﻿ Insolation ( input of solar energy) as a Function of Latitude and Season
San José State University

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Thayer Watkins
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 Insolation (input of solar energy) as a Function of Latitude and Season

The motivation for this material was when a friend told of seeing a video in which it was revealed that open water had been found at the North Pole. The video presented this as confirmation of global warming. The open water at the North Pole had been viewed by a couple of American scientists who were not meteorologists who journeyed on a commercial tour on a Russian ice-breaker in the summer time. The fact that it was summertime and that the Russians were taking customers on a regular basis to the North Pole should have alerted them that open water at the North Pole was not that unusual. But if one has a mindset concerning catastrophic global warming any observation that can be construed as evidence for global warming is accepted as evidence for global warming.

Open water at the North Pole may have to do with ocean and wind currents as well as temperature. However it is not widely known that the North Pole in the summer time was never deficient in solar warming. The input of radiant energy from the Sun is called insolation.

Insolation is the amount of radiant energy from the Sun which impacts upon a unit surface area. This will depend upon the angle of the Sun with respect to the vertical over the surface. This angle is called the zenith angle. If the Earth's axis of rotation had no inclination with respect to the plane of its orbit then the insolation at high noon is simply αcos(φ) where φ is the latitude angle and α is the intensity of the Sun's radiation above the atmosphere. The insolation as a function of latitude would be as shown below.

When the Earth's axis is tilted 23.5° toward the Sun (summer solstice for the Northern Hemisphere) the points at 23.5° are getting the same radiation as the points at the equator get when the axis is not tilted toward the Sun (equinoxes). This means that the North Pole at summer solstice is effectively at 66.5° N, about the same latitude as Stockholm, Sweden or Fairbanks, Alaska or Archangel, Russia at the equinoxes. But at summer solstice the North Pole is getting 24 hours per day what Stockholm, Fairbanks and Archangel get only 12 hours at the equinoxes. It would be surprising to find open water at Stockholm or Archangel on September 21st.

Using a formula developed elsewhere for the zenith angle of the Sun at each hour of the day the insolations (Watts per square meter per day) at the solstices and equinoxes were computed. All refinements such as the varying path lengths and average cloud cover were ignored. The computation does take into account the fact that the Earth is closer to the Sun at the Northern Hemisphere's winter solstice (December 21) than at its summer solstice (June 21). This means that the summer solstice for the Southern Hemisphere gets more intense solar radiation than the Northern Hemisphere gets for its summer solstice.

The insolation per day is measured in kilowatt-hours of energy per square meter (kW-hr/m²). The rate of energy input varies from 1.412 kW/m² at the closest approach to the Sun to 1.321 kW/m² at the furtherest. If an area is receiving energy at a rate of 1.4 kW/m² for one hour that is 1.4 kW-hr/m² of energy input. If its energy input falls from 1.4 kW/m² to 1.3 kW/m² for an hours then the combined energy received is 2.7 kW-hrs/m²

In the following latitudes in degrees north are given as positive figures; latitudes in degrees south are given as negative figures.

The rate of energy input per unit area depends upon the angle of the Sun. The solar constant is multiplied by the cosine of the zenith angle of the Sun, the angle between the Sun's rays and the vertical.

Amount of Solar Energy Received Per Day
Per Unit Area by Season and Latitude
(Kilowatt-hours/meter²)
Solar
Constant
1.321 kW/m² 1.366 kW/m² 1.412 kW/m²
Latitude
(deg)
NH Summer
Solstice
EquinoxesNH Winter
Solstice
Average of
these four
90 12.64 0 0 3.1600
80 12.45 1.8 04.0125
70 11.88 3.55 04.7450
60 11.49 5.19 0.585.6125
50 11.59 6.67 2.046.7425
40 11.65 7.95 3.767.8275
30 11.39 8.99 5.428.6975
20 10.99 9.75 7.129.4025
10 10.25 10.22 8.619.8250
0 9.20 10.38 9.849.9500
-10 8.06 10.22 10.969.8650
-20 6.67 9.75 11.759.4800
-30 5.07 8.99 12.188.8075
-40 3.52 7.95 12.457.9675
-50 1.91 6.67 12.396.9100
-60 0.54 5.19 12.285.8000
-70 0 3.55 12.70 4.9500
-80 0 1.80 13.314.2275
-90 0 0 13.513.3775

Here is the graph of the values for the solstices and equinoxes.

The blue line is for June 21, the Northern Hemisphere summer solstice, and the green line is for the Southern Hemisphere summer solstice, December 21. The red line is for insolation for both equinoxes, March 21 and September 21.

Some of the notable facts of these insolation values is that the North Pole at the Northern Hemisphere summer solstice gets more solar energy on that day than any other location on Earth. At that time it is getting significantly more than locations on the equator with their twelve hour days are getting. Of course at that time points on the equator are effectively at a latitude of 23.5° South. The point on Earth that gets the highest one-day energy input from the Sun is the South Pole. One-day energy inputs do not count for much in terms of annual climate. Here is the graph of the averages of the energy inputs for the solstices and the equinoxes. This average is a reasonable approximation of the annual average daily energy inputs.

This profile is essentially the same as the profile of average temperature by latitude.

The phenomenon of high insolation at high latitudes in the summer explains how giant cabbages and such short growing season plants can be grown in Alaska.

(To be continued.)