Physics of the atmosphere

1.1A thin film heated from below#

If the Earth were an orange, all the weather that concerns us would fit within the thickness of its peel. This layer is called the troposphere. It reaches from the ground up to the tropopause, at around 11 km in our latitudes — higher at the equator (16 to 17 km), lower at the poles (about 8 km), and a little lower in winter than in summer. It is the layer in which temperature falls with height and water changes state, and so the layer of clouds, wind and convection.

Above it, the stratosphere is stable and dry: the temperature stops falling there, and higher up it even rises again. No thermal can push into it for long. It is against this ceiling that the tops of cumulonimbus clouds flatten out, spreading into an anvil (Fig. 1.1).

Why it is colder higher up

A stubborn misconception holds that it is cold at altitude because you are further from the sun. In reality, sunlight passes through the air almost without warming it: it is the ground that absorbs the energy and gives it back to the air, by contact and by infrared radiation. The atmosphere is heated from below, like a saucepan on the stove. Two consequences underpin this whole book.

First, temperature decreases with height on average. The mean lapse rate is 0.65 °C / 100 m, or 6.5 °C per kilometre. But this is only a statistical average: the real profile of the day, the environment curve (section 1.6), departs from it all the time, and it is precisely this departure that makes or breaks a flying day.

Second, convection always starts from the ground. The ground warms the air in contact with it, that air becomes less dense than its neighbours and rises: that is a thermal. Free-flight weather is the science of what happens next to this bubble of air.

1.2Pressure: the weight of the air#

The pressure at a point is the weight of the whole column of air above it. At sea level, this column weighs about 10 tonnes per square metre, which gives the standard value of 1013.25 hPa. As you climb, there is less air above you: the pressure falls.

It doesn’t fall evenly. Air is compressible: the lower layers, squashed by the weight of those above, are denser. Picture a pile of duvets: the ones at the bottom are flattened, the ones at the top are fluffed up. Cut the atmosphere into six layers of equal weight: the first is 1,500 m thick, the fifth almost 5 km (Fig. 1.2).

Near the ground, you lose about 1 hPa every 8 m; at around 2,000 m, it is more like 1 hPa every 10 m. The pressure is halved at about 5,500 m. That is why meteorologists describe altitude by pressure levels, which you will find on every chart and every sounding:

These altitudes vary by a few tens to a few hundreds of metres depending on the temperature of the air: a warm column is thicker than a cold one. This is in fact valuable information, put to use in chapter 5.

Your altimeter is a barometer

The altimeter on your watch, your GPS or your harness does not measure altitude: it measures pressure and converts it into altitude according to the standard atmosphere. If the pressure drops by 5 hPa overnight because a low is approaching, the altimeter “climbs” by fifty metres or so without you having moved.

1.3Humidity and dew point#

Air always contains water vapour, an invisible gas. The maximum amount it can hold depends almost entirely on its temperature, and in a very non-linear way. A kilogram of air at 30 °C can hold about 27 g of vapour; at 10 °C, only 7.6 g; at −10 °C, barely 1.8 g. Every 10 °C or so, the capacity doubles (Fig. 1.3).

Remember the picture: cooling moist air pushes it relentlessly towards saturation. Morning fog, dew on the tent, the midday cumulus and the mist on your glasses are all the same phenomenon.

Three quantities describe humidity, and you must keep them strictly apart:

That is why meteorologists think in Td, not in RH: saying “RH = 60%” tells you nothing until you know the temperature; saying “Td = 14 °C” fixes the amount of water once and for all. The difference T − Td, called the dew-point spread, is the quantity that matters in practice: it measures how much the air must be cooled to make a cloud.

Relative humidity goes up and down like a yo-yo

Over a fine day, the valley air neither gains nor loses much water: Td barely moves. The temperature, though, rises by 10 to 15 °C between dawn and mid-afternoon. The result: relative humidity falls from nearly 100% in the early morning to 40% or less around 15:00, then rises again in the evening (Fig. 1.4).

1.4The bubble and the bicycle pump#

To reason it through, we follow an air parcel (also called a particle): an imaginary bubble that rises without mixing with the surrounding air and without exchanging heat with it. It’s an idealisation — we’ll see its limits — but its predictive power is remarkable.

When the bubble rises, the pressure around it falls: it expands, like the air escaping from a valve. As it expands, it pushes back the air around it, and that work draws on its own energy: it cools. Conversely, the air compressed in a bicycle pump heats up. This transformation without any exchange of heat is called adiabatic. The cooling owes nothing to contact with colder air: it is purely mechanical, and its rate is a physical constant (Fig. 1.5).

One last detail matters. The bubble’s dew point also falls a little as it rises, by about 0.2 °C / 100 m, because expansion dilutes its vapour. Its temperature and its dew point therefore close in on each other by 1.0 − 0.2 = 0.8 °C every 100 m. Remember this figure: in a moment, it will give you the height of the clouds.

1.5The cumulus base#

A bubble that leaves the ground with a T − Td spread of 11 °C catches up with its dew point after 11 / 0.8 ≈ 14 slices of 100 m, so about 1,350 m higher up. At that height it saturates: this is the condensation level, the flat base of the cumulus. All the bubbles from the same place start out in much the same way: they all condense at the same height, hence that characteristic horizontal base (Fig. 1.6).

Three cautions for use. The formula gives a height above the weather station: add its elevation. It holds for values measured in a standard weather screen, once the sun has already warmed things up: a spread taken at 07:00 greatly underestimates the afternoon base. Finally, it assumes that the air is well mixed from the ground to the base, which is the case as soon as the thermals are working.

1.6Stable or unstable: the race between two rates of cooling#

The adiabats describe what a bubble would do if you lifted it. What remains is to know what it meets on the way: the real temperature profile of the atmosphere that day, measured by a radiosonde or calculated by the models. This is the environment curve. It follows no rail: it is the result of the air mass’s whole history — the ground warming up, cooling at night, air sinking under an anticyclone, warm or cold air brought in by the wind…

The verdict comes down to comparing slopes. Lift a bubble 100 m in your mind: it loses 1 °C. And the surrounding air, 100 m higher up — is it colder or less cold than the bubble? (Fig. 1.7)

From temperature difference to vertical speed

A bubble warmer than its environment is lighter: it is pushed upwards with a force proportional to the temperature difference. A difference of 1 °C gives an acceleration of about 0.03 m/s² — three hundredths of gravity. That’s modest, but applied over 1,000 m of climb, it would in theory be enough to reach 6 to 8 m/s.

If real thermals top out between 1 and 4 m/s instead, with peaks of 5 to 8 m/s on big Alpine days, it is because of entrainment: at its edges the thermal draws in colder, drier surrounding air, which dilutes its excess heat, and it rubs against the still air around it. The narrower a thermal, the more it is diluted. A wide, well-fed thermal is protected at its core: it climbs harder and higher.

1.7Inversions: a lid on the valley#

An inversion is a layer in which the temperature increases with height. It is stability taken to the extreme: a bubble entering it immediately becomes colder than its surroundings and sinks back. Three mechanisms create them, each with its own signature (Fig. 1.8).

A radiation inversion forms at the ground on clear, calm nights. The ground radiates its heat out to space, cools, and cools the air in contact with it. The cold, heavy air drains away and pools on the valley floors, in a layer a few tens to a few hundreds of metres deep. In the early morning, the valley floor can be 5 to 10 °C colder than a slope 300 m higher up. The sun erodes the inversion from below in mid-morning: it is what delays the first thermals.

A subsidence inversion forms under anticyclones. The air there sinks slowly, over hundreds of kilometres; as it sinks, it is compressed and warms by 1 °C every 100 m (the bicycle pump in reverse), and it dries out. It ends up resting, warm and dry, on the cooler air of the low layers, often between 1,000 and 3,000 m. This is the lid of long spells of fine weather: blue sky, dry haze under the inversion, a capped ceiling that changes little from one day to the next and may even come down day after day as the anticyclone ages (section 3.7).

A frontal inversion forms when warm air slides up over colder air, ahead of a warm front (chapter 4). It is often moist: stratus, mist or drizzle in the cold layer, layered cloud above.

1.8The parcel method#

Everything so far can be summed up on a single graph, the emagram, on which the day’s environment curve is overlaid on the adiabatic rails. On the real document, the temperature lines slant and altitude is given as pressure; to understand it, you can “unskew” it onto temperature / altitude axes without losing anything of the method (Fig. 1.9). Chapter 2 will teach you to read the real ones.

Two quantities sum up the diagram. The area where the bubble is warmer than the surrounding air measures the energy available for convection: the CAPE, in joules per kilogram. The area where it is colder — typically in the morning inversion — measures the energy needed to break through the lid: the CIN. A large CAPE under a CIN that holds until the middle of the day is the recipe for a late-afternoon thunderstorm outbreak: all afternoon, energy builds up under the lid, then everything goes at once.

Finally, the trigger temperature is the ground temperature from which the dry adiabat starting at the ground breaks through the nocturnal inversion. Compare it with the forecast rise in temperature through the morning: that gives you the time of the first usable thermals. And the margin between the maximum temperature and the trigger temperature tells you whether the day will be generous or sluggish.

1.9Where the thermal stops: soft ceiling, concrete ceiling#

Lift stops when the bubble is no longer warmer than the surrounding air. There are three ways for this to happen, each with a very different signature in flight (Fig. 1.10).

The soft ceiling is the ceiling of days with no marked lid: the surrounding air cools more and more slowly with height, and the bubble’s excess melts away gradually. In flight, the thermal widens, weakens and becomes hard to centre; with care you can still gain a few tens of metres, then nothing more.

The concrete ceiling is the ceiling of inversions: the excess disappears within a few tens of metres. The thermal climbs well right to the end, then stops abruptly, often in a choppy zone where the wing gets shaken about. Any cumulus spread out underneath it.

The reprieve in the cloud comes from latent heat: above the base, the saturated bubble loses only 0.5 to 0.6 °C per 100 m. If the surrounding air cools faster than that, the bubble becomes warmer and warmer again: the cloud climbs, sometimes very high. This is the conditional instability of section 1.6, and it is what turns a cumulus into a congestus, then into a cumulonimbus.

Two practical nuances. First, entrainment: the ceiling on the emagram is that of the ideal bubble; real, diluted thermals often top out a little lower, and only the most vigorous ones reach the theoretical ceiling. Second, the ceiling isn’t fixed: it rises through the day, as convection warms the layer and nibbles away at the inversions from below. The ceiling at 12:00 is not the ceiling at 15:00.

1.10Latent heat, the hidden engine#

Water is the atmosphere’s great carrier of heat (Fig. 1.11). To evaporate, it borrows heat from its surroundings: that is why sweat cools you down and why damp ground warms up less than dry, stony ground. Once in the air, the vapour travels, invisible, with the thermals. When it condenses, it gives back exactly the heat it borrowed, about 2,500 J per gram of water.

A typical value makes the effect concrete: condensing 1 gram of water in a kilogram of air warms it by about 2.5 °C. A bubble of moist air that makes a few grams of droplets as it passes through its cloud thus gets several degrees of free heating. The cloud is a heat engine that warms itself by making its own droplets: this is the fuel of cumulonimbus clouds, and the reason why a thermal picks up again when it enters its cloud.

The engine also runs in reverse. When rain falls through dry air, part of it evaporates on the way and cools the air it passes through. This cooled air, heavier, plunges towards the ground and spreads out in gusts. The drier the air below the base, the more violent the effect: high-based thunderstorms, over dry air, produce the most brutal gusts.

1.11Depth brings rain#

All clouds contain water, but very few produce rain. The droplets of a cumulus are a few hundredths of a millimetre across: they float. To make a raindrop, you need to bring a million of them together, and that takes time and depth. In the mid-latitudes, the most efficient route goes through ice: in the part of the cloud colder than about −10 °C, ice crystals grow at the expense of the droplets, then fall and melt as they pass through the 0 °C isotherm (Fig. 1.12).

Hence a field rule, to be used as a typical value: a convective cloud less than 1,500 to 2,000 m deep almost never produces rain; beyond 3,000 m, especially if its top is colder than −10 °C, showers become likely; a cumulonimbus 8 to 10 km deep means a thunderstorm. The depth can be read on the emagram (top − base, section 1.8), and most free-flight forecast websites give it directly.

Stratiform rain — the rain of fronts, which lasts for hours over whole regions — obeys the same physics, but in deep layers lifted slowly over hundreds of kilometres: that is the business of chapter 4.

The hiker’s two questions, answered with numbers

“Will I be walking in cloud?” The base of convective clouds is the condensation level: base ≈ valley elevation + 122 × (T − Td). Compare this figure with the height of your route, bearing in mind that the base rises through the morning, that slopes facing a moist flow catch clouds lower than the calculation suggests, and that a T − Td spread of less than 4 °C first thing in the morning promises shrouded summits.

“Will it rain?” For convective rain, look at the forecast depth of the clouds and the height of the freezing level. Cumulus 1,000 m deep under a freezing level at 4,000 m: nothing. Clouds 3,000 m deep or more whose tops rise above the freezing level: showers possible in the afternoon. If, on top of that, the CAPE is high and the air is moist aloft, the risk of thunderstorms is real; in the mountains, it is decided early, and chapter 9 sets out the signs in detail.

1.12Exercises#

1.13Quick reference and glossary#

Adiabatic

Describes a transformation without any exchange of heat with the outside. A rising bubble cools adiabatically, simply by expanding.

CAPE and CIN

Energy available for convection (the area where the bubble is warmer than the surrounding air) and energy needed to break through a stable layer (the area where it is colder), in J/kg.

Latent heat

Heat absorbed by water as it evaporates and given back when the vapour condenses, about 2,500 J per gram.

Environment curve

The real profile of temperature against altitude, at a given place and time.

Dew-point spread

The difference T − Td: how much the air must be cooled for it to become saturated.

Entrainment

Mixing of surrounding air into a thermal through its edges; it dilutes the excess heat and slows the lift.

Relative humidity

Ratio of the vapour present to the maximum possible at the air temperature, as a percentage.

Inversion

Layer in which temperature increases with height; a lid on convection.

Condensation level

Height at which a rising bubble reaches saturation; the cumulus base. Also called the lifting condensation level (LCL).

Parcel (or air parcel)

Imaginary bubble of air that is followed as it rises, assuming it is isolated from its environment.

Dew point

Temperature to which the air would have to be cooled to become saturated; it measures the amount of vapour.

Mixing ratio

Mass of water vapour per kilogram of dry air, in g/kg.

Subsidence

Slow, large-scale sinking of air, typical of anticyclones; the air warms and dries as it sinks.

Troposphere, tropopause

Lowest layer of the atmosphere, in which temperature falls with height and clouds form; the tropopause is its ceiling, at around 11 km.

End of chapter 1 · Chapter 2 puts these tools into practice on real emagrams.