Top of the Atmosphere Solar Radiation

The solar radiation reaching Earth varies over the course of a day and the course of a year according to Earth-Sun geometry. The amount of extraterrestrial solar radiation at the top of the atmosphere on a horizontal surface is:

where S_c = 1364 W m^-2 is the solar constant and r_v is the radius vector. The cosine of the zenith angle adjusts the radiation that would be received on a surface perpendicular to the solar beam to that received on a horizontal surface. The radius vector accounts for the fact that as Earth moves in an elliptic orbit around the Sun, it is slightly closer to the Sun in January than in July (Figure 4.2). Since the strength of the Sun’s radiation decreases with the square of the distance from the Sun, Earth receives slightly more radiation in January than July. This distance, expressed as a fraction of the mean Earth-Sun distance, is called the radius vector and is at a minimum in early January. At this time, Earth receives about 3.5 percent more solar radiation relative to the average Earth-Sun distance. It is at a maximum in early July, when Earth receives about 3.25 percent less solar radiation. However, seasonal changes in radiation due to Earth’s tilt are much larger. Indeed, if Earth’s axis of rotation were perpendicular to the plane of rotation (i.e., no tilt), there would be no seasons since all points would be illuminated an equal amount of time throughout the year.

Figure 4.6 illustrates the diurnal cycle of solar radiation on June 21 for several latitudes in the Northern Hemisphere. Peak solar radiation at all latitudes occurs at solar noon, when the Sun is at its highest point in the sky. The Sun rises earlier in the day and sets later in the day with higher latitudes. At latitude 75° N, the Sun never sets. The lowest maximum insolation occurs at high latitudes, and insolation increases with southerly latitudes. This is because the Sun’s beam is spread over a larger area at high latitudes than at lower latitudes (i.e., the zenith angle is large) so that less radiation is received per unit surface area. However, latitudes 15° N and 30° N receive more solar radiation at solar noon than does the equator. This is because the solar declination angle (23.5°) is far north of the equator, and the Sun has a zenith angle of zero at solar noon at latitude 23.5° N.

Fig. 4.6. Diurnal cycle of solar radiation at the top of the atmosphere on the summer solstice for latitudes from the equator (0°) to 75° N

Daylength (in hours), defined as the period during which the Sun is above the horizon, is given by:

Daylength decreases with northern latitudes in winter and increases with northern latitudes in summer (Figure 4.7). Tropical latitudes have relatively little seasonal variation in daylength. Seasonal variation increases with higher latitudes in the Northern and Southern Hemispheres. The most extreme seasonal variation occurs in polar regions, where the Sun is below the horizon in winter and never sets in summer.

Fig. 4.7. Daylength as a function of latitude (vertical axis) and day of year (horizontal axis). Dark shading shows when the Sun never rises. Light shading shows when the Sun is above the horizon for 24 hours

Earth’s orbit around the Sun over the course of a year drives changes in the apparent motion of the Sun in the sky that affects the amount of solar radiation received. From December 21 to June 21, as declination increases from -23.5° to 23.5°, zenith angle decreases, days become longer, and regions in the Northern Hemisphere receive more solar radiation (Figure 4.8) . From June 21 to December 21, declination decreases, days get shorter, and radiation decreases in the Northern Hemisphere. Latitudes near the equator have relatively little seasonal variation in solar radiation. At higher latitudes, the amplitude of the seasonal cycle increases.

Fig. 4.8. Daily solar radiation at the top of the atmosphere in relation to latitude (vertical axis) and day of year (horizontal axis). Units are megajoules (10⁶ joules) per square meter

The most extreme seasonality occurs near the poles, where the Sun is below the horizon until the equinoxes (March 21, September 22) and where the long summer days result in much radiation. Figure 4.8 also shows a strong poleward decrease in solar radiation during winter, and a much weaker equator-to-pole temperature gradient in summer.