INTRODUCTION

Energy from the Sun reaching the Earth drives almost every known physical and biological cycle in the Earth system. By making solar radiation calculations and examining radiation measurements, students can gain a better understanding of many physical cycles and concepts associated with the Earth system.

A detailed study of solar irradiance will give Earth & Space Science and Physics students a better understanding of:

• Solar radiation
  
• Electromagnetic spectrum
  
• Mathematical concepts that apply to solar radiation
  
• Climate variation due to latitude
  
• Seasonal weather changes
  
• Global energy balance
  
• Daily changes in solar radiation
  
• Changes in solar irradiance due to solar cycles
  
• Effects of solar irradiance variations on the earth system
  

This educational brief is designed to serve as a source of background information on solar radiation studies and as a reference for student investigations on this subject. Links to student investigations can be found at the end of this brief. Before beginning a detailed investigation of solar radiation, there are three terms that must be understood.

• Irradiance - The amount of electromagnetic energy incident on a surface per unit time per unit area. In the past this quantity has often been referred to as "flux".
  * When measuring solar irradiance (via satellite), scientists are measuring the amount of electromagnetic energy incident on a surface perpendicular to the incoming radiation at the top of the Earth's atmosphere, not the output at the solar surface.
  
  
• Solar Constant - The solar constant is the amount of energy received at the top of the Earth's atmosphere on a surface oriented perpendicular to the Sun’s rays (at the mean distance of the Earth from the Sun). The generally accepted solar constant of 1368 W/m² is a satellite measured yearly average.
  
  
• Insolation - In general, solar radiation is received at the Earth's surface. The rate at which direct solar radiation is incident upon a unit horizontal surface at any point on or above the surface of Earth. *I will refer to insolation as direct solar radiation at the Earth's surface.
  

The solar constant is an important value for current studies of global radiation balance & climate models. The problem that faces scientists studying Earth’s radiation budget and climate is that while satellites can “accurately” measure solar irradiance and calculate a solar constant, the surface insolation is much more difficult to assess. When the solar constant is calculated there are four major problems in trying to relate this radiation intensity to its effect on the Earth's surface or surface insolation.

• First, the calculation is made for the top of the atmosphere and not for the surface of the Earth.
  
• Second, the calculation assumes that the surface receiving the radiation is perpendicular to the radiation.
  
• Third, the calculation assumes that the surface receiving the radiation is at a mean Sun-Earth distance.
  
• Fourth, the calculation assumes that radiation emission from the Sun remains constant.
  

Trying to relate calculations made for the top of the atmosphere to the surface is a problem because up to 70% of incoming radiation can be blocked by the atmosphere and cloud cover. In attempts to create global energy budget models, scientists must insert estimations for the amount of energy actually reaching the surface.

Assuming that the surface receiving the radiation is perpendicular to the incoming radiation is a problem because this is a rare occasion even at tropical latitudes due to the rotation of the Earth (time of day), tilt of the Earth's axis in relation to the incoming solar radiation (season), and the latitude and orientation of the surface. All of these factors change the angle of the surface receiving the radiation, which changes the intensity of the energy received.

Assuming that the radiation emission of the Sun is constant is a problem because this value fluctuates with cycles in solar activity. NASA satellites have measured incoming radiation since 1978 and have recorded changes in solar irradiance. This data can be accessed on the internet from Goddard Space Flight Center.

SOLAR RADIATION AND THE ELECTROMAGNETIC SPECTRUM

The electromagnetic spectrum consists of the entire range of frequencies and wavelengths at which electromagnetic waves can travel. The electromagnetic spectrum organizes energy types by wavelength and frequency. The peak wavelength of radiation emitted from an object is dependent upon the temperature of the object and can be calculated using the Wien Displacement Law when the temperature of the object is known. (In astronomy these are solid objects such as stars and planets.)

Wien Displacement Law:

maximum = 2897 / T
maximum = The peak wavelength of energy in
micrometers
T = The temperature of the object radiating energy

 

Using this law, the peak wavelength of radiation emitted from an object is inversely proportional to the temperature of the object. The irradiance or radiation output of an object can be calculated using the Stefan-Boltzman Law when the temperature is known.

Stefan-Boltzman Law: E = T⁴

E = Surface Irradiance of the object
* = Emissivity of the object
= Stefan-Boltzman Constant (5.67x10^-8 W/m²K⁴ )

T = Temperature of the object

 

*Emissivity is the factor of how well a surface can absorb and emit energy. Emissivity numbers range from 0 to 1. Very black objects such as charcoal have an emissivity near 1 while shiny objects have an emissivity near 0.

 

The Wien Displacement & Stefan-Boltzman laws strictly apply only to black bodies. Black bodies are capable of absorbing and emitting radiation at all wavelengths. Because the Sun & Earth are not perfect black bodies, applying these laws to them only allows approximate values to be obtained. The fact that the Sun is not a perfect black body is especially important when studying solar cycles. The most significant variations in solar radiation during these cycles occur in the UV & X-Ray portions of the solar spectrum. In order to compare solar emissions to black body emissions at the same temperature go to the Solar Spectrum/Black Body Graph.