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Evaporation of intercepted snow: measurement and modelling
Journal of
Hydrology ELS EVI E R
Journal of Hydrology 206 (1998) 151-163
Evaporation of intercepted snow: measurement and modelling Angela Lundberg a'*, Ian Calder b, Richard Harding b "Division of Water Resources Engineering, Lulegt Universi~ of Technology, Lule~t, Sweden blnstitute of Hydrology, Wallingford, Oxfordshire, UK Received 14 May 1996; accepted 25 January 1997
Abstract Snow storage on a coniferous forest canopy was measured using y-ray attenuation and tree weighing systems, along with measurements of throughfall, using two plastic sheet net rainfall gauges. Meteorological parameters were measured with an automatic weather station. Estimates of evaporation of intercepted snow show an average rate of 0.24 mm h -~ and a maximum cumulative total of 3.9 mm in 7 h. Comparison with evaporation determined by a combination method with two different estimates of aerodynamic resistance (the " s t a n d a r d " rain aerodynamic resistance raL and a snow aerodynamic resistance r ~ s - - a n order of.magnitude larger than raL) showed that raL overestimated the evaporation by a factor of 2.6, whereas ras gave fair agreement with the measured evaporation. A multilayer model may be needed to take into account the variations of latent heat source area. Using the long-term measurements of the weight of snow on a single tree the total interception evaporation was estimated to be of the order 200 m m year 1. © 1998 Elsevier Science B.V. All rights reserved.
Keywords: Snow storage; Interception evaporation; Modelling; Forest
1. Introduction
Several studies during the last decade have emphasised the importance of evaporation of intercepted snow (Calder, 1985; Calder, 1990; Schmidt et al., 1988; Schmidt, 1991; Lundberg, 1993; Nakai et al., 1993; Nakai et al., 1995; Nakai et al., 1996; Lundberg and Halldin, 1994; Claassen and Downey, 1995). Pomeroy and Gray (1995) estimate that one-third of the winter snowfall in central Canada is lost through evaporation of snow intercepted on forest canopies. It is evident, therefore, that water resources models used in northern forested areas must describe correctly the lodging, and subsequent evaporation of snow. Bonan et al. (1992) and Thomas and Rowntree (1992) have *
Corresponding author.
0022-1694/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PH S0022- 1694(97)00016-4
used general circulation models to investigate the role of boreal forest in a global climate. Both these studies highlighted the importance to climate of the interaction between the forest and snow cover. General circulation models are increasingly incorporating realistic surface schemes and it is essential that the energy and water budget of snow on a coniferous forest canopy is correctly described. When assessing the amount of snow that is lost by evaporation, process studies of the intercepted snow become important. Classical interception studies of the type used for rainfall, in which precipitation beneath the canopy is compared with that outside, are less successful in the case of snow where the measurements of precipitation input are particularly prone to error. To circumvent this problem process, studies of snow interception generally aim to measure
152
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163
the amount of snow on the forest canopy; such studies are presented by Calder (1990), Schmidt (1991) and Lundberg and Halldin (1994). Schmidt (1991) treated dry snow conditions and Lundberg and Halldin (1994) considered wet snow, whereas Calder (1990) attempted to model both dry and wet snow conditions. W h e n snow covers a canopy the resulting surface generally becomes aerodynamically much smoother than that of a rain-wetted canopy. It would therefore be expected that the evaporation rates from a snowcovered canopy would be lower than from a rainwetted canopy. However, the water equivalent of the snow stored on a forest canopy can be an order of magnitude larger than that of a rain-wetted canopy and thus the potential is considerably larger for evaporation when the precipitation stops. Since the ventilation term is dominant in the equation for evaporation of intercepted snow, the evaporation values are very sensitive to the way the aerodynamic resistance is calculated, (Lundberg and Halldin, 1994). Using data from Aviemore, Scotland, Calder (1990) by optimisation found an order of magnitude difference in aerodynamic resistance between a snowcovered and a rain-covered canopy and these findings are partly confirmed at a site in Sweden by Lundberg and Halldin (1994). According to Schmidt (1991) a large exposed snow surface area gives a higher evaporation rate per unit intercepted mass than a small exposed surface area. Both the total snow-covered area and the roughness of the surface elements contribute to the efficiency of the transfers between the snow on the canopy and the atmosphere. A number of researchers have suggested that the roughness length for heat is approximately one order of magnitude less than that for momentum (see Lankreijer et el., 1993). Lankreijer et el. (1993) found that an aerodynamic resistance for heat one-half that of momentum (corresponding to an order of magnitude change in roughness length) improved the models of interception loss from a rain-wetted forest canopy. This paper presents a re-analysis of the "y-ray attenuation measurements described by Calder (1990) to describe in detail the climatic conditions during events with evaporation of dry intercepted snow and to discuss how to model the aerodynamic resistance during snow conditions. Longer term measurements of the duration of snow cover on a single tree are used to estimate the losses
from a snow-covered canopy over two entire winter seasons.
2. Measurements This paper presents some detailed snow measurements made in north-east Scotland over two winters. The measurement system, a ~,-ray attenuation rig, was operated intermittently during the winters of 1 9 8 3 1984 and 1984-1985. A total of 16 storms, some incomplete, were recorded. Periods with high precipitation are omitted, since measurement of solid precipitation is inaccurate (Hanson et al., 1983) and periods with low canopy storage were also excluded to avoid uncertainties with modelling the reduction in evaporation due to incomplete canopy cover. To isolate the snow evaporation process from the rain evaporation process, occasions when most of the snow was melted, were omitted. This paper presents in detail the measurements from three events. During the first ( 1 6 - 1 9 March, 1985), 15 m m water equivalent of snow was deposited on the forest canopy in the first day and during the subsequent 3 days a substantial amount evaporated. The two other events (28 and 30 March, 1985) were shorter events with initial storage of approximately 9 mm; again a substantial proportion of the canopy storage evaporated. All events had mainly dry snow on the trees with little precipitation after the initial snowfall. In addition to these intensive measurements, a system monitoring the weight of a single tree was operated for both winters.
2.1. Experimental site The experimental site was located at Queens Forest near Aviemore in the Highland Region of Scotland, longitude 3°42'W, latitude 57°11'N and altitude 345 m. The trees were mature Sitka Spruce, (Picea sitchensis (Bong.) Carri6re) age 3 0 - 3 2 years with average tree height 16.5 m, mean tree girth at breast height 46 cm and a tree density of 3100 stems per hectare (Fig. 1).
2.2. Interception measurements The intercepted mass was measured with 7-ray
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163
153
Fig. 1. Experimental field at Queens Forest with tower, radioactive source and meteorological sensors (with permission from Calder, 1990). attenuation and tree weighing systems. The "r-ray system gives a good spatial average of the canopy snow storage, but is not practical to operate over an entire winter. The tree weighing system can give a continuous measurement, but the representation of a single tree is a problem. Also, because the tree weighing system is automatic it is difficult to interpret the changes, particularly when there may have been precipitation. The 3,-ray attenuation system (Fig. 2) was based on an original design by the Applied Physics Department of Strathclyde University (Olszyczka, 1979) and is described in detail in Calder and Wright (1986). A radioactive source ( 6 6 0 k e V from a
200 mCu CS 137) and a detector (0.3 m 2 plastic scintillator attached to a photomultiplier), mounted on rails on two towers, were winched up and down to allow the beam to scan different levels in the canopy. The distance between the towers was 40 m and the beam length through the forest was 35 m. The beam was arranged to sample a representative volume of the canopy, in relation to the distance of the beam from the tree trunks, by aligning the beam at an angle to the tree lines. The beam therefore intersected a representative sample of both the canopy and trunks. The number of counts from the scintillation counter at each metre within the canopy and at one level above the
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163
154
Automatic Weather I o-,-o
k -,--O
, '~l Ii--,. Clearing
Winch Raingauge !1 ;'1 i
: i i =
(S
"~~~ ,d
I
A i i i i
'
~
K.'
'
Control Caravan
Fig. 2. Schematic sketch of the -y-rayattenuation system (not to scale) (with permission from Calder, 1990). canopy (4 m) were registered and stored. A scan at one level took approximately 1 min, and a scan o f the entire canopy was thus accomplished in approximately 20 min. The data acquisition system was automated with a computer controlling the movements of the source and the detector. The computer also recorded the time, level, and count rate o f the pulses from the scintillation counter. The tree weighing system was based on the technique of tree cutting, described by Roberts (1977). A selected tree was supported from a tower, cut and then placed in a container of water resting on a load cell platform. A scaffolding frame was constructed to prevent gross lateral movements of the tree in high winds. To estimate the horizontal projected area of the tree and, as far as possible, ensure that it was representative of the canopy, a survey of the chest height girths was made o f the block of forest and a tree with mean girth was then selected for cutting. The three load cells on the weighing platform were logged individually and the system calibrated by hanging known weights on the tree. The trees were cut at the beginning of each winter (October 1993 and December 1994) and the system was operated throughout until the following April. During this time there was no obvious degradation of the structure of the tree.
2.3. Meteorological measurements The meteorological parameters measured by an automatic weather station (Strangeways, 1972) 4 m above the canopy (Fig. 2) were: net radiation, air temperature (dry and wet) and wind speed. In addition, an aspirated temperature screen was attached to the 3~-ray scanning equipment; this gives a measurement of the temperature profile as the equipment scans through the canopy. Precipitation was recorded with a heated tipping bucket gauge located in a nearby clearing with a 0.1 m m resolution tipping bucket. The throughfall was measured with plastic sheet net rainfall gauges (Calder and Rosier, 1976) (Fig. 2) equipped with 0.029 m m resolution tipping buckets. The plastic sheet was heated, but, unfortunately, it proved impossible to provide sufficient heat to give a real-time estimate of the snow throughfall and there was always lag of a few hours for this measurement.
3. T h e o r y
3.1. Interception depth The total mass per unit cross-sectional area normal
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163 to the beam m(kg m -2) (comprising intercepted water and snow, trunks and canopy) at each metre of vertical height through the canopy was calculated from the attenuated count rate n, the count rate with only air in the beam ha, the background count rate rib, and the attenuation coefficient for water /~ (Calder and Wright, 1986):
l
( n-nb~
Ix
\ na - rib/
m= - log
(1)
In dry conditions, without snow, the canopy dry mass (trunk and canopy) per unit area, m0, at the different levels was also measured. The mass per unit area of intercepted snow and water in the beam at each level could then be obtained by subtracting the dry canopy mass per unit area (kg m-2). The total intercepted mass per unit ground area was calculated by adding the intercepted mass per unit area normal to the beam at the different levels and dividing by the beam length through the forest, this resulted in the integral intercepted density times height profile, which is numerically equal to the depth of intercepted snow or water (kg m -2 or mm). The total error in the density measurement of material in the beam was estimated to be 1.1% (Calder and Wright, 1986). This results in an error of approximately 0.1 mm in the measurement of interception depth.
155
resistance to transport of vapour and X(J kg l) is the latent heat of sublimation. Eq. (2) can be rewritten as three terms: ~kEI - z~tRN
AQiL
A+3'
A+~/
- -
- -
~
pCp(6e/ra) A+~,
(3)
where the first term represents the part of the evaporation driven by net radiation, the second term is the heat required to melt the intercepted mass and the last term is the aerodynamic term (the efficiency of the turbulent transport). Lundberg and Halldin (1994) discussed the relative importance of the different terms and concluded that the time-rate-of-change of latent heat storage in the intercepted snow Q i L ( W m -2) is small compared with the other terms and the evaporation can be calculated:
)xEI = ARN + OCp(~e/ra)
(4)
A+-y Lundberg and Halldin (1994) also showed that for their data (northern Sweden) the aerodynamic term was much larger than the radiation term. 3.3. Aerodynamic resistance
The aerodynamic resistance for rain raL is commonly calculated according to Monteith (1965) ( lnz-d~2~-o /
3.2. Combination equation
raL --
The evaporation flux El(kg m -2 s -1) from wet snow intercepted in a canopy, when the intercepted mass exceeds a threshold value, can be calculated (Lundberg and Halldin, 1994) with a combination equation similar to the equation originally developed by Penman (1948): )~EI = A(RN -- QiL)
+pCp(~e/ra)
(2)
A+-y where A(Pa °C -l) is the change of saturation-vapour pressure with temperature, RN(W m -2) is the net radiation at height z, Q i L ( W m -2) is the time-rate-ofchange of latent heat storage in the intercepted snow, o(kg m -3) is the density of air at the air temperature T, Cp(J kg -l °C -l) is the specific heat of air, 6e(Pa) is the vapour pressure deficit (with respect to water) at measurement height z, ra(S m -1) is the aerodynamic
K2U(Z)
(5)
where z(m) is the reference height above the surface, r is yon Karman's constant (dimensionless, taken as 0.41) and u(z)(m s -l) is wind speed at height z. The displacement height d(m) and roughness length zo(m) can be related to stand height h/m. The values: d--0.75h and Zo = 0.1h, first proposed by Rutter et al. (1971), are used here. With the average tree height h = 16.5 m and measurement height z = 20.5 m the rain aerodynamic resistance raL becomes 15.9/u(z). Thom (1975) commented that Eq. (5) should be restricted to neutral conditions and suggested empirical stability functions to compensate for the thermal buoyancy. Calder (1990) used a constant aerodynamic resistance for rain raL and suggested a value an order of magnitude higher for snow ras. Since the transition of intercepted snow into liquid form is often associated with the arrival
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163
156
20
°r ,
New snow
EEl2
~8
o ~ 4 ~ 0 '~ 0 0
3
6 9 C (mm)
12
Fig. 3. Ratio o f m e a s u r e d sublimation E A to calculated sublimation
Esp plotted versus canopy storage C. The sublimation is measured from an artificial 1 m high tree and the calculated value equals the sublimation from a 1 mm ice sphere (modified from Schmidt, 1991). of warm fronts with high wind speeds, the difference in aerodynamic resistance between raL and ras might have been overestimated. Here the wind influence is included in the aerodynamic resistance ra (Eq. (5)), but the order of magnitude difference between snow and liquid conditions is adapted from Calder (1990). Thus: 15.9 raL = U - - ~
(S m - 1)
159 1 ras = u - ~ (s m - )
4
15
8 12 16 2 0 24 28 32 Snow precipitation (mm W.E.)
Fig. 4. "Snow build-up" function for Aviemore (after Calder, 1990).
Schmidt (1991) as a function of canopy storage (Fig. 3).
3.4. Mass balance The evaporation flux E ( m m h -l) from the area was determined from the water balance of the snow on the canopy. Strictly, the water balance should contain the precipitation rate P, the evaporation rate E, the change in storage on the canopy, 6C/6t, and on the ground, 6g/ 6t, plus the discharge Q:
(6)
E=p+ CI-C2-t gl-g2 6t 6t
(7)
where C] and C2 are the canopy storage, gj and g2 are the ground snow storage determined at the beginning and end of the measurement period 6t respectively. However, in the cases considered here the precipitation was insignificant, after the initial snow build up, and in dense spruce forests the evaporation from snow on the forest floor would be expected to be small (although no measurements are available). Thus the evaporation is calculated from:
Schmidt (1991) studied evaporation of snow at subzero temperatures. He found that the measured sublimation, EA, from a 1 m high, freely standing artificial tree (normalised using the calculated sublimation from a 1 mm ice sphere, Esp) for new snow was roughly twice the value of that for old snow (Fig. 3). The normalised evaporation was also found to depend on the mass of snow on the canopy, increasing up to a m a x i m u m value (at approximately twice the rain-saturation value) and then decreasing as the intercepted mass increases further. The greater sublimation rate from new snow was attributed to the fact that the exposed microscopic surface area for the same intercepted mass was greater for new snow than for old snow. The decrease in the normalised evaporation for large intercepted mass was attributed to the fact that the exposed macroscopic area of the snow decreased when bridging of snow between branches started to occur. Schmidt (1991) expressed the evaporation rates as functions of intercepted mass. In order to make the expression independent of tree size Lundberg and Halldin (1994) expressed the data of
E=
C1 - C 2
6t
Q
(8)
(9)
4. Results During 1 6 - 1 9 March, 1985, a single event took place resulting in a large snow canopy storage. A considerable snowfall occurred during the 16 March and the morning of the 17 March; in all, 19.3 mm water equivalent fell, of which 14.5 m m lodged on the canopy and 4.8 m m reached the forest floor (this later figure was estimated from a snow survey), see Fig. 4. After the snowfall, no precipitation was recorded during the following 59 h. During this period
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163
7.5
RN (w/m 21 R~
a)
5.0
19 March
18 March
17 March U (m/s)
157
.....
2.5
.... . ..- ........ .....y
0.0 6e (Po), RH (~) 200
500 400 500 200 100 0 -I00
b)
150
RH
100
50 0 5.0 2.5 0.0 -2.5 -5.0 2O 15 10 5 0 5.0
~
t ~
"w.__ ! \
tI
I
T. dT (°C)
o)
C w, C l . g (ram
C[ .....
g
Q (mm/h), (~CC (ram) ,e)
_ ~
q
2.5
. . . . . . . .
.i- . . . .
- - - r
. . . . . . . . . . . . . . . . .
ACC// /
0.0 E (~./h) 2 0
I
r~,.
-,
~
/ ~ - - _
-
0 -I E^ec (ram) 50
g)
20
rl m
I
~
10 0
J . - - ~
7--I--w-~
12
24
5"r-"q 12
J
J
I 24
I
I
I r.w
i
lZ
i
(h)
Fig. 5. Measured meteorological parameters, canopy and ground storage, discharge, calculated and accumulated calculated evaporation: (a) R N is the net radiation, u is the wind velocity; (b) 6e is the vapour deficit, RH is the relative humidity; (c) T is the air temperature at reference height z, dT is the difference in temperature between reference height z and average canopy air temperature; (d) CM is the measured canopy storage, CI is the interpolated canopy storage, g is the calculated ground storage; (e) Q is the discharge, QACCis the accumulated discharge; (f) EWB is the evaporation rate determined with the water budget method (Eq. (9)), Er0L is the evaporation rate determined with the combination equation (Eq. (4)) and the aerodynamic resistance for rain r,L (Eq. (6)), Er0~ is the evaporation rate determined with the combination equation and the aerodynamic resistance for snow conditions ras (Eq. (7)); (g) E Acc is the accumulated evaporation determined with same methods as above.
the canopy storage C decreased by 10.8 m m from 14.5 m m to 3.7 m m (Fig. 5(d)). The accumulated runoff recorded from the heated plastic sheets was 4.6 m m (Fig. 5(e)). The accumulated evaporation, E ACC, during the period was 10.8 mm, corresponding to 0.19 m m h -1. The redistribution of the canopy storage, C, during this event can be observed in Fig. 6. Initially the storage was largest at the top of the canopy, but by
the evening of the first day some of the high branches were bare. During the third day the decrease in storage was roughly the same at all the remaining levels. An idea of the accuracy of the canopy storage measurements can be obtained by noting that a negative storage of 0.25 m m was recorded at 13 m height; this is probably due to the movement of branches, either due to snow loading or wind. During these 3 days the average net radiation, RN,
158
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163
Table 1 Estimates of accumulated evaporation with water budget equation and with combination equation using different aerodynamic resistances; March 1985 Term/date
17
18
19
ACC EwB (mm) 4cc (mm) Erjs
5.0 3.0
1.3 3.2
4.5 3.9
E mcc (mm) EACC/E Acc
5.1 0.60
10.2 2.46
12.3 0.86
was 97 W m -2 (Fig. 5(a)) with average daytime values of approximately 175 W m -2 and night values of -75 W m -2. The average wind velocity, u, was 2.7 m s -j (Fig. 5(a)). The average relative humidity, RH, was 91% (Fig. 5(b)), resulting in an average vapour pressure deficit be of 60 Pa with pronounced peaks during the days and zero values during the nights. The average air temperature, T, was -0.6°C (Fig. 5(c)), with night values below and daytime values above zero. The temperature difference, dT, between the air temperature at the reference level z and the temperature within the canopy was small except for the 19 March when the canopy was approximately I°C warmer than the air above. There was fairly good agreement between the accumulated evaporation calculated with the water budget method (Eq. (9)) and that calculated with the combination equation (Eq. (4)) with snow aerodynamic resistance ras (Eq. (7)) (Fig. 5(g)). The calculated value underestimated the evaporation during the first day and overestimated it during the second day. The accumulated evaporation E raL ACC calculated with the combination equation (Eq. (4)) and Eq. (6)--the 16
/"
J::
.
0 0.0
]
I
0.5
1.0
.
.
.
.
.
i ..........
1.5
19/3 19/,..3
2.0
1loo 19i00 2.5 C ( r a m / m )
Fig. 6. Canopy storage changes during 17-19 March, 1985.
17-19
28
30
Average (mm h -I)
10,8 -+ 1.4 10,1
3.9 -+ 0.8 2.3
3.1 _+ 0.8 1.1
0.24 0.18
27,8 0.94
7.8 0.59
1.5 0.35
0.51
standard equation for the aerodynamic resistance for rain raL, however, gave values 2.6 times larger than the accumulated evaporation calculated with the water budget method (Fig. 5(g) and Table 1). The variation in the hourly daytime values calculated with the water budget method (Fig. 5(f)) were great, reflecting the random errors in the individual canopy mass determinations. Two more days (28 and 30 March, 1985) fulfilled the requirements of large canopy storage: dry snow in the canopy and little precipitation during the observation period (Fig. 7(d,h)). The average net radiation, RN, was 168 W m -2 and 103 W m -2 respectively (Fig. 7(a)). On 28 March the average wind speed, u, was high (4.6 m s -~) and the average vapour pressure deficit, 6e, large (90 Pa) (Fig. 7(a,b)), whereas on 30 March both the wind speed (0.8 m s -1) and the vapour pressure deficit (42 Pa) were low. The air-temperature during both days was approximately I°C and the temperature difference between the canopy and the air above was very small (Fig. 7(c)). During both these days the canopy storage, C, decreased from approximately 9 mm to approximately 4 mm (Fig. 7(d)). The accumulated precipitation (Fig. 7(h)) was less than 0.1 mm during both days and the initial ground snow storage, g, was small (approximately 1.0 ram) on both days (Fig. 6(d)). For 28 March the accumulated evaporation (Fig. 7(g)), determined with the water budget method, agreed fairly well with the accumulated evaporation determined with the combination equation with the aerodynamic resistance for snow conditions ras. However the rain aerodynamic resistance again overestimated the evaporation. On 30 March the calculated evaporation using both the rain and the snow aerodynamic resistance gave lower rates than the water budget method. The summary of the accumulated evaporation in Table 1 and Fig. 8 shows
159
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163
28
March
30
RN(W/m~
10
0 200
March 3 0 March Q (mm/h),QaCC(mm) ) QAC~
March
28 500
I
30O 20O IO0 0 -100
~(P.), SH (r.)
/ 1
/////~°t
E (ram/h)
)
150
~r~L
1 O0
50 0 10
T,dT (°C)
lO
5
EACC{mm) raL
5 I)
/ ~"
. ~ -
0 -5 10
o
(mm) d)~ ~CM
CI~, ~,
1.o
pACC(~tm)
P (ram/h),
0.5
12
14
16
18
i------i-~..J 12 14 16
I 18
o.o
FL)I l J --I 12
14
16
18
l l l l 12
14
16
18
Fig. 7. Measured meteorological parameters, canopy and ground storage, discharge, calculated and accumulated calculated evaporation: (a) R N is the net radiation, u is the wind velocity; (b) 6e is the vapour deficit, RH is the relative humidity; (c) T is the air temperature at reference height z, dT is the difference in temperature between reference height z and average canopy air temperature; (d) CM is the measured canopy storage, Cr is the interpolated canopy storage, g is the calculated ground storage; (e) Q is the discharge, QACCis the accumulated discharge; (f) EWB is the evaporation rate determined with the water budget method (Eq. (9)), Er,L is the evaporation rate determined with the combination equation (Eq. (4)) and the aerodynamic resistance for rain r~L (Eq. (6)), Er,S is the evaporation rate determined with the Combination equation and the aerodynamic resistance for snow conditions ras (Eq. (7)); (g) E Acc is the accumulated evaporation determined with same methods as above.
that, even if the variations of individual hours are large, the average accumulated evaporation determined with the combination equation using the snow aerodynamic resistance agrees well with the average evaporation determined with the water budget method, whereas the standard aerodynamic resistance overestimates the evaporation. The values reported for 28 and 30 March refer to 7 h periods. The length of the period is given by the length of the interception measurements (Fig. 5(d)). The ratio between E ras Acc and E A c c plotted versus the canopy storage C in Fig. 9 shows very large variation and the sample is small. A tendency to underestimate the evaporation estimates for old snow (on the lower branches), when using the combination equation and the "snow aerodynamic resistance", can be detected (cf. Fig. 3). No trend in the ratio as a function of canopy storage is observed. The tree weighing experiment gave an almost
complete record of the weight of water (solid and liquid) on the forest canopy through the two winters 1983-1984 and 1984-1985. January 1984 (Fig. 10(a)) illustrates the typical patterns which can be observed. Events A and B follow a commonly found pattern with a snowfall followed by very rapid decrease in the snow storage associated with the
0 V" 0
L
5
I
10
I
15
I
20
25 E~c( mr")
Fig. 8. Accumulated evaporation determined with different methods. E Ace is measured with the water budget method. ErA,cc is calculated with the combination equation: O, aerodynamic resistance for snow conditions; @, aerodynamic resistance for rain conditions. Bars denote error associated with water budget method and figures denote dates.
160
A. Lundberg et al./Journal of l4ydrology 206 (1998) 151-163
I
I
I 0
I
1
2 1
0
0
I ,.5
0
I 6
assuming that when the storage is greater than 2 m m it is snow. It is unlikely that storage of liquid water can exceed 2 mm, except during short periods with high rainfall rates. Overall, during the December to March periods the canopy had snow cover for 32% of the 1983-1984 winter and 35% of the 1984-1985 winter.
|
I 9
I 12 C ( m m )
Fig. 9. Ratio of accumulated evaporation determined with different methods plotted against canopy storage C. E~vcc is measured with the water budget method. ErA,cc is calculated with the combination equation and the aerodynamic resistance for snow conditions. N indicates new snow (<24 h), O indicates old snow (>24 h). arrival of warm air in a frontal system. The periods of rapid fall are associated with above zero air temperatures (averaging +2°C), moderate wind speeds ( 3 - 4 m s -~) with some rainfall. During such periods there is almost certainly liquid water on the canopy from snow melt and rainfall and with possible evaporation rates up to 0.5 m m h -l (Calder, 1990). The third event (C) is a complex event extending over 15 days. The air temperatures were mostly below zero during this period, apart from the major loss period on 28 January which had positive temperatures and rainfall. Fig. 10(b) shows the tree weighing measurement for March 1995 which includes the three periods investigated in detail above. The agreement between the 7-ray and tree weighing estimates of canopy storage are very good, suggesting that the single tree gives a good representation of the forest during this period. The tree weighing measurements have been used to identify the percentage of the winter period in which the canopy is snow covered (Table 2). Periods when snow is on the forest canopy have been estimated by W,E. (mm)
5. Discussion and conclusion The m a x i m u m evaporation rate determined with the water budget method (0.56 m m h -E during 7 h) is much higher than the maximum evaporation from an open snow pack (0.06 m m h -1) reported by Harding (1986); it is also higher than the 0.3 m m h -l reported from intercepted snow by Lundberg and Halldin (1994) but is similar to the rate (0.5 m m h -l) reported by Calder (1990). Since Lundberg and Halldin (1994) worked with wet snow (lower aerodynamic resistance) it could be expected that they would report higher evaporation rates, but their measurement equipment did not allow measurements during high wind-speed conditions and may have excluded the highest rates. Nakai et al. (1995) quote values averaging 0.7 m m h -1 and 2.3 m m day -1. The tree weighing results suggest that the trees are snow covered one-third of the winter; the average measured evaporation rate is 0.24 m m h -1. If this is representative of the entire winter it would correspond to a total evaporation of 58 m m per month. A disadvantage with determining evaporation as a residual term from the water budget consideration is that the errors in the individual terms have to be added, resulting in a large possible maximum error. b)
a)
20-
10-
05
10
15 January
20
25
30
5
10
15
20
25
30
March
Fig. 10. The water equivalent of snow on the forest canopy as recorded by the tree weighing experiment for (a) January 1984 and (b) March 1985. Also shown (dots) are the ",/-raymeasurements in March 1985. The letters refer to storm numbers discussed in the text.
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163
161
Table 2 Hours of snow cover, percentage of time there is snow on the canopy and maximum storage in the month estimated from the tree weighing experiment Period
December, 1983 January, 1984 February, 1994 March, 1984 December, 1984 January, 1985 February, 1985 March, 1985
Snow cover
Maximum storage
(h)
(%)
(mm)
21 74 18 17 20 63 4 37
6 23 11 9 7 > 30 2.5 15
155 551 126 128 98 474 20 276
Notes
data starts 11/12 system overtopped 22/1 to 29/1 6.5 days missing
This is a considerable potential problem in cases involving snowfall, where there can be large systematic errors in the precipitation measurements; however, since no precipitation occurred during the periods 1 7 - 1 9 and 28 March and only 0.03 m m on the 30 March, the effects of precipitation errors in these cases are small. The random error estimate of the 3,-ray attenuation system was calculated to be 0.1 m m (Calder and Wright, 1986), and from consideration of the variability in the measurement of the canopy storage between successive scans the measurements largely lie within this error. For individual scans, larger, random variations are found (up to 0.5 mm), These are due to drifts in the gain of the photomultiplier (arising from loss of temperature control) and on some occasions due to the movement of branches in the beam. Thus, although individual hourly rates may have large, random errors, the error in the long-term cumulative evaporation will be small. The determination of the effects of atmospheric stability would have required measurements not made in this study. An indication of the stability conditions can be obtained from the records of the difference 6T between the temperature above the canopy and the temperature in the stand. For all days except the 19 March the temperature difference was small, indicating neutral conditions. For 19 March the canopy was approximately I°C warmer than the air above, indicating unstable conditions, but there is no indication from the ratio between Eras and EWB (Table 1) that this affected the evaporation. In the wet-snow study by Lundberg and Halldin (1994) only stable conditions were observed (estimated using temperature difference to indicate the stability
of the air). This latter study reported a slight decrease in the evaporation in the most stable conditions. The calculated evaporation rates using the combination equation were very sensitive to the choice of aerodynamic resistance. This indicates that the aerodynamic term is more important than the radiation term and this is in agreement with the findings of Lundberg and Halldin (1994). The agreement between the accumulated evaporation determined with the water budget method and modelled by the combination equation using the snow aerodynamic resistance (ten times larger than the rain aerodynamic resistance) was generally good. During the 3 day period, 1 7 - 1 9 March, the agreement was very good on the last two days, but on the first day, immediately following the snowfall, the use of the aerodynamic resistance for rain provided a better agreement with observations. The source area for evaporation in these cases will vary with time (in contrast with that of momentum). At the beginning of the 3 day event the snow covered the entire canopy, whereas at the end snow only remained at the lowest branches (Fig. 6). The evaporation during the first day was well simulated with a low aerodynamic resistance (appropriate for rain), whereas during the following two days this value greatly overestimated the evaporation. A multilayer model with higher resistance from the lower branches might be useful to simulate this. A further uncertainty is the presence of liquid water on the canopy. No verification that the snow in the trees was completely dry was made; for part of the time the temperature was above 0°C and it is possible that parts of the snow on the highest branches may
162
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163
have melted, resulting in wet rather than dry snow conditions. A weighted snow and rain aerodynamic resistance should then have been used. This might indicate that the snow aerodynamic resistance should be even larger than determined here and it may also have masked any possible differences between new and old snow (Fig. 9) and possible differences in aerodynamic resistance as function of canopy storage. The evaporation determined with the combination method on the 30 March was lower than the evaporation determined with the water budget method using both rain and snow aerodynamic resistance. The meteorological conditions on this day were substantially different from the other periods (with lower wind speeds and higher relative humidity) and hence the calculated evaporation will be less sensitive to the aerodynamic resistance. A difficulty with the determination of evaporation of intercepted snow using the combination equation is the determination of vapour pressure in freezing conditions. If dry and wet thermometers are used an error in the temperature of 0.2°C alters the vapour deficit by approximately 30 Pa, compared with the observed vapour deficit on the 30 March of 42 Pa. Capacitance probes for humidity determinations are an alternative but are not reliable when measuring in very cold and humid environments, according to Lundberg and Halldin (1994). The transition between the solid and liquid phases is very important when dealing with the evaporation of intercepted snow and there is no existing direct method (Lundberg, 1993) to measure this. To partition it into liquid and solid phases will require further investigations and will probably require the use of a combination of methods, such as microwave and 3,-ray attenuation (Lundberg, 1993). This paper has presented some of the very few measurements of evaporation from a snow-covered canopy. The maximum evaporation rate (0.56 m m h -l) was similar to the rate (0.5 m m h -1) reported by Calder (1990), with an overall mean rate of 0.24 mm h -1. An order of magnitude calculation suggests that the total winter losses from snow intercepted on a forest canopy might be over 200 mm. It is obviously essential that physically based water resource and climate models include a proven and robust parameterisation of this process. Comparison of the measured intercepted snow evaporation and an
estimate made with a combination equation using different aerodynamic resistances showed that evaporation of dry intercepted snow can be calculated with the combination method provided a much larger aerodynamic resistance (ten times) than the standard aerodynamic resistance (Eq. (5)) is used. Such models will require more accurate measurements of air humidity (at temperatures close to and below zero), an improved consideration of the evaporation from partially covered canopies and measurements and models which separate liquid from solid interception.
Acknowledgements Thanks are due to all the staff at the Institute of Hydrology, Wallingford, UK, who were engaged on the data collection and analysis. The simulations were performed at the Division of Water Resources Engineering, University of Technology, Lule~, Sweden and was funded by The Swedish Natural Science Research Council (NFR) and Coldtech. Kimberly Miles, exchange student, University of Alaska, Fairbanks, Canada, helped with converting the data into PC standard. John Gash, Institute of Hydrology, Wallingford, UK is acknowledged for first pointing out the importance of the variable source area for latent heat.
References Bonan, G.B., Pollard, D., Thompson, S.L., 1992. Effects of boreal forest vegetation on global climate, Nature, 359, 716-718. Calder, I.R., 1985. What are the limits of forest evaporation?Comment, Journal of Hydrology, 82, 179-192. Calder, I.R., 1990. Evaporation in the Uplands. Wiley, Chichester, UK. Calder, I.R., Rosier, P.T.W., 1976. The design of large plastic-sheet net rainfall gauges, Journal of Hydrology, 30, 403-405. Calder, I.R., Wright, I.R., 1986. Gamma ray attenuation studies of interception from Sitka spruce-some evidence for an additional transport mechanism, Water Resources Research, 22, 409-417. Claassen, H.C., Downey, J.S., 1995. A model for deuterium and oxygen 18 isotope changes during evergreen interception of snowfall, Water Resources Research, 31 (2), 601-618. Hanson, C.L., Zuxel, J.F., Morris, R.P., 1983. Winter precipitation catch by heated tipping-bucket gages, Trans. American Society of Agricultural Engineering, 26 (5), 1479-1480. Harding, R.J., 1986, Exchange of energy and mass associated with
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163 a melting snowpack. Proceedings from Budapest Sympymposium, IAHS Publication, vol. 155, pp. 3-15. Lankreijer, H.J.M., Hendriks, M.J., Klaassen, W., 1993. A comparison of models simulating rainfall interception of forests, Agricultural Forest Meteorology, 64, 187-199. Lundberg, A., 1993. Measurement of intercepted snow--review of existing and new measurement methods, Journal of Hydrology, 151,267-290. Lundberg, A., Halldin, S., 1994. Evaporation of intercepted snow: analysis of governing factors, Water Resources Research, 30 (9), 2587-2598. Monteith, J.L., 1965. Evaporation and environment, The state and movement of water in living organisms. In: G.E. Fogg (Ed.), Symposium from Society of Experimental Biology, Cambridge, vol. 19, pp. 205-234. Nakai, Y., Kitahara, H., Sakamota, T., Saito, T., Terajima, T., 1993. A study on evaporation of snow intercepted by forest canopy, Journal of Japanese Forest Society, 75, 191-200. (in Japanese with abstract in English). Nakai, Y., Sakamoto, T., Terajima, T., Kitamura, K., 1995. Evaporation of snow intercepted by a Todo-fir forest (1) Water balance measurements, Journal of Japanese Forestry Society, 77, 581-588. (in Japanese with abstract in English). Nakai, Y., Sakamoto, T., Terajima, T., Kitamura, K., 1996. Evaporation of snow intercepted by a Todo-fir forest--estimations by an energy balance model and their comparison with water balance measurements, Journal of Japanese Forestry Society, 78 (1), 15-19. (in Japanese with abstract in English). Olszyczka, B., 1979. Gamma-ray determinations of surface water
163
storage and stem water content for coniferous forests. PhD thesis, Department of Applied Physics, University of Strathclyde, Scotland. Penman, H.L., 1948. Natural evaporation from open water, bare soil and grass, Proceedings Royal Society Ser. A, 193, 120-145. Pomeroy, J.W. and Gray, D.M., 1995. Snow cover: accumulation, relocation and management. NHRI report No. 7, Saskatoon, Canada. Roberts, J.M., 1977. The use of tree cutting techniques in the study of the water relations of mature Pinus Selvestris L, Journal of Experimental Biology, 28, 751-767. Rutter, A.J., Kershaw, K.A., Robins, P.C., Morton, A.J., 1971. A predictive model of rainfall interception in forest. I Derivation of the model from observations in a plantation of Corsican pine, Agricultural Meteorology, 9, 367-384. Schmidt, R.A., 1991. Sublimation of snow intercepted by an artificial conifer, Agricultural Forest Meterology, 54, 1-27. Schmidt, R.A., Jairell, R.A. and Pomeroy, J.W., 1988. Measuring snow interception and loss from an artificial conifer. In: Proc. 56th Western Snow Conference, Kalispell, MT, April, 1988. Colorado State University, Colorado, pp. 166-169. Strangeways, I.C., 1972. Automatic weather stations for network operation. Weather 27, 403-408. Thom, A.S., 1975. Momentum, mass and heat exchange of plant communities. In: J.L. Monteith (Ed.), Vegetation and the Atmosphere, Vol. 1. Academic Press, New York, pp. 57-108. Thomas, G., Rowntree, P.R., 1992. The boreal forest and climate, Quarterly Journal of the Royal Meteorological Society, 118, 469-498.
Hydrology ELS EVI E R
Journal of Hydrology 206 (1998) 151-163
Evaporation of intercepted snow: measurement and modelling Angela Lundberg a'*, Ian Calder b, Richard Harding b "Division of Water Resources Engineering, Lulegt Universi~ of Technology, Lule~t, Sweden blnstitute of Hydrology, Wallingford, Oxfordshire, UK Received 14 May 1996; accepted 25 January 1997
Abstract Snow storage on a coniferous forest canopy was measured using y-ray attenuation and tree weighing systems, along with measurements of throughfall, using two plastic sheet net rainfall gauges. Meteorological parameters were measured with an automatic weather station. Estimates of evaporation of intercepted snow show an average rate of 0.24 mm h -~ and a maximum cumulative total of 3.9 mm in 7 h. Comparison with evaporation determined by a combination method with two different estimates of aerodynamic resistance (the " s t a n d a r d " rain aerodynamic resistance raL and a snow aerodynamic resistance r ~ s - - a n order of.magnitude larger than raL) showed that raL overestimated the evaporation by a factor of 2.6, whereas ras gave fair agreement with the measured evaporation. A multilayer model may be needed to take into account the variations of latent heat source area. Using the long-term measurements of the weight of snow on a single tree the total interception evaporation was estimated to be of the order 200 m m year 1. © 1998 Elsevier Science B.V. All rights reserved.
Keywords: Snow storage; Interception evaporation; Modelling; Forest
1. Introduction
Several studies during the last decade have emphasised the importance of evaporation of intercepted snow (Calder, 1985; Calder, 1990; Schmidt et al., 1988; Schmidt, 1991; Lundberg, 1993; Nakai et al., 1993; Nakai et al., 1995; Nakai et al., 1996; Lundberg and Halldin, 1994; Claassen and Downey, 1995). Pomeroy and Gray (1995) estimate that one-third of the winter snowfall in central Canada is lost through evaporation of snow intercepted on forest canopies. It is evident, therefore, that water resources models used in northern forested areas must describe correctly the lodging, and subsequent evaporation of snow. Bonan et al. (1992) and Thomas and Rowntree (1992) have *
Corresponding author.
0022-1694/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PH S0022- 1694(97)00016-4
used general circulation models to investigate the role of boreal forest in a global climate. Both these studies highlighted the importance to climate of the interaction between the forest and snow cover. General circulation models are increasingly incorporating realistic surface schemes and it is essential that the energy and water budget of snow on a coniferous forest canopy is correctly described. When assessing the amount of snow that is lost by evaporation, process studies of the intercepted snow become important. Classical interception studies of the type used for rainfall, in which precipitation beneath the canopy is compared with that outside, are less successful in the case of snow where the measurements of precipitation input are particularly prone to error. To circumvent this problem process, studies of snow interception generally aim to measure
152
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163
the amount of snow on the forest canopy; such studies are presented by Calder (1990), Schmidt (1991) and Lundberg and Halldin (1994). Schmidt (1991) treated dry snow conditions and Lundberg and Halldin (1994) considered wet snow, whereas Calder (1990) attempted to model both dry and wet snow conditions. W h e n snow covers a canopy the resulting surface generally becomes aerodynamically much smoother than that of a rain-wetted canopy. It would therefore be expected that the evaporation rates from a snowcovered canopy would be lower than from a rainwetted canopy. However, the water equivalent of the snow stored on a forest canopy can be an order of magnitude larger than that of a rain-wetted canopy and thus the potential is considerably larger for evaporation when the precipitation stops. Since the ventilation term is dominant in the equation for evaporation of intercepted snow, the evaporation values are very sensitive to the way the aerodynamic resistance is calculated, (Lundberg and Halldin, 1994). Using data from Aviemore, Scotland, Calder (1990) by optimisation found an order of magnitude difference in aerodynamic resistance between a snowcovered and a rain-covered canopy and these findings are partly confirmed at a site in Sweden by Lundberg and Halldin (1994). According to Schmidt (1991) a large exposed snow surface area gives a higher evaporation rate per unit intercepted mass than a small exposed surface area. Both the total snow-covered area and the roughness of the surface elements contribute to the efficiency of the transfers between the snow on the canopy and the atmosphere. A number of researchers have suggested that the roughness length for heat is approximately one order of magnitude less than that for momentum (see Lankreijer et el., 1993). Lankreijer et el. (1993) found that an aerodynamic resistance for heat one-half that of momentum (corresponding to an order of magnitude change in roughness length) improved the models of interception loss from a rain-wetted forest canopy. This paper presents a re-analysis of the "y-ray attenuation measurements described by Calder (1990) to describe in detail the climatic conditions during events with evaporation of dry intercepted snow and to discuss how to model the aerodynamic resistance during snow conditions. Longer term measurements of the duration of snow cover on a single tree are used to estimate the losses
from a snow-covered canopy over two entire winter seasons.
2. Measurements This paper presents some detailed snow measurements made in north-east Scotland over two winters. The measurement system, a ~,-ray attenuation rig, was operated intermittently during the winters of 1 9 8 3 1984 and 1984-1985. A total of 16 storms, some incomplete, were recorded. Periods with high precipitation are omitted, since measurement of solid precipitation is inaccurate (Hanson et al., 1983) and periods with low canopy storage were also excluded to avoid uncertainties with modelling the reduction in evaporation due to incomplete canopy cover. To isolate the snow evaporation process from the rain evaporation process, occasions when most of the snow was melted, were omitted. This paper presents in detail the measurements from three events. During the first ( 1 6 - 1 9 March, 1985), 15 m m water equivalent of snow was deposited on the forest canopy in the first day and during the subsequent 3 days a substantial amount evaporated. The two other events (28 and 30 March, 1985) were shorter events with initial storage of approximately 9 mm; again a substantial proportion of the canopy storage evaporated. All events had mainly dry snow on the trees with little precipitation after the initial snowfall. In addition to these intensive measurements, a system monitoring the weight of a single tree was operated for both winters.
2.1. Experimental site The experimental site was located at Queens Forest near Aviemore in the Highland Region of Scotland, longitude 3°42'W, latitude 57°11'N and altitude 345 m. The trees were mature Sitka Spruce, (Picea sitchensis (Bong.) Carri6re) age 3 0 - 3 2 years with average tree height 16.5 m, mean tree girth at breast height 46 cm and a tree density of 3100 stems per hectare (Fig. 1).
2.2. Interception measurements The intercepted mass was measured with 7-ray
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163
153
Fig. 1. Experimental field at Queens Forest with tower, radioactive source and meteorological sensors (with permission from Calder, 1990). attenuation and tree weighing systems. The "r-ray system gives a good spatial average of the canopy snow storage, but is not practical to operate over an entire winter. The tree weighing system can give a continuous measurement, but the representation of a single tree is a problem. Also, because the tree weighing system is automatic it is difficult to interpret the changes, particularly when there may have been precipitation. The 3,-ray attenuation system (Fig. 2) was based on an original design by the Applied Physics Department of Strathclyde University (Olszyczka, 1979) and is described in detail in Calder and Wright (1986). A radioactive source ( 6 6 0 k e V from a
200 mCu CS 137) and a detector (0.3 m 2 plastic scintillator attached to a photomultiplier), mounted on rails on two towers, were winched up and down to allow the beam to scan different levels in the canopy. The distance between the towers was 40 m and the beam length through the forest was 35 m. The beam was arranged to sample a representative volume of the canopy, in relation to the distance of the beam from the tree trunks, by aligning the beam at an angle to the tree lines. The beam therefore intersected a representative sample of both the canopy and trunks. The number of counts from the scintillation counter at each metre within the canopy and at one level above the
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163
154
Automatic Weather I o-,-o
k -,--O
, '~l Ii--,. Clearing
Winch Raingauge !1 ;'1 i
: i i =
(S
"~~~ ,d
I
A i i i i
'
~
K.'
'
Control Caravan
Fig. 2. Schematic sketch of the -y-rayattenuation system (not to scale) (with permission from Calder, 1990). canopy (4 m) were registered and stored. A scan at one level took approximately 1 min, and a scan o f the entire canopy was thus accomplished in approximately 20 min. The data acquisition system was automated with a computer controlling the movements of the source and the detector. The computer also recorded the time, level, and count rate o f the pulses from the scintillation counter. The tree weighing system was based on the technique of tree cutting, described by Roberts (1977). A selected tree was supported from a tower, cut and then placed in a container of water resting on a load cell platform. A scaffolding frame was constructed to prevent gross lateral movements of the tree in high winds. To estimate the horizontal projected area of the tree and, as far as possible, ensure that it was representative of the canopy, a survey of the chest height girths was made o f the block of forest and a tree with mean girth was then selected for cutting. The three load cells on the weighing platform were logged individually and the system calibrated by hanging known weights on the tree. The trees were cut at the beginning of each winter (October 1993 and December 1994) and the system was operated throughout until the following April. During this time there was no obvious degradation of the structure of the tree.
2.3. Meteorological measurements The meteorological parameters measured by an automatic weather station (Strangeways, 1972) 4 m above the canopy (Fig. 2) were: net radiation, air temperature (dry and wet) and wind speed. In addition, an aspirated temperature screen was attached to the 3~-ray scanning equipment; this gives a measurement of the temperature profile as the equipment scans through the canopy. Precipitation was recorded with a heated tipping bucket gauge located in a nearby clearing with a 0.1 m m resolution tipping bucket. The throughfall was measured with plastic sheet net rainfall gauges (Calder and Rosier, 1976) (Fig. 2) equipped with 0.029 m m resolution tipping buckets. The plastic sheet was heated, but, unfortunately, it proved impossible to provide sufficient heat to give a real-time estimate of the snow throughfall and there was always lag of a few hours for this measurement.
3. T h e o r y
3.1. Interception depth The total mass per unit cross-sectional area normal
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163 to the beam m(kg m -2) (comprising intercepted water and snow, trunks and canopy) at each metre of vertical height through the canopy was calculated from the attenuated count rate n, the count rate with only air in the beam ha, the background count rate rib, and the attenuation coefficient for water /~ (Calder and Wright, 1986):
l
( n-nb~
Ix
\ na - rib/
m= - log
(1)
In dry conditions, without snow, the canopy dry mass (trunk and canopy) per unit area, m0, at the different levels was also measured. The mass per unit area of intercepted snow and water in the beam at each level could then be obtained by subtracting the dry canopy mass per unit area (kg m-2). The total intercepted mass per unit ground area was calculated by adding the intercepted mass per unit area normal to the beam at the different levels and dividing by the beam length through the forest, this resulted in the integral intercepted density times height profile, which is numerically equal to the depth of intercepted snow or water (kg m -2 or mm). The total error in the density measurement of material in the beam was estimated to be 1.1% (Calder and Wright, 1986). This results in an error of approximately 0.1 mm in the measurement of interception depth.
155
resistance to transport of vapour and X(J kg l) is the latent heat of sublimation. Eq. (2) can be rewritten as three terms: ~kEI - z~tRN
AQiL
A+3'
A+~/
- -
- -
~
pCp(6e/ra) A+~,
(3)
where the first term represents the part of the evaporation driven by net radiation, the second term is the heat required to melt the intercepted mass and the last term is the aerodynamic term (the efficiency of the turbulent transport). Lundberg and Halldin (1994) discussed the relative importance of the different terms and concluded that the time-rate-of-change of latent heat storage in the intercepted snow Q i L ( W m -2) is small compared with the other terms and the evaporation can be calculated:
)xEI = ARN + OCp(~e/ra)
(4)
A+-y Lundberg and Halldin (1994) also showed that for their data (northern Sweden) the aerodynamic term was much larger than the radiation term. 3.3. Aerodynamic resistance
The aerodynamic resistance for rain raL is commonly calculated according to Monteith (1965) ( lnz-d~2~-o /
3.2. Combination equation
raL --
The evaporation flux El(kg m -2 s -1) from wet snow intercepted in a canopy, when the intercepted mass exceeds a threshold value, can be calculated (Lundberg and Halldin, 1994) with a combination equation similar to the equation originally developed by Penman (1948): )~EI = A(RN -- QiL)
+pCp(~e/ra)
(2)
A+-y where A(Pa °C -l) is the change of saturation-vapour pressure with temperature, RN(W m -2) is the net radiation at height z, Q i L ( W m -2) is the time-rate-ofchange of latent heat storage in the intercepted snow, o(kg m -3) is the density of air at the air temperature T, Cp(J kg -l °C -l) is the specific heat of air, 6e(Pa) is the vapour pressure deficit (with respect to water) at measurement height z, ra(S m -1) is the aerodynamic
K2U(Z)
(5)
where z(m) is the reference height above the surface, r is yon Karman's constant (dimensionless, taken as 0.41) and u(z)(m s -l) is wind speed at height z. The displacement height d(m) and roughness length zo(m) can be related to stand height h/m. The values: d--0.75h and Zo = 0.1h, first proposed by Rutter et al. (1971), are used here. With the average tree height h = 16.5 m and measurement height z = 20.5 m the rain aerodynamic resistance raL becomes 15.9/u(z). Thom (1975) commented that Eq. (5) should be restricted to neutral conditions and suggested empirical stability functions to compensate for the thermal buoyancy. Calder (1990) used a constant aerodynamic resistance for rain raL and suggested a value an order of magnitude higher for snow ras. Since the transition of intercepted snow into liquid form is often associated with the arrival
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163
156
20
°r ,
New snow
EEl2
~8
o ~ 4 ~ 0 '~ 0 0
3
6 9 C (mm)
12
Fig. 3. Ratio o f m e a s u r e d sublimation E A to calculated sublimation
Esp plotted versus canopy storage C. The sublimation is measured from an artificial 1 m high tree and the calculated value equals the sublimation from a 1 mm ice sphere (modified from Schmidt, 1991). of warm fronts with high wind speeds, the difference in aerodynamic resistance between raL and ras might have been overestimated. Here the wind influence is included in the aerodynamic resistance ra (Eq. (5)), but the order of magnitude difference between snow and liquid conditions is adapted from Calder (1990). Thus: 15.9 raL = U - - ~
(S m - 1)
159 1 ras = u - ~ (s m - )
4
15
8 12 16 2 0 24 28 32 Snow precipitation (mm W.E.)
Fig. 4. "Snow build-up" function for Aviemore (after Calder, 1990).
Schmidt (1991) as a function of canopy storage (Fig. 3).
3.4. Mass balance The evaporation flux E ( m m h -l) from the area was determined from the water balance of the snow on the canopy. Strictly, the water balance should contain the precipitation rate P, the evaporation rate E, the change in storage on the canopy, 6C/6t, and on the ground, 6g/ 6t, plus the discharge Q:
(6)
E=p+ CI-C2-t gl-g2 6t 6t
(7)
where C] and C2 are the canopy storage, gj and g2 are the ground snow storage determined at the beginning and end of the measurement period 6t respectively. However, in the cases considered here the precipitation was insignificant, after the initial snow build up, and in dense spruce forests the evaporation from snow on the forest floor would be expected to be small (although no measurements are available). Thus the evaporation is calculated from:
Schmidt (1991) studied evaporation of snow at subzero temperatures. He found that the measured sublimation, EA, from a 1 m high, freely standing artificial tree (normalised using the calculated sublimation from a 1 mm ice sphere, Esp) for new snow was roughly twice the value of that for old snow (Fig. 3). The normalised evaporation was also found to depend on the mass of snow on the canopy, increasing up to a m a x i m u m value (at approximately twice the rain-saturation value) and then decreasing as the intercepted mass increases further. The greater sublimation rate from new snow was attributed to the fact that the exposed microscopic surface area for the same intercepted mass was greater for new snow than for old snow. The decrease in the normalised evaporation for large intercepted mass was attributed to the fact that the exposed macroscopic area of the snow decreased when bridging of snow between branches started to occur. Schmidt (1991) expressed the evaporation rates as functions of intercepted mass. In order to make the expression independent of tree size Lundberg and Halldin (1994) expressed the data of
E=
C1 - C 2
6t
Q
(8)
(9)
4. Results During 1 6 - 1 9 March, 1985, a single event took place resulting in a large snow canopy storage. A considerable snowfall occurred during the 16 March and the morning of the 17 March; in all, 19.3 mm water equivalent fell, of which 14.5 m m lodged on the canopy and 4.8 m m reached the forest floor (this later figure was estimated from a snow survey), see Fig. 4. After the snowfall, no precipitation was recorded during the following 59 h. During this period
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163
7.5
RN (w/m 21 R~
a)
5.0
19 March
18 March
17 March U (m/s)
157
.....
2.5
.... . ..- ........ .....y
0.0 6e (Po), RH (~) 200
500 400 500 200 100 0 -I00
b)
150
RH
100
50 0 5.0 2.5 0.0 -2.5 -5.0 2O 15 10 5 0 5.0
~
t ~
"w.__ ! \
tI
I
T. dT (°C)
o)
C w, C l . g (ram
C[ .....
g
Q (mm/h), (~CC (ram) ,e)
_ ~
q
2.5
. . . . . . . .
.i- . . . .
- - - r
. . . . . . . . . . . . . . . . .
ACC// /
0.0 E (~./h) 2 0
I
r~,.
-,
~
/ ~ - - _
-
0 -I E^ec (ram) 50
g)
20
rl m
I
~
10 0
J . - - ~
7--I--w-~
12
24
5"r-"q 12
J
J
I 24
I
I
I r.w
i
lZ
i
(h)
Fig. 5. Measured meteorological parameters, canopy and ground storage, discharge, calculated and accumulated calculated evaporation: (a) R N is the net radiation, u is the wind velocity; (b) 6e is the vapour deficit, RH is the relative humidity; (c) T is the air temperature at reference height z, dT is the difference in temperature between reference height z and average canopy air temperature; (d) CM is the measured canopy storage, CI is the interpolated canopy storage, g is the calculated ground storage; (e) Q is the discharge, QACCis the accumulated discharge; (f) EWB is the evaporation rate determined with the water budget method (Eq. (9)), Er0L is the evaporation rate determined with the combination equation (Eq. (4)) and the aerodynamic resistance for rain r,L (Eq. (6)), Er0~ is the evaporation rate determined with the combination equation and the aerodynamic resistance for snow conditions ras (Eq. (7)); (g) E Acc is the accumulated evaporation determined with same methods as above.
the canopy storage C decreased by 10.8 m m from 14.5 m m to 3.7 m m (Fig. 5(d)). The accumulated runoff recorded from the heated plastic sheets was 4.6 m m (Fig. 5(e)). The accumulated evaporation, E ACC, during the period was 10.8 mm, corresponding to 0.19 m m h -1. The redistribution of the canopy storage, C, during this event can be observed in Fig. 6. Initially the storage was largest at the top of the canopy, but by
the evening of the first day some of the high branches were bare. During the third day the decrease in storage was roughly the same at all the remaining levels. An idea of the accuracy of the canopy storage measurements can be obtained by noting that a negative storage of 0.25 m m was recorded at 13 m height; this is probably due to the movement of branches, either due to snow loading or wind. During these 3 days the average net radiation, RN,
158
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163
Table 1 Estimates of accumulated evaporation with water budget equation and with combination equation using different aerodynamic resistances; March 1985 Term/date
17
18
19
ACC EwB (mm) 4cc (mm) Erjs
5.0 3.0
1.3 3.2
4.5 3.9
E mcc (mm) EACC/E Acc
5.1 0.60
10.2 2.46
12.3 0.86
was 97 W m -2 (Fig. 5(a)) with average daytime values of approximately 175 W m -2 and night values of -75 W m -2. The average wind velocity, u, was 2.7 m s -j (Fig. 5(a)). The average relative humidity, RH, was 91% (Fig. 5(b)), resulting in an average vapour pressure deficit be of 60 Pa with pronounced peaks during the days and zero values during the nights. The average air temperature, T, was -0.6°C (Fig. 5(c)), with night values below and daytime values above zero. The temperature difference, dT, between the air temperature at the reference level z and the temperature within the canopy was small except for the 19 March when the canopy was approximately I°C warmer than the air above. There was fairly good agreement between the accumulated evaporation calculated with the water budget method (Eq. (9)) and that calculated with the combination equation (Eq. (4)) with snow aerodynamic resistance ras (Eq. (7)) (Fig. 5(g)). The calculated value underestimated the evaporation during the first day and overestimated it during the second day. The accumulated evaporation E raL ACC calculated with the combination equation (Eq. (4)) and Eq. (6)--the 16
/"
J::
.
0 0.0
]
I
0.5
1.0
.
.
.
.
.
i ..........
1.5
19/3 19/,..3
2.0
1loo 19i00 2.5 C ( r a m / m )
Fig. 6. Canopy storage changes during 17-19 March, 1985.
17-19
28
30
Average (mm h -I)
10,8 -+ 1.4 10,1
3.9 -+ 0.8 2.3
3.1 _+ 0.8 1.1
0.24 0.18
27,8 0.94
7.8 0.59
1.5 0.35
0.51
standard equation for the aerodynamic resistance for rain raL, however, gave values 2.6 times larger than the accumulated evaporation calculated with the water budget method (Fig. 5(g) and Table 1). The variation in the hourly daytime values calculated with the water budget method (Fig. 5(f)) were great, reflecting the random errors in the individual canopy mass determinations. Two more days (28 and 30 March, 1985) fulfilled the requirements of large canopy storage: dry snow in the canopy and little precipitation during the observation period (Fig. 7(d,h)). The average net radiation, RN, was 168 W m -2 and 103 W m -2 respectively (Fig. 7(a)). On 28 March the average wind speed, u, was high (4.6 m s -~) and the average vapour pressure deficit, 6e, large (90 Pa) (Fig. 7(a,b)), whereas on 30 March both the wind speed (0.8 m s -1) and the vapour pressure deficit (42 Pa) were low. The air-temperature during both days was approximately I°C and the temperature difference between the canopy and the air above was very small (Fig. 7(c)). During both these days the canopy storage, C, decreased from approximately 9 mm to approximately 4 mm (Fig. 7(d)). The accumulated precipitation (Fig. 7(h)) was less than 0.1 mm during both days and the initial ground snow storage, g, was small (approximately 1.0 ram) on both days (Fig. 6(d)). For 28 March the accumulated evaporation (Fig. 7(g)), determined with the water budget method, agreed fairly well with the accumulated evaporation determined with the combination equation with the aerodynamic resistance for snow conditions ras. However the rain aerodynamic resistance again overestimated the evaporation. On 30 March the calculated evaporation using both the rain and the snow aerodynamic resistance gave lower rates than the water budget method. The summary of the accumulated evaporation in Table 1 and Fig. 8 shows
159
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163
28
March
30
RN(W/m~
10
0 200
March 3 0 March Q (mm/h),QaCC(mm) ) QAC~
March
28 500
I
30O 20O IO0 0 -100
~(P.), SH (r.)
/ 1
/////~°t
E (ram/h)
)
150
~r~L
1 O0
50 0 10
T,dT (°C)
lO
5
EACC{mm) raL
5 I)
/ ~"
. ~ -
0 -5 10
o
(mm) d)~ ~CM
CI~, ~,
1.o
pACC(~tm)
P (ram/h),
0.5
12
14
16
18
i------i-~..J 12 14 16
I 18
o.o
FL)I l J --I 12
14
16
18
l l l l 12
14
16
18
Fig. 7. Measured meteorological parameters, canopy and ground storage, discharge, calculated and accumulated calculated evaporation: (a) R N is the net radiation, u is the wind velocity; (b) 6e is the vapour deficit, RH is the relative humidity; (c) T is the air temperature at reference height z, dT is the difference in temperature between reference height z and average canopy air temperature; (d) CM is the measured canopy storage, Cr is the interpolated canopy storage, g is the calculated ground storage; (e) Q is the discharge, QACCis the accumulated discharge; (f) EWB is the evaporation rate determined with the water budget method (Eq. (9)), Er,L is the evaporation rate determined with the combination equation (Eq. (4)) and the aerodynamic resistance for rain r~L (Eq. (6)), Er,S is the evaporation rate determined with the Combination equation and the aerodynamic resistance for snow conditions ras (Eq. (7)); (g) E Acc is the accumulated evaporation determined with same methods as above.
that, even if the variations of individual hours are large, the average accumulated evaporation determined with the combination equation using the snow aerodynamic resistance agrees well with the average evaporation determined with the water budget method, whereas the standard aerodynamic resistance overestimates the evaporation. The values reported for 28 and 30 March refer to 7 h periods. The length of the period is given by the length of the interception measurements (Fig. 5(d)). The ratio between E ras Acc and E A c c plotted versus the canopy storage C in Fig. 9 shows very large variation and the sample is small. A tendency to underestimate the evaporation estimates for old snow (on the lower branches), when using the combination equation and the "snow aerodynamic resistance", can be detected (cf. Fig. 3). No trend in the ratio as a function of canopy storage is observed. The tree weighing experiment gave an almost
complete record of the weight of water (solid and liquid) on the forest canopy through the two winters 1983-1984 and 1984-1985. January 1984 (Fig. 10(a)) illustrates the typical patterns which can be observed. Events A and B follow a commonly found pattern with a snowfall followed by very rapid decrease in the snow storage associated with the
0 V" 0
L
5
I
10
I
15
I
20
25 E~c( mr")
Fig. 8. Accumulated evaporation determined with different methods. E Ace is measured with the water budget method. ErA,cc is calculated with the combination equation: O, aerodynamic resistance for snow conditions; @, aerodynamic resistance for rain conditions. Bars denote error associated with water budget method and figures denote dates.
160
A. Lundberg et al./Journal of l4ydrology 206 (1998) 151-163
I
I
I 0
I
1
2 1
0
0
I ,.5
0
I 6
assuming that when the storage is greater than 2 m m it is snow. It is unlikely that storage of liquid water can exceed 2 mm, except during short periods with high rainfall rates. Overall, during the December to March periods the canopy had snow cover for 32% of the 1983-1984 winter and 35% of the 1984-1985 winter.
|
I 9
I 12 C ( m m )
Fig. 9. Ratio of accumulated evaporation determined with different methods plotted against canopy storage C. E~vcc is measured with the water budget method. ErA,cc is calculated with the combination equation and the aerodynamic resistance for snow conditions. N indicates new snow (<24 h), O indicates old snow (>24 h). arrival of warm air in a frontal system. The periods of rapid fall are associated with above zero air temperatures (averaging +2°C), moderate wind speeds ( 3 - 4 m s -~) with some rainfall. During such periods there is almost certainly liquid water on the canopy from snow melt and rainfall and with possible evaporation rates up to 0.5 m m h -l (Calder, 1990). The third event (C) is a complex event extending over 15 days. The air temperatures were mostly below zero during this period, apart from the major loss period on 28 January which had positive temperatures and rainfall. Fig. 10(b) shows the tree weighing measurement for March 1995 which includes the three periods investigated in detail above. The agreement between the 7-ray and tree weighing estimates of canopy storage are very good, suggesting that the single tree gives a good representation of the forest during this period. The tree weighing measurements have been used to identify the percentage of the winter period in which the canopy is snow covered (Table 2). Periods when snow is on the forest canopy have been estimated by W,E. (mm)
5. Discussion and conclusion The m a x i m u m evaporation rate determined with the water budget method (0.56 m m h -E during 7 h) is much higher than the maximum evaporation from an open snow pack (0.06 m m h -1) reported by Harding (1986); it is also higher than the 0.3 m m h -l reported from intercepted snow by Lundberg and Halldin (1994) but is similar to the rate (0.5 m m h -l) reported by Calder (1990). Since Lundberg and Halldin (1994) worked with wet snow (lower aerodynamic resistance) it could be expected that they would report higher evaporation rates, but their measurement equipment did not allow measurements during high wind-speed conditions and may have excluded the highest rates. Nakai et al. (1995) quote values averaging 0.7 m m h -1 and 2.3 m m day -1. The tree weighing results suggest that the trees are snow covered one-third of the winter; the average measured evaporation rate is 0.24 m m h -1. If this is representative of the entire winter it would correspond to a total evaporation of 58 m m per month. A disadvantage with determining evaporation as a residual term from the water budget consideration is that the errors in the individual terms have to be added, resulting in a large possible maximum error. b)
a)
20-
10-
05
10
15 January
20
25
30
5
10
15
20
25
30
March
Fig. 10. The water equivalent of snow on the forest canopy as recorded by the tree weighing experiment for (a) January 1984 and (b) March 1985. Also shown (dots) are the ",/-raymeasurements in March 1985. The letters refer to storm numbers discussed in the text.
A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163
161
Table 2 Hours of snow cover, percentage of time there is snow on the canopy and maximum storage in the month estimated from the tree weighing experiment Period
December, 1983 January, 1984 February, 1994 March, 1984 December, 1984 January, 1985 February, 1985 March, 1985
Snow cover
Maximum storage
(h)
(%)
(mm)
21 74 18 17 20 63 4 37
6 23 11 9 7 > 30 2.5 15
155 551 126 128 98 474 20 276
Notes
data starts 11/12 system overtopped 22/1 to 29/1 6.5 days missing
This is a considerable potential problem in cases involving snowfall, where there can be large systematic errors in the precipitation measurements; however, since no precipitation occurred during the periods 1 7 - 1 9 and 28 March and only 0.03 m m on the 30 March, the effects of precipitation errors in these cases are small. The random error estimate of the 3,-ray attenuation system was calculated to be 0.1 m m (Calder and Wright, 1986), and from consideration of the variability in the measurement of the canopy storage between successive scans the measurements largely lie within this error. For individual scans, larger, random variations are found (up to 0.5 mm), These are due to drifts in the gain of the photomultiplier (arising from loss of temperature control) and on some occasions due to the movement of branches in the beam. Thus, although individual hourly rates may have large, random errors, the error in the long-term cumulative evaporation will be small. The determination of the effects of atmospheric stability would have required measurements not made in this study. An indication of the stability conditions can be obtained from the records of the difference 6T between the temperature above the canopy and the temperature in the stand. For all days except the 19 March the temperature difference was small, indicating neutral conditions. For 19 March the canopy was approximately I°C warmer than the air above, indicating unstable conditions, but there is no indication from the ratio between Eras and EWB (Table 1) that this affected the evaporation. In the wet-snow study by Lundberg and Halldin (1994) only stable conditions were observed (estimated using temperature difference to indicate the stability
of the air). This latter study reported a slight decrease in the evaporation in the most stable conditions. The calculated evaporation rates using the combination equation were very sensitive to the choice of aerodynamic resistance. This indicates that the aerodynamic term is more important than the radiation term and this is in agreement with the findings of Lundberg and Halldin (1994). The agreement between the accumulated evaporation determined with the water budget method and modelled by the combination equation using the snow aerodynamic resistance (ten times larger than the rain aerodynamic resistance) was generally good. During the 3 day period, 1 7 - 1 9 March, the agreement was very good on the last two days, but on the first day, immediately following the snowfall, the use of the aerodynamic resistance for rain provided a better agreement with observations. The source area for evaporation in these cases will vary with time (in contrast with that of momentum). At the beginning of the 3 day event the snow covered the entire canopy, whereas at the end snow only remained at the lowest branches (Fig. 6). The evaporation during the first day was well simulated with a low aerodynamic resistance (appropriate for rain), whereas during the following two days this value greatly overestimated the evaporation. A multilayer model with higher resistance from the lower branches might be useful to simulate this. A further uncertainty is the presence of liquid water on the canopy. No verification that the snow in the trees was completely dry was made; for part of the time the temperature was above 0°C and it is possible that parts of the snow on the highest branches may
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A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163
have melted, resulting in wet rather than dry snow conditions. A weighted snow and rain aerodynamic resistance should then have been used. This might indicate that the snow aerodynamic resistance should be even larger than determined here and it may also have masked any possible differences between new and old snow (Fig. 9) and possible differences in aerodynamic resistance as function of canopy storage. The evaporation determined with the combination method on the 30 March was lower than the evaporation determined with the water budget method using both rain and snow aerodynamic resistance. The meteorological conditions on this day were substantially different from the other periods (with lower wind speeds and higher relative humidity) and hence the calculated evaporation will be less sensitive to the aerodynamic resistance. A difficulty with the determination of evaporation of intercepted snow using the combination equation is the determination of vapour pressure in freezing conditions. If dry and wet thermometers are used an error in the temperature of 0.2°C alters the vapour deficit by approximately 30 Pa, compared with the observed vapour deficit on the 30 March of 42 Pa. Capacitance probes for humidity determinations are an alternative but are not reliable when measuring in very cold and humid environments, according to Lundberg and Halldin (1994). The transition between the solid and liquid phases is very important when dealing with the evaporation of intercepted snow and there is no existing direct method (Lundberg, 1993) to measure this. To partition it into liquid and solid phases will require further investigations and will probably require the use of a combination of methods, such as microwave and 3,-ray attenuation (Lundberg, 1993). This paper has presented some of the very few measurements of evaporation from a snow-covered canopy. The maximum evaporation rate (0.56 m m h -l) was similar to the rate (0.5 m m h -1) reported by Calder (1990), with an overall mean rate of 0.24 mm h -1. An order of magnitude calculation suggests that the total winter losses from snow intercepted on a forest canopy might be over 200 mm. It is obviously essential that physically based water resource and climate models include a proven and robust parameterisation of this process. Comparison of the measured intercepted snow evaporation and an
estimate made with a combination equation using different aerodynamic resistances showed that evaporation of dry intercepted snow can be calculated with the combination method provided a much larger aerodynamic resistance (ten times) than the standard aerodynamic resistance (Eq. (5)) is used. Such models will require more accurate measurements of air humidity (at temperatures close to and below zero), an improved consideration of the evaporation from partially covered canopies and measurements and models which separate liquid from solid interception.
Acknowledgements Thanks are due to all the staff at the Institute of Hydrology, Wallingford, UK, who were engaged on the data collection and analysis. The simulations were performed at the Division of Water Resources Engineering, University of Technology, Lule~, Sweden and was funded by The Swedish Natural Science Research Council (NFR) and Coldtech. Kimberly Miles, exchange student, University of Alaska, Fairbanks, Canada, helped with converting the data into PC standard. John Gash, Institute of Hydrology, Wallingford, UK is acknowledged for first pointing out the importance of the variable source area for latent heat.
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A. Lundberg et al./Journal of Hydrology 206 (1998) 151-163 a melting snowpack. Proceedings from Budapest Sympymposium, IAHS Publication, vol. 155, pp. 3-15. Lankreijer, H.J.M., Hendriks, M.J., Klaassen, W., 1993. A comparison of models simulating rainfall interception of forests, Agricultural Forest Meteorology, 64, 187-199. Lundberg, A., 1993. Measurement of intercepted snow--review of existing and new measurement methods, Journal of Hydrology, 151,267-290. Lundberg, A., Halldin, S., 1994. Evaporation of intercepted snow: analysis of governing factors, Water Resources Research, 30 (9), 2587-2598. Monteith, J.L., 1965. Evaporation and environment, The state and movement of water in living organisms. In: G.E. Fogg (Ed.), Symposium from Society of Experimental Biology, Cambridge, vol. 19, pp. 205-234. Nakai, Y., Kitahara, H., Sakamota, T., Saito, T., Terajima, T., 1993. A study on evaporation of snow intercepted by forest canopy, Journal of Japanese Forest Society, 75, 191-200. (in Japanese with abstract in English). Nakai, Y., Sakamoto, T., Terajima, T., Kitamura, K., 1995. Evaporation of snow intercepted by a Todo-fir forest (1) Water balance measurements, Journal of Japanese Forestry Society, 77, 581-588. (in Japanese with abstract in English). Nakai, Y., Sakamoto, T., Terajima, T., Kitamura, K., 1996. Evaporation of snow intercepted by a Todo-fir forest--estimations by an energy balance model and their comparison with water balance measurements, Journal of Japanese Forestry Society, 78 (1), 15-19. (in Japanese with abstract in English). Olszyczka, B., 1979. Gamma-ray determinations of surface water
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storage and stem water content for coniferous forests. PhD thesis, Department of Applied Physics, University of Strathclyde, Scotland. Penman, H.L., 1948. Natural evaporation from open water, bare soil and grass, Proceedings Royal Society Ser. A, 193, 120-145. Pomeroy, J.W. and Gray, D.M., 1995. Snow cover: accumulation, relocation and management. NHRI report No. 7, Saskatoon, Canada. Roberts, J.M., 1977. The use of tree cutting techniques in the study of the water relations of mature Pinus Selvestris L, Journal of Experimental Biology, 28, 751-767. Rutter, A.J., Kershaw, K.A., Robins, P.C., Morton, A.J., 1971. A predictive model of rainfall interception in forest. I Derivation of the model from observations in a plantation of Corsican pine, Agricultural Meteorology, 9, 367-384. Schmidt, R.A., 1991. Sublimation of snow intercepted by an artificial conifer, Agricultural Forest Meterology, 54, 1-27. Schmidt, R.A., Jairell, R.A. and Pomeroy, J.W., 1988. Measuring snow interception and loss from an artificial conifer. In: Proc. 56th Western Snow Conference, Kalispell, MT, April, 1988. Colorado State University, Colorado, pp. 166-169. Strangeways, I.C., 1972. Automatic weather stations for network operation. Weather 27, 403-408. Thom, A.S., 1975. Momentum, mass and heat exchange of plant communities. In: J.L. Monteith (Ed.), Vegetation and the Atmosphere, Vol. 1. Academic Press, New York, pp. 57-108. Thomas, G., Rowntree, P.R., 1992. The boreal forest and climate, Quarterly Journal of the Royal Meteorological Society, 118, 469-498.