The Prairie Blowing Snow Model: characteristics, validation, operation

Transcription

1 Journal of Hydrology, 144 (1993) Elsevier Science Publishers B.V., Amsterdam 165 [3] The Prairie Blowing Snow Model: characteristics, validation, operation J.W. Pomeroy", D.M. Gray b and P.G. Landine 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 WO, Canada (Received 2 May 1992; revision accepted 5 September 1992) ABSTRACT Pomeroy, J.W., Gray, D.M. and Landine, P.G., The Prairie Blowing Snow Model: characteristics, validation, operation. J. Hydrol., 144: 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 3 and 1 m, then remains relatively constant or slowly declines. Within the first 3 m of fetch 38-85% of annual snowfall is removed by snow transport, the amount increasing with wind speed. Beyond 1 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 4 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 1 m fetch value for fetches 5 to 4 m. The transition from primarily transport to primarily sublimation losses at the 1 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 Correspondence to: J.W. Pomeroy, National Hydrology Research Institute, Environment Canada, I 1 Innovation Boulevard, Saskatoon, Sask. S7N 3H5, Canada. Present address: Department of Civil Engineering, University of Saskatchewan, Saskatoon, Sask., Canada /93/$ Elsevier Science Publishers B.V. All rights reserved

2 166 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, 196; 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 PRAIRIE BLOWING SNOW MODEL 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, 199; 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.

3 THE PRARIE BLOWING SNOW MODEL 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 (199) found the following expression valid for snow-covered prairies, Qsalt Csalt PUt* (//,2, u. -- u.2) (1) u*g where Qsalt is the saltation transport rate (kg m-i s- ~ ), Csalt is an empirically derived constant found equal to.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(z)k u* - (2) ln(z ) where k is yon Kgrmfin's constant (.4), u(z) is the wind speed at height z and z 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 Z -- 2g -~- CstNstAst (3) in which Q is a dimensionless coefficient found equal to.123 for prairie snowcovers, Cst is a coefficient equal to.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 32 stalks m -2. Ast is the product of the stalk diameter (3 mm) and the exposed height of stalk (25 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.15 to

4 168 J.W. POMEROY ET AL. 1 E UtlO = 11 m/s _ ~ J f LU p- < er rr O 3 Z < rr lc Z O F- _J < WIND SPEED AT 1-m HEIGHT (m/s) Fig. 1. Saltation transport rate as a function of the 1 m wind speed for several transport threshold wind speeds and exposed heights of wheat stubble..25 m s I for fresh, loose, dry snow and for movement during snowfall and from.25 to 1.ms -~ 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 = NstAst 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 LJL 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.

5 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 - k q(z) In dz (6) h* in which h* is the lower boundary for suspension (approximate top of the saltation layer), z b is the top of the surface boundary-layer for suspended snow, q(z) is the mass concentration of suspended snow (kg m -3) at height z (m) and z 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) exp{- A[(Bu* ) Z-.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.5628 s As a calculation procedure, Pomeroy and Male (1992) set r/(zr) =.8 kg m-3, based on measured values in the saltation layer (Pomeroy and Gray, 199). 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* = chu *127 where ch is a coefficient found equal to.8436 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() = ku*t (9) 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, Z b ~- Zp(t) = Zp() + k2[x(t) - X()] Iln ~zp() 1 In [ZP(t--~)]~- 5 (1) l [_ z o J k z o 3) (8)

6 17 J.W. POMEROY ET AL. g 1_ W ~ 1 z z 1: Z W Stub = Stub / s,u;,oc // j." WIND SPEED AT lo-m HEIGHT (m/s) Fig. 2. Suspension transport rate as a function of the 1 m wind speed for an unobstructed upwind fetch of 5 m, transport threshold wind speed (1 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, 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. (1) to this zone, the model specifies x() = 3m and zp() =.3 m, based on Takeuchi's (198) 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 1 m wind speed of 1 m s -1, z b increases from a height of about 1 m for a fetch distance of 325m to over 1m for a fetch distance of 7 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 of small mass fluxes at this height). Using eqns. (2), (3) and (6)-(1), and an absolute upper limit for Zb of 5 m, the modelled suspension transport rates for a 5m fetch distance, u* =.2ms -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

7 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 dm dt 2nra?sM ) 2-r TNu \ R T 1 Ls (LsM ) 1, 2vTN u \~--f 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 ( jkg-~); M is the molecular weight of water (18.1kgkmol-l); 2 v is the thermal conductivity of the atmosphere (2v =.63T +.673); 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.7 and 1 Nu --- Sh = 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 sin s-t). V r is the sum of the mean terminal particle fall velocity, co, and the root mean square fluctuating velocity relative to the (11)

8 172 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~ = 9 + 3xrcos(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 where c~ is a coefficent equal to m- 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 ) = cru(z) 136 (16) where cf is a coefficient equal to.5 S 36m -"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, 199) as csatt u* 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 r m = CpZ -"258 (18) in which Cp equals 4.6 x 1-5 m 258 and r m and 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.5 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 (15)

9 THE PRARIE BLOWING SNOW MODEL 173 Prairies consistently showed a decrease in relative humidity with increasing height during blowing snow. The most common gradient, expressed in terms of the undersaturation of water vapour at z, o-(z), is simulated by, a(z) -- a(z = 2)( In z) (19) where o-(z = 2) is the undersaturation measured at a 2 m height and must lie between and 1. For a column of blowing snow extending from the snow surface to the top of the boundary layer for suspended snow, the sublimation rate per unit area of snowcover, qsubl (kg m 2 s- i ) is Zb q~ubi = t~ Csubl (z)n(z) dz (2) 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 [m m (z)]/dt calculated by eqns. (11)-(19). These equations are applied using the blowing snow particle of mean mass at height z. This blowing snow particle of mean mass may be found from the mean snow particle radius rm. Assuming the frequency distribution of snow particle sizes can be described by a gamma distribution (Budd, 1966; Schmidt, 1982), the relative frequency of particles with radius rm, f(rm) is r~- exp (- ~) f(rm) = (22) fl r( ) in which ~ is a shape parameter, fl is a scale parameter (m), and F is the gamma function. Given the gamma size distribution, the mean mass of a snow particle may be described by a series, truncated as 4no~r3m 1 + _3 + (23) mm in which Pi is the density of ice (kg m-3), and from Schmidt's (1982) measurements, c~ = c~z (24) where ca is a coefficient equal to 12.6m ~.

10 174 J.W. POMEROY ET AL, oq C, 7% RH -1 C 5 % R H ~ ~ C, 7% RH ~... S.:; ;;::::... " a LIJ }-- < cr z I.- <.._I m oo ii iiii WIND SPEED AT 1-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 1 m wind speed for an unobstructed upwind fetch of 5 m, transport threshold wind speed of 5.5ms t, no exposed vegetation, incoming solar radiation of 12Jm 2s t and several 2m air temperatures and relative humidities. Equation (2) 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. (1). Figure 3 shows qsubl for a fully developed column of blowing snow plotted as a function of the 1m wind speed, for a fetch distance of 5 m, an incoming solar radiation of 12 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

11 THE PRARIE BLOWING SNOW MODEL 175 Z=Z b ~ Snowfall ~ qv(x,zb) Air Flow e x susp( ) y v dqsusp /dx Suspended Snow qsubl(x) I l Sublimation Diffusion %usp(x+l) Air FI L Qsalt (x) z=r z-~=o d~,ait/dx $Saltating Snow ~ --~ Qsalt (x+l) x=x ~ 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, ) 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, ) - dqsa~t dqsusp d~ (x) + ~ (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 (198) reports distances varying from 15 to 3 m for transport rates to reach equilibrium in the lowest.3 m of the atmosphere; Pomeroy (1988) suggests a distance of 5m 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.

12 176 J.W. POMEROY ET AL E g loo- - Sublimation._> 8- W O r- CO Suspension - Saltation - Residual i, i, f i i i ~ i,, i i i i, i,, Fetch Distance (m) 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 mm of snow water equivalent. Note the magnitude of snow fluxes and residual snow~ice/melt/evaporation for each land surface element of 1 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 1m 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.

13 THE PRARIE BLOWING SNOW MODEL 177 (1) External snow fluxes. Snow enters the fetch only as precipitation in the vertical direction. Therefore, at the upwind edge of the fetch (x = ), 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+ 1 Qsalt(X + 1) + Qsusp(X + 1) [qv(x, ) - qv(x, Zb) -- qsubi(x)] dx x -k- Qsalt(x) + Qsusp(X) The snow surface erosion flux, qv(x, ), is unknown, but, (26) t+l f qv(x, O) dt < f - t t qv(x, O)dt - MELT where t is time elapsed from the start of the snow season, the integral from time () to time (t) of -qv(x, ) is the cumulative snow accumulation and MELT 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, 3 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 3m is required to re-establish fully developed flow when accumulation is induced by a surface roughness change. The density of wind-deposited snow is 25 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. (1). (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. (27)

14 178 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 1 kg m -3. (8) Snowmelt. When the daily maximum air temperature exceeds 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 (199) show a mean difference of 2.5% with a coefficient of variation in difference of 14.5% between 2 modelled and measured saltation fluxes. Pomeroy and Male (1992) compared 75 modelled and measured suspended mass concentrations and found the values were associated with a coefficient of determination of.84 and standard error of.16kgm -3 over a range from 1 x 1 6 to 1 kgm -3 (variance scaled with mass concentration). Snow accumulation simulation Tabler et al. (199) 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 4m tall with a north-south axis, trapped snow transported from approximately 1 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 3 m where the slope declined. The major obstructions to wind near the hedge were a large farmyard to the northeast and a gravel road 6 m east of the hedge. Snow surveys were conducted along a 5 m transect oriented in the east-west direction. The transect was situated 1 m north of the southern edge of the

15 THE PRARIE BLOWING SNOW MODEL 179 hedge and 5 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.15 m; (2) that the fetches of stubble and fallow were I 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 5-1% at wind speeds when most events occurred. An underestimate of

16 18 J.W. POMEROY ET AL ' 4' 35, 13 JANUARY NEAR SASKATOON Carragana Hedge Stubble I ~ Z~h'~t = 235 kg/m 3 3, Density = 181 kg/m 3, Fallow 25' Density = 244 kg/m 3 U~ 15 lo, 5' o o West 5 1 1, ,5 4 4,5 5 Distance (m) East 25' 13 MARCH 1989 NEAR SASKATOON Carragana Hedge 2' l ~ 7 9 kg/m ~ 1' Stubble I~ Fallow Densi72 kg/m3 I I~ 1 Density = 282 kg/m West Distance (m) East! Fig. 6. Transects of snow depth near a Caragana hedge east of Saskatoon, Canada on 13 January and 13 March 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

17 THE PRARIE BLOWING SNOW MODEL 181 TABLE 1 Cumulative snowfall and comparisons of snow water equivalent accumulated on fields from PBSM simulations and snow surveys Date Cumulative Surface (1989) snowfall (mm) type Snow water equivalent (mm) PBSM Survey 13 January 38. Fallow January 28. Stubble March 5.4 Fallow March 5.4 Stubble TABLE 2 Comparison of blowing snow transport totals from the PBSM simulations and snow surveys Date (1989) Snow trapped at hedge (kg m -~) PBSM Survey 13 January March Mass of snow trapped is in kilogram permetre perpendicular to the axis ofthe hedge. climatic variations. For this demonstration the meteorological stations of Prince Albert and Regina, Saskatchewan are selected and the years are used for PBSM operation. This time period represents a range of high and low snowfall years with average meteorological conditions close to the 3 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 1 m fetches of fallow (stubble height set to.2 m) and stubble (stubble height set to.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 4% 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 of annual snow transport fluxes Figure 7 shows vertical profiles of the percent of annual blowing snow transport on 1m fetches of stubble and fallow land use at Prince Albert

18 182 J.W. POMEROY ET AL 8 b,,--, -~ ~,,,.",,-*-~ =,. ~ ='- ='-,- ~S 2 t-, E &.-, E r-, o 8 5 E I I," > 8 Z o...;,_.] < [., <...,.. '-'

19 THE PRARIE BLOWING SNOW MODEL 183 I-- rv~ I-- "r- 1 ~, ],- ~(..5 4 [] STUBBLE: REGINA W~ O~ IIW W.-J 13-2 o~ '' O FALLOW: REGINA STUBBLE AND FALLOW: PRINCE ALBERT I i i i r l i l l l l l l l L I i i l ~ HEIGHT ABOVE SNOW SURFACE (m) Fig. 7. Vertical profiles of the mean annual blowing snow transport fluxes for fetches of 1 m, over fallow and.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.5 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.5 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

20 184 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 1m 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 1 m fetch of.4 m stubble is 52% less than that off a.1 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.1 m, otherwise the curve is very similar to that for Prince Albert, with the annual transport over.4m stubble being 63% less than that over.1 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 1 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

21 THE PRARIE BLOWING SNOW MODEL 185 i-," 1 ooooo r 1 O~ 8oooof (a) i O REGINA l[ <. ooooot / 2 I-_ ~,-~ / t ~ r~,,,v,,~,,, ~..... ~ o,o 2o 3o 4o STUBBLE HEIGHT (cm) "~. 8 F-"'.~E ~.,,..-?,. <,,, g~ me 2op----o. x2~,--.---~ o STUBBLE HEIGHT (cm) O/,,,,,,, i,,,,,,,,, i i / / oof 'c> ''4 STUBBLE HEIGHT (cm) 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 1m 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.5 and.! m. With short stubble (.5-.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 1 m fetch, is plotted against stubble height in Fig. 8(c). The residual increases with stubble height as both transport and sublimation

22 186 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 (.5 m) to 73 % on tall stubble (.4 m). At Regina, there is little change in the residual for stubble heights from.1 to.5m, but for heights exceeding this range the residual increases by 1 mmm 2 over the fetch for every.1 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 6% for tall stubble (.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 3 times the exposed height of snowfences and 1-2 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.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 3 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 9 and 1kgm -1 for stubble and between 12 and 13 kg m- ' for fallow. Annual snow transport at Regina as shown in Fig. 9 changes notably with

23 THE PRAR1E BLOWING SNOW MODEL / PRINCE ALBERT 31,NA 2 z 1 ~ o (a) FETCH DISTANCE (m) ~ 4~,.~ "~ 35 E ~ 3 ~ g25 ~2 < 15 ~ ~- PRINCE ALBERT REGINA :~ (b) FETCH DISTANCE (m) 4 Fig. 9. The mean annual blowing snow transport off fetches at Prince Albert and Regina, Canada of: (a) fallow land use (stubble height =.1 m), (b) stubble land use (stubble height =.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 3m distance. Snow transport increases with fetch distance up to a maximum at 1m, then declines with increasing distance. The increase in transport with fetch distance up to 1 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 3m 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 1m is not as dramatic as for fallow land use. For fetch distances beyond 1m 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

24 188 J.W. POMEROY ET AL. aoo~ 9t An n_nual SWE = 11mm ~" 81 F.ALI-OW TRAN SPORT ~ 7] FALLOW SUBLIMATiON X 61 STUBBLE TRANSPORT 51STU BBLE SUBLIMATION... 4ot r~... _... 3ot/....x/iil;il... I I (a) FETCH DISTANCE (m) loo / g 9 > F '..' FALLOW $UBUMATION..'" STLI B LE TRANSPORT STUBBLE SUBUMATION (b) FETCH DISTANCE (m) Fig. 1. 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 =.l m) and stubble (stubble height =.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. 1 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

25 THE PRARIE BLOWING SNOW MODEL 189 transported off the fetch (saltation + suspension) domingtes for fetches up to between 6 and 1 m in length. This is especially prominent for the first 3 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 3m of fallow at Regina and 42mm (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.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 6-1m, loss due to blowing snow sublimation increases to dominate the depeletion of snowcover. Sublimation losses are 85 mm water equivalent over a 4 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 4 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 times those for stubble, while at Prince Albert, losses on fallow are 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 1 m fetch value (Table 3) for fetches from 5 to 4m. The implication of the transition from primarily transport loss for fetches less than 1 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.

26 19 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 3 m then remains relatively constant. (5) For a high wind speed and temperature regime, annual snow transport increases with fetch distance up to 1 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 3 m of fetch by a high wind speed regime whilst only 38% is transported by a lower wind speed regime. (7) For fetches beyond 1 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 4 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

27 THE PRARIE BLOWING SNOW MODEL m fetch value for fetches of from 3 to 4 m. However, the transition from primarily transport to primarily sublimation losses at the 1 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., The drifting of non-uniform snow particles. In: Studies in Antarctic Meteorology. Antarctic Research Series No. 8, American Geophysical Union, Washington, DC, pp Goodison, B.E., Ferguson, H.L. and McKay, G.A., Measurement and data analysis. In: D.M. Gray and D.H. Male (Editors), Handbook of Snow, Principles, Processes, Management and Use. Pergamon, Toronto, pp Granberg, H.B., 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 Gray, D.M., 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 Greeley, R. and Iversen, J.D., Wind as a Geological Process on Earth, Mars, Venus and Titan. Cambridge University, Cambridge, 333 pp. Landine, P.G. and Gray, D.M., Snow Transport and Management. Report prepared by the Division of Hydrology, University of Saskatchewan for the National Hydrology Research Institute, Saskatoon, 8 pp. Lee, L.W., Sublimation of Snow in Turbulent Atmosphere. Ph.D. Thesis, University of Wyoming, Laramie, 162 pp. (unpubl.). Lettau, H., Note on aerodynamic roughness-parameter estimation on the basis of roughness element description. J. Appl. Meteorol., 8: Lyles, L. and Allison, B.E., Wind erosion: the protective role of stimulated standing stubble. Trans. ASAE, 19: Kuz'min, P.P., 196. Snowcover and Snow Reserves. Gidrometeorologischeskoe Izdatelsko, Leningrad: (translation, US National Science Foundation, Washington, DC, 1963). Pasquill, F., Atmospheric Diffusion, 2nd edn. Ellis Horwood Ltd., Chichester, 429 pp. Pomeroy, J.W., Wind Transport of Snow. Ph.D. Thesis, Division of Hydrology, University of Saskatchewan, Saskatoon, 226 pp. (unpubl.). Pomeroy, J.W., A process-based model of snow drifting. Ann. Glaciol., 13: Pomeroy, J.W., Transport and sublimation of snow in wind-scoured alpine terrain. In:

28 192 J.W. POMEROY ET AL. H. Bergmann, H. Lang, W. Frey, D. Issler and B. Salm (Editors), Snow, Hydrology and Forests in High Alpine Areas. IAHS Publication No. 25, IAHS, Wallingford, pp Pomeroy, J.W. and Gray, D.M., 199. Saltation of snow. Water Resour. Res., 26(7): Pomeroy, J.W. and Male, D.H., Steady-state suspension of snow. J. Hydrol., 136: Schmidt, R.A., Sublimation of wind-transported snow -- A model. U.S., For. Serv. Rocky Mount. For. Range Exp. Stn., Res. Pap. RM-9, 24 pp. Schmidt, R.A., Vertical profiles of wind speed, snow concentration and humidity and blowing snow. Boundary-layer Meteorol., 23: Schmidt, R.A., Sublimation of snow intercepted by an artificial conifer. Agric. For. Meteorol. 54: Schroeter, H.O., An Operational Snow Accumulation-Ablation Model for Areal Distribution of Shallow Ephemeral Snowpacks. Ph.D. Thesis, University of Guelph, Guelph, Ont., 325 pp. (unpubl.). Steppuhn, H., Snow and agriculture. In: D.M. Gray and D.H. Male (Editors), Handbook of Snow, Principles, Processes, Management and Use. Pergamon, Toronto, pp Steppuhn, H. and Dyck, G.E., Estimating true basin snowcover. In: Advanced Concepts and Techniques in the Study of Snow and Ice Resources. National Academy of Sciences, Washington, DC, pp Tabler, R.D., Estimating the transport and evaporation of blowing snow. In: Snow Management on the Great Plains, July 1985, Swift Current, Sask. Great Plains Agricultural Council Publication No. 73, University of Nebraska, Lincoln, NE, pp Tabler, R.D. and Schmidt, R.A., Snow erosion, transport and deposition in relation to agriculture. In: H. Steppuhn and W. Nicholaichuk (Editors), Proc. Symp., Snow Management for Agriculture. Great Plains Agricultural Council Publication No. 12, Water Studies Institute, Saskatoon, pp Tabler, R.D., Benson, C.S., Santana, B.W. and Ganguly, P., 199. Estimating snow transport from wind speed records: Estimates versus measurements at Prudhoe Bay, Alaska. In: Proc. 58th Western Snow Conf., pp Takeuchi, M., 198. Vertical profiles and horizontal increase of drift snow transport. J. Glaciol., 26(94):