AOS 101-304

March 22

Moisture and Stability

Humidity

• The amount of water vapor in the atmosphere.

• Mixing ratio, w: ratio of mass of WV to mass of dry air (g/kg)

w =

grams of water vaporkilograms of dry air

Vapor Pressure

• Vapor pressure, e: partial pressure of water vapor (Pa)

• The total air pressure of the atm. equals the partial pressures of each constituent gas

Pair = PN2 + PO2

+ PAr + e + PCO2 + ...

• Typical air pressures are around 1000 hPa, vapor pressure is typically 1-25 hPa.

Saturation Vapor Pressure, es

• Definition: For a given temperature, the amount of WV required so that the rates of condensation and evaporation are equal.

• Warmer air has a higher saturation vapor pressure than cooler air.

• Exponential relationship between es and temperature, i.e. es = f(T)

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Temperature (oF)

Sat

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apo

r P

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ure

(h

Pa)

• Relative Humidity: ratio of observed vapor pressure and the saturation vapor pressure (for a given temperature)

• Dewpoint (Td): Temperature of air to which a parcel must be cooled to reach saturation.

• Completely relies on vapor pressure.

e = f(Td)

RH =

ef(T)

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Temperature (oF)

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apo

r P

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Pa)

Given T = 70oF and RH = 20%, what are es, e and Td?

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-10 0 10 20 30 40 50 60 70 80 90

Temperature (oF)

Sat

. V

apo

r P

ress

ure

(h

Pa)

Given T = 70oF and RH = 20%, what are es, e and Td?

T = 70oF → es = 25 hPa

RH = .2 = e/25 → e = 5 hPa

e = 5 hPa → Td = 27oF

• If you know 2, you know all 5.

T ↔ es

Td ↔ e

RH ↔ e / es

T = 70oF → es = 25 hPa

RH = .2 = e/25 → e = 5 hPa

e = 5 hPa → Td = 27oF

Stability

• Refers to an equilibrium position

• Stable equilibrium: perturbing an object will result in the object returning to original position

• Unstable equilibrium: perturbing an object will result in the object continuing to move away.

In the atmosphere…

• Perturbed objects are parcels (bubbles of air that can’t mix with surroundings).

• Atmospheric stability has to do with buoyancy– A parcel warmer (less dense) than its

surroundings will rise.– A parcel cooler (more dense) than its

surroundings will sink.

• Stability assessed by moving parcels vertically and comparing parcel temperature with the temperature of its surroundings.

However…

• As a parcel rises it does not keep the same temperature, instead it cools ADIABATICALLY.

• Adiabatic: reversible process which results in no loss/gain of heat energy by the parcel

• Instead, during ascent the parcel expands resulting in cooling (or warming by compressing during sinking)

• Dry Adiabatic Lapse Rate (DALR): The rate at which an unsaturated parcel cools as it rises (or warms as it sinks) is constant:

Γd = 9.8oC / km

• If a parcel is saturated, latent heat is released as water vapor condenses slightly counteracting the cooling during ascent. This is the Moist Adiabatic Lapse Rate (MALR):

Γm ~ 6.0oC / km (varies 4-7oC/km)

Note: if condensed water leaves the parcel the process is no longer reversible.

Assessing stability

• On a given day, the atmosphere will have a certain environmental lapse rate (Γe).

• Negative sign needed so that if temperature decreases with height the lapse rate is positive.

Γe =T(z2) – T(z1)z2 – z1

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For a certain atmospheric layer…

• If Γe > Γd , atmospheric layer is absolutely unstable.

• If Γe < Γm , atmospheric layer is absolutely stable.

• If Γd > Γe > Γm , atm. layer is conditionally unstable, atm. only unstable if saturated.

Absolutely UnstableΓe > Γd (9.8oC/km)

1 km

25201510

DALR MALR

Γe

T(z=0 km) = 25oC

T(z=1 km) = 10oC

Absolutely StableΓe < Γm (6.0oC/km)

1 km

25201510

DALR MALR

Γe

T(z=0 km) = 25oC

T(z=1 km) = 25oC

Conditionally Unstable(9.8) Γd > Γe > Γm (6.0)

1 km

25201510

DALR MALR

Γe

T(z=0 km) = 25oC

T(z=1 km) = 17oC

On average…

• The environmental lapse rate is 6.5oC/km, meaning the atmosphere is usually conditionally unstable or barely stable.

• The closeness to saturation determines if the atmosphere is unstable or not

Atmospheric Soundings

• Radiosondes measure the temperature and moisture profiles of the atmosphere

• These profiles can be used to assess the stability of the atmosphere

Next Week…

• Severe thunderstorms usually result from instability in the atmosphere.

• The summer sun warms parcels near the ground, allowing them to become unstable and rise to the tropopause