Available via license: CC BY 3.0
Content may be subject to copyright.
1
1 The impacts of moisture transport on drifting snow
2 sublimation in the saltation layer
3
4 N. Huang and X. Dai
5 Key Laboratory of Mechanics on Disaster and Environment in Western China,
6 Lanzhou University, Lanzhou 730000, China
7 Corresponding to: N. Huang (huangn@lzu.edu.cn)
Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-795, 2016
Manuscript under review for journal Atmos. Chem. Phys.
Published: 11 February 2016
c
Author(s) 2016. CC-BY 3.0 License.
2
1
2 Abstract
3 Drifting snow sublimation (DSS) is an important physical process related to moisture
4 and heat transfer that happens in the atmospheric boundary layer, which is of
5 glaciological and hydrological importance. It is also essential in order to understand
6 the mass balance of the Antarctic ice sheets and the global climate system. Previous
7 studies mainly focused on the DSS of suspended snow and ignored that in the
8 saltation layer. Here, a drifting snow model combined with balance equations for heat
9 and moisture is established to simulate the physical DSS process in the saltation
10 layer. The simulated results show that DSS can strongly increase humidity and
11 cooling effects, which in turn can significantly reduce DSS in the saltation layer.
12 However, effective moisture transport can dramatically weaken the feedback effects.
13 Due to moisture advection, DSS rate in the saltation layer can be several orders of
14 magnitude greater than that of the suspended particles. Thus, DSS in the saltation
15 layer has an important influence on the distribution and mass-energy balance of snow
16 cover.
Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-795, 2016
Manuscript under review for journal Atmos. Chem. Phys.
Published: 11 February 2016
c
Author(s) 2016. CC-BY 3.0 License.
3
1 1 Introduction
2 Drifting snow is a special process of mass-energy transport in the hydrological
3 cycle of snow. It not only changes the snow distribution but also results in phase
4 changes of ice crystals into water vapor, which is known as DSS. Snow sublimation
5 not only significantly influences the mass-energy balance of snow cover (e.g., Zhou
6 et al., 2014) by changing surface albedo (Allison, 1993) and the runoff of snowmelt
7 in cold regions (Marks and Winstral, 2001), but also has a pivotal status on moisture
8 and heat transfer in the atmospheric boundary layer(Pomeroy and Essery, 1999;
9 Anderson and Neff, 2008). Thus, it is of glaciological and hydrological importance
10 (Sugiura and Ohata, 2008). In high cold area, the reduction of snow cover may cause
11 the surface temperature to increase in the cold season(Huang et al., 2008, 2012). The
12 thickness of seasonally frozen ground has decreased in response to winter warming
13 (Huang et al., 2012). On the other hand, both dust and biomass burning aerosols may
14 impact the surface albedo when deposited on snow; soot in particular has large
15 impacts on absorption of radiation (Huang et al., 2011). In addition, a large, but
16 unknown, fraction of the snow that falls on Antarctica is removed by the wind and
17 subsequently sublimates. Therefore, a detailed knowledge of DSS is also essential in
18 order to understand snow cover distribution in cold high area as well as the mass
19 balance of the Antarctic ice sheets, and further the global climate system (Yang et al.,
20 2010).
21 In drifting snow, snow particles can experience continuous sublimation, which
22 induces a heat flux from the surrounding air to the particle and a moisture flux in the
23 opposite direction (Bintanja, 2001a). Thus, DSS can cause increases in humidity and
24 cooling of the air (Schmidt, 1982; Pomeroy et al., 1993) and has an inherent self-
25 limiting nature due to the feedback associated with the heat and moisture budgets
26 (Déry and Yau, 1999; Groot Zwaaftink et al., 2011, 2013). On one hand, snow
27 sublimation absorbs heat and decreases the temperature of the ambient air, which in
28 turn reduces the saturation vapor pressure and hence the sublimation rate; on the
29 other hand, the increment in the moisture content of the ambient air decreases the
30 sublimation rate of drifting snow, as it is proportional to the under-saturation of the
31 air.
32 Saltation is one of the three modes of particle motion, along with suspension and
33 creep. Among the three modes, saltation is important and the DSS in the saltation
Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-795, 2016
Manuscript under review for journal Atmos. Chem. Phys.
Published: 11 February 2016
c
Author(s) 2016. CC-BY 3.0 License.
4
1 layer may constitute a significant portion of the total snow sublimation (Dai and
2 Huang, 2014). Previous studies of DSS mostly focused on the sublimation of
3 suspended snow, which was mainly due to the consideration that sublimation will
4 soon vanish in the saltation layer because the feedback of DSS may lead to a
5 saturated layer near the surface (Bintanja, 2001b). However, the field observation
6 data of Schmidt (1982) showed that relative humidity only slightly increases during
7 snowdrift events and the maximum humidity was far below saturation. Further
8 studies (Groot Zwaaftink et al., 2011; Vionnet et al., 2013) also showed that the
9 relative humidity does not reach saturation even at the lowest atmosphere level after
10 DSS occurs. Some scientists argued that it was caused by moisture transport, such as
11 diffusion and advection of moisture, which inevitably accompany the drifting snow
12 process (Vionnet et al., 2013). Therefore, it is necessary to study the feedback
13 mechanism of DSS in the saltation layer and the effect of moisture transport on it.
14 In this study, a wind-blown snow model, balance equations for heat and moisture
15 of an atmospheric boundary layer, and an equation for the rate of mass loss of a
16 single ice sphere due to sublimation were combined to study the sublimation rate of
17 drifting snow by tracking each saltating particle in drifting snow. Then, the effects of
18 DSS on the humidity and temperature profiles, as well as the effects of diffusion and
19 advection of moisture on DSS in the saltation layer, were explored in detail.
20
21 2 Methods
22 2.1 Model Description
23 Saltation can be divided into four interactive sub-processes, i.e., aerodynamic
24 entrainment, particle trajectories, particle-bed collisions, and wind modification
25 (Huang et al., 2011).
26 The motion equations for snow particles are (Huang et al., 2011)
27 , (1)
p f p
p D
r
dU U U
m F
dt V
28 , (2)
p f p
p g B D
r
dV V V
m W F F
dt V
Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-795, 2016
Manuscript under review for journal Atmos. Chem. Phys.
Published: 11 February 2016
c
Author(s) 2016. CC-BY 3.0 License.
5
1 , (3)
p
p
dx
U
dt
2 . (4)
p
p
dy
V
dt
3 where and are the mass and weight of the snow particle, respectively; , ,
p
m
g
W
f
U
f
V
4 and are the horizontal and vertical velocities of the airflow and snow particle,
p
U
p
V
5 respectively;
2 2
r f p f p
V U U V V
is the relative velocity between the
6 airflow and snow particle;
p
x
and
p
y
are the horizontal position and vertical height of
7 the snow particle, respectively;
3
1
6
B f
F D g
and
2 2
1
8
D D f r
F C D V
are the
8 buoyancy force and the drag force applied on the snow particle, respectively;
f
is the
9 air density;
D
is the diameter of the snow particle;
g
is the acceleration of gravity; and
10
D
C
is the drag coefficient.
11 Within the atmospheric boundary layer, the mean horizontal wind
12 velocity
u
satisfies the Navier-Stokes equation (Werner, 1990). According to
13 Prandtl’s mixing length theory for the steady flow fully developed over an infinite
14 planar bed,
u
is
15
2 2
( ) 0
f x
du du
y F
y dy dy
, (5)
16 where
x
is the coordinate aligned with the mean wind direction,
y
is the vertical
17 direction,
is the von Karman constant, and
x
F
is the force per unit volume that the
18 snow particles exert on the fluid in the stream-wise direction and can be expressed as
19
1
n
x p i
i
F m a
. (6)
20 where
n
is the number of particles per unit volume of fluid at height
y
, and
i
a
is the
21 horizontal acceleration of particle
i
.
Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-795, 2016
Manuscript under review for journal Atmos. Chem. Phys.
Published: 11 February 2016
c
Author(s) 2016. CC-BY 3.0 License.
6
1 When the bed shear stress is greater than the threshold value, snow particles begin
2 lifting off the surface. The number of aerodynamically entrained snow particles
a
N
is
3 (Shao and Li, 1999)
4
2
3
*
*
2
*
1
t
a
u
N u D
u
. (7)
5 where
is a dimensionless coefficient (
3
1 10
in our simulations),
*
u
is the friction
6 velocity, and
*t
u
is the threshold friction velocity. Following the previous saltation
7 models (McEwan and Willetts, 1993), the vertical speed of all aerodynamically
8 entrained particles is
2gD
.
9 The following three splash functions for drifting snow proposed by Sugiura and
10 Maeno (2000) based on experiments are used to determine the number and motion
11 state of the splashed particles.
12
1
1
exp
v
v v v
e
S e e
, (8)
13
2
2
2
1
exp
2
2
h
h h
e
S e
, (9)
14
1
e
e
e
m n
n
e e m n
S n C p p
. (10)
15 In Eq. (8),
v
S
is the probability distribution of the vertical restitution coefficient
v
e
,
16
( )
is the gamma function, and
and
are the shape and scale parameters for the
17 gamma distribution function. In Eq.(9),
h
S
is the probability distribution of the
18 horizontal restitution coefficient
h
e
, and
and
are the mean and variance,
19 respectively. In Eq. (10),
e
S
is the probability distribution function of the number of
20 ejected particles
e
n
, a binomial distribution function with the mean
mp
and the
21 variance
(1 )mp p
.
22 The potential temperature
and specific humidity
q
of the ambient air satisfy the
23 following prognostic equations (Déry and Yau, 1999)
Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-795, 2016
Manuscript under review for journal Atmos. Chem. Phys.
Published: 11 February 2016
c
Author(s) 2016. CC-BY 3.0 License.
7
1
s
f
L S
K
t y y C
, (11)
2
q
f
q q S
K Q
t y y
. (12)
3 where
* T
K u y K
and
*q V
K u y K
are the heat and moisture diffusivities (the
4 sum of eddy diffusivity and molecular diffusivity), respectively,
S
is the sublimation
5 rate summed over all particles at each height above the surface,
s
L
is the latent heat of
6 sublimation (2.835×10
6
J kg
-1
),
C
is the specific heat of air,
q
Q u
x
is the horizontal
7 advection of moisture at each height above the surface, and
q
x
represents the
8 horizontal gradient in specific humidity. When the external dry air with specific
9 humidity
out
q
enters into the study domain, we hypothesize that the specific humidity
10 in the study domain is linearly distributed along the horizontal direction and
11 possesses the value of
in
q
at the exit. Thus, the horizontal advection of moisture can be
12 simplified to
( ) /
in out
Q u q q l
, with
l
being the length of the domain.
13 The total DSS rate
S
Q
(kg s
-1
) of the saltation layer within the computational
14 domain is obtained by summing the mass loss of all saltating particles in the domain.
15
S
i
i
dm
Q
dt
, (13)
16 where
i
dm
dt
is the mass loss rate corresponding to the i-th particle. At the air
17 temperature
T
and undersaturation
(
1 RH
), the rate of mass change of a single
18 particle with radius
r
due to sublimation is (Thorpe and Mason, 1966)
19
2
( 1)
s s v
v v s
dm r
L L R T
dt
KTNu R T D She
, (14)
20 where
RH
is the relative humidity of air,
K
is the molecular thermal conductivity of
21 the atmosphere (0.024 J m
−1
s
−1
K
−1
),
v
D
is the molecular diffusivity of water vapor in
22 the atmosphere,
v
R
is the gas constant for water vapor (461.5J kg
-1
K
-1
),
s
e
is saturated
Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-795, 2016
Manuscript under review for journal Atmos. Chem. Phys.
Published: 11 February 2016
c
Author(s) 2016. CC-BY 3.0 License.
8
1 vapor pressure with respect to an ice surface, and
Nu
and
Sh
are the Nusselt number
2 and the Sherwood number, respectively, both of which are dimensionless and depend
3 on the wind velocity and particle size (Thorpe and Mason, 1966; Lee, 1975).
4
0.5
0.5
1.79 0.606 Re 0.7 Re 10
1.88 0.580 Re 10 Re 200
Nu Sh
. (15)
5 where
Re /
r
DV
is the Reynolds number and
is the kinematic viscosity of air.
6 For the purpose of comparison with the sublimation of suspended particles, the
7 initial relative humidity profile in accordance with that of Xiao et al. (2000) is
8
0
1 ln( / )
S
RH R y y
, (16)
9 where
0
y
is roughness length and
0.039469
S
R
.
10 The conversion relation between relative humidity and specific humidity is
11
0.622
s
s
e
q RH
p e
, (17)
12 where
610.78exp 21.87 273.16 7.66
s
e T T
.
13 The constant initial potential temperature
0
is 263.15K (but is 253.16 K in the
14 comparison with Xiao et al. (2000)) and the initial absolute temperature is
15
0.286
0 0
0
p
T
p
, (18)
16 where
p
is the pressure and its initial distribution is based on the hypsometric
17 equation
18
0
0
exp
d
yg
p p
R
. (19)
19 where
0
p
is taken as 1000 hPa and
d
R
is the gas constant for dry air (287.0 J kg
-1
K
-1
).
20 2.2 Calculation Procedure
21 The procedure for the calculations is enumerated below.
Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-795, 2016
Manuscript under review for journal Atmos. Chem. Phys.
Published: 11 February 2016
c
Author(s) 2016. CC-BY 3.0 License.
9
1 1. The length, width and height of the computational domain sampled from the
2 saltation layer above the surface are 1.0 m, 0.01 m, and 1.0 m, respectively. The
3 initial and boundary conditions of temperature and humidity are set from Eqs. (16)-
4 (19).
5 2. Snow particles are considered as spheres with diameter of 200
m
and density
6 of 910 kg m
-3
. The threshold friction velocity of snow is 0.21 m s
-1
and the snow bed
7 roughness is 3.0 × 10
−5
m (Nemoto and Nishimura, 2001).
8 3. The initial wind field is logarithmic. If the bed shear stress is greater than the
9 threshold value, particles are entrained from their random positions on the snow
10 surface at vertical speed
2gD
and the number of aerodynamically entrained snow
11 particles satisfies Eq. (7).
12 4. The snow particle trajectory is calculated using Eqs. (1)-(4)every 0.00001 s in
13 order to obtain the velocity used in the calculation of sublimation rate and the new
14 location of each drifting snow particle to determine whether the snow particle falls on
15 the snow bed.
16 5. As the snow particles fall on the snow bed, where they impart their energy to
17 other snow particles and splash or eject other snow particles, the velocity and angle of
18 the ejected particles satisfy the splash functions, i.e., Eqs. (8)-(10), according to the
19 motion state of the incident particles and the actual wind field at that time. The
20 number of snow particles is re-counted every 0.00001 s.
21 6. The reactive force
x
F
that the snow particles exert on the wind field induces
22 wind modification according to Eq. (5).
23 7. Based on the process above, the velocity and location of each drifting snow
24 particle are derived and then used in Eqs. (13)-(15) to calculate their sublimation rate
25 every 0.00001 s. Under the effect of DSS, potential temperature and specific
26 humidity at different heights under the diffusion or advection moisture transport are
27 calculated every 0.00001 s.
28 8. The new values of wind field calculated in step 6 are used in step 3, and then
29 steps 4 to 7 are recalculated. Such a cycle is repeated to finish the calculation of DSS
30 under thermodynamic effects. Each calculation takes 60 s.
31 3 Results and Discussion
Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-795, 2016
Manuscript under review for journal Atmos. Chem. Phys.
Published: 11 February 2016
c
Author(s) 2016. CC-BY 3.0 License.
10
1 3.1 Relative Humidity and Temperature
2 The relative humidity at 1 cm height for different defined wind velocities generally
3 reaches saturation within 10 s when moisture transport is not included (Fig. 1a).
4 Snow sublimation will not occur, and the temperature will not change (Fig. 1b).
5 However, when moisture transport is included, the snow sublimation occurs
6 throughout the simulation period, and temperature decreases continually. Moreover,
7 under the same moisture transport mechanism, the greater the wind friction velocity,
8 the higher the relative humidity and temperature change (Fig. 1). The relative
9 humidity at 1 cm shows a trend of rapid decrease, then rapid increase, and finally a
10 slow increase (Fig. 1a), but does not reach saturation in the simulation period of 60 s.
11 Early in the wind-blown snow stage, the sublimation rate is smaller as only a few
12 saltating particles sublime and the moisture at the lower height largely moves
13 outwards due to the effect of moisture transport, resulting in relative humidity
14 decrease. With continuing wind-blown snow, more snow particles leave the surface,
15 which increases the sublimation rate and hence the relative humidity. When it reaches
16 a steady state, the amount of snow particles in the saltation layer will no longer
17 increase, but fluctuate within a certain range. Thereafter, because of the increase in
18 humidity and cooling, DSS weakens (Fig. 2). The results indicate that DSS in the
19 saltation layer has a self-limiting nature.
20 3.2 Sublimation Rate
21 Moisture transport could remove some moisture, attenuating the increase of relative
22 humidity and thus negative feedback, leading to higher sublimation rates with
23 moisture transport than without (Fig. 2). With moisture removal only by diffusion,
24 the sublimation rate at 60 s is roughly the same at 3 wind velocities, meaning that
25 sublimation still shows obvious negative feedback. However, with moisture transport
26 by diffusion and advection, the sublimation rate increases significantly as the
27 negative feedback effect is effectively reduced. Moreover, the sublimation rate
28 increases with the friction velocity and can be even greater than that at the highest
29 wind velocity without advection. For example, the sublimation rate at 60 s with
30 advection is 0.6110
-5
kg m
-2
s
-1
at a friction velocity of 0.3 m s
-1
, greater than that of
31 0.4410
-5
kg m
-2
s
-1
at a friction velocity of 0.5 m s
-1
without considering advection.
32 The sublimation rate even reaches 0.9610
-5
kg m
-2
s
-1
, equaling the 0.83 mm d
-1
Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-795, 2016
Manuscript under review for journal Atmos. Chem. Phys.
Published: 11 February 2016
c
Author(s) 2016. CC-BY 3.0 License.
11
1 snow water equivalent (SWE) at a friction velocity of 0.5 m s
-1
with advection
2 included (Fig. 2). Furthermore, sublimation continues to occur. Thus, it can be seen
3 that effective moisture transport can weaken the negative feedback of sublimation,
4 hence significantly affecting DSS. Because the occurrence of wind-blown snow must
5 coincide with the airflow, DSS in the saltation layer is not negligible, and the
6 assumption that the saltation layer is a saturation boundary layer is inadvisable.
7 Air temperature decreases with decreasing height, along with air saturation degree
8 during wind-blown snow, which is adverse to sublimation in contrast to higher
9 heights above the surface. Nevertheless, the volume sublimation rate increases with
10 decreasing height (Fig. 3). This is in agreement with the vertical profiles of the
11 horizontal mass flux of snow particles (Huang et al., 2011). That is, there are more
12 snow particles that can participate in sublimation at lower heights, leading to higher
13 sublimation rates even in environments adverse to sublimation. The results indicate
14 that the particle density is an important controlling factor for sublimation rate, which
15 is consistent with a previous study (Wever et al., 2009). A comparison between our
16 simulated results and that of four models for suspended snow, i.e., PIEKTUK-T,
17 WINDBLAST, SNOWSTORM and PIEKTUK-B, shows that the local sublimation
18 rate of the suspended snow at 60 s can reach 10
-6
kg m
-3
s
-1
at most (Xiao et al.,2000)
19 (Fig. 3), smaller than that of our calculated results (10
-4
kg m
-3
s
-1
) by 2 orders of
20 magnitude at the same initial temperature and relative humidity. This result shows
21 that the assumption that sublimation in the saltation layer can be ignored by
22 considering it a saturation boundary layer is inadvisable. Therefore, DSS in the
23 saltation layer is of non-negligible importance and requires further detailed study.
24 4 Conclusions
25 In this study, we established a wind-blown snow model and balance equations for
26 heat and moisture to study the effect of different moisture transport mechanisms on
27 DSS in the saltation layer. As has been reported (e.g., Schmidt, 1982), DSS could
28 lead to strong increases in humidity and cooling, which in turn can significantly
29 reduce the DSS rate, i.e., DSS has an inherently self-limiting nature. Moreover, the
30 relative humidity in the saltation layer quickly reaches saturation when moisture
31 transport is not considered. However, effective moisture transport, such as advection,
32 can dramatically weaken the negative feedback of sublimation and prolong the
33 duration of the higher DSS rate and hence has a profound effect on DSS. Because of
Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-795, 2016
Manuscript under review for journal Atmos. Chem. Phys.
Published: 11 February 2016
c
Author(s) 2016. CC-BY 3.0 License.
12
1 the presence of advection, DSS rate increases with the friction velocity and the
2 volume sublimation rate of saltating particles is several orders of magnitude greater
3 than that of the suspended particles due to the higher particle density in the saltation
4 layer. Thus, DSS in the saltation layer plays an important part in the energy and mass
5 balance of snow cover and needs to be further studied.
6 Acknowledgments
7 This work is supported by the State Key Program of National Natural Science
8 Foundation of China (91325203), the National Natural Science Foundation of China
9 (41371034), and Innovative Research Group of the National Natural Science
10 Foundation of China (11421062).
Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-795, 2016
Manuscript under review for journal Atmos. Chem. Phys.
Published: 11 February 2016
c
Author(s) 2016. CC-BY 3.0 License.
13
1
2 References
3 Allison, I., Brandt, R. E., and Warren, S. G., East antarctic sea ice: albedo, thickness
4 distribution, and snow cover, J. Geophy. Res., 98(C7), 12417-12429, 1993.
5 Anderson P. S., Neff W. D., Boundary layer physics over snow and ice, Atmos.
6 Chem. Phys., 8(13):3563-3582, 2008.
7 Bintanja, R.: Modelling snowdrift sublimation and its effect on the moisture budget
8 of the atmospheric boundary layer, Tellus, Ser. A, 53, 215-232, 2001a.
9 Bintanja, R.: Snowdrift Sublimation in a Katabatic Wind Region of the Antarctic Ice
10 Sheet, J. Appl. Mete., 40, 1952-1966, 2001b.
11 Dai, X. and Huang, N.: Numerical simulation of drifting snow sublimation in the
12 saltation Layer, Sci. Rep., 4, 6611, doi:10.1038/srep06611, 2014.
13 Déry, S. and Yau, M.: A bulk blowing snow model, Boundary Layer Meteorol.,
14 93,237-251, 1999.
15 Groot Zwaaftink, C. D., Löwe, H., Mott, R., Bavay, M. and Lehning, M.: Drifting
16 snow sublimation: A high-resolution 3-D model with temperature and moisture
17 feedbacks, J. Geophys. Res., 116, D16107, doi:10.1029/2011jd015754, 2011.
18 Groot Zwaaftink, C. D., Mott, R. and Lehning, M.: Seasonal simulation of drifting
19 snow sublimation in Alpine terrain, Water Resour. Res., 49, 1581–1590,
20 doi:10.1002/wrcr.20137, 2013.
21 Huang, J., et al.: An overview of the semi-arid climate and environment research
22 observatory over the Loess Plateau, Adv. Atmos. Sci., 25 (6), 906-921,
23 doi:10.1007/s00376-008-0906-7, 2008.
24 Huang, J., Fu, Q., Zhang, W., Wang, X., Zhang, R., Ye, H. and Warren, S.: Dust and
25 black carbon in seasonal snow across northern China, Bull. Amer. Meteor. Soc., 92
26 (2), 175-181, doi:10.1175/2010BAMS3064.1, 2011.
27 Huang, J., Guan, X. and Ji, F.: Enhanced cold-season warming in semi-arid regions,
28 Atmos. Chem. Phys., 12 (12), 5391-5398, doi:10.5194/acp-12-5391-2012, 2012.
29 Huang, N., Sang, J. and Han, K.: A numerical simulation of the effects of snow
30 particle shapes on blowing snow development, J. Geophys. Res., 116, D22206,
Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-795, 2016
Manuscript under review for journal Atmos. Chem. Phys.
Published: 11 February 2016
c
Author(s) 2016. CC-BY 3.0 License.
14
1 doi:10.1029/2011JD016657, 2011.
2 Lee, L.: Sublimation of snow in a turbulent atmosphere, Ph.D. thesis, Univ. of Wyo.,
3 Laramie, 1975.
4 Marks D, Winstral A. Comparison of snow deposition, the snow cover energy
5 balance, and snowmelt at two sites in a semiarid mountain basin, J.Hydrometeorol.,
6 2(3): 213-227, 2001.
7 McEwan, I. K. and Willetts, B. B.: Adaptation of the near-surface wind to the
8 development of sand transport, J. Fluid Mech., 252, 99-115, 1993.
9 Nemoto, M. and Nishimura, K. Direct measurement of shear stress during snow
10 saltation, Boundary Layer Meteorol., 100, 149-170, 2001.
11 Pomeroy, J. W., Gray, D. M. and Landine, P. G.: The Prairie Blowing Snow Model:
12 characteristics, validation, operation, J. Hydrol., 144, 165-192, 1993.
13 Pomeroy J. W., Essery R. L. H., Turbulent fluxes during blowing snow: field tests of
14 model sublimation predictions, Hydrological Processes, 13(18): 2963-2975, 1999.
15 Schmidt, R.: Vertical profiles of wind speed, snow concentration and humidity in
16 blowing snow, Boundary Layer Meteorol., 23, 223-246, 1982.
17 Shao, Y., and Li, A.: Numerical modelling of saltation in the atmospheric surface
18 layer,Boundary Layer Meteorol., 91, 199-225, 1999.
19 Sugiura, K. and Maeno, N.: Wind-tunnel measurements of restitution coefficients and
20 ejection number of snow particles in drifting snow: determination of splash functions,
21 Boundary Layer Meteorol., 95, 123– 143, 2000.
22 Sugiura, K. and Ohata, T.:Large-scale characteristics of the distribution of blowing-
23 snow sublimation, Ann. Glaciol., 49, 11-16, 2008.
24 Thorpe, A. D. and Mason, B. J.: The evaporation of ice spheres and ice crystals, Br. J.
25 Appl. Phys., 17, 541-548, 1966.
26 Vionnet, V., Martin, E., Masson, V., Guyomarc’h, G., Naaim-Bouvet, F., Prokop, A.,
27 Durand, Y. and Lac, C.: Simulation of wind-induced snow transport in alpine terrain
28 using a fully coupled snowpack/atmosphere model, The Cryosphere Discuss., 7,
29 2191–2245, doi:10.5194/tcd-7-2191-2013, 2013.
Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-795, 2016
Manuscript under review for journal Atmos. Chem. Phys.
Published: 11 February 2016
c
Author(s) 2016. CC-BY 3.0 License.
15
1 Werner, B. T.: A steady-state model of wind-blown sand transport, J. Geol., 98, 1-17,
2 1990.
3 Wever, N., Lehning, M., Clifton, A., Ruedi, J. D., Nishimura, K., Nemoto, M.,
4 Yamaguchi, S. and Sato, A.: Verification of moisture budgets during drifting snow
5 conditions in a cold wind tunnel, Water Resour. Res., 45, W07423,
6 doi:10.1029/2008WR007522, 2009.
7 Xiao, J., Bintanja, R., Déry, S. J., Mann, G. W. and Taylor, P. A.: An
8 intercomparison among four models of blowing snow, Boundary Layer Meteorol.,
9 97(1), 109-135, 2000.
10 Yang, J., Yau, M. K., Fang, X. and Pomeroy, J. W. A triple-moment blowing snow-
11 atmospheric model and its application in computing the seasonal wintertime snow
12 mass budget, Hydrol. Earth Syst. Sci., 14, 1063-1079, doi:10.5194/hess-14-1063-
13 2010, 2010.
14 Zhou, J., Pomeroy, J. W., Zhang, W., Cheng, G., Wang, G. and Chen C.: Simulating
15 cold regions hydrological processes using a modular model in the west of China. J.
16 Hydrol., 509, 13-24, 2014.
Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-795, 2016
Manuscript under review for journal Atmos. Chem. Phys.
Published: 11 February 2016
c
Author(s) 2016. CC-BY 3.0 License.
16
1
2
3 Figure 1.Temporal evolution of relative humidity (a) and temperature (b) at 1 cm
4 above the surface for three wind force levels neglecting the effects of moisture
5 transport, considering only moisture diffusion, and both moisture diffusion and
6 advection.
Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-795, 2016
Manuscript under review for journal Atmos. Chem. Phys.
Published: 11 February 2016
c
Author(s) 2016. CC-BY 3.0 License.
17
1
2
3 Figure 2.Temporal evolution of drifting snow sublimation rate for three wind force
4 levels neglecting moisture transport, considering only moisture diffusion, and both
5 moisture diffusion and advection.
Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-795, 2016
Manuscript under review for journal Atmos. Chem. Phys.
Published: 11 February 2016
c
Author(s) 2016. CC-BY 3.0 License.
18
1
2
3 Figure 3. Comparison of the sublimation rate for the saltation layer and suspension
4 layer (the inset figure) at 60 s as a function of height. The inset figure shows the
5 sublimation rate of four models for the suspension layer with initial friction velocity
6 of 0.87 m s
-1
reported in Xiao et al. (2000). Our results for the sublimation rate in the
7 saltation layer are obtained for three wind force levels (<0.87 m s
-1
) with moisture
8 diffusion and advection included with the same initial temperature (253.16 K) and
9 relative humidity as Xiao et al. (2000).
Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2015-795, 2016
Manuscript under review for journal Atmos. Chem. Phys.
Published: 11 February 2016
c
Author(s) 2016. CC-BY 3.0 License.