Definition and characteristics of solar constant and solar spectrum

Definition and characteristics of solar constant and solar spectrum

1.1 Solar Constant

Since the earth revolves around the sun in an elliptical orbit, the distance between the sun and the earth is not constant, and the distance between the sun and the earth is different every day of the year. As we all know, the radiation intensity at a certain point is inversely proportional to the square of the distance from the radiation source, which means that the solar radiation intensity above the earth’s atmosphere will vary with the distance between the sun and the earth. However, due to the large distance between the sun and the earth (the average distance is 1.5×108km), the intensity of solar radiation outside the earth’s atmosphere is almost constant. Therefore, people use the so-called “solar constant” to describe the solar radiation intensity above the earth’s atmosphere.

To understand the true meaning of the solar constant, it is necessary to explain the meaning of the two concepts of “average distance between the sun and the earth” and “upper boundary in the atmosphere”.

(1) The average distance between the sun and the earth from the sun and the earth is called “astronomical unit” in astronomy. Obviously, the astronomical unit refers to the distance, which is the distance from the sun to the earth, that is, the average distance between the sun and the earth. The number representing the size of this distance is a very important number, and many astronomical numbers are based on it. There are several ways to measure the distance between the sun and the earth. One is to use the Venus transit method (that is, the sun, Venus, and the earth are just in a straight line); the other is to use asteroids to measure the distance between the sun and the earth. Historically, the former method was used to measure the distance from the earth to the sun to calculate the average distance between the sun and the earth, that is, a beam of radar wave is emitted from the earth, hits Venus, and is reflected back from Venus. The average distance between the sun and the earth measured by this method is 149,597,870 km, which is about 150 million kilometers.

(2) The upper limit of the atmosphere means that the influence of the atmosphere on solar radiation is not considered, that is, the value of the solar constant in the absence of an atmosphere.

The solar constant refers to the solar radiation energy received per unit time and unit area on the plane perpendicular to the sun’s rays outside the atmosphere. That is to say, under the condition of the average distance between the sun and the earth, on the upper boundary of the earth’s atmosphere, on the area of ​​1cm2 perpendicular to the sun’s rays, the solar radiation energy received within 1min is called the solar constant. It is a physical quantity used to express solar radiation energy. The solar constant is determined by the World Meteorological Organization as (1367±7)W/m2. The solar constant represents, to a certain extent, the intensity of solar radiation reaching the upper boundary of the atmosphere vertically. However, there is the following mathematical relationship between the solar constant and the solar radiation intensity reaching the horizontal plane:

         Ⅰ= Io sinh

In the formula, h is the solar altitude angle; Io is the solar constant; I is the solar radiation intensity projected on the upper boundary of the atmosphere. The above formula shows that the intensity of solar radiation on the horizontal plane of the upper boundary of the atmosphere increases with the increase of the sun’s altitude. When the solar altitude angle is 90°, the solar radiation intensity is equal to the solar constant. Therefore, the solar constant is the maximum value of solar radiation intensity reaching the horizontal plane. The solar radiation reaching the upper boundary of the atmosphere is the solar constant. However, because the solar radiation reaching the upper boundary of the atmosphere is inversely proportional to the square of the distance between the sun and the earth, the solar radiation intensity at aphelion and perihelion has a certain difference with the solar constant. The solar radiation intensity perpendicular to the upper boundary of the atmosphere at perihelion is 3.4% larger than the solar constant; while at aphelion it is 3.5% smaller than the solar constant.

According to the above formula of the relationship between the solar radiation intensity and the solar constant, the solar radiation reaching the upper boundary of the atmosphere is proportional to the sine of the solar altitude angle. The altitude of the sun changes with latitude and time. In fact, the solar constant changes due to the following reasons: day and night are generated due to the rotation of the earth, and the seasons are generated due to the angle between the rotation axis of the earth and the rotation axis of the earth’s orbit around the sun.

The rotation axis of the earth and the earth's orbit around the sun

Figure 1-1 The rotation axis of the earth and the earth’s orbit around the sun

The earth rotates once a day from west to east around the “earth axis” that passes through it. Each revolution (360°) is day and night (24h), so the earth rotates 15° per hour. In addition to its rotation, the earth also revolves around the sun once a year in an elliptical orbit with a small eccentricity. The normal of the earth’s rotation axis and the orbital plane is always 23.5°. When the earth revolves, the direction of the rotation axis remains the same, always pointing to the north pole of the earth. Therefore, when the earth is in different positions of the orbit, the direction of sunlight projected on the earth is also different, thus forming the four seasons on the earth (Figure 1-2). At noon every day, the height of the sun is always the highest. In low tropical latitudes (that is, the area between 23°27′ north and south latitudes of the equator), the sun has two perpendicular incidences in a year. In higher latitudes, the sun is always close to the equator. In the Arctic and Antarctic regions, the sun stays below the horizon for a long time in winter, while it stays above the horizon for a long time in summer.

Schematic diagram of the earth moving around the sun

 Figure 1-2 Schematic diagram of the earth moving around the sun

Since the earth revolves around the sun in an elliptical orbit, the distance between the sun and the earth is not constant, and the distance between the sun and the earth is different every day of the year. As we all know, the radiation intensity at a certain point is inversely proportional to the square of the distance from the radiation source, which means that the solar radiation intensity above the earth’s atmosphere will vary with the distance between the earth. However, because the distance between the sun and the ground is too large (the average distance is 1.5×108km), although the solar constant value is affected by factors such as radiation measurement, the accuracy of the scale itself, and atmospheric interference, due to the large distance between the sun and the ground, other influences The factor can be controlled within the accuracy range, so for those who design and use solar photovoltaic power generation, it can be treated as a constant.

Therefore, people use the so-called “solar constant” to describe the intensity of solar radiation above the earth’s atmosphere. It refers to the energy received on the unit surface area of ​​the upper boundary of the earth’s atmosphere perpendicular to the solar radiation at the average distance between the sun and the earth.

1.2 Solar spectrum

(1) Definition of solar spectrum

Everyone knows that the sun looks white, but if a beam of sunlight passes through a glass prism, then a strip of red, orange, yellow, green, blue, indigo, etc. will appear on the white curtain (Figure 1-3). Purple colored light band. In physics, such colored light bands (light band diagrams in which the colors of light are arranged in the order of frequency or wavelength) are called the solar spectrum (Figure 1-4). In fact, this visible spectrum only occupies a small part of the solar spectrum. The wavelength of the entire solar spectrum is very broad, from a few tenths of a nanometer to tens of meters. There are infrared radiation, microwaves, radio waves, etc., which have wavelengths shorter than visible light, and ultraviolet, X-rays, etc., which have shorter wavelengths than visible light.

Colored light belt

Figure 1-3 Colored light belt

(2) Classification of spectra

According to the method of generation, the spectrum can be divided into two categories: emission spectrum and absorption spectrum. The spectrum directly generated by the light emitted by the luminous body is called the emission spectrum. The emission spectrum is divided into continuous optical harmonic and bright line spectrum.

The continuous spectrum is generated by the light emitted by a solid or liquid at a high temperature, and it contains continuous colored light bands including a variety of colors from red to purple. The bright line spectrum is generated by the light emitted by gas or vapor at high temperature, and there are only some discontinuous bright lines on a dark background.

Solar spectrum

Figure 1-4 Solar spectrum

The bright lines in the bright line spectrum are called spectral lines. The high-temperature steam of each element has its own unique bright line spectrum. Since the number and location of the spectrum of each element are different, it is possible to identify which element is emitted by these spectral lines.

In the context of continuous spectrum, there are many scrambled lines, this kind of spectrum is called absorption spectrum. It is the white light emitted by a very high temperature light source, which is generated after passing through a relatively low temperature gas or vapor.

The solar spectrum is an absorption spectrum. It is on the background of a continuous spectrum with many dark lines distributed. The reason is that the white light emitted by the sun passes through the solar atmosphere, which has a much lower temperature than the sun. The gas containing many elements evaporated from the sun. When the sunlight passes through it, the light that is the same as the spectrum line of these elements is absorbed by these gases, so the absorption spectrum is formed when the sunlight reaches the earth.

Solar radiation spectrum

Figure 1-5 Solar radiation spectrum

The wavelength of more than 99% of the solar radiation spectrum of the upper boundary of the earth’s atmosphere is between 0.15 and 4.0um. About 50% of the solar radiation energy is in the visible spectrum (wavelength 0.4~0.76um), 7% is in the ultraviolet spectrum (wavelength<0.41um), 43% is in the infrared spectrum (wavelength>0.76um), and the maximum energy is at the wavelength of 0.475 um (Figure 1-5). Because the wavelength of solar radiation is much smaller than the wavelength of ground and atmospheric radiation (3~120um), it is usually called solar radiation as short-wave radiation, and ground and atmospheric radiation as long-wave radiation. Changes in solar activity and the distance between the sun and the earth will cause changes in the solar radiation energy of the upper boundary of the earth’s atmosphere. It can be seen from the structure of the sun that the sun is not a black body with a constant temperature, but a multi-layered radiator with different wavelength emission and absorption. However, in solar energy utilization, it is usually regarded as a black body with a temperature of 6000K and an emission wavelength of 0.3~3um.

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