Modelling Snowmelt-Induced Processes (Proceedings of the Budapest Symposium,
July 1986). IAHS Publ. no. 155,1986.
The energy balance of a melting snow cover in
different environments
ESKO KUUSISTO
Hydrological
Office,
PO Box 436,
Helsinki
10,
Finland
SF-00101
ABSTRACT
The energy balance of a melting snow cover has
been studied at two observation sites in flat, open fields
in Finland. The radiation balance contributed 48% of the
total energy flux at Jokioinen (61°N) and 58% at Sodankyla
(67°N). The difference was due to the later occurrence
of the melting season in the north; therefore days were
longer and solar radiation more intense. In addition, 20
energy balance studies from different environments have
been compared. It can be concluded that radiation and
turbulent exchange processes play a major role. In
special conditions the other components may also have
considerable effect on snowmelt.
Bilan d'énergie
d'une couche de neige fondante dans des
milieux
différents
RESUME
Le bilan d'énergie d'une couche de neige fondante
a ete étudie d'abord en deux sites d'observation dans deux
champs plats et dégages. Le bilan de rayonnement a
contribue a 48% au flux d'énergie total à Jokioinen (61°N)
et à 58% à Sodankyla (67°N). La différence était due à
l'occurrence plus avancée de la saison de fonte dans le
nord; pour cette raison les jours ont ete plus longs et le
rayonnement solaire plus intense. Enfin, 20 etudes du
bilan d'énergie des milieux différents ont été comparées.
On peut conclure que le bilan de rayonnement et les
procèdes d'échange tumultueux jouent un role majeur. Dans
les conditions spéciales, les autres composants peuvent
aussi avoir un effet considerable sur la fonte des neiges.
INTRODUCTION
Snowmelt depends on the energy exchange between the snowpack and its
environment. Therefore, all the variables affecting this energy
exchange should be considered if an accurate computation of the rate
of snowmelt is required.
The energy balance of a snowpack can be written as follows:
H = H
+ H, + H + H + H + H - H
m
sn
In
c
e
p
g
where
Hm
Hsn
H^n
H„
c
=
=
=
=
energy available for snowmelt,
net shortwave radiation,
net longwave radiation,
sensible heat exchange,
(1)
t
37
E.Kuusisto
38
He
Hp
H_
Ht
= latent heat exchange,
= heat content of precipitation,
= heat exchange at the ground surface,
= change in the internal energy of the snowpack.
Of these components, H l n , H c and H e can be considered to be
limited to the snow surface or to the uppermost snow layer with a
thickness of a few millimetres. H m , H s n and H t can be distributed
throughout the whole vertical extent of the snowpack. Thus
snowmelt within the snowpack may occur due to solar radiation
even if the temperature of the snow surface is below zero. The
component H„ is obviously limited to the base of the snowpack.
The energy balance of the snowpack was studied at two experimental
sites in open fields in Finland. One site was located in southern
Finland (Jokioinen, 61°N), the other in northern Finland (Sodankyla,
67°N). Snowmelt at these sites was estimated by observations at a
stake station together with precipitation measurements. Complete
meteorological data were available, because Jokioinen and Sodankyla
are the two meteorological observatories in Finland.
RADIATION BALANCE
The radiation balance at the snow surface can be expressed by the
equation :
H
= H - H
+ H, - H, - H
(2)
r
s
sr
1
lr
b
where
H
= incoming shortwave radiation,
H s r = reflected shortwave radiation,
H-L = incoming longwave radiation,
H, = reflected longwave radiation,
H b = outgoing longwave radiation.
Shortwave radiation is generally considered to fall within the
wavelength range 0.3-2.2 urn, longwave radiation between 6.8 and
100 um. The interval between 2.2 and 6.8 um contains both types of
radiation, but these wavelengths account for less than 5% of the
total radiation (Geiger, 1966).
The diurnal distributions of the incoming shortwave radiation at
Jokioinen and Sodankyla are shown in Fig.l. The lengthening of daytime and the increasing solar angle increase the intensity of
radiation considerably from March to April; hourly intensities were
100-150 W m~2 greater in April. In March about 55% of the daily
total was obtained within 4 h (10 a .m. to 2p.m.), in April about 45%.
The components of the radiation balance were calculated for a
number of days with intense snowmelt at Jokioinen and Sodankyla
during the period 1959-1978. H g , H g r and H r were measured; H b and Hj
were computed using the Stefan-Boltzmann equation; H l r was assumed to
be equal to zero.
o
The mean values of the components, in W m
Jokioinen
Sodankyla.
H
s
sr
Hi
H
121.7
66.4
276.0
201.7
118.3
263.9
H
b
H
r
were as follows :
Jokioinen
Sodankyla
309.4
21.9
309.5
37.7
The energy
balance
of a melting
snow cover
39
p.m. 12
FIG.l
The average hourly intensities
of the
shortwave radiation
at Jokioinen
and Sodankyl'â
and April
1971-1980.
incoming
in March
Thus incoming shortwave radiation was 66% greater at Sodankyla
during intense snowmelt. Average albedo was 0.55 at Kolioinen and
0.59 at Sodankyla. Differences in the longwave components were
small. The radiation balance was 72% greater at Sodankyla, mainly
due to a higher level of incoming radiation.
100
JOKIOINEN
y"
%
/
1
>.
S 75
o-
/
/
/
y
/ *——
/
1 1 f~~
Hi/
»J H sr / H s /
a, 50
/
>
o
1 I
1 25
Hh
1
*s
/
/
J
s^
J
3
U
y
-50
i/ /
i
i
, /250
100
150 200
Energy flux
/
Wm"2 350
FIG.2
The frequency
distribution
of the daily values of
the radiation
balance and its components at Jokioinen
and
SodankylS. during intense
snowmelt.
Figure 2 shows the frequency distribution of the daily values of
each component. The variation of the longwave components, especially
Hb> was small at both stations. The shortwave components varied
considerably; thus H„ ranged between 20 and 230 W m
at Jokioinen
40
E.Kuusisto
and between 40 and 340 W m~2 at Sodankyla. Even H s r exceeded
200 W m~2 at Sodankyla.
Cloud cover is the main factor causing variation in shortwave
radiation. Figure 3 shows the dependence of the daily values of H g
on daily cloudiness at Jokoionen. All data were from the first
pentad of April in order to eliminate the seasonal variation of H g .
The correlation coefficient between the variables was -0.77, which
is significant at the 99.9% level.
300
Wm
250
|
200
!..
| 100
o
c
50
0
0
1
2
3
4
5
Cloudiness
6
7
8
FIG.3
The dependence of daily incoming
shortwave
radiation
on daily cloudiness
at Jokioinen.
All data
from the first
pentad
of April,
1971-1980.
are
The fact that the incoming shortwave radiation at Sodankyla was
greater that at Jokioinen was mainly due to the later occurrence of
snowmelt at Sodankyla, although reduced cloudiness also had some
influence.
Figure 2 also shows the frequency distributions of the daily
radiation balance at Jokioinen and Sodankyla. Generally, the value
of the radiation balance is small compared to the values of its
components. This implies that the accuracy of measurements or
estimation should be good if the balance is to be calculated using
equation (2). Fortunately, direct measurements of the balance are
also available from some stations.
TURBULENT ENERGY EXCHANGE
Heat and moisture transfer above the snow surface occur as a
consequence of turbulent mixing. They occur simultaneously and may
thus be considered as a single process. This process is affected
mainly by turbulent convection in the presence of wind and mainly by
thermal convection if the wind is very weak. The molecular
processes of heat and moisture transfer - conductivity and diffusion - can usually by neglected (Kuzmin, 1972).
In most investigations, the sensible and latent heat exchanges
The energy balance
of a melting
snow cover
41
over snow have been, estimated by aerodynamic formulae for steady
flow over an infinite, uniform surface. Departures from this ideal
situation are always likely to occur. On the other hand, it is not
known whether these departures are serious enough to make the
application of these formulae questionable.
The well known equations for H c and H e , obtained by assuming
logarithmic profiles for wind velocity, temperature and humidity
under neutral conditions, are as follows:
X,
(v - v ) (T - T )
-A t 2
2
1JK 2
1J
C
pPaX k
ln2(z / z ï
2 1
Xm
V
e 2 (V2
l>%
L P
k
2
f aX~~
ln (z / z j
m
2 1
(3a)
V
(3b)
where
c„
'P = specific heat of air at constant pressure,
= air density,
Pa =
Lf =
= latent heat of sublimation,
Xh = turbulent transfer coefficient for heat,
= turbulent transfer coefficient for momentum,
= trubulent transfer coefficient for water vapour,
= von Karman constant,
= wind velocity,
= potential temperature,
= absolute humidity,
z
l> z 2 = measurement heights.
The ratios of the transfer coefficients depend on the stability
of the lower atmospheric layers. Unfortunately, these dependences
have not been completely agreed upon by different investigators.
Under stable conditions, both X n /X m and X e /X m have been considered
to be 1.0 (Anderson, 1976). In many snowmelt studies this value has
been used regardless of the magnitude of the atmospheric temperature
gradient.
Figure 4 shows the hourly averages and extremes of the air
°C/m
+3
A
'\
\\
,/
\Max
\
\\
J
1
\\
\
Mean
f
A.
/ v
\V /
//
/
\
^^
s—.
/
S.+1
Ê
Min
,t
— -
_ •—'
"' !
a.m. 12
Hour
FIG.4
erature
1
06
p.m. 12
The hourly averages and extremes of the air tempgradients
at Hyrylâ in the snowmelt season of 1981.
42
E.Kuusisto
SODANKYLÀ
100
%
S- 75
C
01
O"
>
I
3
OC
o
"
0
100
J0KI0INEN
%
>. 75
a
cr
s
50
-200
-150
-100
-50
0
Energy flux
50
Wm" !
150
FIG.5
The frequency
distribution
of daily latent
(He)
and sensible
(Hc) heat fluxes
at Jokioinen
and Sodankyla'
during intense
snowmelt.
temperature gradients in an open field at Hyrylâ (61°N) in the
melting season of 1981. Stable conditions prevailed; negative
temperature gradients occurred only in the forenoon hours, when the
average gradient was also at its smallest. Thus at Hyryla the ratio
X h /X m obviously was close to 1.0 in spring 1981. However, the data
series is too short to allow any general conclusions.
Figure 5 shows the frequency distribution of daily latent heat
and turbulent heat fluxes at Jokioinen and Sodankyla. In general,
the turbulent heat flux did not vary markedly, and its daily values
were all positive. The latent heat flux was negative on 44% of days
at Jokioinen and on 72% of days at Sodankyla. On 90% of days this
flux was between -40 and +70 W m" at Jokioinen, but on the
remaining days it deviated considerably from these values. At
Sodankyla large negative values of H were much more frequent that at
Jokioinen. It is obvious that the tails of the distributions of H e
are slightly erroneous, probably reflecting the deficiencies of the
estimation method.
Finally, Fig.6 shows the diurnal variation of sensible and latent
heat fluxes and of the total turbulent heat flux. The precise shape
of the curves, estimated on the basis of observations made only four
times a day, is obviously rather uncertain.
The sensible heat flux was 2-3 times larger in the afternoon that
in night-time. The high afternoon values were compensated by the
negative latent heat flux, especially at Sodankyla. The sum of
these fluxes, however, remained positive both in day- and nighttime. It is interesting to note that the sum had its maximum in the
night-time at Jokioinen.
The energy
balance
of a melting
snow cover
43
+50
JOKIOINEN
Wm'
SODANKYLÀ
/
—
/
/
\
\
//
\
—
\
\
V
\
\
\
\
\
/
^
\
\
/
/
/
/
//
\
/
/
/
^
A---NW
y/
-•--.
i
\
i
/
S
/
\
I/
\
\
\
A
\
\
\
A"v
//
0—O
— A—A
—-••-—
—
Sensible heat
Latent heat
TotaL turbulent heat
i
06
i
a.m. 12
Hour
\\
\\
\
_
\
N
/
^S
i
1
p.m.
12
00
06
1
a.m.
//
/A '
S
S
06
//
y
"*~._
12
Hour
/
/
1
06
p.m.
12
FIG.6
The diurnal variation
of sensible
and latent
heat
fluxes
and of the total turbulent
heat flux at
Jokioinen
and Sodankyla during intense
snowmelt.
OTHER COMPONENTS
The amount of energy transferred to the snowpack by rainwater is
relatively small. The average energy flux due to this process was
1.4 W m~ at Jokioinen and 1.6 W m~ at Sodankyla during intense
snowmelt. Daily averages exceeding 10 W m~ were very rare at both
stations.
During intense snowmelt, the contribution of ground heat flux to
meltwater production is usually negligible. This flux can be either
positive or negative. It was negative, for example, for the shallow
prairie snowpack studies by Granger & Male (1978). Positive values
are likely to occur for thicker snowpacks, but during the last
stages of snowmelt negative fluxes prevail. In this study, the
component H was neglected.
COMPARISON OF ENERGY BALANCE IN DIFFERENT ENVIRONMENTS
It is apparent that the roles of various energy fluxes are different
in different environments. Table 1 is a summary of the results of
20 studies. The following generalities can be presented:
(a) the radiation balance and turbulent exchange processes play a
major role; the contributions of heat from precipitation or heat
exchange at the ground surface are small or negligible;
(b) the radiation balance and sensible heat exchange are almost
positive during snowmelt periods;
(c) both evaporation and condensation may prevail during
44
E.Kuusisto
TABLE 1 The relative
contributions
of different
components of
energy balance of snowpack to snowmelt.
See equation
(1) for
definitions
of the
abbreviations
Elevation
(m)
Observation
period
Average
melt
ran d
-1
the
Percentage contribution
of the component
H +Hsn In
72
H
c
H
e
28 -18
25 -74
Miller (1955)
Open field (California), 37°N
Gold s Williams (1960)
Open field (Canada), 45°H
March 1959
Wendler (1967)
Open field (Alaska), 67°N
March-April 1966
86
14 -24
Anderson (1968)
Open field in mountains
(California), 37°N
Snow seasons 1947-51
- April-May, daytime
31
73
68
23
1
4
Treidl (1970)
Open field (Michigan), 46°N
Dewalle s Meiman (1971)
Forest opening (Colorado),
39° N
de la Casiniëre (1974)
Open field in mountains
(France), 46°N
Open field in mountains
(Spain), 41 N
7
75
January 23, 1969
15
17(10,7)
47
36
June 1968
50
56
44
-3
3 550
July 1968
16
85
15 -15
1860
April 1970
10
100
-11 -42
100
3 260
Weller s Holmgren (1974)
Open field (Alaska), 71°»
June 1971
Granger S Male (1978)
Open field in prairies
Melting season 1974
Melting season 1975
Melting season 1976
(Canada), 51 N
59
95
67
-19
41
5
33
-10
8
5
3
7
46
53
-4
-10
-29
-14
April 1978
Hendrie s Price (1979)
Deciduous forest (Ontario),
46° N
Kuusisto (1979)
Open field (Finland)
60° N
Harstveit (1981)
Open field in mountains
(Norway, 60°N
435
April-May 1979-80
- cloudy days
- clear days
12
35
65
23 20(22,--2) 54
7 37(135,-89)63
0
26
-24
Braun s Zuidema(1982)
Small basin, 23 % forest
(Switzerland), 47°N
800
Days with' intense
snowmelt, 1977-80
23
8
65
20
Eaton & Wendler (1981)
Open field (Alaska), 65° N
April 1980
3
67
Kuusisto (1982)
Open field (Finland),
61° N
Open field (Finland),
67 N
Days with intense
snowmelt, 1959-78
Ohmura (1982)
60
Melting seasons
1968-73
Open tundra (Canada, N.W.T.),
79° N
200
Melting seasons
1969-70
Open field in mountains
(New Zealand), 43° S
500
Oct.-Nov. 1976-80
- rainy days only
- days with greatest
heat supply
Moore & Owens (1984)
Open field in mountains
(New Zealand), 43 S
450
Melting season 1982
Aguado (1985)
Open field (Wisconsin)
Three sites, 43-45 N
Vehvilainen (1986)
Small basin, 82 % forest
(Finland), 64°N
120
Melting seasons
1971-81
Prowse s O œ n s
(1982)
H
p
1
7
33 -68
14 48(121,--73)47
2
3
15 58(128,--70) 40 -23
2
100
31
Melting seasons
1953-64
-90 -77
30
17
57
55
16
60
23
1
16
57
25
2
100
-12
13
25
~1
3
-31(88,--119)
5
15
-13
<1
86(105,,-19)
snowmelt; thus the latent heat flux may be negative or positive;
(d) in forest environments the radiation balance is usually the
most important energy component;
(e) on cloudy or rainy days turbulent heat transfer dominates;
(f) a very intense snowmelt usually also requires a large
turbulent heat transfer.
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g
The energy
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snow
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