How can we get the fire cloud particle size? Typically I write about nanoparticles. The current fire situation in California reminded me that the larger than nano-size range is also affecting our daily life. While smoke forms clouds we can observe light scattering directly. So why is the sun so red in smoky air? Is this related to cloud particle size?

Fires produce smoke

California has had a streak of very hot days, above 100°F = 37°C. That is not so unusual in the summer. But during this heatwave meteorological events triggered an avalanche of (dry) thunderstorms with lightning strikes (estimated to more than 10,000). That is highly unusual for the area. And lightening then caused hundreds of small wildfires. Many combined into larger events – even causing their own weather patterns. These are called pyrocumulus clouds, carrying smoke particles to great heights. Due to the lower temperature at this altitude, condensation of water onto the smoke particle nuclei can increase their size.

What is smoke?

When fires burn, smoke is the result of partial incomplete combustion. These reaction results form a collection of airborne particulates, an aerosol of solid particles and liquid droplets. The primarily visible size range of these particulates is the coarse mode in the micrometer range. This also happens to be where light scattering comes into play.

estimate cloud particle size from this Image of the sun surrounded by a red ring, with angular indicator of ring size

How can we estimate the smoke particle size?

For particles larger than the light illuminating it we can estimate the size of particles from the position of the “first minimum”. This large particle limit is also known as the Fraunhofer approximation: opaque disk-shaped particles, larger than 25 µm, in forwarding scattering only. There is a rough guide for aerosols predicting the angle θ in degrees for particles of diameter d in microns (µm)

θ ~ 35 / d   or  the particle size in µm is     d = 35 /  θ

This equation for cloud particle size is from an article in Aerosol Science. JR Hodkinson “The optical measurement of aerosols” in Aerosol Science ed. CN Davies, Academic Press (1966) page 343. It is the result of using the position of the first minimum at a wavelength of about 0.6 µm and converting radians to degrees. Since the angular size of the sun is about 0.5° we can estimate the size of the ring to be about 1°, so the position of the first minimum is at ~0.5°. Using the above equation we can estimate the particle size to be about 70 µm.

What is Mie scattering?

Mie scattering is a theory which describes the scattering behavior of a particle when irradiated with light. (Well, not just light, electromagnetic radiation in general.)  It predicts how much light is scattered into any direction by a particle. In order to calculate this light scattering pattern, we need to know the properties of the particle material. Specifically the refractive index and absorption of the material. As an example, if we have soot particles, this could be n=1.7 and k=0.5 for red light (Radiative properties of Soot Particles). With lots of micron-sized particles in the air, the forward scattering of this light is the most observable effect. Large particles scatter more in the forward direction, and due to their size they scatter a lot more than any other particles (or molecules) in the air. This becomes especially apparent at dawn or dusk. In the photo above, it can also be seen during the middle of the day: the forward scattering from the smoke particles provides the reddish hue.

On the other hand, the blue color of the clear sky is the result of scattering from very small air molecules. These are isotropic, as they scatter evenly in all directions. And then the lower wavelength region will contribute more than the higher wavelength. This is also known as Rayleigh scattering. And ‘normal’ white clouds are white because multiple scattering scrambles everything…we’ll leave that for another post.

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