Why Do Autumn Leaves Change Colour from the Mountaintop Down?
― Though Closer to the Sun, the Summit Gets About 0.6 °C Colder for Every 100 m You Climb
In autumn, the news says, "The colours have come down from the summit to the mountainside." Cold decides when leaves turn, and the higher you go, the colder it is. But the summit is supposed to be closer to the Sun. So why is it cold? The answer is that air is warmed not from above, but from below.
It is early November. Look at a distant mountain, and only the area near the top is stained red and yellow. The trees at the foot are still green.
About two weeks later, the edge of the colour has dropped to the mountainside. It is as if the colour were slowly flowing down from the top.
But that is a little strange. The summit should be thousands of metres closer to the Sun than the foot of the mountain. So why does the cold arrive at the top first?
There are just two reasons the top is cold
Sunlight passes almost straight through the air and warms the ground first. The air is then warmed from below by that warm ground. The higher air, farther from the heat source, stays cold.
High up, there is less air piled on top, so the pressing force (air pressure) is weaker. When air near the ground rises, it expands. As it expands, the air uses up some of its own heat and cools.
Together, these two effects make the air about 0.6 °C cooler for every 100 m of height on a mountain, on average. Autumn colour is triggered by chilly nights. So when the line of cold moves from top to bottom, the colour comes down with it.
Closer to the Sun, so why is it cold?
The Sun is about 150 million km away. A mountain 3 km high is only one 50-millionth of that distance. The extra sunshine from being closer is almost zero.
What really matters is where the heat is made. Most sunlight slips through the air and reaches the ground. The warmed ground heats the air it touches. That warm air becomes lighter and rises, mixing as it goes and carrying heat upward.
Think of a room with a stove. It is warm next to the stove and cooler the farther away you get. For the atmosphere, the stove is not the Sun but the ground under your feet.
Why does rising air cool?
When a parcel of air expands, it pushes the surrounding air out of the way. Pushing takes work, and the energy for that work comes from the air's own heat. So the air cools by the amount it expands.
The reverse is also true: squeeze air and it warms up. This is why the base of a bicycle pump gets warm when you push the handle again and again. The hot wind that blows down the far side of a mountain range is the same process in reverse.
Wind and rising currents are always mixing air up and down. As a result, height and temperature on a mountain slope follow a fairly fixed relationship. On average, it is about 0.6 °C per 100 m. The summit of Mt. Fuji, at 3,776 m, works out to be more than 20 °C colder than its foot.
How many metres per day does the colour line descend?
Leaves are said to start changing colour when the morning low drops below about 8 °C. As autumn deepens, the temperature in the lowlands falls a little each day. So the "8 °C height" also slips a little lower each day.
Use the slider in Figure 2 to change the lowland's minimum temperature. The dotted line is the boundary: "above this, it is colder than 8 °C." While the lowlands are warm, only the summit changes colour. As the lowlands cool, the dotted line comes down toward the foot.
Let's work it out. In Tokyo, the normal temperature falls by about 0.16 °C a day from October into November. Converted into height, that means the line descends about 27 m a day, or about 800 m a month. This is the speed at which the best viewing moves from the summit to the lowlands over one to two months.
On a clear, windless night, the ground loses heat to the sky, and the air nearest the ground gets the coldest. The valley floor can then be colder than the mid-slope. A band of later colour or frost can form partway up a slope.
If it is 15 °C in the lowlands, the temperature at a viewpoint 1,500 m up works out to about 6 °C. If the wind blows, it will feel even colder. When you go to the mountains to see the autumn colours, dress for a season ahead.
Summary
What warms the air is not the Sun itself but the ground the Sun has warmed. On top of that, rising air expands and cools itself. That is why mountains get colder the higher you go, and why autumn cold reaches the summit first. Autumn leaves trace that line of cold, acting as a "visible thermometer."
The atmosphere's stove is not in the sky but under your feet.
Autumn colour is the "8 °C line" walking down the mountain.
What happens inside a leaf to change its colour is explained in "Why do autumn leaves turn red and yellow?". For how air cools when it expands and warms when it is compressed, see "Why does wind coming over a mountain suddenly turn hot?". For why trees stop growing high on mountains, see "Why don't trees grow high up on mountains?"
- Pick one mountain you can see from home or school, and take a photo from the same spot on a clear day.
- Keep taking photos once a week, and compare where the border between the coloured part and the green part lies.
- Use a map app to look up the altitude near the border. Work out how many metres it dropped in one week.
Also look up the minimum temperatures at a nearby station in the Japan Meteorological Agency's "Past Weather Data". In weeks when the temperature fell more, the border may have dropped further.
For those who want to know more ― Terms, formulas and links to textbooksShows which level each topic is at, from junior-high science to university specialist courses
- Junior highCovered in junior-high science
- High schoolCovered in high-school earth science or physics
- High school+Advanced high-school material, or a textbook sidebar
- UniversityNot taught in high school; university specialist courses (meteorology, atmospheric thermodynamics)
- ResearchNot yet taught as settled knowledge, even at university; researchers are still investigating it
Junior highTerms: this phenomenon has names
- Lapse rate: the rate at which temperature falls as height increases. In Japan's mountains, about 0.6 °C per 100 m is often used.
- Adiabatic expansion: a gas expanding without exchanging heat with its surroundings. It uses its own heat to do the work of expanding, so its temperature drops.
- Autumn-colour front (kōyō zensen): a line on a map joining the days maple and other trees change colour. On flat land it moves from north to south, and on mountains from top to bottom.
Junior highHigh schoolChecking with a formula: how fast the colour line descends
We write the relation between height and temperature as a formula, then find the temperature difference between the top and bottom of Mt. Fuji and the distance the colour line drops per day. The symbols are T = temperature (in °C), h = altitude (m), and Γ = lapse rate (°C/m).
| In symbols | T(h) ＝ T₀ − Γ × h , boundary height h₈ ＝ ( T₀ − 8 ) ÷ Γ |
| In words | Temperature at that height = lowland temperature − (drop per 100 m × height) |
| Where it comes from | Rising air loses pressure and expands, and cools by the amount of work it does (the first law of thermodynamics, and the balance between the weight of air and air pressure). For dry air, in theory Γ = gravitational acceleration ÷ specific heat at constant pressure. In the real atmosphere, the heat released when water vapour condenses adds in, and the average comes to about 0.6 °C/100 m |
| Gravitational acceleration g | 9.8 m/s² |
| Specific heat of dry air at constant pressure cp | 1005 J/(kg·K) |
| Average lapse rate of the real atmosphere | About 0.6 °C per 100 m |
| Tokyo's normal monthly mean temperature (October / November) | About 18.8 °C / about 14.0 °C, reportedly |
| Height of Mt. Fuji | 3776 m |
| Dry-air lapse rate (per 1 m) | 9.8 ÷ 1005 ≒ 0.0098 ℃ |
| Convert to per 100 m | 0.0098 × 100 ＝ 0.98 ℃ |
| How many 100 m units is Mt. Fuji? | 3776 ÷ 100 ＝ 37.76 |
| Temperature difference, summit to foot | 37.76 × 0.6 ≒ 22.7 ℃ |
| Fall over one month, October to November | 18.8 − 14.0 ＝ 4.8 ℃ |
| Fall per day | 4.8 ÷ 30 ＝ 0.16 ℃ |
| Height the line drops per day (in 100 m units) | 0.16 ÷ 0.6 ≒ 0.27 |
| Convert to metres | 0.27 × 100 ＝ 27 m |
| Height dropped in a month | 27 × 30 ＝ 810 m |
The annual mean temperature at the summit of Mt. Fuji is said to be around −6 °C, and the difference from Tokyo is over 20 °C, just as calculated. The colour line comes down about 27 m a day, or about 800 m a month, by this calculation. With dry air alone, the temperature should fall about 1 °C per 100 m, but the real atmosphere is gentler than that. One reason is that water vapour gives off heat when clouds form.
High schoolHigh school+Dry and moist air cool at different rates
High schoolIn earth science you learn to tell apart the dry adiabatic lapse rate (about 1 °C per 100 m), for cloud-free air that is rising, from the moist adiabatic lapse rate (about 0.5 °C per 100 m), for air rising inside a cloud. In moist air, the heat released when water vapour turns into droplets (latent heat of condensation) softens the cooling.
High school+The average fall actually observed (the environmental lapse rate) falls between these two. The International Standard Atmosphere fixes it at 6.5 °C per km up to a height of 11 km. The boundary there is called the "tropopause," and above it the temperature hardly falls any more.
UniversityPotential temperature and atmospheric stability
In atmospheric thermodynamics, the temperature air would have if brought dry-adiabatically down to a reference pressure (1000 hectopascals) is called the potential temperature. It stays the same whether the air goes up or down, so looking at how it changes with height tells you whether the air mixes easily up and down (static stability). The dry adiabatic lapse rate Γd ＝ g ÷ cp follows from the first law of thermodynamics and hydrostatic balance (the balance between the weight of air and the pressure difference).
📖 Derivation of the formula, and further reading: Lapse rate (Wikipedia, in Japanese) ／ International Standard Atmosphere (Wikipedia, in Japanese)
ResearchWhat is still not well understood
- Is temperature the only trigger for colour change? Night length, daytime sunshine and soil dryness are also said to play a part, and how much each counts for different tree species is still being studied.
- How much will warming delay autumn colour? In Japan, maple colour dates have been reported to be getting later over several decades. But whether the delay is the same on high and low parts of a mountain is unclear, because there are few observation points.
- Fine-scale cooling on slopes. On nights when cold air pools in valleys, the relationship between height and temperature flips. Predicting how each mountain's terrain disturbs the bands of colour is still said to be difficult.
In other words, this article is also "an explanation of what we know so far." The figure of 0.6 °C per 100 m is an average, and it changes with the weather on the day.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Junior high | Science, Year 2: "Weather and its changes" (how clouds form) | Rising air expands and cools |
| High school | Earth science: "Structure of the atmosphere"; physics: "Changes of state of gases" | Dry and moist adiabatic lapse rates |
| High school+ | Advanced earth science (standard atmosphere, tropopause) | The 6.5 °C per km rule |
| University | Meteorology, atmospheric thermodynamics | Potential temperature, static stability, hydrostatic balance |
| Research | Plant phenology, climate change research | Triggers of colour change and warming-related delay |
| ― | Links to daily life | Timing and clothing for leaf-viewing, reading mountain weather |
- Yoshimitsu Ogura, General Meteorology (一般気象学), 2nd revised ed., University of Tokyo Press (東京大学出版会)
- Japan Meteorological Agency (気象庁), "Past Weather Data Search" (normals for Tokyo and Mt. Fuji)
- National Astronomical Observatory of Japan (国立天文台), ed., Chronological Scientific Tables (理科年表), Maruzen Publishing (丸善出版) (Meteorology section, standard atmosphere)
- International Standard Atmosphere (国際標準大気) - Wikipedia
*This article is a popular-science explanation for general readers. The figures given are rough guides to help you understand how things work. When heading into the mountains, check the latest weather information from the Japan Meteorological Agency and other sources.