APES 4.7: Solar Radiation and Earth's Seasons

Solar irradiance

Solar irradiance is the electromagnetic power received from the Sun per unit area. Its SI unit is watts per square meter, $\mathrm{W/m^2}$.

Solar irradiation (insolation)

Solar irradiation is the radiant energy received per unit area over a specified time interval. It is obtained by integrating irradiance over time and is commonly expressed in $\mathrm{J/m^2}$ or $\mathrm{kWh/m^2}$.

How are irradiance and irradiation mathematically related?

Irradiation is the time integral of irradiance: $H=\int I\,dt$. For constant irradiance, $H=It$.

Total solar irradiance (TSI)

TSI is the total solar power per unit area, summed over all wavelengths, incident on a surface perpendicular to incoming sunlight at the top of Earth's atmosphere.

Solar constant

The solar constant is the conventional mean value of TSI at Earth's average distance from the Sun, approximately $1361\ \mathrm{W/m^2}$.

How does distance from the Sun affect solar irradiance?

Solar irradiance follows an inverse-square relationship with distance: $I\propto1/r^2$. Relative to a reference distance, $I=I_0(r_0/r)^2$.

What is the approximate annual-average solar irradiance at the top of Earth's atmosphere?

It is about $1361\ \mathrm{W/m^2}$ on a surface perpendicular to the Sun's rays, or about $340\ \mathrm{W/m^2}$ when averaged over Earth's entire spherical surface.

Why is Earth's average incoming solar flux about one-fourth of the solar constant?

The solar constant applies to Earth's cross-sectional disk, with area $\pi R^2$. Averaging the same incoming power over Earth's spherical surface, area $4\pi R^2$, gives $1361/4\approx340\ \mathrm{W/m^2}$.

Solar zenith angle

The solar zenith angle, $z$ or $\Theta$, is the angle between the Sun's rays and the local vertical. It is $0^\circ$ when the Sun is directly overhead and approximately $90^\circ$ at sunrise or sunset.

How does solar zenith angle determine instantaneous irradiance on a horizontal surface?

Above the atmosphere, irradiance on a horizontal surface is $Q=S_0(R_0/R)^2\cos\Theta$ when $\cos\Theta>0$. When $\cos\Theta\le0$, the location is on the night side and the direct irradiance is zero.

How can solar zenith angle be calculated from latitude, solar declination, and hour angle?

For a horizontal surface, $\cos\Theta=\sin\phi\sin\delta+\cos\phi\cos\delta\cos h$, where $\phi$ is latitude, $\delta$ is solar declination, and $h$ is hour angle.

Solar declination

Solar declination is the latitude at which the Sun is directly overhead at a given time. It changes throughout the year as Earth's tilted axis changes the Sun's apparent position relative to the equator.

What condition determines the hour angle at sunrise or sunset?

At sunrise and sunset, the Sun is on the horizon, so $\cos\Theta=0$. For an idealized spherical Earth, this gives $\cos h_0=-\tan\phi\tan\delta$, where $h_0$ is the sunrise or sunset hour angle.

How do latitude and solar declination affect daylight?

The daylight duration depends on $\cos h_0=-\tan\phi\tan\delta$. At high latitudes, the geometry can produce 24-hour daylight in one season and 24-hour darkness in the opposite season.

How can daily-average top-of-atmosphere irradiance be found conceptually?

Daily-average irradiance is found by integrating the instantaneous irradiance over the daylight portion of Earth's rotation and dividing by the length of a full rotation. The daylight limits depend on the hour angle at sunrise and sunset.

What causes seasons in terms of solar radiation?

Earth's approximately $23.5^\circ$ axial tilt changes both the Sun's declination and the angle at which sunlight reaches each latitude. These changes alter daylight duration and the intensity of incoming radiation.

Why are the seasons opposite in the two hemispheres?

When one hemisphere is tilted toward the Sun, it receives more direct sunlight and longer days, producing summer. At the same time, the opposite hemisphere is tilted away from the Sun and experiences winter.

What happens at the solstices?

At a solstice, one hemisphere is tilted maximally toward or away from the Sun. That hemisphere experiences its longest or shortest day and its greatest or least solar elevation at noon.

What happens at the equinoxes?

At an equinox, neither hemisphere is tilted toward the Sun. The Sun is directly overhead at the equator, and day and night are approximately equal in length worldwide.

Why is axial tilt, rather than Earth-Sun distance, the primary cause of the seasons?

Axial tilt changes the angle and duration of sunlight in each hemisphere. Although Earth's elliptical orbit causes small changes in solar irradiance, it does not explain the opposite seasons in the two hemispheres.

How does Earth's elliptical orbit affect solar irradiance?

Earth receives more solar irradiance near perihelion and less near aphelion because of the inverse-square dependence on distance. This effect is smaller than the seasonal effect of Earth's axial tilt.

Milankovitch cycles

Milankovitch cycles are long-term variations in Earth's orbital eccentricity, axial tilt, and precession. They change the geographic and seasonal distribution of insolation and contribute to glacial-interglacial climate cycles.

How much does total solar irradiance vary over an approximately 11-year solar cycle?

TSI changes by roughly $0.1\%$ peak-to-peak over a solar cycle. Ultraviolet irradiance varies more strongly than total irradiance.

What solar processes primarily produce short-term changes in TSI?

Changes in solar surface magnetic activity, especially the competing effects of sunspots and bright faculae, account for most observed TSI variability.

Direct normal irradiance (DNI)

DNI is the solar irradiance measured on a surface perpendicular to the Sun's rays. It represents the direct beam and excludes diffuse radiation scattered by the atmosphere.

Direct horizontal irradiance (DirHI)

Direct horizontal irradiance is the direct-beam component received on a horizontal surface. It is related to DNI by $\mathrm{DirHI}=\mathrm{DNI}\cos z$.

Diffuse horizontal irradiance (DHI)

DHI is the radiation reaching a horizontal surface after being scattered by the atmosphere, excluding radiation coming directly from the Sun's disk. In the absence of an atmosphere, DHI would be nearly zero.

Global horizontal irradiance (GHI)

GHI is the total solar irradiance received by a horizontal surface. It is related to DNI and DHI by $\mathrm{GHI}=\mathrm{DHI}+\mathrm{DNI}\cos z$, where $z$ is the solar zenith angle.

Global tilted irradiance (GTI)

GTI is the total irradiance received by a surface with a specified tilt and azimuth, whether the surface is fixed or tracks the Sun. It is especially relevant to photovoltaic panels.

How does the atmosphere alter solar irradiance before it reaches Earth's surface?

Atmospheric gases, aerosols, and clouds absorb and scatter sunlight. The reduction is greater when the Sun is low because the radiation travels through a longer atmospheric path.

Typical comparison of solar irradiance above the atmosphere and at Earth's surface

The top-of-atmosphere normal irradiance is about $1361\ \mathrm{W/m^2}$. Under clear conditions, maximum direct normal irradiance at sea level is approximately $1000\ \mathrm{W/m^2}$, though actual values depend on solar angle and atmospheric conditions.

How are direct and global solar irradiance measured at Earth's surface?

A pyrheliometer mounted on a solar tracker measures direct normal irradiance. A pyranometer measures global irradiance, such as radiation received on a horizontal surface.

Why does a horizontal surface receive less direct irradiance when the Sun is low in the sky?

The direct horizontal component is $\mathrm{DNI}\cos z$. As $z$ increases, the rays strike the surface more obliquely and their energy is spread over a larger area.

Why can global surface irradiance exceed direct-beam irradiance?

Global irradiance includes both direct sunlight and diffuse light scattered or reflected by the atmosphere and surroundings. Therefore, GHI can be greater than the direct horizontal component alone.

Albedo

Albedo is the fraction or proportion of incident radiation reflected by a surface. Radiation that is not reflected may be absorbed and converted primarily into thermal energy.

What happens to absorbed solar radiation?

Absorbed radiation commonly increases a substance's thermal energy and temperature. In some systems, such as photovoltaic cells or plants, part of the absorbed energy is converted into electrical energy or chemical bond energy.

Projection effect of solar radiation

When sunlight strikes a surface obliquely, the same beam is distributed over a larger area, lowering irradiance. For a surface receiving direct sunlight, the relevant dependence is proportional to $\cos\theta$, where $\theta$ is the angle from the surface normal.

Absorption effect caused by a low Sun angle

At low solar elevation, sunlight travels through more atmosphere before reaching the surface. The longer path increases absorption and scattering, further reducing surface irradiance beyond the geometric projection effect.

Why are Earth's polar regions generally colder than equatorial regions?

Sunlight reaches the poles at lower elevation angles, so its energy is projected over a larger surface area. The poles also generally experience less annual insolation and longer periods of low or zero sunlight.

How does solar energy drive Earth systems?

Unequal solar heating creates temperature and pressure differences that drive atmospheric circulation, winds, and much of the water cycle. Solar energy also powers photosynthesis and influences weather and climate.

Why does the angle of incoming solar radiation influence climate?

The angle controls both the concentration of solar energy on Earth's surface and the atmospheric path length. Direct, concentrated radiation produces greater heating, whereas oblique radiation is spread over a larger area and undergoes more atmospheric absorption and scattering.

Why is solar irradiance important in applied science?

Solar irradiance is used to predict photovoltaic power production, estimate building heating and cooling loads, model climate and weather, study radiative cooling, and plan spacecraft or space-mission energy systems.