Journal of Hydrology, 144 (1993) 165-192
165
Elsevier Science Publishers B.V., A m s t e r d a m
[3]
The Prairie Blowing Snow Model: characteristics,
validation, operation
J . W . P o m e r o y " , D . M . G r a y b a n d P . G . L a n d i n e b'j
aNational Hydrology Research Institute, Environment Canada, 11 Innovation Boulevard, Saskatoon,
Sask. S7N 3H5, Canada
bDivision of Hydrology, University of Saskatchewan, Saskatoon, Sask. S7N 0 WO, Canada
(Received 20 May 1992; revision accepted 5 September 1992)
ABSTRACT
Pomeroy, J.W., Gray, D.M. and Landine, P.G., 1993. The Prairie Blowing Snow Model: characteristics,
validation, operation. J. Hydrol., 144: 165-192.
Physically based algorithms that estimate saltation, suspension and sublimation rates of blowing snow
using readily available meteorological and land use data are presented. These algorithms are assembled into
a model, the Prairie Blowing Snow Model (PBSM), and used to describe snow transport on fields in a
Canadian Prairie environment. Validation tests of PBSM using hourly meteorological data indicate
differences between modelled and measured seasonal snow accumulations between 4 and 13%.
Application of the blowing snow model using meteorological records from the Canadian prairies shows
that the annual proportion of snow transported above any specific height increases notably with mean
seasonal wind speed. An observed decrease in annual blowing snow transport and sublimation quantities
with increasing surface roughness height becomes more apparent with higher seasonal wind speeds and
temperatures. The annual quantity of snow transported off a fetch increases with fetch length up to lengths
of between 300 and 1000 m, then remains relatively constant or slowly declines. Within the first 300 m of
fetch 38-85% of annual snowfall is removed by snow transport, the amount increasing with wind speed.
Beyond 1000 m of fetch, blowing snow sublimation losses dominate over transport losses. In Saskatchewan,
sublimation losses range from 44 to 74% of annual snowfall over a 4000 m fetch, depending on winter
climate. Notably, as a result of steady-state transport, the sum of snowcover loss due to blowing snow
transport and sublimation does not change appreciably from its 1000 m fetch value for fetches 500 to
4000 m. The transition from primarily transport to primarily sublimation losses at the 1000 m fetch distance
may be useful in assessing the effect of scale in snow hydrology.
INTRODUCTION
In open and windswept environments, blowing snow processes control the
C o r r e s p o n d e n c e to: J.W. Pomeroy, N a t i o n a l H y d r o l o g y Research Institute, E n v i r o n m e n t
C a n a d a , I 1 I n n o v a t i o n Boulevard, S a s k a t o o n , Sask. S7N 3H5, C a n a d a .
Present address: D e p a r t m e n t of Civil Engineering, University o f Saskatchewan, Saskatoon,
Sask., C a n a d a .
0022-1694/93/$06.00
© 1993 - - Elsevier Science Publishers B.V. All rights reserved
166
J.W. POMEROY ET AL.
evolution and distribution of snowcover. Most studies in snow hydrology
have focused on the areal distribution of snow water equivalent as an input
to snow melt calculations (Kuz'min, 1960; Steppuhn and Dyck, 1974;
Granberg, 1978; Schroeter, 1988). In recent years, however, the loss of water
by sublimation of snow during wind transport has received increased
attention (Schmidt, 1972; Tabler, 1975; Steppuhn, 1981; Pomeroy, 1991).
Landine and Gray (1989) have applied an ensemble of physically based
blowing snow transport and sublimation algorithms, termed the Prairie
Blowing Snow Model, PBSM (Pomeroy, 1988, 1989), to calculate the disposition of seasonal snowfall in agricultural areas of the Canadian prairies. They
estimate annual sublimation from I km fetches of non-vegetated fallow land
due to wind transport ranging from 23 to 41% of annual snowfall. These
losses increase by 1.4-fold for a fetch of 2 km and 1.75-fold for a fetch of 4 kin.
This paper describes the PBSM, its ability to estimate snow accumulation, and
the operation of the model to predict: (1) mean vertical profiles of snow
transport flux; (2) the effect of grain stubble height on blowing snow transport
and sublimation losses from snowcovers; (3) the effect of land use and unobstructed fetch distance on blowing snow transport and sublimation losses
from snowcovers; for two climatically different stations in a Canadian prairie
environment.
THE P R A I R I E B L O W I N G SNOW M O D E L
The transport and sublimation algorithms within the PBSM calculate rates
for steady-state conditions over relatively flat terrain with known surface
roughness and upwind fetch (therefore, boundary-layer height) assuming an
unlimited upwind snow supply. For implementation on natural fields the
algorithms are modified for variable snow supply, fetch distance and surface
roughness. All algorithms are process-based, being derived from theory and
the results of extensive measurements in western Canada (Pomeroy, 1988,
1989; Pomeroy and Gray, 1990; Pomeroy and Male, 1992). The PBSM divides
snow transport into: saltation - - the movement of particles in a 'skipping'
action just above the snow surface, and suspension - - the movement of
particles suspended by turbulence in the atmospheric layer extending to the
top of the surface boundary-layer. Sublimation rates are calculated for a
column of saltating and suspended blowing snow extending to the top of the
boundary layer. The following development emphasizes the implementation
of the process algorithms using readily available meteorological information
such as wind speed, temperature, humidity measured at a single height,
occurrence of blowing snow and land use information. The detailed development of the algorithms, however, is referenced to original sources.
THE PRARIEBLOWINGSNOWMODEL
167
Saltation
The saltation transport rate is derived by partitioning the atmospheric
shear stress into that required to free particles from the snow surface, that
applied to non-erodible surface elements and that available to transport
particles. Pomeroy and Gray (1990) found the following expression valid for
snow-covered prairies,
Qsalt
-
-Csalt
-
PUt* (//,2
u*g
--
u . ,2
--
u .2)
(1)
where Qsalt is the saltation transport rate (kg m-I s- ~), Csalt is an empirically
derived constant found equal to 0.68 m s- I, p is atmospheric density (kg m - 3),
g is the acceleration due to gravity (ms--Z), u* is the atmospheric friction
velocity (ms ~) and the subscripts n and t refer to the friction velocity (shear
stress) applied to the non-erodible surface elements and to the snow surface,
respectively, at the transport threshold.
Mechanical turbulence dominates atmospheric exchange processes during
blowing snow, hence the friction velocity is associated with the wind speed
profile as
u* -
u(z)k
ln(z)
(2)
where k is yon Kgrmfin's constant (0.4), u(z) is the wind speed at height z and
z0 is the aerodynamic roughness height. The aerodynamic roughness during
blowing snow differs from that for non-transport conditions because it is
influenced by a surface roughness created by saltating snow. Pomeroy (1988)
found for blowing snow over complete snowcovers
Cz u*2
Z0 --
2g
-~- CstNstAst
(3)
in which Q is a dimensionless coefficient found equal to 0.1203 for prairie
snowcovers, Cst is a coefficient equal to 0.5 m, N~t is the number of vegetation
elements per unit area and Ast is the exposed silhouette area of a single typical
vegetation element. The second term on the right-hand side of eqn. (3) is the
roughness created by exposed vegetation (Lettau, 1969). A typical value of Nst
for wheat fields in Saskatchewan is 320 stalks m -2. Ast is the product of the
stalk diameter (3 mm) and the exposed height of stalk (250 mm minus the
depth of snowcover (mm)).
The threshold friction velocity, u*, is the friction velocity at the termination/initiation of transport. Typical values for u* range from 0.15 to
J.W. P O M E R O Y ET AL.
168
100
E
UtlO = 11 m/s
_ ~ J f
LU
p-
<
er
rr
O
03
Z
<
rr
lC
Z
O
F_J
<
5
10
15
20
WIND SPEED AT 10-m HEIGHT (m/s)
25
Fig. 1. Saltation transport rate as a function of the 10 m wind speed for several transport threshold wind
speeds and exposed heights of wheat stubble.
0.25 m s I for fresh, loose, dry snow and for movement during snowfall and
from 0.25 to 1.0ms -~ for older, wind-hardened, dense or wet snow. The
non-erodible friction velocity, u* is expressed as a function of the friction
velocity and the arrangement of surface roughness elements that protrude
above the snow surface by
where Cr is a dimensionless roughness coefficient. Lyles and Allison (1976)
suggest Cr can be estimated by
cr =
1.638 + 17.04NstAst - 0.117 Ly
(5)
in which Ly is the distance between stalks parallel to the wind vector and L x
is the distance between stalks perpendicular to the wind vector. For wheat
fields the ratio L J L x is taken equal to unity.
The saltation transport rate calculated by eqns. (1)-(5) for several threshold
conditions and exposed heights of wheat stubble is plotted against wind speed
in Fig. 1. Saltation transport is shown on a logarithmic axis for comparison
with suspension transport, however, the increase in saltation transport rate
with increasing wind speed is approximately linear. High threshold conditions
inhibit transport at low wind speeds, but they enhance transport at high wind
speeds because of more efficient, particle-surface interaction.
THE PRARIE BLOWING SNOW MODEL
169
Suspension
The transport rate of suspended snow is found by integrating the mass flux
over the depth of flow, which extends from the top of the saltation layer to
the top of the surface boundary-layer. The mass flux is the mass concentration
multiplied by the mean downwind particle velocity; on average this velocity
is equal to that of a parcel of air (Schmidt, 1982). Therefore, using eqn. (2),
the transport rate of suspended snow (kg m-I s-~ ), Qsusp, is
Qsusp -
q(z) In
k
dz
(6)
h*
in which h* is the lower boundary for suspension (approximate top of the
saltation layer), zb is the top of the surface boundary-layer for suspended
snow, q(z) is the mass concentration of suspended snow (kg m - 3 ) a t height z
(m) and z0 is calculated using eqn. (3). The steady-state mass concentration of
suspended snow may be approximated as (Pomeroy and Male, 1992)
q(z)
=
q(Zr) e X p { - A[(Bu* )
0.544 - -
Z-0.544]}
(7)
in which q(Zr) is the reference mass concentration for suspension, A is equal
to 1.55m °544 and B is equal to 0.05628 s -°544. As a calculation procedure,
Pomeroy and Male (1992) set r/(zr) = 0.8 kg m-3, based on measured values
in the saltation layer (Pomeroy and Gray, 1990). However, r/(z) may exceed
q(zr) for z < z~, as the lower limit for z is set by the lower boundary height
for suspension, h*, estimated following Pomeroy and Male (1992) as
h*
=
(8)
cHu *127
where cH is a coefficient found equal to 0.08436 m -°'27 s 127.
The upper boundary height for suspended snow, exclusive of inversions or
flow separation due to upwind topography, is determined by the time
available for diffusion of a snow particle from the lower boundary. The top
of a plume of diffusing particles, Zp, may be found from the elapsed time and
turbulence characteristics if the variance of particle velocity approximately
equals that of an atmospheric fluid point velocity. Following Pasquill (1974),
Zp(t) - Zp(0) =
(9)
ku*t
where t is elapsed time. Assuming Zp = z b for blowing snow up to several
metres in height, the top of the surface boundary-layer for suspended snow is
found in terms of the logarithmic wind profile as,
Zb
~-
Zp(t) = Zp(0) +
k2[x(t)
-
X(0)] Iln ~zP(0)1 In [ZP(t--~)]~-°5
l
[_ z o
J
k
z o 3)
(10)
J.W. POMEROY ET AL.
170
1000_
g
W
//
~
100
j."
Stub = 0
0
z
z
0
Z
W
10:
/
s,u0;,oc
Stub
10
15
20
WIND SPEED AT lO-m HEIGHT (m/s)
25
Fig. 2. Suspension transport rate as a function of the 10 m wind speed for an unobstructed upwind fetch
of 500 m, transport threshold wind speed (10 m) of 5.5 m s ~and several exposed heights of wheat stubble.
where x is the distance downwind from the beginning of the fetch over which
the surface roughness and the aerodynamic roughness height, z 0, can be
considered uniform. A comparison of Lagrangian and snow particle time
constants suggests that the assumption of equal particle and wind velocity
variance is not met at heights near to, or below, the saltation layer (Pomeroy,
1988). To avoid applying eqn. (10) to this zone, the model specifies
x(0) = 300m and zp(0) = 0.3 m, based on Takeuchi's (1980) measurements
of blowing snow flow development. The modelled upper boundary height
shows a log-linear increase with friction velocity and a decreasing rate of
increase with fetch distance. For a 10 m wind speed of 10 m s -1, z b increases
from a height of about 1 m for a fetch distance of 325m to over 10m for a
fetch distance of 700 m.
Pomeroy (1988) suggested that in typical prairie conditions, snow particles
lifted to heights above approximately 5 m are unlikely to settle back to the
surface before sublimation removes much of their mass. Hence when
transport rates are calculated for surface hydrology purposes, only the mass
flux below 5 m height need be considered (the exact height is unimportant
because o f small mass fluxes at this height). Using eqns. (2), (3) and (6)-(10),
and an absolute upper limit for Zb of 5 m, the modelled suspension transport
rates for a 500m fetch distance, u* = 0 . 2 m s -1 and various exposed grain
stubble heights are shown in Fig. 2. Suspension transport increases as a power
function of wind speed. While exposed stubble roughness increases the wind
THE PRAR1E BLOWING SNOW MODEL
17l
speed below which suspension transport can not occur, increased turbulence
due to stubble stalks increases the suspended transport rate for a given wind
speed above this limit. Suspension transport is considered zero unless
saltation transport has started.
Sublimation
Schmidt (1972, 1991) has shown that the rate of sublimation of a snow
particle may be modelled by a balance between radiative energy exchange,
convective heat transfer to the snow particle, turbulent transfer of water
vapour from the snow particle and consumption of heat by sublimation.
Assuming that blowing snow particles are in thermodynamic equilibrium, the
time rate of change in mass of a particle is given by
2nra
dm
dt
?sM )
2-r TNu \ R T
Ls (LsM
2vTN u \ ~ - - f
)
1
1,
(11)
1 + DpsS------h
(see Schmidt, 1991 for derivation) where r is the radius of a snow particle
possessing mass, m; o- is the ambient atmospheric undersaturation of water
vapour with respect to ice; Qr is the radiative energy absorbed by the particle;
L~ is the latent heat of sublimation (2.838 × 106jkg-~); M is the molecular
weight of water (18.01kgkmol-l); 2v is the thermal conductivity of the
atmosphere (2v = 0.00063T + 0.0673); Nu is the Nusselt number; R is the
universal gas constant (8313Jmol I K-~); T is the ambient atmospheric
temperature; Ps is the saturation density of water vapour at T; and Sh is the
Sherwood number.
Equation (11) requires specification of the Nusselt and Sherwood numbers,
the radiant energy input, and the temperature and humidity of the air. Lee
(1975) confirmed that adjacent to a blowing snow particle in a turbulent
atmosphere Nu -- Sh. Both terms are related to the particle Reynold's
number, Re, and for Re between 0.7 and 10
Nu
--- Sh =
1.79 + 0.606 Re °5
(12)
in which,
Re -
2rVr
(13)
v
where Vr is the ventilation velocity and v is the kinematic viscosity of air (taken
as 1.88 × 10-sin×s-t). Vr is the sum of the mean terminal particle fall
velocity, co, and the root mean square fluctuating velocity relative to the
172
J.W. POMEROY ET AL,
atmosphere. Lee's (1975) study of blowing snow particle turbulent movement
provides a method of calculating the ventilation velocity, where
V~ =
09 + 3 x r c o s ( 4 )
(14)
and x r is a component of the root mean square particle velocity relative to the
atmosphere in one cartesian direction. Pomeroy and Male (1992) solve for the
mean terminal fall velocity of suspended snow from an analysis of snow
particle drag as
co
=
co, r 18
(15)
where c~ is a coefficent equal to 1.1 × 107m-°8s -I. Lee's model for fluctuating relative wind speeds may be simplified (Pomeroy, 1988) to mean Prairie
surface roughness conditions for suspended snow as
xr(z )
=
c r u ( z ) 136
(16)
where cf is a coefficient equal to 0 . 0 0 5 S ° 3 6 m -0"36 and both xr and u ( z ) are in
metres per second. For saltating snow the ventilation velocity is separated into
vertical and horizontal mean components. The vertical component is then
derived from the mean saltation height (Pomeroy and Gray, 1990) as csattu*
and the horizontal component from the mean saltation speed as 2.3u*, thus
V~ =
csajtu* + 2.3u*
(17)
It is evident that the ventilation velocity is strongly dependent upon height
and mean particle size. Mean particle size may be calculated from height
above the snow surface as
rm
=
CpZ -0"258
(18)
in which Cpequals 4.6 x 10 -5 m °258 and r mand z are in metres. The expression
is an empirical compilation (Pomeroy and Male, 1992) of measurements of
blowing snow particles made over a range of heights from 0.05 to 1 m above
the surface by Schmidt (1982).
The ambient air temperature at any height is calculated using a reference
temperature and an assumed lapse rate. Measurements of vertical temperature profiles over three winters in southern Saskatchewan showed a
relative cooling near the snow surface during the majority of blowing snow
events; however, there was no overall consistency in the resulting gradients,
which ranged from unstable to stable. Therefore, for simplicity, no change in
temperature with height is assumed by the model.
Equation (11) requires specification of the undersaturation of water
vapour. Measurements of vertical humidity profiles over three winters on the
THE PRARIE BLOWING SNOW MODEL
173
Prairies consistently showed a decrease in relative humidity with increasing
height during blowing snow. The most c o m m o n gradient, expressed in terms
of the undersaturation of water vapour at z, o-(z), is simulated by,
a(z) -- a(z = 2)(1.02 - 0.027 In z)
(19)
where o-(z = 2) is the undersaturation measured at a 2 m height and must lie
between 0 and 1.
For a column of blowing snow extending from the snow surface to the top
of the b o u n d a r y layer for suspended snow, the sublimation rate per unit area
of snowcover, qsubl(kg m 2 s- i ) is
Zb
t~
| Csubl(z)n(z) dz
q~ubi =
(20)
0
where Cs.b~(z) (s -I ) is the sublimation loss rate coefficient at a specific height
that is defined by,
CsubJ(Z) --
d[mm(Z)]/dt
(21)
mm(Z)
in which m m(Z) is the mean blowing snow particle mass at height, z. Equation
(21) is solved using d [mm(z)]/dt calculated by eqns. (11)-(19). These equations
are applied using the blowing snow particle of m e a n mass at height z. This
blowing snow particle of m e a n mass m a y be found from the mean snow
particle radius rm. Assuming the frequency distribution of snow particle sizes
can be described by a g a m m a distribution (Budd, 1966; Schmidt, 1982), the
relative frequency of particles with radius rm, f(rm) is
r ~ - ° exp ( f(rm)
=
~)
fl r( )
(22)
in which ~ is a shape parameter, fl is a scale parameter (m), and F is the g a m m a
function. Given the g a m m a size distribution, the m e a n mass of a snow particle
m a y be described by a series, truncated as
mm---- 54no~r3m 1 + _3 +
(23)
in which Pi is the density of ice (kg m-3), and from Schmidt's (1982) measurements,
c~ =
4.08 + c~z
where ca is a coefficient equal to 12.6m ~.
(24)
174
J.W. POMEROY ET AL,
10.
oq
1
-1 °C, 70% RH
-10°C 5 0 % R H ~ ~
. -10 °C, 70% RH ~
..... S.:; ;;::::.... "
a
LIJ
}-<
cr
. . . . . . . . . . .ii. . .iiii
. ..................
0.1
z
0
I.<
.._I
m
0.01
oo
0.001
10
15
20
25
W I N D SPEED AT 10-m HEIGHT (m/s)
Fig. 3. Sublimation rate for a column of blowing snow extending to the top of the boundary-layer, over
a unit area of snow surface, as a function of the 10 m wind speed for an unobstructed upwind fetch of 500 m,
transport threshold wind speed of 5 . 5 m s t, no exposed vegetation, incoming solar radiation of
1 2 0 J m 2s t and several 2 m air temperatures and relative humidities.
Equation (20) integrates over height the predicted Csubl(Z), calculated for a
snow particle of mean mass at height z given the ambient atmospheric
environment, and the mass concentration of blowing snow calculated from
the saltation or suspension algorithms to provide the blowing snow sublimation rate for a column extending from the snow surface to the top of the
boundary-layer as specified using eqn. (10). Figure 3 shows qsubl for a fully
developed column of blowing snow plotted as a function of the 10m wind
speed, for a fetch distance of 500 m, an incoming solar radiation of 120 W m -z
and three different air temperatures and relative humidities. In western
Canada, variations in temperature or humidity through their normal range
cause at least an order of magnitude change in the sublimation rate, whereas
variations in daily radiation input cause only a small change in sublimation
rate.
Snow surface erosion~accumulation
Consider a control volume of the atmosphere extending vertically from the
snow surface to the top of the surface boundary-layer for blowing snow. At
the top of this boundary-layer the flux of snow due to vertical diffusion is zero
(Fig. 4). Assume the fluxes perpendicular to the direction of flow are negligible
and the reference for z, the vertical direction, is the snow surface. The surface
erosion/deposition rate at distance x, downwind of the leading edge of a fetch
175
THE PRARIE BLOWING SNOW MODEL
~ Snowfall ~ qv(X,Zb)
Z=Z
b
dQsusp /dx
Suspended Snow
susp(x )
v
Air Flow
e
%usp(X+l)
qsubl(X)
y
l
Sublimation
I
Diffusion
Air FI°L
z=r
Qsalt(x) z-~=o d~,ait/dx $Saltating Snow ~
x=x
--~
Qsalt(x+l)
~ Snow Surface Erosion/ x=x+l
/
Accumulation
Fig. 4. Cross-sectional view of a control volume for blowing snow transport and sublimation over a unit
area of snow surface. The process algorithms may be conceived in terms of internal and boundary fluxes
to a volume of blowing snow extending to the top of the boundary-layer.
qv(X, 0) is established by the net mass of snow entering or leaving the volume
in x and z directions and through sublimation occurring within the volume
(see Fig. 4). The mass balance for the volume gives the surface erosion/deposition rate per unit area as
qv(X, 0 )
-
dQsa~t
d ~ (x) + ~dQsusp (x) + qsub,(X) + qv(X, Zb)
(25)
in which the vertical flux at the top of the volume, qv (x, z b), equals the negative
of the snowfall rate. Fully developed flow occurs when the surface erosion rate
is equal to the sublimation rate less the snowfall rate, and develops under
invariant atmospheric and surface conditions and an adequate fetch of mobile
snow. The fetch required for full development varies with snow supply and
land use; non-vegetated ground, hard or incomplete snowcovers may prevent
fully developed snow transport. Takeuchi (1980) reports distances varying
from 150 to 300 m for transport rates to reach equilibrium in the lowest 0.3 m
of the atmosphere; Pomeroy (1988) suggests a distance of 500m for full
development to a height of 5 m.
Snow accumulation occurs where exposed surface roughness elements or
topographic depressions cause a decrease in wind speed and saltation and
suspension transport rates, or when the snowfall rate is greater than the
surface erosion rate.
J.W. POMEROY ET AL.
176
140120E
g
lOO-
._>
80-
- Sublimation
W
60-
- Suspension
- Saltation
O
rCO
40- Residual
20-
i
,
i
0
,
f
i
i
i
~
i
,
,
i
i
i
i
500
1000
1500
Fetch Distance (m)
,
i
,
,
2000
Fig. 5. Cross-sectional view of the Prairie Blowing Snow Model applied to a fetch, with annual quantities
of sublimation, suspension and saltation expressed as m m of snow water equivalent. Note the magnitude
of snow fluxes and residual snow~ice/melt/evaporationfor each land surface element of 100 m in length and
their variation with fetch distance.
Implementation
Implementing the PBSM for application to natural systems involves
adapting the transport and sublimation algorithms for conditions of limited
upwind snow supply and incomplete flow development, adding surface snow
supply accounting procedures and interfacing the surface condition to the
transport processes. The PBSM calculates blowing snow transport, sublimation and erosion/deposition on an hourly basis for land surface elements
(LSE) of 100m in length. Calculations are run over a season using: (a)
standard Atmospheric Environment Service, Environment Canada (AES)
hourly observations of wind speed, direction, air temperature and relative
humidity; daily observations of snow depth and snowfall amount; and
observed occurrences of snowfall and blowing or drifting snow; (b) simulated
surface conditions, such as snowcover extent, snow depth, snow water
equivalent, immobile ice content and aerodynamic surface roughness, from
the previous hour. The LSEs are assembled into a flat plane of land (fetch) of
unit width whose major axis is oriented in the direction of the prevailing wind.
A roughness height is specified for each LSE within the fetch. Figure 5
demonstrates conceptually how the fluxes of saltation, suspension and
sublimation change with fetch distance.
Certain operating procedures are specified to calculate seasonal snow
balances. These are listed below.
177
THE PRARIE BLOWING SNOW MODEL
(1) External snow fluxes. Snow enters the fetch only as precipitation in the
vertical direction. Therefore, at the upwind edge of the fetch (x = 0), the
saltation and suspension fluxes downwind and those perpendicular to the
fetch are zero.
(2) Internal snow fluxes/transformations. Snow is: relocated within the
fetch, transported to the downwind edge, sublimated over the fetch or melted
on the fetch. Surface evaporation, infiltration and runoff over the winter are
considered negligible. Therefore
x + 100
[qv(X, 0) - qv(X, Zb) -- qsubI(X)] dx
Qsalt(X + 100) + Qsusp(X + 100)
x
-k- Qsalt(x) + Qsusp(X)
(26)
The snow surface erosion flux, qv(X, 0), is unknown, but,
t+l
t
f qv(X, O) dt < f - qv(X, O)dt - M E L T
t
(27)
0
where t is time elapsed from the start of the snow season, the integral from
time (0) to time (t) of -qv(X, 0) is the cumulative snow accumulation and
M E L T is the cumulative snow melt. Equation (27) limits the snow that may
be eroded over a unit time interval to the seasonal snow accumulation less the
seasonal snow melt.
(3) Flow development. For flow to fully develop, 300 m of fetch (3 LSE) is
required. If insufficient snow is eroded from the first three LSEs to support
fully developed flow, LSEs are added in sequence until a steady condition
exists. Sublimation losses are small until full development occurs.
(4) Snow erosion/accumulation. Blowing snow is deposited on any LSE
whose surface roughness prevents erosion. A fetch of 300m is required to
re-establish fully developed flow when accumulation is induced by a surface
roughness change. The density of wind-deposited snow is 250 kg m 3.
(5) Upper and lower boundary conditions. The 'exposed' roughness height
on an LSE is the stubble height less the depth of snowcover. Blowing snow
transport is integrated to a maximum height of 5 m because snow above this
is not normally redeposited. Sublimation is integrated to the top of the
boundary-layer as set by eqn. (10).
(6) Snow transport occurrence. Snow transport occurs during any hour the
hourly meteorological observations indicate blowing or drifting snow,
provided an LSE is snow-covered and the wind speed high enough to
overcome elevated transport threshold levels caused by exposed stubble
roughness (see Figs. 1 and 2). This indexes snow availability for transport on
terrain other than that at airport meteorological stations.
178
J.W. POMEROY ET AL.
(7) Snowfall. Snowfall occurs at a uniform rate over the duration of a
storm. Newly fallen snow has a density of 100 kg m -3.
(8) Snowmelt. When the daily maximum air temperature exceeds 0°C and
a decrease in snowcover depth is observed by AES, this decrease is converted
to an equivalent depth of water that is retained on an LSE as 'immobile ice'.
VALIDATION
Transport algorithms
Transport rates calculated by the saltation and suspension algorithms have
been compared with mass flux measurements made under fully developed
conditions over continuous snowcover. Pomeroy and Gray (1990) show a
mean difference of 2.5% with a coefficient of variation in difference of 14.5%
between 200 modelled and measured saltation fluxes. Pomeroy and Male
(1992) compared 750 modelled and measured suspended mass concentrations
and found the values were associated with a coefficient of determination of
0.84 and standard error of 0.0016kgm -3 over a range from 1 x 10 6 to
1 k g m -3 (variance scaled with mass concentration).
Snow accumulation simulation
Tabler et al. (1990) used regressions derived from the transport algorithms
to calculate accumulation at a snow fence on the northern Alaska tundra. In
3 out of 4 years, estimated snow transport was within 11% of measured snow
accumulation. The authors attribute the results of the one year, where
estimated accumulation exceeded that measured, to an insufficient upwind
snow supply for full development of flow.
Landine and Gray (1989) evaluated the performance of the PBSM by
comparing model estimates of snow transport and accumulation with snow
survey measurements made over a transect of prairie land. Snow surveys were
conducted on 13 January and 13 March 1989 in fields under dryland farming
located near the city of Saskatoon in western Canada. A Caragana hedge,
approximately 4 m tall with a north-south axis, trapped snow transported
from approximately 1000 m fetches in east and west directions. The field to the
west was covered by grain stubble and provided a flat fetch. To the east, the
field was in fallow on terrain which rose slightly ( < 1%) for about 300 m
where the slope declined. The major obstructions to wind near the hedge were
a large farmyard to the northeast and a gravel road 60 m east of the hedge.
Snow surveys were conducted along a 500 m transect oriented in the east-west
direction. The transect was situated 100 m north of the southern edge of the
THE P R A R I E B L O W I N G S N O W M O D E L
179
hedge and 500 m south of the farmyard. Snow depth was measured every 5 m
along the transect and several measurements of snow density were made in
each type of land use (fallow, stubble, hedge) with a portable gamma attenuation probe.
The hedge acted as a trap for incoming blowing snow and its wake sheltered
snow from erosion for a distance of l15m (about 29 times its height)
downwind on either side. As wakes produced by large objects are not taken
into account by the PBSM, only the snow survey measurements made at least
115 m away in either direction from the hedge were used to characterize field
snow accumulation. Measurements of drifts showed distinctly large accumulations adjacent to the hedge and in the road ditch. These were used to
characterize snow transported from the fields. Snow depth and snow density
on the transects on 13 January and 13 March are shown in Fig. 6. The data
show that snow depth is more variable and that snow density is higher on
fallow fields than on stubble. The fact that substantial amounts of snow
accumulated on each side of the hedgerow suggested multidirectional snow
transport.
Simulations were conducted from 1 November 1988 up to the date of each
snow survey. In these simulations it was assumed: (1) that the height of
stubble was 0.15 m; (2) that the fetches of stubble and fallow were I000 m in
length; (3) that after 15 January, the stubble was inundated by snow and snow
transport to the hedge and ditch snow occurred over non-vegetated surfaces;
(4) that all snow transported in saltation and suspension was trapped by the
hedge and road ditches. Table 1 shows cumulative snowfall and compares
simulated and measured snow water equivalent on the fetches of stubble and
fallow land uses. For fallow, the values are in reasonable agreement on both
dates, with the PBSM underestimating the survey estimates by from 4 to 5%.
For stubble the differences between modelled and measured values are larger,
being approximately 13 % with the PBSM overestimating the measured value
on 13 January and underestimating the measured value on 13 March.
Simulated and measured values of thd total mass of snow transport are
given in Table 2. The totals are in close agreement; on 13 January the
difference is less than 2.5% of the survey estimate and on 13 March the
difference is less than 4%.
Interestingly on 13 March, after significant snow redistribution by wind,
the PBSM underestimated both the amount of snow transported to the hedge
and the amount of snow left on the fields. This difference may possibly be due
to an undercatch of snowfall monitored by a Nipher precipiation gauge.
Goodison et al. (1981) suggest that undercatch by the Nipher is of the order
of 5-10% at wind speeds when most events occurred. An underestimate of
J.W. POMEROYET AL.
180
50.
13 JANUARY NEAR SASKATOON
45'
Carragana Hedge
40'
35,
Stubble
30, Density= 181kg/m3
£
25'
U~
I ~ Z~h'~t = 235 kg/m 3
,
Fallow
Density= 244kg/m3
15
lO,
5'
o
o
50 100 1,50 200 250 300 3,50 400 4,50
Distance (m)
West
250'
500
East
13 MARCH 1989 NEAR SASKATOON
Carragana Hedge
l ~ 7 9
kg/m3
200'
150.
~ 100'
Stubble
I~
D e n s i 7 2 kg/m3 II~1
0
50
West
100
150
200 250 300
Distance (m)
Fallow
Density= 282kg/m3
350
!
400
450
500
East
Fig. 6. Transects of snow depth near a Caragana hedge east of Saskatoon, Canada on 13 January and 13
March 1989. Snow density was measured using a portable gamma attenuation gauge.
snowfall would cause underestimations in both snow transport and sublimation by the PBSM.
OPERATION
Operation of the PBSM using several years of meteorological data can
provide insight into the blowing snow phenomenon in relation to terrain
variables such as aerodynamic surface roughness and fetch and to broad
THEPRARIEBLOWINGSNOWMODEL
181
TABLE 1
Cumulative snowfall and comparisons of snow water equivalent accumulated on fields from
PBSM simulations and snow surveys
Date
(1989)
13 January
13 January
13 March
13 March
Cumulative
snowfall (mm)
38.0
28.0
50.4
50.4
Surface
type
Fallow
Stubble
Fallow
Stubble
Snow water equivalent (mm)
PBSM
Survey
28.0
28.5
31.4
38.4
29.4
25.3
32.7
44.2
TABLE 2
Comparison of blowing snow transport totals from the PBSM simulations and snow surveys
Date (1989)
13 January
13March
Snow trapped at hedge (kg m -~)
PBSM
Survey
590
8147
577
8485
Mass of snow trapped is in kilogram permetre perpendicular to the axis ofthe hedge.
climatic variations. F o r this demonstration the meteorological stations of
Prince Albert and Regina, Saskatchewan are selected and the years 1970-1976
are used for PBSM operation. This time period represents a range of high and
low snowfall years with average meteorological conditions close to the 30 year
average. Prince Albert lies at the northern edge of the Saskatchewan agricultural zone in the partially wooded Parkland Region and regina in the southern
agricultural zone in the prairie grassland region. Table 3 describes the climate
and regional characteristics and the average annual disposition of snowfall as
calculated by the PBSM for 1000 m fetches of fallow (stubble height set to
0.02 m) and stubble (stubble height set to 0.15 m) land uses. At Prince Albert
in the cooler, less windy parklands, blowing snow transport and sublimation
consume 32% on stubble land use and 40% on fallow land use of the annual
snowfall, whilst at Regina in the warmer, windier prairies, these processes
consume 53% and 77%, respectively.
Vertical distribution o f annual snow transport fluxes
Figure 7 shows vertical profiles of the percent of annual blowing snow
transport on 1000m fetches of stubble and fallow land use at Prince Albert
J.W. P O M E R O Y E T A L
182
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183
THE PRARIE BLOWING SNOW MODEL
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(m)
Fig. 7. Vertical profiles of the mean annual blowing snow transport fluxes for fetches of 1000 m, over fallow
and 0.25 m high stubble land uses at Prince Albert and Regina, Canada. Fluxes are calculated by the PBSM
using 6 years of hourly meteorological data.
and Regina. In this figure the percentage of total annual transport occurring
below a given height above the snow surface is plotted against this height. At
Prince Albert, the simulations produced very small differences between flux
profiles for stubble and fallow land uses and hence the results are represented
by a single curve. Most of the transport at Prince Albert occurs very near to
the snow surface with 83% of the transport occurring below a height of
0.05 m, travelling either in saltation or in the lowest suspended layers. This
figure supports the observation that at Prince Albert most transport occurs at
relatively low wind speeds and hence the fluxes near to the surface are
relatively more important than at locations experiencing higher wind speeds.
The strong correlation between the fallow and stubble transport flux profiles
suggests that most transport over stubble occurs after the stubble roughness
elements are nearly filled by snow and the surface aerodynamically resembles
a fallow land use snowcover.
The profiles for Regina show smaller percentages of annual blowing snow
transport below specific heights than for Prince Albert. For example, 64% of
the annual transport occurs between the snow surface and a height of 0.05 m
on fallow land use and 59% on stubble land use. The differences between the
profiles for the two stations can be attributed to the integrated effects on the
blowing snow phenomenon of differences in climate such as wind and temperature regimes, the depth and permanency of snowcover and other factors.
In particular, strong winds during transport at Regina cause greater upward
184
J.W. POMEROY ET AL.
turbulent diffusion of snow than at Prince Albert. This is evident by
comparing the Regina fallow land use and the Prince Albert profiles.
However, the strong winds at Regina also permit snow transport over exposed
stubble stalks, the stalks generating additional turbulence which promotes the
upward diffusion of snow. These effects are evident in comparing the vertical
distribution of blowing snow flux for Regina stubble and fallow land use, the
larger percentage of total annual flux occurring above specific heights on
stubble land use.
Effect of surface roughness on transport and sublimation
The height of grain stubble in western Canada varies with location, crop
type, crop height and cultural practice, hence it is valuable to understand the
effect of varying surface roughness, as indexed by stubble height, on the
blowing snow phenomenon. A specific non-snow surface roughness will have
a range of aerodynamic roughness heights associated with it over the winter,
this range depending on burial of the roughness element by snow which in
turn depends on snowfall, blowing snow accumulation, wind speeds and
mid-winter melt and evaporation. Hence, the interaction between surface
roughness and blowing snow will vary with climate region. Figure 8 shows an
example of the interaction as simulated by the PBSM for uniform 1000m
fetches of varying stubble heights, using climatological data from Prince
Albert and Regina. In Fig. 8(a) annual blowing snow transport is that snow
eroded from and blown to the edge of the fetch, expressed as the mass of snow
per unit width perpendicular to the wind direction. The snow transport at
Prince Albert decreases approximately linearly with increasing stubble height,
the decrease displaying a very low slope. The annual quantity of snow eroded
and transported off a 1000 m fetch of 0.4 m stubble is 52% less than that off
a 0.01 m stubble. Although this is a significant change in terms of potential
snow accumulation at the downwind end of the fetch, the change only
represents 6.2% of the mean annual snowfall over the fetch. At Regina there
is a sharper drop in transport with stubble height for stubble heights less than
0.1 m, otherwise the curve is very similar to that for Prince Albert, with the
annual transport over 0.4m stubble being 63% less than that over 0.01 m
stubble. However because of the greater magnitude of the snow transport at
Regina this change is more notable in terms of annual snowfall over the fetch,
being 22% of such.
Figure 8(b) shows the average annual blowing snow sublimation loss, in
terms of depth of water per unit area averaged over the 1000 m fetch, plotted
against stubble height. At both Prince Albert and Regina the general trend is
for decreasing sublimation with increasing stubble height. However, there is
THE PRARIE BLOWING SNOW MODEL
i¢,"
185
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20000I-_
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STUBBLE HEIGHT (cm)
0"~.
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, , i , , , , , , , , , i
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. . . . . . .
10
20
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STUBBLE HEIGHT (cm)
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<,,,
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mE
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Fig. 8. The effects of grain stubble height on mean annual values of: (a) blowing snow transported off the
fetch, (b) blowing snow sublimated over the fetch, and (c) residual un-eroded snow water over 1000m
fetches at Prince Albert and Regina, Canada. Values are calculated by the PBSM using 6 years of hourly
meteorological data.
an apparent divergence from this trend at Regina, where greater sublimation
occurs over stubble heights between 0.05 and 0.! m. With short stubble
(0.05-0.1 m) land use, a portion of the snowcover is protected from erosion by
winds of low velocity that cause some snow transport but insignificant sublimation. When a high wind speed event does occur (more likely at Regina
than Prince Albert), snow is scoured from the stubble, the stubble generates
additional turbulence and hence snow particle ventilation, and high sublimation losses result. At Regina, the increased consumption of blowing snow by
sublimation over short stubble is mirrored by rapidly declining blowing snow
transport with stubble height over short stubble as shown in Fig. 8(a).
Conversely the linear decreases in transport (Fig. 8(a)) and sublimation (Fig.
8(b)) with stubble height at Prince Albert mirror each other.
The residual, the seasonal snowfall minus the sum of blowing snow
transport and sublimation and expressed as depth of water per unit area
averaged over the 1000 m fetch, is plotted against stubble height in Fig. 8(c).
The residual increases with stubble height as both transport and sublimation
186
J.W. POMEROY ET AL.
decline. At Prince Albert, warm weather events occur infrequently during
winter and most of the residual remains as snowcover over the fetch. This
residual snowcover varies only a small amount with stubble height, changing
from 56% of snowfall on short stubble (0.05 m) to 73 % on tall stubble (0.4 m).
At Regina, there is little change in the residual for stubble heights from 0.01
to 0.05m, but for heights exceeding this range the residual increases by
1 m m m 2 over the fetch for every 0.01 m increase in stubble height. This
results in a substantial gain in residual for an increase in stubble height, from
22% of annual snowfall for short stubble to 60% for tall stubble (0.4m).
However, it should be noted that components of the residual other than
snowcover, such as mid-winter evaporation, infiltration and runoff will also
be higher at Regina and an increase in residual does not necessarily translate
to an increase in snowcover water equivalent.
Effect of fetch distance on transport and sublimation
The fetch distance is defined here as the downwind distance over uniform
land use from a location where blowing snow is not occurring. The fetch
distance varies notably across western Canada with cultural features such a
field size, shelterbelts, snowfences and road network density as well as with
natural features such as escarpments, river valleys and woods. This idealized
definition of fetch does not include the downwind distance over which flow is
disturbed by wakes of potential obstructions to blowing snow. Tabler and
Schmidt (1986) suggest that the downwind wakes occupy a distance typically
30 times the exposed height of snowfences and 10-20 times the exposed height
of hedges. The appropriate wake distance should be added to the fetch
distances stated here before comparison or application to real landscapes.
Variation in mean annual blowing snow transport as simulated by the PBSM
with fetch length is demonstrated for Prince Albert and Regina in Fig. 9 for
fallow (Fig. 9(a)) and 0.25 m high stubble (Fig. 9(b)) land uses. The value
plotted is the summation of seasonal transport; i.e. the snow transported off
the fetch of a given distance. Its units are mass of snow per unit width
perpendicular to the flow; this value should be resolved into directional
components before comparing with actual accumulations in shelterbelts, etc.
that might occur at the end of the fetch distance. Of note at both stations is
the increase in transport in the first 300 m of fetch distance; with adequate
snow supply this is the distance over which fully developed flow is established.
Once established, the annual snow transport at Prince Albert remains
reasonably constant with distance at between 9000 and 10000kgm -1 for
stubble and between 12 000 and 13 000 kg m - ' for fallow.
Annual snow transport at Regina as shown in Fig. 9 changes notably with
187
THE PRAR1E BLOWING SNOW MODEL
351
/
PRINCEALBERT
301
,NA
20
z
1
~
o
0
(a)
~
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40~
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35
E
1000
2000
3000
FETCH DISTANCE (m)
4000
PRINCE ALBERT
~ 30
~ g25
~20
REGINA
<°15
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0
:~
0
(b)
~-
1000
2000
3000
FETCH DISTANCE (m)
4000
Fig. 9. The mean annual blowing snow transport off fetches at Prince Albert and Regina, Canada of:
(a) fallow land use (stubble height = 0.01 m), (b) stubble land use (stubble height = 0.25m). Snow
transport is mass per unit width perpendicular to the flow direction; this value should be distributed
according to actual transport vectors before comparison with snow drift accumulations at the edge of fields.
fetch well beyond the 300m distance. Snow transport increases with fetch
distance up to a m a x i m u m at 1000m, then declines with increasing distance.
The increase in transport with fetch distance up to 1000 m is attributed to the
effects of high winds and insufficient snowcover to sustain fully developed
flow. Because requirements for fully developed flow are given priority by the
PBSM, if there is not sufficient snow in the first 300m to satisfy transport
requirements then subsequent distances are added until full development is
achieved. This modelling feature simulates the snow-depleted areas that can
cover large areas of the semiarid southern Canadian Prairies in winter and are
often the limiting factor to snow transport. For stubble land use at Regina,
the increase in snow transport up to a fetch distance of 1000m is not as
dramatic as for fallow land use. For fetch distances beyond 1000m the
decrease in transport with distance is more pronounced over stubble than over
fallow land use. These differences are attributed to the requirement to reduce
J.W. POMEROY ET AL.
188
aoo~
90t Ann_nualSWE = 110mm
~"
801 F.ALI-OWTRANSPORT
~ 70] FALLOWSUBLIMATiON
X
601 STUBBLETRANSPORT
501STUBBLE SUBLIMATION
4ot r~
........................................
.............................. _.........................................
3ot/ .
0
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......x/iil;il...........................................
I
1000
2000
3000
FETCH DISTANCE (m)
4000
I
lOO/
90
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1000
(b)
2600
3600
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4000
Fig. 10. The water equivalent of mean annual blowing snow transport and sublimation as a function of
fetch distance and land use: (a) Prince Albert, Canada, (b) Regina, Canada. Values shown are average
annual blowing snow transport and sublimation in depth of snow water equivalent averaged over the fetch
for fallow (stubble height = 0.0l m) and stubble (stubble height = 0.25 m) land use.
aerodynamic roughness by deposition in stubble before snow transport can
easily proceed and the cumulative depletion of available snow by sublimation
during transport over the fetch (sublimation is higher at Regina than at Prince
Albert). The probability that the snow supply available for transport can
overcome losses due to snow accumulation in exposed stubble and to sublimation decreases with increasing fetch distance.
The effect of snow transport and sublimation on the average water balance
over fetches of varying distances and land uses is shown in Fig. 10 for Prince
Albert and Regina. The values plotted are snowcover losses to blowing snow
transport and sublimation, respectively, in terms of water equivalent per unit
area averaged over the fetch distance. Snowcover loss due to snow eroded and
THE PRARIE BLOWING SNOW MODEL
189
transported off the fetch (saltation + suspension) domingtes for fetches up to
between 600 and 1000 m in length. This is especially prominent for the first
300 m of fetch distance because of the increase in transport from the leading
edge. Quantities of water lost from the fetch to snow transport are greater at
windy Regina, for example 94 mm water equivalent (85% of annual snowfall)
is transported off 300m of fallow at Regina and 4 2 m m (38% of annual
snowfall) off the same fetch at Prince Albert. Stubble land use experiences a
greater reduction in transport relative to fallow at Regina, where transport
from fallow is twice that from a 0.25 m height stubble cover. In comparison,
transport from fallow at Prince Albert is only one-fifth more than that over
stubble.
As fetch distance increases beyond 600-1000m, loss due to blowing snow
sublimation increases to dominate the depeletion of snowcover. Sublimation
losses are 85 mm water equivalent over a 4000 m fallow fetch at Regina; this
equals 74% of the annual snowfall input to the fetch. However, there are
important differences in the magnitude of sublimation between the two
stations; sublimation losses over the 4000 m fallow fetch at Prince Albert are
only 49 mm or 44% of the annual snowfall. The larger sublimation (and
transport) losses at Regina can be explained by the extremes of wind speed
experienced at that station. On average, each year several very high wind
speed events scour snow from previously filled roughness elements and
produce high transport and sublimation losses. The net result is that
subsequent winds, which would ordinarily cause saltation, do not produce
transport because of the increase in transport threshold and aerodynamic
surface roughness resulting from the scouring action. The effect of land use on
snowcover loss due to sublimation is more consistent between stations than
the effect on transport. For fetches of identical length at Regina, sublimation
losses over fallow are about 1.2-1.4 times those for stubble, while at Prince
Albert, losses on fallow are 1.2-1.3 the loss for stubble. The small differences
in sublimation between stubble and fallow land uses at Regina are attributed
to increased turbulence during blowing snow events over stubble compensating somewhat for the decreased rate of transport.
At all locations, the sum of losses due to blowing snow transport and to
sublimation does not change appreciably from its 1000 m fetch value (Table 3)
for fetches from 500 to 4000m. The implication of the transition from
primarily transport loss for fetches less than 1000 m to primarily sublimation
loss for longer fetches, is most striking at larger scales rather than the small
scale of the fetch itself. Snow eroded and then transported off the fetch is
available for trapping by local hedges, snowfences, woodlands, river valleys
and other topographic depressions, and after evaporative losses during melt,
provides an important input to surface and soil water supplies at these sites.
190
J.W. POMEROY ET AL.
However, snow eroded and then returned to the atmosphere by sublimation
of blowing snow over longer transport distances is removed from surficial
supplies at all scales.
CONCLUSIONS
Initial validation of a physically based blowing snow transport, sublimation and accumulation model using field measurements of snow transport and
residual field snow and hourly meteorological observations show differences
between snow accumulation measurements and model simulations of from 5
to 13%. The largest differences are underestimates of snow accumulation at
the end of the snow season that may be related to, and are the same order of,
the undercatch of snowfall over the season by Nipher-shielded snowfall
gauges.
Application of the blowing snow model shows the following.
(1) The annual proportion of snow transported above any specific height
increases notably with mean seasonal wind speed.
(2) Under high wind speed regimes, snow is transported at greater heights
over grain stubble stalk surfaces than over smooth, because of increased
turbulence and high wind speeds during transport over roughened surfaces.
(3) The decrease in annual blowing snow transport and sublimation
quantities with increasing surface roughness height becomes more apparent
with higher seasonal wind speeds and temperatures.
(4) For a low wind speed and temperature regime, the annual quantity of
snow transported off a fetch increases with fetch length for distances up to
300 m then remains relatively constant.
(5) For a high wind speed and temperature regime, annual snow transport
increases with fetch distance up to 1000 m then slowly declines.
(6) The percentage of annual snowfall lost to snow transport varies tremendously with wind speed; in the Canadian prairies a peak of 85% of annual
snowfall is transported off the first 300 m of fetch by a high wind speed regime
whilst only 38% is transported by a lower wind speed regime.
(7) For fetches beyond 1000 m, blowing snow sublimation losses dominate
over transport losses, the difference increasing with increasing fetch distance.
(8) The percentage of annual snowfall lost to blowing snow sublimation
varies strongly with wind speed and temperature; in Saskatchewan sublimation losses are 74% of annual snowfall over a 4000 m fetch in a warm and
windy location and only 44% over the same fetch distance at a cooler and
calmer location.
(9) For both climate regimes modelled, the sum of snowcover loss due to
blowing snow transport and sublimation does not change appreciably from its
THE PRARIE BLOWING SNOW MODEL
191
1000 m fetch value for fetches of from 300 to 4000 m. However, the transition
from primarily transport to primarily sublimation losses at the 1000 m fetch
is useful in assessing the effect of scale in snow hydrology.
ACKNOWLEDGEMENTS
The support and encouragement of the Saskatchewan Agricultural
Development Fund, Regina and Dr. W. Nicholaichuk, National Hydrology
Research Institute, Saskatoon are gratefully acknowledged. Mr. Thomas
Brown built the snow particle detectors and data retrieval system and Mr. Dell
Bayne conducted the snow surveys; both are thanked for their assistance in
this work.
REFERENCES
Budd, W.F., 1966. The drifting of non-uniform snow particles. In: Studies in Antarctic
Meteorology. Antarctic Research Series No. 8, American Geophysical Union, Washington,
DC, pp. 59-70.
Goodison, B.E., Ferguson, H.L. and McKay, G.A., 1981. Measurement and data analysis. In:
D.M. Gray and D.H. Male (Editors), Handbook of Snow, Principles, Processes,
Management and Use. Pergamon, Toronto, pp. 191-265.
Granberg, H.B., 1978. Snow accumulation and roughness changes through winter at a foresttundra site near Shefferville, Quebec. In: S.C. Colbeck and M. Ray (Editors), Proceedings,
Modelling of Snow Cover Runoff. U.S. Army, Corps of Engineers, Cold Regions Research
and Engineering Laboratory, Hanover, NH, pp. 83-92.
Gray, D.M., 1978. Snow accumulation and distribution. In: S. Colbeck and M. Ray (Editors),
Modelling of Snow Cover Runoff. U.S. Army, Cold Regions Research and Engineering
Laboratory, Hanover, NH, pp. 3-33.
Greeley, R. and Iversen, J.D., 1985. Wind as a Geological Process on Earth, Mars, Venus and
Titan. Cambridge University, Cambridge, 333 pp.
Landine, P.G. and Gray, D.M., 1989. Snow Transport and Management. Report prepared by
the Division of Hydrology, University of Saskatchewan for the National Hydrology
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