt conditions that can jointly benefit water
and forest management (Lawler and Link, 2011; Ellis et al., 2013).
In line with Rutter et al. (2009), Essery et al. (2008), and many others, we
agree that the mass balance of snow is most relevant when it comes to snow
hydrological applications or to the assessment of snow hazards. In the
forest, snow interception and subsequent sublimation of intercepted snow
majorly affects the sub-canopy mass balance; reductions up to 60 % for
sub-canopy snowfall have been reported as a result of these processes (Hardy
et al., 1997). Radiation, as the main driver of the melt, shapes the
end-of-season snow mass balance, but the latter also critically depends on
peak accumulation from the accumulation phase which our developments barely
touch. We see our contribution as a necessary step in a sequential,
multi-directional development and validation process, whereby the careful and
independent validation of each component of the snow model will gradually
improve its skills; SNOWPACK, now equipped with a more reliable and
sophisticated radiative transfer scheme for the canopy, diagnosing flaws
originating from other processes (mixed-precipitations, rain-on-snow events,
or misrepresented canopy interception), should be easier. Promising work has
just been published very recently as to new ways to parameterize canopy
interception in alpine forests (Moeser et al., 2015). The proposed
methodology should later serve the improvement of snow models like SNOWPACK
in aspects of crucial interest for the snow mass balance.
Other physical processes could further improve SNOWPACK, in the present
version the within-canopy air humidity is equal to the above-canopy one,
while Durot (1999) show a 10 to 20 % increase in within-canopy air
humidity in spring, with peaks during unloading. This should impact the
modeled sub-canopy turbulent and radiative fluxes. Also, the reduction of
albedo as a result of canopy debris should be considered, though tests
performed at Alptal did not show much change upon a specific parameterization
of sub-canopy snow aging.
Further wintertime assessment of model performance in colder, controlled
environments, where mixed-precipitation events are scarce but radiation play
an important role, would help confirm the added value of our new canopy
formulation for the representation of sub-canopy snow dynamics. Data from
the SnowMIP sites could be used for that purpose provided they are combined
with site knowledge and expertise, and ancillary data that help fit
important model parameters to the local canopy conditions (interception,
radiation extinction).
SNOWPACK has a multi-layer and detailed representation of snow and soil,
which features a highly resolved modeling of energy and mass balance in thin
layers including, e.g., snow metamorphism and freezing point depressions during
phase change in the soil (Wever et al., 2014). This detailed and
physics-based description should have a corresponding representation of
canopy processes, which has not been the case in earlier versions of
SNOWPACK. The more detailed model described in this contribution is therefore
a consistent extension of SNOWPACK and leads to an overall more balanced
representation of processes in the air–canopy–snow–soil continuum. A
physics-based, integrated modeling chain featuring such level of homogeneity
and detail is rare. Sivapalan et al. (2003) and Rutter et al. (2009)
underlined that such process-based model (rather than calibrated parametric
models) offer the best possibility to address the current hydrological and
ecosystemic challenges related to snow in a manner that ensures
site transferability and robustness with respect to changing climate. The new
version of SNOWPACK with the two-layer canopy module builds a sound basis for
such investigations. The current two-layer formulation of the canopy is also
a suitable basis for a future model adaptation to deciduous forest
environments.
Our two-layer canopy model exhibits robustness in two ways:
First, it shows little sensitivity to physical parameters that are hard to
assess from standard forestry metrics or for non-investigated forests. The
canopy heat mass is one of such parameters, as stated in Sect. 4. The other
one is the fraction of LAI attributed to the top-most (“leafy”) canopy
layer, as illustrated in Fig. 7. The ratio of woody to total plant area is
hard to measure optically, especially for evergreen canopies (Weiss et al.,
2004). Pomeroy et al. (2009) used a formulation somewhat similar to ours to
attribute LW radiation to emission from leafy or woody elements. They
conclude that, depending on the forest structure and type, the needle-branch
fraction as seen from a ground observer would range from 0.6 to 0.75 of the
total plant elements. Our Alptal calibration attributing 50 % of canopy
LAI to the upper “leafy” layer is consistent with this model-based estimate
for leaves and branches.
Second, the model exhibits a good performance at the Norunda site, while
its free parameters (kLAI and fLAI) have been calibrated
in a different forest ecosystem and climatic context at Alptal. In both
forests, coniferous species are dominant and it is suspected that
extrapolation of our parameterizations to deciduous forests requires further
adaptation. However, our results give confidence in the possibility of using
our physics-based model without prior tuning in different alpine and
sub-arctic catchments majorly covered by conifers.
Finally, it is a quite general finding that two-layer formulations of
physical continuums often bring substantial improvements over single-layer
ones. The step from big-leaf soil–vegetation–atmosphere transfer models to
dual-source models (e.g., Blyth et al., 1999; Bewley et al., 2010) is a
typical illustration of this phenomenon for the computation of the land
surface energy balance. Similarly, Dai et al. (2004) improved their modeling
of forest CO2 absorption by considering different regimes for sunlit and
shaded leaves. Our results here are in line with this more general
observation.
Sensitivity of model performance over 2003–2007 (with
kLAI=0.85) to fLAI. The MB and RMSE are for the variables
SW↓BC (SW in the legend) and LW↓BC (LW
in the legend).
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