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I left a wheelbarrow outside overnight and it rained heavily. This morning, the water in the wheelbarrow is five (5) inches deep. It's not sitting under an eave where water might have been channeled to it, but out in the back yard fully exposed to the sky. And it's sitting quite level; I'm not measuring "at the deep end". The weather news is saying we had two (2) inches of rain. Are there local pockets of heavier rain that would explain the discrepancy, or is the wheelbarrow not an appropriate way to measure rainfall? Is there some sort of averaging involved?

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    $\begingroup$ See also: what does a mm of rain mean ? $\endgroup$ Dec 19, 2023 at 9:17
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    $\begingroup$ Hi. Requesting three clarifications: (1) Does your wheelbarrow have a perfectly constant horizontal section, like a cylinder or rectangular cuboid?; (2) How large an area did this weather news cover? Rain can be very localised, so saying "it rained an average of 2 inches over the whole city" is not the same thing as saying "it rained 2 inches in my garden"; (3) You left the wheelbarrow overnight: did the weather news use the word "overnight" or "over the last xx hours" or something different? $\endgroup$
    – Stef
    Dec 19, 2023 at 12:58
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    $\begingroup$ Does this answer your question? What does a mm of rain mean? $\endgroup$
    – OrangeDog
    Dec 19, 2023 at 14:34
  • $\begingroup$ I've known rain to follow a road, in that one side was dry while the other side was overflowing the gutters. Weather can absolutely be very localized, and in fact often is. scifi.stackexchange.com/a/270191/47955 $\endgroup$ Dec 20, 2023 at 17:43
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    $\begingroup$ @Stef On the road, sorry for the delay in responding. The wheelbarrow does have a curved "lip" in the front that would increase the catchment surface area by a little, say 10%; not enough to explain the rather egregious difference between the reported 2 inches and my 5. I think the phrase was "in the past 24 hours", but that only increases the discrepancy, since I left the wheelbarrow exposed for only about 12 of those hours. I've been told by a neighbor that the news I heard may rely on the gauges at the international airport which is about 5 miles away. $\endgroup$
    – Tim
    Dec 23, 2023 at 13:38

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A wheelbarrow is usually considerably wider at the top than at the bottom, so the accumulated water at the bottom will likely be deeper than what actually fell.

However, rainfall can also have considerable variation in space. I often see reported rainfall totals being for the local airport or similar. For example, if this rainfall were reported for the airport (northeast of the highway intersection in the little black outline), people a short ways southwest would have gotten half again more rain.

Rainfall distribution for Colorado September 2013 floods

Averaging will depend on what's being reported. As mentioned, it's often at the airport or similar, but you can also see area-wide averages. Any given reporting method could still vary significantly from the precipitation at a given point unless it's measured right there.

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Weather stations measure the depth of rain that falls over a small, set area by setting an open topped cylinder of precise diameter in the open at a standard height above the ground and measuring how high the water rises within it over (usually) a 24 hour period. A standard 8"/203mm diameter is widely used for weather station rain gauges but is not required to give accurate measurements.

At its simplest the height of the water within the cylinder - which must be flat bottomed as well as the same diameter top to bottom is measured. Buckets, wheelbarrows that are wider at the open top than the bottom - or jars that are smaller at the top - are not suitable.

In practice, to make it easier and for greater accuracy a separate calibrated measuring cylinder of smaller diameter is used to measure what has collected. Each mm or inch marked on the measuring cylinder is equivalent to one mm or inch in the collecting cylinder.

(The use of a separate measuring cylinder - or automated measuring equipment - means the collecting container shape or size becomes irrelevant. Measurement is calibrated to the size of the opening - the top rim of brass in the example shown. Automated rain gauges are becoming more common.)

Standard manual rain gauge

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    $\begingroup$ Interesting. I'd expect the funnel to be deeper the tube to prevent rain splashing out. $\endgroup$ Dec 19, 2023 at 4:36
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    $\begingroup$ @chux-ReinstateMonica - I've done the duty myself a few times; the gauge I handled looked well optimised, including a sharpish inside edge to the precise brass rim, that would slice raindrops. The funnel starts a bit down from the rim. Seemed well designed for avoiding splash back out. $\endgroup$
    – Ken Fabian
    Dec 20, 2023 at 2:40
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In addition to what others have mentioned, sometimes measurements are simply wrong, in particular where measurements are automated.

Some weeks ago, two weather stations in Germany reported over 60 mm of rain, when all the others nearby reported zero, radar reported zero, model reported zero, and satellite imagery was not consistent with precipitation. What was going on? You would think that automatic rainfall measurements shouldn't be too hard? Those were automated weather stations with automated rain gauges. During those erroneous measurements, there was a snowpack that was melting. Most likely, rather than measuring rainfall, those gauges had been measuring snowmelt and reporting it as rain. Since there's nobody present at weather stations in Germany any more, this will remain a hypothesis and it's up to the data users to filter out measurements that are clearly wrong.

There are many other things that can go wrong with automated weather stations, but they satisfy politicians who want to reduce public spending, so...

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    $\begingroup$ There was a story back when I was a student where some unexpected rain occurred. Turned out a drunk guy ended up using it for a restroom(!?!) :-p You are right that previous ice can wind up measured as rain (though that's why the highest standard typically are heated). The data that goes public (at least from the main instruments in the US) also gets automatically quality controlled to look for odd anomalies like that. I like weather, but honestly would think there's a lot of better things to spend money/time on. Though I think we may still have weather observers at certain large airports $\endgroup$ Dec 19, 2023 at 9:42
  • $\begingroup$ @JeopardyTempest True, there is quality control, and snowmelt is not supposed to end up being measured as rain when asking the manufacturer, and weather stations are supposed to be fenced to avoid such drunks as you mention, but there certainly wasn't 60 mm of rainfall at those stations some weeks ago. Maybe the explanation is a different one, but in any case quality has gone down since widespread automation (I think airports are also here the only ones that still have humans, but they're working on automating those too; the barrier for doing so is much higher, though). $\endgroup$
    – gerrit
    Dec 19, 2023 at 10:02
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    $\begingroup$ As a scientist, and having supervised student projects, sooner or later something will always go wrong. An additional data source makes a big difference. Here it could be a camera covering the weather station; I've used a combination of weather data and an insistence on logging against wall-clock time to find glitches caused by sunlight getting past the blind onto the experiment in the lab. $\endgroup$
    – Chris H
    Dec 19, 2023 at 13:30
  • $\begingroup$ @chrish I'll be honest, don't know why don't work to add them at asos sensors, as you're absolutely right. Wonder if the power/data profiles would be quite significantly challenged??? $\endgroup$ Dec 20, 2023 at 16:14
  • $\begingroup$ @JeopardyTempest I suspect cost. And someone would have to ensure that every installation was acceptable for privacy (i.e. only looking at the kit, but OTOH you do want to include some background for maximum usefulness). You don't need live video for troubleshooting, or massive resolution, after all $\endgroup$
    – Chris H
    Dec 20, 2023 at 16:24
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Properly designed rain gauges can give accurate results for a given location or point in space, but the problem is that it's hard to have enough of them packed densely enough in an area to give the level of detail that you might see in maps on news stations or weather websites. Models and extrapolation can fill in the gaps to a degree, but there could be a lot of error with it.

On the other hand, Doppler radar (a remote sensing tool) can measure the type and intensity of precipitation at various altitudes across an area with a radius of 100+ miles. By "scanning" periodically (it might miss very short bursts of precipitation!), this data can give a pretty good idea of what the accumulation was to a pretty fine level of spatial detail. It's the data used to create those animated maps showing the progress of a storm you might see on news channels or weather websites. Ground stations/rain gauges are then used to calibrate/verify the Doppler data; you don't need many of them for this purpose.

As others mentioned, a wheelbarrow will likely overestimate how much rain accumulates. But also, the models that use the Doppler data to create precipitation accumulation estimates won't be 100% perfect; averaged across a large area (or time), they're probably really good, but as you start to zoom in towards a small enough area or point, you could very well see some deviation (variance) from the true amount.

Here are a few links related to the topic of weather radar and precipitation accumulation (I'm not an expert by any means):

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  • $\begingroup$ Note that radar measurements also have error, in particular since they cannot measure close to the ground, where precipitation happens. The farther from the radar, the larger the blind zone near the surface. Some rain evaporates on the way down, or rain accumulates in a vertical column. $\endgroup$
    – gerrit
    Dec 19, 2023 at 8:26
  • $\begingroup$ As maybe hinted at, radar also has another issue: the relationship between Z (radar reflectivity) and R (rainfall rate) are not one-to-one; a certain reflectivity can in reality be a range of droplet size\shape distributions. Higher reflectivity of course means higher rate... but it's not as cut and dry to figure out the rainfall values (and different Z-r ratios are used for different weather). The implementation of polarmetric radar helps some, allowing a better idea of shapes and separate contributions of different frozen shapes and such. But it's still a complex science. $\endgroup$ Dec 19, 2023 at 9:11
  • $\begingroup$ In fact, each radar has its own unique patterns too, in part because of slight differences in equipment and environment. So altogether, thus, ground truth is important in calibrating continually. See also $\endgroup$ Dec 19, 2023 at 9:11
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It’s the depth of water in a container of any arbitrary size (more specifically, arbitrary area of ground it covers¹, the height has to be enough to measure the volume of rain that fell) with a perfectly flat bottom and perfectly vertical sides, collected over the course of the entire period of rainfall.

This is a proxy for the volume of water that fell, but is particularly useful because it’s invariant of the total area that the water fell over¹ and can thus be easily used to calculate the volume for any given area of interest (because you can just multiply it by the area, instead of having to know the size of the measurement container and rely on ratios like you would if you just used the volume). This ability to use quick math to figure out the volume for a given area of ground is really useful because it lets you more quickly calculate:

  • How much the level of a lake is likely to rise as a result of runoff from the rainfall.
  • How much the flow rate of a river or stream is likely to change given the rainfall (this is super important for ships navigating the river).
  • How much water needs to be let through a dam to maintain a constant reservoir depth given the rainfall.
  • How much water needs to be used when irrigating a field to ensure the crops are not over or under watered.
  • How likely it is that ponding (buildup of standing water in areas with poor drainage) will occur in a given area.

But, for such measurements to be accurate, the container used for measuring must be designed to actually make the measurements. This means that the bottom must be flat and level, and that the sides must be perfectly vertical and perfectly parallel to each other. A wheelbarrow almost never meets those requirements.

Additionally, these measurements are almost always taken at some central location for the region being covered. Quite often it’s based on the nearest airport, seaport, or military installation as they typically have very accurate weather stations. Otherwise, it may be some government operated weather station in the region, or possibly a station operated by whatever entity is providing the reporting. If you’re more than a few kilometers from the measurement site, you’re actually reasonably likely to see different numbers².


1: I mentioned above that the measurement container can cover any area, and that the depth is invariant of the total area covered. This may seem unintuitive, but it’s actually a logical side-effect of the random nature of precipitation when observing at the scale of individual raindrops or snowflakes. If you have a infinitesimally small point, the probability that it gets hit by a raindrop in a rainstorm follows a (roughly) uniform distribution dependent on the rate of rainfall (unless there are objects nearby that might obstruct the flow, in which case their positions together with the wind direction and speed also influence the probability). Because of the law of large numbers, this means that any two arbitrary points near each other will see roughly the same number of raindrops hit them in a rainstorm, provided enough total raindrops fall proportionate to the area the storm covers (which almost always happens). This same effect is why the ground eventually ends up uniformly wet during a rainstorm no matter the rate of rainfall.

2: In contrast to the point above about small-scale uniformity of precipitation, when measuring at large scales there’s quite a bit of variance (otherwise meteorology would be a much simpler science with far more accurate predictions), and the possible variance increases proportionate to the distance between the measurement sites. What this means is that the further away you are from the site the data you’re seeing is being measured at, the more likely it is that you will see different measurements locally.

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