Wednesday, September 14, 2005

Fun With Stupid Math Errors

So today I set up my rain gauge that came with the groovy Oregon Scientific WMR968 weather station, and I wanted to be sure it worked and was calibrated. So, I thought I would pour some volume of water into the rain gauge, calculated so it should read as close to 1 inch of rainfall as possible.

To do this, I measured the diameter of the circular rain gauge opening. If I had all the cool tools I know I need, I'd have used calipers. Instead, I had to settle for a measuring tape and eyeball it.

I decided after much hemming and hawing that the diameter was as close to 3 and 29/32 inches as I could possibly determine with a measuring tape marked in 1/16ths of an inch. I then plugged this into google:
(3 + 29/32) inches * (3+29/32) inches * 1 inch

The result was almost exactly 250 milliliters, which is 1 cup. This seemed to be too good to be a coincidence - obviously Oregon Scientific engineered this rain gauge to process 1 cup of water per inch of rain that falls. Very clever.

So, I poured 1 cup of water into my rain gauge, as slowly as I could. This still worked out to a rate of 21 inches per hour, according to the weather console. I figured there was some error in the size of my measuring cup, and that since I was pouring the water so fast compared to rainfall that the gauge would underreport - some water must inevitably be not recorded if it falls through the rain gauge in the middle of a "dump", where the gauge self-empties.

I was somewhat surprised to see the result on the computer: 1.14 inches of rain fell.

Then I slapped myself silly. I had calculated the volume required as if my rain gauge had a square opening, and it has a circular opening. Back to google:

((3 + 29/32)/2) inches * ((3 + 29/32)/2) inches * 1 inch * pi

So the answer is now 196 milliliters. Too close to 200 to be a coincidence! Or, given how far off I was the last time I thought of this, nevermind.

So, my 1 cup of water should have measured 1.28 inches. At least this has the error in the direction I was expecting it. Either way, it's close enough for me. The measured error is about 14%, but I believe that with slower rainfall the error will decrease dramatically due to reduced "dump" losses.

If I think of it, I'll put up a standard manual rain gauge next to the new one to see if the results are comparable.

Next step: A weather web page. I'm sure my loyal reader will be thrilled. Actually, I know he will, because he is me.


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