NATARAJAMoisture, DALR & SALR — the stability of the air
Learning outcomes & permitted supports
- State the DRY adiabatic lapse rate as a consequence of g/cp, not a measurement, and say why a rising parcel cools at all
- Explain why the SATURATED rate is smaller — latent heat released inside the parcel — and why it varies with temperature
- Find a cloud base from a thermometer and a hygrometer: 125 × (T − Td), and say where that constant comes from
- Classify the atmosphere as absolutely stable, conditionally unstable or absolutely unstable by comparing ELR with SALR and DALR
- Predict the weather each state gives, and explain advection fog, radiation fog, sea smoke and the Föhn effect from the same two lapse rates
Supports in this lab: Calculator. DALR is g/cp exactly; the SALR is a stated working model (about 4 °C/km warm and moist, approaching the dry rate when cold), and the cloud-base rule 125·(T−Td) carries its own honest 0.5%-of-spread residue. Golden 1031/1031.
Glossary: DALR · SALR · environmental lapse rate · atmospheric stability · condensation level · advection fog
Lift a parcel and see what happens to it
Take a bubble of air at the surface and push it up. It expands into thinner air around it, and expanding costs energy, so it cools — with no heat exchanged at all. That is an adiabatic change, and while the parcel stays unsaturated it cools at a rate fixed by physics alone: the DRY ADIABATIC LAPSE RATE, g/cp = 9.76 °C per kilometre. Not a measurement — a consequence.
The parcel's dew point falls too, but only about 1.8 °C/km, so the gap between temperature and dew point closes at roughly 8 °C per kilometre — which is the whole origin of the bridge rule cloud base ≈ 125 × (T − Td). Here: 125 × 9.0 = 1125 m. Above that the parcel is saturated and cloud forms.
Above the cloud base: the SALR, and why it is smaller
Once condensation starts, the vapour gives back its latent heat inside the parcel — heat that partly offsets the cooling of expansion. So a saturated parcel cools MORE SLOWLY: the saturated adiabatic lapse rate, about 4 °C/km in warm tropical air and approaching the dry rate in cold dry air, because cold air has almost no vapour left to condense.
| At 2000 m the parcel is | 13.4 °C (saturated — inside cloud) |
|---|---|
| The environment there is | 13.0 °C |
| So the parcel is | WARMER than its surroundings by 0.4 °C — it keeps rising by itself |
The three skies
Now race the parcel against the air it is rising through — the environmental lapse rate, which is whatever the atmosphere happens to be doing today and is measured, not derived. Three cases, and they are the whole of stability:
| ELR < SALR | Absolutely stable. Nothing rises on its own — layer cloud, poor visibility, smoke flattening, fog if it cools further. |
|---|---|
| SALR < ELR < DALR | Conditionally unstable. Stable while dry, unstable once saturated. The commonest state, and the one that builds thunderstorms IF something lifts the air past its condensation level. |
| ELR > DALR | Absolutely unstable. Vigorous but shallow and short-lived: the overturning destroys the state that caused it. |
At 7.5 °C/km against SALR 4.1 and DALR 9.76, this air is conditionally unstable. fair-weather cumulus that can grow into towering cumulus and thunderstorms IF something lifts the air past its condensation level — a front, a hill, or the afternoon sun The standard atmosphere's mean is 6.5 °C/km — conditionally unstable, which is why the world has weather at all.
What the mariner does with it
Stability is not an exam word; it is the forecast you make yourself from a thermometer, a hygrometer and the look of the sky. Stable air over a warmer sea gives sea fog and smooth visibility-killing haze; unstable air over a warmer sea gives showers, squalls and sudden gusts on the beam — the difference between a quiet watch and one spent shortening the ship's exposure. Two more mariner's cases follow straight from the two lapse rates:
| Advection fog | warm moist air moving over a colder sea is cooled from below to its dew point — the classical Grand Banks and Arabian Sea fog. It needs a wind to keep coming and dies when the air mass changes. |
|---|---|
| Radiation fog | land cools overnight by radiation, chills the air above it below its dew point, and the fog drifts seaward at dawn — a coastal, calm-night phenomenon that burns off with the sun. |
| Arctic sea smoke | very cold air over a much warmer sea: the water evaporates into air that cannot hold it, and steams. Shallow, dramatic, and a sign of a bitter wind. |
| The Föhn effect | air forced over a range rains out its moisture on the way up (SALR), then descends the far side warming at the full DALR — arriving hot and dry. The two lapse rates, doing the same job in opposite directions. |
| Surface | 28.0 °C, dew point 19.0 °C — 58% humidity |
|---|---|
| Cloud base = 125 × (T − Td) | 1125 m |
| DALR · SALR · ELR | 9.76 · 4.1 · 7.5 °C/km |
| The air is | CONDITIONALLY UNSTABLE |
| Out of the window | fair-weather cumulus that can grow into towering cumulus and thunderstorms IF something lifts the air past its condensation level — a front, a hill, or the afternoon sun |