Theor. Appl. Climatol. 77, 77–105 (2004)
DOI 10.1007/s00704-003-0032-5
1
2
Geophysical Institute, University Alaska Fairbanks, Fairbanks, AK, USA
International Arctic Research Center, University Alaska Fairbanks, Fairbanks, AK, USA
Atmospheric response to soil-frost and snow
in Alaska in March
N. Mölders1 and J. E. Walsh2
With 14 Figures
Received May 26, 2003; revised October 24, 2003; accepted November 3, 2003
Published online February 25, 2004 # Springer-Verlag 2004
Summary
A hydro-thermodynamic soil-vegetation model including
soil freezing=thawing (soil-frost) and snow-metamorphism
has been integrated into the PennState=NCAR Mesoscale
Meteorological Model MM5 in a two-way coupled mode.
A hierarchy of simulations with and without the soil-frost
module, each combined with and without the snow module,
shows the influence of snow-cover and soil-frost on weather
in Alaska. Herein the landscape is featured as it is typically
by mesoscale models.
Theoretical considerations suggest that organic soil types
should be considered in mesoscale modeling because of their
different thermal and hydrological behavior as compared to
mineral soils. The Ludwig-Soret and Dufour effects are
small, but increase appreciably during freezing=thawing
and snow-melt.
The snow and soil-frost processes have a demonstrable
impact on the surface thermal and hydrological regimes
and on the near-surface atmospheric conditions even on the
short (synoptic) timescales. The presence of snow-cover
results in a highly stable stratification. In cloud-free areas,
the enhanced loss of radiant energy and cooling of the air
over snow-cover lead to a positive feedback to relatively
colder, drier conditions. In cloudy areas, a positive feedback
to warmer, moister conditions develops over snow-cover. As
the changes in atmospheric humidity and temperature caused
by snow-cover propagate into the pressure field, sea level
pressure is lower by more than 1 hPa in the simulations with
snow-cover. Although the effect of soil-frost alone is an
order of magnitude smaller, the soil-frost snow system leads
to an increase of the pressure difference to 1.2 hPa. The
changes in the pressure field alter wind speed and direction
slightly.
Soil-frost results in soil temperature differences of 2–5 K
in the upper soil layers, while snow results in differences of
3–10 K. Soil-frost has a notably greater impact in cloud-free
than cloudy areas. When a snow-cover is present, frozen soil
enhances the insulating effect of a snow-cover in cloudy
areas, but reduces it in cloud-free areas. In cloudy areas,
soil-frost without snow-cover leads to cooler, drier atmospheric conditions relative to no frost. In cloudy areas,
soil-frost under a snow-cover reduces the water supply to
the atmosphere as compared to snow-covered conditions
without soil-frost. The combined effects of soil-frost and
snow increase precipitation locally by as much as 12.2 mm=
48 h. If mesoscale modeling does not consider the soil-frost
snow system, predicted water vapor fluxes will be too high in
cloud-free areas, and too low in cloudy areas.
1. Introduction
Soil-frost and snow-cover are the most common
terrestrial surface conditions in Arctic and subarctic regions from October to mid-May. Snowmetamorphism and the depth of snow regulate
soil freezing (e.g. Williams and Smith, 1989)
with implications for soil hydraulic properties,
over-winter survival of some plants (e.g. Kongoli
and Bland, 2000) and water supply to the atmosphere (e.g. M€olders et al., 2003a). A snow-cover
78
N. M€
olders and J. E. Walsh
results in a more stable stratification of the atmospheric boundary layer (ABL) and a reduced
vertical exchange of trace gases (e.g. Segal et al.,
1991). Isolated soil surfaces surrounded by
snow-cover can lead to substantial sensible heat
fluxes, convection, and enhanced vertical mixing
in the ABL, especially when solar radiation is
significant. The strong spatial contrast in the
energy budget of snow-covered and snow-free
areas may generate a significant advection of
moisture and heat similar to sea breezes (Baker
et al., 1999). Thus, the timing and duration
of seasonal snow-cover significantly influence
macro- and micro-climate conditions (e.g. Zhuang
et al., 2001), and air-quality (e.g. Segal et al.,
1991).
Permafrost as well as a frozen active layer
restricts the mobility of soil-water and its infiltration. Moisture stored in frozen soils in winter
can contribute to the peak of spring floods
(Cherkauer and Lettenmaier, 1999). Another
important aspect of frozen ground is the local
equilibrium between the ice, gaseous, and liquid
phase of water. Slight changes in heat diffusion
and conduction caused by a change in snow
thickness or water fluxes affect all three water
phases in the soil and soil temperature simultaneously. Any change in soil temperature results
in freezing or thawing and a release of latent heat
or consumption of energy, again altering soil
temperature. The coupling between soil moisture
and thermal processes is fundamental to highlatitude soil irritations and must be formulated
appropriately in numerical models to capture
the annual temperature cycle in the soil and
2 m temperatures in winter (e.g. Viterbo et al.,
1999).
These high-latitude terrestrial conditions and
the related processes have received little systematic study in the context of their influence
on short-term weather. Most mesoscale meteorological models consider snow only by a change
in surface roughness length, albedo, emissivity
(e.g. Eppel et al., 1995), or in more sophisticated
formulations, by a simple one-layer snow model
(e.g. Koren et al., 1999; Warrach et al., 2001;
Chen and Dudhia, 2001). While the specification
of an albedo and emissivity typical of snowcover improves the prediction, this approach
does not allow for predicting some of the
micro-meteorological and micro-climatological
conditions (e.g. near-surface temperature and
humidity, latent heat fluxes, soil heat fluxes,
etc.) associated with a snow-cover (e.g. Fr€ohlich
and M€olders, 2002). Various authors (e.g. Loth
et al., 1993; Lynch-Stieglitz, 1994; Schlosser
et al., 1998; Slater et al., 2001; Fr€ohlich and
M€olders, 2002) found that multi-layer snow
models more successfully predict these conditions, especially in high latitudes. A comparison
of (1) a snow-model using a mixture theory to
simulate multi-phase water and energy transfer
processes in snow-layers, (2) a simplified threelayer snow-model, and (3) a snow-model determining snowmelt from the energy budget and
snow-temperature by the force-restore method,
showed that all these models simulated time
series of snow-water equivalent, surface-temperature and fluxes well (Jin et al., 1999). The
first-mentioned gives the best results, but needs
the highest computational efforts, while the second
one nearly performs like the first, but requires
comparable computational resources as the third
mentioned snow-model (Jin et al., 1999).
Recently, there have been some efforts to
develop soil-frost parameterizations for use in
mesoscale meteorological models (e.g. Koren
et al., 1999; Boone et al., 2000; Warrach et al.,
2001). Mesoscale meteorological models that
apply the force-restore method are limited in
resolving the various soil horizons (Montaldo
and Albertson, 2001). Moreover, these models
do not simulate the vertical distributions of soil
processes like the diurnal variation of the boundary between an unfrozen upper and a frozen
deeper soil layer as they work with two or three
reservoirs. Surface water and energy fluxes are
extremely difficult to determine without knowing
the exact depth of the freezing line. Therefore,
there are some efforts to enlarge multi-layer soil
models by soil-frost processes. Koren et al.
(1999) tested and evaluated a soil-frost model
offline that is developed for the NCEP (National
Center for Environmental Prediction) Eta
model. Warrach et al. (2001) designed and evaluated a soil-frost and one-layer snow parameterization for use in hydrological and atmospheric
models.
If soil water freezing is included in soil
models, they of course will consider the increase=
decrease in soil temperature associated with
freezing=thawing (e.g. Viterbo et al., 1999;
Atmospheric response to soil-frost and snow in Alaska in March
Boone et al., 2000; Warrach et al., 2001). However, although there are other interactions
between the soil thermal and moisture regimes
like the Ludwig-Soret effect (i.e. a temperature
gradient contributes to the water flux and
changes the soil volumetric water content) and
Dufour effect (i.e. a moisture gradient contributes
to the heat flux and alters soil temperature; e.g.
de Groot, 1951; Prigogine, 1961; Kramm et al.,
1996; M€olders et al., 2003a), and these are noteworthy especially in permafrost regions (e.g.
M€olders et al., 2003a), none of the mesoscale
meteorological models with soil-frost considers
these cross effects. Under many circumstances,
the Ludwig-Soret and Dufour effects are negligible. However, when chemicals are considered,
dry soil conditions suddenly enter the wet mode,
soil temperatures vary around the freezing point,
snow melts, and over the long-term these processes may gain influence on other processes or
variables. The Ludwig-Soret effect, for instance,
was found to affect water recharge by 5% of the
total recharge, and the Dufor effect soil temperature up to 2 K over the long-term (M€
olders et al.,
2003a). The example in Fig. 1 shows how these
cross effects influence soil volumetric water content for a site in Alaska. Here, soil volumetric
liquid water content integrated over the first
2 m of soil differs by up to 0.18 mm=d between
simulations without and with inclusion of these
cross effects. This difference is of the order of
daily evaporation loss in high-latitudes. The largest effects relate to freeze up, snow-melt and
freezing=thawing of the active layer. At soil temperatures below freezing point, soil volumetric
liquid water content decreases at the benefit of
soil ice (Fig. 2). The lower the liquid water content becomes, the greater the Ludwig-Soret effect
becomes (see Eq. A1 in Appendix A). Along the
freezing line, the gradient in soil moisture may
become strong, thereby increasing the Dufour
effect’s influence on soil temperature changes
(see Eq. A2 in Appendix A). The transfer coefficients for liquid water decrease non-linearly with
decreasing relative volumetric liquid water content, and are greater in soils of low than high
pore-size distribution index. At low volumetric
liquid water content, they reduce to the order of
magnitude of those for water vapor, for which the
Dufour effect gains influence on soil temperature
changes (cf. Eq. A2 in Appendix A). During
79
Fig. 1. Differences in soil volumetric liquid water content
as obtained without and with inclusion of the Dufour and
Ludwig-Soret effects for Ivotuk (68 290 N, 155 440 W). The
symbols show differences at various soil layers. The solid
line shows the differences integrated over a depth of 2 m.
HTSVS was driven with observed meteorological data from
(a) July 8, 1999 thru September 23, 1999, and (b) March 23,
2000 to July 13, 2000. Note that the largest differences
occur during freeze up (a) and in the melting season (b)
melt, the relative volumetric liquid water content
changes quickly due to thawing of the frozen
ground and percolation in response to snow-melt
(Fig. 1). The uppermost layers have the greatest
differences during snow-melt, while the deeper
layers are more sensitive to the cross effects during freeze-up (Fig. 1). The coupling of Eqs. A1
and A2 by Ludwig-Soret and Dufour effects has
been neglected in previous formulations of soils
affected by phase transition of water (e.g. Koren
80
N. M€
olders and J. E. Walsh
2. Brief description of HTSVS,
its modifications, and coupling to MM5
HTSVS includes:
Fig. 2. Dependence of maximum relative liquid water content max=s on soil temperature for some selected soil
types and organic materials. Note that relative liquid water
content ranges between 0 and 1 and is dimensionless. It is
determined by the ratio of the liquid water content, , to the
liquid water content at saturation, s
et al., 1999) for the benefit of computational
performance.
We have introduced into the PennState=NCAR
Mesoscale Meteorological Model MM5 version
3 (e.g. Dudhia, 1993) the thermo-hydrodynamic
soil vegetation scheme (HTSVS) (e.g. Kramm
et al., 1996; M€
olders et al., 2003a) that is able
to capture the processes summarized above. In
addition, in order to describe appropriately
snow-metamorphism, we have included a
multi-layer snow-model in HTSVS. By using
the modified model, we study the influence of
the snow soil-frost system on regional weather.
Simulations with and without the consideration of soil-frost processes are performed both
with and without the inclusion of snow (Table 1).
This hierarchy of experiments allows us to
examine the effect of soil-frost and snow separately, as well as to determine the effects of their
interaction.
Table 1. Nomenclature and brief description of the main
simulations performed in this study
CONTROL
FROSTSNOW
SNOW
FROST
Soil-frost module on
Snow module on
No
Yes
No
Yes
No
Yes
Yes
No
1. the exchange of momentum, heat, and moisture
at the vegetation-soil-atmosphere interface,
with special consideration of heterogeneity on
the micro-scale by the mixture approach, i.e. a
grid-cell can be partly covered by vegetation
(e.g. Deardorff, 1978; Kramm et al., 1996),
2. heat conduction and water diffusion (including the Richards-equation) within the soil
as well as cross-effects such as the LudwigSoret and Dufour effects (e.g. de Groot, 1951;
Prigogine, 1961; Kramm et al., 1996; M€
olders
et al., 2003a),
3. soil freezing and thawing, and the related
release and consumption of latent heat energy
(e.g. Flerchinger and Saxton, 1989; M€
olders
et al., 2003a),
4. water vapor fluxes within the soil (e.g.
Flerchinger and Saxton, 1989; Kramm et al.,
1996),
5. the effects of frozen soil layers on the vertical
fluxes of heat and moisture,
6. water uptake by plants, including a vertically
variable root distribution, and
7. the temporal variation of soil albedo, snow
albedo and snow emissivity (e.g. M€
olders
et al., 2003a).
M€olders et al. (2003a, b) evaluated HTSVS with
soil-frost component by using observed soil temperatures and water recharge. They used a simple
one-layer snow model. For the present study, we
replaced this snow model by a substantially modified version of Fr€ohlich and M€olders’ (2002)
multi-layer snow model, because the comparisons
of various stand-alone versions of snow-models
demonstrated that the number of snow-layers
influences the performance of the snow-models
(e.g. Jin et al., 1999; Slater et al., 2000).
Fr€ohlich and M€olders (2002) coupled the
multi-layer snow model with a force-restore
model in GESIMA (Geesthacht Simulation
Model of the Atmosphere, e.g. Kapitza and
Eppel, 1992; Eppel et al., 1995) assuming that
each grid-cell with snow is totally snow-covered.
The modifications made for our study will be
discussed in section 2.2. They serve to address
snow processes important in high-latitudes, but
Atmospheric response to soil-frost and snow in Alaska in March
less so in mid-latitudes (for which they were
neglected in previous work). Only the equations
of those processes are given which are (1) treated
differently, (2) added, and=or (3) describe coupling of the modified snow model to HTSVS or
of HTSVS to MM5. Appendix A reviews the
main features of the soil-frost model.
2.1 Coupling of HTSVS to MM5
Similar to the treatment of the vegetation-soil
system (e.g. Kramm et al., 1996), a resistance
network analogy serves for determining soil
moisture, soil- and snow temperature. The energy
and water budgets are given by
Rss# Rss" þ Rls# Rls" Hs Ls Es
þ Gsnow þ PH ¼ 0;
P þ S Es ¼ 0;
ð1Þ
ð2Þ
where Rss# , and Rls# are the downward directed
fluxes of short- and long-wave radiation predicted by MM5. Furthermore, Rss" ð¼snow Rss# Þ,
and Rls" ð¼"snow T4snow;surf þ ð1 "snow Þ Rls# Þ
are the upward-directed fluxes of short- and
long-wave radiation (for the emissivity, "snow ,
and albedo, snow , of snow see Appendix B), S
and P (in kg=(m2s)) are solid and liquid precipitation, Es is sublimation, Ls is the latent heat of
sublimation, and PH is the heating of the snowpack by rain. The fluxes of sensible and latent
heat are given by
cp a
ðR Tsnow;surf Þ;
ð3Þ
Hs ¼ rmt;snow þ rt
and
Es ¼ a
rmt;snow þ rt
ðqR qsnow;surf Þ;
ð4Þ
where R and qR (both predicted by MM5) are
the potential temperature and water vapor mixing
ratio at the reference height (first half-layer
above ground), and qsnow;surf is the mixing ratio
at the snow surface. Here, a , rt, and rmt;snow , are
air density, the turbulent resistance of air, and
molecular turbulent resistance, respectively. The
snow heat flux is
@Tsnow
@q
Lv w kv snow ;
ð5Þ
Gsnow ¼ snow
@zsnow
@zsnow
where, qsnow is the mixing ratio at saturation
for ice and Tsnow is the snow temperature,
81
w (¼1000 kg=m3), kv, Lv, and snow ð¼ 0:02 þ
2:5 106 2snow Þ are the density of water, molecular diffusion coefficient of water vapor within
air-filled pores of the snowpack, the latent
heat of condensation, and the thermal conductivity of snow depending on snow density, snow
(Anderson, 1976).
The energy and water budgets of the underlying soil are
ð6Þ
Rsg# Rsg" þ Gg Gsnow;g ¼ 0;
SF þ Wsoil ¼ 0:
ð7Þ
Here, Rsg# ð¼Rss# expðkext hsnow ÞÞ, and Rsg"
ð¼g Rsg# Þ are the downward and upward-directed
fluxes of short-wave radiation through the snowcover to and from the ground. Both quantities
depend on the extinction coefficient of snow, kext,
which in our study is a function of grain-diameter
and snow density (see Appendix B). Upwarddirected short-wave radiation also depends on
soil albedo, g , for which the moisture-dependency is now considered (see Appendix A). Wsoil,
Gg, and Gsnow,g denote respectively the soil
moisture and soil heat fluxes, and the snow heat
flux at the soil-snow interface. The treatment of
infiltration follows Schmidt (1990)
8
P=w <Kws
P=w
< 0:5
2
;
SF ¼ P
w Kws Þ
: w 1 þ 2t KðP=
P=w Kws
ws j k jðs 0 Þ
ð8Þ
where 0 is the volumetric water content at the
onset of precipitation or snowmelt; b, s, and s
are the pore size distribution index, porosity and
water potential at saturation (see Table 2 for
values), and k ¼ j s j=ð1 þ 3=bÞ. Ponding of
water starts at the time tp ð¼ Kw;s j k jðs 0 Þ
½P=w ðP=w Kw;s Þ1 Þ, when precipitation or
melt-water exceed the hydraulic conductivity of
soil at saturation, Kws (Table 2). Infiltration then
slows down.
2.2 Main equations of the snow model
Snow depth, hsnow, increases by the deposition of
new snow and decreases by sublimation, outflow
of melt-water, and the increase of snow density
by windbreak, compaction, settling, melt-water
percolation, and freezing. The water equivalent,
hw, is the depth of water that would result after
82
N. M€
olders and J. E. Walsh
Table 2. Soil characteristics for the mineral and organic soils considered in our study. Here, ks, s, b, s and cSS are the
saturated hydraulic conductivity, porosity, volumetric water content at saturation, pore-size distribution index, water potential at
saturation, and volumetric heat capacity of the dry soil material. Parameters are from Clapp and Hornberger (1978), Cosby et al.
(1984), Pielke (1984), Chen and Dudhia (2001), and Beringer et al. (2001)
Soil-type
ks 104 m=s
s m3=m3
b
loamy sand
sandy loam
loam
clay loam
clay
bedrock
glaciers
organic material
peat
lichen
moos
1.563
0.341
0.070
0.025
0.013
0.0974
1.34
3.38
0.2
1.5
2.0
0.410
0.435
0.451
0.476
0.482
0.25
0.421
0.451
0.7
0.9
0.95
4.38
4.90
5.39
8.52
11.40
11.55
11.55
5.25
4
1
0.5
complete melting of the snow-cover (e.g.
Dingman, 1994):
snow
:
ð9Þ
hw ¼ hsnow
w
Snow density depends on the volumetric water
content, , and porosity, , of the snow (e.g.
Dingman, 1994):
snow ¼ ð1 Þice þ w ;
ð10Þ
where ice (¼916 kg=m3) is the density of ice. In
contrasts to saturated soils, the pore-space is not
totally filled by water in saturated snowpacks.
This effective porosity is (e.g. Dunne et al.,
1976)
¼
snow ice
;
ret w ice
ð11Þ
with ret being the maximum volumetric water
content that the matured snowpack can hold
against gravity (e.g. Dingman, 1994)
ret ¼
3:528 104
ð2:67 104 snow 0:0735Þ snow
w
snow 280 kg=m3
:
snow > 280 kg=m3
(12)
Fr€ohlich and M€
olders (2002) neglected sublimation, as it is of minor relevance in midlatitudes. In high-latitudes, sublimation is an
important process of latent heat exchange, and
it can reduce snow depth notably (e.g. Dery
et al., 1998; Pomeroy et al., 1998; Dery and
Yau, 2002). The rate of change of snow depth
s
m
0.090
0.218
0.478
0.630
0.405
7.59
0.036
0.355
0.12
0.12
0.85
cSS 106 Jm3 K1
"g
1.41
1.34
1.21
1.23
1.09
1.9131
1.92556
0.84
1
1
1
0.95
0.95
0.95
0.95
0.95
0.98
0.82
0.97
0.97
0.97
0.97
by sublimation is given by:
@hsnow
Es
¼
:
ð13Þ
@t
snow
We neglect redistribution of snow depth by blowing snow, assuming that the associated variation
in snow depth will average out over the size of a
model grid-cell of several square kilometers. As
we only simulate a short period, we neglect the
contributions of snow-blow to sublimation that
can affect winter (7–8 month) sublimation by
10% (Dery and Yau, 1999).
We replaced the stepwise relation between
wind speed jvj and snow density used by
Fr€ohlich and M€olders (2002) by a continuous
function (Boone, 2000)
pffiffiffiffiffi
ð14Þ
snow;surf ¼ A þ BðTR T0 Þ þ C jvj
with A ¼ 109 kg=m3, B ¼ 6 kg=m3=K and
C ¼ 26 kg s1=2m7=2, TR and T0 are the air temperature at reference height, and the freezing
point temperature in K.
The rate of change in snow density by compaction is calculated by (e.g. Anderson, 1976)
1 @snow
¼ C1 expð0:08ðT0 Tsnow ÞÞWsnow
snow @t
expðC2 snow Þ
ð15Þ
where Wsnow is the weight of the overlying
snowpack, Tsnow is snow temperature, and
and
C2 ¼ 2.1 C1 ¼ 2.777 104 m1 s1 ,
102 m3 kg1 .
Atmospheric response to soil-frost and snow in Alaska in March
Destructive metamorphism is computed by
(Anderson, 1976)
1 @snow
¼ C3 expðC4 ðT0 Tsnow ÞÞ
snow @t
expð0:046ðsnow c ÞÞ snow c
snow < c
1
;
(16)
s , C4 ¼ 0.04 K , and
6 1
1
with C3 ¼ 2.777 10
c ¼ 150 kg=m3.
If Tsnow exceeds T0, any further energy supplied will produce melt-water. Once retention
capacity is exceeded, percolation, J, through
the matured snow-layer sets in:
J ¼ w kw :
ð17Þ
Here, kw is the hydraulic conductivity given by
(e.g. Colbeck, 1978)
3
gw 3 gw
KS ¼
K
;
ð18Þ
kw ¼
w
w
where w ( ¼ 1.792 103 kg=(ms)) is the viscosity of water, and g is acceleration of gravity. The
permeability K (¼ 0:077d2 exp½7:8snow =w )
(e.g. Colbeck, 1978) depends on grain-diameter,
d (¼ 2 104 expð5 103 snow Þ) and snow density (e.g. Wanciewicz, 1978). If the snowpack
becomes colder than T0, melt-water will freeze
until no liquid water exists or the released heat
raises Tsnow to T0.
During snow-melt a fractional snow-coverage
is likely to occur, for which inclusion of a parameterization for a subgrid-scale snow-coverage is
planed for the future. In our study no melting
occurs, and partly melted snow-coverage can be
excluded.
In accord with MM5, new snow has the same
temperature as air at reference height. As an
improvement to Fr€
ohlich and M€
olders (2002),
the equation of heat transport within the
snowpack now also includes the effects of (a)
water flowing with temperature Tw through the
snowpack, and (b) heat transport by radiative
heating
@Tsnow
@ 2 Tsnow
@
¼ snow
Lf w
2
@t
@t
@z
#
@Tw @Rss;z
þ Csnow w
:
ð19Þ
@z
@z
These additional processes are important for
long-lasting snow-covers typical in high-lati-
Csnow
83
tudes. The first term on the right hand side of
Eq. 19 describes heat diffusion. The second term
is the consumption and release of latent heat by
phase transition processes. The third term represents advection of temperature by percolating
melt-water. The last term denotes the temperature change due to the solar energy scattered
and absorbed within the snowpack (e.g. Dunkle
and Bevans, 1956), where
R#ss;z ¼ R#ss ð1 snow Þ expðkext;z ðhsnow zÞÞ;
ð20Þ
with kext,z being the extinction coefficient for the
snow-layer from the surface at hsnow to the level z
in the snowpack.
The constant values for the volumetric heat
capacity of snow, Csnow, used by Fr€ohlich and
M€olders (2002) was replaced by a dependency
on the composition of snow:
Csnow ¼ ð1 Þcice ice þ cw w þ ð Þcp a ;
ð21Þ
where cice (¼2105 J kg1 K1 ) is specific heat
capacity of ice, – is the air-filled pore-space,
and cp (¼1004 J kg1 K1 ) is specific heat
capacity of air at constant pressure.
The change in the volumetric water content in
a snow model-layer is given by
@
@J cice snow @Tsnow
:
ð22Þ
¼ þ
Lf w
@t
@t
@z
3. Experimental design
3.1 Model set up
MM5 (Dudhia, 1993) is the atmospheric model
used in this study. The explicit moisture scheme
of Schultz (1995) is applied to clouds at the
resolvable scale, and Grell’s cumulus scheme
(1993) for subgrid-scale clouds. Grell et al.’s
(1994) simple radiation scheme is used. The
treatment of boundary layer physics follows
Hong and Pan (1996).
The model domain (shown in Fig. 3) has
54 54 points, a grid horizontal spacing of
36 km, and 23 vertical layers reaching to
100 hPa. There are five snow-layers, five soillayers, and one canopy layer. The snow-layers
are of equal thickness depending on snow depth.
The lower boundaries of the soil layers are at
84
N. M€
olders and J. E. Walsh
0.01, 0.23, 0.54, 1.27, and 2.95 m with
the centers at 0.07, 0.15, 0.36, 0.83, and
1.93 m, respectively. We use a time step of
108 s.
Fig. 3 (continued)
3.2 Model input data and initialization
Fig. 3. (a) Soil-type distribution, (b) land-use distribution,
and (c) topography as used in our study
The simulations encompass March 1, 2001 0600
UT thru March 11, 2001 0600 UT. Initial and
boundary conditions are obtained from the NCEP
and NCAR Reanalysis Project (NNRP data). The
vegetation fraction of each grid-cell is a weighted
combination of the February and March monthly
five-year mean green vegetation cover data
(0.15 resolution) derived from AVHRR data
(Gutman and Ignatov, 1998). The 1-km resolution
USDA State Soil Geographic Database (Miller
and White, 1998) and 10-min resolution USGSterrain and vegetation data are used for the
soil-texture, terrain elevation, and land-use type
(Fig. 3). Tables 2 and 3 list the soil physical and
plant physiological parameters used. In accord
with Dingman (1994), field capacity and wilting
point are the volumetric water content for which
water potential drops to 3.4 m and 150 m,
respectively.
Initial snow depths are from the NNRP data.
Snow density of each snow model-layer is set to
300 kg=m3, a value typical for February–March
(e.g. Sturm and Holmgren, 1998).
Interpolated total soil moisture and temperature data from the NCEP operational Eta forecasts served to initialize these quantities. We
modified Chen and Dudhia’s (2001) interpolation
procedure for the grid spacing of HTSVS. In all
Atmospheric response to soil-frost and snow in Alaska in March
85
Table 3. Plant specific parameters for land surface types that occur in the model domain (from Pielke, 1984; Wilson et al., 1987;
Jackson et al., 1996). Here, rst,min, c, m, a, Rr, bst,Tmin, Tmax, Topt, "f, f and zroot are the minimum stomatal resistance, water
potential, at which the production of cytokinis by roots is sufficiently reduced to close stomata, the fine root (ovendry) biomass,
the partitioning of roots between the upper and lower root zone, the mean root radius, a parameter used to calculate stomatal
resistance, the temperatures, at which stomata close, the temperature at which rst reaches its minimum, the albedo and emissivity
of foliage surface, and the maximum root depth, respectively. Average volumetric density of roots (ovendry) is set to 500 kg=m3.
Note that if root depth exceeds the maximum depth of the soil model, maximum root depth is 2 m. Z0 is roughness length
Land-use
rst,min
c
s=m m
grassland
shrubland
deciduous needleleaf forest
evergreen needleleaf forest
mixed forest
water bodies
barren or sparsely vegetated
wooded tundra
mixed tundra
glaciers=sea ice
70
300
232
125
125
-.999
150
150
-.-
92
133
214
163
158
-.92
163
163
-.-
m
a
kg=m2 -.-
bst Tmin Tmax Topt f
Rr
104 m -.- C
C
C -.-
"f
-.-
zroot
m
z0
m
70
4.8
7.1
12.7
8.2
-.3.3
15.5
2.9
-.-
0.925
2.51
3.5
3.5
3.5
-.0.925
3.5
3.5
-.-
0.97
0.95
0.95
0.97
0.96
0.993
0.91
0.97
0.97
0.82
2.6
7.0
2.9
3.9
3.12
-.0.5
1.81
1.81
-.-
0.08
0.03
0.85
1.09
0.8
0.0001
0.01
0.06
0.05
0.01
0.24
0.36
0.02
0.02
0.02
-.0.22
0.4
0.4
-.-
simulations, soil temperature and total soil moisture at the bottom of the soil model are constant
throughout the simulation.
No assumptions on the depth of permafrost are
required, as HTSVS works for both the permafrost and the active layer that is partly frozen in
winter. According to the NNRP data permafrost
is mostly continuous in northern Alaska, discontinuous in central Alaska, and absent in southern
and southeastern Alaska near the coast. In accord
with Woo (1986) it is below 0.5 m over large
areas.
The treatment of soil-frost requires determining the fraction of the total soil water that is
initially frozen at the given initial soil temperature. Freezing increases soil temperature (cf. Eqs.
(A1) to (A5) in Appendix A), and the volumetric
heat capacity differs between the frozen and
unfrozen soil. Maximum liquid water content at
temperatures below zero depends on soil-type
(cf. Eq. (A5)). All soils with high fractions of
clay allow more than 0.6 of the total pore volume
(¼1) to be filled with super-cooled water, even at
low soil temperatures (e.g. Fig. 3). The
maximum relative liquid water content, =s,
decreases rapidly with decreasing soil temperature for soils with high fractions of silt, sand,
loam, or organic material (e.g. Fig. 3). Moss
and lichen allow for less than 0.01 of the relative
soil volumetric water content to be in the liquid
phase at temperatures below freezing (therefore
20
5
10
5
22 10
25 5
23
0
-.- -.20
5
40
5
40
5
-.- -.-
45
45
45
35
40
-.45
40
40
-.-
9
25
25
25
25
-.9
25
25
-.-
0.19
0.25
0.11
0.10
0.12
0.19
0.12
0.16
0.16
0.8
not shown). Freezing of soil water in loamy and
sandy soils and the insulation of peat and moss
may offset each other (e.g. Pauwel and Wood,
1999a, b).
Although HTSVS is able to resolve different
soil types with depth (e.g. M€olders et al., 2003a)
and to consider organic soils (Fig. 3), these
effects cannot be included in mesoscale modeling at the moment. The reason is that data sets
with a vertical resolution of different soil types
are not available at the required horizontal
extent, and organic soils are often of subgridscale with respect to the typical resolution of
mesoscale models.
In initializing soil-frost, care must be taken
that the simulations with and without soil-frost
have the same initial total soil moisture and soil
temperature. The total soil-water is distributed
between the liquid and solid phase using a rearranged form of Eq. (A4) to assure local equilibrium between soil temperature, soil volumetric
liquid water and ice content at the same soil temperature (Fig. 4a).
As part of the soil-water is frozen, the volumetric liquid water content is up to 0.266, 0.270,
0.271, 0.286, and 0.293 m3 m3 lower at the
beginning of the simulations with soil-frost than
without soil-frost (e.g. Fig. 4b, c). The distribution of frozen soil correlates with soil-type and
terrain elevation (cf. Figs. 3a, c, 4b, c). A higher
fraction of the total soil water freezes in loam
86
N. M€
olders and J. E. Walsh
than in the other soil-types (Figs. 2, 3a, 4b, c).
Since less soil-water can be in the liquid phase at
lower soil temperatures (e.g. Fig. 2), and total
Fig. 4 (continued)
soil water increases with depth, the fraction of
frozen soil increases with depth.
The above initialization procedure ensures that
initial total soil water and soil temperature are
the same for all simulations (Fig. 4a). Note that
starting with zero ice content would warm the
soil due to the release of latent heat, and there
would be no ice at the lower boundary because of
the constant soil conditions at the bottom of the
soil model. Under such conditions, an upwarddirected moisture flow would establish, resulting
in a source of energy as the soil-water transports
heat.
3.3 Numerical experiments
Fig. 4. Initial distribution of (a) soil temperature in K
(same for all four simulations), and soil volumetric liquid
water content (m3 m3 ) in the uppermost soil layer for (b)
CONTROL, and (c) FROSTSNOW. Note that the initial
distribution of soil liquid water content of SNOW is the
same as for CONTROL and that of FROST is the same as
for FROSTSNOW. Note that the scaling is different in (b)
and (c) for showing more details
Oceans surround Alaska except to the east
(Fig. 3). To examine the impact of the Alaskan
soil-frost snow system on weather, a synoptic
situation has to be chosen under which no air
that has felt and been directly affected by the
Canadian soil-frost snow system enters the
domain over the lateral boundaries. For such air,
the signal due to the soil-frost snow system
would be difficult to separate from the simulations with and without snow-cover and=or soilfrost in Alaska. The period from March 1,
Atmospheric response to soil-frost and snow in Alaska in March
87
0600UT 2001 to March 11, 0600UT 2001 fulfills
these conditions through its prevailing airflow
from the south.
We run the model alternatively with and without soil-frost in combination with and without
the inclusion of snow (Table 1). These simulations are denoted FROSTSNOW, SNOW,
Fig. 5 (continued)
Fig. 5. Distribution of column integrated cloud hydrometeors in mm at the end of integration (March 11, 2001
0600 UT) for (a) CONTROL, (b) SNOW, (c) FROST, and
(d) FROSTSNOW
FROST, and CONTROL, respectively, as are
their results (i.e. the CONTROL simulation
includes neither soil-frost nor snow). As the
underlying surface affects the overlying air mass,
the initial atmospheric data indirectly include
information on the soil-frost snow system. To
lose this information, several days of simulation
are required. Moreover, soil can have a longer
memory for its initial conditions. Since we
use the soil temperature and total water content
88
N. M€
olders and J. E. Walsh
conditions from NCEP reanalysis (herein the soil
has spun up already), spin-up is only required
because of the introduction of the frozen phase
and a different grid. We allowed the soil to spinup until domain-averaged soil temperatures vary
less than 0.1 K from one day to the next in the
soil layers that do not experience a diurnal cycle.
The model achieves this condition after eight
days of simulation. This leaves March 9, 2001
0600 UT to March 11, 2001 0600 UT for the
investigations of the impact of the soil-frost snow
system on weather.
3.4 Synoptic situation
On March 9, 2001, the synoptic situation was
governed by a low-pressure system in the Pacific
Ocean south of the Aleutian Islands, and highpressure systems over the Arctic Ocean and north
of the Hudson Bay. Therefore, Alaska was under
southerly flow that acquired an easterly component over north-west Alaska (but not at the
model’s eastern lateral boundary). This weather
situation was relatively stationary until the end of
the episode. At the beginning, a cloud system
existed over southern Alaska with some cloud
bands extending into the central Yukon Territory.
The cloudiness moved northwards, covering
most of the Yukon Territory and eastern Alaska
at the end of the episode (Fig. 5a–d). At this time
of year, night and day have about the same
length, and solar angles are low.
FROSTSNOW (Appendix B). Emissivity depends
on vegetation-fraction, vegetation- and soil-type
(Tables 2, 3) in the former simulations, and on
snow-age in the latter (see Appendix B). These
differences affect the energy budget directly.
The high albedo of the snow-cover increases
shortwave upward-directed radiation relative to
snow-free conditions. Whether upward-directed
fluxes of long-wave radiation are smaller or
greater in the simulations with snow-cover than
in those without snow-cover depends on the time
passed since the last snow-event (cf. Tables 2, 3,
Appendix B). Radiative cooling is strong in
response to high surface albedo, leading to on
average lower temperatures in cloud-free areas
with than without snow-cover (cf., e.g. Figs. 5,
6). For all simulations, air temperatures differ
below 700 hPa, especially in cloudy areas. Here,
differences due to the release of latent heat and
consumption of heat during phase transition processes are superimposed on those caused by the
altered surface fluxes.
Domain-averaged long-wave downward radiation differs less than 5 Wm2 between the
four simulations. Domain-averaged short-wave
downward radiation differs less than 10 Wm2
4. Results
We first highlight the general aspects of the four
numerical experiments (Table 1), and discuss the
effects of snow-cover and soil-frost separately
before evaluating their combined impacts. For
brevity, we restrict the discussion to notable differences rather than a complete discussion of all
quantities.
4.1 General findings
While snow covers all land surfaces in
FROSTSNOW and SNOW, glaciers, and sea-ice
are the only frozen water in FROST and
CONTROL. Surface albedo depends on vegetation type (Table 3) and soil liquid volumetric
water content in CONTROL and FROST
(Appendix A), but on snow-age in SNOW and
Fig. 6. Distribution of air temperature in C at 850 hPa at
the end of integration (March 11, 2001 0600 UT) for (a)
CONTROL, and differences (b) CONTROL minus SNOW,
(c) CONTROL minus FROST, and (d) CONTROL minus
FROSTSNOW
Atmospheric response to soil-frost and snow in Alaska in March
89
Fig. 6 (continued)
Fig. 6 (continued)
between the two simulations without snowcover; differences are similarly small between
the two with snow-cover. These differences
represent the effect of soil-frost. In cloudy
(cloud-free) areas (see Fig. 5), domain-averages
of short-wave net radiation are about 110 Wm2
(40 Wm2 ) greater in the simulations without
snow-cover than with snow-cover. This explains
some of the differences found between the simu-
lations without and with snow-cover. Differences
between cloudy and cloud-free areas are up
to 180 Wm2 for long-wave and 80 Wm2 for
short-wave downward directed radiation, resulting in some of the differences found between
cloudy and cloud-free areas. The greatest differences in short-wave and long-wave downward
directed radiation occur along the edges of cloud
fields when one of the simulations provides
clouds while the other does not, and in areas
where cloud properties differ appreciably.
The exchange of water and heat at the surface
occurs at the vegetation-soil-atmosphere interface in CONTROL (FROST) and at the snowatmosphere interface in SNOW (FROSTSNOW).
Over land, sensible heat fluxes are negative
(downward) for all simulations, on average. They
are lower (by up to 15 Wm2 in the domain-average at noon) with snow-cover than without. The
sensible heat fluxes obtained by simulations
without snow-cover differ little in the domainaverage, but locally large differences occur
(e.g. Fig. 7c). The same is true for the simulations with snow-cover (e.g. Fig. 7b, d) where
local differences are greater than 100 Wm2 .
In cloud-free areas, the simulations with snowcover provide lower domain-averaged sensible
heat fluxes than those without (see also Fig. 7).
We conclude that soil-frost has less impact on the
90
N. M€
olders and J. E. Walsh
sensible heat fluxes than snow-cover for the
given synoptic conditions typical for Alaska in
March.
In general, the domain-averaged latent heat
fluxes are higher in cloudy than cloud-free areas
(less than 3 Wm2 before sunrise, 18 Wm2 at
noon). As will be explained later, in cloudy
areas, SNOW and FROSTSNOW supply more
water vapor to the atmosphere than FROST or
Fig. 7 (continued)
Fig. 7. Like Fig. 6, but for turbulent fluxes of sensible heat
in Wm2
CONTROL, on average (e.g. Figs. 5, 8). Latent
heat fluxes of SNOW are usually greater than
those of FROSTSNOW (1 Wm2 at noon on
the domain-average). In cloud-free areas, latent
heat fluxes of CONTROL and FROST exceed
those of SNOW and FROSTSNOW (1 Wm2 in
the domain-average at noon). We conclude that
soil-frost tends to reduce the water supply to the
atmosphere, but has less impact on latent heat
fluxes than the snow-cover (e.g. Fig. 8).
Atmospheric response to soil-frost and snow in Alaska in March
91
In cloud-free areas, incoming energy is partitioned in favor of surface ground=snow heat and
sensible heat fluxes rather than latent heat fluxes.
In cloudy areas, the partitioning shifts to latent
heat fluxes, mainly at the cost of sensible heat
fluxes. This results from the fact that relatively
colder air (cloud-free areas) can take up less
water vapor than relatively warmer air (cloudy
areas).
Fig. 8 (continued)
Fig. 8. Like Fig. 6, but for turbulent fluxes of latent heat in
Wm2
Soil temperature differences due to soil-frost
decrease with depth with the largest differences
occurring in mountainous areas (Fig. 9). At
depth, soil temperatures are related to the longterm climatic conditions. In the uppermost
layers, soil temperature interacts with the surface
atmospheric conditions and, hence, air and soil
temperatures are loosely related. Because air
temperature generally decreases with height
92
N. M€
olders and J. E. Walsh
there is a slight dependency on terrain height also
for the uppermost layers (cf. Figs. 3c, 9a). Soil
volumetric ice and, hence, liquid water content
are sensitive to soil temperature for which they
are indirectly related to terrain height. As will be
discussed later snow depth affects soil temperature by insulating. Thus, in upper soil layers,
relatively lower (higher) soil temperatures occur
where the snow pack is thin (thick; Fig. 10). Note
Fig. 9 (continued)
Fig. 9. Like Fig. 6, but for soil temperature in the uppermost model layer and ocean surface temperature in K
that some soil types correlate with terrain height
(cf. Figs. 3a, c). Other temperature-dependent
quantities like the turbulent fluxes of sensible
and latent heat fluxes also are indirectly affected
by terrain-height.
Ground surface temperatures describe the
conditions at the soil-atmosphere interface in
CONTROL and FROST, and at the ground-snow
interface in SNOW and FROSTSNOW. On average, they are (up to 15 K) lower in cloud-free
Atmospheric response to soil-frost and snow in Alaska in March
93
than cloudy areas for the simulations without
snow-cover, because the ground surfaces are
directly exposed to the atmosphere. Soil-frost
increases the differences. Domain-averaged
ground surface temperatures are (up to 10 K)
lower in cloud-free than cloudy areas in the
simulations including snow-cover. Under a
snow-cover, soil-frost tends to increase the differences slightly (0.2 K in the domain-average),
reducing ground temperatures in cloud-free and
enhancing them in cloudy areas, on average. The
differences in ground-surface temperature indicate an insulating effect of about 4 K by the
snow-cover averaged over all areas. The effect
is less in areas of thin rather than thick snowcover. Differences in snow depth (Fig. 10) result
from altered latent heat fluxes, snow-metamorphism, and in some areas from differences in snowfall (Fig. 11). Snow depth affects soil frost,
and, hence, soil volumetric liquid water and ice
content (Figs. 12, 13)
Surface temperature describes the temperature
at the soil-vegetation-atmosphere interface in
CONTROL and FROST, and at the snow-atmosphere interface in SNOW and FROSTSNOW.
Generally, surface temperatures of cloudy areas
exceed those of cloud-free areas (by up to 20 K);
the surface temperatures are (up to 6 K) higher
for simulations without snow-cover than with
snow-cover. Soil-frost tends to reduce surface
temperatures slightly when no snow-cover is
present, i.e. soil frost contributes to its own
persistence.
4.2 The effect of snow-cover
alone – CONTROL versus SNOW
Fig. 10. Distribution of (a) snow depth (Thickness of glaciers and sea ice are the same in all simulations and excluded from this plot for better illustration.) at the end of
the simulation with SNOW in m (Snow depth plotted includes initial snow depth.), and (b) difference in snow depth
SNOW minus FROSTSNOW in mm at the end of the simulations. Units differ in (a) and (b) for better illustration.
Differences in cloud-free areas are due to sublimation and
snow-metamorphism, and in some areas additionally due to
differences in snowfall (see text for further discussion)
In CONTROL, the atmosphere feels the soilvegetation system, while in SNOW it is in contact with snow-cover. A comparison of these
simulations shows the role of snow-cover alone,
since soil-frost is present in neither.
After spin-up, volumetric liquid water content
of SNOW is (locally as much as 0.142, 0.116,
0.090, and 0.050 m3 m3 from the uppermost soil
layer downwards) greater than in CONTROL.
This pattern remains similar until the end of the
simulation. Differences relate to soil-type, with
the greatest differences occurring in sandy loam
(cf. Figs. 3, 4b, 12b), which permits quick migration of liquid water (Table 2). The differences in
94
N. M€
olders and J. E. Walsh
soil liquid volumetric water content propagate to
different soil moisture gradients. Below the third
soil model layer, soil volumetric water content
hardly differs between CONTROL and SNOW.
Differences in soil liquid volumetric water
content (e.g. Fig. 12) result from the altered soil
moisture and heat fluxes caused by snow-cover.
In SNOW, the snow-cover (Fig. 10) protects the
Fig. 11 (continued)
Fig. 11. Like Fig. 5, but for precipitation accumulated
during the last 48-hours of the simulation (March 9, 2001
0600 UT to March 11, 2001 0600 UT) in mm water
equivalent
soils from losing water by evaporation, and satisfies the atmospheric demands. In the snowpack,
air is saturated with respect to ice, and the water
vapor fluxes from the soil in the snowpack
are small or even directed into the soil. In
CONTROL, the moisture gradient and wind
drive evaporation of soil-water, and the soil loses
water by satisfying the atmospheric demands
(e.g. Fig. 12b).
After spin-up, soils in SNOW are warmer
(locally as much as 11.6, 15.2, 11.5, and 3.6 K
Atmospheric response to soil-frost and snow in Alaska in March
95
from the uppermost soil layer downwards) than
in CONTROL along the Arctic Ocean, in the
Yukon Flats and lower McKenzie river basin,
and colder elsewhere. Again, the general pattern
Fig. 12 (continued)
Fig. 12. Like Fig. 6, but for soil volumetric liquid water
content in the uppermost model layer in m3 m3 . Note that
the scaling is different than in Fig. 4 for showing more
details
remains similar for the rest of the simulation time
(e.g. Fig. 9b). Differences relate to terrain height
(e.g. Figs. 3c, 9b), and mainly result from the
insulating effect of the snowpack. The snowpack
is less thick over the Brooks Range than along
the Arctic Ocean (Fig. 10a). Comparison with the
soil temperature differences shows that SNOW
96
N. M€
olders and J. E. Walsh
The altered moisture gradients slightly (less than
0.1 K) affect soil temperature (Dufour effect; cf.
Eq. A2). The differences in soil temperature gradients contribute to water fluxes and slightly (less
than 0.001 m3=m3) affect soil volumetric water
content (Ludwig-Soret effect; cf. Eq. (A1)). As
differences in soil temperature caused by snow
can last long after melting (e.g. M€olders et al.,
2003a), they may have implications for plant survival and ecosystems (e.g. Kongoli and Bland,
2000; Zhuang et al., 2003).
The surface-atmosphere interface is, on average, colder in SNOW than in CONTROL. In
cloudy areas, ground surface temperatures of
CONTROL exceed those of SNOW, while the
opposite is true in cloud-free areas. This means
that the snow-cover protects the soils from cooling in cloud-free areas, and hinders its warming
in cloudy areas. In the ABL, air temperatures of
SNOW exceed those of CONTROL in cloudy
areas (by more than 2 K); the opposite is true
in cloud-free areas (e.g. Figs. 5b, 6b), indicating
that clouds strongly affect the net surface longwave radiation flux.
Fig. 13. Like Fig. 6, but for soil volumetric ice water content in the uppermost soil layer for (a) FROST, and
(b) FROSTSNOW in m3 m3
predicts lower (higher) soil temperatures in areas
of thin (thick) snowpacks. The thinner the
snowpack is, the greater the soil temperatures
of SNOW and CONTROL differ (Figs. 9b, 10).
Fig. 14. Distribution of surface pressure at sea level in hPa
and wind vectors at about 30 m height above ground at the
end of integration (March 11, 2001 0600 UT) for (a)
CONTROL, and differences in sea level pressure for (b)
CONTROL minus SNOW, (c) CONTROL minus FROST,
and (d) CONTROL minus FROSTSNOW
Atmospheric response to soil-frost and snow in Alaska in March
97
Fig. 14 (continued)
Fig. 14 (continued)
In CONTROL, the greater surface heterogeneity without snow-cover contributes to a pattern of
upward or downward motions relative to SNOW.
In SNOW, the greater stability reduces vertical
mixing, and the smoother surface increases wind
speed and changes wind direction in the ABL
relative to CONTROL. Nevertheless, the greatest
differences in the wind field coincide with the
areas of the greatest differences in temperature.
The differences in temperature propagate into the
pressure field, leading to 1.17 hPa lower pressure
in the meso-low over the interior Alaska in
SNOW than CONTROL (Fig. 14b). Ross and
Walsh (1986) found comparable impact of
snow-cover on East Coast cyclones in a study
that was primary statistical. We conclude that
the altered pressure contributes greater to
changes in wind speed and direction than the
modified roughness.
SNOW shows lower surface latent heat fluxes
(3 Wm2 in the domain-average) in cloud-free
areas, but generally greater fluxes (2 Wm2 at
noon, 6 Wm2 at night in the domain-average)
in cloudy areas than in CONTROL (e.g. Fig.
8b). Sublimation of snow occurs at saturation
for ice, which corresponds to lower humidity
relative to evaporation of water in general. In
the soil, water experiences not only gravitational
forces, but also adhesive and surface tension
forces in the fine- and middle-pores, where it is
less freely accessible for evaporation than open
water. Nevertheless, evaporation of soil-water in
CONTROL exceeds that of sublimation of snow
in SNOW in cloud-free areas (e.g. Fig. 8b),
because cold air can take up less water vapor
than warm air. In cloud-free areas, the colder
air of SNOW leads to lower latent heat fluxes
relative to CONTROL. In cloudy areas, the
98
N. M€
olders and J. E. Walsh
warmer conditions allow the air to take up more
water. As temperatures differ less between
CONTROL and SNOW in cloudy than cloud-free
areas (e.g. Figs. 5b, 6b), the temperature conditions are no longer more favorable for water
uptake in the former than the latter, and cannot
compensate for CONTROL’s ‘‘disadvantage’’ of
the forces hindering evaporation of soil-water
and SNOW’s ‘‘advantage’’ of the lower saturation pressure over ice than water.
In SNOW, clouds are horizontally more extensive (e.g. Fig. 5a, b) and have more precipitable
water (up to 0.7 mm) than in CONTROL. In
cloud-free areas, the atmosphere contains less
water vapor in SNOW than CONTROL. SNOW
predicts more precipitation (up to 5.7 mm=48 h)
and at more places than CONTROL, but locally
values are smaller by more than 6.4 mm=48 h
(Fig. 11b), especially over inland areas of high
terrain.
The following feedbacks contribute to the differences. In cloud-free areas, the higher albedo
and stronger radiative cooling of SNOW lead to
lower surface temperatures, reduced surface
sensible heat flux (e.g. Fig. 7b), a colder (e.g.
Fig. 6b) and more stable ABL than CONTROL.
This result agrees with findings from other studies (e.g. Segal et al., 1991; Baker et al., 1999).
Because of the colder conditions in SNOW, the
atmospheric demands and latent heat fluxes are
less than in CONTROL (e.g. Fig. 8b). Thus, a
positive feedback to cooler, drier conditions
establishes in cloud-free areas. Since at relatively
lower temperature, saturation pressure is lower
than at relatively higher temperatures, the horizontal extension of the cloud fields is slightly
larger in SNOW than CONTROL (e.g. Fig. 5).
This means the clouds occur earlier in SNOW
than in CONTROL as the front moves in. In
cloudy areas, radiative cooling is less and the
ABL is warmer relative to cloud-free areas (e.g.
Fig. 6b). This shift to warmer conditions results
in higher latent heat fluxes at the snow-atmosphere interface of SNOW than at the soilvegetation-atmosphere interface of CONTROL
(e.g. Fig. 8b). It leads to an increase of precipitable water, release of latent heat during condensation=deposition, and warming of the ABL in
SNOW, which again favors sublimation. In addition, long-wave radiational trapping increases as
air’s water vapor content increases. The addi-
tional condensate contributes to a reduction of
cooling and an increase of precipitation in
SNOW relative to CONTROL (Fig. 11b).
4.3 The effect of soil-frost alone –
CONTROL versus FROST
After spin-up, FROST has less liquid water content from the top downwards, locally as much as
0.154, 0.147, 0.153, 0.157, and 0.293 m3 m3
than CONTROL. Soil liquid volumetric water
content of FROST remains less than in
CONTROL for the entire simulation time (cf.
Fig. 12c). On average, differences are the greatest for loam (e.g. Fig. 12c) as for this soil-type
the amount of liquid water decreases more
strongly with decreasing soil temperature than
for all other soil-types occurring in the domain
except for loamy sand (cf. Fig. 2). As loamy sand
exists in areas of more moderate temperatures,
differences are less than for loam (Figs. 3a, 9c).
Differences in volumetric liquid water content
mainly result from soil-frost (e.g. Fig. 13a), but
altered soil moisture and heat fluxes contribute to
them (including the Ludwig-Soret effect). Given
similar atmospheric conditions, soil temperatures
and soil total volumetric water content, the water
supply to the atmosphere from an unfrozen soil
exceeds that from a frozen soil. More water can
evaporate from the unfrozen soil in CONTROL
than the partly frozen soil in FROST.
After spin-up, soil temperatures differ locally
as much as 5 K, 4 K, 3.6 K, and 2 K from the
uppermost soil layer downwards. Differences of
both signs and similar magnitude exist through
the end of the simulations (e.g. Fig. 9c) and result
mainly from the release of latent heat and consumption of heat during freezing and thawing.
Differences in soil liquid water gradients affect
soil temperatures slightly (cf. Eq. (A2); Dufor
effect). As soil temperature differences caused
by soil-frost remain long after the soil-frost event
(M€olders et al., 2003a), we have to conclude that
neglecting of soil-frost processes can lead to
wrong estimates of the onset of phenological seasons (e.g. Zhuang et al., 2003).
FROST predicts generally warmer (up to
3.7 K) near-surface air temperatures in cloudy
areas than CONTROL (e.g. Figs. 5c, 6c). On
average, at 850 hPa the atmosphere is slightly
warmer (about 0.1 K) in FROST than CONTROL
Atmospheric response to soil-frost and snow in Alaska in March
in cloudy areas. In cloud-free areas, FROST provides slightly colder air than CONTROL (e.g.
Figs. 5c, 6c).
As more liquid water is available in the soils of
CONTROL (e.g. Fig. 12c) and less energy is
required for evaporation of soil-water than
sublimation of soil-ice, the latent heat fluxes of
CONTROL exceed those of FROST (Fig. 8c)
yielding a slightly moister atmosphere and lower
total soil volumetric water content in the former
than the latter.
Since soil-frost has no effect on aerodynamic
roughness and affects the thermal and moisture
regime of the ABL only slightly, it hardly affects
the pressure field (Fig. 14c).
FROST predicts slightly lower (up to 0.2 mm)
values of precipitable water in cloudy areas
and less extensive cloud fields than CONTROL,
mainly because evaporation is greater in
CONTROL. Soil-frost hardly affects domainaveraged precipitation, but locally enhances or
reduces it by about 2.9 mm=48 h (Fig. 11c).
4.4 The effect of soil-frost
under a snow-cover – SNOW
versus FROSTSNOW
We examine the role of soil-frost under a snowcover by comparing SNOW and FROSTSNOW.
After spin-up, soil liquid volumetric water content differ locally as much as 0.165, 0.165, 0.184,
0.180, and 0.293 m3 m3 from the uppermost
soil layer downwards. Similar differences exist
until the end of the simulations (compare
Fig. 12b, d). Liquid volumetric water content of
FROSTSNOW exceeds that of SNOW in sandy
loam, while it has lower values elsewhere. The
effect of snow-cover on soil-frost is related to
soil-type (compare Figs. 3a, 10b, 12b, d, 13b)
because the snow-cover insulates the soil and
some soils allow more liquid water at particular
super-cooling than others (Fig. 2).
After spin-up, soil temperatures differ locally
as much as 10, 7.4, 5.8, and 3.6 K from the top
downwards. These differences remain of similar
magnitude until the end of the simulations
(compare Fig. 9b, d). The differences exceed
those caused by soil-frost alone, because the
snow-cover hinders the heating of the soil during
the day. Soils are warmer (up to 3.5 K) in
FROSTSNOW than SNOW in Yukon Flats and
99
in sandy loam. The differences in soil liquid
water content and soil temperature result from
soil-frost, and from differences in snow depths
(Fig. 10). Differences in snow depth are due to
differences in snow-metamorphism processes
and latent heat fluxes in the cloud-free northwestern and northern part of the model domain; in
addition to these, discrepancies in snowfall (cf.
Fig. 11b, d) contribute to the differences in snow
depth in the southeastern part of the model
domain.
Differences in precipitation onset or cessation
cause slight changes in albedo and emissivity
between FROSTSNOW and SNOW, contributing
to small changes in short-wave downward radiation, snow surface temperatures, near-surface
air-temperatures, and surface fluxes. Due to differences in the consumption and release of latent
heat (compare Fig. 8b, d), near-surface air temperatures are locally up to 1 K lower and 4 K
higher in the cloudy ABL in FROSTSNOW than
SNOW; the differences decrease with height
(compare Fig. 6b, d). In cloud-free areas, air temperatures hardly differ.
Freezing and thawing alter the fluxes of heat
and moisture in the soil. The warmer soils of
FROSTSNOW result in slightly warmer snowpacks and less variation in ground heat fluxes
relative to SNOW. In cloudy areas, soil-frost
reduces the latent heat fluxes (up to 1 Wm2 in
the domain-average).
Soil-frost hardly affects precipitable water
(0.1 mm) because, in both simulations, sublimation satisfies the atmospheric demands and
the surface characteristics are similar (e.g. aerodynamic roughness, albedo, emissivity). The
effect of soil-frost on precipitation is similar
whether the soil is snow-covered or not (compare
Fig. 11b, d).
4.5 The role of the system soil-frost
snow – CONTROL vs. FROSTSNOW
After spin-up, soil liquid water content locally
differs by as much as 0.160, 0.145, 0.152,
0.157 and 0.293 m3 m3 from the uppermost soil
layer downwards. Such differences exist thru
the end of the simulations (e.g. Fig. 12d). Soil
volumetric liquid water content is lower in
FROSTSNOW than CONTROL, except for some
places along the Arctic coast and Yukon Territory
100
N. M€
olders and J. E. Walsh
throughout the entire simulation time (e.g. Fig.
12d). On average, differences are the greatest in
loam (cf. Figs. 3a, 12d). The differences mainly
result from a combination of the reasons already
discussed for the effects of soil-frost and snowcover alone.
After spin-up, soil temperatures of CONTROL
are, on average, warmer (locally as much as 12,
10, 8, and 4 K from the top downwards) than
in FROSTSNOW. This warm condition remains
until the end of the episode (e.g. Fig. 9d). Soil
temperature differences depend on elevation
(Fig. 3c). They result from the release and consumption of heat during phase transition processes in FROSTSNOW (cf. CONTROL vs.
FROST), the insulating effect of the snow-cover
(cf. CONTROL vs. SNOW), and altered soil
moisture gradients, soil-moisture- and heat
fluxes. In general, the effect of snow is considerably greater than the effect of soil-frost in shaping the pattern in Fig. 9d.
The surface is colder in FROSTSNOW than
CONTROL (up to 7 K in cloud-free, 4.5 K in
cloudy areas). On average, the air close to
the surface is cooler in FROSTSNOW than
CONTROL in cloud-free areas (up to 13 K). In
cloudy areas, the near-surface atmosphere is generally warmer in the former than the latter (up to
5 K). At 850 hPa, the ABL of FROSTSNOW is
(up to 4 K) warmer in cloudy areas, while it
is (up to 1 K) colder than in CONTROL in
cloud-free areas on average (Figs. 5d, 6d). In
FROSTSNOW, the mixing ratios of cloud and
precipitation particles are higher, and the release
of latent heat during phase transitions contributed
to the warmer air than in CONTROL. The optically thicker clouds of FROSTSNOW (Fig. 5a, d)
also protect the ABL more efficiently from cooling than in CONTROL.
Like the effect of snow-cover alone
(CONTROL vs. SNOW), the greatest differences
in temperature propagate into the pressure field,
leading to an approximately 1.20 hPa deeper
pressure over interior Alaska in FROSTSNOW
than CONTROL (Fig. 14d). Hence, soil-frost
slightly increases the effect of snow-cover on
pressure (cf. Fig. 14b, d).
For the reasons discussed for the effects of
snow-cover alone, domain-averaged latent heat
fluxes of FROSTSNOW exceed those of
CONTROL (up to 6 Wm2 at night) in cloudy
areas, while they are (less than 3 Wm2 ) smaller
for FROSTSNOW than CONTROL in cloud-free
areas nearly all the time (Fig. 8d). The inclusion
of soil-frost slightly reduces the water supply in
cloudy areas during daytime relative to no soilfrost (CONTROL vs. SNOW).
In FROSTSNOW, cloud fields are horizontally
more extensive and have more (up to 0.7 mm)
precipitable water than in CONTROL. On average, FROSTSNOW predicts more precipitation
(Fig. 11d), with differences locally as large as
12.2 mm=48 h.
In general, the soil-frost snow system results
in the same positive feedbacks as discussed
earlier for the effect of snow-cover alone. Slight
changes due to soil-frost are superimposed,
affecting precipitation in both directions and
decreasing pressure even more than snow-cover
alone.
5. Conclusions
To examine the synoptic scale influence of
the soil-frost snow system on weather in Alaska
during March, we have introduced a sophisticated soil-frost-vegetation model and multi-layer
snow model into MM5. We performed simulations with and without inclusion of soil-frost
and snow processes as well as their combinations
(Table 1). The altered treatment of the surface
and subsurface processes provides differences
in atmospheric fluxes (e.g. Figs. 7, 8, 11) and
variables of state (e.g. Figs. 5, 6, 9, 12 to 14).
When snow-cover is included, much of the
solar radiation reflects back to space. In cloudfree areas, these circumstances result in a stronger loss of radiant energy, cooling of the air,
and more stable stratification in simulations with
inclusion of snow-cover than without, in agreement with previous studies (e.g. Segal et al.,
1991; Baker et al., 1999). Sublimation of snow
occurs at saturation relative to ice, corresponding
to lower humidity as compared to evaporation of
water. Since the fine and middle pores hold the
water in the soil, soil water is less freely accessible for evaporation than open water. Despite
this disadvantage, evaporation of soil-water in
the simulations without snow-cover over cloudfree areas exceeds the sublimation in the simulations with snow-cover. The colder air of the
simulations with snow-cover contributes to lower
Atmospheric response to soil-frost and snow in Alaska in March
latent heat fluxes relative to the simulations without snow-cover. Thus, in cloud-free areas, a positive feedback to colder, drier conditions develops
in the simulations with snow-cover. Based on this
different thermal and hydrological behavior of
snow-covered and snow-free areas, we conclude
that parameterizations of fractional snow-cover
are an urgent need for large grid-cells (like in
climate models) to better resolve the snow-line,
as well as the local water and energy cycle relevant quantities.
In cloudy areas, predicted air temperatures differ less between the simulations without and with
inclusion of snow processes than in clear areas.
In general, warmer air can take up more water
vapor than relatively cooler air. This means that
the air temperature is no longer more favorable
for water uptake in the simulation with snowcover than without snow-cover. The snow-cover
provides water vapor to the atmosphere by sublimation, while adhesive forces within the soil
hinder evaporation of soil water. In the snowcovered simulation, the resulting slightly higher
water vapor content of air increases the absorption of incoming solar radiation during daylight
hours relative to the simulations without snowcover. A positive feedback with a warmer,
moister atmosphere establishes over a snowcover. As a small change in temperature means
a much greater change in saturation vapor pressure, this difference is often decisive for whether
or not condensate forms. Snow-cover enhances
accumulated precipitation, on average. Soil-frost
hardly alters the precipitation amount, but can
locally diminish or increase precipitation (e.g.
Fig. 11). We conclude that if soil-frost- and
snow-processes are not considered in mesoscale modeling, the predicted surface water
vapor fluxes to the atmosphere will be too
high in cloud-free areas, and too low in cloudy
areas.
The amount of soil-ice and soil liquid water
coexisting after freezing depends on soil-type
(cf. Eq. (A5); Figs. 2, 4b, c, 12, 13). The smaller
differences in soil liquid water content of
CONTROL minus FROST than in CONTROL
minus FROSTSNOW illustrate that snow-cover
protects the soil from losing water. Comparing
these differences between CONTROL and
SNOW with the differences between FROST
and FROSTSNOW shows that phase transitions
101
within the soil cause small differences relative to
the insulating effect of the snow-cover. The insulating effect amounts to about 4 K on average for
the synoptic situation examined. Snow-cover
protects the soils from cooling in cloud-free areas,
while it prevents soils from warming in cloudy
areas. Snow-cover appreciably, and soil-frost slightly reduces ground heat fluxes, on average.
Soil-frost results in differences of 2–5 K in the
upper soil layers, while snow results in differences of 3–10 K. Because the aforementioned
differences in soil temperature can be important
for the onset of phenological seasons (e.g.
Zhuang et al., 2003), we conclude that all longterm integrations as well as agricultural meteorological models require a sophisticated treatment
of soil-frost.
Over a snow-cover, the greatest differences in
wind speed and direction occur in response to
differences in temperature rather than surface
roughness. Temperature differences propagate into
the pressure field, lowering the pressure by more
than 1 hPa over central Alaska when snow is
included. The effect of soil-frost on pressure
works in the same direction, but is an order of
magnitude smaller (e.g. Fig. 14).
In our simulations, the Dufour and LudwigSoret effects are small (most the time less than
0.1 K, 0.001 m3=m3). Offline studies showed that
these effects can become larger during the
freeze-up and melting season (Fig. 1). Thus, we
conclude that these effects may be of larger
importance during spring, fall and in permafrost
areas during summer than winter as a freezing
line exists in the soils during spring, summer
and fall.
Organic soils and materials like peat, lichen,
and moss allow only for low fractions of supercooled liquid water at temperatures below freezing. Moreover, there are large subgrid-scale areas
covered by these types of soils in Arctic and
sub-Arctic regions. Therefore we conclude that
subgrid-scale parameterizations like the mosaic
approach or explicit subgrid scheme should be
used to treat soil in mesoscale modeling as soon
as data sets are available that include the distribution of these soil types.
Based on our findings we conclude that, on the
short-term, the differences caused by soil-frost
alone are smaller than those produced by a
snow-cover. It remains to be determined whether
102
N. M€
olders and J. E. Walsh
they become of higher importance on the longterm, i.e. in climate simulations. Future studies
should also investigate whether soil-frost processes have a larger impact in summer, when
moisture is available to the atmosphere from
the thawed active layer overlying the permaforst.
The impact of permafrost and the overlying
active layer on long-term climate are a high
priority for future investigations.
changes by freezing=thawing. In Eq. (A2), the first term on
the right hand side describes the changes in soil temperature
by divergence of soil heat fluxes, the second stands for the
divergence of soil heat fluxes due to water vapor transfer, the
third represents the Dufour effect, and the last term encompasses the changes by freezing/thawing.
In the presence of ice, water potential remains in local
equilibrium with the vapor pressure over pure ice (e.g. Fuchs
et al., 1978)
Appendix A: Brief description
of the soil model
The volumetric ice content is defined by the difference of
the total water within the soil layer minus the maximum
liquid water content for temperatures below freezing (e.g.
Flerchinger and Saxton, 1989):
The treatment of the (vertical) heat- and water-transfer processes, soil freezing=thawing is based on the principles of the
linear thermodynamics of irreversible processes. The governing balance equations for moisture and heat including phase
transition processes and water extraction by roots are, in
rearranged from (e.g. Philip and de Vries, 1957; de Vries,
1958; Sasamori, 1970; Sievers et al., 1983; Flerchinger
and Saxton, 1989; Kramm et al., 1996; M€
olders et al.,
2003a),
@
@
@
@
@
¼
D;v
þ
D;w
@t @zS
@zS
@zS
@zS
@
@TS
@Kw ice @ice
DT;v
þ
;
ðA1Þ
þ
@zS
@zS
@zS w w @t
@TS
@
@TS
@
@TS
þ
Lv w DT;v
C
¼
@zS
@zS
@t
@zS
@zS
@
@
@ice
:
ðA2Þ
Lv w D;v
þ Lf ice
þ
@zS
@zS
@t
Here zS is soil depth, represents the water uptake per soil
volume by roots; D,v, D,w and DT,v are the transfer coefficients for water vapor, water, and heat; Kw, TS, , ice and
C(¼ ð1 s ÞS cS þ w cw þ ice ice cice þ ðs ice Þ
a cp ) are the hydraulic conductivity of soil, soil temperature,
soil volumetric liquid water- and ice content, and volumetric
heat capacity of moist soil. Herein, S, and cS are the density
and specific heat capacity of the dry soil material (Table 2).
The thermal conductivity of unfrozen soil relates to water
potential (McCumber and Pielke, 1981)
419 expððpf þ 2:7ÞÞ pf < 5:1
;
ðA3Þ
¼
0:172
pf 5:1
10
with pf ¼ 2 þ log j j. For TS T0 a mass-weighted thermal conductivity depending on the liquid and solid volumetric water content present is calculated using Eq. (A3)
for the liquid and 2.31 J=(msK) for the solid phase.
The first two terms on the right hand side of Eq. (A1)
describe the changes in soil volumetric liquid water content
by the divergence of water vapor fluxes and soil water fluxes.
The third term denotes the Ludwig-Soret effect, the fourth
represents the changes due to hydraulic conductivity, the fifth
stands for the water uptake by roots and the last describes
¼
Lf ðTS 273:15Þ
:
g TS
max ¼ s
Lf ðTS T0 Þ
g s TS
ðA4Þ
1=b
ðA5Þ
:
Soil- albedo depends on surface soil volumetric water
content, g (e.g. Idso et al., 1975)
0:14 1 gs
for g 0:5s
g ¼
:
ðA6Þ
0:07
for g > 0:5s
Appendix B: Albedo and emissivity
of snow
Snow albedo,
tsnow 8
< 0:35 þ 0:18 exp
114048
tsnow
þ0:31 exp 954720
; for TR > T0 ;
snow ¼
:
tsnow
; for TR T0
0:61 þ 0:23 exp 469411
and emissivity
0:99 9:8 107 tsnow
"snow ¼
0:82
ðB1Þ
for tsnow < 173469s
:
for tsnow 173469s
ðB2Þ
depend on snow age, tsnow in s, after the last snowfall
(M€
olders et al., 2003a). A separation of the aging processes
for snow density and snow surface albedo, which can become important under certain conditions (e.g. Yang et al.,
1997) has to be postponed until suitable data for developing
a parameterization for Alaska are availabe. The extinction
coefficient is given by (Bohren and Barkstrom, 1974)
kext ¼ C5 snow d1=2 ;
ðB3Þ
with C5 ¼ 3.8 103 m5=2=kg.
Acknowledgements
We thank J. Dudhia, A. Ebel, H. Elbern, A. Klioutchnikova,
G. Kramm, J. Zhang and the anonymous reviewers for
fruitful discussions and helpful comments. BMBF and NSF
financially supported this study under contracts 01 LD0036
and OPP=0002239.
Atmospheric response to soil-frost and snow in Alaska in March
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105
Authors’ addresses: Nicole M€
olders (e-mail: molders@
gi.alaska.edu), Geophysical Institute, University Alaska
Fairbanks, 903 Koyukuk Drive, P.O. Box 757320, Fairbanks,
AK 99775-7320, USA; John E. Walsh, International Arctic
Research Center, University Alaska Fairbanks, 930 Koyukuk
Drive, Fairbanks, AK 99775, USA.