**Introduction**

**Introduction**

The Earth’s atmosphere has several effects on terrestrial radiation. The figure below depicts the relative importance of atmospheric impacts on the sunlight striking the Earth’s surface. The process poster also depicts the solar energy balance of the Earth-atmosphere system.

The major impacts of the atmosphere on sunlight include:

- A reduction in solar radiation and change in spectral content given atmospheric absorption;
- A change in sunlight quality due to Raleigh scattering (e.g. the introduction of a diffuse sunlight); and
- Cloud and surface albedo, which is the reflection and release of radiation following absorption.

The values in the process poster are dimensionless and relative quantities of energy for illustration purposes. The radiation balance assumes that the sum of all sources minus all sinks equals zero. For example, clouds are in radiative balance since they absorb and emit 64 units of radiation. The components of solar radiation striking the Earth’s surface are defined below.

**Direct Normal Irradiance (DNI)**

**Direct Normal Irradiance (DNI)**

DNI is the solar radiation on a surface element perpendicular or normal to the Sun’s rays, and excludes diffuse insolation. Empirical estimates of DNI begin with the estimated irradiance at the top of the atmosphere, as defined here. The surface level DNI by wavelength, corrected for atmospheric filtering, , is given by:

(1)

where is solar radiation by wavelength at the top of the atmosphere; is the atmospheric optical depth or the attenuation coefficient by wavelength on a cloudless day; is the optical air mass for the solar zenith angle Z; and is the Raleigh optical thickness at air mass AM.

DNI varies depending on the time of year, time of day, atmospheric absorption, and Raleigh scattering. All of these parameters have been defined previously except Raleigh optical thickness, which can be estimated using the improved formula of Kasten (1996):^{1}

For AM < 20

(2)

For AM > 20

(3)

**DNI on Angled Surfaces**

**DNI on Angled Surfaces**

The direct beam irradiance on a horizontal surface in W/m^{2} is calculated as:

(4)

where is the solar altitude angle (radians) and is defined by standard sun position equations.

The beam irradiance on an inclined tilted surface in W/m^{2} is calculated as:

(5)

where is the solar incidence angle measured between the Sun and an inclined surface as defined by the standard sun position equations.

**DNI Measurement**

**DNI Measurement**

DNI is measured in W/m^{2} or kilowatt-hours per square meter per day. The basic conversion between the two measures is shown below:

(6)

DNI observations can be measured directly via an *absolute cavity radiometer (ACR)*. ACRs are considered the most accurate method, but the equipment is not designed for continuous, unattended, outdoor use. Instead, they are used to calibrate and validate more traditional instruments. An ACR connected to a tracker and digital data logger is shown below.

The primary field instrument for DNI field measurement is a *pyrheliometer*. Pyrheliometers employ thermopile sensors at the base of a light-collimating tube and a glass window face (or they are constructed with another photosensitive element in place of the thermopile). The light-collimating tube limits the instrument field of view to 5**° **to ensure focus on the direct beam and circumsolar radiation. The small field of view requires that the pyrheliometer tracks perpendicular to the Sun’s path. An image of a pyrheliometer appears in the second image above.

**Diffuse Horizontal Irradiance (DHI)**

**Diffuse Horizontal Irradiance (DHI)**

As the cloudless sky becomes more turbid with water vapor and aerosols, the diffuse irradiance increases while the beam irradiance decreases. The estimation of the diffuse component on a horizontal surface and measured in W/m^{2} is given by:^{2}

(7)

where

- is irradiance at the top of the atmosphere
- is a diffuse transmission function dependent on aerosol optical depth , and
- a diffuse solar altitude function dependent only on the solar altitude

The estimate of the transmission function gives the theoretical diffuse irradiance on a horizontal surface with the Sun vertically overhead for the AM(2) attenuation factor. The following second order polynomial expression is used:

(8)

The diffuse solar altitude function is determined by:

(9)

where the values of the coefficients , and depend only on the attenuation coefficient as follows:

(10)

**DHI on Angled Surfaces**

**DHI on Angled Surfaces**

The model for estimating the clear-sky diffuse irradiance on an inclined tilted surface in W/m^{2} distinguishes between sunlit and shadowed surfaces. The equations are as follows:^{3}

*For sunlight surfaces, non-overcast skys and in radians*

if (or 5.7 degrees)

(11)

if

(12)

where is the surface or module tilt angle and depends on the azimuth angle (horizontal angle between the Sun and meridian – measured from East) and the azimuth aspect (an angle between the projection of the normal on the horizontal surface and East), as defined by standard sun position equations:

(13)

The variable is a measure beam irradiance on a horizontal surface expressed as a proportion of the extraterrestrial irradiance on a horizontal surface:

(14)

where

(15)

*For surfaces in shadows ( and )*

(16)

where ( in radians)

(17)

**Global Horizontal Irradiance (GHI)**

**Global Horizontal Irradiance (GHI)**

**Irradiance vs Insolation**

**Irradiance vs Insolation**