The relative amounts of insolation received at different latitudes and at different times have been carefully determined. The values all refer to conditions at the upper limit of the earth’s atmosphere, i.e. without the effect of absorption by the atmosphere. The accompanying figure (fig. 1), after Davis, shows the distribution of insolation in both hemispheres at different latitudes and at different times in the year. The latitudes are given at the left margin and the time of year at the right margin. The values of insolation are shown by the vertical distance above the plane of the two margins.
At the equator, where the day is always twelve hours long, there are two maxima of insolation at the equinoxes, when the sun is vertical at noon, and two minima at the solstices when the sun is farthest off the equator. The values do not vary much through the year because the sun is never very far from the zenith, and day and night are always equal. As latitude increases, the angle of insolation becomes more oblique and the intensity decreases, but at the same time the length of day rapidly increases during the summer, and towards the pole of the hemisphere which is having its summer the gain in insolation from the latter cause more than compensates for the loss by the former. The double period of insolation above noted for the equator prevails as far as about lat. 12° N. and S.; at lat. 15° the two maxima have united in one, and the same is true of the minima. At the pole there is one maximum at the summer solstice, and no insolation at all while the sun is below the horizon. On the 21st of June the equator has a day twelve hours long, but the sun does not reach the zenith, and the amount of insolation is therefore less than at the equinox. On the northern tropic, however, the sun is vertical at noon, and the day is more than twelve hours long. Hence the amount of insolation received at this latitude is greater than that received on the equinox at the equator. From the tropic to the pole the sun stands lower and lower at noon, and the value of insolation would steadily decrease with latitude if it were not for the increase in the length of day. Going polewards from the northern tropic on the 21st of June, the value of insolation increases for a time, because, although the sun is lower, the number of hours during which it shines is greater. A maximum value is reached at about lat. 43½° N. The decreasing altitude of the sun then more than compensates for the increasing length of day, and the value of insolation diminishes, a minimum being reached at about lat. 62°. Then the rapidly increasing length of day towards the pole again brings about an increase in the value of insolation, until a maximum is reached at the pole which is greater than the value received at the equator at any time. The length of day is the same on the Arctic circle as at the pole itself, but while the altitude of the sun varies during the day on the former, the altitude at the pole remains 23½° throughout the 24 hours. The result is to give the pole a maximum. On the 21st of June there are therefore two maxima of insolation, one at lat. 43½° and one at the north pole. From lat. 43½° N., insolation decreases to zero on the Antarctic circle, for sunshine falls more and more obliquely, and the day becomes shorter and shorter. Beyond lat. 66½° S. the night lasts 24 hours. On the 21st of December the conditions in southern latitudes are similar to those in the northern hemisphere on the 21st of June, but the southern latitudes have higher values of insolation because the earth is then nearer the sun.
| From Davis’s Elementary Meteorology. |
| Fig. 1.—Distribution of Insolation over the Earth’s Surface. |
At the equinox the days are equal everywhere, but the noon sun is lower and lower with increasing latitude in both hemispheres until the rays are tangent to the earth’s surface at the poles (except for the effect of refraction). Therefore, the values of insolation diminish from a maximum at the equator to a minimum at both poles.
The effect of the earth’s atmosphere is to weaken the sun’s rays. The more nearly vertical the sun, the less the thickness of atmosphere traversed by the rays. The values of insolation at the earth’s surface, after passage through the atmosphere, have been calculated. They vary much with the condition of the air as to dust, clouds, water vapour, &c. As a rule, even when the sky is clear, about one-half of the solar radiation is lost during the day by atmospheric absorption. The great weakening of insolation at the pole, where the sun is very low, is especially noticeable. The following table (after Angot) shows the effect of the earth’s atmosphere (coefficient of transmission 0.7) upon the value of insolation received at sea-level.
Values of Daily Insolation at the Upper Limit of the Earth’s Atmosphere and at Sea-Level.
| Lat. | Upper Limit of Atmosphere. | Earth’s Surface. | ||||
| Equator. | 40°. | N. Pole. | Equator. | 40°. | N. Pole. | |
| Winter solstice | 948 | 360 | 0 | 552 | 124 | 0 |
| Equinoxes | 1000 | 773 | 0 | 612 | 411 | 0 |
| Summer solstice | 888 | 1115 | 1210 | 517 | 660 | 494 |
The following table gives, according to W. Zenker, the relative thickness of the atmosphere at different altitudes of the sun, and also the amount of transmitted insolation:
Relative Distances traversed by Solar Rays through the Atmosphere, and Intensities of Radiation per Unit Areas.