# What does a mm of rain mean?

Lots of people have explained it over many sites but I still can not confidently say that I know what it means when they say Hong Kong experienced 3mm of rainfall last Friday.

Does it mean that 3mm per square meter was experienced in a specific area, or does it mean that the total amount of rain had a volume such that if it was spread over all of Hong Kong the height would be 3mm. Or is it referred to in terms of per square meter?

What is the time period? Is it measured per day, per hour, per minute?

EDIT: The question marked as a duplicate may refer to some aspects of the question but does not effectively ask them. The title of the question refers to something different and the only answer to that question is what I am asking an explanation of.

• it is simply liters per square meter. 1 l/m2=1mm. – arkaia Jul 11 '18 at 15:33
• Can also see this overlapping question: Intuitive explanation of precipitation amount – JeopardyTempest Jul 11 '18 at 16:10
• @Milwrdfan relatively few towns have NWS offices (122 offices) compared to recording stations (4,000ish it appears). But you're right that a large percentage of those stations are at airports (and that most "official climate sites" [i.e. those with the greatest history are reliability] are the airport stations) – JeopardyTempest Jul 11 '18 at 19:34
• volume of water per area. – user3528438 Jul 12 '18 at 1:57
• Possible duplicate of Intuitive explanation of precipitation amount – WBT Jul 12 '18 at 16:35

It's confusing to measure liquid in units of length instead of volume, isn't it? Here's how it works.

"One millimeter of rain" is actually one cubic millimeter per square millimeter. On average, over the area you're talking about, each square millimeter has received one cubic millimeter of rain. If you divide n mm3 by 1 mm2, you get -- n mm!

The field of Dimensional Analysis deals with questions like this.

If there was "1 mm of rain", how much rain did a square meter receive? 1000 mm * 1000 mm * 1 mm = 1 000 000 mm3 = 1 liter. Pour one liter of water into a square container one meter on a side, and it forms a layer one millimeter deep.

To calculate "how much rain fell on Hong Kong" (expressed as total volume), you'd take the area of Hong Kong, and multiply it by 1 mm. That's usually not what people want to know, though -- they want to know how wet things got, and the volume-per-area number is most convenient for that.

• @JimmyB "1mm per m²" is wrong, though. That's a measurement in units of inverse length. "1 liter per m²" is right, because that again is a unit of length. – jeffB Jul 12 '18 at 14:32
• You're right of course :) – JimmyB Jul 12 '18 at 15:21
• When using the "unit of length for rainfall" approach to measuring; you are therefore able to simply place a cup outside and measure how far the collected water's surface is removed from the bottom of the cup, giving you "x millimeters of rain". Assuming the cup has vertical sides, the millimeter measurement would remain correct regardless of the size of cup you use. – Flater Jul 13 '18 at 11:10
• For exactly the same reason, exposure in photography is the same regardless of sensor size. – mattdm Jul 13 '18 at 20:33
• I don't think yet another answer is waranted, but I would mention that the actual measurement is made in mm: we measure length, not volume. Not different from the case where we also measure atmospheric pressure in mm (of mercury). – Martin Argerami Jul 15 '18 at 1:59

It is the amount of rain that it takes to cover the ground X milimeters deep. It is normally measured in 24 hours and is measured each morning at a fixed time like 0900.

But now the measurements are fully automatic, so the meteorological service gets the data more often and can provide data for each hour of the day.

Total rainfall is still measured from 0900 to the next day at 0900.

Two weather stations with some distance between them can often give very different measurements.

• Indeed. Daily sums shall be reported at fixed times, but it can be different from country to country. The amount of rain can be measured at a point (precipitation gauge) or for an area with a weather radar. The volume (eg. liters) of rain in the gauge can be converted to a theoretical depth of water: 3 mm = 3 liters / square meter Source: WMO Guide to Meteorological Instruments and Methods of Observation library.wmo.int/pmb_ged/wmo_8_en-2012.pdf – Lukas Jul 11 '18 at 15:08
• @Lukas i only used the time as an example,the sampling time is fixed to GMT or UTC to avoid trouble when we change from normal time to summertime too. – trond hansen Jul 11 '18 at 16:30
• @JoL You might be thinking about it too hard. It is safe to assume that rain falls in an evenly distributed manner. Lets take an example of "3mm of rainfall". If you held out a test tube that was 1x1 mm, it'd fill up to 3mm in depth of water. If you had a 10x10 meter empty pool before the rain, it would also fill up 3mm. The rain fell in an even manner, so for each square mm of space, 3 mm of rain fell. It doesn't matter how large the area is, the total "depth" of rain is 3mm. (Of course, this isn't totally true, leading to measurements from each side of a city being different). – Doc Jul 12 '18 at 0:17
• "Two weather stations with some distance between them can often give very diferent measurments." Indeed. Mt. Waiʻaleʻale and White Sands beach on the island of Kaua'i, while separated by less than 20 miles, typically show something of a difference in their daily rainfall readings. – dgnuff Jul 12 '18 at 2:50
• +1 for the only answer to actually touch the second half of the question - the time period over which the water is collected. – Semidiurnal Simon Jul 12 '18 at 10:11

Does it mean that 3mm per square meter was experienced in a specific area, or does it mean that the total amount of rain had a volume such that if it was spread over all of Hong Kong the height would be 3mm. Or is it referred to in terms of per square meter?

They're really the same idea. Fundamentally it means that it filled a rain gauge (of some type) to 3mm height. But every place that gets that experience equally would see the same amount of rain. So if the storm hit the entirety of Hong Kong as it hit the airport, the rain gauge at that airport would record 3mm, and so would any other rain gauge in the city. And (on flat, exposed ground... if water didn't absorb into the soil or evaporate over time) every square meter would get a depth of 3mm... and the region as a whole would have been covered with 3mm deep of water. (Of course water truly flows downhill and is deflected by buildings and such, so you'd end up with much more water in some spots, less in others).

In other words, 3mm is the height of whatever 3-dimensional prismatic shape you want to draw that was equally affected by the storm, be it a box with a square base of 1 m$^2$, a cylinder 1 km in diameter, a surface with a base of the entire city, etc.

Now of course in reality, not every place does experience the storm the same. And so Hong Kong airport may get 3mm, but Cheung Chau may only see 2mm.

And it's still true that a storm that affects a larger area with 3mm of rainfall does put down more total water quantity in entirety. If the same storm hits all of China, that's indeed a lot of water! But of course it's also a larger area to absorb that water. So regardless of whether it's a Hong-Kong sized downpour or a China sized rain system, if it puts down 3mm, it tends to have similar impacts throughout the region affected.

As others mention, a day is a very common time period for reporting such values. But they can be reported for whatever time periods people wish. Often you'll hear values for a specific storm, which can be as short as a quick downpour, or as long as a multi-day typhoon/hurricane. It's whatever the person wants to report about. Usually they'll give the time period or subject. 3mm doesn't fall in 1 second, but it can fall in a period much shorter than an hour. Or it can be the accumulation from only a steady drizzle that lasts days. That's where the rainfall rates (often given in mm or inches per hour) can be worthwhile!

• It's kind of like saying I'm going to give £1 to each location I go today. Whether I stay home and just give my roommate £1, or I go all over town, giving £1 throughout the entire city, each person's wallet gained only that £1. It's true that I truly gave a lot more money if I went all over town. But the impact on each person is still the same! – JeopardyTempest Jul 11 '18 at 16:02
• +1 This answer explains best why the area doesn't matter, and shows that length is indeed a good measurement, which I think is the crux of the question. – JoL Jul 11 '18 at 21:47
• It's not just that it allows for comparable statistics for locations with different surface areas. The other benefit is also that every can measure rainfally using a cup (with vertical edges) of any size. I might use a bucket, you might use a test tube, and the result will be the same (again, assuming straight lines and barring local variations in rainfall). – Flater Jul 13 '18 at 13:23

Given any container with straight sides, 3 millimeters of rainfall will fill up that container to 3 millimeters in depth.

The size of the container does not affect this. It holds whether the container is the size of a tennis court, or the size of a small beaker or a test tube with a flat bottom. As long as its sides are vertical and uniform.

It is also not necessary to talk about volume of water (eg cubic millimeters, liters etc) to understand this. You would only be converting to volume in order to convert back to depth later.

All you need to take into account is that any straight edged container will fill to this depth.

If you ever see a conical shaped container measuring rainfall, it's because the depth measurements on the side of that container are non-linear - these markings show what the equivalent depth would be in a straight-edged container.

Note 2: shallow water evaporates relatively quickly. For a rain gauge to be useful it needs to have a way to minimise evaporation, such as by having a funnel in the top. The area of the top of the funnel still matches the cross sectional area of the container in which we're measuring the depth

• This is in my opinion the best answer: We measure rainfall in mm because you can do it with literally any container with a flat bottom and sides that follow the profile of the opening. – Chris Becke Jul 15 '18 at 12:37

Simply, an "amount" of rain is a certain volume, and volume equals area x height.

"3mm of rain" means for any given area, the amount of rain that fell (ie the volume) would fill that area to a height of 3mm.

The area part of the formula is effectively a constant. The only variable is the height.

It means that during the rain event (which may last a minute, an hour, a day), one square meter of ground was filled with water up to a height of 3mm.

The one square meter just next to this first square meter was also filled with a height of 3mm of water. So that over the 2 square meters united, the ground was still filled up to 3mm of water.

A surface of 10 square meters was also filled with water up to a height of 3mm, etc.

In other words, the volume of rain collected obviously depends on the surface of the ground, but the height of the water level fallen onto the ground does not depend on the surface of the collector.

This is of course correct if the rain is uniform over the whole surface (i.e. it might brake for a surface which is much smaller than the distance between the drops, or for a surface that is larger than the scale at which the rain rate uniform).

I will address the aspects of the question that relate to how rainfall is measured and the measurement period. Some of this has been mentioned in other answers.

As previously noted you can think the amount of rain as the volume of water that falls on a given area divided by that surface area. That means that the measurement has units of length (typically mm). This assumes that the amount you measure at one point can represent the amount that falls over the whole area or that you measure many points that represent different parts of a large area and add them together.

The straight-sided graduated cylinders discussed in other answers have a constant area so the depth markings are a constant (1 mm) apart, but you can use other shapes, if they are marked correctly, to show what the depth would be on a straight sided cylinder. One common design is to have a funnel with a large area at the top feed into a narrower container below. In that case the depth of the water captured will be greater than the rainfall in mm. These take the rain volume from a larger area and measure it in a smaller one because it 'magnifies' the depth, making it easier to read for small amounts.

Automated systems work differently, using weighing or 'tipping bucket' systems. Tipping buckets have a funnel like top that feeds the water down into little cups on a pivot below. When one cup fills up the weight causes it to go down like a see-saw and the bucket empties. The other bucket moves up and catches the water until it is full and goes down. They are designed so the weight of rain it takes to get the tipping bucket to pivot is known. All you have to do is count how many times it pivots to measure the rainfall. If you assume that rain is essentially pure water, then the weight is directly related to the volume. Divide that volume by the area of the top of the gauge and you get mm of rain.

Most country's weather services report the amount of rain over a day and add the amounts together to get monthly or annual measurements, but it is possible to take measurements more frequently. More frequent measurements can be used to report rainfall intensity over a shorter period. So you, for example, could report the maximum hourly rainfall intensity within a day. You can also use more frequent measurements to calculate how quickly streamflow responds to a rainstorm.

Your question seems to be a conceptual one, so I'll answer conceptually.

For the sake of the argument let's imagine a flat area with impermeable ground, like rock, and an impermeable wall around it. After it has rained for some time with a certain intensity over that area — everywhere the same —, there will be a certain height of water on the ground, which will be the same height all over this flat area. This height is measured in millimeters and reported. You can now go and divide this area up in square meters, or soccer fields, or square milimeters; the height of the water would obviously not change. That's the beauty of this measurement: It is independent of any particular area.

These are unrealistically ideal assumptions. The intensity or duration differed from place to place, the ground is not level, water seeps away etc.

So the statement actually says: "This station measured a rain event which would cover any area with x mm of rain if it had rained everywhere the same amount as it did here." The duration is irrelevant with respect to the amount but must be mentioned together with the measurement because it makes a huge difference in meaning and impact: 100 mm in a month are just wet while 100 mm in a day are catastrophic. In your case, "last Friday", one may assume a 24 hour calendar day.

It's also often not possible to make a reliable statement for a larger area, especially in the case of local severe weather events. One can make an estimation based on measurements from different stations in the area and qualitative observations, but the only reliable accurate statements which can be made are factual measurements at weather stations; everything else is inferred, as in your example about all of Hong Kong.

I can imagine though that among Meterologists the sentence "Hong Kong reports 3 mm of rain" is taken to mean "The Hong Kong Observatory reports 3 mm of rain", and equivalently for other places.

Rainfall is measured with a rain gauge. This one goes up to 12 cm or 120 mm, so 3 mm would just be a few drops at the bottom.

As you can imagine, it doesn't matter how big this gauge is, as long as the sides are straight. A larger cylinder will hold more water, but it has a larger opening to collect rain, so the measured rainfall is the same in either case.

Inversely, multiplying the rainfall (3 mm) by an area (100 square meters) gives a volume (= 0.3 cubic meters, or 300 liters), assuming a uniform rainfall over the area.