Same Rain, So Why Do City Roads Turn Into Rivers So Fast?
― Ground Without Soil Leaves 100 Pools' Worth of Water Nowhere to Go in One Hour
On hills and farmland, the ground keeps drinking in water even in very heavy rain. In a city, the same rain can turn a road into a river in no time. The amount of rain is the same. What differs is a little-known number: how many millimetres the ground can absorb in an hour.
On a summer evening, a sudden downpour begins. Within ten minutes, water is rushing noisily along the edge of the road.
At the same time, the same rain is falling on a copse a short distance away. The woodland floor is muddy, but no water is flowing over it.
It is one rain cloud. The amount of rain is the same. Yet only one of the two places becomes a river.
There are only two reasons
Soil soaks up water, but not infinitely fast. There is a cap on how many millimetres it can take in per hour. If the rain is lighter than that cap, 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 runs across the surface. Where it ends up is left entirely to the drains.
Both reasons are about speed, not quantity. I think this is the hardest part of the whole phenomenon to grasp. What matters is not the size of the bucket but the width of its mouth.
How fast can soil absorb water?
The top speed at which soil can take in water is called its infiltration capacity. Its unit is millimetres per hour, the same as rain. Well-kept woodland soil is known to manage 50 mm or more per hour, while a heavily trampled schoolyard manages around 10 mm per hour.
Set those numbers beside the strength of the rain. If the forecast says "30 mm in an hour", a woodland can take nearly all of it, but on trampled ground two-thirds overflows. The same rain shows a different face on different ground.
Look at Figure 1. On the left is soil, on the right is paved ground, and the same amount of rain falls on both.
Where does the water go in a city?
Rain that cannot soak in does not vanish. It gathers along the slope of the road, enters the gutters and flows into the sewers. City drainage is designed on the assumption that it can carry this water away.
But that design has a limit too. Sewers in many cities are said to be built to handle rain of around 50 mm per hour. When heavier rain falls, the water cannot fit into the pipes and begins to pool in low spots.
That is why city puddles form in the same places every time: at the bottom of a slope, on roads that dip under a railway, in front of stairs leading underground. Low ground gives the same answer every time it rains.
Some recent pavements and car parks use surfaces deliberately built to let water through. There are also systems that store rainwater in underground tanks and release it slowly. Both are attempts to restore, by human hands, the "absorption speed" of soil that has been lost.
When a road floods, a drain cover may have come off and you cannot see it from the surface of the water. You also cannot tell the depth by looking. Underpasses and underground car parks are places where water collects easily, so in heavy rain keep away from them and move to higher ground. If you sense danger, such as someone being trapped, call 119 without hesitation.
Summary
Roads turn into rivers in cities not because the rain is unusually heavy, but because the land has lost its "speed of absorbing water". The unseen receiving dish of the soil can no longer do its work under the pavement.
The problem is not how much rain falls.
It is how many millimetres per hour the ground can absorb.
When the ground of a city changes, it is not only the rain that changes but the temperature too. Read Why Are Cities Hot? ― The Difference Is Bigger at Night Than in the Day as well, and you will see the whole picture of what paving brings. If you want to know a little more about soil and water, try Why Do Landslides Happen Even After the Rain Has Stopped? too.
- Prepare a plastic bottle with the bottom removed (cut off both ends to make a tube). Push it a few centimetres into soil in a garden or park, with the cut end pointing down.
- Pour water into the tube and time how many seconds it takes for the water surface to drop by 2 cm. From the time it takes for 10 cm of water to drop, you can roughly estimate how many millimetres per hour the soil absorbs.
- Repeat this on trampled soil beside a path and on soil under a tree covered in fallen leaves. The undisturbed soil should absorb far faster.
* Do not do this on other people's land. After the experiment, fill in the hole and leave it as you found it.
For those who want to know more ― terms, formulas and links to textbooksIt shows which level each topic sits at, from lower-secondary science to university courses
- Middle schoolCovered in lower-secondary science
- High schoolCovered in upper-secondary Earth Science Basics
- High school+Advanced upper-secondary material, or a textbook side column
- UniversityNot taught in high school; university courses (hydrology, river engineering)
- ResearchNot yet taught as settled fact even at university; researchers are still investigating it
Middle schoolTerms: this phenomenon has names
- Infiltration: surface water moving down into the ground through gaps in the soil. Its speed depends on how many gaps there are and how much water is already in the soil.
- Infiltration capacity: the upper limit on the depth of water the soil can take in per hour. Its unit is millimetres per hour, a number you can compare directly with rainfall intensity.
- Surface runoff: water that cannot soak in and flows over the ground surface. The share of rainfall that becomes surface runoff is called the runoff coefficient.
Middle schoolHigh schoolChecking with a formula: how many tonnes flow out of 1 square kilometre of city in one hour?
Let's actually calculate how different the runoff is between woodland and a city when heavy rain falls for an hour.
| In symbols | Q ＝ C × r × A |
| In words | Volume of runoff ＝ runoff coefficient × rainfall intensity × area |
| Where it comes from | It is conservation of water: the rain that falls splits into the part that soaks in, the part that pools and the part that runs off. In a short downpour, evaporation is almost negligible, so whatever cannot soak in becomes runoff. A formula of this form is called the rational method. |
| Q | Volume of water flowing out in one hour. Unit: cubic metres |
| C | Runoff coefficient. The share of the rain that runs off; it 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 | 50 mm per hour (the strength the Japan Meteorological Agency calls "very heavy rain") |
| Area of land | 1 square kilometre ＝ 1000000 square metres |
| Runoff coefficient of a heavily paved urban area | Said to be about 0.9 |
| Runoff coefficient of woodland or farmland | Said to be about 0.2 |
| Water in one 25-metre pool | About 360 cubic metres |
| Convert the rain depth to metres | 50 ÷ 1000 ＝ 0.05 |
| Volume of rain falling in one hour (cubic metres) | 0.05 × 1000000 ＝ 50000 |
| Runoff from the urban area | 50000 × 0.9 ＝ 45000 |
| Runoff from woodland or farmland | 50000 × 0.2 ＝ 10000 |
| The difference | 45000 － 10000 ＝ 35000 |
| How many pools the urban runoff would fill | 45000 ÷ 360 ＝ 125 |
③ In everyday terms: with the same rain, the city sends out 4.5 times as much water at once as woodland. The difference of 35000 cubic metres is about 97 25-metre pools. Within that one hour, this water has to be carried away through the gutters and sewers alone. The reason cities flood easily lies in this share, not in the amount of rain.
High schoolHigh school+Absorption speed changes as the rain goes on
High schoolDry soil at first drinks up water eagerly. Its gaps hold only air, so the water is pulled in not just by gravity but also by the force with which narrow gaps draw water in. This force is called capillary force.
High school+But as the gaps fill with water, that pulling force weakens, and the absorption speed falls until it settles at a steady value. This settled value approaches the soil's hydraulic conductivity. This is why, in long-lasting rain, the water that suddenly starts running off partway through increases. Even at the same rainfall intensity, the ground behaves differently at the start of the rain and two hours later.
UniversityHow infiltration capacity changes with time, and predicting runoff
How infiltration capacity falls with time is expressed by Horton's infiltration equation. It has the form in which the gap between the initial and the final infiltration capacity shrinks exponentially with time. Combined with rainfall records, it lets you predict when surface runoff begins. A more physical approach solves the movement of water in soil with a partial differential equation called the Richards equation. The rational method used in the main text boils such calculations down drastically to "a single coefficient", and it is still widely used in design work today.
📖 Derivations and further reading: Rational method (Japanese Wikipedia) ／ Infiltration capacity (Japanese Wikipedia)
ResearchWhat is still not clear
- How to set the runoff coefficient. The values used in practice are mostly determined empirically from past observations. There is still no established way to determine from physics which value to move to when land use changes.
- How short, intense rain is increasing. A warmer atmosphere can hold more water vapour, but how far that pushes up rainfall intensity on an hourly scale varies a lot by region, and research continues.
- The lifespan of permeable pavement. Its performance drops when the gaps clog with soil and dust. How many years it lasts in a real city, and how maintenance can restore it, lacks enough long-term observation.
So the content of this article too is "an explanation within what is known today". The runoff coefficients used are typical guide values; on real land they vary greatly with soil type and slope.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Middle school | Science: changes in the land / nature and humans | Gaps in soil and water soaking in; land use and disasters |
| High school | Earth Science Basics: Earth's water and atmosphere | The water cycle and a breakdown of where rain goes |
| High school+ | Advanced Physics Basics: surface tension / capillary action | Why dry soil absorbs fast only at first |
| University | Hydrology and river engineering | The rational method, Horton's infiltration equation, the Richards equation |
| Research | Urban hydrology / climate change impact assessment | Physical ways to set runoff coefficients; future changes in short, intense rain |
| ― | Connection to daily life | Telling which places flood easily; deciding whether to travel in rain |
- Rational method (Japanese Wikipedia): the formula for estimating peak flow, and what the runoff coefficient means
- Infiltration capacity (Japanese Wikipedia): the definition of infiltration capacity and how it changes with time
- Japan Meteorological Agency (気象庁), "Rain intensity and how it falls" (雨の強さと降り方): the classes of hourly rainfall and a description of conditions at each
- Japan Society of Civil Engineers (土木学会), ed., Handbook of Hydraulic Formulas (『水理公式集』): typical runoff coefficient values and the range of application of the rational method
- Japan Society of Hydrology and Water Resources (日本水文科学会), ed., Hydrological Sciences (『水文科学』): the basic treatment of infiltration and runoff
* This article is a general-audience science explainer. The figures given are guides and rough estimates for understanding how things work. Actual flood risk varies greatly from place to place. Check the hazard map published by your local authority, and in rain follow the information and instructions issued by the Japan Meteorological Agency, your local authority and the fire service.