Why Is the Sea of Japan So Rough in Winter?
― Wave height is set by wind strength and the "distance the wind travels"
Every November, forecasts for the Sea of Japan coast start to show figures like "wave height 5 metres". On the same day, beaches on the Pacific side are often calm. The winter wind is the same. What differs is how long, and how far, the wind has travelled over the open sea.
A late-autumn shore in Niigata or Kanazawa. Under a grey sky, white, broken waves leap over the breakwater.
On the same day, you visit a beach in Shizuoka or Chiba. The cold wind is strong, yet the water's edge is surprisingly quiet.
Blow on a bath of hot water and you only get tiny ripples. So where, and how, do the big waves of the sea grow?
There are two main reasons
The winter north-westerly crosses the Sea of Japan from the continental coast to the Japanese shore. Waves keep growing as the wind pushes them along, so the longer the distance, the higher they get.
Waves also need time to reach full size. The winter monsoon often blows in the same direction for days on end, giving waves plenty of time to grow.
In short, wave height is set by three things: "wind strength", "distance the wind travels" and "how long it keeps blowing". The winter Sea of Japan is a place where all three come together easily.
Waves "grow" as the wind pushes them
When wind brushes the water, small ripples appear first. Ripples make the surface uneven. The wind pushes on the windward side of each bump and lifts the wave a little more. The higher a wave gets, the more surface it presents to the wind, so it keeps growing.
This growth doesn't finish in a moment. As a wave moves downwind, it keeps taking energy from the wind. So waves are small near the shore where the wind starts, and bigger the farther downwind you go. Look at Figure 1.
Same wind, different distance, very different waves
Oceanographers use formulas that estimate wave height from wind strength and the distance the wind travels. Take a strong wind of 15 metres per second. Over a lake 10 km across, waves reach only about 80 centimetres. Over 300 km of the Sea of Japan, they top 4 metres. The distance is 30 times longer, yet the height is only about 5 times greater. That is because height grows in proportion to the square root of the distance.
Waves do not grow without limit, though. For a given wind strength there is a ceiling, and for a 15 metre-per-second wind it is about 5 metres. Try the slider in Figure 2 to change the distance.
The Pacific shore is calm because the wind blows "out to sea"
The winter monsoon also spills down over the mountains of Japan to the Pacific side. But on the Pacific shore, the wind blows from land to sea, that is, out to open water. The sea right in front of the shore is where the wind has only just started to blow. The distance is almost zero, so the waves haven't grown.
Even with the same 15 metre-per-second wind, the waves 5 km offshore are estimated at only about 50 centimetres. That is why a Pacific beach can be quiet on a cold, windy day. The waves grow as they head out to sea, and are big far out over the water.
In Toyama Bay, on a clear day with light wind, large waves can suddenly roll in. Strong north winds over the sea west of Hokkaido build the waves, which then travel a long way south across the Sea of Japan and reach the bay. Known as "Yorimawari waves", they are said to have caused heavy damage along the coast in February 2008. They are a kind of "swell", waves that grew far away and arrive from afar.
A wave-height forecast gives the "average size" of many waves. In practice, waves about 1.5 to 2 times that height are said to turn up from time to time. When a wave warning or advisory is out on the winter Sea of Japan coast, do not go near breakwaters or rocks to watch the sea or to fish.
Summary
Ocean waves grow as the wind pushes them. So wave height depends not only on wind strength but on the distance the wind travels over the sea and how long it keeps blowing. The winter Sea of Japan combines a long run from the continent with a monsoon that lasts for days. On the Pacific shore, by contrast, the same wind blows out to sea, so the waves stay small before they have a chance to grow.
Waves are a record of how far the wind has travelled over the sea.
Even with the same wind, the look of the sea changes with where it came from.
How waves that grew far away reach a windless shore is explained in "Why Does a High Wave Suddenly Arrive When There's No Wind?", and the limit to how high waves can get in "How High Can Ocean Waves Get?". For how the same monsoon brings snow, see "Why Does the Sea of Japan Side Get So Much Snow?".
- Pour 2 to 3 centimetres of water into a long, shallow tray or a storage box.
- From the end of a short side, fan air just above the water. Compare the size of the ripples at the upwind end and the downwind end.
- Next, fan the same way from the end of a long side. When the distance gets longer, how do the waves at the downwind end change?
The waves should stand out more downwind. It is also worth comparing the "wave height" in weather forecasts for the Sea of Japan side and the Pacific side.
For those who want more ― terms, formulas and links to textbooksEach part is labelled with its level, from middle-school science to university specialist courses
- Middle schoolCovered in middle-school science
- High schoolCovered in high-school basic physics and earth science
- High school+Advanced high-school material, or a textbook sidebar
- UniversityNot covered in high school; university specialist courses (physical oceanography, coastal engineering)
- ResearchNot yet settled even at university; what researchers are working on now
Middle schoolTerms: this phenomenon has names
- Wind waves: waves still growing under the wind blowing at that spot. They are sharp-peaked and not aligned in one direction.
- Fetch: the distance the wind has blown over the sea in roughly the same direction. The word appears in specialist books on coasts and harbours.
- Significant wave height: the average height of the highest third of many waves. The "wave height" in weather forecasts is this, and it is said to be close to what the eye sees.
Middle schoolHigh schoolCheck with a formula: how different are waves on a lake and on the Sea of Japan?
We use a formula based on measurements that estimates wave height from wind strength and fetch. The wind speed is fixed at 15 metres per second, and only the fetch changes.
| In symbols | H ＝ 0.0016 × U × √( F ÷ g ) |
| In words | Wave height ＝ 0.0016 × wind speed × square root of (fetch ÷ gravitational acceleration) |
| Where it comes from | The energy the wind passes to the waves builds up in proportion to the distance travelled. Wave energy is proportional to the square of the height, so height grows with the square root of distance. The coefficient 0.0016 was fixed from large-scale observations in the North Sea. |
| H | Significant wave height (metres) |
| U | Wind speed at 10 metres above the sea surface (metres per second) |
| F | Fetch (metres) |
| g | Gravitational acceleration (metres per second squared) |
| Wind speed | 15 metres per second |
| Gravitational acceleration | 9.8 metres per second squared |
| Lake fetch | 10 km (10000 metres) |
| Sea of Japan fetch | 300 km (300000 metres) |
| Multiply coefficient and wind speed | 0.0016 × 15 ＝ 0.024 |
| Lake: divide distance by gravity | 10000 ÷ 9.8 ≒ 1020 |
| Lake: its square root | The square root of 1020 is about 32 |
| Lake wave height | 0.024 × 32 ≒ 0.77 metres |
| Sea of Japan: divide distance by gravity | 300000 ÷ 9.8 ≒ 30600 |
| Sea of Japan: its square root | The square root of 30600 is about 175 |
| Sea of Japan wave height | 0.024 × 175 ＝ 4.2 metres |
| Height ratio | 4.2 ÷ 0.77 ≒ 5.5 times |
| Wave energy ratio (height squared) | 5.5 × 5.5 ≒ 30 times |
With 30 times the distance, the height is about 5.5 times and the energy almost exactly 30 times. The idea behind the formula, that energy builds up in proportion to distance, shows up directly in the numbers. 4.2 metres is about two and a half times a person's height.
High schoolHigh school+Wave energy, and a fully grown sea
High schoolIn a water wave, the water itself is not carried far; the up-and-down motion is what travels. A wave's energy is proportional to the square of its amplitude (height). A wave twice as high hits the shore with four times the energy.
High school+When the wind blows long enough and far enough, the energy waves receive from the wind balances the energy they lose by breaking, and they stop growing. This is called a "fully developed sea". Its wave height is proportional to the square of the wind speed: about 5 metres at 15 metres per second, and close to 9 metres at 20 metres per second. For waves to reach full size over a 300 km fetch, the same wind is estimated to need to blow for more than half a day.
UniversityWave hindcasting and forecasting: how waves are "predicted"
Estimating waves from wind is called "wave hindcasting". Sverdrup and Munk laid its foundation for amphibious landings in the Second World War, and Bretschneider later improved it. It is called the SMB method after the three names. The formula above is a fetch law based on the JONSWAP spectrum, obtained from a North Sea observation campaign in the 1970s. Waves in a fully developed sea are described by the Pierson-Moskowitz spectrum. The wave forecasts of the Japan Meteorological Agency today come from "spectral" numerical models that track wave energy by frequency and direction.
📖 Derivations and further reading: Japan Meteorological Agency, "Knowledge of Ocean Waves" ／ Significant wave height (Wikipedia)
ResearchWhat is still not clear
- The fine details of how wind grows waves. One theory says bumps on the surface create pressure differences in the wind; another says the layer of air flowing just above the wave matters. Which one matters more under strong wind is still being studied with observations and calculations.
- Whitecaps in strong wind, and exchange between air and sea. The heat and gas that breaking waves take into the sea matter for climate prediction, but the exact amounts under strong wind are still uncertain.
- Predicting unexpected giant waves. Under what conditions, and how often, "freak waves" more than twice the height of their neighbours occur is still being researched.
So this article, too, is an explanation of "what is known so far". The formula above is also an estimate fitted to measurements, and real ocean waves also change with the shape of the seabed and coast and with tidal currents.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Middle school | Year 2 science, "Weather in Japan (monsoons)" | The winter north-westerly monsoon crosses the Sea of Japan |
| High school | Basic physics, "Properties of waves"; basic earth science, "Atmosphere and ocean" | A wave is a travelling oscillation; energy goes with height squared |
| High school+ | Physics, "Energy of waves" | Fully developed sea, time needed to reach full size |
| University | Physical oceanography, coastal engineering | Wave hindcasting (SMB method, JONSWAP, spectral method) |
| Research | Air-sea interaction | Energy transfer from wind to waves, freak waves |
| ― | Links to daily life | Reading winter wave forecasts, behaviour at the shore on high-wave days |
- Japan Meteorological Agency (気象庁), "Knowledge of Ocean Waves" (波浪の知識)
- Hasselmann, K. et al. (1973) report of the Joint North Sea Wave Project (JONSWAP), Deutsche Hydrographische Zeitschrift supplement
- Pierson, W. J. & Moskowitz, L. (1964) paper on the spectrum of fully developed wind waves, Journal of Geophysical Research
- Goda, Yoshimi (合田良實), "Wave-Resistance Engineering: Wave-Resistant Design of Port and Coastal Structures" (耐波工学 ― 港湾・海岸構造物の耐波設計), Kajima Institute Publishing (鹿島出版会)
- Wikipedia, "Significant wave height" (有義波高), Japanese edition
* This article is a popular-science explanation. The figures given are rough guides to help you understand how things work. Actual wave heights vary greatly with terrain, tidal currents and changes in wind. At the seaside, follow the Japan Meteorological Agency's wave warnings and advisories and the instructions of local authorities.