Where Does River Water Come From?
― For nearly 2,000 years, everyone "knew" rain wasn't enough. One official with a rain gauge overturned that
No matter how many sunny days pass, rivers keep flowing. Scholars of old decided that rain could not explain this. The answer came from a person who kept measuring rain with a single tube, and from a calculation on paper.
After a week of clear autumn weather, you peer into a nearby river. The water is a little lower, but it is still running along as smoothly as ever.
The last rain fell many days ago. So where is all this water coming from?
Is there some endless spring deep in the mountains? In fact, until only about 350 years ago, many scholars seriously thought so.
Rain alone can keep a river flowing, for two reasons
A single rainfall is only a few millimetres to a few tens of millimetres deep. But the land that drains into a river covers tens or hundreds of square kilometres. Multiply even a thin layer of water by a huge area and you get many times the volume of the river.
Most of the rain that falls does not run straight into the river. It first soaks into gaps in the soil and rock, then seeps out as spring water over days or months. This store is what keeps a river going on sunny days.
This sounds obvious today. But it took nearly 2,000 years before someone checked it with numbers.
Why did early scholars think rain wasn't enough?
The ancient Greek philosopher Aristotle thought that air cooled in mountain caves and turned into water, which then became rivers. Another idea was believed for a long time as well: seawater flows through underground channels to the mountaintops and gushes out of springs. The left side of Figure 1 shows this idea.
They also had reasons for doubting rain. When people dug into the ground, the rain seemed to have soaked in only a few tens of centimetres. And sunny days are far more common than rainy ones, yet rivers flow without rest. It seemed impossible that rain, which comes and goes, could support a nonstop flow.
An official who measured rain for three years
The person who challenged this idea with numbers was Pierre Perrault of France. Perrault was not a scholar but an official who worked in tax collection.
Perrault measured rainfall for three years on land near the source of the Seine. The yearly rain is said to have been about 520 millimetres deep. Next, he estimated from a map the size of the land from which water gathers into that river. Then he multiplied "depth of rain × area of land" to get the volume of rain that falls in a year.
He also estimated how much water flows down the river and compared the two. The result: the rain was said to be about six times the river's water. Far from being too little, the rain was more than enough to supply the river, with plenty left over. In 1674, Perrault set out this calculation in a book.
Where did the leftover rain go?
As you can see by moving the slider in Figure 2, rain fails to supply the river only when there is very little of it, close to desert conditions. So where did the other five-sixths, the rain that did not become river, go?
The answer is the sky. Water evaporates from the ground and from water surfaces, and plants draw it up through their roots and release it from their leaves, turning it back into vapour. That vapour forms clouds again and falls as rain. Around the same time, Edmond Halley in England measured evaporation of water over the Mediterranean. He is said to have shown that the amount evaporating was large enough to supply rivers and rain. In this way, the idea of a "water cycle" linking sea, sky and land was built up with numbers.
The second reason explains what a river really is on a sunny day. Rain that soaks into the soil moves slowly downhill and seeps out at valley bottoms and riverbanks. So however many days have passed since the last rain, the river keeps flowing. What people once took for an "endless spring" was in fact a store of past rain.
One of Pierre Perrault's brothers was Charles Perrault, who collected the tales of "Cinderella" and "Puss in Boots". Another brother, Claude, is said to have been an architect involved in designing the Louvre Palace in Paris. So the brother with the plainest job opened a big door in natural science.
Japan's average yearly rainfall is said to be about 1,700 millimetres. The water falling on the whole country is estimated at about 650 billion cubic metres. Lake Biwa holds about 27.5 billion cubic metres, so that is about 24 lakes' worth. About a third of it is said to return to the sky through evaporation and the like.
Summary
River water did not come from secret underground channels. It came from the sky. Rain is thin, but it falls on a wide area, so all of it added together is many times the river. And the soil stores that rain and sends it into the river bit by bit, even on sunny days. What confirmed this obvious fact was not a flash of inspiration, but three years of patient measuring and a single multiplication.
A river on a sunny day is made of rain from many days ago.
"It shouldn't be enough" is something you can't know until you measure.
To find out what happens to the water once it reaches the sea, see "Rivers pour into the sea every day, so why doesn't the sea overflow?". For the temperature of water in the ground, see "Why does well and spring water feel cold in summer and warm in winter?". And for what happens to rain in a city with no soil, see "Why do roads turn into rivers so quickly in a city, even in the same rain?".
- Put a flat-bottomed, straight-sided cylindrical glass or jar in a spot with no roof or trees around it.
- When the rain stops, measure the depth of the collected water with a ruler. This is that rain's "rainfall". One millimetre of rain is one litre of water per square metre.
- Now multiply by the area of your balcony or garden (in square metres). Even just 10 millimetres of rain turns out to be more water than you would expect.
A few days after the rain, look at a nearby stream or roadside ditch and see whether water is still coming out. That is rain stored in the soil. Do not go near rivers or waterways during or after rain; watch from a safe place.
For those who want to know more ― terms, formulas and links to textbooksEach part is labelled with its level, from lower secondary science to university courses
- Middle schoolCovered in lower secondary school science
- High schoolCovered in upper secondary "Basic Earth Science"
- High school+Advanced upper secondary material, or treated as a textbook sidebar
- UniversityUniversity-level specialist material (hydrology and groundwater science), not covered in high school
- ResearchNot yet taught as settled fact even at university; being studied by researchers right now
Middle schoolTerms: this phenomenon has names
- Precipitation (rainfall): Rain or snow that has fallen, expressed as the depth of water collected on the ground. The unit is millimetres.
- Catchment (drainage basin): The area of land from which rainwater gathers into a given river. Mountain ridges form the boundaries.
- Water cycle: The circulation in which water from sea and land evaporates into clouds, falls as rain or snow, and returns to the sea as rivers and groundwater.
Middle schoolHigh schoolChecking with a formula: how many times more rain falls than the river carries?
Let us follow Perrault's calculation using round numbers. The catchment area is said to have been estimated at about 120 square kilometres.
| In symbols | V ＝ P × A ／ River's share ＝ Q ÷ V |
| In words | Volume of rain in a year ＝ rainfall (depth) × catchment area. River's share ＝ the river's yearly flow ÷ volume of rain |
| Where the formula comes from | The water balance (water is neither created nor destroyed). The only water entering the catchment is rain, and the water leaving splits into "river + evaporation + change in storage". Averaged over several years, the change in storage is almost 0 |
| Symbol | Meaning and unit |
| P | Rainfall (depth) in one year. Unit: metres |
| A | Catchment area. Unit: square metres |
| V | Volume of rain falling on the catchment in one year. Unit: cubic metres |
| Q | Volume of water the river carries in one year. Unit: cubic metres |
| Yearly rainfall (said to be Perrault's three-year average) | about 520 mm ＝ 0.52 m |
| Catchment area | about 120 km² ＝ 120,000,000 m² |
| Ratio of river flow to rain (Perrault's estimate) | The river is said to be about one-sixth of the rain |
| Seconds in a year | 31,536,000 seconds |
| Volume of rain in a year | 0.52 × 120,000,000 ＝ 62,400,000 m³ |
| Water the river carries | 62,400,000 ÷ 6 ＝ 10,400,000 m³ |
| The rest, which returned to the sky and so on | 62,400,000 − 10,400,000 ＝ 52,000,000 m³ |
| River flow per second | 10,400,000 ÷ 31,536,000 ≒ 0.33 m³ |
| Converted to litres | 0.33 × 1000 ＝ 330 L |
| Smallest rainfall that can still supply the river | 520 ÷ 6 ≒ 87 mm |
By this calculation, about 330 litres per second flow in the river near its source. That is about one and a half household bathtubs (about 200 litres each). Even so, it is only one-sixth of the rain that fell. If a year's rain is more than 87 millimetres, rain alone can supply the river. This is the value behind the bar in Figure 2 dropping below the dotted line at about 90 millimetres or less.
High schoolHigh school+Seeing the water cycle in amounts
High schoolIn Basic Earth Science, you learn a diagram of the global water cycle expressed as amounts of evaporation, precipitation and runoff. On land, more water falls than evaporates, and the difference flows to the sea as rivers and groundwater. Over the sea it is the reverse: evaporation exceeds precipitation. Perrault's calculation can be seen as the first measurement of the "land" part of this diagram, made for a single river.
High school+The share of rain that leaves as river flow is called the "runoff ratio". It is low on forested land and high in paved cities. Perrault's estimate was about one-sixth, which is less than 20 percent. Later, Mariotte is said to have re-measured the Seine in Paris and obtained a similar result. Mariotte also investigated how deep rainwater soaks into the ground.
UniversityHydrology and the flow of groundwater
The study of the amounts of rain, rivers, groundwater and evaporation is called "hydrology", and Perrault is regarded as one of its founders. The equation that records the difference between water entering and leaving a catchment is called the "water balance equation", and it takes the form precipitation ＝ runoff ＋ evapotranspiration ＋ change in storage. The flow that supports a river on sunny days is called "baseflow". The speed at which groundwater moves through soil is described by "Darcy's law", and is proportional to how easily water passes through (hydraulic conductivity) and to the slope of the water surface. How a river's level changes after rain is predicted using runoff analysis such as the "unit hydrograph method".
📖 Derivations and further reading: Hydrology (Wikipedia, in Japanese) ／ Water cycle (Wikipedia, in Japanese)
ResearchWhat is still not clear
- How old is river water, in terms of the rain it came from? Some studies use isotopes in the water to work out the "age" of river water. Some rivers are said to contain rain from decades ago, and how this differs from place to place is still poorly understood.
- The exact amount of evapotranspiration The combined amount of evaporation from the ground and water released by plants is hard to measure directly, and the range of estimates is said to be wide.
- How will runoff change with warming? Higher temperatures increase evaporation, but they also change how rain falls. Where river water will increase and where it will decrease is a field in which predictions still vary widely.
In other words, the content of this article too is "an explanation within what is known today". Perrault's figures were also estimates made with the tools of his time, and the finer values carry uncertainty.
Links to textbooks (by level)
| Level | Subject and unit | Where in this article |
|---|---|---|
| Middle school | Science, Year 2: "Weather and its changes", water cycle | The cycle in which rain evaporates and returns to the sky |
| High school | Basic Earth Science: "Atmosphere and oceans", water cycle | The difference between rain falling on land and evaporation |
| High school+ | Runoff ratio | One-sixth of the rain becomes the river |
| University | Hydrology and groundwater science | Water balance equation, baseflow, Darcy's law |
| Research | Isotope hydrology and climate change | The age of river water, the future of runoff |
| ― | Links to daily life | Sources of tap water, preparing for drought |
- Pierre Perrault, De l'origine des fontaines, Paris, 1674.
- Asit K. Biswas, History of Hydrology, North-Holland, 1970.
- Ministry of Land, Infrastructure, Transport and Tourism, Water and Disaster Management Bureau (国土交通省 水管理・国土保全局), "Current State of Water Resources in Japan" (日本の水資源の現況), various years
- Water cycle (Wikipedia, in Japanese)
- Precipitation (Wikipedia, in Japanese)
* This article is a general-audience science explainer. The figures given are rough guides to help you understand how things work. Historical measurements are converted and counted differently depending on the source, and representative values are shown here in rounded form.