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Arduino Based Weather Station
Designed by Mark Little
The figure to the left comes from a ResearchGate published  thesis "Analysis of local weather radar data in support of sewer system modelling" by Toon Goormans - click the figure to see the article. The figure demonstrates the principle of the tipping bucket rain gauge.
As the rain falls, it is gathered in the funnel (1) and falls into the bucket mechanism that consists of the two triangular buckets (2) sitting on a pivot.
Because of the sloped floor of the bucket catching the water, eventually the weight of the collected water will over-balance the bucket and it will tip over so that it hits the bump stop (3) allowing the water will drain out.
The other bucket will now catch the rain falling though the funnel and the process will repeat as the water continues to fall.

To determine the rainfall, it is necessary to count the number of times that the bucket tips. This is commonly done by mounting a small magnet on the peak of the tipping bucket so that as it passes the vertical position during tipping, it activates a magnetic reed switch that is connected to some form of counter.

Because the rainfall is gathered from the funnel's relatively large area, it is possible to detect small amounts of rain, however, it does mean that measurements and calculations need to be done to estimate the rainfall amount from the number of bucket tips counted. It should also be noted that the rainfall measurement has a minimum amount of rain that it can detect. That amount is the amount of rainfall that is need to fill the bucket until it tips over.
References
"Analysis of local weather radar data in support of sewer system modelling"  by Toon Goormans

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Tipping Bucket Rain Gauge
Calculating Rainfall for the Two-Bucket Rain Gauge
The tipping bucket rain gauge is a common means of measuring rainfall and rainfall rate.

The top of the instrument is used to gather rainfall and then funnelling the captured rain into the measuring device.

Usually, the rain gauge outputs a pulse when a particular amount of rain has been collected. The rate at which the pulses are generated depends of the rate at which that amount of rain is collected.
As can be seen in the figure above, the tipping bucket mechanism has a magnet mounted on the tipping bucket mechanism. With the buckets tip from one side to the other, the magnet passes the reed switch, which closes and generates a pulse, which signifies that a bucket is full and will down to empty its water, placing the other bucket in place to collect the collected rainfall. The resistor and capacitor that can be seen on the circuit board is a low-pass filter which reduces the probability of getting multiple pulses if the reed switch bounces when the reeds are pulled together.
Alternate Tipping Bucket Design
An alternate design to the two section tipping bucket is a single section tipping bucket as seen above. In this case, when the bucket fills, it will drop (as seen in the right image) and the magnet will rise to the reed switch mounted above the tipping bucket and cause a pulse. In this case, however, when the bucket empties, it will rise into its normal position and the magnet will fall back away from the reed switch.
There are two factors which govern the amount of rain that will cause the bucket to tip. The first is the surface area of the top of the collecting funnel, and the other is the volume of water required to fill the bucket to the tipping point.

Both of these are relatively easy to measure. For a circular tipping bucket rain gauge the surface area of the top of the funnel can be calculated by:
AreaFunnel = π*r^2
Where r is the radius of the funnel. The diameter of the rain gauge above is about 104 mm, or a radius 52.0 mm. This gives an area of 8,494.87 sq. mm.

The water required to tip the bucket was 9.0 ml, which is a volume of 9000 cu. ml. Given that the collection surface area is 7,697.687399 sq. mm. The equivalent depth of rain can be calculated by:
Rainmm = RainVolume / AreaCollection
Using the measurements, the bucket will tip when approximately 1.059 mm of rain falls into the rain gauge. Looking at the specifications of the old weather station this rain gauge came from, it gave the accuracy of the rain gauge as ±7% which would seem to fit, given that the resolution is given as 1 mm.

When this rain gauge is in action, it can be compared to other rain gauges and the calibration factor can be adjusted to reflect the measured rainfall.
Comparison with the Single-Bucket Rain Gauge
The single bucket rain gauge taken from a more modern weather station has a smaller bucket (3.4 mm) and a wider collection funnel (120mm). This would suggest that this unit will have a resultion of about 0.3 mm which is consistent with the measurements displayed by the weather station.
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