Introduction
In forested areas significant variations in snow accumulation can result from
the processes of forest canopy interception and sublimation of intercepted
snow . Snowfall in forested areas is either
intercepted 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 atmosphere, intercepted snow can be subject to
high sublimation losses, especially in dry continental climates. Generally,
sublimation 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 . Intercepted snow can also be removed from the
canopy by direct unloading and dripping of meltwater to the ground
. 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 . Likewise,
humidity and temperature underneath a canopy differ from those in the
open . In the boundary layer, forest canopies
moreover strongly modify the interactions between snow-covered
surfaces and the atmosphere. Even the litter on the forest floor has
a significant effect on the radiative properties of the snow cover
beneath a canopy .
The influences of a forest canopy on the snow cover dynamics beneath are very
complex. The snow cover duration 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
. On the other hand, shorter snowpack duration in the
forest was observed by .
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 sublimation
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 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 consideration of these complex
snow–canopy–atmosphere interactions, the ESCIMO.spread spreadsheet-based
point energy balance snow model developed by (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 algorithm for precipitation phase detection that applies wet-bulb
temperature as a criterion to distinguish solid and liquid precipitation.
Another model improvement is a new parameterization for cold and liquid water
content of the snow cover allowing the consideration of refreezing of liquid
precipitation or meltwater in the snowpack. Compared to other existing
spreadsheet-based snow models e.g., the glacier and snowmelt study
model by, ESCIMO.spread (v2) is particularly fast and
can easily be modified 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 demand on meteorological input is covered by those
variables most commonly recorded at any state-of-the-art automatic weather
station. While have presented a spreadsheet energy
balance model that requires even fewer meteorological input data (daily
minimum/maximum temperature 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, compared to the canopy model
implemented in ESCIMO.spread (v2), the consideration of canopy effects in the
model is reduced to a canopy-induced extinction of
solar radiation only. Canopy effects on other meteorological 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,
ESCIMO.spread allows the calculation of sensitivity tests for changes in
temperature and precipitation for any site of interest. 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 Numbers,
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
operated with laptop computers, e.g., to visualize and make plausible
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 sublimation,
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,
documented and freely available snow model for application in both science
and education. This paper describes the newly implemented algorithms and
evaluates the model results against available hydrometeorological
observations inside and outside the forest canopy at a site in the Black
Forest mountain range (southwestern Germany; see Fig. )
with a mostly temperate snow cover at an elevation of 800 ma.s.l.
The applied hydrometeorological data have been recorded by a set of low-cost
snow monitoring systems (SnoMoS) recently developed by .
The model can be downloaded from www.alpinehydroclimatology.net
together with 1 year of example meteorological recordings and snow
observations.
The Vordersteinwald site in the Black Forest mountain range
(southwestern Germany, 800 m a.s.l.).
The ESCIMO.spread model (v2)
General description
The new version of ESCIMO.spread (v2) builds upon the ESCIMO.spread model as
published by . 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 surface applying simple parameterizations of
the relevant processes. The energy balance of the snow surface is calculated
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 sublimation/resublimation and a constant soil heat
flux . Thereby, absorbed and reflected shortwave
radiation is calculated from incoming shortwave radiation on the basis of the
snow albedo, which is estimated for each hourly time step using an albedo
ageing curve approach. Solid precipitation increases the amount of snow water
equivalent (SWE) on the land surface, while liquid precipitation is (up to
a certain maximum amount depending on actual 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
273.16 K, the newly implemented method for snow temperature
estimation (see Sect. ) allows the removal
of this condition in ESCIMO.spread (v2). The model results are visualized in
the form of diagrams for the majority of model variables, together with four
quantitative measures of goodness of fit.
Precipitation phase
detection
The new version of ESCIMO.spread (v2) includes an improved distinction
between liquid and solid precipitation. As air temperature Ta
is often an insufficient indicator of the precipitation water phase
, wet-bulb temperature Tw is used in
ESCIMO.spread (v2) as a combined measure of air temperature and humidity to
distinguish liquid from solid precipitation. Figure shows
the relation between air temperature, wet-bulb temperature and relative
humidity for different altitudes to account for the dependence of wet-bulb
temperature on air pressure. Each of the displayed lines in
Fig. could be interpreted as a borderline to separate
liquid and solid precipitation assuming a certain threshold 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.
Relation between air temperature, wet-bulb temperature and relative
humidity at different altitudes. The latter represent
different 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 temperature.
Generally, wet-bulb temperature can be derived by solving the
psychrometric equation
ea(Ta)-es(Tw)-A⋅(Ta-Tw)=0
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 psychrometric equation
and iterations are unfavorable in a spreadsheet
model, a pragmatic assumption 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. (). Beside temperature and
humidity, wet-bulb temperature also depends on air pressure pz (Pa) that
is required to calculate the psychrometric constant, A, as
A=pz⋅cp0.622⋅Lv,
where cp is the specific heat capacity of air at constant pressure
(1004 Jkg-1K-1) and Lv (Jkg-1)
represents the latent heat of vaporization. In ESCIMO.spread (v2) the
temperature 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 . Air
pressure, p (Pa), at a given elevation, z (m), can be derived from
standard atmospheric pressure, p0 (Pa), by integration of the hydrostatic
equation assuming a linear decrease in temperature with increasing altitude
(γ=-0.0065 Km-1)
pz=p0TaTa-γ⋅z-gγ⋅R,
where R is the gas constant of dry air (287 Jkg-1K-1) and
g is gravity (ms-2). To account for the air pressure
dependence, the implemented lookup tables have been prepared for several
elevation bands with a 500 m interval. Figure shows
a comparison of wet-bulb temperatures calculated using the lookup table
approach to those achieved with an iterative solution for different
elevations. The differences between both approaches shown for a common
snowfall situation are relatively 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 required for precipitation
phase detection in ESCIMO.spread (v2) is one of the user-defined input
parameters and is here set to 273.16 K. 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 ± 0.5 K) in which liquid precipitation decreases from 100 to
0 % with solid precipitation increasing accordingly. When temperature is
exactly at the defined temperature threshold (here 273.16 K), this approach
results in 50 % liquid and 50 % solid precipitation.
Comparison of iteratively calculated wet-bulb temperature to the
results of the lookup table approach implemented in ESCIMO.spread (v2).
Cold and liquid water
content
A physically based method for estimating the snow temperature and deriving
the cold content of a single-layer snowpack has been implemented in
ESCIMO.spread (v2) following an approach presented by .
The snow temperature 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=minTst-1+dT,273.16.
The temperature change in Eq. () is derived as
dT=Et-1⋅dt+RFt-1⋅ci(SWEt-1+Ps)⋅cs,
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 liquid water refrozen in the previous time step,
ci is the melting heat of ice (3.337×105 Jkg-1), SWEt-1 (mm) is the SWE of the previous
time step, Ps (mm) is the solid precipitation in the current time
step and cs is the specific heat of snow
(2100 Jkg-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 273.16 K. Snow temperature and cold
content can be considered as equivalent and physically consistent
representations of the snowpack's energy state as defined by
Eq. (). 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 and
, melting snow is not immediately removed from
the snowpack, but a certain amount of liquid water can be retained (and
possibly 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 inferred
directly from calculated snow temperature in the form of
Cc=(Ts-273.16)⋅(SWEt-1+Ps)⋅csci.
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=minClwt-1,(-E⋅dt)/ci,
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,
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).
Clw is then updated in the form of
Clw=minClwt-1+M,SWEt-1⋅HCw,
where HCw(-) is a water holding capacity that limits
liquid water storage and is specified as a fraction of the total snowpack
weight. This parameter is to be defined by the user in the model's parameter
section and set to HCw=0.1 as recommended by
by default.
Finally, the outflow (i.e., the excess water that is actually removed from
the snowpack), O (mm), can be calculated as
O=maxClwt-1+Pl+M-SWEt-1⋅HCw,0.
Modification of meteorological conditions inside the
forest canopy
The canopy model newly implemented in ESCIMO.spread (v2) by
has already been successfully applied under alpine
conditions (see , or ). The
development of the approach was motivated by the fact that meteorological
observations inside forest canopies only sparsely exist, necessitating the
estimation of inside-canopy conditions from available meteorological
observations in the open. The method requires information on leaf area index
and canopy height that can either be derived from field measurements or be
taken from the literature for a wide range of plant species (e.g., from
, or ).
Wind speed inside the canopy uc (ms-1) is
derived from above-canopy wind speed u (ms-1) as
uc=uexp(-a⋅(1-z/h)),
where h (m) is the canopy height and z (m) is the canopy reference
level assumed to be 0.6 h .
The canopy flow index, a(-), is calculated as a function of the effective
leaf area index LAI∗ (m2m-2) and a scaling
factor, β (=0.9), that is introduced by to
make LAI∗ compatible with the canopy flow index proposed by
:
a=LAI∗⋅β.
LAI∗ includes stems, leaves and branches as described
by .
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,
where Qsif is the incoming shortwave radiation impinging on the
snow surface beneath the canopy . τv
representing the fraction of Qsi reaching the land surface is
derived as
τv=exp(-k⋅LAI∗),
with k being a vegetation-dependent extinction coefficient
. 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), have yielded
the best overall performance using a k value 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
as
Fc=a+b⋅ln(LAI∗),
where a(-) and b(-) are constants with values of 0.55 and 0.29,
respectively. A value of Fg can be derived as
Fg=1-Fc,
with both calculated fractions used to estimate inside-canopy incoming
longwave radiation Qlif (Wm-2) from
Qlif=(Fg⋅Qli)+(Fc⋅σ⋅Tc4),
where Qli (Wm-2) represents the top-of-canopy
incoming longwave radiation. The latter is provided as input for
ESCIMO.spread (v2) and is here estimated as a function of temperature and
cloud cover as proposed by due to a lack of
observations. σ represents the Stefan–Boltzmann constant and
Tc (K) the inside-canopy temperature. Assuming a linear
dependency on canopy fraction, Tc is derived from top-of-canopy
temperature Ta (K) as proposed by :
Tc=Ta-Fc⋅(Ta-(Rc⋅(Ta-Tmean)+Tmean-δT)),
where Tmean (K) is the mean daily air temperature,
Rc(-) is a dimensionless scaling parameter set to 0.8 and
δT(-2K≤δT≤+2K) is a temperature
offset defined as
δT=Tmean-273.163.
has further shown that relative humidity inside 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
RHc=maxRH⋅(1+0.1⋅Fc),100.
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 t is
derived introducing a canopy-intercepted load, I (mm), expressed as
I=It-1+0.7⋅(Imax-It-1)⋅(1-exp(-Ps/Imax)),
where t-1 represents the previous time step and Imax is the
maximum interception storage calculated as
Imax=4.4⋅LAI∗.
Sublimation of intercepted snow Qcs (mm) is calculated as
described by as
Qcs=Ce⋅I⋅Ψs⋅dt,
where dt (s) is the time increment (here: 3600 s),
Ψs (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 500 µm as proposed
by .
The canopy exposure coefficient is calculated as
Ce=kc⋅(I/Imax)-0.4,
where kc(-) is a dimensionless coefficient related to the
shape of the intercepted snow deposits . Sublimation
at the canopy scale is hence estimated based on sublimation from individual
ice spheres. Analyzing observed and modeled
sublimation rates for a 2.7 m tall subalpine fir tree at the USDA Fraser
Experimental Forest, have found that the
application of kc=0.010 seems to best reproduce observed
sublimation rates at both, higher and lower elevated tree sites. This value
is very close to the value of kc=0.011 derived by
for the Canadian boreal forest and is used as the
kc value for the calculations with ECIMO.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 Ψs is
calculated from the particle mass m (kg) in the form of
Ψs=(dm/dt)/m,
where the particle mass is given by
m=34⋅π⋅ρi⋅r3,
with ρi (kgm-3) being ice density and r
(m) representing the radius of a spherical ice particle (assumed to be
500 µm as proposed by ).
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
and :
dmdt=2⋅πRH100-Sp⋅Ωhs⋅Ω+1D⋅ρv⋅S⋅h,
where hs is the latent heat of sublimation (2.8355×106 Jkg-1).
The diffusivity of water vapor in the atmosphere, D (m2s-1),
is derived following as
D=2.06×10-5(Ta/273)1.75.
Simulated filling and depletion of the interception storage through
snowfall, sublimation and melt-induced unload at site Vordersteinwald in the
Black Forest mountain range (southwestern Germany).
The molecular weight of water M (18.01 kgkmole-1), the
universal gas constant R (8313 Jkmole-1K-1), air
temperature Ta (K) and the thermal conductivity of the
atmosphere λt (0.024 Jm-1s-1K-1)
are used to calculate Ω as proposed by :
Ω=1λt⋅Ta⋅Nu⋅hs⋅MR⋅Ta-1.
The Nusselt number Nu and Sherwood number Sh are both
calculated as
Nu=Sh=1.79+0.606⋅Re0.5,
where Re (0.7<Re<10) is the Reynolds number expressed
by
Re=2⋅r⋅ucv,
with v representing the kinematic viscosity of air (1.3⋅10-5 m2s-1) and uc the ventilation
velocity inside the canopy, which is set equal to inside-canopy wind
speed as proposed by .
Following , the saturation density of water vapor
ρv (kgm-3) is derived as
ρv=0.622⋅esRd⋅Ta,
where Rd is the gas constant for dry air
(287 JK-1kg-1) and es (Pa) is the saturation
vapor pressure over ice, estimated following as
es=611.15exp22.452⋅(Ta-273.16)Ta-0.61.
The shortwave radiation absorbed by a snow particle with radius r is
defined as
Sp=π⋅r2(1-αp)⋅Si,
where αp is the snow albedo, and Si
(Wm2) is the solar radiation at the earth's surface, which in the
case of ESCIMO.spread (v2) is among the required meteorological input
parameters.
To account for a melt-induced unloading of intercepted snow from the
canopy, a melt-unloading rate Lm (kgm-2) is
introduced by :
Lm=5.8⋅10-5(Ta-273.16)⋅dt.
We assume an unloading rate of 5 kgm-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
illustrated in Fig. exemplarily for a period in
February 2013.
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. ). This site is eminently 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 demanding, and (ii) has
been subject to intense snow surveys over the years 2010–present, including
simultaneous observation of meteorological and snow conditions inside and
outside the forest canopy .
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 conditions, the applied SnoMoS were installed
pairwise with one SnoMoS located in the open and another set up at a close
distance inside the forest canopy (see Fig. ). The data
recorded by these low-cost monitoring sensors include hourly values of snow
depth, surface temperature, air temperature and humidity, global radiation,
wind speed and barometric pressure.
Schematic overview of the SnoMoS setup locations inside and
outside the forest canopy at site Vordersteinwald in the Black
Forest mountain range (southwestern Germany, 800 m a.s.l). The light
green areas indicate grassland, the dark green areas forest, the
grey lines streets and the light blue area
a lake.
The continuous monitoring of snow depth with the SnoMoS was accompanied by
bi-weekly snow density surveys that allow translation of snow depth into SWE.
A comprehensive description of the technical specifications and the
instrumental setup of the SnoMoS is provided by .
Precipitation recordings for the study site originate from nearby weather
station Freudenstadt , operated by the German Weather Service
(DWD). Precipitation observations have been corrected for differences in
terrain elevation between the sites of measurement and model application by
applying monthly elevation adjustment factors as proposed by
. The latter have been taken from ,
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 (3 km distance) to station
Freudenstadt. Hemispherical images were taken at the forest location and were
utilized to derive the effective LAI of the forest stand
(LAI∗=2.6 m2m-2). Moreover, a logarithmic
function considering snow ageing and new snowfall was used to compute daily
snow densities between the surveys. All data used as model input and for
model validation are freely provided along with the model.
Results
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.
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.
Figure shows outside-canopy global radiation modified
for canopy effects with the new ESCIMO.spread (v2) algorithms in comparison
to inside-canopy observations. As global radiation under mid-latitude
prealpine conditions usually provides 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 variation in global
radiation inside the forest canopy seem well reproduced with a certain
tendency of the model to underestimate global radiation in the forest. The
latter is also reflected by the scatterplot shown in
Fig. opposing simulated 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 = 8.23 Wm-2)
(see for a detailed explanation of the efficiency
criteria applied). The values of these efficiency criteria are provided in
Table with the corresponding scatterplots for the
different meteorological input variables modified for canopy effects shown in
Fig. . As shown in Fig. , 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 values of
0.79, 0.82, 0.94 and 1.74 (K), respectively, further underline 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
R2 and 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 predictor than the model . The course of
relative humidity and wind speed conditions illustrated in
Figs. and explains the diametrical
picture of model performance described by means of R2 and IA compared to
NSME. While the temporal variation in relative humidity and wind speed is
well reflected in the simulations (resulting in good correlation and
acceptable values of R2 and IA), the exact values in the observed time
series are seldom reproduced by the model results, a condition that is
considered in the calculation of NSME . 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.
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.
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.
Performance of ESCIMO.spread (v2) in the modification of outside-canopy global radiation, temperature, relative humidity and wind speed for canopy effects.
Variable
NSME
R2
IA
RMSE
Global radiation
0.64
0.66
0.89
8.23 (W m-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)
The good overall model performance as well as the differences in model
performance for the different meteorological 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 efficiency 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 .
Comparing the values of the different efficiency criteria calculated for the
four meteorological variables to those shown in
Table reveals that while values of R2 are
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, measured 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 with consideration of
the canopy fraction to estimate inside-canopy relative humidity (see
Eq. ).
Predictive capabilities of outside-canopy observations for inside-canopy conditions.
Variable
NSME
R2
IA
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)
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.
Simulated vs. observed meteorological conditions inside the forest canopy
for the winter period 2012/13 at site Vordersteinwald.
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.
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.
The simulated snow cover is displayed in Fig. for the open
and in Fig. for inside the canopy in comparison to
observations at the respective sites. As can be seen from
Fig. , the newly developed version of ESCIMO.spread (v2)
reproduces much better the observed snow conditions outside the forest at
site Vordersteinwald compared to ESCIMO.spread v1. This increase in model
performance 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 maximum value defined by the water holding capacity,
with the rest leaving the snowpack as outflow (see Eq. ).
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 ), at lower elevated sites
the comparatively high amounts of liquid precipitation in winter make these
model modifications essential. As a result of these further developments, 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 . 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. and
Table ), applying the canopy model reasonably
reproduces observed snow conditions inside the forest. Compared to the
results achieved using observed outside-canopy snow conditions as a predictor
for inside-canopy snow conditions (see Table ),
application of the proposed canopy model increases NSME values from -0.49
to 0.81 and reduces RMSE from 23.07 to 8.26 mm.
Performance of ESCIMO.spread v1 and ESCIMO.spread v2 at site
Vordersteinwald for the winter period 2012/2013. As ESCIMO.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
R2
IA
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)
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.
The fact that the model results inside the canopy are even better than for
the outside (see also the scatterplots in Fig. ) might at
least partly be the result of multiple error compensation effects (including
errors from precipitation measurement, the transfer of precipitation
information from precipitation gauge Freudenstadt to site Vordersteinwald as
well as from translating snow depth into SWE). The green line in
Fig. shows the simulations achieved using observed
meteorological 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 input for the simulations inside the canopy in
this experiment 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 radiation, 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. and explanations
below). Comparing the results achieved using observed and simulated
meteorological conditions inside the forest as model input (see
Fig. ), the meteorological observations allow only slightly
better model performance, with NSME increasing from 0.81 to 0.82 and RMSE
decreasing from 8.26 to 8.02 mm. The results of both model runs show
a distinct overestimation of SWE between 15 and 26 December. A closer look at
the conditions during this period reveals 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
precipitation. While the model acceptably reproduces snow accumulation
between 10 and 30 January in the open, a noticeable overestimation of SWE can
be observed in the results using 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 observations.
Conclusions
A new version of the ESCIMO.spread spreadsheet-based point energy balance
snow model has been presented (ESCIMO.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 meteorological 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 variables 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 radiation
(NSME = 0.64 Wm-2, RMSE = 8.23 Wm-2) and
temperature (NSME = 0.79 K, RMSE = 1.74 K), representing the most
important meteorological variables for the estimation 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 0.59 m s-1
for 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 as potential biases in the measurements of
the applied low-cost monitoring systems, which are described in detail by
. 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 18.07 mm for simulated SWE inside 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 multiple error compensation effects
(including errors from precipitation measurement, the transfer of
precipitation information from precipitation gauge Freudenstadt to site
Vordersteinwald 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 important processes of the
snow–vegetation interaction. In the current version, the model only
considers unloading of intercepted 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 direction) makes this a complex process hard to consider in
numerical models . The modification of shortwave and
longwave radiation assumes a plant-specific extinction coefficient and
a constant canopy fraction, respectively. While these assumptions can be
expected to reasonably reproduce the general observed patterns in local
radiation, they are not capable of accurately capturing the actual 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 observations used in this study. The
model has been tested on OpenOffice 4.1.1 as well as on different versions of
Microsoft Excel for Windows and Mac.