Understanding Solar Radiation: Types, Laws, and Effects

Understanding Solar Radiation

Direct radiation: Solar radiation received directly from the sun without being scattered by the atmosphere.

Diffuse radiation: Solar radiation received after its direction has been changed due to reflection and refraction in the atmosphere.

Total radiation is the sum of direct and diffuse radiation at the surface.

Solar Constant

The solar constant is the amount of energy received per unit time on a unit area perpendicular to the sun's direction at Earth's mean distance, outside the atmosphere. The currently accepted value is: S = 1.94 Ly min^-1 = 1368 W/m²

Absorption, Reflection, and Transmission

When radiation strikes a body, it can be absorbed, reflected, or transmitted. The ratio is: e + r + t = 1, where:

• e = absorptivity
• r = reflectivity
• t = transmissivity

Black Body

If e = 1, the body is a black body. A black body absorbs all radiation that strikes it:

e = 1, r = 0, and t = 0

E_a = E_i, E_r = 0

White Body

If r = 1, the body is a white body.

E_r = E_i, E_a = 0

Radiant Intensity

Radiant intensity is the radiant energy that passes through an imaginary plane in space per unit area, unit time, and unit solid angle perpendicular to the plane. It is expressed in W/m² sr^-1.

I = dQ / (dA * dt * dw)

Where:

• dQ = incident energy
• dA = area
• dt = time
• dw = solid angle

Radiant energy flux is the energy radiated by a body per unit time.

Monochromatic emittance is the radiant energy emitted at a given wavelength per unit time, unit area, and unit wavelength interval, measured in W m^-2 μm^-1.

The radiant energy emitted by any body depends on:

• The nature of the body
• Its surface
• Its absolute temperature
• Size
• Time

Planck Function

The Planck function describes the radiation emitted by a black body, according to wavelength and temperature:

E = C₁λ^-5 / (e^C2/(λT) - 1)

Where:

• C₁ = 1.1910439 x 10^-16 W m² sr^-1
• C₂ = 1.438769 x 10^-2 m K
• T = temperature (K)
• λ = wavelength (m)

Stefan-Boltzmann Law

The Stefan-Boltzmann Law indicates the amount of energy per unit area, E, emitted by a black body, regardless of direction. It corresponds to the area under the curve resulting from integrating the Planck equation:

E = σT⁴

Where σ is the Stefan-Boltzmann constant (5.67051 x 10^-8 W m^-2 K^-4)

Wien's Displacement Law

Wien's displacement law states:

λ_max * T = 2897.9 K

The spectral distribution of black body radiation depends on temperature. Higher temperature corresponds to higher energy at shorter wavelengths.

Factors Affecting Solar Radiation

Radiation intensity of the sun is a function of altitude: h

I_h = I₀ sin h

Daily Distribution of Solar Radiation

Solar radiation varies throughout the day, with a maximum at midday.

Atmospheric Effects on Solar Radiation

Energy is lost during atmospheric passage due to:

• Reflection
• Absorption

Absorption:

• Ozone absorbs UV radiation (< 0.29 μm)
• Water vapor absorbs infrared radiation
• CO₂ absorbs infrared radiation
• Clouds absorb and reflect (30-60%)