SOLAR RADIATION ON SLOPES, NORTHERN HEMISPHERE
The intensity of solar radiation received on a unit of surface area in the mountains varies
considerably across the landscape because of the differing inclination and azimuth angles of
mountain slopes. Because solar radiation receipt is the main driving force for surface energy
balance differences in a mountainous region that lead to local wind systems, algorithms for the
calculation of solar radiation receipt on slopes assume an important role in mountain
meteorology. In this appendix, the differing rates of receipt of solar radiation on variously
oriented slopes at different times of year are discussed.
Any sloping plane surface can be defined by specifying its inclination and azimuth angles. The
inclination angle is the surface’s tilt angle relative to the horizon; the azimuth angle is the
direction that the surface faces, as determined from a compass bearing. A vertical, north-facing
wall would have an inclination angle of 90° and an azimuth angle of 0°. A slope with an azimuth
angle of 90° faces east, a 180°-azimuth slope faces south, etc.
On a horizontal surface, sunrise, sunset and day length, the length of the daily period of direct
solar radiation, vary significantly with latitude and day of year. In mountainous terrain, sunrise,
sunset and day length are also affected by the slope azimuth and inclination angles. This is
illustrated for slopes at 40° N latitude in Figure1, where the calculations assume a transparent
atmosphere, a solar constant of 1353 W m-2 and a longitude that is a multiple of 15° (times must
be advanced 4 minutes for each degree of longitude west and delayed by 4 minutes for each
degree of longitude east of these standard longitudes). The gray shading in the figure indicates
nighttime or a shaded slope, and the gray-white boundary at the tops (bottoms) of the sub-figures
indicates sunrise (sunset) times. The left-hand side of each sub-figure indicates insolation on a
slope with a 0° inclination angle (a horizontal surface) and is identical for each set of four subfigures in a column. The right-hand side of each sub-figure gives the insolation on a vertical wall
oriented as stated to the right of its row (e.g., north-facing). The dates at the tops of the columns
are approximate dates of the solstices and equinoxes. The sub-figures for west- and east-facing
slopes are asymmetric in time and slope inclination angle and are mirror images. Maximum
insolation occurs in the morning on an east-facing slope, in the afternoon on a west-facing slope
and at noon on a south-facing slope. On north- and south-facing slopes the insolation is
symmetric about noon. The day length on a sloping surface can be much shorter than on a
horizontal surface at the same date and latitude. Low-angle north-facing slopes are in sunlight for
only a short period in mid-winter, and higher-angle slopes receive no direct sunlight at all, even
though an adjacent horizontal surface may be illuminated for hours. For south-facing slopes,
peak insolation occurs on slopes of different inclination angles at different times of year. The
inclination angle for maximum insolation at 40°N latitude is about 15° on June 21 and 65° on
December 21. At the winter solstice, sunrise and sunset occur at the same time on all southfacing slopes because the sun rises in the southeast and sets in the southwest. At the summer
solstice, the sun rises in the northeast and sets in the northwest, so sunrise on south-facing slopes
is delayed and sunset is advanced. The delay in sunrise time and advance in sunset time increase
with steeper slopes. Double sunrises and sunsets can occur on steep north-facing slopes in the
summer half-year. The slopes are in direct sunlight early in the morning when the sun rises to the
northeast and in the evening when the sun sets to the northwest, but are in shade during much of
the day when the sun takes a path through the southern sky during midday.
Meteo 3000, page 1/2
Figure 1. Theoretical (i.e., extraterrestrial) solar radiation (W m-2) at 40°N latitude on slopes of
different inclination (0-90°) and azimuth (north-, west-, east- and south-facing) angles at
different times of day (0400 to 2000 LST) for the approximate dates of the solstices and
equinoxes. See text.
Meteo 3000, page 2/2