SNOW ACCUMULATION AND DISTRIBUTION

Don M. Gray and Others

Paper presented to the Workshop/Meeting on "Modeling Snow Cover Runoff" U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, U.S.A., 26-29 September, 1978.

SNOW ACCUMULATION AND DISTRIBUTION

Don M. Gray and other& I

I INTRODUCTION

Snowcover comprises the net accumu- lation of snow on the ground as it repre- sents precipitation which has been depo- sited as snowfall, ice pellets, hoarfrost, glace ice and, in addition includes water from liquid precisitation (rainfall) much of which subsequently has frozen and con- taminants stored in the cover. Its str.uc- ture and dimensions are complex and highly variable with respect to space and time. This variability is a function of many factors: the variability of the "parent" weather, in particular, atmospheric wind, temperature and moisture conditions at the time of precipitation and immediately following deposition; the nature and frequency of the parent storms; the weather conditions between storms during which radiative exchanges may alter the structure, the density and the optical properties and wind action may lead to scour and redeposition as well as modifi- cation in snow density and crystalline structure; the process of metamorphism and ablation which can alter the physical characteristics of the snowcover to the extent that it bears little resemblance to the freshly-fallen snow; and topo- graphical, vegetal and physiographical

factors. Being the end product of both accumulation and ablation snowcover em- braces the complexity of the many factors affecting accumulation and loss.

Prior to embarking on a discussion of snowcover accumulation and distribu- tion it is important to emphasize that the areal variabilty of snowcover must be considered on three geometric scales. (1) Macroscale or Regional variability, which may include areas from 1 to 1 x 1 0 ~ k m ~ with characteristic linear distances of lo4 to lo5m depending on latitude, elevation, orography, etc. in which the dynamical meteorological effects such as the formation of standing waves, the directional flow of wind streams around a barrier and lake effects are important factors. (2) Mesoscale or Local (within region) variability which may involve character- istic linear distances of lo2 to 10% in which redistribution may occur by wind or avalanches along meso relief features and where deposition and accunu- lation may be related to the terrain variables of elevation, slope and aspect and to vegetal cover variables such as canopy and crop density, tree species or crop type, height of cover and complete- ness of the vegetal cover.

1 - - Don M. Gray is Professor of Agricultural Engineering and Chairman of the Division of Hydrology, University of Saskatchewan, Saskatoon, Canada. Parts of this manuscript are bascd extensively on contributions received from diffcrcnt scientists for a Book on Snow, (thc exact title undecided) of which the senior author is the Editor. Although these contributions are duly rcfercnccd within thc manuscript it is imperative in any rcpro- duction or rcfercnce to thc material that proper acknowledgement be given these persons.

(3) Microscale variability in which major differences occur over distances of 10 to 102m where the accumulation patterns are the result of numerous interactions, primarily the effect of surface roughness conditions as they effect the transport phenomenon.

Inasmuch as snowcover is the residual product of snowfall it is axiomatic that the discussion of its accumulation begin with a brief resume of snowfall formation.

11 SNOWFALL (Schemenaur, Maxwell and Berry).

11.1 General Principles of Precipitation Format ion

The physics of snowfall is simply a special case of precipitation forma- tion in that the meteorological condi- tions producing snowfall are the same as those which generate other forms of precipitation. In general, the occur- rence of precipitation is determined by the availability of moisture in the atmosphere and the presence of mechan- isms capable of converting this mois- ture into precipitation. Thus, although the formation of snow in the atmosphere depends on many variables, the most important are the presence of super- cooled water and an ambient temperature less than 0 OC.

In the northern hemisphere, during winter the oceans particularly those portions of the Pacific and the Atlantic north of latitude 40" N and the Gulf of Mexico, are the main sources of atmos- pheric moisture at middle and high latitiudes. The continental air masses that move over the oceans generally . have a much lower temperature and vapor pressure than the underlying water surface. As a result large upward fluxes of heat and moisture to the lower layers of the a'aosphere occur. The extent to which this moisture is transferred to higher levels depends both on the nature of the surface energy exchange processes and on the large scale vertical motion of the atmosphere which is influenced by the configuration of the upper atmospheric flow. Although on a hemispheric scale oceans serve as the principal sources of moisture supply other bodies of water can be important particularly in the early parts of winter before they freeze. For example in North America Hudson's Bay and the Great Lakes.

The amount of water vapor present in the atmosphere in a particular region

Figure 1. Distribution of mean precipitable water (mm) over ~anada in January (after Hay, 1970).

is influenced by both the temperature of the air, which determines the upper limit . of its vapor capacity and the accessabil- ity of source areas of moisture. When considering the broad-scale distribution of atmospheric moisture it is common to use the concept of precipitable water, the depth to which water would stand if all water vapor were condensed from a ver- tical column of uniform cross-section of the earth's atmosphere. Hay (1970) has prepared maps of the mean precipitable water for different months for Canada, the distribution for January is given in Figure 1. The largest values for the month (8 to 12 nun) which occur along the British Columbia coast can be attributed to warm moist air originating from the Pacific. A second maximum of 4 to 7 mm which occurs over the Atlantic Provinces reflects the effects of the Atlantic and, to a lesser extent, the Gulf of Mexico on the atmospheric moisture supply. Through- out much of the remainder of Canada the values fall in the range from 2 to 4 mm and decrease with increasing latitude. This decrease can be attributed to the low temperatures experienced by those regions in January and to the fact they are distant to major moisture sources.

Precipitation normally occurs when the vertical motion in the atmosphere causes cooling of elements of an air mass by adiabatic expansion (an expan- sion process is termed adiabatic when there is no heat exchange with the surrounding mass). Four types of verti- cal motion associated with the formation of signifi'cant amounts of precipitation are :

(1) Horizontal convergence: wind fields are oriented to direct the flow into a particular area thereby causing lift.

(2) Orographic lift: when the movement of air is directed

against a ridge, group of hills or mountains and air is forced to rise. .

(3) Convective lift: lift produced by differential heating or ad- vection which causes a portion of the atmosphere to become more buoyant than its environment.

(4) Frontal lift: lift produced by the interaction of separate large masses of air having sig-

. nificantly different physical characteristics (density and motion).

Of these four lifting mechanisms the last three are most important to snowfall formation. In North America the effects on snowfall accumulation origina- ting from orographic effects are well recognized in the mountainous regions ad- jacent to the Pacific Ocean. Likewise, major accumulations of snowfall resulting from convective activity are common in areas south and east of Lake Huron and Lake Ontario. Frontal storms tend to give widespread snowfall to large areas of the interior parts of Canada and the United States. In the absence of insta- bility, the precipitation patterns origi- nating from frontal activity show steady precipitation within 250 km ahead of a warm front and within 40 to 80 km of the cold front. However, conditions may vary markedly in any given storm depend- ing on the moisture supply and the vigor of the frontal wave. Strong convective activity indicative of instability comp-

licates the pattern and leads to the occurrence of pockets of heavy prccipita- tion. Figure 2 illustrates the ty1,ical cloud structure through warm and cold fronts. Correspondingly, it is possible to characterize the snowfall associated with the different cloud types (see Table 1).

11.1 Physics of Formation

The preceding section provides a very brief resume of the macroscopic factors affecting the formation of precipitation. It is important however to consider in greater detail the physics of snowfall as the formation process governs not only the depth or amount of snowfall but also the physical proper- ties of the snow crystals such as their shape, mass, density, crystal habit, etc. The snow crystal that arrives at the ground may be a simple product of ice crystal formation or it may be the result of a complex life history during which its original 'physical character is greatly modified and changed.

The formation of snow in the atmos- phere depends on many atmospheric vari- ables, the most important being that the ambient temperature is less than 0 OC and that supercooled water is present. The schematic diagram shown as Figure 3 outlines the mechanisms by which differ- ent types of snow develop.

At a temperature of -5 "C ice-forming nuclei present in the atmosphere form

LEGEND: - FRONTAL SURFACE - AIR FLOW

PRECIP ITATION

Figurc 2. Typical cloud structure associatcd with warm and cold fronts. (cloud abbreviations givcn in Table 1.)

Tab le 1. Snowfa l l a s s o c i a t e d w i t h v a r i o u s c loud t y p e s

Cloud Type Assoc i a t ed Snowfal l

T y p i c a l C i r r u s and warm de r iv$ ives ( C i ) f r o n t a l c loud Al tocumulus (Ac) P r e c i p i t a t i o n is u s u a l l y v i r g a

Altocumulus a l t h o u g h l i g h t snow showers a r e C a s t e l l a n u s (Acc) p o s s i b l e from t h e Acc

A l t o s t r a t u s ( A s ) L i g h t con t inuous o r i n t e r m i t t e n t snow may f a l l from A s ; however, when t h e snow i s heavy, t h e A s h a s p r o b a b l y g radua ted t o a n i m b o s t r a t u s - t y p e c loud .

N imbos t r a tu s . ( N s ) Cont inuous snow may f a l l . V i rga o c c u r s from bo th N s and A s .

S t r a tocumulus (Sc) I n t e r m i t t e n t l i g h t powdery snow ( f i n e f l a k e s ) p o s s i b l e .

S t r a t u s ( S t ) Cont inuous l i g h t powdery snow is p o s s i b l e . (Th i s i s t h e f r o z e n p r e c i p i t a t i o n ana log of warm p r e c i p i t a t i o n d r i z z l e . )

T y p i c a l Cumulus (Cu) L i g h t snow showers p o s s i b l e c o l d Towering a l t h o u g h t h e s e a r e more l i k e l y f r o n t a l Cumulus (Tcu) t o o c c u r from t h e Tcu. c loud

Cumulonimbus (Cb) Moderate t o heavy snow showers are p o s s i b l e .

t i n y i c e c r y s t a l s t h rough t h e p r o c e s s of i c e n u c l e a t i o n . The n u c l e a t i o n of t h e i c e phase on t h e s e p a r t i c l e s o r n u c l e i is c a l l e d he t e rogeneous n u c l e a t i o n which i s t h e pr imary p r o c e s s l e a d i n g t o t h e form- a t i o n of i c e c r y s t a l s . Three b a s i c t y p e s of he t e rogeneous n u c l e a t i o n may o c c u r : ( a ) i f a n i c e n n c l e u s i s p r e s e n t i n a c loud d r o p l e t which i s coo led be low 0 "C t h e

' d r o p l e t w i l l f r e e z e a t a t e m p e r a t u r e de termined by t h e n a t u r e of t h e n u c l e u s , i n which c a s e t h e i c e n u c l e u s h a s a c t e d a s a n "immersion f r e e z i n g " nuc l eus ; ( b ) i f an i c e n u c l e u s t o u c h e s t h e o u t e r

s u r f a c e o f a d r o p l e t and c a u s e s it t o f r e e z e , it h a s s e rved a s a " c o n t a c t n u c l e u s " ; and ( c ) i f wa te r vapor i s de- p o s i t e d d i r e c t l y on a p a r t i c l e and e v e n t u a l l y forms an i c e l a y e r on t h e s u r f a c e t h e p a r t i c l e h a s a c t e d a s a "de- p o s i t i o n nucleus" . The n u c l e a t i o n p ro - c e s s e s are ex t r eme ly complex.

An i c e c r y s t a l i n a c l o u d of w a t e r d r o p l e t s grows a t t h e expense o f t h e d r o p l e t s because t h e vapor p r e s s u r e a t t h e i c e s u r f a c e is l e s s t h a n t h a t above t h e wa te r s u r f a c e . A t t e m p e r a t u r e s con- d u c i v e t o t h e fo rma t ion o f snow a c loud

wa te r vapor + i c e n u c l e i + c loud d r o p l e t s a t T < 0 OC I

( n u c l e a t i o n ) I

I ( s u b l i m a t i o n )

I I SNOW CRYSTALS I

( r iming ) I

( s u b l i m a t i o n ) I

( a g g r e g a t i o n )

A\ I

SNOW CRYSTALS I R I b E D SNOW FLAKES

CRYSTALS GRAUPEL

F igu re 3. Schemat ic f low diagram of t h e fo rma t ion o f d i f f e r e n t t y p e s o f snow.

may exhibit only slight supersaturation with respect to water and supersatura- tions of 10 to 20% with respect to ice. The net result is a transfer of water vapor from the droplets to the surface of the ice crystal. The preferential growth of the ice crystals is the basis of the Bergeron mechanism (Bcrgeron, 1935) of prccipitation formation, a theory which describes the development of much of the precipitation in the temperate latitudes. When the crystals attain sufficient mass they fall and during this movement grow primarily by a riming process. If during its fall the ice crystal passes through a layer of the atmosphere in which the temper- ature is greater than O°C it may melt completely and fall as rain. The basic habit (shape) of an ice crystal is determined by the temperature at which it grows whereas the rate of growth and secondary crystal features are deter- mined by the degree of supersaturation. Further different relative growth rates of the crystal faces leads to extremes to plate-like or prism-like crystals.

The rate of change in mass of a crystal by diffusion is directly related to the difference in vapor density of the atmosphere and the air at the snr- face of the crystal. When a crystal reaches a size of a few hundred of pm its mass growth by diffusion becomes relatively less important to accretion or the capture of droplets through collisions. The riming process is im- portant in that riming affects the fall velocity and motion of the crystals, it is through the riming process that graupel and most hailstones originate. Recent experimental evidence has indicated that during freezing of a cloud droplet onto a snow crystal secondary ice par- ticles are ejected leading to a "multi- plication" of ice particles in a cloud. The onset of riming occurs at different sizes for crystals of different shape.

A snowflake is formed by the aggre- gation or the collision of snow crystals followed by their adhesion. Adhesion can result by the interlocking of parts of the crystals, riming, vapor deposi- tion and sintering. The maximum sizes of snowflakes generally occur at temper- atures near ODC. Hobbs (1974) shows that in a typical cloud a 1 mm diameter snowflake can grow to 10 mm in about 20 minutes.

he process governing the formation of a snowflake in the atmosplrere as well as affecting the crystal habit also governs thc sizes, masses, the densities,

the terminal velocities and the concen- trations of snow c~ystals. Individual snow crystals observed at the earth's surface range in dimension from -50 pm to -5 nun. Unfortunately, the dcnsity of snow crystals of a given type is diffi- cult to specify because of the problems in determining a representative volume. The particle densities for heavily rimed crystals and for graupel, whose volumes can be measured with reasonable accuracy have been found to range from approxi- mately 100 kg/m3 to 700 kg/rn3.

Snowflakes can consist of from two to several hundred snow crystals joined together. They may range in size (maxi- mum diameter) from 0.10 mm to several cm. The largest snowflakes occur at temperatures near 0°C with decreasing sizes as' the temperature decreases, (Hobbs, 1973). Magnano and Nakamura (1965) showed that the density of a snowflake decreased with size according to the relationship:

where p is the particle density in mg/m3 and d is in nun.

A knowledge of snow formation in the atmosphere is essential to winter weather modification activities including the artificial redistribution of snowfall and the initiation and increase of snowfall from a given cloud system.

11.2 Areal Distribution

Fulkes (1935) derived the following approximate relationship for the precipi- tation rate of an ascending layer of saturated air of unit cross section:

where: i = precipitation rate, b = a coefficient whose magnitude

depends on the temperature and pressure of the layer,

w = the vertical velocity, and Az = the thickness of the layer.

The variation in tile coefficient b with temperature and pressure height is shown in Figure 4 . As shown in the figure under conditions when most snow forms (temperatures below O°C and heights below 6 k m ) , the rate of precipitation decreases rapidly with decreasing temperature; at temperatures of -lO°C and lower the rate is rclativcly uninfluenced by height. The vertical velocity is determined primarily by thc characteristics of individual weather systems and the extent to which

TEMPERATURE (.C)

Figure 4. Rates of precipitation from adiabatically ascending air for a 100-m layer with a vertical velocity of 1 m/s (after Fulkes, 1935).

terrain factors affect the airflow. The duration of snowfall depends on a number of factors including the speed and track of the system and the size and shape of .the associated snowfall area.

In the case of convective stoms the intensity of snow formation depends on the availability of moisture and the degree of instability of the air. Con- vection which produces snow often occurs with the movement of cold air over warm bodies, for example lake effects..The amount by which the moisture and stab- ility of the air is modified depends on factors such as the initial temperature and moisture characteristics of the air, the temperature of the water and the length of overwater trajectory. Instab- ility can also be produced by large- scale motion associated with frontal systems.

11.2.1 Effects of Ploisture and Precipi- tation Mechanisms on Snowfall Distribution

The distribution of the mean annual snowfall amounts over Canad& and the United States is illustrated in Figure 5. In the figure two areas of relatively heavy snowfall can be identified. Cer- tain parts of western British Columbia thc Yukon and Alaska adjacent to the mount air^ ranges which parallel the Pacific Coast, reccivc seasonal values exceeding 400 cm. These areas are di- rectly cxposc>d to moisture-laden distur- banccs moving castward from t11c Pacific source region. The verrical motion

associated with low-pressure systems is enhanced by the coastal terrain and the snowfall can be very heavy, in some loca- tions exceeding 1000 cm annually. For example, along the southern coast of British Columbia near sea level, the air temperatures are normally above freezing so that a majority of winter precipitation occurs as rain, and the seasonal average snowfall is less than 60 cm. Snowfalls are also relatively light in areas to the lee of the mountains where eastward moving air has a downward component.

Widespread heavy snowfall also occurs in Eastern Canada throughout an area en- compassing central Ontario, southern Quebec, much of the Atlantic provinces, Labrador, and the east coast of Baffin Island where the seasonal falls range from 250 cm to in excess of 400 cm (see Figure 5). Moisture is available to these areas in varying amounts from the Pacific, the Atlanzic and the Gulf of Mexico. In addition, to the west, the Great Lakes serve as an important source of moisture for local precipitation. For example, average seasonal snowfalls in excess of 250 cm occur to the southeast of Lake Huron. The snowfall amounts decrease rapidly in the southward direction from :. the eastern Ontario-northern New England area to th2 southeastern United States. For the most part, this is a result of increasing temperatures, as opposed to decreasing precipitation.

Over the prairie provinces and the northern plains the seasonal snowfall is, considerably lower than in the eastern or western regions of the country, averaging between 70 to 140 cm in most areas (see Figure 5). The small amounts of snowfall over this region can be attributed, in part, to the infrequent occurrence of vigorous weather systems. Likewise, the relatively flat terrain does not induce snowfall formation as the Pacific air moving inland tends to subside as a result of the downward slope in topography from the Rocky Mountains to Elanitoba-Minnesota.

The western half of the Arctic Islands receives less snow (<80 cm) than most other parts of Canada. Although win- ter is long in this area, it is remote from major moisture sources, and the extremely low temperatures which prevail over the region reduce the moisture hold- ing capacity of the air to low values.

Figure 5. Mean annual measured snowfall (a), 1941-1970.

I1 I FACTORS AFFECTING SNOWCOVER ACCUMU- LATION AND DISTRIBUTION

111.1 Wind (Kind)

The characteristics of the wind near the earth's surface are of major importance in determining the amount of snow movcmcnt and in determining the scour and depositional patterns. In addi- tion, when snow crystals are moved by wind, their physical shape and properties may be changed markedly.

At hcights grcatcr than about 1 km above thc earth's surface thc motion of the atmosphere is govcrncd by the prcssurc distribution of large-scale weather systcms and the wind charactcr- istics are independent of terrain condi- tions at the surface. Throughout the

boundary layer the wind speed increases from zero at the earth's surface to t,he geostrophic wind speed at its outer limit. The thickness and distribution of the velocity profile depend on the nature of the earth's surface. Numerous studies have been conducted on the in- fluence of different surface conditions, particularly vegetative cover, on the wind velocity distribution with height (see Figure 6 ) . For detailed information on these effects the reader is referred to the works of Geiger (1966) and Reifsnyder (1955). Over relatively rough terrain the boundary layer is thicker and the wind speed increases relatively slowly with height; over flat, open terrain the opposite is truc. The boundary layer thickness and vclocity profile arc also influenced by thc

E - 30 = 20 V W

W l N D SPEED ( m / r e c )

W l N D SPEED ( m / s c c l

Figure 6. Vertical wind profiles in different forest stands (after Reifsnyder, 1955).

thermal stratification of the atmosphere, for example, if unstable stratification prevails (temper~ture increasing with height above the surface) the boundary layer tends to be thicker than under the stable condition.

The presence of velocity gradients within the boundary layer implies the existence of shear stresses in the wind flow. The shear stress is a maximum at the earth's surface and decreases with height becoming zero in the geostrophic wind above the boundary layer. It is the shear stress exerted by the wind on the surface which causes the movement of loose snow. Virtually all natural sur- faces act as rough surfaces with respect to wind. Under these conditions, and when the wind speed is high enough to induce drifting or movement of snow the flow near the surface is dominated by the shear forces and the effects of thermal stratification are negligible. Under such conditions field observations have shown the following relationship applies:

where: U = the mean wind speed at a height, z,

U* = the "friction" or "shear" velocity, equal to ~m in

0 which T is the shear stress

0 at the surface and p is the dcnsity of air,

k = a roughness parameter; and C(A) = a constant whose magnitude

depends on the non-dimensional spacing of the roughness ele- ments, A.

The maximum height to which the logar- ithmic velocity profile equation (equa- tion 3) applies is limited by the up- stream fetch over which the surface roughness is reasonably uniform. That is, Tani and Meketa (1971) suggest that the equation is valid for z?fetch/20 or z = 50 m, whichever is least. The lower limit of applicability of the equation is for z 7 2k. That is the equation will not describe the profile near or below the tops of roughness elements where the flow pattern is very complex and often three dimensional, for example, where bushes, trees, buildings and other obstacles affect the wind pattern.

The limitless variety and combin- ations of surface features that can be encountered in nature make it impossible to define and to discuss all the inter- actions between aiz flow patterns and snowdrift patterns. T'ne snow accumula- tion patterns are a complex function of deceleration and acceleration of the air stream, its velocity profile and the formation of separation bubbles and vortices (Richter, 1945).

111.1.1 Transport of Snow by Wind

Individual particles of snow lying on the surface are initially caused to move by the drag force exerted on them by the moving air. The drag force per unit area is the shear stress, T

0' existing between the moving air and the snowcover, which, in turn, is a function of such factors as surface rouahness, the mass density of air and the wind velocity. Before movement can occur it is necessary that the shear stress attain some critical value to overcome the particle weight and inter-particle cohesive forces; at snow temperatures less than about -2OC the cohesive forces in newly-fallen snow may be considered negligible. Normally, in snow drifting studies, it is customary to utilize the shear velocity, u * E ~ , instead of the shear stress. Tile threshold shear velo- city (U* ) required to disturb the sur- face anhhtransport particles is highly variable depending on the size, shape and wcight of the snow crystals and the cohesive forccs, thc lattcr bcing dcpen- dent on the wctncss of the snow. These aspccts stress the iinporta~~cc of the

formation process with respect to snow drifting. Numcrous studies (Richter, 1945; Kotlyakov, 1961; Oura et al, 1967; and Isyumov, 1971) have bec-n directed to evaluating U* for Jiffcrent snow condi-

th tions. The values of U* found in these

t studies vary from 0.07 mps for a light, dry snow to 0.40 to 1.0 m/s for wlnd- hardened snow of similar density (350- 400 kg/m3) but differing hardness (98 kPa compared to 245 kPa). In fact, the data report& by Kotlyakov (1961) for the Antarctica show a linear relationship between snow hardness and U* . This relationship is complicatedtky the fact that in the absence of new snowfall, com- paction by wind and energy exchange pro- cesses lead to a hardening of the snow surface. It is interesting to note that Oura et a1 (1967) report an increase in U* of newly fallen snow from 0.22 m/s to 0f9 m/s after only several hours of aging.

The shear stress, T and the shear velocity U* are related ?A the wind velocity, U. Owen (1964) and Kind (1976) suggest that the following relationship can be used to describe the velocity profile over and within the saltation layer

Obviously, equation 4 is the same as equation 3 provided ~*'/2~ is interpreted as being proportional to the effective roughness height, k. Mellor (1965) pro- vides an extremely useful summary of the roughness of snow.

111.1.1.1 Modes of transport. The three modes of snow transport recognized in the movement of snow are: ground creep - the physical movement or rolling of particles along the surface saltation - the bound- ing of partscles along the surface tra- velling in a curved trajectory under the influence of wind and gravity forces and turbulent diffusion - in which par- ticles are held in suspension in the air stream without necessarily contacting the ground. Generally, it is accepted that most of the snow is transported by saltation or turbulent diffusion. In effect, these two modes of transport have led to the devclopmcnt of two snowdrift theorics. the dyn'mical and diffusion theories based on the works of Dhgnold (1941) and Schmidt (1925). As detailed by Radok (1977) the basic equations of the two thcorics arc of somewhat mar- ginal relevance from a practical point of vicw. In essence, the most tclling

difference is in terms of the dominant processes and vertical scales, the dy- namic theory views snow drifting as a near surface phenomenon due to small eddies in the lowest 10 cm producing mainly saltation, the diffusion theory (relating to conditions on polar ice shects) attaches the main importance to the larger eddies in the free air stream extending to tens or even hundreds of metres above the surface. Radok (1977) in his evaluation of the two theories stresses that the real power of the diffusion theory comes from its detailed predictions of drift concentrations and velocity profiles and a greater under- standing of the snow drift process.

In practice snow particles can only rise to great heights above the earth's surface khen the vertical velocity com- ponents are approximately equal to or greater than the terminal falling velo- city, w, of the particles. Bagnold (1973) suggests that the turbulent velo- cities become roughly equal to the ter- minal falling velocity of particles only when the shear velocity U* is greater than about 5 U* Generally, the dominant

jh' . particle size nomlnal diameter) of a wind blown snow may be of the order of magnitude of 0.5 mm for which values of Uth may range from 0.1 m/s to 0.2 m/s. Wlnds capable of producing a shear velo- city of 0.74 m/s (corresponding to approximately 14 m/s at a height of 1 m) are infrequent in nature. In recent years considerable study has been devoted to the mass transport of snow. Owen (1964) has shown that for saltating uniform, spherical particles, assuming no phase change and two dimensional flow the mass transport rate or the ability of the wind to transport snow is approxi- mately proportional to u*~. However, it Is recognized that during the scouring or erosional process layers of very fine particles (snow dust) may be exposed which, because of their low fall veloci- ties, may rise to great heights in the atmosphere and become suspended in the turbulent air flow. Kind, using field data reported by Oura (1967) and Kobayshi (1973) plotted a curve showing the distri- bution of the horizontal mass flux of blowing snow with height (see Figure 7). It is evident from the figure that approxi- mately 90% of the total flux occurs within about 2 cm of the surface (saltation).

111.1.2 Condensation/sublimation Losses.

Obviously, were it possible to de- fine mathematically 'thc distribution of

P E R C E N T OF TOTAL FLUX OCCURING ABOVE H E I G H T z

- too- ! - 5 0 - I

u < u a t 10. 3 VI

W 8

> 0 m 6 - a

c 4 - I C3 i-! 2- I

OO

Figure 7. Approximate variation of hori- ii zontal mass flux of blowing snow with height (after Kind).

- 5 snow particle concentration the mass , 'Y "- 3 , flux would be calculable by integrating

the function with height. Unlike solid

:J kt particles, when a snow crystal is trans-

9 *!L ported, its.mass changes because of vapor transport with the surrounding air { $.+ and other particles. Schmidt (1972) presented a model of the major processes : j$ contributing to the evaporation or sub- limation of a single particle. Some

< importmt findings from this work in-

$ -8 &\ clucied: tho sublimation rate appeared to double for each 10 degree temperature e s; rise in the range from -20°C to O°C. It more than doubled when the particle

j a r diameter doubled and the percentage mass loss in unit time increased markedly with decreasing particle size. In

8 4 8 essence, a snow particle evaporates because of vapor pressure gradients . . existing with the surrounding air and

P other particles. Schmidt assumed that all the sublimated vapor is transferred

0 vertically by turbuient exchange hence it would be hypochesizcd that a substan-

h tial amount of water to a snowcover may

\I be lost in the transport process. Equations for estimating the condensation/

8 sublination loss of a mass of blowing

3 snor; have been proposed by 3yunin (1961) and Tabler (1971). In both cases use is

i$ made of the concept of a "transport

3 distance", Ru, the distance over which ,the average sized drift particle is completely evaporated. Obviously, the transport distance frequently differs from the contributing distancc and thus the amount of blown snow completely col- lestcd by some barrier or obscacle must be adjusted by the amount: vllich llas evap- orated. In a later paper Tablcr (1975) suggcsts that the ratio bctwccn the

pcrccntage of relocated precipitation lost to cvapcration as a function the ratio of che fetch to the transport dis- tance is an cxponcntial function - derived from a consideration between evaporation and particlc size distribution. For con- ditions encountered in Wyoming where en- vironmental conditions were constant over the fetch distance downwind of a boundary, for fetch distances of 0.5 Ru, Ru, 2 Ru and 3 Ru the portion of relocated snow evaporating in transit would be about 37, 57, 75 and 83 percent respectively.

1 1 1 1 1 . . .

(WIND SPEED = IOm/r ) > I

111.1.3 Combined Transport and Evaporation

-

The work by Tabler (1975) led to the development of a combined transport and evaporation equation of the form:

;

where Q = the total water equivalent volume of snow arriving at a point after a transport dis- tance, R, (m3/m),

n = number of interval distances of AR within which R can be divided over which P and evaporation can be agsumed constant,

(Pr)i = the wa'ter equivalent of the precipitation swept off the i th - AR interval (m) - for annual transport calculations P is the total winter precipi- t5tion less the amount held by the vegetation and terrain irregularities plus the mount of melt,

R = the travel distance, (m), Ru = the transport distance required

for complete evaporation of the average size particle (evalu- ated using measured field data) (m) ,

dr = incremental length (m). In his paper Tabler proceeds to demon- strate thz application of the model for determining transport volumes an3 evapo- ration losses for different combinations of vegetation and terrain features.

In manner of summary, Miller (1976) lists the actual transport distances and the transport flux rates for different physiographic and climatic regions (see Tables 2 and 3). Stcppuhn and Gray (1978) have estimated thc potential transport fluxes over tllc winter season on the Canadian Prairies to vary in the range

' 2 ' 0 ' 4 0 60 8 0 A I 0 0 .

Table 2. Average distances of snow transport in different terrain, km, (after Miller, 1976).

In mountainous dissected topography (Kotlyakov, 1973) 0.1 to 0.5 On plains of western Siberia (Dyunin et al, 1973) 1 to 3 On plateaus of southeastern Wyoming (Tabler & Schmidt, 1973)

---small particles (0.1 mm diam.) 0.5 ---larger particles (0.2 mm diam.) 1.4

On ice domes (Kotliakov, 1968) Up to 5 On polar ice caps (Kotliakov, 1968) To 30-50

Table 3. Mean winter season transport flux rates, tons/m (after Miller, 1976).

Central European Russia (Mikel', et al, 1969, p.54) 100 to 200 Kamennaia Steppe (Mikel', et al, 1969, p.54) 230 Tundra (Mikel' , et al, 1969, p.54) 600 to 1000 Arctic Coast (Mikel' , et al, 1969, p. 54) 1000 Wyoming - (Tabler , 1973) 150 Rocky Mountains (Martinelli, 1973) 300 Northern Idaho ridge: Increase in transport rate into a lee cornice when windward slope was cleared (Haupt, 1973) 14 to 120

from 2.6 to 21.7 tonnes/r,. because of other factors such as the manner with which snow accumulates,

111.1.4 Interaction in Forest Environment collects and adheres to different types of vegetation and the cohesion and ad-

In the forest environment maximum hesionproperties of different types of accumulations of snow are often reported snow. Although several investigations at the edges of a forest as a result of have been conducted of the critical wind snow being blown in from adjacent areas. speed required to. remove intercepted These accumulatioris are highly dependent snow the writer is unaware of any field on the porosity of the stand borders. measurenents which provide quantitative Within the stand itself snow accunula- measures of the amount of transport by tions may not be uniform although it is wind and its affect on snowcover distri- generally conceded that the snowcover bution. Hoover and Leaf (1967) in Colo- distribution is more uniform within hard- rado did conclude from timed-sequence woods than in coniferous forests where photographic neasurements of snow inter- the effect of 6ense cro'~;ns is to create ception that there was a possibility that a "ridge and hollow" effect. Further, mechanical removal predominated over most studies have reported that more vaporization in removing snow from tree snow is found within forest openings than Crowns. within the stand itself.

A unique transport phenomenon affec- 111.1-5 ~ffects on Snow Density ting the distribution of snowcover within a forest which is affected primarily by To the hydrologist a discussion of wind is the transport of intercepted wind on a snowcover would be inconplete snow. Wind causes a tree to vibrate, without some consideration of its effect thereby resulting in a loosening and erosion of intercepted snow, blowing and transporting fragments ciownwind. Miller (1966) in his review paper on the trans- port of intercepted snow sununarizes the results of different studies concerning the transport process. It is obvious from this review that a physical under- standing of the process is complicated not only by tl~c comploc nature of thc air flow pdttcrns and velocity distributions within diffcrcnt forcst covers but also

on snow density and consequently the snow water equivalent. \\%en snow crystals are moved by wind their physical shape and properties are changed and they are rede- psited in accumulations which have den- sities greater than the parent materials. For cxample. Church (1941) found fresh snow with densities of 36 kg/m3 and 56 kg/m3 to increasc to a density of 176 k9/m3 within 24 hours after being subjected to wind action- Gray et a1 (1371) rcportcd similar findings for the Prairies

I"'

I - A L B E R T A

&-&--i CALIFORNIA

M COLORAOO

IDACIO

*NEW MEXICO

densities of snow as influenced by wind. The time dcnrlfication of a snowcover,

although initiated by the wind action is also influenced by condensation, melting and other processes. These diffcrences are well illustrated by considering the curves for different vegetation zones (see Figure 3).

111.2 Topographic Factors

111.2.1 Elevation

The primary to~ographic factors affecting snow accumulation and distribu- tion are elevation, slope and aspect. Of these three normally, in a mountain terrain, elevation is considered the major factor and, at a specified location and within a given elevation interval frequently a linear association between

I 1 snow accumulation and elevation can be I , , , I found (see for exaxple U.S. Corps of

Oo 100 2 0 0 3 0 0 Engineers, 1956). The transposability of AVERAGE INCREASE OF SHOW WATER

Imm/hm)

Figure 8. Average increase of snow water with elevation in different years (data obtained from Meiman, 1970).

in which the density of newly fallen snow increased froin 45 kg/m3 to 230 kg/m3 within a period of 24 hours under blizz- ard conditions. In comparison, Goodison and Ferguson report changes in density of newly-fallen snow during storms sheltered site in Ontario to increase, on the average, by a factor in the range of 1.3 to 2.4, depending on the depth of snow and snowfall duration. Table 4 lists characteristic values of the

these relationships is highly suspect as the influence of elevation alone is indeterminate because of the interdepen- dency of climate, slope and elevation. Figure 8, constructed from data reported by bleiman (1970) shows the increase in snow accumulation with elevation as measured in eleven separate investigations undertaken in Alberta, California, Colorado, Idaho and New Mexico. In one study (Colorado) measurements were made within selected elevation bands for three consecutive years. The information reflects not only the large variation encountered between major physiographic areas as well as the spatial-temporal variations within a given area. Meiman

Table 4. Densities of Snow Cover

Snow Type

Wild snow

Density (kg/m3)

10 to 30 Ordinary new snow immediately after falling

in the still air. 50 to 65

Settling snow 70 to 90

Very slightly toughened by wind immediately after falling

63 to 80

Average wind-toughened snow 280

Hard wind slab 350

New firna snow

Advanced firn snow 550 to 650

Thawing firn snow 600 to 700

a snow consolidated partly into ice (after Scligman, 1962)

cites that numerous workers have substan- tially improved the correlations by including other land surface features. Howcvcr, as Peck (1964) and others have cml>hacizcd, and as the writer has alluded to in'prior discussion it is.important to recogliize the influence of zlimatic factors or elements of the parcnt wcather system in interpreting snow distribution and accumulation patterns., For exmnle, the dccrease in temperature found with elevation results in a decrease in melt losses. Also, it can be argued that since the moisture available for the precipitation process decreases with elevation the increases observed with elevation reflect the combined influence of slope and elevation on the efficiency of the precipitation mechanism.

To the hydrologist, the density of a snowcover is equally important as depth. Storr and Golding (1974) show a linear association between snow water equivalent and depth in the IJarmot Basin in Alberta. Grant and Rhea (1974) report a substantial variation of snow density in mountain passes in the central Colorado Rockies. Greater densities were observed at the lower elevations which was attri- buted to a higher frequency and degree of riming of ice crystals than occurs at higher elevations.

111.2.2 Slope

Mathematically, the orographic precipitation rate is predominately related to terrain slope and windflow rather than elevation. That is, if the air is saturated the rate at which precipitation is produced is directly proportional to the rate of rise of the air and the rate of rise of the air flowing over a upsloping terrain is directly proportional to the product of the windspeed and the magnitude of the slope.

Rhea and Grant (1974) have provided a general expression for orographic mountain snowfall to include the effects of large-scale vertical air mass novsaent, convective activity and orographic lift, passage of air mass over upwind moui~tain barriers, interception and gauge exgosure. The orographic conponent is mati,t-matically related to the spccific humidity grcLient, a vertical velocity component-a function of slopc and time, thc prcssure dcpth of the air mass, the precipitation effic- iency and the elcvation of the site. Tllcy found frorn analysis of winter prccipitation data in Colorado that t11c long-term avcrdge precipitatio~l at a

point was strongly correlated (positively) with topographic slope computed in the first 20 km upwind, using the slope valucs obtained from 30' directional classes and weighted according to the directional frequency in precipitation days and an estimated cloud depth for each direction. The correlation between mcasured winter precipitation and computed "orographic" preci2itation was slightly improved (r=O. 082 to r=0.90) by incorpor- ating a factor to account for the partial depletion of available condensate because of precipitation induced by upstream barriers. They concluded that long term average precipitation is not well corre- lated to station elevation except for points on the same ridge.

Even where orography is the principle lifting fnechanism and an increase in snowfall amounts with elevation may be expected the depth of accumulation or deposition may not exhibit this pattern. In addition to the many factors affecting distribution at the higher elevations winds of high velocities and long dura- tion are more frequent causing transport and redistribution. Table 5 reported by Miller (1976) shows the high variability in the relative mounts of snow deposited on different topographic facets in the Ural Mountains in the USSR.

In topographically-similar areas to the Prairies in which snow occurs prim- airly by frontal activity and the ex2osed snowcover is subjected to high wind shear forces slope and aspect are impor- tant terrain variables affecting the snowcover distribution. The depth of snowcover along a slope oriented in the direction of the prevailing wind tends to decrease alony its length. Steppuhn (1978) shows that the relative amounts of snow retained by level plains, gradual slopes and hill tops, all in summer fallow, to that measured by a Nipher snow gauge to be of the order of 0.6, 0.70 and 0.2 respectively (see Table 8). In many years on the Prairies it is common to note, even at the time of maximum accumulation, hilltops may be free of snow. Further, it should be noted that in this region the lee of steep slopes and gullies form major collection areas. IblcKay (1970) cites the case where the snow water equivalent rcnaining in a prairie valley in the spring after the adjacent plains were frce of snow amounted to 14,000 m3 per km of channel. Steppuhn provides examples which suggest that the retention in srn~ll drainage-ways and steep hills and valley slopes cornpar'ed to gradual slopes

Table 5. Relative snow deposition on topographic facets along a traverse across the Ural Mountains (Kotliakov, 1968, p.161) (from Miller, 1976).

Topographic Facet Length, Precipitation Accumulation km

Eddy (Relative) (Relative)

Flat 10. lower slope 2. Upper slope 1. Ridge 1.3 Lee of main Second ridge 1. Lee of second ridge 0.8 Downwind plateau 0.7 Valley of Igan River 0.7 Windward slope 0.5 Ridge and its lee slope 1.3 Lower lee slope 0.5

Standard deviation 0.43 0.52

a H-Horizontal-axis eddy, V-Vertical axis eddy.

may be of the order 1.5 to 2.4 and 3 to Table 6. Mean Accumulation of Snow (an) 4.5 respectively (see Table 8). under different cover conditions in

Woo and March (1977) suggest a simi- the Eastern Rockies as related to lar division of terrain units in study of aspect (after Stanton, 1966). snow storage on a high arctic basin. There are hilltops, high flats on plateau Aspect

Cover surface, low flats or flat areas at lower N S E elevations, gullies, valleys and long

Forest slopes.

41 4 1 39 Cut Forest 45 53 6 5

111.2.3 Aspect

The importance of aspect on accumu- lation is evinced by the wide differences found between the snowcover on windward and leeward slopes of coastal mountain ranges. In these regions the interaction and influence of aspect in relation to the directional flow of snowfall producing air masses, the frequency of snowfall occurrences and its effect on the energy exchange processes influencing snowmelt and ablation are assumed the major factors contributing to the differences. In fact Neiman (1970) suggests the effect of aspect appears to be prcd2ninantly a melt effect as the works of Goodell, 1952; Stanton, 1966; and Wilm and Collet, 1940, indicate that aspect did not affect the maximum snowcover in natural forest con- ditions where the melt opportunity is minimized whereas thc effects increased in areas where winter melt is common. Xeiman reported that rnultifactor studies of snow accumulation indicate that the effect of aspect on accumulation in mast arcas tends to be considerably less than that of elevation. For oxample purposds, the results of Stanton (1366) provide an exmple of the inport~lnce of aspect, alon? thc esstcrn slopes of tt~c Rockies (sec Table 6).

The importance of aspect with respect to producing major changes in climatic regimes and energy exchange processes is less apparent when local conditions are considered. Within the Prairie environ- ment it is accepted that the influence of aspect on accumulation is dominated by its influence on the latter and, in addition, the snow transport phenomenon.

N3 attempt will be made within this manuscript to discuss the complex inter- actions between melt, ablation and accumu- lation and distribution. The melt and ablation phenomena are a separate topic of this Workshop.

111.3 Vegetative Cover

Vegetation affects the surface roughness and wind velocity thereby affecting the erosional, transport and depositional characteristics of the sur- face. If the biomass extends above the depth of <he snowcover it affects the energy exchange processcs. the magnitudes of thc energy terms and the position (height) of the most active exchange surfacc. Also, a vegetative canopy affects thc 'mount of snow reaching the ground. In most cases the works conccr~ling the

interaction of vegetation and snow accu- mulation are divided to study of forest and non-forest (short vegetative cover) ecosystems.

111.3.1 Forest

A forest differs from other vegeta- tive covers primarily in its protrusion of large intercepting and radiating bio- mass above the snowcover surface and into the atm'osphere.

Kitteredge in 1953 showed using illustrations, the effects of a forest canopy on local snowcover distributions. Since that time numerous studies have been conducted on the canopy effects on interception and accumulation. These are summarized by ~lille; (1966) and Meiman (1970). Most of the works have concen- trated on differences between the amounts of snowcover under different species of forests and the amounts measured in openings. Though more snow is consis- tently found in forest openings than within the stand itself absolute estimates of the interception aounts are unknown because of the lack of knowledge of the interception loss processes.

Kuzmin (1960) reported that the amount of snow accumulated in a forest clearing depends on the size of the . wooded area. Thc average depth in clearings in a wooded area 100 m x 200 m was 53 cm compared to a depth of 36 cm in an area 1000 x 2000 m. He also repor- te? that the accumulations depend on the type of tree species; deciduous for- ests giving greater accumulations than pine or fir forests; the latter showing accumulations of 82 and 63 percent of that measured in a birch forest. Multi- factor analyses have disclosed snowcover amounts to increase from 8 to 56 nun of water equivalent for a 10% decrease in canopy depending on tree species (Meiman, 1970) .

llany investigators (Goodell, 1959; Molchanov, 1903) have found snow accumu- lation to be inversely related to canopy density. Hence, it may be expected that forest density can be used as an index of the amount of interception. Kuzmin (1960) reports that the relationship between the water equivalent in a fir forest (MEf) and the water equivalent of the snowcover in a clearing, (WE ) , can be related to tree density ( p ) , $xpressed as a fraction by the expression

In addition to the cffects of a forest cover on the wind vclocity distri- bution and interception the other major effect of cover on snow accumulation and distribution originates from its effect on the energy exchange processes and thereby the way in which the snowcover is modified by the energy fluxes to change its erodability, mass and state. The classical work of the U.S. Corps of Engineers (1956) and Reifsnyder and Lull (1965) serve as excellent guides to the effects of a forest canopy on the radia- tive exchange components. More recently Bohren (1972) presented a theoretical analysis of radiation transfer and snow- cover and has suggested that the total surface area of the canopy is a relevant parametqr which determines the amount of radiant energy incident on a snowcover. The turbulent transfer of the sensible and latent heat between snowcover and the atmosphere in a forest are largely unknown quantities.

In manner of summary it is suggested that at the present time because of the lack of understanding of snow transport processes and the lack of information on the magnitudes of radiative and turbulent fluxes the accretion of snowcover in a forest is indeterminate. lliller (1966) summarized the types of research studies needed of heat and mass transfer quan- tities to obtain an understanding of the interception and transport phenomena in forests. This work serves a useful guide- line to the development of an accumulation mode 1.

111.3.2 Prairies (Grassland) and Steppes

Kuzmin (1960) and McKay (1963) have emphasized the importance of terrain and wind in establishing snowcover patterns on the Prairies. However, over the highly-exposed, relatively-flat or moder- ately-undulating terrain, meso and micro- scale differences in vegetation as it increases aerodynamic roughness may pro- duce wide variability in accumulation patterns. kccumulations are most pro- nounced where there is a long u stream fetch of loose snow which is suEjected to sustained strong winds from one direc- tion; they are less pronounced when wines change direction especially if the wind velocities are low.

Lakshman (1973) cites examples where on areas stratified according to land use and topography, a linear relationship map be used to rclate snow water equivalcnt and snow depth. Steppuhn and Dyck (1974) suggest consistent similarities exist in

t h e a r e a l v a r i a t i o n of snowcovers w i t h i n a r e a l u n i t s h a v i n g s i m i l a r l a n d s c a p c f e a - t u r c s . T h a t is, f o r c s t s , pastures, c u l t i - v a t e d f i e l d s , p o n d s , c t c . , w i t h i n t h e same c l i m a t i c r e g i o n t e n d t o a c c u m u l a t e snow a c c o r d i n g t o r e c u r r i n g p a t t c s n s u n i q u e t o s p e c i f i c t e r r a i n and l a n d u s e . The a u t h o r s d e m o n s t r a t e t h e v a l u e i n u s i n 7 a s t r a t i f i e d o r u n i t i z e d samplinr j t e c h n i q u e i n e s t i m a t i n g t r u e b a s i n snowcover . The p r o c e d u r e i s b a s e d on t h e d i v i s i o n o f a w a t e r s h e d i n t o d i f f e r e n t l a n d s c a p e c l a s s e s and s a m p l i n g w i t h i n g i v e n a r e a l u n i t s o f a g i v e n c l a s s . T a b l e 7 , t a k e n from Steppuhn (1976) shows t h e snowcover d e p t h s t a t i s t i c s by l a n d s c a p e t y p e measured on t h e C r e i g h t o n T r i b u t a r y o f t h e Bad hake Watershed l o c a t e d i n w e s t c e n t r a l S a s k a t - chewan. I t is o b v i o u s f rom t h e s e d a t a ,

T a b l e 7. Snowcover d e p t h s t a t i s t i c s by l a n d s c a p e t y p e , 1974 , Bad Lake, S a s k a t c h e w a n ( a f t e r S t e p p u h n , l 9 7 6 )

Landscape No. Mean C o e f f . o f TYPe Obs. Depth V a r i a t i o n

P l a i n f a l l o w s t u b b l e

R o l l i n g P l a i n

f a l l o w s t u b b l e p a s t u r e

G r a d u a l S l o p e

f a l l o w s t u b b l e s c r u b

S lough f a l l o w s t u b b l e

S h a r p S l o p e

p a s t u r e s c r u b

Broad Lowland

f a l l o w s t u b b l e p a s t u r e s c r u b

Topland f a l l o w s t u b b l e p a s t u r e

Farm - Yard -

A l l t y p e s n o n - s t r a t i f i e d

68.1

t h a t t h e d e p t h o f snow c o l l e c t e d by s c r u b b r u s h i s consistently h i g h e r t h a n t h a t c o l l c c t c d on f a l l o w , s t u b b l e o r p a s t u r e i n d e p c n d e n t o f t e r r a i n . C o n v e r s e l y , t h e s t r o n g i n t e r d e p e n d e n c y o f v e g e t a t i o n a n d t e r r a i n i n r e l a t i o n t o t h e c o m p a r a t i v e amounts o f snow r e t a i n e d by f a l l o w , s t u b b l e and p a s t u r e c a n be n o t e d . I t is wor thy t o n o t e t h a t 1973-1974 was a w i n t e r w i t h s n o w f a l l much above normal , t h e mean snow w a t e r e q u i v a l e n t on t h e b a s i n was a b o u t 134 mrn. Using d a t a from 1973/74 a n d 1974/75, t h e l a t t e r a w i n t e r i n which t h e mean a r e a l snow w a t e r e q u i v a l e n t was measured a s 71.2 mm Steppuhn (1978) n o r - m a l i z e d t h e mean w a t e r e q u i v a l e n t measured on t h e d i f f e r e n t a r e a l u n i t s t o t h a t mea- s u r e d by a Nipher g a u g e , ( s e e T a b l e 8 ) . It c a n b e n o t e d t h a t (1) t h e r a t i o s f o r a g i v e n l a n d s c a p e t y p e d i f f e r i n t h e two y e a r s , ( 2 ) w i t h i n t h e d i f f e r e n t l a n d s c a p e c l a s s e s t h e r a t i o s remain r e l a t i v e l y con-

a s i s t e n t i n o r d e r o f magni tude w i t h r e s p e c t t o v e g e t a t i o n t y p e s , and ( 3 ) t h e r e is a r e a s o n a b l e d e g r e e of o r d e r w i t h which t h e d i f f e r e n t l a n d s c a p e t y p e s a c c u m u l a t e snow; t h e a c c u m u l a t i o n s on s t e e p h i l l and v a l l e y s l o p e s t e n d i n g t o b e much g r e a t e r r e l a t i v e t o t h o s e o f o t h e r l a n d s c a p e t y p e s i n t h e y e a r o f lower s n o w f a l l . I t s h o u l d b e r e c o g n i z e d t h a t t h e s e d a t a a r e p r e s e n t e d f o r example p u r p o s e s o n l y and a r e l i m i t e d i n t h e i r a p p l i c a t i o n a s t h e y . r e p r e s e n t o n l y t h e r e s u l t s o f two y e a r s o f s t u d y .

111 .3 .3 Zona l Snowcover

The d i s c u s s i o n s i n d i c a t e t h a t c l i m a t e p h y s i o g r a p h y and v e g e t a t i o n i n t e r a c t i n a complex manner i n g o v e r n i n g snowcover a c c u m u l a t i o n and d i s t r i b u t i o n . Many i n v e s t i g a t o r s ( R i c h t e r , 1945; Khodakov, 1975; and McKay a n d F i n d l a y , 1971) h a v e found t h a t it is p o s s i b l e t o e s t a b l i s h and t o map some g e n e r a l c h a r a c t e r i s t i c s o f snowcover on a z o n a l b a s i s i n which t h e z o n e s a r e d e f i n e d a c c o r d i n g t o vege- t a t i o n . T h i s p r o c e d u r e is o f t e n e f f e c t - i v e b e c a u s e t h e t y p e o f v e g e t a t i o n is f r e q u e n t l y i n d i c a t i v e o f c l i m a t e . U s u a l l y t h i s s i m p l e z o n a t i o n i n c l u d e s t h e f o l l o w i n g : Tundra , T a i g a and B o r e a l F o r e s t , G r a s s l a n d a n d S t e p p e s , Mixed F o r e s t and Mountain Areas . I t c a n b e e x p e c t e d t h a t be tween t h e d i f f e r e n t z o n e s , a n d i n f a c t w i t h i n z o n e s , t h e d a t e of f o r m a t i o n , d u r a t i o n , d a t e of d i s a p p e a r - a n c e , d e p t h and d e n s i t y o f t h e snowcover v a r y w i d e l y d e p e n d i n g on s u c h f a c t o r s a s l a t i t u d e , a l t i t u d e a n d o t h e r p h y s i o g r a p h i c f e a t u r e s . N e v e r t h e l e s s , i n d c p c n d e n t o f t t i e wide d i f f e r e n c c s , i n t l ~ c p l ~ y s i c a l p r o - p e r t i e s o f t h e snowcover w i t h i n t h e

Table 8. Ratios of mcan snow water equivalent on given landscape class to snow water equivalent measured in a Niptlcr gauge - Crcighton Tributary, Bad Lake Watershed, Saskatchewan, 1974 and 1975.

Landscape Type Ratio of mcan snow water equiva- lent on landscape type to that measured by Nipher gauge.

1974~ 1975~

Upland and Lowland Plains (shallow sloughs) fallow 0.59 stubble hayland, pasture

Undulating Plains fallow stubble Hayland, pasture

Gradual Hill and Valley Slopes fallow stubble hayland ,

hayland, pasture Steep Hill and Valley Slopes

fallow stubble hayland, pasture bush

Small Shallow Drainageways fallow stubble hayland, pasture scattered brush

Wide Valley Terraces and Bottoms (ravines, coulees) fallow 0.74 stubble 0.75 hayland, pasture 0.75 brush 0.75

Farm Yards 2.10

a)Ratio of areal mean water equivalent to Nipher gauge : 1974-0.729 1975-0.82

different zones it is also possible to distinguish major differences in certain properties between zones. For example, Figure 9 exhibits the differences in the time-density variations in different vegetation regions. Although such infor- mation can be used by a hydrologist only for grossly simplified computations of water equivalent they serve the purpose of illustrating the effects of vegeta- tion on the ripening process under different conditions.

IV SIMULTTION, SYNTHESIS AND PREDICTION

The snow transport and accumulation phcnomena arc highly complex and the exact rnccl~ar~islns of movement are dif f i- cult to cxplclin even under thc simplest situation of a smooth flat infinite

plane. The following section discusses some of the physical, mathematical and empirical, to include measurement and con- ceptual approaches, used to describe the areal accumulation of snowcover.

The approach adopted to study m d to determine snowcover distribution will de- pend largely on such factors as: the study objectives, thc available resources and the use of the results. That is, an cngi- neer whose primary interest is to study distribution pattcrns surrounding b~ildifigs, air terminals and runways, roadways and other engineering works resulting from a single storm may take advantage of the use of physical models. Conversely, to a hydrologist, whosc interest is in the areal snowcover distribution, primary snow water equivalent, at thc time of nuximum accumulation the usc of a physics1

shallow snowcovcr at a point identified that the depth and density (snow water equivalent) are the most critical proper- ties affecting the changes in internal energy of a shallow snowcover and the sensitivity of the encrgy budgct approach for determining snowmelt. He exemplified

5 2 0

4 4 0

-.- .... ,,. $6 that the cumulative uncertainty to be 400--0- c.... r ...a - .,

I, L....-c. placed on estimates of the internal energy - n may be several multiples (ranging between I 3 6 0 - 2 to 16), of both the net radiation and . - Z

sensible heat fluxes depending on the t magnitudes of the different components; g 3 2 0 - Y the larger the fluxes the smaller the 0

ratio. The results of this study define 280 - the importance of the depth and density

of snow in relation to the time of occurr- ence of melt and the amount produced.

2 4 0 - Erickson et a1 (1978) reported the results of a study conducted on small units on the

zoo - Prairies which show that the runoff vol- umes and rates are greatly affected by land use and'to a lesser extent terrain.

D ~ C J ~ N F ~ B M ~ R M ~ T J ~ N E Table 9, taken from these works illustrates 15 15 15 I5 15 j

the volumetric differences which may be Figure 9. Time density variations in found under differing land use or vegetal different vegetation zones. covers based on the degree day approach

for estimating the runoff quantities. model is coqletely impractical not only The data indicate: (a) the differences in because of its physical size and cost but ,it runoff volmes in forest and Prairie moreso because most natural systems defy regions - the runoff volumes per degree the construction of a model that will day, in all cases but one (stubble) exceed- satisfy the geometric, kinematic and

'

ing those experienced in a forest and (b) dynamic similitude criteria. the effects of land use on runoff within

the h ~ ~ ~ ~ ~ o g ~ ~ ~ ~ the the Prairies - the average values being tant uses of snowcover data are for fore- 3.90 for stubble, 4.78 for pasture and casting, or updating forecasts of water 10.96 for fallow (,,,,its in of water yield or the magnitude and time of occurr- per 'C-day above 0°C) with maximum rates ence of flood peaks. In many climatic for the three land use conditions reported environments absolute data of areal snow- as 5.04 6.50 and 18.62 respectively. cover distribution, by itself, will not These rates are in reverse order of magni- necessarily lead to significant improve- tude relative to the depth of snow accu- ments in forecasts than can be obtained mulation on the different land use classes; through the use of one-dimensional snow- depth on pasture and stubble being melt models currently available. The significantly greater than on fallow. point to be emphasized is that the areal Many factors have contributed to the distribution of snowcover and snow water differences in the release rates and a equivalent does not necessarily accurately comprehensive discussion of each is be- reflect the major source areas of snowmelt yond the scope of this paper. The impor- runoff. Snowcover, prior to becoming tant aspects of the study are that on the streamflow, is modified by ablation (snow- Prairies the magnitudes of rates and vol- melt and infiltration) and storage Pro- of runoff from different land units cesses. Hence it is only where the bun- may be in complete opposition.to the dary conditions affecting these other snowcover depth distribution patterns. processes remain sensibly constant, both McKay (1970) has pointed out that in spatially and temporally, or where the many years on the Prairies the snow accu- effects or interactions between the snow- mulated in gullies and drainageways covcr and these proccsscs can be explained (major accumulation areas) serve as major will it be possible to make efficient source areas of runoff. In addition these quantitative usc of areal snowcover accumulations ray retain largc quantities diffcrcntiation in stl-eamflow prediction. of water which originate from snowmelt To excrnplify, Male (1972) in a study of runoff from adjacent. stubble, jmsturc the thermodynamics of the melt of a and fallow land ant1 dclay thc time of

. . L .I cr,... D r, a-..,... TIuL-DCNSITT VaIIATIONS . -..... I 7. IN V E G L T A T L O N REGIONS

--.--,a. l.". 11 . I . 4110--- .,,... ~1 I

I --- c..., I I

-..- C.,.",,. . I I

.-.--'.a(. I

/' ! + -C rm*. 11

/' ; -.- ..... t.... TI

Table 9. Comparison of basin snowmelt runoff degree day factors between forest and prairie environments.

Location

:

Central Sierra (Calif a :I- Upper Columbia (Mon. ) -

a Willamette Basin (Ore.)- Bad Lake (Sask. ) Bad Lake (Sask. ) Bad Lake (Sask. )

Land Use Month

Runoff/OC day above O°C/unit snow covered

area (nun)

forest April 4.07 forest Apr i 1 1.69 forest April .78 stubble Mar. , Apr . 3.91 pasture Mar. , Apr . 4.79 fallow Mar. , Apr . 10.96

k, Taken from U.S. Corps of Engineering (1356).

release to streamflow. Field observations have substantiated that measureable stream- flow and floods will occur only after water has channelled the snow in the drainage ways; a situation that may occur when a large part of the snowcover has been removed from adjacent areas. To date, procedures for routing of snowmelt through snow-clogged channels to account for the storage effects have not been developed.

The preceding discussion emphasizes the problems of applying a snowcover dis- tribution model to assist forecasting and of water yield and floods in the Prairie environment; the time elements of any release pattern may be directly related to snowcover depth whereas the volumetric elements may be indirectly related to depth. Certainly, in a mountain, forested region a similar dilemma exists indepen- dent of the fact that different factors may assume greater importance in the accumulation-ablation-runoff interaction than those in the Prairies.

It appears possible, however, that for hydrological purposes a snow accumu- lat'ion and distribution model may be developed giving consideration to soil- vegetation-topography factors. Many investigators (Adams, 1976; Leaf, 1975; Steppuhn and Dyck, 1974 and operational agencies in the USSR) are proponents of this practice for application to rclling forest, mountain forest and prairie areas. The number of units or classes selected will depend not only on the areal vari- ability of the different physical vari- ablcs but also on such factors as the sensitivity of the given water management modcl to the variations in the input data, the type and availability of data acqui- sition, handling and processing facilities and the needs and requirencnts of the user.

IV.l Physical Models (Kind)

blellor (1965) has pointed out that

the value of wind tunnel testing in snow drifting studies has been widely recog- nized for about 40 years although rela- tively few studies have been conducted during that time. By using sawdust and flake mica to simulate snow in a wind tunnel, Finney (1939) was able to suggest improved methods for snowdrift control along highways. More recently Theakston (1962) has studied snow accu- mulation around structures first by the use of wind tunnels and later by use of water flumes. Quite extensive studies on drifting snow have been conducted at New York University by Gerdel and Strom (1961). In the early tests modelling criteria were apparently not explicitly considered. It is entirely impracticable to satisfy the large number of similarity criteria yielded by a simple dimensional analysis of the system. However, a similarity analysis which draws more heavily on physical analysis and experi- mental evidence promises to be more fruit- ful. Strom et a1 (19621, Odar (1962, 1965), Isyumov (1971) and Kind (1976) have considered this problem.

Kind (1976) has presented three design criteria which must be satisfied to correctly model the ratios drag force: weight, drag force:inertia force and velocity fields in studying the free- flight portion of the trajectory of a saltating particle (the saltation pro- cess). A requirement for similarity of model and prototype velocity fields is that the model be geometrically similar to the prototype. In addition, the velo- city profile of the wind approaching the model must be similar to that found in the prototype. Thus, the model profile must give the samc value of Uf/V (where; U* is the shear velocity and V is the wind velocity) as the prototype profile. Thc model must also include a substantial fetch of correctly modelled terrain, com- plete with particles, upstream of the

region of interest. This is necessary in order that saltation bc properly es- tablished by the timc the flow reaches the region of interest. The rcquirement that v2/~g (where V is a reference wind velocity, L is a reference dimension and g is the gravitational constant) be the same in model and prototype will usually conflict that U * 3 /2gV (where U* is the

th threshold shear velocity and v is the kinematic viscosity) be greater than 30 - a condition required for the flow over rough surfaces to be independent of the kinematic viscosity of the air.

Kind also discusses methods of selecting model particles. Of special interest is the fact that the mass den- sity of the 'snow' particles will usually be different in the model and prototype cases and this must be taken into account when determining the times for volume accumulations of snow from the model tests.

The requirements for correct simula- tion of the free-flight of falling par- ticles are included in the overall simulation requirements. Snowfall and snow drifting can therefore be modelled simultaneously 'without additional diffi- culty. Simulation of the snowfall pro- cess is acconplished by dropping par- ticles into the flow at an appropriate rate from the roof of the wind tunnel.

Sometimes only the simulation of airborne blowing snow is necessary where ground-drift is irrelevant. If the air- borne snow particles of interest are very small they essentially follow the air flow and smoke or dye tracers could be used instead of particles.

The ratio of drag force to lift force on snow particles is largely due to the large ratio of particle density. This would not be true if water were used as the model fluid and therefore the use of water to model ground drifting of snow is open to some question. Neverthe- less, model studies in water flumes have been and will continue to be useful (Theakston, 1962; Isyumov, 1971). The flow of water over buildings and other surface fcatures is certainly basically the same as that of air. The saltation process is also qualitatively the same in both fluids although there are substan- tial diffcrenccs in magnitudes for cer- tain effects. Therefore drift pattcrns obtained in a watcr flume should be rcasonably realistic if the velocity profile in t h e f l ~ w approacl~ing the mc)del is adccuatcly simulated and if the modcl itself is geometrically similar to the prototype. Such model tests would

not, however, be expected to yield re- liable quantitative results for rates of snow accumulation or drift depths. Results for drift shape and location also tend to be somewhat inaccurate in water flumes although they are usually quali- tatively correct.

IV.2 Mathematical, Fxnpirical and Other Approaches

The complex nature of the transport and deposition processes and the large number of factors affecting these pro- cesses defies the development of a gen- eralized, physically-based mathematical model for describing areal snowcover accumulation and distribution. However, the works of Tabler (1975) on a combined transport and evaporation model and Rhea and Grant (1974) on a method for accoun- ting for the effects of the orographic lift component on snowfall represent creditable contributions in providing a physical base for a better understanding of the accumulation process. It is recog- nized that such models involve a number of simipifying assumptions and they require field input data. As is frequently the case in hydrological studies many of the simplifications used in a theoretical analysis cannot be verified because of the lack of field data. Likely, this deficiency imposes one cf the greatest constraints on future model developments.

If sufficient point field data have been obtained over an area, isopleths of such variables as depth, density or water equivalent can be drawn and these maps used as an estinate of the distribu- tion of the snowcover parameter. Such maps provide gross simplifications of snowcover distribution yet when compli- mented with data obtain& from aerial photographs or satellites serve a useful operational function. Ancther method of using point data to obtain basin averages is the standard Thiessen polygon approach.

Lacking an understanding of the physical processes governing snowcover distribution, of necessity, hydrologists have opted to the use of empirical rela- tionships to define the spatial distri- butions of snowcover properties. AS it would be expected, based on the material prescnted in earlier parts of this paper, these relationships make use of the association between the snowcover pro- perty and topographical, vegetative and land use features. It is reiterated that such relationships generally invoke the concept that within the same climatic region consistent similarities m y be

found in the areal variation of snowcover within areal units having common landscape features. The extrapolation use and appli- cation of thesc empirical associations outside of the region in which they were developed is highly questionable. In many cases, the associations are estab- lished through standard regression tech- niques. The works of Meiman (1970) and the U.S. Corps of Engineers (1956) pro- vide an excellent summary of the rela- tionships developed between snowcover depth and elevation, slope, aspect and other factors in forested mountain regions. Much work in these regions has been di- rected to study of the effects of clear- ing size on accumulation. In the less densely forested regions of rolling topo- graphy of Eastern Canada, Adams and Rogerson (1968)' and Adams (1976) focussed their work in study of differences in snowcover character in different vegeta- tional zones. On the prairies, Ste~puhn and Dyck (1974) demonstrated the value of sampling within areal units of water- shed having similar land use, terrain and vegetal cover features to obtain an accu- rate estimate of the basin mean water equivalent (see Table 7). Broader scale studies (McKay, 1972 and Billelo, 1969) demonstrate differences in certain snow- cover properties that may be expected.in different climate and vegetation regions (see Figure 9). Any review of literature concerning the interaction of snowcover accumulation patterns and vegetation and topography would be incomplete without citing the work of Kuz'min (1960) con- taining the much cited table of "snow retention coefficients" for a range of landscape classes.

The observation that snow accumula- tion patterns may be explained in terms of landscape features serves as a useful tool toward gaining an insight of areal snowcover. The relative amounts accumu- lated by the different units may differ appreciably from year to year because of the variability in the aerodynamic pro- cesses affecting accumulation and, in addition, changes in land use. The transport-condensation model proposed by Tabler explained in an earlier section of this paper delineates some of these factors. In addition, as Adams (1970) points out, significant differences can be expected, for example in the masimum depths of snowcovers on selected vegcta- tion typcs in individual years, and that the nature of the differences between strata (vegetative typcs) may not be con- sistcnt bctwcen years. He points out that the consistcncy of the differences

bctwcen the depth, density and water c~quivalent of different vegetative-based snowcovers will depend largely on the con- sistency in the evolution of the snowcover from initiation to peak accumulation. In a region where a snowcover is subject to periods of melt or to rain the changes to its physical properties caused by these factors may mask the differences caused by vegetation. His findings would suggest that a colder environment is more conducive to the preservation of different depositional conditions on different landscapes.

In ~rinciple, the application of landscape-based classes to differentiate areal snowcover distribution or to deter- mine the mean basin water equivalent is relatively straight forward. Through the use of areal photographs and vegeta- tive maps the hydrologist identifies, interprets, geographically locates and determines the areas of the different landscape classes. Selected units of the different classes are sampled to obtain statistically valid estimates of the mean depth, density or water equivalent for each class. These values are used for mapping and calculations. In many cases the procedure may not be accepted for operational purposes by management agencies:

(1) The division of a basin to different landscape classes requires prior knowledge and experience of snow accumulation facets and the preparation of maps is a time consuming task, inde- pendent of whether computer mapping facilities are available. New maps may need to be prepared each year depending on land use or vegetal cover changes caused, for example, by farming practices, forest manipulations, fires or other natural or artificial practices.

(2) The method requires comprehen- sive snowcover data from representative classes to establish reliable statistical estimates of the snowcover properties.

(3) Provision must be made for up- dating the snowcover conditions to account for precipitation, sublimation/ condensation and melt following the date of the last survey.

Members of the Division of Hydrology, University of Saskatchewan are currently investigating the application of the areal differentiation of snowcover by landscape classes for prairie watersheds, in areas not subject to chinook activity, major wintcr sublimation losses, or melt. Attempts are being madc to use Landsat imagery obtained in thc fall to idcntify broad land use classes (ie. fallow, stubble,

sloughs and lakcs, etc). The,advantages in use of these data are that they are in computcr compatible form, a pixel gives a linear resolution of approximately 50-80 m (at - 50DN) thereby providing rclatively- fine-scale arcal delincation,, the geogra- phical position of each pixe.l' is defined and the large number of brightness levels of the pixel provide flexibility and alternatives of investigating different features. The decision to apply satellite imagery in this manner rather than to attempt to use it directly to measure areal snow water equivalent was based on the uncertainty that the imagery would provide adequate estimates of water equivalent and, because of the orbital resolution, the uncertainty of obtaining quality imagery at the time of maximum accumulation. In the fall, prior to the occurrence of permanent snowcover and following harvest several passes of the satellito are made which usually pro- vide one or more images under clear sky conditions. Terrain data will be stored in an identical matrix array (although on a gross scale) and combined with land use data to generate relevant landscape classes. In effort to eliminate the problem of undertaking comprehensive snow surveys of each landscape class attempts are being ma6e to relate the relative accumulations in the different landscape units to the accumulated water equiva- lents measured by b S C Standard Nipher precipitation gauges (see 'Table 7). These gauges would be dispersed throughout a large watershed to obtain an estimate of spatial distribution of the water equiva- lent. Appropriate retention values would be assigned the different landscape units used to map the areal distribution of the snowcover water equivalent. The fact that all data are filed in computer digestible form permits immediate updating. At the present time this approach is only in the research stage of development.

Young (1974) describes a method of obtaining snow accumulation maps on glaciers from irregularly-spaced sampling points. A grid square technique is used to describe terrain characteristics based on altitude, slope, azurnith and local relief, and to establish field sampling locations. The method is based on the assumptions: a strong linear association between snow depth (or watcr equivalent) and altitude exists, the total accumula- tion on the glacier can bc calculated by such a relationship and local patterns arc fairly constant from year to year and closely associated with thc local con- figuration of the glacier qc-omctry. The

depth of the snow surface is defined'by thc equation:

where d = the depth of snowcover, z = the altitude of the point, R = the local relief, S = the surface slope angle, and

a,b,c,d = empirically-derived coefficients.

The magnitudes of the coefficients c and d are mean values that describe the per- sistence in the local patterns of snow distribution on the glacier. Values of the coefficients a and b are established each year from depth and density samples taken at selected sampling points in different altitude zones. Using a linear relationship between dcpth and water equivalent with altitude the values are applied to all points on the grid to determine an estimate of the snow water equivalent for the entire glacier. The snowcover is then redistributed according to the equations while keeping the total amount of water constant. Maps are pre- pared from the adjusted values. A standardized data bank structure and the use of high speed data reduction systems make the method suitable for real time melt prediction studies.

It is appropriate to mention that the use of the grid square technique has been popularized for use in the spatial extrapolation of hydrometeoroloqical data because of its adaptability for computer operations. Solomon et a1 (1968) for example, has applied the procedure in .estimating precipitation, temperature and runoff for Newfoundland, Canada.

Even in the use of the more sophis- ticated mathematical models with distri- buted parameters, such as those used in streamflow forecasting, it is evident that the snowcover input values will be spatially-averaged either by smoothing or dividing a watershed to specified land- scape units. Stratification, simply by means of providing improved areal repre- sentativeness reduces the systematic errors in estimating areal snowcover. Likewise the technique reduces the interpolation error within a physiographic region and provides a basis for statistical estimates of the same. Steppuhn and Dyck (1974) an3 Woo and Marsh (1977) have substantiated that significant improvements in the cal- culation of the arcal mean are obtained.

Any discussion of the use of land- scape-course snow surveys would be incom- plete without recognizing that the pro- cedure is in operational use in the USSR. Uryvacv and Vershinina (1971) report that

landscape course snow surveying can be used to determine the water equivalent over areas of 250-1000 km3 with an error of 5-10% compared with the results from continuous, comprehensive snow surveys.

Vershinina (1971) presents a compre- hensive review, which includes both theoretical considcrations and field results of the accuracy in determining the water equivalent of snowcover at a point, over a course and the average water equivalent of an area (based on landscape snow courses). His findings indicate an exponential type decrease in the root mean square error with increa- sing area for a constant network density; the magnitude of the error increases with a decrease in density. Some other impor- tant findings of the study are: 1. Errors in determining the snow water

equivalent of an area are approximately the same for fields and forests for any network density. 2. The accuracy in determining the

water equivalent of snow over an area with small absolute snowcover and during winter thaws is very low and depends markedly on the size of the area and net- work density. The errors under these con- ditions may be 50-100% higher than those calculated during the time of maximum water equivalent on the area.

3. The relative errors during maximum accumulation may be of the order of 15 to 20% in highly exposed areas where a shallow snowcover nay be subject to fre- quent drifting. 4. The errors in determining snow

water equivalent of an area are close to those for rainfall with a given network density.

5. The magnitudes of the errors for areas of equal size having the same net- work density exhibit regional differences. In a later paper Chermerenko (1975) sub- stantiated these findings. His work extends that of Vershinina by including the effects of gauge location on network configuration on the magnitude of the error.

IV.3 Remote Sensing of Snowcover (Goodison and Ferguson)

Ground based techniques of snowcover measurement will not always detect significant areal variations in snowcover. In mountain regions large variations in snow depth and water equivalent occur because of variations in slope, aspect, elevation, exposurc and surface cover. In some areas, accessibility can limit both the number and rcpresentativencss of

ground measurements. In plains regions, variations in snowcover are dominated by local land use and topographic variations, in addition to initial spatial variations in snowfall.

For hydrologic analyses, the per- centage snowcover in a basin is an important variable. It is an areal parameter which ground measurements alone may not provide with sufficient accuracy, especially in sparsely-instrumented regions. However, the rapid development during the last 20 years of renote sens- ing techniques as applied to snowcover has provided new methods for observations, measurement and analysis, The successful application of these methods depends on accurate "ground truth" data for calibr- ation and the verification,

IV.3.1 Aircraft Observations of Snowcover

With improvements in both photo- graphic methods and airplane technology during the past 60 years. aerial photo- graphy has developed into a major method of photographing, interpreting, and mapping topography and other landscape features. However, to take vertical imagery over a large area is both time consuming and expensive.

The most common use of air photos is for topographic mapping; photography being done in late spring after the snow- cover was gone, but before the leaves were on the trees. Such photography is of no value in the analysis of snowcover. Instead, special flights are usually required to obtain snowcover data. However, the rapid development of satellite remote sensing provides a promising alter- native for the areal analysis of snowcover over large regions. Aircraft observations can then be used to obtain supplementary large scale data over selected areas of interest.

IV.3.2 Aerial Markers, Snowline Flights

In mountainous or remote regions where adequate snow course networks may be very expensive and difficult to ser- vice, and hence impractical, observations from aircraft may be a reasonable alter- native. Snow depth at selected locations can be obtained by aircraft observations of previously installed aerial markers. An estimate of water equivalent for these sites is possible by using density infor- mation from nearby (within 40 hn) snow courses located at similar elevations. Canadian and US agencies use daily runoff simulation modcls to predict runoff for

selected mountainous drainage basins in which an important parameter in the mudel is the snowline elevation that is, the boundary between the lower snow-free area and the higher snow-covered area. This elcvation, in conjunction with the hypso- metric curve for the drainage basin is used to calculate the percent of sriow covered area for the basin. Field obser- vations of the snowline from aircraft in British Columbia have bsen shown to greatly-improve the prediction of a run- off simulation model (Sporns, 1976). For the Columbia River Basin both the United States Army Corps of Engineers and British Columbia Hydro and Power Author- ity conduct "snowline flights" to deter- mine the snowline elevation. Personnel, flying in small aircraft at the altitude of lowest snowcover, estimate the snow- line elevation for different aspects at preselected points marked on a topogra- phical map. Two to four flights are made each year for each area being studied, May and June being the nost common months because the snowline is most distinct.

Snowline flights are effective; yet are relatively expensive and time con- suming. They may present a safety pro- blem, and as well, a reliability problem as they are subject to suitable flying conditions, and the accuracy is somewhat dependent on the experience of the observer. As an alternative, efforts are being made to abstract snowlines from satellite imagery. Not only can a large area be mapped, but also more frequent observations are possible.

IV.3.3 Natural Gamma Radiati0n:Airborne Survey

The aerial qamma survey was deve- loped in the USSR in the 1960's (Kogan et al, 1965) and since then experimental aerial surveys to measure snowpack water equivalent have been done in PJomay, the USA and Canada.

Natural gamma radiation is emitted from the ground by potassiu.-40, bismuth- 214 and thallium-206. Tne ?amma radia- tion is attenuated by the mass of mater- ial between the source and the detector. Water, in either the solid or liquid phase, will attenuate gamna rays ecitted from the soil surface. If the amount of attenuation is known, the amount of water causing the reduction can be calculated. The basic theory of the method and pro- cessing procetlures of Canadian airborne messurcmcnts arc summarized by Loijcns an? GI-asty (1373). For snow water cqui- valcnt mcasurtmcnt, thc potassium and

integral (total count) data have been shown to be the most useful (Peck et al, 1971; Grasty et dl, 1974; Jones et al, 1974).

As with the terrestrial survey, a no-snow measurement of the gamma levels along the traverse is necessary and adjustments for changes in soil moisture in the top 15 cm of the ground is re- quired. The aerial survey method pre- sents additional problems for which corrections must be made. The mass of air between the aircraft and the ground will attenuate g&ma rays. Based on the temperature and pressure of the air at the flying height (typically 150 m), a correction for air mass attenuation can be calculated. Radon gas in the atmos- phere also emits gamma radiation and it particularly affects those computations using the total count data. Entrapment of radon gas by an inversion layer near the surface can cause measurement problems since the background radiation will change. Background radiation is most easily measured by flying over a lake, since the mass of water will attenuate all gamna radiation emitted by the underlying ground. The reading over the lake establishes the zero value for the survey. If this method for establishing the zero value is not possible, other methods can be used, but with greater uncertainty (Jones et all 1974). Finally, deviation from the pre-snow flight track, especially in areas of variable ground radioactivity, may introduce significant error in the snow water equivalent calculation. Variation in the count rate associated with changes in the background radiation, the mass of air below the aircraft, and the counting statistics of the equipment may introduce a? error up to twice that associated with soil moisture variability.

An experimental gmna-ray spectro- meter survey of snowcover over Southern Ontario gave encouraging results. The survey was done with a highly sensitive gamma spectrometer normally used for uranium surveys. The results indicated that the average snowcover water equiva- lent over 16 km sections could be mea- sured to a precision of 12 mm using the potassium count and to 17 mm using the total count (Grasty et al, 1974). In this experiment, comparative ground based information was obtained from snow survcys along the flight track; snow water equiva- lents up to 140 mm were smpled.

The United States National Weather Service has conducted an aerial gamma survey over the Souris River Basin in the

central plains area of Canada and theUSA at the time of peak snow accumulation. The aim of the survey is to provide near real time snow water equivalent data as an aid in snowmelt forecasting. Good results have been obtained; the estimated errors are of the same order of magnitude as found in the Canadian experiment (Loi jens, 1975) .

In contrast to snow course measure- ments, the gamma survey measures the mean water equivalent over an area. When used with fixed wing aircraft the requirement for low level flight restricts the tech- nique to relatively flat areas; helicop- ters can be used in mountainous terrain. Precise navigation is required for dupli- cating tracks and comparing results to ground truth data. The great advantage of the aerial gamma technique is its coverage of large areas. By averaging the measured water equivalent in sections along the line the problem of high local variation in snowpack water equivalent, which commonly affects snow survey mea- surements, can be minimized. The present status of the gamma method indicates that in some cases it can be operationally feasible for obtaining the snowpack water equivalent over a basin.

However, as pointed out by Steppuhn (1976) sensing the snowcover attenuation of terrestrial gamma radiation may ease sampling, but will not eliminate it. He points out that in certain cases the extent of area sampled is relatively small in relation to the basin size. For example, the aerial gamma survey over the Souris River Basin covered only 0.42% of . the watershed. The point made is that inherently the method suggests a grossly inflated sampling density. In most cases the accuracy with which the method will provide an estimate of the true basin water equivalent will depend directly on the representativeness of areas sampled.

IV.3.4 Microwave Sensing of Snowcover from Aircraft

Both radar and passive microwave systems operate in the portion of the electromagnetic spectrum-from 0.1 cm to 100 cm. Passive microwave systems sense a portion of the natural radiation emitted by objects; radar is an active system which emits a beam of radiation and measures the reflected and back- scattered return. For snowcover applica- tions both techniques are still in the research and development stage. Micro- wave emission (or brightness temperature) has been shown to change with snowpack

accumulation and with the wetness of the snowpack (Meier, 1975). The great advantage with microwave systems is their day-or-night operational capability and their ability to sense through a cloud cover. Studies are currently being conducted on the usefulness of synthetic- aperature radar in measuring snowpack water equivalent. Side-looking airborne radar (SLAR) has been used for observing ice cover over the Great Lakes and ocean areas.' Such systems can provide high resolution image~y (tens of meters) over sizeable swath widths (tens of kilometers) with no scale variation across the image.

IV.3.5 Satellite Observations of Snowcover

Studies of the application of satel- lite imagery to snowcover analysis began in the 1960's. A brief state-of-the-art review is provided herein. However, rapid changes in technology will soon render this summary obsolete. Continued sensor development will undoubtedly result in new techniques applicable to snowcover analyses. For example, at the present time a microwave scatterometer is cur- rently being tested in sea-ice and sea- state experiments and eventually the sensor might be applicable to the analy- sis of the physical properties of a snowcover.

In 1977 the two principal satellite systems used for snowcover studies and operational analysis in North America were the polar orbiting Landsat and NOAA systems. The geostationary SMS/GOES satellites can provide useful data for snowcover analysis south of about 50 ON, with an excellent time resolution of 30 minutes, but the viewing angle causes distortion problems for Canadian appli- cations. The resolution of a few kilo- meters over southern Canada is not as good as that provided by Landsat or NOAA.

The first Earth Resources Technology Satellite (ERTS) was launched in 1972 and later renamed Landsat 1. Landsat covers a surface swath width of 185 km with a resolution of about 90 m at nadir. The Multispectral Scanner Subsystem (MSS) provides data in four spectral bands:

MSS 4:O. 5 - 0.6 pm - green MSS 5:0.6 - 0.7 pm - red (strong

reflectance of dry and melting snow; similar to NOAA-VHRR visible band)

MSS 6:0.7 - 0.8 pm - near infrared MSS 7:O.E - 1.1 pm - near infrared

(least water penetration, low reflectance from melting

. or metamorphose snow)

This multi-spectral imagery can be used separately, to obtain representative signatures in each of the four bands, or combined to give black and white or false colour composites. Landsat provides data for a given area at mid-latitudes once every 18 days. Convergence of swaths at high latitudes provides for more frequent coverage. When two Landsats are in orbit a temporal resolution of twice every eighteen days is provided, but even coverage at nine day intervals may be insufficient for many applications in operational hydrology over southern Canada and, in particular the Prairies. A significant proportion of the imagery (typically 50% or more) is unusable because of cloud cover. In addition, the data were not available in real time in 1977. "Quick-look" imagery could be obtained within about ten days, while corrected and annotated images were available within two or three months. In general, Landsat data are being used for research and to supplement NOAA VHRR and conventional ground data for operational snowcover analyses.

Landsat also has a data retrans- mission capability. It can collect surface observations for example, from precipitation gauges or snow pillows, and from automatic telemetering stations, and retransmit them to distant data collec- tion centers. This capability is useful in areas of significant snow storage that are remote or relatively inaccessible where it may not be feasible to install manned observing stations. With the

. Landsat system, simultaneous remotely- sensed imagery and ground based infor- mation can be collected, eliminating the significant problem of time lag in cor- relating the observations.

The NOAA satellites provide twice- daily coverage (mid-morning and late evening over southern Canada) of all areas in a swath width of about 1900 km, a width where distortion due to the earth's curvature is acceptable for snowcover analysis. The NOM-5 satellite in orbit in 1977 carried two observing systems, the Scanning Radiometer (SR) and the Very High Resolution Radiometer (VHRR). Both sensors provide data in the visible (0.6 - 0.7 pm) and the thermal infrared (10.5 - 12.5 urn). The resolution of the VHRR is 900 m at nadir, while the SR has a maximum reso- lution of 3 km.

IV.3.5.1. Recent snow studies and current applications. In 1968 the World Meteoro-

logical Organization initiated a project on "snow siudies by satellites", and subsequently published a status report and a report on an International Seminar (WMO, 1973, 1976) which incorporated results from a number of countries. The main emphasis in this project was the determination of the areal extent of snowcover, expressed as a fraction of the total basin area that was snow-covered to a depth of at least 5 cm, In a few cases the feasibility of determining other parameters, such as snow depth, was also examined. Canadian studies in support of the UMO project were cond-acted on the Saint John, Souris, Lake-of-the-Woods and Columbia basins. In general these studies were based primarily on MAA-VHRR data (Ferguson and Lapczak, 1977) using limited "ground truth" information. Landsat imagery was used to supplement the analy- sis and image analyzers (density slicers) were employed to carry out grey scale analyses of the images. Optical equipment was used to superimpose original or density sliced images on base maps. The feasibility of determining areal extent of snowcover by the method was demonstra- ted. Its accuracy is highest over non- forested terrain and lowest over areas of dense coniferous forests where the snow- cover may only be visible in larger clearings.

In some situations correlations have been found between image brightness and snow depth (McGinnis et al, 1975, Ferguson and Lapczak, 1977) but interpre- tation problems are formidable and a general operational technique has not been developed. Because of the inherent limitation of the penetration of visible light into the snowcover it seems likely that the determination of snow depth by remote sensing will have to rely on other portions of the spectrum, particularly the microwave wavelength band.

Operational snowcover mapping is being carried out by U.S. National Environment Satellite Service. A pre- cision of + 5% is claimed for areas greater than 5000 km2 (Wiesnet, 1974).

McGinnis et a1 (1975) suggest the improved VHRR of later NCAA satellites permits mapping of snow limits to better than 10 krn.

It has been recommended (WMO, 1976) that for operational hydrological pur- poses Landsat should be agplicd to basins with areas of 10 km2 or larger, NOAA VHRR imagery should not be used on watersheds smaller than 1000 krn2 and the minimum basin size for NOAA SR data

should be of the order of 10,000 km2. For hydrologic applications it would be desirable to adapt forecasting models to accept remote sensing inputs.

Satellite snowcover applications also include regional or hemispheric delineations of snow and ice cover. Hemispheric maps of snowcover are dis- tributed weekly by the National Oceanic and Atmospheric Administration (NOAA, 1977) which also prepares 10-day compo- site minimum brightness charts for detecting hcmispheric snowcover under changeable cloud conditions. These charts are updated daily, recorded on tape and displayed as photographic images.

At present, relatively simple optical-electrical interpretation tech- niques are being used for operational snowcover mapping using satellite data. These methqds involve elements of oper- ator skill and subjectivity. More sophisticated and objective digital analysis mathods have the potential to produce more accurate results, but they are still in the research and development stage. Suitable cost-effective digital analysis routines (based on the raw data with appropriate correction factors) will likely develop over the next few years. In that event, the imagery will still.be useful for visual comparison. Ground based information will still be needed for calibration and verification and for filling ga2s in the satellite data. Satellites are thus seen as one component of a total observing system which will continue to include surface observations.

This paper attempts to document the "state-of-the-art" on evaluating areal snowcover accumulation and distribution .A review of the major processes and fac- tors which govern accumulation patterns under mountain-forest and prairie envi- ror~rncnts is prcsented. Consideration is also given to methods of simulating and mcbsuring the areal differentiation of snowcover.

From this review it is evident that at the present time, because of the lack of knowledge of the snow transport and deposition proccsscs and the complex nature of the accumulation phcnon~ellon, it is impossible for thc hydrologist to dcfine by a physically-bdsed, matll~~~natical model snowcovcr distribution patterns. llencc, certilinly for the imnediatr future o1)el-cltianal hydro1ogist.s will continue to

rely very heavily on the use of ground measurements combined with cmpirical re- lationships and other mcasurcment tech- niques for obtaining estimates of basin snowcover. There is an urgent need howcvcr, for hydrologists and other users of snowcover data to establish the sensi- tivity of the system output to space-tine variable snowcover inputs. For examnle, for streamflow forecasting purposes, what lcvel of precision is needed in defining areal snowcover distribution to optimize streamflow prediction? Such information would serve the useful purpose in defining the sophistry and effort that need to be given to the snow accumulation and distri- bution problem.

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