Rain gauge issue

[Wowbagger]

For some years I have had one of these



Over the years, the plastic support, which is used to attach it to a post, has broken and it's too flimsy and light in windy weather to stay upright if just placed on the ground.

So I bought one of these


I've been comparing results and the plastic rain gauge invariably records something like 20% less rain than the copper one. They have been standing immediately adjacent to one another.

Yesterday, I had a moan to the company that sold the copper one to me - I'm pretty sure that it's more likely that this one is wrong as the plastic one records figures acceptably close to my Davis weather station, which is at roof level, and also very similar figures to those my sister records. Her house is about 200 metres north of mine, the difference being that she has a north-facing rear garden, mine is south facing. I don't think that is likely to make a significant difference most of the time.

The initial response from them annoyed me greatly as its implication was that two different rain gauges would record differently because they had different outer diameters. I pointed out that the inner measure should be calibrated correctly and both gauges should record the same amount.

Can some clever mathematician please help me with the calculation that needs to be done to find out which of the two rain gauges is calibrated correctly? The plastic one is 102mm in diameter outside, 35mm inside. The inner cylinder is filled at 25mm, but each of the 1mm graduations is actually 1cm.

Would I be right in thinking that the area of the outer cylinder would need to be 10* the area of the inner cylinder for this to be an accurate measure?

The copper rain gauge has an outer diameter of 127mm but the inner plastic cylinder has a diameter of 69mm. This is complicated by the fact that the inner's base is conical, allegedly allowing for easier reading of the first 5mm rain. After 5mm, the next 30mm's worth of graduations are linear and measure 104mm.

I presented the discrepancy to the company that sold me the rain gauges and their initial response annoyed me a lot because I felt it was patronising and the implication was that two different rain gauges would always record differently because they were different diameters. I have had another response this morning more to my satisfaction, offering a refund for the copper one, which I bought in February.

I hope my gobbledegook above is comprehensible. Thanks in advance to anyone who tackles this. I suppose it could be a GCSE question...

[Ham]

Pour the same amount of water into each (use weight to measure) and observe the reading. Repeat with a minimal and maximal amount. That will establish a comparison. Next, you would need to see which is the more accurate.

[philip]

The ratio of the areas is what matters.  If the collector diameter is D and the tube diameter is d then the ratio of the areas is D²/d². In your case 102 and 35 give 8.5, i.e. 1mm rain produces 8.5mm in the inner tube, while 127 and 69 gives 3.4, i.e. 1mm rain produces 3.4mm in the inner tube. Your small gauge appears to underestimate by about 15% while the larger one looks to be more accurate (30mm * 3.4 = 102mm compared to your measured 104mm).

The conical bit causes d to vary, which causes the markings to be spaced further apart in that region.

[Cudzoziemiec]

I merely note that both gauges have the same manufacturer.

[Wowbagger]

I've come up with the test, adapted from Ham's suggestion, of filling each inner to 25mm 10 times and pouring it into the relevant outer, and measuring the depth. Both came out as one might have expected at 25cm deep. So I think the issue is with the graduations where the copper rain gauge inner has the conical base. This is much harder to calculate. Since the vast majority of rain days are under 5mm, this exaggerates the problem. In fact, since I bought the copper rain gauge in February, we have had only 2 days with more than 1cm of rain.

[philip]

Is the conical part a complete cone or a frustum?

If it tapers to a point, i.e a complete cone, it has a volume of 1/3 the cylinder.  5mm in the cylinder of the larger gauge would have a depth of 5mm*3 or 15mm as a cone, i.e. the connical part should be 15mm from the start of the taper to the point.

If the shape is a frustum you need to measure the depth and size of the smaller end.

[Edit: 17->15 typo]

[philip]

Oops, that's not right. The scale represents mm, but is not mm.

5 'in the cylinder' should be 5*3.4mm i.e. 17mm. The cone should be 3 time this, i.e 51mm.

[Wowbagger]

I had to look up "frustrum"! It's a complete cone, but instead of coming to a point, it's rounded. I don't think that would make much difference at all.

But - I think I have a solution.

I weighed 25mm in the inner cylinder - 293g. So - 2.5mm should have been 29g. In fact, 29g reached the 3mm line. So that is a 25% exaggeration at that level. See above for the vast majority of rain days being under 5mm.

[philip]

If the cone is an irregular shape there is no formula for the volume.

If the outer is a simple cylinder with no obstructions is can be used to calibrate the inner, similar to the process you used already. Fill the outer to a known depth, say 10cm, and decant and weigh the water. Divide by 100 and that quantity of water is 1mm of rain. Pour that quantity into the inner and mark the level as 1, pour anothe lot and mark the level as 2, etc.

[philip]

Alternatively, given your measured outer diameter of 127mm, the 10cm of water should have a volume 6.35*6.35*3.14*10cc i.e. 1266cc. Thus 12.66cc, or 12.66g, of water should correspond to a 1mm of rain. Pour 12.66g into the inner, mark 1, pour another 12.66g, mark 2, etc.

[Wowbagger]

The company has offered me a refund, which I have accepted. I don't know if they want me to send the CM1037 (copper) rain gauge back yet.

[Ham]

Just FYI, I've been happy with this https://www.weathershop.co.uk/5-in-1-explore-scientific-colour-wifi-weather-station

[Wowbagger]

I've got a Davis Vantage Pro 2. The problem I have is that I put it at ground-floor-extension roof level. The rain gauge has a tendency over time to get blocked by debris and I need to get a ladder out to access it. I generally only notice that it has become blocked when we have a very wet day that tests it, and of course that completely buggers up my data (the last time was due to a large dead moth blocking the hole). This is why I have another manual rain gauge.

It seems that the Met Office have pretty much completely dispensed with manual rain gauges. Perhaps I should invest in a Davis tripod especially for mounting weather stations on. The trouble is that our garden isn't huge and I would like to keep the anemometer where it is, so the tripod would have to be pretty close to the house. I'm sure this would affect the rainfall readings.

The anemometer should be higher than its current 4 or 5 metres above ground level, but I'm not prepared to get up a ladder and mount it at gable level so that it's in excess of 8 metres up, and I expect someone would charge me quite a lot of money if I paid them to do so.

[Kim]

Problem with tipping-bucket rain gauges is they eventually get clogged by spiders.  So you really do want them accessible.

I've pretty much given up on weather stations.  Our position is too sheltered to do anything reasonable for wind/rain other than mount it on the chimney, and I don't have the ladders for that.

I'll stick to measuring particulates and counting vehicles.  I've got temperature/humidity/pressure/ambient light sensors alongside the particulate sensor, and a slightly better-positioned temperature sensor on the back of the satellite dish.  They're good enough for temperature-compensating the central heating, lighting control and detecting barbecues and volcanic eruptions, which really ought to be enough for anyone.

[aidan.f]

How about one of these? As installed at a river Tweed monitoring station, surrounded by trees... waste of a good gauge!
https://www.bellenviro.co.uk/arg314-wmo-compliant-tipping-bucket-rain-gauge.html

[Wowbagger]

I had to look up "frustrum"! It's a complete cone, but instead of coming to a point, it's rounded. I don't think that would make much difference at all.

But - I think I have a solution.

I weighed 25mm in the inner cylinder - 293g. So - 2.5mm should have been 29g. In fact, 29g reached the 3mm line. So that is a 25% exaggeration at that level. See above for the vast majority of rain days being under 5mm.

I sent these findings, in a bit more detail, to the company that sold me the rain gauge.

Today I had this reply:

Thank you for letting us know your findings, which we do find interesting. However the calibration for the inner measure for the CM1037 was carried out via a specialist company, so we have every faith that the calibration is correct. The CM1037 is also our best selling Copper rain gauge and we haven't come across this problem before.
So we would like to apologies for any inconvenience this may of caused. 
We have issued you a refund for the product and are happy for you to keep the rain gauge if you wish to do so.

Kind Regards
The UK Weather Store

I'd imagine that they haven't come across this problem before because hardly anyone has two rain gauges side by side, or a family so geeky that four of us kept weather records and compared notes frequently. Most people just take a reading and assume it to be correct.

[Kim]

I expect the specialist company hand over a certificate officially proclaiming that it over-reads by $foo to within a margin of $bar.

[Wowbagger]

I expect the specialist company hand over a certificate officially proclaiming that it over-reads by $foo to within a margin of $bar.

Surely, that latter measure would be for their $barometer?

[Wowbagger]

But at least I now know that my copper rain gauge measures 25mm rain and it weighs 290g. All I have to do now is weigh the water in the rain gauge every morning and divide the mass by 11.6 to find out how many mm rain there has been. That's actually rather better than holding it up and guessing how far up the imprecise graduations the water level has reached.

I must present this issue to my good pal Mel who, before his retirement, was head of A level maths at our local sixth form college, and whose son is https://www.imperial.ac.uk/people/edward.smith05 . I reckon that between them they will come up with a definitive answer.

[aidan.f]

All I have to do now is weigh the water in the rain gauge every morning and divide the mass by 11.6 to find out how many mm rain there has been. That's actually rather better than holding it up and guessing how far up the imprecise graduations the water level has reached.

That's got me thinking I 'spose you could automate the weighing -

Strain gauges are a lot of fun to play with but they often need complex conditioning and conversion ICs. Qwiic Scale takes care of all the hardware and software concerns and gets you measuring weight!
We've written an extensive Arduino library to make reading a load cell over I2C a breeze. Calibrate, get weight, and you're set.

https://github.com/sparkfun/Qwiic_Scale

The process could include a conductivity rain sensor to zero the reading periodically.

manual empty or maybe a syphon?

 

[Wowbagger]

You'd need to make all that circuitry rainproof. And I quite like the daily ritual of checking the rain gauge, even though it hardly ever seems to rain.