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Very technical, a litle difficult to understand

Drop size distribution

Drop size distribution

This article is very technical. It talks about math but doesn't give very much information about the actual math involved. It talks about the formulae for scaling constant but only says they are named after the researchers who devised them. Who cares?

Tell what one of the formulas look like and maybe how it is used. The definition of mathematics paragraph is helpful and does give some very good information. especially when talking about the decibel scale. The exponential algorithm from the computer says the math depends on whether we are expecting snow, hail or rain. What is it is sleeting? It shouldn't what kind of precipitation is falling only that there is precipitation. All precipitation eventually turns to liquid anyway, so you should only worry about amount of liquid precipitation is accumulating.

Math is the only way to predict the weather. Not sure how I know this but its true. Math gives us average temperatures, rainfall probabilities, and weather destructiveness. How is a tornado measured? The Fujita scale, and how the Fujita scales takes many factors to calculate.

People should care about math in the weather because weather is constant. Weather is always around us. It may not seem like it is, but there is still math involved when calculating barometric pressure and humidity or wind chill.

Barry's Response - The world's most powerful computers are used to produce weather forecasts, by a process which started out nearly a century ago as
Numerical Weather Prediction.

It can all be reduced to math and that works quite well. Here is the Marshall-Palmer reflectivity relationship asked about earlier.

Radar Reflectivity is Z in decibels (dBZ):

(Z) = ∫ N(D) * D6 dD R

= π/6 * ∫ N(D) * D3 * W(D) dD

D is a raindrop diameter
N(D) is the number of drops of that size per m3
W(D) is the raindrop falling velocity at that size
R is the
rainfall rate

There are many empirical formulae converting dBZ and thus skipping this convoluted theoretical thing. One of which I pick up from wikipedia https://en.wikipedia.org/wiki/DBZ_(meteorology) :

R (mm/hr) = ((10(Z/10)) ÷ 200))(5/8)

Many commonly used ones take the form of Z = A * Rb where A and b are the empirical constants. 300 and 1.4 respectively are used in some rain situations, while 200 and 1.2 in others. Other sets of numbers may be used for hail and snow.

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