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24 - Point irradiance radiometer

IrradianceRadiometer measures the spectral irradiance within a conical field of view at a given position and in a given direction, like an ideal cosine-response radiometer. It can be used to study how platform obstruction, sensor orientation and field of view affect radiation measurements. The probe itself does not block any light.

Measuring upwelling and downwelling irradiance

Two probes are placed 5 m above the sea surface, one facing up and one facing down:

import less

scene = less.Scene()
scene.size = 1000
scene.terrain = less.Terrain(property=less.WaterSurface())
scene.illumination = less.Illumination(
    source=less.Sun(zenith=30, azimuth=180),
    atmosphere=less.PrescribedAtmosphere(
        direct_beam_transmittance=0.75, diffuse_horizontal_transmittance=0.25))

downwelling = scene.simulate(less.IrradianceRadiometer(
    position=(500, 500, 5), orientation="up", fov=180,
    bands=[450, 550, 650], quality=32768))
upwelling = scene.simulate(less.IrradianceRadiometer(
    position=(500, 500, 5), orientation="down", fov=180,
    bands=[450, 550, 650], quality=32768))

print(downwelling.irradiance, downwelling.units)
print(upwelling.irradiance, upwelling.standard_error)
upwelling.save("upwelling.npz")

The upward probe receives direct sunlight and skylight within its field of view; the downward probe receives light reflected by the sea and other objects. The result is the total and is not split into parts. The transmittances here are only example values; their meaning is explained in chapter 16.

Parameters and results

Parameter Meaning
position Probe position (m)
orientation "up" measures downwelling irradiance, "down" upwelling irradiance
normal 3-D vector of the probe direction, for tilted mounting; replaces orientation when given
fov Full angle of the conical field of view (degrees), 0–180
bands Wavelengths (nm)
quality Number of samples; larger values reduce random error

irradiance and standard_error are spectral arrays in W m⁻² nm⁻¹, and wavelengths gives the corresponding wavelengths. The standard error only describes the random error of the simulation.

The probe measures a cosine-weighted integral over its field of view, not an average radiance. Only when both probes have a full hemispherical field of view, the same position and the same illumination is the ratio of upwelling to downwelling an albedo; with a restricted field of view it is only an apparent ratio for that field of view. Broadband albedo must be integrated with the spectral response rather than averaged over wavelengths.

Assessing the effect of a platform

  1. Measure upwelling and downwelling irradiance in a scene without the platform;
  2. add a model of the platform (size, mounting height, surface reflectance), keep the sun, sky, water and probe position unchanged, and measure again;
  3. the difference between the two is the effect of the platform, including both obstruction and reflection from the platform itself.

Even when the sun is completely blocked by the platform, skylight and light reflected by surrounding objects still reach the probe, so the reading is not zero. When the probe is high or its field of view is close to a hemisphere, the sea surface must be large enough.

When the probe looks directly at the sun, the sun is treated as a disc of finite size, so partial obstruction of the sun at the edge of the field of view or of the platform is reproduced. The platform's shadow on the sea is computed for a sun in a single direction, without a penumbra. The probe does not include a finite receiving area, the angular response of real instruments or polarisation.

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