Talk:Raindrop size distribution

Carl W. Ulbrich

His last name is misspelled throughout this article as 'Ulbricht'; could someone with Wikipedia skills please correct this? Thanks. — Preceding unsigned comment added by 2607:F2C0:931B:4F00:24A2:18D:C948:34A1 (talk) 17:36, 24 May 2020 (UTC)[reply]

Done Correct according to the reference. Pierre cb (talk) 22:12, 24 May 2020 (UTC)[reply]

Defining N(D)

This article is very poor in defining what N(D) actually is. All over the literature I find it is measure din raindrops per cubic meter per mm. And I can't and here there is a graph of it in drops per cubic meter. I can't understand what the per mm thing is about, but it's something to with the notion of a DSD and this function mapping a distribution of expected droplet sizes. To get an actual predicted droplet density (droplets per cubic meter) you need thus to integrate this function between two bounds a and b and that would provide the number of raindrops per cubic meter that were between a and b in diameter. To wit if you want a total raindrop density you have to integrate this function from 0 to infinity effectively or practically speaking from Dmin to Dmax being the minimum and maximum sizes of raindrops known known to exist or modelled with this DSD.

That is itself a very interesting thing to present and providing the definite integral between to bounds D1 and D2 would add some true value to this page along with helping really explain WTF N(D) actually is! Which is currently neglected almost everywhere. I just read dozens of pages and papers and all of them are content with totally abstract unhelpful definitions of N(D) and the DSD and number of raindrop per drop size interval or some such twist of language without providing nay clarification of what that actually means in terms of drops per unit volume!

Would be great to see this page stepping up to fill tha gap in easily found literature on-line.

N(D) is per unit of volume which can be any unit you want. See the reference in the text by Mashall-Palmer. As for N(D) it is clearly written in the article that it is the number of drops of a certain diameter in mm in a unit volume (cubic meter), thus the Number per cubic meter per mm that you talk about and the graphs showing the number N at a certain diameter. As for your second mention, the text says: ".. the drop size distribution is represented as a truncated gamma function for diameter zero to the maximum possible size of rain droplets." and the sum of N(D) is done in the Z-R relation where it is needed. Pierre cb (talk) 12:21, 15 June 2020 (UTC)[reply]

I'll respectfully disagree that it's clear and that N(D) is the number of drops of a specific size (which is a misreading of continuous or even discrete distribution). The claim is even mathematically erroneous as "he number of drop with diameter D {\displaystyle D}" is dimensionless and presented against a graph that claims per cubic meter, and every similar graph I find in the literature presents the same quantity as cubic meters per mm, which is more accurate but far from lucid for a lay reader. As to the integration appearing in Z, yes, but not unsullied as a raindrop count per unit volume which is of some interest in aiding comprehension of N(D), which is clearly elusive given even a defender of the current content is content with an erroneous introduction and a unit confused graph.--203.220.1.58 (talk) 00:44, 16 June 2020 (UTC)[reply]

Excuse me but did you look at the M-P reference given for the definition of N₀ and the graphs? The only thing confused is your query and the only thing wrong with the article is the units in the first graph, that you pointed, and that I corrected. Pierre cb (talk) 03:13, 16 June 2020 (UTC)[reply]

Yes, (albeit not with your link as it doesn't work). It states explicitly (and as no surprise): "N(D)*𝛿D is the number of drops of diameter between D and D+𝛿D in unit volume of space". The introduction displays an misunderstanding of N(D)and of units and integrals. N(D) as a value has no physical meaning, N(D) multiplied by a small interval has meaning as described. And as a consequence it would be, specifically to avoid this ongoing confusion in readers let alone editors be of benefit to table a formula for N(D)*𝛿D possibly as the definite integral from 0.25mm to 7mm (the rough range of validity of the approximation that M-P make. It is precisely this confusion that drew me to comment, as the volumetric density of drops is of interest in some applications (I have such a one) but all the literature I can find stops short of clarifying N(D) well, always defining it indirectly as "number of drops per unit volume per unit interval of drop diameter ," a high Google hit on my search being: https://www.hindawi.com/journals/amete/2015/253730/. The general notion being that the actual number of drops of diameter D is typically not a meaningful quantity (reality does not flatter us with that kind of precision in physical sciences and the true answer for any arbitrarily chosen value of D in the Real number space will be zero, the DSD describing a distribution with its shape and offering densities through the area beneath it over an interval. Which is a property it shares probability distributions for real or continuous quantities. Thanks for your patience, and no desire nor intention to seem disrespectful. But the point of confusion her is one well worth resolving on a page like this that could if it did that be a valuable resource to lay readers encountering N(D) and rain DSDs. --203.220.1.58 (talk) 04:49, 16 June 2020 (UTC)[reply]

I will also add that the first image is subtitled: Two average distributions adjusted to Marshal-Palmer equation. But they are categorically NOT the M-P equation, as can be seen by a) looking at the MP equation (it is an exponential and has no maximum)and b) Consulting the cited paper, and its Fig 2 illustrates precisely how the M-P equation is a fit for D > ~1.75mm and a poor approximation for smaller D. And so the figure in the article has some other source and plots some other function which seems not cited. --203.220.1.58 (talk) 02:36, 17 June 2020 (UTC)[reply]

I found be the source and the legend should be "Two average real distributions that can be adjusted to the Marshal-Palmer equation". Pierre cb (talk) 12:44, 17 June 2020 (UTC)[reply]