Adiabatic change and the dry adiabatic lapse rate
Everything about cloud, showers and turbulence comes down to one question: if a parcel of air is pushed upward, does it keep going or fall back? The answer depends on how fast the parcel cools as it rises compared with the air around it. This chapter builds both rates and then compares them.
What adiabatic means
An adiabatic temperature change is one caused only by compression or expansion, with no heat exchanged with the surroundings.
- Pump up a bicycle tyre and the valve gets hot. Compressing the air heated it.
- Discharge a CO2 extinguisher and the horn frosts over. The gas expanded rapidly and cooled.
In the atmosphere pressure falls with height, so a parcel forced to rise expands and cools, and a parcel forced to descend is compressed and warms. No heat is added or removed. The parcel simply trades pressure for temperature.
The dry adiabatic lapse rate
The DALR is the rate at which a rising unsaturated, or dry, parcel of air cools.
Two consequences that get examined directly:
- A dry parcel taken up a hillside and back down to its starting height ends up at the same temperature it began with. Dry adiabatic ascent and descent are reversible.
- Given a surface temperature and the DALR you can read off the parcel's temperature at any height. Surface 30°C, up 2 km at the DALR, gives about 10°C.
The rate at which temperature of a parcel of air decreases with height when it is made to ascend adiabatically is known as DALR. For unsaturated air it is 9.8 C per km, 3 C per 1000 ft.IC Joshi, Aviation Meteorology, chapter 9
The Dry Adiabatic Lapse Rate is the lapse rate for rising dry, unsaturated, air. It has a constant value of 1 C per 100 m, about 3 C per 1000 ft.Oxford ATPL Vol 9, 7
The saturated rate, and the environmental rate
A rising parcel behaves differently once it is saturated, because condensation starts pouring latent heat back into it. And neither rate is the same as the temperature profile of the air the parcel is moving through.
The saturated adiabatic lapse rate
When saturated air rises it still cools, but the cooling makes water vapour condense, and condensation releases latent heat into the parcel. That heat partly offsets the cooling, so the SALR is less than the DALR.
The SALR varies with temperature. Warm air holds a lot of vapour, so a lot condenses when it cools, releasing a lot of latent heat and slowing the cooling further, a small SALR. Cold air holds little vapour, so little latent heat is released and the SALR steepens towards the DALR. Below about −40°C, and at high latitude or high altitude, the SALR and DALR are effectively equal.
Descending saturated air
When a saturated parcel descends, its cloud droplets evaporate, and evaporation absorbs latent heat. So a descending saturated parcel warms more slowly than a dry one, following the SALR until it has dried out.
The environmental lapse rate
The ELR is the actual temperature profile of the real atmosphere, as measured by a radiosonde ascent. It is not a parcel property at all, it is the state of the surrounding air, and it varies with time and place. It can be anything:
- Super adiabatic, steeper than the DALR, over a strongly heated surface
- Normal, close to the ISA value of 0.65°C per 100 m
- Zero, an isothermal layer
- Negative, an inversion, where temperature rises with height
Comparing the rates, the stability criteria
Stability is resistance to vertical displacement. Push a parcel up. If it comes back, the air is stable. If it keeps rising on its own, the air is unstable. If it stays put, the air is neutral. Which one you get depends entirely on how the ELR sits relative to the DALR and the SALR.
| Relationship | State | Meaning |
|---|---|---|
| ELR > DALR | Absolute instability | Unstable for dry and saturated air alike |
| DALR > ELR > SALR | Conditional instability | Stable if the air is dry, unstable if it is saturated |
| ELR < SALR | Absolute stability | Stable for dry and saturated air alike |
| ELR = DALR | Neutral | For dry air. ELR = SALR is neutral for saturated air |
Joshi adds two layer scale cases beyond the simple parcel picture:
- Latent instability. A parcel that is stable at first but becomes unstable once forced high enough. It is real latent if the energy released later exceeds the effort to lift it, pseudo latent if it does not.
- Potential, or convective, instability. A whole layer that becomes unstable when it is lifted bodily. It needs the layer to be moist in its lower part and dry in its upper part, so lifting saturates the bottom and steepens the layer's lapse rate.
What stability does to the weather
Stable and unstable air produce clouds of opposite shape and completely different flying conditions. This is the payoff of the whole chapter, and it is asked as a straight recall.
| Element | Stable air, ELR < SALR | Unstable air, ELR > DALR |
|---|---|---|
| Cloud | Layer, stratiform. Wide, shallow | Heap, cumuliform. Tall, narrow |
| Precipitation | Continuous or intermittent, light | Showers, moderate to heavy |
| Visibility | Moderate to poor, fog likely in winter | Good, except in the showers |
| Turbulence | Light, except at an inversion or in mountain waves | Moderate to severe in and below the cloud |
Inversions and advection
- An inversion is absolutely stable. It traps smoke, haze, dust and fog beneath it, giving poor visibility, and a strong low level inversion produces wind shear and turbulence across it.
- Warm air advected over the top of a layer increases the stability within it, because it widens the temperature gap that a rising parcel has to overcome.
The tools
Upper air soundings are worked on a tephigram, or T phi gram, which carries the isotherms, the dry adiabats, the saturated adiabats and the mixing ratio lines together. Normand's theorem on that chart gives the Lifting Condensation Level, the height at which a surface parcel lifted dry adiabatically first becomes saturated, which is an estimate of convective cloud base.