ESTIMATING EFFECTIVE NET RADIATION FOR
A MOUNTAINOUS WATERSHED
D. STORR
Atmospheric Environment Service, Canada Department of Environment,
Calgary, Alberta, Canada
(Received 1 November, 1971)
Abstract. Net radiation estimates are frequently required in watershed research, e.g., in calculating
evapotranspiration and snowmelt. In mountainous areas, the effective net radiation, i.e., the horizontal
projection of the flux through a surface parallel to the slope, is a more accurate measure of the
available energy than that measured with a horizontal sensor. In a non-homogeneous area, however,
a basin average of effective net radiation is difficult to estimate.
The annual curves for net and global solar radiation under clear skies at one point in the Marmot
Creek Experimental Watershed in Alberta, Canada, show variations from 55 to 650 lyday-' for net
radiation, and from 100 to 760 ly day-' for global radiation. A factor to convert measured net
radiation at the point to a basin average of effective net radiation is obtained by comparing these
curves with that for effective clear sky global radiation for the basin, and by considering the ratio
of net to global radiation over the various types of vegetation in the basin. This conversion factor
varies throughout the year with the elevation of the Sun and the basin albedo, ranging from a maximum
of 1.27 in December to a minimum of 0.93 in April, and averaging 1.06 for the year.
1. Introduction
In watershed research there may be some dispute with the statement by Geiger (1965)
that "radiation is undoubtedly the most important of all meteorologic elements"
because of the importance of precipitation, but there can be no denying that radiation
is of prime importance in studies of evapotranspiration and snowmelt.
The problem which confronts the researcher is: which element in the radiation field
should be used and how should it to be measured or calculated? Net radiation is the
most useful element because it integrates all wavelengths of both incoming and outgoing energy. The World Meteorological Organization (1961) defines net radiation as
"the net radiant flux through a horizontal surface", but in mountainous terrain, the
"effective net radiation", hereby defined as "the horizontal projection of the flux
through a surface parallel to the slope", is a more meaningful measure of the available
energy. The difference between radiation measured with a horizontal sensor and one
parallel to the slope may be positive or negative, and is of course greatest when slopes
are steep and the sun is low in the sky. The problem has been studied for incoming
short-wave radiation by Lee (1963), Ohmura (1968), Rouse and Wilson (1969), Ferguson et al. (1971), and others. Kondrat'yev (1965) discussed the radiation balance of a
slope, and Hay (1971) presented a complex model for computing the mean monthly
intensities of the component fluxes of net radiation for drainage basins. This paper
presents a simple method of estimating a basin average of effective net radiation for
periods as short as one day from net global radiation data measured by horizontal
sensors, along with calculated effective global solar radiation.
Boundary-Layer Meteorology 3 (1972) 3-14. All Rights Reserved
Copyright © 1972 by D. Reidel Publishing Company, Dordrecht-Holland
4
D. STORR
The following nomenclature is used for surface fluxes: QN is net all-wave radiation
and a gain of energy by the ground is positive, QT is short-wave radiation from Sun
and sky (global solar radiation), QR is short-wave radiation reflected from the Earth,
QL1 is long-wave radiation received from the atmosphere, and QLT is long-wave radiation emitted and reflected by the surface.
Then
QN = Q T - QR + QL1 - QLT.
(1)
2. Site and Instrumentation
Marmot Creek (Figure 1) is a mountainous watershed of 9.4 km 2 about 80 km west
of Calgary, Alberta, at latitude 500 57' N, longitude 115 ° 10' W. Elevations range from
1585 to 2805 m MSL with an average slope of 39%. The general aspect is easterly but
individual slopes may face any direction from north through east to southwest. The
vegetative cover is mainly spruce-fir but there are important amounts of lodgepole pine,
larch, and alpine meadow. The treeline is between 2135 and 2285 m. An inventory of
vegetation by Kirby and Ogilvie (1969) is summarized in Figure 2.
Net radiation has been measured with a horizontal CSIRO sensor on a 20-m mast at
Con 5 (Figure 2) from 1963 to 1967 and from 1967 to the present on a 46-m tower at
Fig. 1. Aerial view of Marmot Creek, looking westward to the continental divide.
ESTIMATING EFFECTIVE NET RADIATION FOR A MOUNTAINOUS WATERSHED
5
2134m
o
Qr
Fig. 2.
Marmot Creek vegetation distribution and site locations.
Twin 12. The Con 5 sensor was approximately 1.5 m above spruce which had been thinned in an early selective cutting program.
The Twin 12 instrument is about 10 m above virgin spruce. Because a sensor receives 99% of its upward flux from a surface area with radius ten times its height above
the surface, the Twin 12 sensor therefore sampled the outgoing radiation from an area
44 times larger than the Con 5 sensor. Measurements were recorded continuously.
Although five different sensors have been used, the data are believed reliable (with the
exceptions noted later in Section 4). There are a few gaps in the record, but not as
many as might be expected in an area where winter access is limited to one visit a month.
Short-wave radiation has been measured at Twin 12 since June 1970 with a horizontal Kipp solarimeter about 7.5 m above the tree tops.
3. Variability of Net Radiation
Both sites were in operation in 1967 from July 1 to September 15, providing the data
for the relationship shown in Figure 3. Federer (1968) found little variation in QN over
similar cover types. Since Ferguson et al. (1971) calculated that there would be no significant difference in the theoretical insolation at the two sites for any season, the difference between the Con 5 and Twin 12 data can be attributed mainly to the difference
in albedo of the thinned and unthinned forests. Making the assumption that this
6
D. STORR
difference in albedo is relatively constant through the year, the Con 5 data for 1963
to 1967 were used to estimate (by the Figure 3 relationship) the values at Twin 12, to
provide a longer period of comparable data for the calculation of temporal variations.
The average daily curve for QN consists of a negative portion at night when shortwave radiation is absent and outgoing long-wave radiation from the earth is greater
than incoming long-wave radiation from clouds and the atmosphere, and a positive
portion during the day when incoming radiation is much greater than the sum of the
outgoing components. Part of this daytime surplus moves downward into the soil
(eventually to be released as upward long-wave radiation) or may be used for snowmelt, part is transferred to the air, and the remainder is used for evapotranspiration. It
is therefore the positive portion which is of most interest to hydrometeorologists. It is
greatly affected by topographic shading as shown in Figure 4, the curves for two clear
days. Even sharper cut-offs have been noted with portable sensors in deeper valleys.
Because QLT is a function of temperature, the curves are slightly skewed, with the afternoon decline being more rapid than the morning increase.
Twin 12
60
I.
500
400
. .
,
I
300
v =31 +
1.057
r = 982
200
S/. = 20.8langley
I'
1(0
I'
I/~
100
I
200
300
400
500
Con
Langley
Fig. 3. Daily positive QN at Twin 12 vs Con 5, July 1-Sept. 15, 1967. (Some points omitted to
avoid overlapping). Sy, z is the standard error in estimating y from x.
A wide temporal variability in positive net radiation is shown in Figure 5, giving
monthly means, standard deviations, and the highest and lowest recorded values. Such
variability is probably to be expected in such a complex function as net radiation.
The effect of scattered cumulus is shown in Figure 6. On occasion the trace becomes
negative when a small cumulus passes over the sun, causing an almost complete absence of Qr while QLT is greater than QLI. It is also of interest to note that peak values
ESTIMATING EFFECTIVE NET RADIATION FOR A MOUNTAINOUS WATERSHED
7
I
2I
(MST)
Fig. 4.
Effect of season and topographic shading on net radiation.
l l
l
l
li
M
A
14
13
12
11
,
o 9 _
z
8 _
5
4 3 _
I
Fig. 5.
I
'
J
F
,
,
M
J
J
, \,
A
S
O
N
D
Monthly totals of positive net radiation at Marmot Creek, 1963-1970.
on cumulus days are higher than on clear days, the result of reflected radiation from
the sides of the white clouds.
4. Annual Curves of Clear-Sky Positive Net Radiation and Insolation
From the 7j yr of record, a total of 196 days were found with clear skies and reliable
8
D. STORR
record. The measured daily totals of positive net radiation for these days were plotted
to give the annual curves of clear-sky positive net radiation at Twin 12 (B) and Con 5
(A) (Figure 7). Considering the accuracy attainable by net radiometers and the fact
that QN on clear days depends on insolation, surface emissivity, air and ground temperatures, and the amount of precipitable water, dust and carbon dioxide in the air, there
is remarkably little scatter from the best-fit curves. The scatter is somewhat greater in
April, May, September and October, probably due in part to large variations in albedo
2I
2I
r
M.S.T.
Fig. 6.
Effect of scattered cumulus on net radiation.
ir
:3
1
..
.
.
..........
Fig. 7. Clear-sky radiation at Marmot Creek.
.
..
.
.
.
..
..
ESTIMATING EFFECTIVE NET RADIATION FOR A MOUNTAINOUS WATERSHED
9
associated with intermittent snow cover on the ground. Intermittent snow cover on
the treetops is probably the cause of some scatter in the winter months.
Except in December and January, there are noticeable differences in clear-sky net
radiation values between Twin 12 and Con 5 in agreement with the simple correlation
found for all-weather daily totals in Figure 3. On a few occasions when the data for
clear days did not fit the curve, a check showed faulty data extraction procedures. Over
another period of some months, the clear-sky data were consistently lower than given
by the curve, and testing showed that the sensor had changed its calibration. The curve
can therefore serve as both a test of the sensor and of data extraction procedures.
Also in Figure 7 is the annual curve for Qr at Twin 12 (C). Because of the short
period of record, it has been partly estimated. The curve for effective global radiation
for the whole basin under clear skies as derived by Ferguson et al. (1971) is shown as D.
The values derived from curve B do not plot as a straight line (Figure 8) against cos
(6 - S) where 6 is the declination of the Sun and 0 is latitude, so they are not quite sine
curves. They are also slightly skewed like the daily curves in Figure 4, again the result
of the temperature dependence of QLT and also the slight skewness of insolation found
by Ferguson et. al. (1971).
l
·
, .900
l
June 22'
Jua 24
~~.800
.800
May
Au12
Sr~Sept
10
1
1,6
pr
2
.700Arg
.700
May21
Apr 4
Sept23Mar21
.600
Oct r
.500
Feb 23
Oct 20
Feb 9
Nov3
.400
No 19
MarS
Jan21
.300
.
100
.
,
I
200
,
I
i,
300
400
,
. I
500
QN
at Twin 12.
I
600
Langleys
Fig. 8.
Cos(J--g) vs positive
5. Determining a Basin Average for Effective Net Radiation
Considering the temporal variability in measured net radiation shown in Figure 4, and
also the spatial variability in effective insolation found by Ferguson et al. (1971) as
illustrated in Figure 9, and the variability in albedo due to cover and slope differences,
it is obviously impractical to determine a basin average for effective net radiation by
direct measurement.
10
D. STORR
ESTIMATING EFFECTIVE NET RADIATION FOR A MOUNTAINOUS WATERSHED
11
It is a reasonable assumption for periods of a day or more, that:
Clear sky Q12)
Clear sky Q(for Twin 12)
=
Clear sky effective QN (for Twin 12),
Clear sky effective QT
(2)
and that the same relationship holds for the basin as a whole:
Clear sky QN
Clear sky effective QN
(for basin) =
(for basin).
Clear sky QT
Clear sky effective QT
(3)
Shaw (1965), Davies (1967), Polavarapu (1970) and others have discussed the relationship between QN and QT, but all for standard observing sites over clipped grass,
so their data bear little resemblance to the relationship found at Marmot Creek over
a mountain forest.
Rouse and Wilson (1969) found a regression of QN= 0. 6 4QT- 11 over a deciduous
forest at Mont St. Hilaire for the May-August period; considering the difference in
albedo, this is not dissimilar to the clear-sky relationship between curves B and C in
Figure 7.
The annual dimensionless curve for QNIQT under clear skies over the spruce at Twin
12 is shown as E in Figure 10. Comparable clear-sky curves for pine, meadow, rock
and larch were estimated considering the average times and amounts for snow cover
in the basin, and using the relationship from (1):
Fig. 10. Dimensionless curves (left-hand scale) of QN/QT ratio for spruce (Twin 12) (E), and
weighted basin average (J), and of factor L to convert measured QN at Twin 12 to effective basin QN.
K is effective clear-sky QN for the basin (right-hand scale).
12
D.STORR
(4)
QN/QT = 1 - a + (QL1 - QLI) Q T
along with published figures (Budyko, 1958; Geiger, 1965) for the annual march of
albedo a as guides. For clear days, the net long-wave component in (4) is small and
negative, so QN/QT is slightly less than 1 -a. The mean QN/Qr curve for the basin (J)
was then calculated using Kirby and Ogilvie's (1969) analysis of the cover types as
weighting factors.
Finally, effective clear-sky net radiation for the basin was obtained from Equation
(3) and is shown as curve K in Figure 10.
Table I gives the average data for the curves for the equinoxes, the solstices and for
16 dates representing solar declination angles of _ 20, _ 15, _ 10, and _ 5 deg.
The final step is to obtain effective net radiation for the basin for all-weather conditions. If it is assumed that cloud cover over the basin is reasonably uniform, effective
basin QN for all-weather conditions equals:
Effective clear-sky basin QN1
effective clear-sky basin
L
Clear-sky QN at Twin 12
x (All-weather QN at Twin 12).
The first factor in brackets is shown as 'L' in Table I and Figure 10.
TABLE I
Daily clear-sky radiation values at Marmot Creek
Curve
Date
Jan. 21
Feb. 9
Feb. 23
Mar. 8
Mar. 21
Apr. 4
Apr. 16
May 1
May 21
Jun. 22
Jul. 24
Aug. 12
Aug. 28
Sept. 10
Sept. 23
Oct. 6
Oct. 20
Nov. 3
Nov. 19
Dec. 23
B
clear-sky
QN at
Twin 12
(ly)
C
clear-sky
QT at
Twin 12
(ly)
D
effective
clear-sky
basin QT
(ly)
E
J
QN/QT
QN/QT
at
Twin 12
for
basin
K
L
effective
(K/B)
clear-sky FN
for basin
(ly)
75
135
190
250
315
375
430
495
565
600
540
465
395
335
275
220
155
100
65
47
130
200
265
340
415
480
540
615
695
760
710
635
550
470
390
320
240
175
117
85
200
278
352
441
521
596
681
745
800
848
787
715
638
559
488
414
342
266
191
146
0.576
0.675
0.717
0.735
0.759
0.781
0.796
0.805
0.813
0.789
0.760
0.732
0.718
0.713
0.705
0.687
0.640
0.571
0.555
0.552
439
504
534
549
568
586
599
630
683
737
716
680
647
617
570
524
484
432
418
405
88
140
188
242
296
349
408
469
546
625
563
486
413
345
278
217
165
115
80
59
1.173
1.048
0.990
0.968
0.939
0.930
0.949
0.948
0.966
1.042
1.043
1.045
1.045
1.030
1.011
0.986
1.064
1.150
1.230
1.255
ESTIMATING EFFECTIVE NET RADIATION FOR A MOUNTAINOUS WATERSHED
13
Therefore, to determine effective basin net radiation for any period, the 'L' value
for the period is multiplied by the net radiation data from Twin 12.
6. Conclusions
(1) The annual curves of clear-sky positive net radiation and global radiation are
the keys to this paper. A study of such curves for various latitudes and over various
surfaces would be of value to many researchers.
(2) This method could be applied to other areas where the basic assumptions are
valid. If the vegetation is uniform over the area, the required calculations are much
simpler.
(3) During the mid-winter period when the sun is low in the sky and Twin 12 is
shaded for much of the day, 26% more energy is available for basin processes than that
measured at Twin 12. Conversely, in April and May when the sun is higher but the
ground is still mainly snow-covered, 7% less energy is available for the basin than that
measured at Twin 12.
To eliminate some areas of uncertainty and to reduce reliance on theoretical assumptions, the following further work is suggested:
(1) More measurements of clear sky QT at Twin 12.
(2) Measurements of clear sky QNIQT over various cover types to reduce reliance
on the assumption used in the construction of Figure 10.
To test this method, annual water balances using evapotranspiration estimates based
on the effective basin net radiation are being prepared. Preliminary results are very
encouraging.
References
Budyko, M. I.: 1958, The Heat Balance of the Earth's Surface, English translation by U. S. Dept. of
Commerce, Washington, D.C., pp. 35-37.
Davies, J. A.: 1967, A Note on the Relationship Between Net Radiation and Solar Radiation',
Quart. J. Roy. Meteor. Soc. 93, 109-115.
Federer, C. A.: 1968, 'Spatial Variation of Net Radiation, Albedo and Surface Temperature of
Forests', J. Appl. Meteor. 7, 789-95.
Ferguson, H. L., Cork, H. F., Mastoris, S., Anderson, R., and Weisman, B.: 1971, 'Theoretical
Clear Sky Insolation in Marmot Creek Basin', Canadian Meteorological Service, Climatological
Studies, No. 21, 45 pp.
Geiger, R.: 1965, The Climate Near the Ground, English translation by Harvard Univ. Press, Cambridge, Mass., pp. 5 and 15-18.
Hay, J. E.: 1971, 'Computation Model for Radiative Fluxes', New ZealandJ. Hydrol. 10, No. 1.
Kirby, C. L. and Ogilvie, R. T.: 1969, 'The Forests of Marmot Creek Watershed Research Basin',
Canadian Forestry Service Publication 1259, Department of Fisheries and Forestry, Ottawa, Ont.
Kondrat'yev, K.: 1965, Radiative Heat Exchange in the Atmosphere, transl. from Russian, Pergamon
Press, Oxford.
Lee, R.: 1963, 'Evaluation of Solar Beam Irradiation as a Climatic Parameter on Mountain Watersheds', Hydrology papers, Colorado State University, Fort Collins, Colo.
Ohmura, A.: 1968, 'The Computation of Direct Insolation on a Slope', Climatological Bulletin,
No. 3, McGill University, Montreal, Que., 42-53.
Polavarapu, R. J.: 1970, 'A Comparative Study of Global and Net Radiation Measurements at
Guelph, Ottawa, and Toronto', J. Appl. Meteor. 9, 809-814.
14
D. STORR
Rouse, W. R. and Wilson, R. G.: 1969, 'Time and Space Variations in the Radiant Energy Fluxes
over Sloping Forested Terrain and Their Influence on Seasonal Heat and Water Balances at a
Middle Latitude Site', GeografiskaAnnaler, 51, Ser. A, 160-175.
Shaw, R. H.: 1956, 'A Comparison of Solar Radiation and Net Radiation, Bull. Amer. Meteor.
Soc. 37, 205-206.
World Meteorological Organization:
Practices, W.M.O., No. 8 TP 3.
1961, Guide to Meteorological Instrument and Observing