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The atmosphere — an ocean of air above us

We live at the bottom of an ocean of air. It presses on every square meter with a force of about 100 kN — the weight of about 10 tonnes. Rise from Rysy, Poland's highest peak, to the orbit of the ISS, find out why the sky is blue and sunsets are red, work out how many degrees the greenhouse effect adds to Earth, whip up a foehn wind over Zakopane and compare the atmospheres of other worlds.

“The sky is blue because it reflects the ocean”air scatters short waves more strongly: ∝ 1/λ⁴

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The ozone layer — a shield against UV stratosphere, about 15–35 km

Ozone (O₃) absorbs nearly all UV-C and most UV-B — the radiation that damages DNA. That is what heats the stratosphere, which is why the temperature there rises with altitude. If all the ozone above us were compressed to surface pressure, it would form a layer only about 3 mm thick (about 300 Dobson units). Since the 1980s an ozone hole has opened over Antarctica every spring: chlorine and bromine compounds from CFCs (freons) and halons destroy ozone on the surfaces of icy polar stratospheric clouds.

Montreal Protocol1987CFC ban, ratified by every UN member state
Ozone over Antarctica≈ 2066back to 1980 levels (WMO/UNEP 2022)
Rest of the world≈ 2040the Arctic ≈ 2045 — per the same assessment

It is one of the greatest successes of international cooperation in protecting the environment. The size of the hole varies from year to year, because it also depends on stratospheric weather, and the recovery dates are projections.

1–6 modes ↑↓ altitude (mode 1) Shift+↑↓ bigger step +− zoom L log / linear scale

How does the ocean of air work?

The atmosphere weighs about 5.1 · 10¹⁸ kg. Pressure at the surface is simply the weight of the column of air above each square meter: 101,325 Pa, or about 100 kN per m² — like the weight of about 10 tonnes. We don't feel it, because it pushes equally from all sides, and the fluids and air in our bodies are at a similar pressure.

The barometric formula

p(h) = p0 · e−h/H,   H = RTMg ≈ 8.4 km

Every further H ≈ 8.4 km up reduces the pressure about e ≈ 2.72 times. The formula is exact only for a constant temperature. The simulation computes it more precisely, layer by layer, using the U.S. Standard Atmosphere 1976: in each layer the temperature changes linearly with altitude, and the pressure satisfies the equation of hydrostatic equilibrium:

p = pb · (TbTb + L(h − hb))gM/(RL)L — temperature gradient of the layer, e.g. −6.5 K/km in the troposphere

This gives T = 216.65 K (−56.5 °C) and p ≈ 22.6 kPa at an altitude of 11 km (strictly: 11 geopotential km, i.e. about 11.02 km above sea level), and half the sea-level pressure at about 5.5 km. The mass of air above us is proportional to the pressure, so half of the entire atmosphere lies below about 5.5 km, and 90% below about 16 km.

Why does the temperature fall in some places and rise in others?

Water boils at a lower temperature when pressure drops

log10 pmmHg = 8.07131 − 1730.63233.426 + tAntoine equation for water (1–100 °C)

Water boils when its vapor pressure equals the pressure of its surroundings. On Rysy that is about 92 °C, on Everest about 70–72 °C, and at about 19 km — at 37 °C. Below the triple point (611.657 Pa, about 34–35 km) water cannot be a liquid at all.

The color of the sky: Rayleigh scattering

Iscat ∝ 1λ4,   I(450 nm)I(700 nm) = (700450)4 ≈ 5.9

Nitrogen and oxygen molecules are thousands of times smaller than the wavelength of light and scatter blue light several times more strongly than red. When the Sun is low, its light passes through a layer of air dozens of times thicker (about 38 times at the horizon) and loses most of its blue on the way — orange and red remain. Cloud droplets and aerosols are comparable to the wavelength or larger (Mie scattering) and scatter all colors almost equally, which is why clouds are white and haze is grayish.

Energy balance and the greenhouse effect

F = σT4,   Te = (S0(1 − A)4σ)1/4 ≈ 255 K

The Stefan–Boltzmann law (σ = 5.67 · 10⁻⁸ W/(m²·K⁴)) says how much a body at temperature T radiates. Earth absorbs on average S0(1 − A)/4 ≈ 238 W/m² (the factor 4 is the ratio of the sphere's surface to the disk that intercepts the light). Without an atmosphere absorbing infrared, its temperature would be about 255 K (−18 °C), while the observed average is about 288 K (+15 °C). In a model with one gray layer that absorbs a fraction ε of the infrared:

Ts = Te · (22 − ε)1/4ε ≈ 0.78 gives about 288 K ΔF ≈ 5.35 · ln(CC0) W/m²,   ΔT ≈ ECS · ΔFΔF2×5.35 · ln 2 ≈ 3.71 W/m²

Equilibrium climate sensitivity (ECS) is the warming after CO₂ doubles and equilibrium is reached. According to IPCC AR6 the best estimate is 3 °C, with a likely range of 2.5–4 °C. The dependence on concentration is logarithmic: each further doubling adds a similar amount of forcing.

Rising air and the foehn

Γd = gcp ≈ 9.8 K/km,   Γw ≈ 4–7 K/km,   zcloud ≈ 125 m · (T − Td)

Rising air expands and cools by about 9.8 °C per km (the dry adiabat). Once it reaches its dew point, vapor condenses and releases heat — from then on it cools by only about 5–6 °C per km at typical temperatures (the moist adiabat; the colder it is, the closer to the dry one). In a foehn (in Poland called halny), the air loses its moisture as rain on the Slovak side, and on the Polish side it descends and warms by the full 9.8 °C per km. So at the bottom it is warmer and much drier than on the other side of the mountains.

Model simplifications
  • The temperature profile is the U.S. Standard Atmosphere 1976 (mid-latitudes, moderate solar activity). The real atmosphere changes with season, latitude and weather; the temperature of the thermosphere depends strongly on solar activity. Above 86 km we take pressure and density from this model's tables and interpolate.
  • We compute the partial pressure of oxygen from a 20.95% share, which is accurate up to about 85 km. Higher up the composition changes (atomic oxygen dominates, then helium and hydrogen), so there we give it only as a rough guide.
  • Sky color: single scattering only, three wavelengths (680, 550 and 440 nm), exponential density profiles, white balance matched to sunlight. We ignore multiple scattering, which is why twilight here is darker than in nature. Dust on Mars is described by a simple phenomenological model.
  • Greenhouse effect: gray layers transparent to visible light that absorb all infrared equally; no convection, clouds or feedbacks. It is a model for understanding the mechanism, not a forecast.
  • Foehn: a single air parcel, pseudo-adiabatic ascent (all condensed water falls out as precipitation), pressure from the standard atmosphere. In reality the foehn's warmth also comes from air descending from higher layers.
  • Can and bottle: an ideal gas at constant volume; the shape of the dent is arbitrary.

Did you know…?

  1. The whole atmosphere compressed to its surface density would be only about 8.4 km thick — less than the height of Mount Everest (8,849 m). This is exactly the “scale height” H = p0/(ρ0g).
  2. 90% of the mass of the air is below about 16 km, and half below about 5.5 km. So an airliner flies above about 3/4 of the entire atmosphere.
  3. The sky on the Moon is black even at noon: without an atmosphere there is nothing to scatter light, so you could see stars right next to the Sun (if the bright ground doesn't dazzle you).
  4. At about 19 km, water boils at human body temperature. This is the Armstrong limit — above it a person cannot survive without a pressure suit.

Challenges 0/8

  • Rise to the Kármán line

    Set an altitude of 100 km or more — the conventional edge of space.

    not completed
  • Find the altitude where the pressure drops by half

    Look for a place where the pressure is 50% (±1%) of its sea-level value.

    not completed
  • Find the altitude where water boils at 37 °C

    A boiling point between 36 and 38 °C is enough.

    not completed
  • Set up a sunset with a red sky

    On Earth, lower the Sun to the horizon so that the sky above it turns red.

    not completed
  • See a blue sunset on Mars

    Switch to Mars and lower the Sun — what happens to the sky around it?

    not completed
  • Calculate Earth's temperature without the greenhouse effect

    With S₀ = 1,361 W/m² and albedo 0.30, switch off infrared absorption.

    not completed
  • Whip up a foehn: a warm, dry wind in Zakopane

    Zakopane must be at least 4 °C warmer than the Slovak side, with humidity of at most 50%.

    not completed
  • Compare the pressure on Venus and Mars

    Select both planets and see how many times they differ.

    not completed

Sources of values: U.S. Standard Atmosphere 1976, NOAA (Mauna Loa), IPCC AR6, WMO/UNEP (2022 ozone layer assessment), NASA. Numbers are rounded; many of them change with time, season and place.