Same rain, so why does the road turn into a river in the city?
― Bare ground with no soil sends 100 pools' worth of water nowhere, in just an hour
In hills and fields, even heavy rain mostly soaks into the ground. But in the city, the same rain turns the road into a river within minutes. The amount that falls is identical. What differs is a little-known number: how many millimetres of rain the ground can absorb per hour.
It's a summer evening. Rain suddenly starts falling hard. Within ten minutes, water is roaring along the edge of the road.
At the same time, the same rain is falling on a nearby patch of woodland. The forest floor turns muddy, but no water is flowing over it.
It's the same rain cloud. The same amount falls. Yet only one of the two places turns into a river.
There are just two reasons
Soil does absorb water, but not at unlimited speed. There's an upper limit to how many millimetres it can take in per hour. If the rain is weaker than that limit, the water simply disappears into the ground.
Asphalt and concrete have no gaps for water to pass through. Their absorption speed is close to zero, so almost all the rain that falls runs across the surface. Where it goes next is left entirely to the drains.
Neither of these is about "amount" — it's about "speed." I think that's the hardest part of this phenomenon to grasp. It's not the size of the bucket that matters, but the width of its opening.
How fast can soil actually absorb water?
The maximum speed at which soil can take in water is technically called infiltration capacity. It's measured in the same unit as rainfall: millimetres per hour. Well-maintained forest soil is known to manage 50mm per hour or more, while a well-trodden schoolyard manages only around 10mm per hour.
Compare that number with the strength of the rain. If a forecast says "30mm per hour," a forest can absorb almost all of it, but on trodden ground, two-thirds of it overflows. The same rain shows a completely different face depending on the ground beneath it.
Look at Figure 1. On the left is soil ground, on the right is paved ground, and the same amount of rain is falling on both.
In the city, where does that water go?
Rain that can't soak in doesn't just vanish. It gathers along the slope of the road, then enters the sewer system through gutters. City drainage is designed on the assumption that it will carry this water away.
But that design also has a limit. Many cities' sewers are said to be built to handle around 50mm of rain per hour. Beyond that, water can't fit into the pipes and starts pooling in low-lying spots.
That's why puddles in the city always form in the same places: at the bottom of slopes, in underpasses beneath railway lines, in front of stairs leading underground. Low ground gives the same answer every time it rains.
Some newer pavements for footpaths and car parks are deliberately designed to let water pass through. There are also systems that temporarily store rainwater in underground tanks and release it slowly. Both are human attempts to restore the soil's lost absorption speed.
When a road floods, you can't tell from the surface if a drain cover has come loose — and you can't judge the depth by looking, either. Underpasses and underground car parks tend to collect water quickly, so in heavy rain, stay away from them and move to higher ground. If you sense danger, such as someone being trapped, call 119 without hesitation.
Summary
Roads don't turn into rivers because the rain is unusually heavy. It's because the land has lost its "speed of absorption." Soil — an invisible reservoir — can no longer do its job underneath the pavement.
The issue isn't how much rain falls.
It's how many millimetres per hour the ground can absorb.
When a city's ground changes, temperature changes too, not just rainfall. Read Why are cities hot? ― The gap is bigger at night than in the day alongside this one, and you'll see the full picture of what paving brings. If you'd like to know more about how soil and water interact, try Why do landslides sometimes happen after the rain has stopped? too.
- Take a plastic bottle with the bottom cut off (cut both ends to make a tube). Push the open end a few centimetres into soil in a garden or park.
- Pour water into the tube and time how many seconds it takes for the water level to drop 2cm. From the time it takes for 10cm of water to drop, you can roughly estimate how many millimetres per hour the soil absorbs.
- Compare this with soil beside a well-trodden path, and soil under a tree covered in fallen leaves. Undisturbed soil should absorb far faster.
※ Please don't do this on someone else's land. Fill the hole back in after the experiment.
Want to know more? ― Terms, formulas, and links to the textbooksWe've labelled exactly what level each part belongs to, from junior-high science to university specialist courses
- JHSCovered in junior-high science
- HSCovered in high-school "Earth Science Basics"
- HS+Advanced high-school content, or textbook sidebar material
- UnivNot taught in high school — university specialist content (hydrology, river engineering)
- ResearchNot yet settled as textbook fact even at university — an active research question
JHSTerminology: this phenomenon has names
- Infiltration: the process by which surface water passes through gaps in the soil and enters the ground. Its speed depends on how many gaps there are and how much water has already entered.
- Infiltration capacity: the upper limit, in depth of water, that a given soil can absorb per hour. Measured in millimetres per hour — directly comparable with rainfall intensity.
- Surface runoff: water that can't soak in and instead flows across the surface. The share of rainfall that becomes surface runoff is called the runoff coefficient.
JHSHSCheck it with a formula: how many tonnes flow out of 1 square kilometre of city per hour?
Let's actually calculate how much the runoff differs between a forest and a city when heavy rain falls for one hour.
| In symbols | Q = C × r × A |
| In words | Runoff volume = runoff coefficient × rainfall intensity × area |
| Where the formula comes from | It's conservation of water volume: rain that falls splits into what soaks in, what's stored, and what runs off. In short, intense rainfall, evaporation is nearly negligible, so whatever doesn't soak in becomes runoff directly. This form of the equation is called the rational formula. |
| Q | Volume of water flowing out per hour. Unit: cubic metres |
| C | Runoff coefficient. The share of rainfall that runs off; has no unit |
| r | Rainfall intensity. Unit: metres per hour (millimetres per hour divided by 1000) |
| A | Area of land receiving the rain. Unit: square metres |
| Rainfall intensity | 50mm per hour (what the Japan Meteorological Agency calls "very heavy rain") |
| Land area | 1 square kilometre = 1,000,000 square metres |
| Runoff coefficient for a heavily paved urban area | roughly 0.9 |
| Runoff coefficient for forest or farmland | roughly 0.2 |
| Volume of one 25m swimming pool | roughly 360 cubic metres |
| Convert rain depth to metres | 50 ÷ 1000 = 0.05 |
| Volume of rain falling per hour (cubic metres) | 0.05 × 1,000,000 = 50,000 |
| Runoff from the urban area | 50,000 × 0.9 = 45,000 |
| Runoff from the forest or farmland | 50,000 × 0.2 = 10,000 |
| The difference | 45,000 − 10,000 = 35,000 |
| How many pools' worth is the urban volume? | 45,000 ÷ 360 = 125 |
③ Put in plain terms: for the same rain, the city sends out 4.5 times as much water at once as the forest does. The difference, 35,000 cubic metres, is about 97 25-metre swimming pools' worth. All of that has to be carried away by gutters and sewers alone, within a single hour. The reason cities flood so easily isn't the amount of rain — it's this ratio.
HSHS+Absorption speed changes as the rain keeps falling
HSDry soil absorbs water vigorously at first. Because the gaps are filled only with air, water is drawn in not just by gravity but also by the force with which narrow gaps pull water in. This force is called capillary action.
HS+But as the gaps fill with water, this pulling force weakens, the absorption speed drops, and it eventually settles at a steady value. That steady value approaches the soil's hydraulic conductivity. This is why, during a long spell of rain, runoff can suddenly increase partway through. Even at the same rain intensity, the ground behaves differently at the start of the rain than it does two hours in.
UnivHow infiltration capacity changes over time, and predicting runoff
The way infiltration capacity falls over time is described by Horton's infiltration equation, in which the gap between the initial and final infiltration capacity shrinks exponentially with time. Combined with rainfall records, this lets you predict when surface runoff will begin. A more physically grounded treatment solves for water movement within the soil using a partial differential equation called Richards' equation. The rational formula used in the main text is an extreme simplification of these calculations, boiled down to "just one coefficient" — and it's still widely used in design work today.
📖 For the derivation and further reading: Rational formula (Japanese Wikipedia) / Infiltration capacity (Japanese Wikipedia)
ResearchWhat's still not fully understood
- How runoff coefficients are decided. The values used in practice are mostly determined empirically, from past observations. There's still no established, physics-based method for deciding which value to switch to when land use changes.
- How short, intense bursts of rain are increasing. Warmer air can hold more water vapour, but how far that pushes up hour-by-hour rainfall intensity varies a lot by region, and research is ongoing.
- The lifespan of water-permeable pavement. Performance drops once the gaps clog with soil and dust. There isn't yet enough long-term observation of how many years it lasts in real cities, or how maintenance restores it.
In short, this article, too, describes things "as currently understood." The runoff coefficients used here are representative benchmarks; actual land varies greatly depending on soil type and slope.
Links to the textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| JHS | Science: Changes in the Earth / Nature and Humans | Gaps in soil and water infiltration, land use and disasters |
| HS | Earth Science Basics: Earth's water and atmosphere | The water cycle and where rainfall ends up |
| HS+ | Physics Basics, advanced: surface tension / capillary action | Why dry soil only absorbs quickly at first |
| Univ | Hydrology, river engineering | The rational formula, Horton's infiltration equation, Richards' equation |
| Research | Urban hydrology, climate change impact assessment | Physical grounding for runoff coefficients, future changes in short bursts of intense rain |
| ― | Everyday relevance | Spotting flood-prone spots, deciding whether to travel in the rain |
- Rational formula (Japanese Wikipedia, 合理式): the peak-flow estimation formula, and the meaning of the runoff coefficient
- Infiltration capacity (Japanese Wikipedia, 浸透能): the definition of infiltration capacity and how it changes over time
- Japan Meteorological Agency, "Rainfall intensity and how it feels" (気象庁「雨の強さと降り方」): classification of hourly rainfall amounts and what conditions look like at each level
- Japan Society of Civil Engineers (ed.), Hydraulic Formulas Handbook (土木学会編『水理公式集』): representative runoff-coefficient values and the scope of the rational formula
- Japanese Association of Hydrological Sciences (ed.), Hydrological Science (日本水文科学会編『水文科学』): the basic treatment of infiltration and runoff
※This article is a general-audience science explainer. The figures given are approximations meant to illustrate the mechanism. Actual flood risk varies greatly by location. Please check the hazard map published by your local authority, and follow the information and instructions issued by the Japan Meteorological Agency, your local government, and fire services during heavy rain.