Answer · confidence: partial

How do tiny light-bouncing bits make the whole sky's colors and brightness?

Research question: How do multiple-scattering models combine single-particle dipole radiation into the full color and brightness pattern of the whole sky?

The records show that total sky scattering is the sum of primary scattering and multiple scattering ¹. The induced electrostatic dipole formed when the field distorts an atom's electron cloud radiates, and this induced radiation is what constitutes Rayleigh scattering ⁸. Multiple-scattering sky radiance is obtained by numerically evaluating a two-dimensional integral over the scattering geometry, as in the double-scattering circumsolar case ³. The share of multiple scattering rises from almost zero at 300 nm to roughly 5–60% at visible and near-IR wavelengths, which bears on the color pattern ⁵. The supplied facts describe the dipole source ⁸ and the integral method ³ but do not show how the individual dipole contributions are summed into the full sky color and brightness pattern ¹⁵. The newest fact is dated 2017, about nine years before October 2026 ⁹.

Checked 2026-10-14. Only documented and supported facts are used.

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Sources

[1] supported

Total sky scattering is the sum of primary scattering and multiple scattering, so the primary share is 100 minus the multiple-scattering share.

"Total Scattering (TS) is equal to Primary Scattering (PS) plus Multiple Scattering (MS), i.e. PS/TS = 100 - MS/TS (%)."

The ratio of primary scattering to total scattering of sky radiance (1974)

[2] documented

Monte Carlo simulations of radiation transfer found relative errors in sky radiance over the ocean of as high as 39% in the blue part of the spectrum when radiometers are placed on islands.

"Relative errors in sky radiance of as high as 39% were found in the blue."

Island perturbation to the sky radiance over the ocean: simulations (1995)

[3] supported

Multiple-scattering sky radiance is computed by numerically evaluating a two-dimensional integral over the scattering geometry, specifically for double scattering contributions to circumsolar sky radiance.

"a 2-dimensional integration as it occurs in the physical process of computing the double scattering contributions to circumsolar sky radiance."

A comparative study of Conroy and Monte Carlo methods applied to multiple quadratures and multiple scattering (1978)

[4] supported

Spectral sky radiance for a turbid atmosphere including multiple scattering was computed from theory by Eschelbach.

"Recently Eschelbach has computed from theory spectral radiance values for a turbid atmosphere taking into account the effect of multiple scattering."

The ratio of primary scattering to total scattering of sky radiance (1974)

[5] documented

Simulations show that the share of multiple scattering in total scattering rises from almost zero at 300 nm to roughly 5–60% at visible and near-IR wavelengths, depending on solar geometry and surface albedo.

"Simulations show that the multiple to total scattering ratio increases from almost zero at 300 nm to ∼5–60% at visible and near‐IR wavelengths (depending on solar geometry and albedo of Earth's surface)."

Multiple scattering radiance in limb‐viewing geometry (1999)

[6] documented

A single-scattering model is not adequate for analyzing limb radiance measurements, so multiple scattering must be included.

"A single‐scattering model is not sufficient for the analysis of limb radiance measurements."

Multiple scattering radiance in limb‐viewing geometry (1999)

[7] documented

When the solar zenith angle is small, limb radiance is very sensitive to the surface albedo, and a bright 50 km spot on a dark surface already noticeably increases intensity.

"When the solar zenith angle is small, limb radiance is very sensitive to the surface albedo. A bright spot of diameter 50 km on an otherwise dark surface already causes a noticeable increase of intensity."

Multiple scattering radiance in limb‐viewing geometry (1999)

[8] supported

The induced electrostatic dipole formed when the electromagnetic field distorts an atom's electron cloud radiates, and this induced radiation is what constitutes Rayleigh scattering.

"Le dipôle électrostatique ainsi créé rayonne, c'est ce rayonnement induit qui constitue la diffusion Rayleigh."

Diffusion Rayleigh

[9] documented

The authors found that including scattering effects from different hydrometeor types is significant for simulating cloud-affected microwave radiances in all-sky simulations.

"Correlation between different types of hydrometeors and simulated brightness temperatures at respective atmospheric levels highlights the significance of inclusion of scattering effects from different hydrometeors in simulating the cloud-affected radiances in all-sky simulations."

All-sky radiance simulation of Megha-Tropiques SAPHIR microwave sensor using multiple scattering radiative transfer model for data assimilation applications (2017)

[10] supported

The transient molecular pairs that produce incoherent scattering are binary collisions, so their density is proportional to the square of the pressure, and incoherent Rayleigh scattering falls off rapidly as pressure drops.

"Les collisions les plus fréquentes à basse pression sont binaires, leur densité est proportionnelle au carré de la pression de sorte que la diffusion Rayleigh incohérente décroît rapidement lorsque la pression décroît."

Diffusion Rayleigh