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Geosci. Model Dev., 9, 633–646, 2016
www.geosci-model-dev.net/9/633/2016/
doi:10.5194/gmd-9-633-2016
© Author(s) 2016. CC Attribution 3.0 License.
ESCIMO.spread (v2): parameterization of a spreadsheet-based
energy balance snow model for inside-canopy conditions
T. Marke1, E. Mair1, K. Förster1,3, F. Hanzer1,3, J. Garvelmann2, S. Pohl4, M. Warscher2, and U. Strasser1
1Institute of Geography, University of Innsbruck, Innsbruck, Austria
2Institute of Meteorology and Climate Research (IMK-IFU), Karlsruhe Institute of Technology (KIT),
Garmisch-Partenkirchen, Germany
3alpS – Centre for Climate Change Adaptation, Innsbruck, Austria
4Hydrology Department, University of Freiburg, Freiburg, Germany
Correspondence to: T. Marke (thomas.marke@uibk.ac.at)
Received: 30 June 2015 – Published in Geosci. Model Dev. Discuss.: 25 September 2015
Revised: 19 January 2016 – Accepted: 20 January 2016 – Published: 16 February 2016
Abstract. This article describes the extension of the ES-
CIMO.spread spreadsheet-based point energy balance snow
model by (i) an advanced approach for precipitation phase
detection, (ii) a method for cold content and liquid water
storage consideration and (iii) a canopy sub-model that al-
lows the quantification of canopy effects on the meteorolog-
ical conditions inside the forest as well as the simulation of
snow accumulation and ablation inside a forest stand. To pro-
vide the data for model application and evaluation, innova-
tive low-cost snow monitoring systems (SnoMoS) have been
utilized that allow the collection of important meteorologi-
cal and snow information inside and outside the canopy. The
model performance with respect to both, the modification of
meteorological conditions as well as the subsequent calcula-
tion of the snow cover evolution, are evaluated using inside-
and outside-canopy observations of meteorological variables
and snow cover evolution as provided by a pair of SnoMoS
for a site in the Black Forest mountain range (southwestern
Germany). The validation results for the simulated snow wa-
ter equivalent with Nash–Sutcliffe model efficiency values
of 0.81 and 0.71 and root mean square errors of 8.26 and
18.07mm indicate a good overall model performance inside
and outside the forest canopy, respectively. The newly de-
veloped version of the model referred to as ESCIMO.spread
(v2) is provided free of charge together with 1 year of sam-
ple data including the meteorological data and snow obser-
vations used in this study.
1 Introduction
In forested areas significant variations in snow accumula-
tion can result from the processes of forest canopy inter-
ception and sublimation of intercepted snow (Marsh, 1999;
Pomeroy et al., 1998). Snowfall in forested areas is either in-
tercepted by stems, needles and branches or passes through
the canopy,directly reaching the underlying forest floor. Due
to its large surface area exposed to the surrounding atmo-
sphere, intercepted snow can be subject to high sublimation
losses, especially in dry continental climates. Generally, sub-
limation losses of previously intercepted snow can be as high
as 30% of snow precipitation, depending on the efficiency
of interception, its duration and the atmospheric boundary
conditions (Liston and Elder, 2006b; Pomeroy and Gray,
1995; Strasser et al., 2008). Intercepted snow can also be re-
moved from the canopy by direct unloading and dripping of
meltwater to the ground (Liston and Elder, 2006b; Pomeroy
et al., 2002). Compared to snow in the open, snow in forest
canopies is exposed to different meteorological conditions.
It is sheltered from wind and incoming shortwave radiation
while receiving increased longwave radiation emitted from
the surrounding trees (Link and Marks, 1999a, b). Likewise,
humidity and temperature underneath a canopy differ from
those in the open (Liston and Elder, 2006b). In the bound-
ary layer, forest canopies moreover strongly modify the inter-
actions between snow-covered surfaces and the atmosphere.
Even the litter on the forest floor has a significant effect on
Published by Copernicus Publications on behalf of the European Geosciences Union.
634 T. Marke et al.: A spreadsheet-based snow model for inside-canopy conditions
the radiative properties of the snow cover beneath a canopy
(Melloh et al., 2002; Hardy et al., 2001).
The influences of a forest canopy on the snow cover dy-
namics beneath are very complex. The snow cover dura-
tion in the forest depends on various factors. A delay of the
spring snowmelt under a dense forest canopy compared to
open areas due to the reduction of incoming solar radiation
was shown by Link and Marks (1999a). On the other hand,
shorter snowpack duration in the forest was observed by
Dickerson-Lange et al. (2015). Strasser et al. (2011) showed
in a numerical modeling experiment for a virtual mountain
that in snow-rich winters, the shadowing and its protective
effect are dominant. In winters with little snow, snow subli-
mation losses become dominant and, consequently, the snow
lasts longer in the open than inside the forest, mainly for
northern exposures (in the Northern Hemisphere). Similar
patterns were observed by Pohl et al. (2014) in the Black
Forest region.
To develop a free and easy-to-use tool for the simulation of
the temporal evolution of the snow cover with explicit con-
sideration of these complex snow–canopy–atmosphere in-
teractions, the ESCIMO.spread spreadsheet-based point en-
ergy balance snow model developed by Strasser and Marke
(2010) (in the following referred to as ESCIMO.spread (v1))
has been extended with a canopy sub-model. Moreover, the
model has been improved by integrating an advanced algo-
rithm for precipitation phase detection that applies wet-bulb
temperature as a criterion to distinguish solid and liquid pre-
cipitation. Another model improvement is a new parameter-
ization for cold and liquid water content of the snow cover
allowing the consideration of refreezing of liquid precipita-
tion or meltwater in the snowpack. Compared to other ex-
isting spreadsheet-based snow models (e.g., the glacier and
snowmelt study model by Brock and Arnold, 2000), ES-
CIMO.spread (v2) is particularly fast and can easily be mod-
ified by a simple change of the parameters and formulae
with results immediately visualized. With hourly recordings
of temperature, precipitation, wind speed, relative humidity
and global as well as longwave radiation, the model’s de-
mand on meteorological input is covered by those variables
most commonly recorded at any state-of-the-art automatic
weather station. While Walter et al. (2005) have presented
a spreadsheet energy balance model that requires even fewer
meteorological input data (daily minimum/maximum tem-
perature and precipitation), their approach operates at a daily
time step only and does not allow a quantification of sub-
daily variations in snow cover conditions. Moreover, com-
pared to the canopy model implemented in ESCIMO.spread
(v2), the consideration of canopy effects in the Walter et al.
(2005) model is reduced to a canopy-induced extinction of
solar radiation only. Canopy effects on other meteorolog-
ical variables or vegetation–snow cover interactions (e.g.,
the interception of snow in the canopy) are not accounted
for. By providing the option to define trends in precipitation
and/or temperature in the model’s parameter section, ES-
CIMO.spread allows the calculation of sensitivity tests for
changes in temperature and precipitation for any site of in-
terest. As ESCIMO.spread (v2) is in simple table format and
does not include any macros, it can be applied by all common
spreadsheet programs (e.g., Microsoft Excel, Apple Num-
bers, OpenOffice Calc) on a variety of platforms (Windows,
Linux, Mac OS). Due to its simplicity, ESCIMO.spread (v2)
is particularly suitable for application in education (e.g., in
practically oriented student courses) and can even be oper-
ated with laptop computers, e.g., to visualize and make plau-
sible measured meteorological parameters and the simulated
snow cover directly in the field.
With its new features of
–sophisticated precipitation phase detection using a wet-
bulb temperature threshold,
–snow temperature estimation,
–cold content and liquid water content calculation with
consideration of refreezing of water from melt or liquid
precipitation, and meltwater outflow,
–transformation of standard meteorological observations
(precipitation, relative humidity, temperature, wind
speed, global radiation) from the open into conditions
inside a forest canopy,
–calculation of snow interception and subsequent sub-
limation, melt or dropping of intercepted snow to the
ground, and
–calculation of the beneath-canopy snow energy and
mass balance,
the new version ESCIMO.spread (v2) reaches beyond
the capabilities of most other freely available point-scale
spreadsheet-based snow models and can be expected to set
forth the history of ESCIMO.spread as a well-accepted, doc-
umented and freely available snow model for application
in both science and education. This paper describes the
newly implemented algorithms and evaluates the model re-
sults against available hydrometeorological observations in-
side and outside the forest canopy at a site in the Black For-
est mountain range (southwestern Germany; see Fig. 1) with
a mostly temperate snow cover at an elevation of 800ma.s.l.
The applied hydrometeorological data have been recorded
by a set of low-cost snow monitoring systems (SnoMoS) re-
cently developed by Pohl et al. (2014). The model can be
downloaded from www.alpinehydroclimatology.net together
with 1 year of example meteorological recordings and snow
observations.
Geosci. Model Dev., 9, 633–646, 2016 www.geosci-model-dev.net/9/633/2016/
T. Marke et al.: A spreadsheet-based snow model for inside-canopy conditions 635
Figure 1. The Vordersteinwald site in the Black Forest mountain
range (southwestern Germany, 800ma.s.l.).
2 The ESCIMO.spread model (v2)
2.1 General description
The new version of ESCIMO.spread (v2) builds upon the
ESCIMO.spread model as published by Strasser and Marke
(2010). It is a 1-D, one-layer process model that calculates
snow accumulation and melt for a snow cover assumed to
be a single and homogeneous pack. To do so, it solves
the energy and mass balance equations for the snow sur-
face applying simple parameterizations of the relevant pro-
cesses. The energy balance of the snow surface is calcu-
lated for each hourly time step considering shortwave and
longwave radiation, sensible and latent heat fluxes, energy
conducted by solid or liquid precipitation, as well as subli-
mation/resublimation and a constant soil heat flux (Strasser
and Marke, 2010). Thereby, absorbed and reflected short-
wave radiation is calculated from incoming shortwave radi-
ation on the basis of the snow albedo, which is estimated
for each hourly time step using an albedo ageing curve ap-
proach. Solid precipitation increases the amount of snow wa-
ter equivalent (SWE) on the land surface, while liquid precip-
itation is (up to a certain maximum amount depending on ac-
Solid precipitation
Liquid precipitation
Figure 2. Relation between air temperature, wet-bulb temperature
and relative humidity at different altitudes. The latter represent dif-
ferent air pressure levels derived using the hydrostatic equation. The
colored lines can be interpreted as borderlines to separate liquid and
solid precipitation assuming a certain threshold wet-bulb tempera-
ture.
tual SWE) added to the liquid water storage of the snowpack.
While melt in ESCIMO.spread (v1) has been calculated from
the energy balance remainder only if air temperature exceeds
273.16K, the newly implemented method for snow temper-
ature estimation (see Sect. 2.3) allows the removal of this
condition in ESCIMO.spread (v2). The model results are vi-
sualized in the form of diagrams for the majority of model
variables, together with four quantitative measures of good-
ness of fit.
2.2 Precipitation phase detection
The new version of ESCIMO.spread (v2) includes an im-
proved distinction between liquid and solid precipitation. As
air temperature Tais often an insufficient indicator of the
precipitation water phase (Steinacker, 1983), wet-bulb tem-
perature Twis used in ESCIMO.spread (v2) as a combined
measure of air temperature and humidity to distinguish liq-
uid from solid precipitation. Figure 2 shows the relation be-
tween air temperature, wet-bulb temperature and relative hu-
midity for different altitudes to account for the dependence of
wet-bulb temperature on air pressure. Each of the displayed
lines in Fig. 2 could be interpreted as a borderline to sepa-
rate liquid and solid precipitation assuming a certain thresh-
old wet-bulb temperature. The largest differences between
air temperature and wet-bulb temperature occur at low air
humidities, clearly pronouncing the added value associated
with application of wet-bulb temperature as a criterion for
phase detection.
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636 T. Marke et al.: A spreadsheet-based snow model for inside-canopy conditions
Generally, wet-bulb temperature can be derived by solving
the psychrometric equation
ea(Ta)−es(Tw)−A·(Ta−Tw)=0 (1)
for Tw(K), where A(PaK−1) is the psychrometric constant,
and ea(Tw)(Pa) and es(Tw)(Pa) the vapor pressure of the air
and the saturation vapor pressure at wet-bulb temperature,
respectively. As there is no explicit solution to the psychro-
metric equation (Campbell and Norman, 1998) and iterations
are unfavorable in a spreadsheet model, a pragmatic assump-
tion has been made: for a broad range of combinations of
air temperature and relative humidity values, lookup tables
have been generated outside the spreadsheet model using an
iterative solution scheme for Eq. (1). Beside temperature and
humidity, wet-bulb temperature also depends on air pressure
pz(Pa) that is required to calculate the psychrometric con-
stant, A, as (Kraus, 2004)
A=pz·cp
0.622·Lv,(2)
where cpis the specific heat capacity of air at constant pres-
sure (1004Jkg−1K−1) and Lv(Jkg−1) represents the latent
heat of vaporization. In ESCIMO.spread (v2) the tempera-
ture dependence of the psychrometric constant is neglected
since this dependency is by far less important compared to
that associated with air pressure at higher altitudes (Kraus,
2004; Campbell and Norman, 1998). Air pressure, p(Pa), at
a given elevation, z(m), can be derived from standard atmo-
spheric pressure, p0(Pa), by integration of the hydrostatic
equation assuming a linear decrease in temperature with in-
creasing altitude (γ= −0.0065Km−1)
pz=p0Ta
Ta−γ·z−g
γ·R
,(3)
where Ris the gas constant of dry air (287Jkg−1K−1) and
gis gravity (ms−2). To account for the air pressure depen-
dence, the implemented lookup tables have been prepared for
several elevation bands with a 500 m interval. Figure 3 shows
a comparison of wet-bulb temperatures calculated using the
lookup table approach to those achieved with an iterative so-
lution for different elevations. The differences between both
approaches shown for a common snowfall situation are rel-
atively small. Therefore, the lookup table approach allows
a sufficiently accurate estimation of wet-bulb temperature
in the model. The threshold for wet-bulb temperature as re-
quired for precipitation phase detection in ESCIMO.spread
(v2) is one of the user-defined input parameters and is here
set to 273.16K. To avoid sudden changes in precipitation
phase when temperatures fall below the defined temperature
threshold, in ESCIMO.spread (v2) a temperature range can
be defined (e.g., 273.16±0.5K) in which liquid precipita-
tion decreases from 100 to 0% with solid precipitation in-
creasing accordingly. When temperature is exactly at the de-
fined temperature threshold (here 273.16K), this approach
results in 50% liquid and 50% solid precipitation.
Figure 3. Comparison of iteratively calculated wet-bulb tempera-
ture to the results of the lookup table approach implemented in ES-
CIMO.spread (v2).
2.3 Cold and liquid water content
A physically based method for estimating the snow tempera-
ture and deriving the cold content of a single-layer snowpack
has been implemented in ESCIMO.spread (v2) following an
approach presented by Walter et al. (2005). The snow tem-
perature Ts(K) for a given time step is derived using the snow
temperature calculated for the previous time step, Tst−1(K),
and a temperature change dT(K) as
Ts=min{Tst−1+dT , 273.16}.(4)
The temperature change in Eq. (4) is derived as
dT=Et−1·dt+RFt−1·ci
(SWEt−1+Ps)·cs,(5)
where Et−1(Wm−2) is the energy balance of the previous
time step, dt(s) is the time step length, RFt−1(mm) is the liq-
uid water refrozen in the previous time step, ciis the melting
heat of ice (3.337×105Jkg−1), SWEt−1(mm) is the SWE
of the previous time step, Ps(mm) is the solid precipitation
in the current time step and csis the specific heat of snow
(2100Jkg−1K−1).
Using this approach, heat losses resulting from a negative
energy balance can be used to build up a cold content, which
represents the amount of energy required to increase snow
temperature to 273.16K. Snow temperature and cold con-
tent can be considered as equivalent and physically consistent
representations of the snowpack’s energy state as defined by
Eq. (6). The cold content first needs to be reduced to zero
by positive energy inputs before actual melt can occur. By
implementing a concept for liquid water content as proposed
by Braun (1984) and Blöschl and Kirnbauer (1991), melting
snow is not immediately removed from the snowpack, but
Geosci. Model Dev., 9, 633–646, 2016 www.geosci-model-dev.net/9/633/2016/
T. Marke et al.: A spreadsheet-based snow model for inside-canopy conditions 637
a certain amount of liquid water can be retained (and pos-
sibly refreeze again). Combining these approaches for cold
content estimation and liquid water content accounts for the
delay between beginning surface melt and drainage of a snow
cover.
The cold content Cc(mm) for each model time step is in-
ferred directly from calculated snow temperature in the form
of
Cc=(Ts−273.16)·(SWEt−1+Ps)·cs
ci.(6)
In the case of a negative energy balance, a refreezing of
liquid water in the snowpack, RF (mm), is calculated in the
form of
RF =min{Clwt−1, (−E·dt )/ci},(7)
where Clwt−1(mm) is the liquid water content of the previous
time step. Clw for a given time step can be derived as
Clw =Clwt−1+Pl−RF,(8)
where Pl(mm) is liquid precipitation.
In the case of a positive energy balance, actual melt, M
(mm), is calculated considering the change in cold content
between the current and previous time step as
M=min{(E ·dt /ci)−(Cc−Cct−1),
(SWEt−1−Cct−1)}.(9)
Clw is then updated in the form of
Clw =min{Clwt−1+M, SWEt−1·HCw},(10)
where HCw(−)is a water holding capacity that limits liquid
water storage and is specified as a fraction of the total snow-
pack weight. This parameter is to be defined by the user in
the model’s parameter section and set to HCw=0.1 as rec-
ommended by Blöschl and Kirnbauer (1991) by default.
Finally, the outflow (i.e., the excess water that is actually
removed from the snowpack), O(mm), can be calculated as
O=max{(Clwt−1+Pl+M)−SWEt−1·HCw,0}.(11)
2.4 Modification of meteorological conditions inside
the forest canopy
The canopy model newly implemented in ESCIMO.spread
(v2) by Liston and Elder (2006b) has already been success-
fully applied under alpine conditions (see Strasser, 2008, or
Strasser et al., 2011). The development of the approach was
motivated by the fact that meteorological observations inside
forest canopies only sparsely exist, necessitating the estima-
tion of inside-canopy conditions from available meteorolog-
ical observations in the open. The method requires informa-
tion on leaf area index and canopy height that can either be
derived from field measurements or be taken from the litera-
ture for a wide range of plant species (e.g., from Breuer et al.,
2003, or Liston and Elder, 2006b).
Wind speed inside the canopy uc(ms−1) is derived from
above-canopy wind speed u(ms−1) as (Cionco, 1978)
uc=uexp(−a·(1−z/h)), (12)
where h(m) is the canopy height and z(m) is the canopy
reference level assumed to be 0.6h (Liston and Elder, 2006b;
Essery et al., 2003).
The canopy flow index, a (−), is calculated as a function
of the effective leaf area index LAI∗(m2m−2) and a scal-
ing factor, β(=0.9), that is introduced by Liston and Elder
(2006b) to make LAI∗compatible with the canopy flow in-
dex proposed by Cionco (1978):
a=LAI∗·β. (13)
LAI∗includes stems, leaves and branches as described by
Chen et al. (1997).
To consider the extinction of solar radiation by the forest
canopy, top-of-canopy incoming shortwave radiation, Qsi, is
reduced following the Beer–Lambert law as
Qsif =Qsi ·τv,(14)
where Qsif is the incoming shortwave radiation impinging
on the snow surface beneath the canopy (Hellström, 2001).
τvrepresenting the fraction of Qsi reaching the land surface
is derived as
τv=exp(−k·LAI∗), (15)
with kbeing a vegetation-dependent extinction coefficient
(Liston and Elder, 2006b). Aiming at a best fit to observed
radiation inside forest canopies of different species (e.g.,
spruce, subalpine fir, pine) at a site in the U.S. Department of
Agriculture (USDA) Fraser Experimental Forest near Fraser
(Colorado, USA), Liston and Elder (2006b) have yielded the
best overall performance using a kvalue of 0.71, which is
also used for the simulations here.
Incoming longwave radiation inside the canopy is assumed
to be composed of a fraction Fg(−)directly reaching the
ground through gaps in the forest stand and a fraction Fc(−)
emitted by the forest canopy. The canopy-emitted fraction is
calculated following Liston and Elder (2006a) as
Fc=a+b·ln(LAI∗), (16)
where a (−)and b (−)are constants with values of 0.55 and
0.29, respectively. A value of Fgcan be derived as
Fg=1−Fc,(17)
with both calculated fractions used to estimate inside-canopy
incoming longwave radiation Qlif (Wm−2) from
Qlif =(Fg·Qli)+(Fc·σ·T4
c), (18)
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638 T. Marke et al.: A spreadsheet-based snow model for inside-canopy conditions
where Qli (Wm−2) represents the top-of-canopy incoming
longwave radiation. The latter is provided as input for ES-
CIMO.spread (v2) and is here estimated as a function of
temperature and cloud cover as proposed by Liston and El-
der (2006a) due to a lack of observations. σrepresents the
Stefan–Boltzmann constant and Tc(K) the inside-canopy
temperature. Assuming a linear dependency on canopy frac-
tion, Tcis derived from top-of-canopy temperature Ta(K) as
proposed by Obled (1971):
Tc=Ta−Fc·
(Ta−(Rc·(Ta−Tmean)+Tmean −δT )), (19)
where Tmean (K) is the mean daily air temperature, Rc(−)is
a dimensionless scaling parameter set to 0.8 and δT (−2 K ≤
δT ≤ +2K)is a temperature offset defined as (Durot, 1999)
δT =Tmean −273.16
3.(20)
Durot (1999) has further shown that relative humidity in-
side the canopy, RHc(%), is often higher compared to the
open due to sublimation and evaporation of melted snow.
We therefore propose to modify top-of-canopy humidity RH
(%) with consideration of the canopy fraction in the form of
(Durot, 1999)
RHc=max{RH ·(1+0.1·Fc), 100}.(21)
2.5 Simulating canopy effects on the snow cover
The following describes the newly implemented approaches
to describe snow interception through the forest canopy as
well as melt-induced unloading of intercepted snow from the
canopy.
Interception of solid precipitation Ps(mm) at time tis
derived introducing a canopy-intercepted load, I(mm), ex-
pressed as (Pomeroy et al., 1998)
I=It−1+0.7·(Imax −It−1)·(1−exp(−Ps/Imax)), (22)
where t−1 represents the previous time step and Imax is the
maximum interception storage calculated as (Hedstrom and
Pomeroy, 1998)
Imax =4.4·LAI∗.(23)
Sublimation of intercepted snow Qcs (mm) is calculated
as described by Liston and Elder (2006b) as
Qcs =Ce·I·9s·dt, (24)
where dt(s) is the time increment (here: 3600s), 9s(s−1)
is the sublimation-loss rate coefficient for an ice sphere
and Ce(−)represents the canopy exposure coefficient. Ice
spheres are assumed to be characterized by a constant radius
of 500µm as proposed by Liston and Elder (2006b).
The canopy exposure coefficient is calculated as
Ce=kc·(I/Imax)−0.4,(25)
where kc(−)is a dimensionless coefficient related to the
shape of the intercepted snow deposits (Liston and Elder,
2006b). Sublimation at the canopy scale is hence estimated
based on sublimation from individual ice spheres. Analyz-
ing observed (Montesi et al., 2004) and modeled sublimation
rates for a 2.7 m tall subalpine fir tree at the USDA Fraser Ex-
perimental Forest, Liston and Elder (2006b) have found that
the application of kc=0.010 seems to best reproduce ob-
served sublimation rates at both, higher and lower elevated
tree sites. This value is very close to the value of kc=0.011
derived by Pomeroy et al. (1998) for the Canadian boreal for-
est and is used as the kcvalue for the calculations with EC-
IMO.spread (v2) here. This parameter can be easily adapted
by changing the respective setting in the parameter section of
the model.
The sublimation-loss rate coefficient 9sis calculated from
the particle mass m(kg) in the form of
9s=(dm/dt)/m, (26)
where the particle mass is given by
m=3
4·π·ρi·r3,(27)
with ρi(kgm−3) being ice density and r(m) representing the
radius of a spherical ice particle (assumed to be 500µm as
proposed by Liston and Elder, 2006b).
Mass loss from an ice particle is described as a function
of intercepted solar radiation, humidity gradients between
the ice surface and the surrounding atmosphere, the size of
the considered ice particle and a ventilation term, following
Thorpe and Mason (1966) and Schmidt (1972):
dm
dt=2·πRH
100−Sp·
hs·+1
D·ρv·S·h
,(28)
where hsis the latent heat of sublimation (2.8355×
106Jkg−1).
The diffusivity of water vapor in the atmosphere, D
(m2s−1), is derived following Thorpe and Mason (1966) as
D=2.06×10−5(Ta/273)1.75.(29)
The molecular weight of water M(18.01kgkmole−1), the
universal gas constant R(8313Jkmole−1K−1), air tempera-
ture Ta(K) and the thermal conductivity of the atmosphere
λt(0.024Jm−1s−1K−1) are used to calculate as proposed
by Liston and Elder (2006b):
=1
λt·Ta·Nu ·hs·M
R·Ta−1.(30)
Geosci. Model Dev., 9, 633–646, 2016 www.geosci-model-dev.net/9/633/2016/
T. Marke et al.: A spreadsheet-based snow model for inside-canopy conditions 639
Figure 4. Simulated filling and depletion of the interception storage through snowfall, sublimation and melt-induced unload at site Vorder-
steinwald in the Black Forest mountain range (southwestern Germany).
The Nusselt number Nu and Sherwood number Sh are both
calculated as
Nu =Sh =1.79+0.606·Re0.5,(31)
where Re (0.7<Re <10)is the Reynolds number expressed
by
Re =2·r·uc
v,(32)
with vrepresenting the kinematic viscosity of air (1.3·
10−5m2s−1) and ucthe ventilation velocity inside the
canopy, which is set equal to inside-canopy wind speed as
proposed by Liston and Elder (2006b).
Following Fleagle and Businger (1981), the saturation
density of water vapor ρv(kgm−3) is derived as
ρv=0.622·es
Rd·Ta,(33)
where Rdis the gas constant for dry air (287 JK−1kg−1) and
es(Pa) is the saturation vapor pressure over ice, estimated
following Buck (1981) as
es=611.15exp22.452 ·(Ta−273.16)
Ta−0.61 .(34)
The shortwave radiation absorbed by a snow particle with
radius ris defined as
Sp=π·r2(1−αp)·Si,(35)
where αpis the snow albedo, and Si(Wm2) is the solar
radiation at the earth’s surface, which in the case of ES-
CIMO.spread (v2) is among the required meteorological in-
put parameters.
To account for a melt-induced unloading of intercepted
snow from the canopy, a melt-unloading rate Lm(kg m−2)
is introduced by Liston and Elder (2006b):
Lm=5.8·10−5(Ta−273.16)·dt. (36)
We assume an unloading rate of 5kgm−2day−1K−1
whenever temperatures are above freezing, with unloading
snow adding to snow accumulation at the land surface. The
simulated filling and depletion of the interception storage
through snowfall, sublimation and melt-induced unload is il-
lustrated in Fig. 4 exemplarily for a period in February 2013.
3 Data and test site description
Snow cover simulations in this study are carried out for
the forest site Vordersteinwald in the Black Forest mountain
range (southwestern Germany) (see Fig. 1). This site is em-
inently suitable for testing of the newly developed version
of ESCIMO.spread as it (i) usually experiences alternation
of accumulation and melting periods over the winter season,
making the simulation of snow conditions particularly de-
manding, and (ii) has been subject to intense snow surveys
over the years 2010–present, including simultaneous obser-
vation of meteorological and snow conditions inside and out-
side the forest canopy (Pohl et al., 2014).
The forest stand at the study site is mostly conifer with
spruce, fir and pine, representing the most common conifer
tree species. To quantify the vegetation effect on snow condi-
tions, the applied SnoMoS were installed pairwise with one
SnoMoS located in the open and another set up at a close dis-
tance inside the forest canopy (see Fig. 5). The data recorded
by these low-cost monitoring sensors include hourly values
of snow depth, surface temperature, air temperature and hu-
midity, global radiation, wind speed and barometric pressure.
The continuous monitoring of snow depth with the
SnoMoS was accompanied by bi-weekly snow density sur-
veys that allow translation of snow depth into SWE. A com-
prehensive description of the technical specifications and the
instrumental setup of the SnoMoS is provided by Pohl et al.
(2014). Precipitation recordings for the study site originate
from nearby weather station Freudenstadt (DWD, 2015), op-
erated by the German Weather Service (DWD). Precipitation
observations have been corrected for differences in terrain
elevation between the sites of measurement and model appli-
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640 T. Marke et al.: A spreadsheet-based snow model for inside-canopy conditions
Figure 5. Schematic overview of the SnoMoS setup locations in-
side and outside the forest canopy at site Vordersteinwald in the
Black Forest mountain range (southwestern Germany, 800ma.s.l).
The light green areas indicate grassland, the dark green areas forest,
the grey lines streets and the light blue area a lake.
cation by applying monthly elevation adjustment factors as
proposed by Liston and Elder (2006a). The latter have been
taken from Marke (2008), who has investigated altitudinal
differences in precipitation for the upper Danube watershed.
No interpolation using other station data has been carried out
due to the closeness of the study site (3km distance) to sta-
tion Freudenstadt. Hemispherical images were taken at the
forest location and were utilized to derive the effective LAI
of the forest stand (LAI∗=2.6m2m−2). Moreover, a loga-
rithmic function considering snow ageing and new snowfall
was used to compute daily snow densities between the sur-
veys. All data used as model input and for model validation
are freely provided along with the model.
4 Results
ESCIMO.spread (v2) has been applied to modify outside-
canopy meteorological conditions for canopy effects at site
Vordersteinwald as well as for a subsequent simulation of
the SWE evolution for the winter season 2012/2013. Fig-
ure 6 shows outside-canopy global radiation modified for
canopy effects with the new ESCIMO.spread (v2) algorithms
in comparison to inside-canopy observations. As global ra-
diation under mid-latitude prealpine conditions usually pro-
vides the largest share of energy for snowmelt, an accurate
representation of inside-forest global radiation is essential
for a realistic reproduction of snow ablation with any energy
balance model. The general dimension and temporal varia-
tion in global radiation inside the forest canopy seem well
Table 1. Performance of ESCIMO.spread (v2) in the modification
of outside-canopy global radiation, temperature, relative humidity
and wind speed for canopy effects.
Variable NSME R2IA RMSE
Global radiation 0.64 0.66 0.89 8.23 (Wm−2)
Air temperature 0.79 0.82 0.94 1.74 (K)
Relative humidity −1.10 0.61 0.74 6.31 (%)
Wind speed −0.29 0.60 0.80 0.59 (m s−1)
reproduced with a certain tendency of the model to under-
estimate global radiation in the forest. The latter is also re-
flected by the scatterplot shown in Fig. 10 opposing simu-
lated and observed global radiation. The satisfactory overall
model performance in the modification of global radiation
for canopy effects is also confirmed by the high values of the
coefficient of determination (R2=0.66), the Nash–Sutcliffe
model efficiency (NSME=0.64) and the index of agreement
(IA=0.89), as well as by the low root mean square error
(RMSE=8.23Wm−2) (see Krause et al., 2005 for a detailed
explanation of the efficiency criteria applied). The values of
these efficiency criteria are provided in Table 1 with the cor-
responding scatterplots for the different meteorological in-
put variables modified for canopy effects shown in Fig. 10.
As shown in Fig. 7, the simulated and observed courses of
temperature match fairly well until late January, whereas the
simulations overestimate daily temperature peaks in spring.
The efficiency criteria of R2, NSME, IA and RMSE with val-
ues of 0.79, 0.82, 0.94 and 1.74 (K), respectively, further un-
derline the good performance of ESCIMO.spread (v2) with
respect to the modification of outside-canopy temperature
conditions. Compared to global radiation and temperature,
the model performance for relative humidity and wind speed
with R2and IA values on the order of 0.6 and 0.7–0.8 for
both criteria, respectively, is distinctly weaker. In the case of
both variables the NSME with values below 0 indicates that
the mean value of the observations would be a better predic-
tor than the model (Krause et al., 2005). The course of rela-
tive humidity and wind speed conditions illustrated in Figs. 8
and 9 explains the diametrical picture of model performance
described by means of R2and IA compared to NSME. While
the temporal variation in relative humidity and wind speed is
well reflected in the simulations (resulting in good correla-
tion and acceptable values of R2and IA), the exact values
in the observed time series are seldom reproduced by the
model results, a condition that is considered in the calcula-
tion of NSME (Krause et al., 2005). The high temporal and
spatial variability in wind speed naturally makes any spatial
interpolation or modification for canopy effects particularly
challenging. In the case of both variables, higher maximum
values can be observed in the simulated time series.
The good overall model performance as well as the dif-
ferences in model performance for the different meteoro-
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T. Marke et al.: A spreadsheet-based snow model for inside-canopy conditions 641
Figure 6. Simulated and observed global radiation for the winter period 2012/13 at site Vordersteinwald. The grey areas indicate periods
with presence of a snow cover.
Figure 7. Simulated and observed temperature inside the forest canopy for the winter period 2012/13 at site Vordersteinwald. The grey areas
indicate periods with presence of a snow cover.
logical variables might at least partly be explainable by the
presence/absence of pronounced daily cycles in the hourly
values. While systematic daily variations in the temperature
and global radiation data can be expected to bias some effi-
ciency criteria towards higher model performance, the lower
model performance for wind speed and relative humidity
might partly be due to weaker or missing daily cycles in
the analyzed data. To further look into these assumptions,
the predictive capabilities of outside-canopy observations for
the estimation of inside-canopy conditions are provided in
Table 2. Comparing the values of the different efficiency
criteria calculated for the four meteorological variables to
those shown in Table 1 reveals that while values of R2are
equally high for all meteorological variables, the significant
increase in NSME values clearly shows the improvements
resulting from application of the canopy model, particularly
when estimating global radiation inside the forest canopy.
Only in the case of relative humidity do the outside-canopy
measurements seem to slightly better predict inside-canopy
conditions. This can be explained by the fact that, looking
at the SnoMoS data for the winter season 2012/2013, mea-
sured humidity outside the canopy is often higher than that
observed inside the forest stand, whereas the canopy model
in ESCIMO.spread (v2) increases outside-canopy humidity
Table 2. Predictive capabilities of outside-canopy observations for
inside-canopy conditions.
Variable NSME R2IA RMSE
Global radiation −28.24 0.66 0.39 73.79 (W m−2)
Air temperature 0.74 0.85 0.95 1.92 (K)
Relative humidity −0.81 0.65 0.76 5.84 (%)
Wind speed −13.66 0.60 0.48 2.01 (m s−1)
SWE −0.49 0.87 0.82 23.07 (mm)
with consideration of the canopy fraction to estimate inside-
canopy relative humidity (see Eq. 21).
The simulated snow cover is displayed in Fig. 11 for
the open and in Fig. 12 for inside the canopy in com-
parison to observations at the respective sites. As can be
seen from Fig. 11, the newly developed version of ES-
CIMO.spread (v2) reproduces much better the observed
snow conditions outside the forest at site Vordersteinwald
compared to ESCIMO.spread v1. This increase in model per-
formance is mostly due to the fact that liquid precipitation in
ESCIMO.spread (v1) increases SWE by the total value of
observed precipitation, whereas in the new model version,
liquid precipitation is only added to the SWE up to a maxi-
mum value defined by the water holding capacity, with the
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642 T. Marke et al.: A spreadsheet-based snow model for inside-canopy conditions
Figure 8. Simulated and observed relative humidity inside the forest canopy for the winter period 2012/13 at site Vordersteinwald. The grey
areas indicate periods with presence of a snow cover.
Figure 9. Simulated and observed wind speed inside the forest canopy for the winter period 2012/13 at site Vordersteinwald. The grey areas
indicate periods with presence of a snow cover.
rest leaving the snowpack as outflow (see Eq. 11). While
these improvements are less important for simulations at high
alpine sites, where the largest share of precipitation in the
winter season falls in the form of snow (see Strasser and
Marke, 2010), at lower elevated sites the comparatively high
amounts of liquid precipitation in winter make these model
modifications essential. As a result of these further develop-
ments, the severe overestimation in simulated SWE observed
in the results of ESCIMO.spread (v1) is no longer found in
the results of ESCIMO.spread (v2), leading to a significant
increase in model performance as confirmed by the values of
the different efficiency criteria in Table 3. The simulations
carried out with ESCIMO.spread (v2) sometimes even show
a tendency to underestimate observed snow conditions for
the winter season 2012/2013, particularly with respect to the
second snow peak at site Vordersteinwald in February 2013.
Looking at the results achieved for inside the canopy (see
Fig. 12 and Table 3), applying the canopy model reasonably
reproduces observed snow conditions inside the forest. Com-
pared to the results achieved using observed outside-canopy
snow conditions as a predictor for inside-canopy snow con-
ditions (see Table 2), application of the proposed canopy
model increases NSME values from −0.49 to 0.81 and re-
duces RMSE from 23.07 to 8.26mm.
Table 3. Performance of ESCIMO.spread v1 and ESCIMO.spread
v2 at site Vordersteinwald for the winter period 2012/2013. As ES-
CIMO.spread v1 does not include formulations of inside-canopy
processes, model performance for inside-canopy conditions is only
available for ESCIMO.spread v2. The simulations inside the canopy
are based on modified outside-canopy meteorological conditions.
Variable NSME R2IA RMSE
SWE (v1) outside canopy −15.20 0.34 0.37 134.28 (mm)
SWE (v2) outside canopy 0.71 0.81 0.90 18.07 (mm)
SWE (v2) inside canopy 0.81 0.83 0.95 8.26 (mm)
The fact that the model results inside the canopy are even
better than for the outside (see also the scatterplots in Fig. 13)
might at least partly be the result of multiple error compen-
sation effects (including errors from precipitation measure-
ment, the transfer of precipitation information from precipi-
tation gauge Freudenstadt to site Vordersteinwald as well as
from translating snow depth into SWE). The green line in
Fig. 12 shows the simulations achieved using observed me-
teorological conditions inside the canopy (as provided by the
SnoMoS inside the forest). Due to a lack of precipitation
recordings inside the forest, the precipitation data used as in-
put for the simulations inside the canopy in this experiment
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T. Marke et al.: A spreadsheet-based snow model for inside-canopy conditions 643
Figure 10. Simulated vs. observed meteorological conditions inside the forest canopy for the winter period 2012/13 at site Vordersteinwald.
Figure 11. Simulated and observed snow water equivalent outside the forest canopy for the winter period 2012/13 at site Vordersteinwald.
The blue and red lines represent the results achieved with the previous (v1) and newly developed (v2) versions of the ESCIMO.spread model,
respectively.
also represent recordings from station Freudenstadt modified
for canopy effects. Hence, precipitation inside the canopy as
used as input for the snow simulations has to be considered
a model result rather than an observation. The same applies
to the incoming component of inside-canopy longwave ra-
diation, which to a certain fraction represents the simulated
top-of-canopy incoming longwave radiation due to a lack of
observations outside the forest stand (see Eq. 18 and expla-
nations below). Comparing the results achieved using ob-
served and simulated meteorological conditions inside the
forest as model input (see Fig. 12), the meteorological obser-
vations allow only slightly better model performance, with
NSME increasing from 0.81 to 0.82 and RMSE decreasing
from 8.26 to 8.02mm. The results of both model runs show
a distinct overestimation of SWE between 15 and 26 Decem-
ber. A closer look at the conditions during this period re-
veals significant snowfall at temperatures close to 0◦C and
air humidity close to saturation. Hence, an explanation for
the observed overestimation of SWE in this period might be
a false interpretation of liquid precipitation as solid precipita-
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644 T. Marke et al.: A spreadsheet-based snow model for inside-canopy conditions
Figure 12. Simulated and observed snow water equivalent inside the forest canopy for the winter period 2012/13 at site Vordersteinwald.
The two curves illustrate the snow simulations achieved with the parameterized (red) and observed (green) meteorological conditions inside
the canopy.
Figure 13. Snow water equivalent simulated with ESCIMO.spread (v2) vs. observed snow conditions outside and inside the forest canopy
for the winter period 2012/13 at site Vordersteinwald.
tion. While the model acceptably reproduces snow accumu-
lation between 10 and 30 January in the open, a noticeable
overestimation of SWE can be observed in the results us-
ing the modified outside-canopy meteorological conditions.
Moreover, a period of snow accumulation can be observed
in the observations and simulations for the open in March,
whereas inside the canopy this increase in SWE is merely
predicted by the model and not confirmed by the observa-
tions.
5 Conclusions
A new version of the ESCIMO.spread spreadsheet-based
point energy balance snow model has been presented (ES-
CIMO.spread (v2)) that allows improved precipitation phase
detection, estimation of snow temperature, consideration of
cold and liquid water content in the snow cover, estimation
of inside-canopy meteorological conditions from meteoro-
logical observations in the open and the simulation of snow
accumulation and ablation inside a forest canopy. It thereby
does not require meteorological observations in the canopy,
but instead derives inside-canopy meteorological conditions
from available observations in the open requiring only LAI
and canopy height as plant-specific input parameters. The
derived meteorological conditions inside the canopy are not
only applicable as input for snow cover simulations, but can
also be expected to be of interest for a variety of scientific
disciplines, e.g., forest ecology or pedology. To provide the
data required for model application and evaluation, a pair
of SnoMoS have been utilized as an innovative technology
that allows the collection of important meteorological vari-
ables at low financial costs. Comparison of simulated inside-
canopy meteorological conditions to observations at a site
in the Black Forest region (Germany) reveals good overall
model performance, particularly with respect to global radia-
tion (NSME=0.64Wm−2, RMSE =8.23Wm−2) and tem-
perature (NSME =0.79K, RMSE=1.74K), representing
the most important meteorological variables for the estima-
tion of snowmelt. In the case of relative humidity and wind
speed, the model efficiency with NSME values of −1.10
and −0.29 and an RMSE of 6.31% and 0.59ms−1for the
two variables, respectively, was noticeably lower. This lower
model performance might at least partly be the result of
weaker or missing daily cycles in the hourly data as well
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T. Marke et al.: A spreadsheet-based snow model for inside-canopy conditions 645
as potential biases in the measurements of the applied low-
cost monitoring systems, which are described in detail by
Pohl et al. (2014). A satisfactory model performance unfolds
when comparing the simulated snow cover evolution inside
and outside the canopy to snow observations provided by
the SnoMoS. NSME here reaches values of 0.81 and 0.71
with an RMSE of 8.26 and 18.07mm for simulated SWE in-
side and outside the canopy, respectively. While snow cover
evolution is well reproduced for both, outside and inside
the forest canopy, model performance is slightly higher for
inside-canopy conditions, even though the empirical model
parameters have not yet been adjusted to (pre)alpine forest
species. This might at least partly be explainable by multi-
ple error compensation effects (including errors from pre-
cipitation measurement, the transfer of precipitation infor-
mation from precipitation gauge Freudenstadt to site Vorder-
steinwald and the translation from snow depth to SWE). To
further improve the implemented parameterization of inside-
canopy processes, the simultaneous observations of snow and
meteorological conditions as provided by the SnoMoS are
currently used to develop model parameters that are tailored
to the specific conditions in (pre)alpine forests.
Despite its physically based character and advanced model
features, ESCIMO.spread (v2) still oversimplifies some im-
portant processes of the snow–vegetation interaction. In the
current version, the model only considers unloading of inter-
cepted snow as a result of melting. While the fact that wind
also induces unloading of intercepted snow is well known,
the combined dependence on plant characteristics (e.g., plant
structure and plant element flexibility) and meteorological
conditions (e.g., snow temperature, wind speed and direc-
tion) makes this a complex process hard to consider in nu-
merical models (Liston and Elder, 2006b). The modifica-
tion of shortwave and longwave radiation assumes a plant-
specific extinction coefficient and a constant canopy fraction,
respectively. While these assumptions can be expected to rea-
sonably reproduce the general observed patterns in local ra-
diation, they are not capable of accurately capturing the ac-
tual radiation conditions whenever canopy densities strongly
vary or sunlight is shining through open areas in the trees as
a result of changing solar zenith angles.
Code availability
ESCIMO.spread (v2) can be downloaded free of charge
at www.alpinehydroclimatology.net together with 1 year of
sample data including the meteorological and snow obser-
vations used in this study. The model has been tested on
OpenOffice 4.1.1 as well as on different versions of Mi-
crosoft Excel for Windows and Mac.
Acknowledgements. The authors thank the Austrian Climate and
Energy Fund for the financial support of the presented research
(ACRP6 – STELLA – KR13AC6K11109) within the Austrian
Climate Research Programme. Moreover, we thank the German
Weather Service (DWD) for the provision of the precipitation
recordings at station Freudenstadt.
Edited by: J. Neal
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