Rain measurement with wind blowing

Question

Rain measuring simple unit with a measuring jar fitted with a funnel collect rain pouring. Here I presume the rain falling vertically down with zero speed. However, usually the wind is blowing. If it blows with higher speed, then naturally rain pours down not vertically, but at some angle. With more speed of wind, slanting of rain increases. In that case will this not affect the collected amount in measuring the rain? Or is there any correction one has to apply considering the wind speed and angle made by the rain with vertical line?

Answer 1

Two parts to this answer. First - the idealized situation where wind adds a purely horizontal component to the rainfall; next, what actually happens around a pluviometer when there is wind.

Part 1: ideal situation

Imagine the density of rain drops per unit volume is $N$, and the vertical velocity is $v$. The rate at which drops arrive on a unit area of ground or rain gage will be

$$R = N \cdot v$$

This is illustrated by this diagram: all these rain drops will make it into the box in unit time:

Now we add a horizontal component (due to wind) to the rain velocity. Let us call this additional component $v_h$. As a result, the rain will be falling at an angle $\theta$ to the vertical, and it will have a new velocity $v_t = \sqrt{v^2 + v_h^2}$. The angle $\theta$ is given by

$$\theta = \cos^{-1}\frac{v}{v_t}$$

or

$$v_t = \frac{v}{\cos\theta}$$

In this diagram you see the same number of rain drops as before; they start in different places, but they all arrive in the collector in the next unit of time.

But there is another way of looking at this - we can rotate the entire picture (and move a few drops - I colored them green; but there is once again the same number of drops as before):

Since this rain is arriving at the collecting aperture of the pluviometer at an angle, the apparent area is smaller - by $\cos\theta$. But the velocity $v_t$ is greater - by $\cos\theta$. These two terms exactly cancel out - and for this ideal case, the rate at which rain is collected is independent of the speed of the (horizontal) wind. The only thing this ignores is the situation where the size of the drops becomes significant compared to the area: the chance of hitting an edge becomes nonzero, and how such a drop breaks up (and what fraction ends up in the container) is hard to predict. In particular, the behavior may be different on the leading edge compared to the trailing edge. But that really belongs in

Part 2: real world

So - why doesn't it work out like this in real life (as pointed out by @pentane, and supported by numerous references)?. The problem is that there is no such thing as "perfectly horizontal wind" - especially not in the vicinity of objects. Wind tends to tumble and turn; in short, it has vertical components which will change the local rate at which rain falls. Looking for example at figure 6.11 from [these lecture notes](http://www.jma.go.jp/jma/jma-eng/jma-center/ric/material/1_Lecture_Notes/CP6-Precipitation.pdf), we see the following cartoon:

This shows that the direction of the rain drops is a function of the position relative to the gage, because the wind direction changes around the gage. As a result, some rain is pushed away, leading to a collection deficit. But quoting from the same source:

Wind exerts a significant influence on the observation of precipitation with snow and rain gauges, and there is no way to avoid its effects. However, accurate collection of precipitation in a rain gauge is possible when the wind around the receptacle is horizontal and its speed is equal to that at ground level or when no vortices develop near the gauge. A windshield is effective in reducing the influence of wind.

If you have a typical rectangular collector (a large tin can, for example) the air flow might look something like this:

(image adapted from this website)

Typically, the air draft will be up, leading to an underestimate of the collection efficiency. There are companies dedicated to solving this problem for you - see for example NovaLynx Alter-Type Wind Screens which shows the following:

and states on their website:

The 260-952 Rain Gauge Wind Screen minimizes the formation of strong updrafts that can distort the trajectories of precipitation particles falling toward a gauge. The screen also generates turbulent air motions over the gauge orifice to break up streamlines and thus improve the catch. Use of a wind screen is recommended with all precipitation gauges located in windy areas.

After reading @Azad's comment above, another factor sprang to mind. As long as horizontal wind velocity is constant, the rain drops will continue to fall at their average terminal velocity. However, if the wind speed changes (either because that is what wind does, or systematically because if accelerates around an obstacle) then the rain will experience a greater vertical drag (because of the quadratic nature of drag, a "cross wind" increases forward drag). And that in turn would slow the rate at which the rain falls and make the reading low.

In short - the answer is "it depends". There are various mechanisms that make rain collection dependent on the wind, but there is no "easy formula" as it depends on the details of the geometry and the magnitude as well as variation (temporal fluctuations), of the wind speed

Answer 2

Change in direction won't impact the amount collected per unit area. Amount collected per unit area can be affected only if there is some lensing/dispersion. Since, mass of water that falls, and the area on which it falls (any increase in area in direction of wind is compensated by corresponding decrease in opposite direction) are both constant w.r.t. direction and speed of wind, therefore mass/area is also constant.