Ask A Scientist Weather Archive

name         Donald W. C.
status       educator
age          old

Question -   My wife and I want to know the principle of the rain gauge.  We have two. One is an 
1 1/2" in diameter, 24 inches tall and measures 5 inches of rain.  The other is 3/4" in diameter, 
5" tall and measures 5" of rain.  How can that be?  If poured the contents of each into 
separate cups the result is obvious.  Can you help us?
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Donald,

Here is one way to look at the situation: Although the gauges may look like they are measuring 
the collected rain in columns of water measured by height in inches, in reality, they are 
calibrated to collect the rain that falls on an area of one square inch of soil and then display 
the reading as a column of water that is one inch tall and one square inch in area. In other 
words, the calibration marks are supposed to represent water columns that are in cubic inch 
volumes -- not necessarily as water depth in inches.

For example: Imagine the gauge (let us call it gauge "A" for "actual") as being a tall, skinny 
box 12 inches tall with a base area of one square. Furthermore, imagine it to be calibrated each 
inch, bottom, to top. When that "box" is half full, it will read 6 inches of rainfall. If you 
were to pour an equal volume of water into a similar (square-base) box whose base area is 2 
square inches -- still 12 inches tall --  the water level in that box would stand at the 3 inch 
mark. However, if the actual 3 inch depth mark on the larger volume box was labeled "6 inches", 
the gauge would read the same as gauge "A" even though the water depth in each box was different.

So as you can see, it is all a matter of where the calibration marks are put on the gauge. Rain 
gauges can be any shape or size, so long as they are calibrated in volumes of cubic inches.

Regards,
ProfHoff 634
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Donald,

Your observation is correct...the two gauges represent different volumes of water, with volume 
being a cubic measurement, whereas the depth of the water, a simple measurement, is about the 
same for both.

A pair of rain gauges like you describe, both placed in the same area, should adequately measure 
the depth of the rainfall, which is what is most often expressed by our meteorologists.  The 
theory behind each gauge showing a similar rain depth would be that for a given area (a square 
measurement of length times width), the number of droplets should be about the same (and their 
size should be uniform).  Given a larger diameter gauge we would expect more rain droplets to be 
caught, but because of the larger horizontal square area represented, the rain depth is spread 
over the internal area and produces a depth equal to a narrower diameter gauge; in this case the 
narrow diameter gauge catches rain drops over a smaller square area( fewer droplets), but those 
drops produce an equivalent depth because the drops caught are then spread over a smaller 
internal [horizontal] area which therefore fills equally in the vertical direction. There is a 
point at which a gauge becomes too small to accurately represent the rain falling over a larger 
area.

Thanks for using NEWTON!

Ric Rupnik
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Donald,


There are as many types, styles, and shapes of rain gages as there are days in the year.  Some 
of these were designed as they were for specific reasons, such as the wedge shaped gage that I 
have, which is narrow and has large graduations at the bottom (to allow one to detect small 
amounts of precipitation more  accurately) and wide at the top (to allow a large amount of 
precipitation to be collected).


You did not describe the shape of your gages so it is a little difficult to judge why they 
measure rain differently.  However, it sounds as though your 3/4 inch gage is a cylinder and has 
straight sides, so 5 inches of rain ends up being a water column 5 inches high in the gage.


The 1 1/2 inch gage sounds like it has a large diameter top, perhaps even a funnel at the top, 
and a smaller diameter tube below.  The larger area of the top receives several times the area 
of rain than the bottom tube cross-sectional area.


For instance, a 1 1/2 inch diameter top has a 1.77 inch square cross-sectional area. If the tube 
below it is 3/4 inch in diameter, it has a cross-sectional area of only 0.44 inches square. This 
gives a top to tube ratio of 4, meaning that 5 inches of rain coming into the top of the gage 
would result in a 20 inch tall column of water in the tube (4 x 5 inches = 20). This technique, 
like my wedge rain gage, allows you to more accurately determine the amount of rainfall, by 
effectively expanding the column of water.

David R. Cook
Atmospheric Research Section
Environmental Research Division
Argonne National Laboratory
=====================================================
A rain gauge collects the water that falls in a unit of area.  If the collector opening is the 
same area as the rest of the unit (e.g., a
straight vertical tube), then there's a 1:1 relationship, 1" collected is 1" of rain.  However, 
if you have a funnel for example that is 5 times larger (in area, not diameter) than the tube it 
empties into, then you have a 5:1 relationship, that is, 5" collected is 1" of rain.  Your 
larger rain gauge sounds something like that, if the scale marking 5" of rain is almost 25" 
long.

Don Yee
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The only way that can work is if the collection funnel of the 24" gauge is bigger than the 
collection funnel of the 5" gauge.  When a gauge measures "inches of rain", what it is actually 
measuring is cubic inches of rain per square inches of flat surface.  Rain falling into the 
collection funnel is collected in the gauge column.  The gauge column measures the volume of 
rain falling on the area of the collection funnel.  5 cubic inches of rain falling on an area 
of five square inches is the same as one inch of rain falling on one square inch of area.  
However, it is still five times as much volume.  If you pour the collected rainwater from each 
into the same column,
one will show five times as much water.

If the collection funnel has a mouth with twice the cross-sectional area of the gauge column, 
then one inch of rain falling into the funnel will equal enough water to fill the gauge column 
two inches high.  So, to convert height of the column to actual inches of rain, you need to 
divide by the ratio of the cross-sectional area of the collection funnel's mouth to the cross-
sectional area of the gauge column.

Richard E. Barrans Jr., Ph.D.
PG Research Foundation, Darien, Illinois
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Dear Donald-

The most likely answer to your question about the rain gauges is that the 
larger, or longer one uses a larger "collector funnel" than the smaller 
gauge. If you say the larger gauge is 24 inches tall, and is graduated to 
measure 5 inches of rain, then the collection surface area is about 5 
times as large as the surface area of the measuring tube. For instance, if 
a collection funnel had a surface area of 10 inches, and was collected in 
a tube with a surface area of one inch, the ratio would be 10:1...  That 
is, 10 inches of water in the measuring tube would equal one inch of rain.

The smaller gauge must be a tube with the collection area equal to the 
measuring area...that is, one inch of water in the collecting tube equals 
one inch of rain.

Wendell Bechtold, meteorologist
Weather Forecast Office, St Louis, MO
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