Influence of avalanche snow transport on snowmelt runoff

Journal of Hydrology, ~37 (1992) 73-97

73

Elsevier Science Publishers B.V., A m s t e r d a m

[1]

Influence of avalanche snow transport on snowmelt runoff Fes A. de ScaUy Department of Geography, Okanagan University-College, 1000 K.L.O. Road, Kelowna, B,C. VI Y 4X8, Canada (Received 19 November 1991; accepted 8 January 1992)

ABSTRACT De Scally, F.A., 1992. Influence of avalanche snow transport on snowmelt runoff. J. Hydrol., 137: 73-97. The influence of avalanche snow transport on snowmelt runoff is investigate~ in a large basin (2500 km 2) in the Punjab Himalaya, Pakistan. The results of modelling based on field measurements show that, of the two main changes occurring during avalanching which affect the subsequent generation of snowmelt runoff---concentration of the snow and an ambient temperature increase resulting from the avalanches' fall to a lower elevation--the former is dominant on most avalanche paths. As a result, very high rates of surficial melting on avalanche snow are outweighed by the small surface area of the deposits, significantly decreasing the rate of meltwater production and delaying the disappearance of avalanche snow compared with undisturbed snow. The length of the delay is difficult to estimate accurately but is of the order ~f ~wo to three months on large avalanche paths. Calculations of the volume of avalanche snow in the basin indicate that, following a winter of maximum avalanche activity, such snow represents about 8 and 6% of the snowmelt runoff and a~mual runoff, respectively. In normal years these proportions are of" the order of I-2% and may still be exceptional for a basin of this size.

INTRODUCTION

Avalanche snow transport can have four types of impact on high-mountain hydrological systems. First, avalanches can provide a significant source of snow accumulation for glaciers (Kick, 1962; Iveror~ova, 1966; Kotlyakov, 1973; Tushinsky, 1975). Second, they can disturb the winter runoff regime through such effects as damming of rivers (Iveronova, 1966; Martinec, 1985). Third, through disruption of slope materials they can increase the incidence of mudflow and debris flow activity (iveronova, i 966; Sosedov and Seversky, 1966). Fourth, avalanches create snow deposits in which the processes of densification, ablation and runoff generation can differ from an Correspondence to: F.A. de Scally, D e p a r t m e n t o f Geography, O k a n a g a n University-College, 1000 K.L.O. Road, Kelowna, B.C. V I Y 4X8, Can~,da.

0022-1694/92/$05.00

© 1992 - - Elsevier Science Publishers B.V. All rights reserved

7~

F.A. DE SCALEr

undisturbed snow cover (Iveronova, 1966; Sosedov and Seversky, 1966; de Scally and Gardner, 1990). In ungla¢iated basins these differences may be the most important hydrological impact of avalanching (Iveronova, 1966; Sosedov and Seversky, 1966; Obled and Harder, 1979). The purpose of this paper is to report the ett~¢~ of avalanche activity on runoff in the Kunhar River basin, Punjab Himalaya, Pakistan. The research formed a part of the Snow and Ice Hydrology Project (1985-1989), a joint undertaking between the International Development Research Centre (Canada), the Water and Power Development Authority (Pakistan) and the Wilfrid Laurier University (Canada) researching the glacial and nival runoff sources of the upper Indus River basin. The generation of melt water from avalanche snow deposits is controlled by three changes which occur during avalanching (Zalikhanov, 1975; Martinec and De Quervain, 1975; Martinet, 1976; 1985; De Scally and Gardner, 1990). These are: (1) an increase in ambient air temperature owing to transpea of the snow from higher to lower elevations; (2) a reshaping and/or concentration of the snow body, increasing the snow density and reducing the surface area that is exposed to atmospheric energy exchanges; (3) a reduction in the snow surface albedo resulting primarily from the entrainment of debris, which increases the energy gain from solar radiation. Other changes in snow properties also occur which are usually manifested in the increased density. A number of Soviet studies show that avalanche deposits represent water temporarily withdrawn from spring snowmelt, producing a decrease in spring rul~off but an alimentation of flows during the summer and autumn (Lossev, 1960; lveronova, 1966; Sosedov and Seversky, 1966; Zalikhanov, 1975). Whether the production of snowmelt runoff is delayed or i:a fact accelerated by avalanching depends on which of the three changes outlined above is dominant. While (2) delays snowmelt, (1) aad (3) will accelerate it. The counteracting effects of the two most significant changes (1) and (2) are equal when a" T" A~sz) = a- (T + h. y). A(RZ)

(1)

where a is the melt factor or amount of snowmelt per day per degree of positive mean daily air temperature (i.e. daily average of positive temperature), T is the air temperature at the mean elevation of the starting zone, A~sz~and A~Rz)are the surface area oi the starting and runout zones respectively, h is the difference in elevation between A~sz)and A~z,~ and v is the tempere~ure lapse rate with elevation (Martinet, 1976). Martinet and De

AVALANCHE SNOW IRANSPORT

75

Quervain (1975) showed that avalanche activity can accelerate snowmelt if h or A¢RZ)or both are large. The uelay in melting noted in the Soviet literature appears to result from the significant concentration of the snow during avaianehing, producing a sinai! AtRz). The extent to which the changes described above affect snowmelt runoff from a basin depends largely on the proportion of the basin's snow cover which is avalanched. Various estimates put this proportion between 10 and 32% (Allix, 1924; Iveronova, 1966; Sosedov and Seversky, 1966; Lossev, 1967; Kotlyakov, 1973), with some estimates as high as 64% (ZahKhmz~,., ": '~. . . . 1975). The large range is due to differences in: the size and density of avalanche paths between regions; winter snowfall and other climatic parameters; the orientation of mountain slopes; the size of the basin being considered; methods of estimation. In some very small basins (of the ,,~vderof 1 kin2), avalanche snow has been estimated to represent 10-34% of the snowmelt runoff and 3-11% of the total annual runoff, depending on the severity of the winter (Sosedov and Seversky, 1966). The significance of basin size is discussed later in this paper. RESEARCH AREA

The Kunhar River (basin area = 2500 km 2) is a major tributary of the Jhelum River in the Punjab Himalaya of North-West Frontier Province, Pakistan (Fig. 1). The Kunhar was chosen for several reasons: snowmelt is a major component of the annual runoff regime; intense avalanche activity results in a major area-altitude redistribution of winter snow cover; the question of avalanche snow transport aad its effect on snowmelt runoff has direct relevance to run~,~ff foreca~tin~ r~odc!s for Mangla Dam (Fig. I). In addition, the Kunhar basin has relatively easy springtime access. The elevation of the Kunhar basin ranges from 800 to 5300m. In the vicinity of Naran village, where avalanche activity is most intense (Fig. 1), the vegetation consists primar~iy of coniferous forest and extensive cleared pasture and alpine tundra. A winter snow cover develops above i800m elevation from early November onwards, reaching a maximum depth in M~:rch or April. Snow wgter storage is greatly dependent on elevation, with the annual maximum in the Naran area showing an average iv:crease from 390ram at 2460m tc~ 1010mm at 3220m (Water and Power Development Authority, 1969). ;'gnowfat! and snow water storage also increase significantly in a northeasterly direction toward Babusar Pass (De Scally, 1989). Snowmelt begins in early April and lasts into July or even later at high elevations where it overlaps with the Indian m,msoon period. Temperatures ar~ generally high during the snowmelt period, averaging 13.9°C between May and October at

F.A. DE SCALLY

76 m

a=

• Town or Village "Saif,d Maluk Main" Climate Station Below 1850 m elevation: No signiffcant avalanche activity

(tI

tt

"~Above 1850

elevation:

Affected

10

/

20 k;TI

I

I

I

~~Elurawal 'v~8" " I "- ~''"~9

I r . , ~,.(

'! '~~

\

~.

'~.1"" •'P 2 'tpjMal' a5260m r bkaa ! l : /%

"~ "- '~

JDY AVALANCHE PATHS

Kaghan • I K . ..4

~ 1 2 3 4 5 6 7 8 9

i t

i

~

/. ~- "~

fNar'a:Z

I

Pass £ A _~l

I

i

N

~ a r -

by avalanches

I-7"iArea mapped for avalanche I _ I activity: Kaghan Valley l"~"IArea mapped for avalanche i ~-- l activity. Saiful Maluk basin 0 i

~

~

Chappran Nala Gorfan Kapan Jabbah Di Narr P,,3h~. Sa~ful Maluk Dhumduma Bagnar Kamra I

";"" U.S.S.R. :,', , " ~ 1t •i . . , . r "11 :;:.,"

| ',

.FGHAN,~;-""......... ie~" ;-; CH,.A 'TAN

I

t'"l o/

s.S Garb, Habib Ullah LMuzaffa~abad

1

¢',~-~o," .-,"

~;."" g.e c Ig.,.~p,~ ~

",..¢K2 a~.m

A NonoOu~

~'.,.~b~_l ~. -"

' r °,

.

.o-,otp,.d,~" ~I~~,.--- ~o,.,9,o[:)o~

i' el

/"

"-.._

Fig. I. Kunhar River basin in North-West Frontier Province. Pakistan, showing the location of the study area.

Battakundi (2660 m elevation). The amount of monsoon p~ecipitation (raostly rain) decreases markedly to the northeast, with the average May to October totals decreas,ing from 870mm at Balakot to 200ram at Battakundi (De Scally, 1989) As a result of this seasonal reversal of precipitation patterm,, the annual flow of the Kunhar River is dominated by snowmelt (Fig, 2)° T'otal annual flow at Garhi Habib Uiiah near the mouth of the basin is on aver'age 3.330 x 109 m 3 (Fig. 1).

A~/ALANCHE

SNOW

77

TRANSPORT

300

250 -

oow O tr <

/

\

150

O

t'~

Mean annual disch_Lar.ge-

C

•

¢,.~h./a~9.,. . . . . . . . . . . . . .

loo - ..........

~.

. . . . . . . . . . . . . . .

I

t

i

t

,

I

I

t

t

I

I

I

J

F

M

A

id

J

O

A

S

O

N

D

Fig. 2. Mean monthly discharge of the Kunhar River at Garhi Habib Ullah (1961-1968, 1976-1982). (Data from Water and Power Development Authority, 1969, 1975, and unpublished data.)

The Kunhar basin experiences intense avalanche activity above 1850m elevation (Fig. 1). Individual avalanche aeposits can represent in excess of i06 m 3 of water storage (De Scaliy and Gardner, 1989) and frequently persist into late summer and aatumn tm the larger avalanche paths. The largest paths have vertical falls approaching 2000 m and starting zone area~ in excess of 5 k m 2.

Nine avalanche paths were selected for study (Table 1 and Fig. l). Most have a northwest aspect which represents the most active orientation with respect to avalanche activity in the main valley. The paths are also judged to be representative in terms of their size and morphology. Data from three valley-bottom climate stations provide the climatic parameters required in the modelling. The Battakundi station (2660m) is operated by the Seed Potato Research Program. The Naran station (2,410 m) is operated by the Surface Water Hydrology branch of the Water and Power Development Authority. The 'Saiful Maluk Main' stzAion was operated by this project at an elevat~ion of 2830 m. The choice of station for the h~odelling of each path is based on its proximity~ i:a terms of elevation and distance, to the path's runout.

78

F.A. DE SCALLY

TABLE 1 Parameters of the study avalanche paths required in eqns. (2)-(8) Path

Chappran Nala Gorian Kapan Jabbah Di Narr Rahi Saiful Maluk Dhumduma Bagnar Kamra I

Year

1986 1987 1986 1987 1986 1987 1986 1987 1986 1987 1986 1987 1986 1987 1986 1987 1986 1~,7

Vertical fall h a (m)

Starting zone area A(sz, (m E)

550

165 356

1050

5 236 570

920

3 009 687

260

39 203

730

9 ! 1 140

570

240 350

1020

4306 106

1020

328 600

580

205 031

Runout zone area A,RZ,b (m:)

Concentration

16 593 23 027 262 959 239 118 119 005 139 540 335 a 0 8 365 d 12896 a 41 925 31 739 166616 136 041 44 318 36 879 6684 d ! 4 470 e

10.0 7.2 19.9 21.9 25.3 2 !.6 5.7 7.6 25.8 31.7 7.4 8.9 14.2

factor k c

" Measured from the mid-elevation of the starting zone to the top of the runout zone. h The surlace area of the avalanche deposit in each year is substituted for the runout zone area. Calculated by Aisz)/AtRz~. J The surface area of the deposit is too small to approxirtate the runout area; used only for calculating the total area of the paths. The avalanche deposit is small and the;efore the concentration factor may be too large.

METHODS

A two-part methodology is adopted in this study. First, the effect of avalanching on ablation is assessed for each avalanche path in order to understand any effect on the time distribution of runoff. The term ablation instead of snowmelt is subsequently used since the volumetric decrease in snow water equivalent involves not oa'y melting but meltwater percolation and evaporative losses. The relative importance of evaporation in the study area during the ablation season is dalscussed by.De Scally and Gardner (1990). ~;econd, the proportion of the basin sr:ow cover and hence snowmelt runoff whkh is affected by avalanching is analysed.

79

AVALANCHE SNOW TRANSPORT

Effects on ablation

Equation (1) shows that the increase in ambient air temperature and concentration of snow which occurs during avalanching, and which mainly control subsequent ablation of avalanche snow, are related primarily to the morphology of the avalanche path. The ambient temperature ir~.crease is related to the vertical fall; the concentration of the snow, measured by the concentration factor (A(sz)/A(Rz)), is related to the shape of the starting, track and runout zones. With these parameters available for seven of the ~ine study paths (Tabie 1) the effects on ablation are investigated using models modified from Martinec and De Quervain (1975). The modified equations are described below. Theoretically, snow is displaced as a full-depth avalanche from a starting zone with a surface area A(sz) Lnto a runout zone with a surface a r e a A(RZ)over a vertical distance h. The rtmout zone A(Rz) is assumed to include the track zone above it since the track frequently acts as a deposit area for avalanche snow. The starting zone area A(sz) of each patl~ was measured by field surveys as described by De Seally and Gardner (1989). The surface area of the avalanche deposits, measured in the spring of i986 and i987, is substituted for the runout zone area A(Rz)~vhich was impossible to survey in its entirety on most of the paths. The effects of this substitution are described later in this paper. The vertical fall h is taken as the difference between the mid-elevation of the starting zone and the highest elevation of the runout zone instead of its mid-elevation. This is done to reflect the significant volumes of avalanche snow stored in the track zones. The values of A(sz), A(Rz), h and the derived concentration factor (k = A(sz)/A(Rz)) are shown for the study paths in Table 1. In all ihe equations which follow, subse6pts have the following meaning: SZ and RZ stand for the starting and runout zones, respectively; U stands for a non-avalanche case or undisturbed snow; A stands for an avalanche case or avalanche snow. The average monthly rate of meltwater production (Q) on the av~ianche paths is mode!led for the 1986 and 1987 ablation periods using the equation Qu(sz) =

A(sz)" (au/100)" [T(Rz) -- Y" hi

QA(RZ)

A(RZ) ~ ( a A / 1 0 O ) " T(Fz~

--

(2) "

(3)

where Qu(sz) and QA(RZ)are in cubic metres per day (m 3day-~ ), A(sz) and A(RZ; are in square m e t r e s ( m 2) (Table 1), a is in centimetres per day per degree ,, -,_~ centigrade (cm day -~ ,., ), T is the average of the positive mean daily temo perature in each month (°C), and 7 is in degrees centigrade per metre (°C m-~ ). Values of 0.44crnday -t °C-~ and 0.56cmday-t °C -~ are used for au and aA

80

F.A. DE SCALLY

respectively, as detcrmined from detailed study by De Scally and Gardner (1990). A value of 0.0073 °C m -~ is used for y, as determined from an analysis of air temperature data from eleven pairs of stations over a wide range of elevations in 1986 and 1987 (De Scally, 1989). Mean monthly temperatures from the Naran, Battakundi and Saiful Maluk climate stations are used for T(RZ), since their elevations coincide closely with the elevations of the runout zones. Mean monthly temperature closely reflects the average of the positive mean daily temperature in each month because temperatures during the ablation periods only rarely fell below 0cC. The modelling is initiated when the mean monthly temperature rises above 0°C (March in 1986 and February in 1987) and is continued arbitrarily until September. The time of cessation of ablation (IE) or disappearance of snow on an avalanche path in the non-avalanche and avalanche cases is modelled with the equations

-tL

_i +

/'EA(RZj : t(P 2T_°_(RcZ])

CaU

-

C

q-2"[~(jip,;~JC.aA~° -i' ~/Vu(s_z).0"Sf "~ ]

t,,-' '<' l

~~ '0I(tRZ)c

(6)

where IEUtSZ), IEU(RZ) and /EAtRZ) are in days, To is the temperature at the beginning of the ablation period (°C), c is the rate of increase in positive mean daily temperature over the ablation period in degrees centigrade per day (°Cday-~), W is the water equivalent of the snow cover in centimetres (cm), and k is the concentration factor (Table I). All other terms are the same as in eqns. (2) and (3). The first above-freezing mean monthly temperature at the Battaktmdi station is used for Z,(RZ) (l.9°C in March iq86 and 1.6°C in February 1987). A value of 0.07°C day -~ for c is based on the calculated increase in mean daily temperature from April to September over a 7 year period at Battakundi, assuming that c can be represented by a linear function. The total winter precipitation (snow and rain) in 1986 and 1987 at Battakundi is corrected for the starting and runout zone elevations of each path (see previous sect,~rl ~'; entitled 'Research Area') and substituted for !~.¢sz~ and I'VU(RZ ) •

Equation (6) should produce large values of IE:~(RZ; siace it assumes that the entire snowpack Wu,sz) from the starting zone ,~(sz)avalanches into the runout eone A(RZ). Moreover, substitution of the ava::~nche deposit surface area for A(RZ) will p,'oduce slight overestimates of the concentration factor k for the study paths (Table 1), further increasi,g va~aes of tEA(RZ). To reflect the real

AVALANCHE SNOW TRANSPORT

8l

TABLE 2 Avalanche deposit volumes used in eqn. (7) Path

Year

Chappran Nala

1986 1987 1986 19E7 1986 1987 1986 1987 1986 1987 1986 1987 1986 ! 987 1986 1987 1986 1987

Gorian Kapan Jabbah Di Narr Rahi Saiful Maluk Dhumduma Bagnar Kamra I

Track zone deposit

Runout zone deposit

Total deposit volume V,RZ~

(m3) a

(m3) a

(m3) a

42 978 98 240 643 271 919 185 323 240 516 429 0 0 2952 0 52 513 47 888 268 941 5!9 20~ 72 881 91 ! 89 0 0

2038 3096 356 170 279460 211 355 123 096 1181 0 I 1 807 28813 58 471 61 930 332 447 150 741 21 496 8699 14 359 i I 741

45 9 ~6 101 336 999 44 l 198 645 534 595 639 525 11[~1 0 14 759 28813 i l0 984 109 818 601 388 669 946 94 377 99 879 14 359 11 741

a Water equivalent.

situation more closely, /EA(RZ)is also calculated for 1986 and t987 using the real volume of the avalanche deposits ('fable 2). The volume measurements were carried c~ut using the cross-section survey technique described by Schaerer (1988) and De Scally and Gardner (1989). The equation for tEA(RZ) in this case is /EA(RZ)

--

(I T°tRzi]2 _

¢

+

2{ WuIRZ) W [(V(Rz)/AtRz)) . IO0] }

)o.5 T°(Rz) (7)

¢ . aA

¢

where V is the avalanche deposit volume (cubic metres water equivalent). The other terms are the same as in eqns. (2)-(6). The relationship between h and k, which is the primary control on ablation following avalanching, is shown theoretically in eqn. (1) and diagrammatically by the results of eqn. (3). It can be investigated more closely by calculating the ratio of the rate of meltwater production in the noil-avalanche case to the avalanche case at specific times during the ablation period.

(Qu/QA)

82

F.A. DE SCALLY

The ratio is calculated by

Qu/QA = k . [T(sz)/T(Rz)] = k'{LT0tRZ)+ C . t] --

h}/[r0(RZ) + c. t] (8)

where the terms are the same as in eq~_s. (4)-(6) and t (in days) is equal to or greater than tEU(RZ)in eqn. (5). Whether the rate of meltwater production is increased or decreased in the avalanche case only becomes apparent at t > tEUtRZ).This is because, under the assumption that all of the snow in Atsz) avalanches, the total rate of meltwater production i~ the non-avalanche case is Qu(sz) + Qu(RZ), but only QA(RZ)(the same as Qu(RZ)) in ~he avalanche case. Therefore until the snow cover in the runout zone has disappeared at tEUtRZ) in eqn. (5), the rate of meltwater production is theoretically always greater in the non-avalanche case (Qu/QA > 1). Equation (8) is calculated |br 1986 and 1987 at t == tEU(SZ)and t = tEU(RZ)from eqns. (4) and (5).

Proportion of basfn runoff affected by avalanching The orooortion of snowmelt runoff and nnm~l r~,nr~ff' rr,-,,~ ,I.,,. ~.,_L.... basin that is affected by avalanche snow transport requires an estimate of avalanche snow storage in the entire basin. The total volume of such s:aow (VA in cubic metres water equivalent) is estimated using two techniques in order to provide a check on the assumption,,; necessary for both. First, for specific winters Vg is estimated by VA --- A A ' W u ' f

(9)

where AA is the area of the basin affected by ~valanching in square metres (m2), Wu is the average basin precipitation that winter in metres and f i s the average yield coe~cient, or proportion of Wu which is transported on avalanche paths, expressed as a fraction. Equation (9) is applied to eight winters from t.961 to 1968 when data on Wu and, for comparison, runoff data are available (Water and Power Development Authority, lq60, 1075). Estimation of average values of A A is described below. Wu in each year is taken as the total November to April precipitation or maximum snowpack water equivalent, whichever is greater, at measurernent sites in the Naran area (Fig. 1). The sites are located approximately at the hypsometric mean elevation of the Kuphar basin. A value of 0.0Q9 for f is obtained from other research on the study avalanche paths (De Scally and Gardner, 1989). The total area of avalanche slopes in the basin A A could not be directly meast:red owing to the lack of aerial photographs and high-resolution satellite imagery. Tkerefore an estimate is derived from ground mapping in two

AVALANCHE SNOW TRANSPORT

83

representative parts of the basin: a 50 km length -,f the main valley between Kaghan and Burawai representing a below-treeline environment, and the entire Saiful Maluk tributary basin representing an above-treeline environment (Fig. 1). The mapping is based on a variety of evidence for avalanche activity including: avalanche deposits; terrain conducive to avalanching; vegetative indicators; damaged dwellings; intbrmation provided by the local inhabitants. Avalanche path identification and evaluation in this densely populated environment is discussed further by De ScaUy and Gardner (1986). Both potential and active avalanche areas are drawn onto l :45000 scale topograpb, ic maps and the fraction of the total mapped area affected by avalanching measured. This fraction is then multiplied by the total area of the basin which is at a sufficiently high elevation to e×peiic~:ve avalanching, as determined from observations in the main valley (Fig. i). Any avalanche activity below this elevation (1850 m) appears to be insignificant both in terms of magnitude and frequency. The second method used to estimate Vx is extrapolation of the summed areas of the study avalanche paths and volumes of the snow ~eposits on them to AA (Tables 1 and 2). The assumption is made that the magnituae of snow transport on these paths was representative of the rest of the basin in 1986 and 1987. Runoff data from Garhi Habib Ullah are used for comparison with the estimated avalanche snow volumes. Data both on total snowmelt runoff and total annual runoff are available from 1961 to 1968 (Water and Pow.zr Development Authority, 1969, 1975). The separation of snowmelt runoff from sterm flows and baseflow in these records is judged to be relatively accurate even though some discrepancies exist between the snowmelt runoff and snow accumulation in the Naran area (Table 6). For 1986 and 1987, only data on total April to September runoff and total annual runoff are available. RESULTS Effects on ablatio;~ i

The results of eqns. (2) avd (3) show that on all of the avalanche paths in both years, the effect of the concentration factor k is dominant over the effect of the temperature increase which is a function of the path veitieal fall h. The result is much lower rates of meltwater production in the avalanche case compared with the non-avalanche case. This is illustrated by the 'Gorian' and 'Saiful Maluk' paths in Fig. 3, which are representative of large and moderate sized paths respectively. Meltwater production Iron the undiso turbed snow in each path's starting zone (Qu~sz)) is delayed uiLtil the tern-

84

F.A. DE SCALLY 250

,.~oOo

QU,SZ i

".,,o .°°°°%

/

"D

o on -

o

O.

2O

I

B

"

~

~:

I.-

I

I

I

..... °o,°°°°°°°°°°°~,O,o°

16 -

QUISZ)

......," . . . . . . .

"'".,.

12

8

_I, o

L FEB

............... ~ MAR

. ...............~ ............................... - -! i

APR

MAY

dUN

,JUL

AUG

.J

SEP

1986 .............

1987'

Fig. 3. Average monthly rate of meltwater production in the a i~che case (QA~z~) and non-av~la-che case (Qu(sz)), 1986 and 1987 ablation periods. A, 'Gorian' path; B, 'Salful Maluk' path. ....

perature climbs above 0°C. However, when ablation there does begin, the rote of meltwater production increases rapidly owing to :he large surface area A(szj (Fig 3). Ablation begins earlier in the runeut zones (QA(RZ)) because of their lower elevation, but the rate of meltwater production remains low owing to the small surtace area A(RZ) (Fig. 3). The results of eqns. (4)-(7) are shown in Table 3. On all avalanche paths in both years, undisturbed snow in the runout zor.e (i.e. without avalanching) disay,pears much sooner than undisturbed snow in the starting zone (leu(Rz) < IEU(SZ)),as a result of greater winter precipitation and lower temperatures in the latteL If all of the snow in the starting zone is assumed to avalanche into the runout where it is added to the existing undisturbed snow cover (eqn. (6)), the cessation of ablation is greatly delayed compared with the non-avalanche case (tE~(RZ) > tEU(SZ))on all paths. This delay averages 163 days (Table 4). If, on the other hand, the real volumes of the avalanche deposits are added to the existing undisturbed snow in the runouts ~eqn. ' (7)), the cessation of ablation in the avalanche case is accelerated compared with

AVALANCHE SNOW TRANSPORT

85

TABLE 3

Time of cessation of ablation according to eqns. (4)-(7) Path

Year

Equation (4) tEU(SZ)(days)

Equation (5) tEUiRZ)(days)

Equation (6) tEA(RZ) (days)

Equation (7) tEAtl~Z) (days)

Chappran Nala

1986 1987 1986 1987 1986 1987 1986 1987 1986 1987 1986 ! 987 1986 1987 i~8o 1987 1986 1987

! 31 146 214 230 192 208 77 90 163 179 140 i 56 209 225 2~9 225 141 158

49 59 49 59 49 59 49 59 49 59 56 67 49 59 .. 59 59 71

250 240 384 456 435 452 202 267 440 55| ""~ 287 367

109 116 128 153 ! 39 147 124 90 106 1! 1 132 125 152

Gorian Kapan Jabbah Di Narr Rahi

Saiful Maluk Dhumduma Bagnar Krmra I

oQ 115 103 R3

the non-avalanche case (/EA(RZ) < tEU(SZ))on all paths but one. The acceleration averages 57 days (Table 4). Only the 'Jabbah Di Narr' path in 1986 shows a delay. Actual observations on the study paths in 1986 and 1987 and information from local inhabitants indicate an approximate delay of two to three months to the cessation of ablation following avalanching. In other words, the undisturbed snow cover in the starting zones of the avalanche paths disappeals well before the avalanche depc~sit~ in the valley bottom do~ The ratios of the rate of meltwater production in the non-avalanche case to the avalanche: case, as calculated by eqn. (8), are shown in Table 5. The negative r a ~ s at tEU(RZ)reflect the fact that ablation in the starting zone of the large patb~ r,G o n•a n , 'Kapan', 'Dhumduma' and 'Bagnar') has not even cc,mmenced at the time that the undisturbed snow in the runout zone (nonavalanche case) disappears, because the mean daily temperarure at higher elevations (i.e. T(sz)) is still below 0°C~ On the moderate sized paths at tEU~RZ), the ratio Qu(sz)/Q/~,(Rz)ranges from 1.6 to 5.0, indicating that the concentration factor k is dominant over the vertical fall h arid therefore meltwater production in the avalanche case is slowed (Table 5). At tEu¢SZ)very large ratios of Qu(sz)!QA(az)are produced by eqn. (8) on all

86

F.A. DE S C A L L Y

TABLE

4

Acceleration or delay of the cessation of ablation following avalanching Path

Year

Chappran Nala Gorian Kapan Jabbah Di Narr

/EA(RZ) n

IEU(SZ) a

IEA(RZ ) _

(eqn. ( 7 ) - e q n

(days)

(days)

+ 119

-22

1987

+ 94

- 30

1986

+ 170

- 86

1987

+ 226

- 77

1986 1987

+ 243 +244

- 53 -61

i986

-

+47

1987

-

1986

Rahi

1986

-

- 73

-

Saiful Maluk

1987 1986

+ 62

- 73 - 29

Dhumduma

1987 1986

+ 111 + 231

- 24 - 84

1987

+ 326

Basnar

!986

+ 21

-

1987

+ 62

- 1 l0

Kamra

I

= Delay;-

(4))

- 73

II1

1986

-

- 38

1987

+ 209

- 75

+ 163

- 57

Mean "+

tEU{SZ) a

( e q n . (6)-eqn./~-~-~,,

-acceleration.

paths (Table 5). The ratio at this time averages 9.3, reflecting the clear dominance of the concentration factor k over the vertical fall h. Further calculations show that as the temperature T increases, the effect of the concentration factor k becomes even more dominant and hence the ratio Qu(sz)/ QA(RZ)even larger. Basin area affected by avalanches

The total area mapped for avalanche activity is 288 km 2 which represents 14% of the Kunhar basin at a sufficiently high elevation to experience avalanching (Fig. 1). In the main valley, 63% of the total mapped area is affected by active or potential avalanching whereas in the Saiful Maluk basin this figure is 73%, with an overall average of 65%. The average size of individual avala_nehe paths is 0.48 km z. The average proportion of slope area potentially affected by avalanching (65%) combined with the area of the basin high enough to experience

87

AVALANCHE SNOW TRANSPORT

TABLE 5 Ratio o f the rate o f m e l t w a t e r p r o d u c t i o n in the n o n - a v a l a n c h e case to the avalanche case using eqn. (8) Path

Chappran Nala Gorian Kapan Saiful M a l u k Dhumduma Bagnar Kamra I Mean

Qutsz) / QAtRZ)" a t tEU(RZ) b

Qutsz) / QA(RZ)a at tEU(SZ)c

I986

1987

1986

1987

2.5 - 8.7 d - 6.6 d 1.6 - 10.3 d - 2.9 d -

2.2 - 7.4 d - 3.7 d 2.6 - 9.5 d - 2.7 d 5.0

6.4 10.9 14.2 3.7 14.2 4.1 -

4.8 12.4 12.6 5.1 18.1 5.1 9.4 9.3

a R a t i o o f the rate o f m e l t w a t e r p r o d u c t i o n in the non-avalanche case to the avalanche case. bSee eqn. 5. ¢ See eqn. 4. d Negative ratios represent situations where m e l t w a t e r production is occurring in the r u n o u t zone b u t not in the starting zone.

avalanche activity (2110km 2) yields a total avalanche area of 1372km 2, representing 54% of the entire Kunhar basin. This represents a maximum, since all avalanche paths are assumed to be active. The basin area actually affected by avalanching during the 1961-1968 winters is not known. Therefore, a conservative density of one avalanche per 2.5 km 2 during a normal winter is assumed (LaChapelle, 1968). For comparison, this density appears to have been about two to three times higher in i986 and i987, following two moderate to bad avalanche winters according to local sources. If the 21 l0 k m 2 is combined with the assumed density of path~ and the average mapped path size (0.48 km2), the result is 389 km 2 of total avalanche area, representing 15% of the entire Kunhar basin.

Proportion of basin runoff affected The total volumes of avalanche snow in the basin calculated tar the 19611968 winters using eqn. (9) are shown in Table 6. Values of 1372 and 389 km 2 are used for AA, representing intense and normal avalanche conditions respectively (see above). Table 6 shows that with intense avalanching, on average 7.6% of the snowmelt runoff and 4.8% of the annual runoff of the Kunhar River are supplied by avalanche snow. The proportion of the snowmelt runoff agrees quite closely with the percentage of basin snow cover

88

F.A. DE SCALLY

TABLE 6 Proportion of Kunhar River runoff gtored as avalanche snow, 1961-1968 Year

Winter snow accumulation Wu a (m water equivalent)

Kunhal River i tmoff h (10Sm 3) Snowmelt c

Annual

1961

0.897

17.76

28.86

1962

0.594

15.17

27.26

1963

1.541

19.86

22.32

1964

1.123

23.07

36.26

1965

1.590

27.14

40.46

1966

1.448

22.82

35.52

1967

1.372

22.70

37.37

1968

0.996

19.49

31.58

Mean

Volume o| ° avalanche snow VAa'r (10 s m 3 water equivalent) Intense e

NormaF

1.22 (6.9, 4.2) 0.81 (5.3, 3.0) 2.09 (10.5, 6.5) 1.52 (6.6, 4.2) 2.16 (8.0, 5.3) 1.97 (8.6, 5.5) 1.86 (8.2, 5.0) 1.35 (6.9, 4.3) 1.62 (7.6, 4.8)

0.34 (2.0, 1.2) 0.23 (1.5, 0.8) 0.59 (3.0, 1.8) 0.43 (Y.9, 1.2) 0.61 (2.3, 1.5) 0.56 (2.4, 1.6) 0.53 (2.3, 1.4) 0.38 (2.0, 1.2) 0.46 (2.2, !.4)

~'See eqn. (9); November-April precipitation in Naran (2460 m) or maximum snowt~ack water storage at Lake Saifui Maluk (3220m), whichever is greater (source: Water and Powe~ Develo~,nent Authority, 1969). b Measured at Garhi Habib Ullah (source: Water aad Power Development Authority. 1969, 1975). CTotal snown ielt runoff only. ,See eqn. (9). °h ~nse = i372km2; Nornlal = 389km ~, affected by avalanching. f Ve~ues in parentheses represent the percentage supp!ied by avalanche snow to snowmelt (first value) and annual runoff (~econd value) for the Kunhar River.

which is potentially affected by avalanching (6.4%). This percentage is obtained by multiplying the fraction of slopes potentially affected by avalanche activity (0.65) with the average yield coefficient f i n eqn. (9) (0.099). FolloMng a normal winter, avalanche snow supplies on average 2.2% of the snowmelt runoff and 1.4% of the,, annual runoff (Table 6). The mean percentage of the Kunhar's annual flow derived from snowmelt (65%; Table 6) agrees closely with more recent estimates by Hewitt (1985).

AVALANCHE SNOW TRANSPORT

89

The total volume of avalanche snow (water equivalent) on the study paths was measured to be 2412446m 3 in 1986 and 2820568m 3 in 19,87 (Table 2). Extrapolation of these totals to the 1372 k m 2 a r e a potentially affected by intense avalanche activity y~elds total basin snow volumes of 2.12 x ] 0 S m 3 (1986) and 2.48 x 10Sm s (1987). These represent on average 7.8% of the April to September runoff and 6.6% of the annual runoff of the Kunbmr in those two years. Extrapolation of the avalanche snow volumes from the study paths to the 389km 2 area affected by hypothetically normal avalanching yields total basin snow volumes of 6.02 x 107 m 3 (1986) and 7.03 x 10 7 m 3 (1987). These represent on average 2.2% of the April to September runoff and 1.8% of the annual runoff. DISCUSSION

Effects on ablation

The results at' eqns. """ '~x and (8) show that the concentration of snow during avalanching results in significantly lower rates of meltwater release from the avalanche deposit compared with the undisturbed snow cover in the starting zone. Figure 3 and Table 5 show this difference to increase as air temperature increases during the ablation season. Whether the avalanche deposit actually persists longer than the undisturbed snow cover in the starting zone depends on the total volume of the deposit. The substitution of ,~ the surface area of the avalanche deposits for the runout zone area reflects reality relatively well, because on six of the nine study paths most of the track and runout was covered by avalanche snow in 1986 and 1987. At any rate the runout of most confined paths is very small in comparison with the starting zone. :I'he mean concentration factor on the study paths (15.9; Table 1) agrees with the range of values (IG-18) reported by Zalikhanov (1975). The average for the large paths (24.4 for 'Gorian', 'Kapan' and 'Dhumduma') may in fact be the most realistic s~nce almost all of the runout was covered by avalanche snow in 1986 and 1987. However, eqns. (2), (3) and (8) fail to take into account the changing ratio of the snow covered areas in th: starting and runout zones as ablation proceeds. Equations (4) and (5) provide realb:tic estimates of the time of disappearance of the undisturbed snow cover in the starting and runout zones of avalanche paths if there is no avalanching (Table 3). However, eqns. (6) and (7) both have problems predicting the actual time of disappearance of avalanche snow in the runout. The anrealistically large delays produced by eqn. (6) result from the assumption that all of the snow in the starting zone

90

F.A. DE SCALLY

avalanches into the runout zone (Table !). Therefore, even though the concentration factors may be realistic, the depth of the snow deposit generated in eqn. (6) is still too great. Nevertheless, the equation is useful because it illustrates the magnitude of the delay in the disappearance of winter snow which could be produced by very intense avalanche activity. Equation (7) is more realistic than eqn. (6) because it takes into account the t,~ runout and track zones. However, me real volume of avalanched snow in "'-apparent disappearance of this snow faster than in the non-avalan~zhe case i~ misleading because eqn. (7) assumes the avalanche deposits to be evenly distributed (i.e. of uniform depth throughout). Extensive field observations indicate that although the thin, spread-out portions of' each deposit do disappear rapidly, snow concentrated in gullies and other terrain concav!,ties provides a very small surface area and therefore melts slowly (Fig, 4). Degosits in gullied track zones are especially significant in this regard and are mainly responsible for the two to three months observed delay in the disappearance of snow on the large paths following avalanche activity Avalanche snow in the track zone accounts on average for 51% of the total de~;~o;;iton the study paths in both years, and 74% on those paths with deeply gullied tracks ('Chappran Nala', 'Gorian', 'Kapan' and 'Dhumduma') (Table 2). This percentage appears to increase in years of less-severe avalanche activity because less snow is transported all the way into the runout zone. Therefore, the term 'track zone' in many cases applies only to d~e morphology of the paths (Martinelli, 1974) and not to snow deposition characteristics. The two to three months delay is also evident from anecdotes of valley bottom deposits lingering into October and even later in some years. Also~ probing of the large avalanche deposits in 1987 appears to indicate that some of the avalaeche snow from the 1985-1986 winter survived through to the following winter. The results of this study are in contrast to those of Martinec and De Quervain (1975) who demonstrated that avalanche activity can accelerate the disappearance of winter snow. Acceleration only occurs on smaller, lessconfined paths in the Kunhar basin where the snow is not concentrated to any great degree during avalanching. The delay in the disappearance of avalanche snow in this study agrees with delays reported by Lossev (1960), Sosedov and Seversky (1966) and Zalikhanov (1975). However, in all of the,,;e studies including this one, the basin-wide delay is difficult to estimate. Furthermore the extent to which this delay is compensated for by rapid melting of unconfined and low-elevation avalanche deposits early in the ablation period is not known. A further complicating factor is the poz~sible delay caused by infiltration of the avalanche deposit melt water into alhwial deposits in the valley bottoms. This delay is probably not all that significant s~nce the characteristically coarse sediments and confined valley bottoms would ensure .

.

AVALANCHE SNOW TRANSPORT

91

,,+

(b)

......

•

"

+

~.~t))))~

Fig. 4. Effect of avalanche deposit concentration on ablation. A sequence of photographs from the 'Kapan + path which shows the rapid disappearance of thin, spread-out portions ol the deposit and slow ablation ofconcentra,eu .... i,,,,,,h~ ~naw. In ohotograph a, 81% of the total deposit is concenfrated in the deeply gullied track zone (see Table 2). a, 28 May 1987; b, 1 July 1987. +

+

<,11

u

t. t.gJ ¢.k~ . ~ , l t , ~

•

92

F.A. DE SCALLY

relatively rapid routing of sub-surface water to stream channels. Iveronova (1966) and Sosedov and Seversky (1966) estimated that very little, if any, avalanche snow melt water infiltrates into the ground and therefore avalanche activity may slightly increase the total basin runoff compared with normal snowmelt. A number of simplifying assumptions in eqns. (2)-(8) may affect the results presented here. First, the elevation ranges of both the starting zones and deposit areas are significant and so their characteriz~.tion by an average elevation is overly simplistic. On the larger paths in this study ('Gorian', 'Kapan' and 'Dhumduma') the elevation range of the starting zone or deposit area is as much as 1000m. Second, the assumption in eqns. (4)-(8) that continuous ablation is initiated when the mean monthly temperature rises above 0°C may be erroneous, because in this environment the snowpack may continue to accumulate even in relatively warm conditions. Data from the Water and Power Development Authority (1969) indicate that at lower elevations the snowpack depth peaks in February or March, even though the average temperature has risen above 0°C by this time. Third, the total winter precipitation in the starting zone (Wu(sz)) is derived from elevationally corrected data from Battakundi. The Battakundi station and the precipitation gradient used for the corrections (see previous section entitled 'Research Area') are assumed to be representative of the study area. Fourth, the use of a linear function to represent the increase in positive mean daily temperature (c) during the ablation period is overly simplistic. For example mean daily air temperature in the study area in 1986 and 1987 began to decline after August, meaning that eqn. (6) in this respect is underestimating the date of disappearance of avalanche snow. The air-temperature-based melt factor (a) should produce good estimates of real ablation rates since a strong statistical relationship is shown to exist between temperature and ablation; in addition, the melt factor does not show any consistent pattern of change over the course of the ablation season (De Scally and Gardner, 1990). Improvement of the models to eliminate some of these assumptions is probably not worthwhile, since the major weakness of the models appears to be their inability to account for the distribution of avalanched snow in the deposit area.

Basin area affected by avalanches The percentage of slopes surveyed to be potential avalanche areas (on average 65%) is according to observations quite representative of the Kunhar basin above 1850m elevation. Percentages of 12-15% in moderate winters and 42-43% in snowy winters are reported from the northern Tien Shan Mountains (Sosedov and Seversky, 1966). However, with an average area of

AVALANCHE SNOW TRANSPORT

93

1.2 k m 2 and average gradient of 33° the 'basins' which these figures are derived from appear to be individual awdanche paths rather than stream basins of any significant size. The percentage in this study is therefore extremely high, representing 54% of the Kunhar basin's total 2500 km 2 area. Even the conservative assumption of one avalanche per 2.5 km 2 in a normal winter means that 15% of the total basin area would consist of avalanche slopes. The intense and widespread zvalanche activity is due to a combination of steep slopes, heavy winter snowfalls with frequent thaws, extensive above-treeline areas and widespread removal of forests and other vegetation anchoring the snowpack on slopes.

Proportion of basin runoff affected The percentage of the total snow cover above 1850m elevation that is potentially affected by avalanching (6%) is lower than the 7-12% (normal winters) and 20-65% (snowy winters) reported by Iveronova (1966), Sosedov and Seversky (1966), Lossev (1967) and Kotlyakov (1973). This figure for the Kunhar basin should not exceed 19% which is based on maximum values of the percentage of slope area affected by avalanche activity (73%) and the avalanche path yield coefficient f (0.258; de Scally and Gardner, 1989). The Soviet literature again appears to refer to individual large avalanche paths and not stream basins of any significant size. Their reported percentages are therefore more appropriately compared with the avalanche path yield coefficient f alone, which is described in more detail by Schaerer (1988) and De Scally and Gardner (1989). The two different methods of estimating the percentage of the Kun!~ar River's runoff stored as avalanche snow give very similar results. Therefore i~t appears reasonably certain that following a severe winter (i.e. all potential avalanche slopes are active) avalanche snow makes up approximately 8% of snowmelt runoff and 5-7% of annual runoff. Following a normal winter these proportions are of the order of 1-2%. However, it is difficult to judge how closely the assumed intensity of avalanching reflects a normal winter without longer-term observations in the area. Sosedov and Seversky (1966) estimated that 10-34% of snowmelt runoff and 3-11% of annual runoff are derived from avalanche-transported snow in their study. In light of the very small size of their study basins the percentages for the Kunhar basin are much more significant. The primary weakness of eqn. (9) is its reliance on average values of the basin ,~rea affected by avalanches (AA), yield coefficient ( f ) and winter precipitation (Wu), all of which are highly variable, both spatially and from year to year. The accuracy of the second technique, in which the avalanche deposit volumes from the study paths are extrapolated to the basin, is difficult

94

F.A. DE SCALLY

to assess because, although the paths are quite representative of the basin, it is not clear whether the deposits on them in 1986 and 1987 were. The results of this research have implications for water supply in the Kunhar-Jhelum system. The release of melt water from avalanche snow overlaps considerably with inputs of monsoon rainfall beginning in late June, but the magnitude oi" the overlap cannot be estimated precisely. A number of scenarios for warm-.season flows are possible. First, following a winter with heavy snowfall and intense avalanche activity, above-average flows early in the summer from low-elevation snowmelt may be followed by very high la~e-summer flows from avalanche deposit melting, monsoon rain and continued melting of the undisturbed snowpack at high elevations. Second, a ~inter with light snowfall and little avalanche activity will produce belowaverage flows until the arrival of the monsoon, and even then monsoon storms :~nay ,,~'~ penetrate su~ciently far into the Kunhar basin to increase flows substahLially (De Scally, 1989). Third, contributions from avalanche deposit melting would be most significant in a summer of low monsoon rainfall preceded by a winte/" of intense avalanche a~:tiv~ty. Such activity is possible without heavy snowfall because, although avalanching is to some degree related to total winter snowfall, it is more specifically the result of all of the meteorological factors which toge~.her govern the development of the snowpack structure, snowpack loading and avalanche triggering. Hahn and Shukla (1976), Dey and Bhanu Kumar (1982, 1983) and Bhanu Kumar (1987) suggested that a negative feedback mechanism operates between the amount or extent of winter snow cover and the intensity and timing of subsequent monsoon rainfall in southern Asia. If this is the case, low snowmelt-generated river flows would be compensated for by greater monsoon rainfall and vice versa. The operation of such a natural regulatory mechanism would affect all of the scenarios outlined above. CONCLUSIONS

The results of ~his research show that, on most moderate to large avalanche paths in the Kunhar River basin, the effect of the concentration of snow during avalanching significantly outweighs tS.e effect of the increase in ambient air temperature resulting from the avalanches' fall. The high degree of concentration is related to the path morphology which in the study area is generally deeply confined. As a result, a :ignificant delay occurs in the melting of large quantities of avalanche-transported snow compared with the undisturbed snow cover. The simple models used in this study cannot estimate the length of this delay precisely; however, field observations suggest that avalanche snow continues to contribute significantly to runoff two to three

AVALANCHE SNOW TRANSPORT

95

months after the disappearance of undisturbed snow cover from the avalanche paths. A large proportion of slopes in the Kanhar basin is affected by avalanche activity but the percentage of snow cover which is transported by avalanches on these slopes is on average only 10%. As a result avalanche-transported snow represents about 8% of snowmelt runoff and 6% of annual runoff from the basin following a winter of severe avalanching. These percentages in more-or-less normal avalanche years are of the order of 1-2%, which may still be exceptionai for a basin of this size. The effect of avalanche snow melting on the flow of the Kunhar River is complicated by the summer monsoon as well as a possible negative feedback mechanism between winter snow cover and the strength of the monsoon. ACKNOWLEDGEMENTS

This research was funded by the International Development Research Centre (IDRC) (Canada) and the Water and Power Development Authority (WAPDA) (Pakistan) through the Snow and Ice Hydrology Project (Wilfrid Laurier University (WLU), Waterloo, Canada), and by a personal research award from IDRC. The field assistance of G. Veale and I. Bell (University of Waterloo, Waterloo, Canada), H. Afzal, M. Mohammed, M. Anwar and M. Younis (WAPDA) and R. Lall (WLU) is much appreciated. Other data were supplied by the Seed Potato Research Program (Abbottabad) and WAPDA Hydrology and Investigations Directorate (Lahore), Pakistan. P. Schaerer (National Research Council Canada, Vancouver) made valuable suggestions to a draft of this paper. REFERENCES Allix, A., 1924. Avalanches. Geog. Rev., XIV: 519-560. Bhanu Kumar, O.S.R.U., 1987. Seasonal variation of Eurasian snow cover and its impact on the Indian summer monsoon, in: Large Scale Effects of Seasonal Snow Cover. international Association of Scientific Hydrology, Gentbrugge, Publ. 166, pp. 51-60. De Scally, F.A., 1989. The Role of Avalanche Snow Transport in Seasonal Snowmelt, Himalaya Mountains, Pakistan. Ph.D. Thesis, University of Waterloo (unpublished). De Scally, F.A. and Gardner, J.S., 1986. Avalanche hazard in Kaghan Valley, Himalaya Range, Pakistan. In. Proc. Int. Snow Science Workshop, 22-25 October 1986, Lake Tahoe, California. ISSW Workshop Committee, Homewood, CA/University of California, Santa Barbara, CA, pp. 21-28. De Scally, F.A. and Gardner, J.S., 1989. Evaluation of avalanche-mass determination approaches: an example from the Itimalaya, Pakistan. ~. Glaciol., 35: 248-252. De Scally, F.A. and Gardner, J.S., 1990. Ablation of avalanched and undisturbed snow, Himalaya Mountains, Pakistan. Water Resour. Res., 26: 2757-2767. Dey, B. and Bhanu Kumar, O.S.R.U., 1982. An apparent relationship between Eurasian spring

96

F.A. DE SCALLY

snow ceve~" and the advance of the Indian summer monsoon. J. Appl. Meteorol., 21: 1929-1932. Dey, B. and Bhanu Kumar, O.S.R.U., 1983. Himalayan winter snow cover area and summer monsoon rainfall over India. J. Geophys. Re~., 88: 5471-5474. Hahn, D.G. and Shukla, J., 1976. An apparent relationship be:ween Eurasian snow cover and Indian monsoon rainfall. J. Atmos. Sci., 33: 2461-2462. Hewitt~ K., 1985. ~now and Ice Hydrology in Remote, High Mountain Regions: the Himalayan Sources of the R~vcr Indus. Snow and ice Hydrology Project, Working Paper l, Wilfrid Laurier University. Iveronova, M.I., 1966. The hydrological role of avalanches, in: Int. Symp. Scientific Aspects of Snow and Ice Avalanches. International Association of Scientific Hydrology, Gentbrugge, Publ. 69, pp. 73-77. Kick, W., 1962. Variations of some central Asiatic glaciers. In: Variations of the Regime of Existing Glaciers. International Association of Scientific Hydrology, Gentbrugge, Publ. 58, pp. 223-229. Kofiyakov, V.M., 1973. Snow accumulation on mountain glaciers. In: The Role of Snow and Ice in Hydrology. International Association of Scientific Hydrology, Gentbrugge, Publ. ! 07, vol. l, pp. 394-400. LaChapelle, E.R., 1968. The character of snow avalanching induced by the Alaska earthquake. In: Great Alaska F,arthquake of 1964. Hydrology. National Research Council, National Academy of Sciences, Washington, Pub!. 1603, pp. 355-361. Lossev, K.S., 1960. Avalanches as the hydrological factor. Meteorol. Hydrol., 5. Lossev, K.S., 1967. The role of avalanches in mass budget of glaciers. In: Physics of Snow and Ice. Proc. Int. Conf. on Low Temperature Science, Sapporo (Vol. I). Institute of Low Temperature Science, Hokkaido University, lap. 385-388. Martinec, J., 1976. Snow and ice. In: J.C. Rodda (Editor), Facets of Hydrology. Wiley, Bristol, pp. 85-118. Martinec, J., 1985. Time in hydrology. In: J,C. Rodda (Editor), Fa.',ets of Hydrology II. Wiley, Chichester, pp. 249-290. Martinet, J. and de Quervain, M.R., 1975. The effect of snow displacement by avalanches on snowmelt and runoff. In: Snow and Ice Syrup., Moscow, 1971. International Association of Scientific Hydrology, Gentbrugge, Publ. 104, pp. 364-377. Martinelli, M., Jr., 1974. Snow avalanche sites: their identification and evaluation. US Department of Agriculture, Agricultural Information Bulletin 360, US Government Printing Office, Washington. Obled, Ch. and Harder, H., 1979. A review of snowmelt in a mountain environment. In: S.C. Colbeck and M. Ray (Editors), Proc., Modeling of Snow Cover Runoff, Hanover, 1978. US Army Cold Regions Research and Engineering Laboratory, Hanover, OP. 179-204. Schaerer, P.A., 1988. The yield of avalanche snow at Rogers Pass, British Columbia, C~nada. J. Glaciol., 34:188-193. Sosedov, I.S. and Seversky, I.V., 1966. On hydrological role of snow avalanches in the northern slope of the Z~iliyusky Alatau. In: Int. Symp. Scientific Aspects of Snow and Ice Avalanches. h~ternational Association of Scientific Hydrology, Gentbrugge, Pubi. 69, pp. 78-85. Tushinsky, G.K., 1975. The part avalanches play in the formation and dynamics of mountain glaciers and snow patches in the territory of the U.S.S.R. In: Snow and Ice Syrup., Moscow, 1971. International Association of Scientific Hydrology, Gentbrugge, Publ. 104, pp. 381-389.

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97

Water and Power Development Authority, 1969. Snow Surveys of West Pakistan, 1961-1963. Surface Water Hydrology, Water and Power Development Authority, Lahore. Water and Power Development Authorit), 1975. Sediment Appraisal of West Pakistan Rivers, 1960-1972. Planning and Investigation Division, Water and Power Dcveiopment Authority, Lahore. Zalikhauov, M.Ch., 1975. Hydrological role of avalanches in the Caucasus. In: Snow and Ice Syrup., Moscow, 1971. International Association of Scientific Hydrology, Gentbrug~e, Publ. 104., pp. 390-394.