Chapter 7: Stability and Cloud Development
A parcel of air: Air inside can freely expand or contract, but heat and air molecules do not cross boundary.
A rising parcel of air expands because the air pressure falls with elevation.
This expansion causes cooling: (Adiabatic cooling)
V V
V-2v
V v
Wall Stationary Wall Moving Away
An air molecule that strikes an expanding wall will lose speed on bouncing off wall (temperature of air will fall)
V
V+2v
v
Wall Moving Toward
A falling parcel of air contracts because it encounters higher pressure.
This falling air heats up because of compression.
Stability: If rising air cools more quickly due to expansion than the environmental lapse rate, it will be denser than its surroundings and tend to fall back down.
10°C Definitions: Dry adiabatic rate = 1000 m 10°C Moist adiabatic rate : smaller than because of release of latent heat during 1000 m condensation (use 6° C per 1000m for average)
Rising air that cools past dew point will not cool as quickly because of latent heat of condensation.
Same compensating effect for saturated, falling air : evaporative cooling from water droplets evaporating reduces heating due to compression.
Summary: Rising air expands & cools Falling air contracts & warms
10°C Unsaturated air cools as it rises at the dry adiabatic rate (~ ) 1000 m
6°C Saturated air cools at a lower rate, ~ , because condensing water vapor heats air. 1000 m This is moist adiabatic rate.
Environmental lapse rate is rate that air temperature falls as you go up in altitude in the troposphere.
Depending on the lapse rate, the atmosphere is either stable or unstable.
Moist Adiabatic Dry rate Adiabatic Rate
Absolutely Stable
Absolutely Altitude Conditionally unstable unstable
Temperature
If lapse rate is small, temperature of the environment goes down slowly with altitude. A rising parcel will cool faster than lapse rate and this cold, dense parcel will tend to fall back down – this is stability. If lapse rate is large (sloped sharply to left in figure), parcel is warmer than environment and continues to rise – this is unstable.
In conditionally unstable region, dry air is stable and saturated air is unstable.
Conditions for stable air:
- night time radiative cooling of earth’s surface - subsidence inversion - cold air brought in by wind near surface
Subsidence Inversion:
Large layer of unsaturated air sinks (subsides). Top of layer falls further than bottom, so top ends up hotter than bottom.
Heats up dtop dbottom
Negative lapse rate or inversion leads to stability.
Conditions for unstable air:
- daytime solar heating of earth’s surface - warm air blows in by wind near surface - cold air blows in by wind aloft Development of a cloud by convection:
Sun heats ground and a “thermal” starts to rise
If lapse rate is large (hot humid day) thermal will rise.
Temperature and dew point come together at condensation level.
Dew point drops as thermal rises because pressure drops which means actual vapor pressure of parcel drops.
T1 = original dew point of thermal on surface
T2 = dew point of thermal at condensation level
Saturation
Actual Vapor Pressure
T2 T1
Temperature
Topography and Clouds:
Summary: Cloud formation by convection – must have absolutely unstable air for thermal to continue rising if unsaturated.
However, certain conditions can cause air masses to rise even in stable or conditional air.
Example: Orographic uplift- Figure 7.19
8°C Lapse rate is – conditionally unstable (stable for unsaturated, unstable for 1000 m saturated)
Air is forced to rise by wind blowing against a mountain slope. Eventually, dew point is reached & a cloud forms. Heavier water droplets are caught on windward side, while dryer air in cloud blows over & down leeward side of mountain. Because water has condensed out, falling air heats at faster dry adiabatic rate & warm, dry air reaches bottom of leeward side. (Rain Shadow)
Determining Convective Cloud Bases:
2°C Td (dew point temperature) decreases at ~ 1000 m
10°C T = unsaturated air temperature, decreases at , therefore T- Td reduces by 8° C 1000 m per 1000m so, if T and Td differ by 8° C at ground, cloud will form at 1000m. Or for every 1° C difference in T & Td at ground, cloud will form 125m further up 1000 (125 = ) . 8 H (meters) = 125(T – Td)° C
See figure 1 page 177
In dry areas, T - Td large at ground, cloud bases are high
In humid areas, T – Td small at ground, cloud bases are low
Clouds also commonly form when air is lifted because of two air masses meeting. Cold or Warm fronts: warmer air mass will be lifted over colder air and clouds will form.