# Why can't radar's decibel scale be used to determine the intensity of snowfall?

According to the FAA's Aviation Weather Services advisory circular,

Values below 15 dBZ are typically associated with clouds. However, they may also be caused by atmospheric particulate matter such as dust, insects, pollen, or other phenomena. The scale cannot be used to determine the intensity of snowfall. However, snowfall rates generally increase with increasing reflectivity.

Why can't that scale be used to determine the intensity of snowfall?

• Guess: the radar reflection strength strongly depends on the ratio of ice to water, so light wet snow reflects more strongly than heavy dry snow. – Daniel Griscom Jul 1 '16 at 23:16

Snow, unlike rain, has holes as well as different refractive properties. This allows the radar beam to penetrate and reflect the beam differently than an ordinarily oblate rain drop.

• I just stumbled across this question and added a bounty for more details. – uhoh Mar 8 at 4:23
• @BaroclinicCplusplus can you add a reference to your answer ? It looks closer to the literature I have read – gansub Mar 9 at 10:47

The returned energy which is measured by the radar is given by the so-called "radar equation" which states that:

$$P_r=\frac{CK_w^2}{r^2}\sum_{i=1}^Nn_iD_i^6$$

Here $$C$$ is "just" some antenna characteristics and $$r$$ is the distance from the radar.

$$K_w$$ is the dielectric constant, which differs for rain and snow. For rain it is approximately 0.93. For snow, $$K_w$$ varies much more depending on type of snow i.e. wet or dry snow. So that is the first thing that complicates things when it comes to snow.

Secondly, the last term, which is the reflectivity factor $$Z=\sum_{i=1}^Nn_iD_i^6$$ also cause some trouble.

There is a well known empirical formula for the relation between the reflectivity factor and the precipitation rate, $$R$$, given as:

$$Z=aR^b$$

where $$a$$ and $$b$$ are constants determined empirically. However, these are not very well determined. Fujiwara (1965) found that $$a=450$$ and $$b=1.48$$ for stratiform rain and $$a=300$$ and $$b=1.37$$ for rain showers. These "constants" are even less well-defined for snow and the many varieties that exist.

To conclude I would say that while estimating the intensity of snowfall can be done, the estimation is much more uncertain than in the case of rainfall, probably making it practically useless. The main reasons are the dielectric constant and $$a$$ and $$b$$ in the above formula.

And for fun: Plugging in numbers in the radar equation, one can see that 729 drops with a diameter of 1mm have the same reflectivity as 1 drop with a diameter of 3mm!

Battan, L. J., Radar observation of the atmosphere, p. 44-85. The University of Chicago Press, 1973.

Fujiwara, M. Raindrop-size distribution from Individual Storms. Journal of the atmospheric Sciences, 1965.

• Although I upvoted this i think BaroclinicCPlusCplus is closer to the literature I have read. Smaller ice particles have a smaller refractive index. – gansub Mar 8 at 15:16
• @gansub I've awarded the bounty here because although perhaps not complete this answer offers scientific insight and explanation, and a way to research further. I think "snow has holes and has different properties" isn't sufficient, and offers no support whatsoever. Some users have been vilified for unsourced, unsupported answers. I don't see why that answer was so highly rewarded. – uhoh Mar 16 at 0:23
• @uhoh Entirely upto you. It is a pity BaroclinicCplusplus did not choose to develop his answer – gansub Mar 16 at 0:28