Alejandro Morales Sierra

Centre for Crop Systems Analysis - Wageningen University


March 3, 2023

The package Sky provides a function to calculate the solar radiation on a horizontal surface (for clear skies) as a function of latitude, day of year and time of the day and for different wavebands. In addition, it can generate light sources as required by the VPL package to simulate the light distribution in a 3D scene.


The package Sky is not in the Julia registry. To install it, you can use the following command:

Pkg.add(url = "")


Solar radiation

Use the clear_sky function to calculate the solar radiation on a horizontal plane as a function of day of year, latitude (in radians) and the relative solar time of the day (f = 0 is sunrise, f = 1 is sunset). The function returns the total solar radiation in W/m² as well as direct and diffuse components. For example:

using Sky
lat = 52.0*π/180.0 # latitude in radians
DOY = 182
f = 0.5 # solar noon
Ig, Idir, Idif = clear_sky(lat = lat, DOY = DOY, f = f) # W/m2

The values Ig, Idir and Idif are the total, direct and diffuse solar radiation in W/m². The function waveband_conversion can be used to convert these values to specfic wavebands (UV, PAR, NIR, blue, green or red) as well as converting from W/m² to umol/m²/s, assuming particular spectra for direct and diffuse solar radiation. For example:

f_PAR_dir = waveband_conversion(Itype = :direct, waveband = :PAR, mode = :flux)
Idir_PAR = f_PAR_dir*Idir # PAR in umol/m²/s
f_PAR_dif = waveband_conversion(Itype = :diffuse, waveband = :PAR, mode = :flux)
Idif_PAR = f_PAR_dif*Idif # PAR in umol/m²/s

Light sources for ray tracing

Once the direct and diffuse solar radiation in the relevant wavebands and units have been calculated, the function sky can be used to generate the light sources required by VPL to simulate the light distribution in a 3D scene. For example, a simple horizontal tile (representing soil) in VPL may be created as follows:

using VPL
r = Rectangle(length = 2.0, width = 1.0) 
rotatey!(r, -π/2) # To put it in the XY plane
translate!(r, Vec(0.0, 0.5, 0.0))

A 3D scene requires adding optical properties (e.g., a black material property) and linking these to the mesh (for complicated scenes see VPL documentation for examples):

materials = [Black()]
ids = [1,1]
scene = RTScene(mesh = r, ids = ids, materials = materials)

If we want to compute the amount of solar radiation absorbed by this tile, we need to create a series of light sources. The function sky can be used for that purpose:

sources = sky(scene, 
             Idir = Idir_PAR, # Direct solar radiation from above
             nrays_dir = 1_000_000, # Number of rays for direct solar radiation
             Idif = Idif_PAR, # Diffuse solar radiation from above
             nrays_dif = 10_000_000, # Total number of rays for diffuse solar radiation
             sky_model = StandardSky, # Angular distribution of solar radiation
             dome_method = equal_solid_angles, # Discretization of the sky dome
             ntheta = 9, # Number of discretization steps in the zenith angle 
             nphi = 12) # Number of discretization steps in the azimuth angle

The function takes the scene as input to ensure that light sources scale with the scene. Direct solar radiation is represented by a single directiona light source that will emmit a number of rays given by nrays_dir. Diffuse solar radiation is represented by a hemispherical dome of directional light sources that will emmit a total of nrays_dif rays. The angular distribution of the diffuse solar radiation and the discretization of the sky dome can be modified via dome_method, sky_model, ntheta and nphi. See API documentation and VPL documentation for details.

Once the light sources are created, a ray tracing object can be generated combining all the elements above:

settings = RTSettings(parallel = true)
rtobj = RayTracer(scene, sources, settings = settings);

And the ray tracing can be performed by calling the trace! function:


As expected, the amount of solar radiation absorbed by the tile equals the total in the scene (Ig):

materials[1].power[1]/area(r)  Idir_PAR + Idif_PAR

See VPL documentation for more details and tutorials on ray tracing simulations

Roadmap for future dfevelopment

The package is still under development. The following features are planned:

  • Calculate fraction of direct and diffuse radiation from measurements of actual solar radiation.

  • Calculate the solar radiation on a tilted surface.

  • Allow for a different orientation of the 3D scene from VPL.

  • More advanced algorithms for solar radiation and spectrum (e.g., SOLPOS, Bird).