Solar Irradiance

Overview¶

Solar Irradiance is the power per unit area (surface power density) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument. Solar irradiance is measured in watts per square metre (W/m2) in SI units.

(source: Wikipedia)

Global irradiance¶

Global irradiance represents the total solar radiation incident on a surface, combining all three components. It can be measured or calculated for :

Horizontal surfaces (Global Horizontal Irradiance, GHI)
Inclined surfaces (Global Inclined or In-Plane Irradiance, GII)

The global horizontal component serves as a fundamental input for calculating irradiance on tilted surfaces.

PVGIS models solar irradiance incident on a tilted (or inclined) solar surface as the sum of two fundamental components :

\[ \text{Global}\ _{inclined} = \text{Direct}\ _{inclined} + \text{Diffuse}\ _{inclined} \]

The diffuse irradiance, however, is the sum of the sky-reflected and ground-reflected components :

\[ \text{Global}\ _{inclined} = \text{Direct}\ _{inclined} + \text{Sky-Diffuse}\ _{inclined} + \text{Ground-Diffuse}\ _{inclined} \]

Reflected irradiance in PVGIS <= 5.x

The older generation of PVGIS version <= 5.x, names the latter component as Ground-Reflected. In this documentation the terms ground-diffuse and ground-reflected mean the same physical quantity. The same equation appears there in the following form :

\[ \text{Global}\ _{inclined} = \text{Direct}\ _{inclined} + \text{Diffuse}\ _{inclined} + \text{Reflected} \]

Irradiance data in the PVGIS Web application

The PVGIS Web application uses the SARAHx global and direct horizontal irradiance products. This software however, can consume any such time series data, as long as the data format is one that is supported by the Xarray library.

Each irradiance component represents a distinct physical process :

Direct is the radiation arriving straight from the sun's disk.
Diffuse sky-reflected is the radiation scattered by the atmosphere and clouds.
Diffuse ground-reflected is the radiation reflected from the ground surface onto the solar collector.

Real-sky or Clear-sky conditions ?

PVGIS flexibly uses external time series inputs for global and direct horizontal irradiance, temperature, wind speed, Linke Turbidity, and Albedo to model solar irradiance components accurately. When these inputs are not available, PVGIS simulates the complete set of clear-sky irradiance components —including global, direct, sky-diffuse, and ground-diffuse— along with average temperature, wind speed, turbidity, and albedo based on climatological data and scientific models.

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Terminology & Tools

PVGIS CLI and output columns use consistent terminology to distinguish between irradiance components:

Component	Incidence angles	CLI Command	Subcommand/s	Physical Meaning
Global	Horizontal, Inclined	`global`	`horizontal`, `inclined`	Total incident irradiance
Direct	Horizontal, Inclined	`direct`	`horizontal`, `inclined`	Direct radiation from the sun
Diffuse Sky-reflected	Horizontal, Inclined	`diffuse`	`horizontal`, `inclined`	Radiation scattered by the atmosphere
Diffuse Ground-reflected	Inclined	`diffuse`	`ground-diffuse`	Reflected from the ground surfae

Horizontal vs. Inclined Irradiance¶

PVGIS can output both horizontal and inclined irradiance components

Horizontal irradiance is measured on a flat, horizontal surface
Inclined irradiance (also called in-plane irradiance) is calculated for a solar surface positioned at specified orientation and tilt angles

The transposition from horizontal to inclined irradiance involves geometric and radiometric transformations for each component based on solar position and surface orientation.

Direct irradiance¶

Direct irradiance is the portion of solar radiation arriving directly from the sun's disk and without scattering. This component is sensitive to :

Solar position (altitude and azimuth angles)
Atmospheric conditions (clouds, aerosols)
Surface orientation and tilt

The direct irradiance can be expressed as :

Direct Normal Irradiance (DNI) is the radiation perpendicular to the sun's rays
Direct Horizontal Irradiance (DHI) is the radiation incident on a horizontal plane
Direct Inclined Irradiance is the radiation incident on a tilted surface

The relationship between these quantities involves the solar altitude and solar incidence angles:

\[ \text{Direct}\ _{horizontal} = \text{Direct}\ _{normal} \times \sin(\text{Solar Altitude}) \]

\[ \text{Direct}\ _{inclined} = \text{Direct}\ _{horizontal} \times \frac{\sin(\text{Solar Incidence})}{\sin(\text{Solar Altitude})} \]

Diffuse irradiance¶

The diffuse irradiance is the sum of the sky-reflected and ground-reflected components. The sky-reflected component is the radiation scattered by the atmosphere and clouds. and the ground-reflected is the radiation reflected from the ground surface onto the solar collector.

Sky-Reflected irradiance¶

Diffuse irradiance or sky-diffuse represents solar radiation that has been scattered by atmospheric components (molecules, aerosols, clouds) before reaching the surface. The sky-reflected diffuse irradiance component :

Does not come from the sun directly
Arrives from all parts of the sky dome
Is particularly significant under cloudy conditions
Depends on atmospheric turbidity and cloud cover

For inclined surfaces, the diffuse component calculation accounts for :

The portion of the sky hemisphere visible to the surface (sky view factor)
Whether the surface is in shade or sunlit
Atmospheric scattering properties

Diffuse vs. Sky-Diffuse

In PVGIS documentation and CLI outputs, "diffuse" and "sky-diffuse" are used interchangeably to refer to diffuse sky-reflected irradiance, distinguishing it from ground-reflected irradiance.

Ground-reflected irradiance¶

Diffuse ground-reflected irradiance or ground-diffuse is the solar radiation reflected from the ground surface and incident on the tilted solar collector. This component depends on :

the global horizontal component : the total irradiance available for reflection
ground view fraction : portion of ground visible from the tilted surface (depends on the tilt of the solar surface)
albedo, the reflectivity of the ground surface

Calculation¶

PVGIS consumes time series of global and direct horizontal irradiance to calculate the diffuse irradiance components (sky-reflected and ground-reflected). The ground view fraction is calculated as a function of the surface tilt angle from the global horizontal component (Hofierka, 2002). Note that the diffuse ground-reflected component is set to 0 for a flat horizontal surface or one that is tilted close to 0 degrees.

\[ \text{Ground View Fraction} = \frac{1 - \cos(\text{Surface Tilt})}{2} \]

The diffuse ground-reflected irradiance is then:

\[ \text{Ground-Reflected}\ _{inclined} = \text{Albedo} \times \text{Global}\ _{horizontal} \times \text{Ground View Fraction} \]

Key Characteristics

For horizontal surfaces (tilt ≈ 0°): Ground-reflected component is approximately zero because the surface cannot "see" the ground
For vertical surfaces (tilt = 90°): Maximum ground view fraction of 0.5
Increases with tilt angle: The steeper the tilt, the more ground is visible to the surface

When Ground-Reflected Irradiance Matters

Ground-reflected irradiance becomes significant for:

Steeply tilted surfaces (tilt > 30°)
High-albedo environments (snow, sand, water)
Bifacial PV modules that can capture rear-side irradiance
Vertical installations (building facades)

Effects & Corrections¶

Reflectivity effect¶

The photovoltaic performance analysis considers the effect of the solar surface reflectivity itself to both direct and non-direct irradiance components (sky-reflected and ground-reflected).

In PVGIS the reflectivity is calculated as a function of the solar incidence angle (Martin and Ruiz, 2005).

\[ \text{Reflectivity Effect} = \text{f(Incidence)} \]

Note that there is a difference between the mathematical equations applied to the direct and non-direct components.

The photovoltaic performance analysis considers reflectivity losses due to:

Solar incidence angle (larger angles → more reflection)
Surface properties (glass type, anti-reflection coatings)

Reflectivity is calculated as a function of the solar incidence angle (Martin and Ruiz, 2005):

\[ \text{Reflectivity Effect} = f(\text{Solar Incidence Angle}) \]

Note that different mathematical equations apply to:

Direct irradiance (depends on exact incidence angle)
Diffuse components (sky-diffuse and ground-reflected, averaged over hemisphere)

Spectral Effect¶

The spectral effect accounts for differences between:

Natural sunlight spectrum (varies with atmospheric conditions, solar position)
Standard Test Conditions (STC) reference spectrum (AM1.5)

\[ \text{Spectral Effect} = \frac{\text{STC Spectrum}}{\text{Actual Sunlight Spectrum}} \]

This correction is particularly important for different PV technologies that have varying spectral responses.

References¶

Hofierka, J. (2002). Solar radiation model. In Distributed GRASS Modules for Solar Irradiance Modelling.
Martin, N., & Ruiz, J. M. (2005). Annual angular reflection losses in PV modules. Progress in Photovoltaics: Research and Applications, 13(1), 75-84.
SARAH-⅔ Climate Data Records: Surface Solar Radiation. CM SAF, EUMETSAT.