[wxqc] Error from different collector sizes vs. density
Victor Engel
brillig at gmail.com
Mon Oct 10 21:56:49 CDT 2011
It's certified for something or other (don't have the paperwork handy).
You're right that it's something additional that should be checked. Along
those same lines, I should also calibrate the Cocorahs gauge (graduated
cylinder) with something.
Victor
On Mon, Oct 10, 2011 at 9:50 PM, TJ <tjslagle at cox.net> wrote:
> 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:
>
> http://www.pbase.com/victorengel/image/138737343
>
> 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.
>
> http://www.pbase.com/victorengel/image/138737349
>
> 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.
>
> Victor****
>
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