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roughness features protruding above the snow surface, air density, snow particle size, and fetch distance. Consider- ing these sourcee of variability, it is hardly surprising that different empirical equations have been proposed to relate snow transport to wind speed (Table 1).

Clplrlcrl emprnr lm for .nl f l m af blaulm #mu n r f v r t l m of wlnd aped. u 1r wlrd rpcd

(Ma) at b l b t (I) lndlcr td k r h r l p t . t rmpor t rate. q. 18 In k l l ~ r n r af #mu p r metre Of (m).

1 r m a t l J . m Eaustlm no,

K a r w (1954) 0-2 q = 0 . 0 0 0 0 1 0 ~ ~ ~ ~ ' ~ - O.M)(Lb667 (I lb)

D. ~ d n p a h l et el. ( 1 W ) h l t r t l m q a O.OOOmul s (W)

Dlylln md Kat lykw (1980) 0-2 (Of)

Bymln md Kat lykw (1980) 0-2 q 9 0.000077C.ulO - 5jS (c)

M. tak.uckl (1980) 0-2 q o . ~ M ~ ~ Z W ~ ~ ' ~ ~ .settled dry r n d (11)

There is general consensus that transport rate in the first 2 metres above the ground is approximately proportional to the cube of the wind speed; however, to account for the effects of snow surface conditions on the mechanics of particle transport, and the mechanics of turbulent diffusion in relation to transport at greater heights, more complex relationships are needed.

Transport rate depends strongly on surface roughness and hardness. A hard snow surface exhibits greater threshold speeds, but transport rate for a given wind speed will be larger than for a fresh snow surface because less momentum is lost in friction between particles and the surface (Schmidt, 1986). Field measuremente of transport in the lowest 0.5 m verified the relationship

where q = total transport rate in the first 0.5 m above the surface (kg/m*s),

DRIFTING SNOW 101

p = air density (kg/m3),

g = gravitational acceleration (m/s2) , u,t = threshold shear velocity ,(m/s)

The g term is a saltation speed parameter, and tan_a ie a coefficient of friction between the moving particles and the surface. The ratio (a/tan a) declines exponentially with increasing intrinsic surface roughness; for example, (a/tan a) = 30 for zo = 0.04 mm, and (a/tan a) = 5 for zo = 0.3 mm. The latter ratio is appropriate for snowcover on land (as oppposed to ice) surfaces.

A process-based transport model and computer algorithm, termed the Prairie Blowing Snow Model (PBSI), allows parti- tioning of saltation and suspension transport (Pomeroy, 1988; Pomeroy, 1989; Pomeroy and Gray, 1990). According to this model, total mass flux of saltating snow, qsalt, is given by

vhere u,,, is the friction velocity associated with the fixed roughness elements protruding through the snow surface. As an engineering approximation, Pomeroy (1988) found measured transport rates (kg/m*s) at a fallow field site having unlimited fetch and uniform snow cover, to be represented by

applicable for wind speeds 2 6.5 m/s. An approximation for asuspension" transport in the first 5 m above the surface vas derived using regression analysis to relate this quanti- ty, as computed from the PBSM, to u . Transport rates, Q us (kg/m*s) , computed at 0.5 m/sl!ncnments of ulo over tie pange 6.5- to 25 m/s, were approximated by

Finally, regression analysis was used to derive an approximation for total transport in the first 5 m above the surface, q (kg/m-s), calculated as the sum of Equation (11) and aeuepensionn transport as computed from the PBSM over the same range and incrementation for u10 as described above:

Equation (13) is applicable for wind speeds 2 6.5 m/s, the threshold condition of Equation (11).

COLD REOlONS HYDROUXlYMYDRAULlCS

1) i t Equations (11-13) indicate suspended transport comprises about 75% of the total transport at 8 m/s, and more than 90%

I , for wind speeds greater than about 17 m/s. 'Although the I relatively small contribution of saltation to total trans-

port seems to run counter to the conclusions of other inves- tigators, the distinction between these two modes depends on the selection of a height limit for saltation, Equation (2) in this case.

one of the most significant properties of snow transport is its variation with height. Pomeroy'e (1989) process-based transport model permits calculation of the mass flux in the saltation layer. The result of a concentration gradient calculation based on turbulent diffusion theory, multiplied by the wind speed parameter, u,, provides the mass flux of suspended blowing snow. Figure 1 shows the vertical distribution of snow transport for several wind speeds. The maxima in mass flux occurring just above the saltation layer result from greater horizontal particle speeds in suspension, and are also predicted by the particle transport model of Anderson and Hallet (1986). Arbitrarily specifying the amount of transport within the first 10 metres as being the total provides the distributions shown in Table 2. For a 10-metre wind speed of 10 m/s, snow transported in the first metre above the surface constitutes about 772 of the total, whereas only about 402 of the transport is contained in the first metre with a 30 m/s wind. The tendency for the vertical distribution of mass flux to become more uniform with increasing wind speeds has important implications for drift control.

HEIGHT (m)

Pig. 1: Hass flux as a function of height and 10-m wind speed.

DRIFTING SNOW 103

Distribution of the mass flux of blowing snow as a function of height and wind speed, as derived from a numerical integration of Equation (14). Hass flux to height hs was limited to a maximum of 0.85 kg/m-s.

Percentage of blowing snow totaled to height Z Height above 10-m wind sveed fm/sl surface, Z 10 15 20 25 30 35

-m- ------------------ percent-----------------

Mellor and Fellers (1986) derived the following equation from regression analysis of Antarctic drift data:

where q is mass flux (g/m2-s) , X, = In z (m) , and XU = l/uI0 (ule in m/s). Although this expression overestimates transpor in the first few centimetres above the surface, integration provides results comparable with Equation (13) when mass flux in the saltation region (given by Equation (2)) is limited by constraints on mass concentration (equal to air density) and average particle speed (equal to 2.311,~). Assuming a u*t of 0.25 m/s, this limit would be about 0.85 kg/m-s. With this limitation, numerical integration of Equation (14) to 10 metres is approximated by the following expression for total mass flux as a. function of wind speed:

where q is in kg/m*s, and ulo is in m/s.

. - ' 104 COLD REUIONS HYDROUWYMYDRAULICS

s The op t i ca l proper t ies of blowing snow have been described by Takeuchi and Fukuzawa (1985) and Pomeroy and Male (1988): Schmidt (1977) developed an operational system f o r measuring v i sua l range; and Tabler (1979: 1983) and Berg (1986a) have discussed t h e in terpre ta t ion and use of v isual range data . An image processing-based monitor f o r v i s i b i l i t y is described by Ishimoto e t a l . (1989).

Visual range i n blowing snow is even more sens i t ive t o wind than is mass t ranspor t , being inversely proportional t o the f i f t h power of wind speed. For unlimited snow on t h e ground, t h i s re la t ionship is approximated by

v 1.1*108 u - ~ (16)

where V is v i s i b i l i t y i n metres, and u is wind speed i n m/e (Budd, Dingle, and Radok, 1966; Li l jequie t , 1957; Maki, 1971; Tabler, 1984). V i s i b i l i t y is therefore 680 m with 11 m / s winds, 145 m a t 15 m / s , and 11 m a t 25 m / s . The coeff i - c i e n t of propor t ional i ty i n t h e above equation increases with decreasing snow a v a i l a b i l i t y (Tabler, 1979).

A re la t ionship between visual range (a) and snowfall inten- s i t y ( R , mil l imetres water-equivalent per hour) a s measured i n Sapporo, Japan, is (Fujiyoshi e t a l . , 1983)

The conunon experience t h a t i ce cubes evaporate during sub- freezing storage, and consideration of the l a rge r a t i o of surface area t o mass presented by blowing snow, leads t o an i n t u i t i o n t h a t evaporation of blowing snow p a r t i c l e s is s ign i f i can t . The idea t h a t blowing snow p a r t i c l e s evaporate was perhaps f i r s t proposed by Dyunin (1956) and Komarov (1954). Dyunin (1959) s t a t ed t h a t t h e majority of snow p a r t i c l e s evaporated within 10-20 minutes under conditions of low humidity. Evaporation of wind-transported snow has been substantiated by process-based energy-balance models (Schmidt, 1972; Lee, 1975; Pomeroy, 1988), analys is of atmospheric conditions during d r i f t i n g (Schmidt, 1982b), hydrologic evidence (Tabler and Johnson, 1971), and mass balance s tud ies (Benson, 1982: Tabler, 1975). Schmidt (1972) concluded t h a t r e l a t i v e humidity was the dominant f ac to r a f fec t ing evaporation, and t h a t o ther s i g n i f i c a n t f ac to r s determining evaporation from individual p a r t i c l e s were p a r t i c l e s i z e , atmospheric pressure, s o l a r radia t ion, and a i r temperature, with the evaporation r a t e approximately doubling f o r every 10'C increase in temperature. Although evaporation cools t h e a i r and increases humidity, the turbu- l e n t d i f fus ion of heat and water vapor keeps t h e process

DRIITING SNOW 105

from being se l f - l imi t ing. The increase i n turbulent d i f fu- sion with wind speed implies t h a t evaporation m u s t a l s o increase with wind speed.

In the absence of evaporation, a i r temperature decreases with height above the surface during strong winds. In blowing snow, however, evaporation cools t h e a i r , and because the l a rges t concentration of blowing snow is near the ground, the a i r is s i g n i f i c a n t l y colder near t h e surface. With winds averaging 20 m / s , it is not unusual t o f ind temperatures 5'C colder a t 25 cm above the ground than a t 2 n. Hence, the presence of evaporation is read i ly confirmed with a thermometer.

Pomeroy (1988) developed a numerical procedure f o r computing evaporation of blowing snow using the models developed by Schmidt (1972) and Lee (1975), and based on derived atmospheric gradients of water vapor. The evaporation r a t e from a column of blowing snow modeled using Equation ( 1 3 ) , is a function of wind speed, temperature, and humidity a s shown in Figure 2 . Note t h a t evaporation a t 70% r e l a t i v e humidity and -30'C is s imi lar t o t h a t i n humid condit ions a t -15'C, and tha t r a t e s vary over orders of magnitude with weather conditions. Results can be expressed i n terms of the t rans- port r a t e

where qevap is evaporation r a t e (mg/m2.s) over a u n i t area of surface, and q is t o t a l snow t ranspor t i n g/(m.s). values of ~g and k f o r various atmospheric condit ions a r e given in Table 3.

-

~ " " " ~ ~ " " " " ' ~ " " ~ " " ' ~ " " " ' " " ' * ' " " ~ ' 10 15 20 2 5 3 0

WIND SPEED AT lorn HEIGHT (m/s)

I rig. 2: vapora at ion of blowing snow per u n i t of hor izonta l surface , a s a function of wind speed, f o r various temperatures (T) and r e l a t i v e humidities (RH).

I .

lb6 COLD RBalONS HYDROLOaYMYDRAULICS

Coefficients and constants f o r the evaporation equation

Tabler (1975) developed a conceptual model r e l a t i n g evapora- t ion t o t ranspor t distance and relocated precipi ta t ion (Figure 3 ) , assuming a typical d i s t r ibu t ion of p a r t i c l e sizes. The resu l t an t d i f f e r e n t i a l equation allows evapora- t ion t o be computed over increments of fetch having d i f fe r - ent snow re tent ion character is t ics . For a fe tch having uniform conditions,

where Qevap - evaporation l o s s (kg per metre of width across the wind)

Pr - relocated precipi ta t ion (metres water- equivalent)

F fe tch dis tance (m)

T maximum transpor t distance (A ) , usually taken a s 3000 m.

The "fetchn o r lqcontributina d i s t a n c ~ " is the length of the area serving a s a source of blowing snow t o a downwind location. The upwind end of the fe tch is any boundary across which there is no snow t ranspor t , such a s fo res t maraina, deep g u l l i e s o r stream channels, rows of t r e e s , and sho;elines of unfrozen bodies of water.

@I m transwort distancgW is the distance t h a t the average snow p a r t i c l e t r ave l s before completely evaporating. Although not d i r e c t l y neaeurable, t h i s conceptual variable provides the bas is fo r estimating the evaporation of blowing snow. The maximum transpor t d is tance var ies g rea t ly from one storm t o the next (depending on r e l a t i v e humidity, a i r temperature, and wind speed), but season-long averages are l e s s e r r a t i c . Studies i n Wyoming show the maximum transport distance averages about 3000 m. Although it is expected t h a t the seasonal average would vary with locat ion, other compensating factors make the 3000-m value generally applicable. For example, a s imi lar value seems t o apply i n a r c t i c Alaska where lower r e l a t i v e humidity may compensate f o r the colder temperatures.

rig.

DRIFTING SNOW 107

MAXIMUM TRANSPORT DISTANCE, T --I

Diagram of the t ranspor t distance concept used t o est imate seasonal evaporation l o s s from wind- transported snow. llDansvort i s tancen, T, is defined as t h e average-hich a snow p a r t i c l e (shown between the convergent dashed l i n e s ) must t r ave l before it completely evaporates. "contributinu distancen (o r nfetch'l), F, is defined a s the distance upwind t h a t contr ibutes blowing snow t o a s i t e , and may be equal t o o r l e s s than T.

precipitation r e f e r s t o the water-equivalent of the snow- fa l l , and relocated ~ r e c i ~ i t a ' is t h a t portion of precip- i tat ion t h a t is relocated by t y w i n d . Relocated precipi ta- tion excludes snow retained by vegetation and topographic features over the fetch, o r snow t h a t "se ts upn o r melts i n place. Studies i n Siber ia , a s well a s i n Wyoming, show t h a t aven on f l a t areas with low-growing vegetation, the percentage of snowfall relocated by the wind seldom exceeds 702 over the course of a winter (Komarov, 1954).

subtracting the evaporation loss from the t o t a l relocated precipitation provides an estimate f o r t o t a l seasonal transport, Qt (kg/m)

This equation, with an assumed value of T = 3000 m, has been ured t o design many successful snowdrift control projects , and provides an excellent first approximation f o r general rngineering use. Solution curves f o r t h i s equation a r e plotted i n Figure 4. James and Brendecke (1985) incorporat- ad Equation (20) in a streamflow simulation model f o r an alpine watershed i n Colorado.

COLD REOIONS HYDROIXXlYMYDRAULlCS

FETCH DISTANCE, F (kin)

I Fig. 4: snow t r a n s p o r t water-equivalent a s a f u n c t i o n o f f e t c h d i s t a n c e and r e l o c a t e d p r e c i p i t a t i o n , a s

I c a l c u l a t e d from Equation ( 2 0 ) , u s i n g T = 3000 m.

Bromion and D o D o s ~ ~ & ~ ~

I For a f u l l y developed l a y e r o f blowing snow t o a h e i g h t of 5 met res o r SO over a f l a t s u r f a c e , t h e s u r f a c e e r o s i o n r a t e

I ! I ' should e q u a l t h e evapora t ion r a t e , provided t h a t t h e t r a n s -

p o r t r a t e is i n ba lance w i t h momentum t r a n s f e r i n t o t h e d r i f t i n g l a y e r . whi le t r a n s p o r t ratem f l u c t u a t e and c o r r e - sponding e r o s i o n and d e p o s i t i o n p a t t e r n s develop, on a

I uniform e x t e n s i v e s u r f a c e t h e average d e p l e t i o n o f snow cover ba lances t h e t o t a l evapora t ion from t h e blowing snow p a r t i c l e s and from t h e snow s u r f a c e .

Experiments by Takeuchi (1980) show t h a t d i s t a n c e s o f 150- t o 300 m a r e r e q u i r e d f o r t r a n s p o r t r a t e s t o r e a c h e q u i l i b - rium, and Pomeroy (1988) h a s computed t h a t about 500 m is r e q u i r e d f o r a f u l l y developed blowing snow p r o f i l e i n t h e First 3 metres above t h e s u r f a c e . T h i s i m p l i e s a g e n e r a l tendency f o r e r o s i o n over t h i s d i s t a n c e downwind of any boundary d e l i m i t i n g a f e t c h o r c o n t r i b u t i n g d i s t a n c e f o r blowing snow.

DRIFTING SNOW 109

Deposi t ion o c c u r s i f t h e r a t e o f momentum t r a n s f e r t o t h e e a l t a t i o n l a y e r d e c r e a s e s t o a v a l u e less t h a n t h a t t o which t h e t r a n s p o r t r a t e h a s a d j u s t e d . Equat ions (9 ) and (10) sugges t s e v e r a l ways t h i s can occur , such a s a d e c r e a s e i n u,, an i n c r e a s e i n u,,, o r a change i n s u r f a c e hardness . I f a b a r r i e r o r change i n topography c a u s e s t h e wind speed t o decrease , some of t h e t r a n s p o r t e d snow w i l l be depos i ted . Where wind a c c e l e r a t e s , more p a r t i c l e s w i l l be p icked up, causing e r o s i o n . T h i s ba lance is a dynamic one, because t h e energy l e v e l o f t h e wind is c o n s t a n t l y f l u c t u a t i n g a s a r e s u l t o f n a t u r a l tu rbu lence . But i n terms of c o n d i t i o n s averaged over t i m e , d e p o s i t i o n o c c u r s where s u r f a c e s h e a r stress is d e c r e a s i n g i n a downstream d i r e c t i o n , and e r o s i o n occurs where s h e a r stress is i n c r e a s i n g . Radok (1968) argued t h a t a more u s e f u l view is t h a t e r o s i o n r e s u l t s from a d ivergence o f t h e suspended f l u x o f blowing snow, and d e p o s i t i o n r e s u l t s from a convergence o f t h e suspended f l u x .

Snow is d e p o s i t e d s o a s t o reduce t h e aerodynamic d r a g of t h e s u r f a c e . D r i f t s f i l l i n s u r f a c e d e p r e s s i o n s , s t r e a m l i n e o b j e c t s p r o t r u d i n g from t h e s u r f a c e , and f i l l i n s p a c e s between s u r f a c e roughness f e a t u r e s . Any s u r f a c e f e a t u r e t h a t c a u s e s d e p o s i t i o n appears t o have some maximum o r ~ ~ e a u i l i b r i u m ~ d e p o s i t , presumably r e p r e s e n t i n g a s u r f a c e over which s h e a r stress is uniform i n a downstream direc- t i o n . The shape of d r i f t s formed by b a r r i e r s , such a s snow fences , seems t o be r e l a t i v e l y i n s e n s i t i v e t o wind speed , one e x p l a n a t i o n f o r t h i s be ing t h e bonds t h a t deve lop between snow p a r t i c l e s . Observa t ions o f a l i q u i d - l i k e l a y e r on t h e s u r f a c e o f smal l ice s p h e r e s a t s u b f r e e z i n g tempera- t u r e s (Nakaya, 1954; Yamada and Oura, 1969) s u g g e s t snow p a r t i c l e s might f r e e z e t o g e t h e r upon c o n t a c t . Bonds between p a r t i c l e s grow and s t r e n g t h e n through s i n t e r i n g (Kuroiwa, 1962; Ebinuma, 1983) . The r a t e o f bond s t r e n g t h e n i n g is i n d i c a t e d by t h e i n c r e a s e i n work r e q u i r e d f o r d i saggrega- t i o n , which J e l l i n e k (1957) showed doubles w i t h i n 1 day and t r i p l e s w i t h i n 3 days. Because wind-t ransported snow becomes q u i t e r e s i s t a n t t o subsequent e r o s i o n w i t h i n o n l y a few hours o f being d e p o s i t e d , t h e e q u i l i b r i u m d r i f t shape t e n d s t o r e f l e c t t h e maximum a t t a i n a b l e p r o f i l e (presumably t h a t a s s o c i a t e d w i t h lower wind s p e e d s ) .

Theor ies f o r snow d e p o s i t i o n a s a f f e c t e d by b a r r i e r s and s u r f a c e roughness have been d e s c r i b e d by T a b l e r and Schmidt (1986) and Pomeroy (1988). Berg (1986b) used b a s i c aerodynamic p r i n c i p l e s t o p r e d i c t t h e l o c a t i o n and e x t e n t o f d r i f t accumulat ion downwind of topographic i r r e g u l a r i t i e s , and Schmidt and Randolph (1981) r e l a t e d d e p o s i t i o n p a t t e r n s t o p a r t i c l e t r a j e c t o r i e s .

110 COLD REGIONS HYDROLCXJYMYDRAULICS

Although ignored in most textbooks, wind-transported snow has profound effects on the hydrology of windswept areas. As wind redistributes snow over a watershed, eroding snow from exposed locations and depositing it in sheltered areas, the total mass of accumulation is reduced by the evaporation of the blowing snow particles, and this evaporation can constitute a significant or even dominant component of the hydrologic cycle. The resultant snowdrifts, on the other hand, have a greater density and smaller surface area/volume ratio than that represented by a uniform snowpack, reducing evaporation from the snow surface and melt rate.

Because blowing snow ignores watershed boundaries, the *8aerodynanric contributing area" for frozen water input to streams nay differ vastly from basin area, making tradition- al drainage divides irrelevant in windswept areas. Effec- tive precipitation is greater in waterstieds having snow deposition areas, as compared with watersheds lacking such features. On a local scale, the climate of ridge crests and windward-facing slopes is drier than that of leeward-facing slopes and other areas sheltered from the wind. Snowdrifts blocking stream channels cause flooding, and can increase peak flows and water-yield efficiency. By insulating the soil, drifts control soil freezing and the transfer of water vapor across the snow/soil interface. This section describes some of these more significant hydrologic effects.

Although evaporation from the surface of the snowpack is often a relatively small component of the overall water balance, evaporation from blowing e n w particlea ("in- transitn evaporation) can dominate the hydrologic cycle in windy environments. For example, at temperatures just below freezing, 70% relative humidity, and wind speed 20 m/s, the blowing snow evaporation rate is equivalent to a wa er 106s of 0.4 m 2 h to be compared with the 0.012 mm/mr oh maximum snow eurface evaporation rate measured by Nale and Granger (1979) during spring melt.

Annual blowing snow evaporation can be 'estimated from weather records by using Bquation (13) to estimate total snow transDort from hourly wind speed data, and Equation (18) to eetiahte evaporation; ow ever, representative values for averaae tem~erature and humidity are essential for this - ~-~

purpoie, as*deaonstrated by cal~ulations for the 1970-76 winters at Regina, Saskatchewan (Pomeroy et al., 1990). Using the PBSH model and actual hourly weatger data, mean annual transport was eat-imated to be 3.9 10 kg per metre of width across the wind,with evaporation loss averaging 48 u of water-equivalent over the fetch. Using Equation (18),

DRIFTING SNOW 1 1 1

evaporation would be estimated to be 86 mm assuming a mean temperature of -15'C and relative humidity of 702, and 28 mm If 902 relative humidity were assumed with the same temperature.

The effect of enow relocation and evaporation on water yields is demonstrated by a comparison of two adjacent watersheds, the Middle and South Forks of Crow Creek in ~outheast Wyoming (Tabler and Johnson, 1971). Although similar in area, topography, geology, and precipitation, these drainages differ markedly in snow retention. Annual water yield per unit area from the watershed (Middle Fork) having the most trees and rock formations to retain snow, averages about 508 more than that from the more exposed watershed.

vapor at ion rate varies greatly from storm to storm, but the net loss over a winter is much less variable, and Equation (19) provides reasonable approximations. For continental climates, evaporation loss increases with transport distance or "fetch," as shown in Figure 5, with about 572 of the 'relocated snow evaporating over a distance of 3 kin, and 85% over a fetch of 10 km. Measurements by Benson (1982) sug- gest the same magnitude of evaporation losses on Alaska's hrctic Slope. Rechard (1973) used a variation of Equation (19) to estimate that annual eva or tion losses from blowing snow in Wyoming are about 4.3.10' rn3 of water.

FETCH DISTANCE, F (km)

Tiq. 5 : Percentage of relocated snowfall that evaporates annually in Wyoming during transport by wind, as a function of the fetch distance (calculated from quat ti on 19, with T = 3000 m).

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COLD REOIONS HYDROLOOYMYDRAULICS

According to Marsh and Woo (1984), "Owing to a cold sub- strate, the etrong heat flux from the snow into the soil delays the warming of the snow cover and limits runoff after the snow is isothermal at O'C by the refreezing of soil infiltration and the development of a basal ice layer."

Hydrologic consequences of the basal ice under drifts depend on topography. On sloping terrain, the ice layer can greatly reduce infiltration into the underlying soil, concentrat- ing runoff from the perimeter of the drift. This feature is advantageous where snowdrifts are used to augment streamflow or local water supplies. Concentration of meltwater along the top of the ice layer can form tunnels under the drift, forming what Kattelman (1965) refers to as l*macropores.M Woo, Heron, and Marsh (1982) have described hydrologic effects of tunnels formed on top of or underneath basal ice in the High Arctic.

The apportionment of melt from shallow drifts is controlled by infiltration into frozen soils. As described by Gray, Granger, and Landine (1986), frozen mineral soils are grouped into three categories: restricted, limited, and unlimited infiltration potential. In the restricted case, infiltration is impeded by an ice layer at the soil-snow interface or within the soil. Infiltration of melt water is negligible and water either evaporates or becomes runoff. In the limited case, infiltration is controlled by the snowcover water-equivalent and the frozen water content of the top 30 an of soil. For medium- to fine-textured un- cracked soils, infiltration, INF, can be estimated from the snowcover water-equivalent, SWE, and the premelt moisture content of the soil, 8, by

INF = 5(1 - 8 ) s ~ ~ ~ ' ~ ~ ~ (23)

where INF and SWE are3in qillimetres and 8 is the degree of pore saturation in ~III /nun . All snowmelt infiltrates in the case of unlimited infiltration, which occurs in the case of dry, cracked clays, coarse dry sands, and other soils with large non-capillary pores.

The large-grained, porous snow layer (depth hoar) formed at the base of shallow snowpacks by "temperature gradient metamorphisma is conducive to the flow of water under a snow cover. Depth hoar is seldom found under deep drifts, however, because of an unfavorable temperature gradient. The absence of depth hoar, and the greater density of wind- drifted snow, result in a much lower permeability of drifts compared to undisturbed snow. Snowdrifts can therefore provide very effective dams, with spectacular hydrologic consequences. In areas of low topographic relief, a section

DRItTINO SNOW 115

of stream channel blocked by a snowdrift can cause water ponding over a large area upstream, and high peak flows can result when water eventually erodes a channel through the obstructing drift. This phenomenon is even more marked in the case of arctic streams, where impervious snowdrift dams are formed when melt water refreezes as it comes in contact with cores of cold, dense snow. Break-up in the watersheds of north-flowing streams proceeds from south to north as warmer interior temperatures precipitate runoff in the upper watershed. As meltwater progresses downstream, it is forced to overtop progressively larger snowdrift dams, causing an extremely peaked hydrograph in the lower reaches of the watershed (McDonald, 1985) . "oversnow flow" is the term Sturges (1975) applied to snowmelt water running across the surface of snow-filled drainages. Conditions favoring over-snow flow in subarctic latitudes include the following:

Wind-drifted snow obstructing the lower portion of a watershed

b Relatively low topographic relief

b A snow c w e r over the windswept portion of the watershed

b Frozen soil underlying the general snow cover

r Rapidly warming temperatures at the onset of melt

channel development in snow-filled valleys in the High Arctic has been described by Woo and Sauriol (1900).

Channels carved in the surface of wind-drifted snow provide efficient conveyance systems for runoff because water infiltration into the ground is essentially eliminated, and flow velocities are increased by the lower Manning's roughness coefficients for ice and water-smoothed snow surfacee as compared to that for the earth materials constituting the summer streambed (Woo and Sauriol, 1981). On sagebrush- covered watersheds at 2350-m elevation in south-central Wyoming, where well-developed oversnow runoff occurred in 2 of 7 years, maximum flow rates in years with oversnow flow were 3 to 5 times greater, and water yield efficiency was 4 times as large (Sturges, 1975).

The higher velocities of oversnow flow increase both sediment transport capacity and erosion potential. Although the snow protects the ground surface from scour, rapid erosion occurs wherever the oversnow flow cuts through to the ground, particularly where this occurs outside of the summer stream channel. Sturges (1975) reported suspended sediment concentrations of 860 parts per million in a year with

116 COLD REGIONS HYDROUXIYIHYDRAULICS

oversnow flow, compared with 20 parts per million in other years.

Valleye of ephemeral streams on Wyoming's plains typically exhibit an eroded bank on the downwind (east) side, because the location of oversnow flow channels is determined by the slope of snowdrifts that form in the valleys.

This section summarizes methods for controlling wind- transported snow. The following guidelines are u-eful for collecting wind-transported snow to augment water bvlpplies, as well as preventing drift6 causing hydraulic and hydrologic problems.

The management of surface roughness for snow retention is a practical method of snow control having great importance for agriculture and wildland management, but one that falls outside the scope of this presentation. Steppuhn (1981) in recommended as a source of information on this subject.

esleatina Bites for laailitiea and Roads

Many problems arising from wind-transported snow could be prevented or at least minimized by considering environmental factors in site selection. Baeic rules of siting are:

Identify potential effects of wind-transported snov on the operation of the facility or road.

Consider the entire facility (e.g., buildings, pipelines, roads) when evaluating snow problems at alternative locations.

r Study snow conditions at proposed locations for at least one winter before deciding on a final site. Snow deposition areas should be identified on aerial photographs taken during the winter. Drift featurar and wind orientation are discernible at scales up to 1:12,000 if black-and-white film is used; the poor contrast of color film limits its usefulness for snow studies. Photographs must be taken on sunny days at low sun angles.

r Avoid locations where anowdrifts form.

Select locations having the least snow transport; i-e., consider fetch distance, winter precipitation, and wind exposure. Features such as stream channels, buildings, and groves of trees, can have a significant effect on transport even though several

1

DRIFTING SNOW

kilometres from the site. Where possible, select sites in the DDsnow erosion" zone, 150- to 200 m downwind from a deposition area. I

b Where blowing snow is unavoidable, select sites where snow fences or other drift control measures can be installed upwind. Avoid locations downwind of frozen lakes, unless there is adequate space between the shoreline and the facility for adequate snow fence.

~lthough every facility has unique requirements that impose constraints on architecture and layout, there is usually rufficient flexibility to reduce snow problems significant- 1 . Ignoring blowing and drifting snow in the early plan- .Iw stages invariably proves to be a costly mistake. sound! awlneering practice requires that snow be considered in al: rtrges and aspects of design. After a site has been select. ad, the greatest potential for reducing drifting problems 11am in the orientation of the facility with respect to the pravalling winds, and the arrangement or layout of struc- ture. within the facility. The following rules and guide- Ilnam for facility design can minimize drifting problems:

r orienting a facility with the long axis aligned wit the prevailing wind direction generally reduces sno deposition, with a commensurate reduction in snow removal cost.

orienting a facility with the long axis aligned wit4 I the wind reduces the length of snow fence required i for protection. I

I

11 Access roads, pipelines, and similar aboveground 1 utilities should enter the facility on the downwind

\ aide, or at right angles to the prevailing wind. Entrances for roads and railroads are always a priority for drift prevention, and the structures comprising the facility can provide significant protection. If a road must enter on the windward side, it should approach from a cross-wind directio to allow snow fences to be placed upwind without having to leave an opening for the road.

Drifts formed by individual structures should be considered in the layout of buildings, roads, and aboveground pipelines. Primary roads within a plan should be aligned with the wind, and situated so as to avoid horseshoe drifts that form around structures. I

COLD REGIONS HYDR0UX)YMYDRAULICS

: As with on-grade sections, the road surface should be located above the equilibrium drift surface given by Equation (24), to keep the accumulation of plowed snow below the shoulder elevation. A simplified rule is that a straight line connecting the road shoulder and the top of the cut should have a slope of 8:l (12.5t) or flatter, and the backslope should be 5:l or steeper.

Cornices form at the top of steep backslopes on the windward side of the road. Because these overhanging drifts are formed by blowing snow, their density can exceed 350 kg/n3, and falling cornices present a significant safety hazard unless adequate space is provided between the road shoulder and the toe of the slope.

Ditches should be widened as much as possible to provide storage for wind-transported snow. Although it is generally not feasible to provide capacity for the total transport, properly designed cuts can store the modest volume of snow escaping a properly designed snow fence system, allowing control to approach 100% when both methods are employed.

Safety barriers induce deposition of blowing snow, prevent plowed snow from being cast away from the road surface, and generally interfere with snow removal operations. The most important rule of road design for snow control is to minimize the length of required safety barrier. This can be done by altering alignment, widening the road to provide th required recovery distance, providing safety shoulders, and removing obstacles. Even if a safety barrier cannot be eliminated, widening can allow it to be placed farther away from the travel lane. The drift formed by a solid barrier extends for a distance of about 12 times the barrier height on both sides of the barrier, and these dimensions apply to a guardrail after it becomes buried by plowed snow.

In drift-prone areas, box-beam or cable barriers are prefar- able to W-beam barriers (Tabler and Jairell, 1980). Sections requiring concrete wJerseyw barriers should be widened where possible, and snow fences installed upwind.

There are two basic types of snow fences -- d- and collectors. Deflector fences deflect the wind and blowing snow in such a way as to provide a sheltered area. Lateral deflectors, such as livestock shelters, force the snow around the area to be protected. w B 1 o ~ e ~ w fences, commonly used in Japan, deflect snow downward and accelerate the wlni so as to reduce deposition and improve visibility in the immediate vicinity of the fence. Blower-type fences are

DRIITING SNOW 121

rlao used to prevent the formation of cornices in avalanche atarting zones. An opposite approach is to deflect the snow

the area to be protected using solid fences or embank- wnts of snow or earth.

ctor fences reduce snow transport arriving at the protected area by inducing deposition upwind, and can be urod for water supply augmentation as well as drift control. Although collector fences have been used in the United States for at least a hundred years, and in Scandinavia mince at least 1852 (Brown, 1983). the true potential of fences has only become apparent within the last 17 years as r result of successful large-scale projects in Wyoming, Arlzona, Alaska, and Montana (Tabler and Furnish, 1982; Trbler, 1989). Snow fences have been accepted by Federal and State agencies as an environmentally sound method of oontrolling snow near oil and gas facilities in the Arctic, a d passive snow control is being implemented on Alaska's krth Slope as a way to reduce operating costs while pro- tecting the tundra from contamination by snow removed from pdm, roads, and along pipelines. This section summarizes Ule atate of the art for collector fences.

i; or Btorage Capaoity : thr most important requirement for a fence system is that it

&ve sufficient capacity to store snow transported over the 1 damlgn winter. Snow storage capacity is primarily deter- ' mined by the height, length/height ratio, porosity, bottom

p p , and topographic placement of a fence. It has long been

I wognized that fences having 50% open area ("porosity") ,, lorn the largest drifts (Mellor, 1965). Opening size and

rhrp are less important, but they influence the tendency % l o r a fence to become buried in the drift (Tabler, 1988a). -11 openings promote snow deposition near the fence, / nrulting in burial. On flat terrain, the storage capacity

: of the 50%-porous horizontal-slat "Wyoming" fence, described I later, is given by I I I Qc = 8500 H ~ . ~ (25) 1 t

1, *re Qc is snow storage capacity in kilograms per metre of ii towe length, and H is fence height in metres (Tabler, t, 1989). Although the cross-sectional area of a drift is

pportional to the square of fence h i ht (Tabler, 1980), capacity is proportional to Hg.' because the density

snow increases with depth according to Equation

;:I rrquired height of fence can therefore be determined by 1, W t i t u t i n g the estimated transport, as given by Equation

I ( 2O) , for Qc in Equation (25). and solving for H. Annual aov arriving at a site can also be estimated using hourly ruther observations, recorded in computer-retrievable form,

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COLD REGIONS HYDROLOOYMYDRAULICS DRIRING SNOW

~~~~t-~tion of enow fences i n t h e A r c t i c is r e s t r i c t e d to " Unqth of t h e equi l ib r ium d r i f t d e f i n e s t h e c1oae.t p e m i s - t h e win te r per iod from November through Apr i l , when heavy 1 r l b l s placement of a fence t o t h e p ro t ec t ed a r e a , assuming equipment can ope ra t e on snow roads b u i l t on t h e f rozen tha t t h e fence f i l l s to capac i t y . Closer spacing is possi- tund ra s u r f a c e with minimal environmental d i s tu rbance- b h i f t h e fence is s u f f i c i e n t l y t a l l t h a t it does n o t fill

ground a l s o f a c i l i t a t e s d r i l l i n g and s l u r r y i n g Opera- t o capaci ty , t a k i n g advantage of t h e l e e d r i f t being con- t i o n s , Direct c o s t s f o r cons t ruc t i on o f a 4.6-m fence in fined t o w i th in 20H of t h e fence up t o t h e t ime a fence is early 1988 were $138.62 pe r metre o f fence length. 1s t f u l l (F igure 6 ) . D r i f t shape is g r e a t l y a f f e c t e d by

t o P o g r a ~ h ~ t and few q u a n t i t a t i v e r e l a t i o n s h i p s a r e a v a i l a b l e (Tabler, 1974: Table r , 1988a) . For a g iven topographic

aoement. D e f i n i t i v e s t u d i e s o f t h e shape of equilibrium *@ttln91 equ i l i b r i um d r i f t dimensions a r e bel ieved t o be t h e :tifts f o r r e d by snow fences have improved guidelines everywhere, provided t h a t fence he igh t is ad ju s t ed f o r fence placement. The l a t e s t i n f o m a t i o n on d r i f t dimensions abackgroundM snow depth. The s h o r t e r "equi l ibr ium" d r i f t (Tablet-, 1988a; 1989) u se s a d d i t i o n a l yea r s Of data rev ise p rev ious e s t ima t e s (Table r , 1980)- To a ap- snow depth , H,, a s it proximation, lee d r i f t dimensions a r e s ca l ed w i t h fence fence. Takeuchi (1989) he igh t , at l e a s t over t h e range of h e i g h t s f o r which data p ropo r t i ona l to are a v a i l a b l e (Table r , 1980). For t h e o be p ropo r t i ona l t o W y o m i n g anow fence on l e v e l t e r r a i n and f o r a s i n g l e wind direct ion, t h e d r i f t on t h e leeward a i d e o f t h e fence ex- t ends t o about 35H, and t h e windward d r i f t extends abOu

o r i e n t e d perpendicular 1 5 ~ (Figure 11 ) . The windward d r i f t is roughly t r i angu l a r l o s s i n effect iveness in c r o s s sect ion, wi th a maximum depth of about H I 2 . 25'. For dev ia t ions of ~ ~ k ~ ~ c h i (1989) a rgues t h a t because t h e windward drift ie p a r a l l e l t o t h e wind, formed e n t i r e l y by depos i t i on of s a l t a t i n g particles, drift t i o n (Table r , 1980). dimensione a r e p r ima r i l y determined by snow surface and y of a t h i n fence weather condi t ions r a t h e r t han by fence heights l e l t o t h e wind) in -

ique , with a p ropor t ion- shape of t h e lee d r i f t is approximated by though it is pos s ib l e to

ucing t h e p o r o s i t y of y/n = 0.43 + 0.303(X/H) - O . O I I ~ ( X / ~ ) ~ + 0*002193(x/n)3 - t o t h e wind, no such

seems t o be requi red f o r t h e Wyoming fence be- - + 5.105*10-' (x/H) 5 1 (X/H)<34 ( e s i s t a n c e o f f e r ed by t h e t r u s s members, and hence r a t i o , i nc r ea se s a s t h e a t t a c k ang l e becomes

where y is snow depth a t d i s t a n c e X from t h e fence- *lthouqh t h e s e dimensions a r e s t r i c t l y app l i c ab l e only t o

'' t h e Wyoming fence , d r i f t s a r e s i m i l a r f o r o t h e r fence ge n t should al low f o r a 30' v a r i a t i o n on e i t h e r tries having 50% po ros i t y provided they a r e less than ha ' rid@ of t h e mean p r e v a i l i n g d i r e c t i o n (Tabler , 1988a), bur ied . d i s t a n c e fences should extend on e i t h e r s ide of

tb. area t o be p ro t ec t ed , a s we l l a s t h e amount of ove r l ap ~ l r e d f o r openings o r s taggered rows o f fencing.

I x

t h e snow is depos i ted a s o rage f a c i l i t y o r p o i n t of u se i z e conveyance l o s s e s ) .

2- Determine t h e requi red volume of water . , 11: Dimension. of equ i l ib r ium d r

"Wyoming" fences (H - fence 3 . Estimate snow t r a n s p o r t a t t h e fence l o c a t i o n . s e c t i o n a l a r ea ) .

COLD REOIONS HYDROLOOYlHYDRAULlCS 130 DRIFTING SNOW 131

provide t h e required water.

FENCE LENGTH/HEIGHT water produced by t h e p r o j e c t (Tabler , 1968).

The of d r i f t s a t t h e ends of fences ~ e s s snow accumulates near t h e ends of a fence where the reduces s to rage capaci ty a s shown i n t h i s d r i f t is rounded by t h e a i r flow around t h e fence, and p l o t of Equation (27). allowance must be made f o r t h i s reduced s to rage - The folo lowing expression can be used t o c o r r e c t s to rage f o r fen-, length (Tabler and Schmidt, 1 9 8 6 ) ~ a s p l o t t e d i n Figure 121

E 3: 0.288 + 0.039(L/H) - 0 . 0 0 0 9 ( ~ / ~ ) ~ +

+ ~ . ~ - I O - ~ ( L / H ) ~ , 5 1 L/H 5 50

where E is t h e r e l a t i v e capaci ty f o r a fence of length G expressed a s a f r a c t i o n of what a very long fence epects Of water supply augmentation w i t h fences, hold. The required length of t h e fence is given by ents* and surface roughness modifications are dls- In by J a i r e l l and Tabler [1985), Sturgea and

L Qr/(QCaE) (lgel), and Tabler and Schmidt (1986).

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134 COLD REGIONS HYDROLDOYMYDRAULICS DRIFTING SNOW 135

efficiency of the rain fence. The fences were built ? Ik Snow accumulation and streamflow were monitored for 4 during the 1983 summer after a calibration period sufficient to detect a 151 change in streamflow.

increasing water-equivalent snow accumulation by 551, and duration of Elow was extended 17 days. All increases exceeded the 992 confidence limits for pre- treatment relationships between North Draw and the control watershed. The fact that the average increase in streamflow was greater than the percentage increase in snow water-equivalent volume suggests a higher when designing snow fence treatments to increase run- efficiency of water yield from the additional snow

suggesting evaporation losses comparable to those reported for snowdrifts by Rechard (1975).

R.8. and 8 . Aallet, "Sediment Transport by Wind: General Model, , 1986, pp. 523-535.

ld , R.A., The Physics of Blown Sand a d Desert Dunes, on r co. L C

~ o l a Mountain Watarsbad

The dramatic streamflow effects of the North Draw snou

,, m r r , O . B . , and Jo~apht D.D., "Boundary Conditions at a fractured rock result in very little surface runoff fktorrlly Permeable Wall," Journal of Fluid Mechanics, Vol. from snowmelt. After two small watersheds had been calibrated for 7 years, a 3.8-m-tall snoy fyce, 396a long, was built on one watershed (4 5 0 m area) in 1970. The second watermed, 3.6-10' in area, re- mained untreated as a control. Design of the snow fence treatment (Tabler, 1971) was based on the same reasoning used for the North Draw fence. This fence I, C . B . , "The Seasonal Snow Cover of Arctic A l a ~ k a , ~ also was planned to augment snow deposition in the titute of North America. Research Paper No, 51, stream channel immediately above the streamgauge, and was located about 20 m upwind from the channel center- line to minimize snowmelt conveyance losses.

V) m

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b 140 COLD REGIONS HYDROUXIY/HYDRAULICS

MoDonald, G.N., Runofi. Section 2.0 in: Prudhoe Bay Unit, Lisburne Development Drainage and Erosion Control Design and criteria Manual, 1985, ARC0 Alaska, Inc.

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- 1986, 16 pp.

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DRIFTING SNOW 14 1

Radok, U., "De~osition and Erosion of Snow bv the Wind."

Radok, u., "snow Drift," Journal of Glaciolou~, vol. 19, NO. 81, 1977, pp. 123-139.

~audkivi, A.J., Loose Boundarv Hvmulics, 2nd ~dition, Pergamon Press, Oxford, England, 1976, 397 pp.

Reahard, P.A., vOpportunities for Watershed Management in ~yorning,~~ Proceedinas of the Irriaation and Drainage Divi- sion s~ecialtv confern~lce on Asricultural and Urban Consid- erations in Irrigation and Drainaae, ~ u g . 1973, pp. 423- 448.

Rechard, P.A., "A Study of Evaporation from a Snowdrift," Proceedinas. Snow Management on the Great Plains Svm~osium, Great Plains Asricultural council Publication No. 73, 1975, pp. 65-84.

Ruff, J.F., and Qelhar, L.W., @*Turbulent Shear Flow in Porous Boundary," Journal of the Enaineerins Mechanics ~ivision. ASCE, vol. EM 4, 1972, pp. 975-991.

Baulmon, R.W., @@Snowdrift Management Can Increase Water- Harvesting yields, Journal of Soil W d Water Conservati~n, Val. 28, NO. 3, 1973, pp. 118-122.

Bchmidt, R.A., "Sublimation of wind-transported snow -- a model," Q.S. Forest Service. Rockv Mountain Forest an4 Rancfe Ex~eriment Station. Research Paper RM-90, 1972, 24 pp.

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lu%sauJ es,

Trans~ortation Research Board. S~ecial Re~ort 185, May, 1978, pp. 200-207.

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Bahmidt, R.A., "Vertical Profiles of Wind Speed, Snow Con- centration, and Humidity in Blowing Snow,@@ Bound- Meteorolosy, Vol. 23, 1982b, pp. 223-246.

L

142 COLD REGIONS HYDROUXIYWDRAUWCS

Salmidt, R.A., "Transport Rate of Drifting Snow and the Mean Wind Speed Profile," -, V O ~ . 34, 1986, pp. 213-241.

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w e e m snow conference, Vole 49, 1981, PP. 34-42.

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D.H. Male, eds., 1981, Pergamon Press, Toronto, pp. 60-126.

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DRlFnNG SNOW 143

Tablor, R.D., "visibility in Blowing Snow,and Applications in Traffic Operations," m o w Removal Ice Control Re - ~earch. ~vm~osium, S D ~ C ~ U & D O ~ ~ May 1978, ~ational 185. Proceedinas. Academy of S c i e n c a - ~ n t

ton, D.C., pp. 208-214.

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Val. 50, 1982, pp. 139-148.

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~ablor, R.D., "Slide Rule for Snow Fence Design,ll proceedinas. Western Snow Conference, Vol. 55, 1987, pp. 162-165.

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to Snow m a , JUl. 1988. U.S. w e a r c h and E n g w g Laboratory Spe- cial Report 89-6, 1989, pp. 297-306.

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. I Q

o 144 COLD REOlONS HYDROUMYRlYDRAULlCS

Taler, R.D., Benmon, C.B., Santana, B.W., and Qanguly, P., "Estimating Snow Transport from Wind Speed Records: Esti- - mates Versus Measurements at Prudhoe Bay, Alaska," proceedinas, 58th Western Snow Conference, Vol. 58, Apr. 1990, (in press).

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