[wxqc] Error from different collector sizes vs. density

TJ tjslagle at cox.net
Mon Oct 10 21:50:11 CDT 2011

Your scale may have a resolution of 1 gram but what is the accuracy and is
it linear? 


From: wxqc-bounces at lists.gladstonefamily.net
[mailto:wxqc-bounces at lists.gladstonefamily.net] On Behalf Of Victor Engel
Sent: Monday, October 10, 2011 3:28 PM
To: Discussion of weather data quality issues
Subject: [wxqc] Error from different collector sizes vs. density


Last week we had a lively discussion about error introduced by collector
size, reading errors, tipping bucket errors, wind, etc. To test the
potential error introduced by using a gram scale to measure the mass of the
water, I decided to do a little exercise.

First, I came up with a reasonable range of densities we can expect from
rainfall. Maximum density occurs at 39F. For pure water, that is a density
of 1. I will conveniently ignore any issues resulting from dissolved
substances or particulates in the water. I think these are normally
insignificant, but someone can feel free to show otherwise.

The lowest density I took to be likely was the density of water at 80F. I
figure that even with warmer ambient temperatures, it's unlikely for
rainfall to be much warmer than 80F, so I used that as a minimum density
likely to be collected. Suppose, then, that we assume the density is half
way between these two values and use that to determine volume from mass, and
hence depth of precipitation.

The density of 80F water is 0.996635, so we have a maximum error due to
assuming the wrong density of 1/2 1-0.996635 = 0.0016825 or 0.16825 %.

The error we can expect from a random set of discrete data (rain drops) is
about the square root of the total number of rain drops. Continuing with the
numbers I came up with last week, the expected number of rain drops for 0.01
rain from a 4" collector is 62 drops. Due to the random nature of rain, we
would expect this to vary by +/- sqrt(62).

I charted the error due to density (which is linear) to that of the
randomness of the signal (which tends to average out with higher values).
Here is the result for a 4" collector:


The graph goes from 0" of rainfall to 10", which corresponds to the capacity
of a CoCoRaHS rain gauge.

Since the 8" size of the Davis collector was also compared to the 4" size of
the CoCoRaHS gauge, I also created a similar graph for an 8" collector.


The curves are closer together, but the error from the randomness of the
rain drops still exceeds any error from assuming the wrong value for
density. And bear in mind, the graph shows the greatest possible density
error. I suggest it's possible to greatly reduce this by choosing a
reasonable density value -- perhaps the density associated with the dew
point at the time of the rain fall.

The other sources of error we discussed, of course, are still present. This
exercise was meant to illustrate how much of an error we can expect from
density errors, in terms of something we deal with anyway.

I will start logging mass when I do my CoCoRaHS readings. This weekend would
have been a good time to start, since we actually got some rainfall, but I
had a bad back and couldn't take a reading. My scale has a resolution of 1
gram, which, for a 4" collector, is about 1/200", so it should be more
precise than reading the meniscus.


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