metr 2413 3 march 2004

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METR 2413 3 March 2004 Thermodynamics Thermodynamics IV IV

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METR 2413 3 March 2004. Thermodynamics IV. Review. First law of thermodynamics: conservation of energy du = dq – dw dq = c v Δ T + p Δα = c p Δ T - α Δ p = c p Δ T – Δ p/ ρ Adiabatic process, dq = 0, no external energy input to parcel Diabatic process, radiation or latent heating - PowerPoint PPT Presentation

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Page 1: METR 2413 3 March 2004

METR 24133 March 2004

ThermodynamicsThermodynamics

IV IV

Page 2: METR 2413 3 March 2004

Review

First law of thermodynamics: conservation of energydu = dq – dw

dq = cv ΔT + p Δα = cp ΔT - α Δp = cp ΔT – Δp/ρ

Adiabatic process, dq = 0, no external energy input to parcelDiabatic process, radiation or latent heating

Adiabatic lapse rate

Entropy dS = dQ/T remains constant or increases

pcdz

dT g

Page 3: METR 2413 3 March 2004

Adiabatic temperature variations

Consider an adiabatic process againdq = 0 = cp dT – dp / ρ

Then cp dT = R T dp / p using ideal gas law

Divide by cp T gives

So

Integrating from initial level pi to final level pf gives

p

dp

cT

dT

p

R

)(lnR

)(ln pdc

Tdp

pc

R

i

f

i

f

pi

f

p

p

p

p

cT

T

lnln

Rln

Page 4: METR 2413 3 March 2004

Adiabatic temperature variations

So with κ = R/cp = 0.286

Given an initial pressure and temperature, we can calculate the final temperature Tf at pressure pf for adiabatic motion.

Since p decreases with height, T also decreases with height for dry adiabatic temperature variations (as we have shown before).

i

fc

R

i

f

i

f

p

p

p

p

T

T p

i

fif p

pTT

Page 5: METR 2413 3 March 2004

Potential temperature

We define the potential temperature θ to be the temperature an air parcel would have if was raised or lowered under dry adiabatic motion to pressure level of 1000 hPa.

Setting pf = p0 = 1000 hPa, we obtain an equation for the potential temperature of an air parcel with temperature T at pressure p; for adiabatic motion.

The potential temperature of an air parcel is constant for adiabatic motion.This is one of the most important concepts in meteorology!

pT

p

pT

10000

Page 6: METR 2413 3 March 2004

Atmospheric stability

Potential temperature θ constant corresponds to a dry adiabatic lapse rate and a neutrally stable layer.

A stable layer has the temperature decrease with height smaller than Γd and θ increasing with height.

An unstable layer has the temperature decrease with height greater than Γd and θ decreasing with height.

10

100

-60 -40 -20 0 20 40 60

T or T_d in C

P i

n k

Pa

Thermo Diagram –Dry Adiabats

-40 -20 0 8020 60 θ in °C

40

Dry adiabats are lines of constant potential temperature

Page 7: METR 2413 3 March 2004

Atmospheric stability

Potential temperature θ constant corresponds to a dry adiabatic lapse rate and a neutrally stable layer.

A stable layer has the temperature decrease with height smaller than Γd and θ increasing with height.

An unstable layer has the temperature decrease with height greater than Γd and θ decreasing with height.

10

100

-60 -40 -20 0 20 40 60

T or T_d in C

P i

n k

Pa

Thermo Diagram –Moist Adiabats

-40 -20 0

80

20 60 θL in °C

40

Moist adiabats show the temperature variations of a saturated air parcel that is rising through the atmosphere. The temperature decreases less quickly with height than a dry adiabat due to latent heat relase from condensation

Page 8: METR 2413 3 March 2004

Atmospheric stability

Potential temperature θ constant corresponds to a dry adiabatic lapse rate and a neutrally stable layer.

A stable layer has the temperature decrease with height smaller than Γd and θ increasing with height.

An unstable layer has the temperature decrease with height greater than Γd and θ decreasing with height.

0, dz

d

dz

dTd

dpcdz

dT

g

0, dz

d

dz

dTd

Page 9: METR 2413 3 March 2004

Boundary layer

Atmospheric boundary layer is region of turbulent motion due to heating from by the ground or strong winds.

Heating of the ground by solar radiation causes heating of the air close to the ground. This air will warm until the temperature gradient is unstable, causing dry convection to occur (if there is not too much moisture around).

Well-mixed boundary layer has adiabatic lapse rate and constant potential temperature with height.

Usually topped by a strong temperature inversion ( temperature increase with height) and a very stable layer.

Page 10: METR 2413 3 March 2004

Maximum temperature forecast

MAXT = estimated maximum afternoon temperature

Most relevant when using morning sounding

Most accurate on days with clear skies and moderate winds

Assumes mixing depth of planetary boundary layer is ~150 mb

To determine MAXT:Note surface pressureFind sounding temperature 150 mb above the surfaceFrom the temperature 150 mb above surface, follow the dry adiabat down to the surface

Page 11: METR 2413 3 March 2004

Maximum temperature forecast

Once the planetary boundary layer mixes to dry adiabatic lapse rate, further warming is slow

- this is one of the reasons why temperatures tend to increase most rapidly in the first half of the day and more slowly in the second half of the day

Temperatures may be higher if wind is lightTemperatures may be lower if wind is strong (wind strength affects depth of atmospheric mixing)

Number of daylight hours affects accuracy (more accurate in warm season

Technique does not work well near fronts or in cases of strong advection

Technique does not work well in regions with complex topography, or in coastal areas

Page 12: METR 2413 3 March 2004

CAPE

CAPE = Convective Available Potential Energy

On the skew-T, CAPE is indicated by the area where a rising air parcel would be warmer than the environment

CAPE gives an indication on the stability of the atmosphere. In general, the higher the CAPE value, the more unstable the atmosphere is.

To find the CAPE from a skew-T thermodynamic diagram, simply locate the area on the diagram where the parcel sounding is warmer than the atmosphere sounding.

Page 13: METR 2413 3 March 2004

CAPE

The white region is called the "positive energy" region. The size of the positive energy region gives an indication on how buoyant, and hence unstable, a parcel is.

Page 14: METR 2413 3 March 2004

CAPE

CAPE values can be used to objectively determine how convective the atmosphere is. CAPE has unites of Joules per kilogram. Use the following scale to determine convective potential (from Sturtevant, 1994):

CAPE valueConvective potential

< 300 Little or none

300-1000 Weak

1000-2500 Moderate

2500-3000 Strong

A CAPE value above 3000 would indicate a potentially highly unstable atmospheric condition, and storms will build vertically very quickly.

Page 15: METR 2413 3 March 2004

CAPE

CAPE > 2500 J/kg hail potential increases (large hail requires large CAPE)

CAPE > 2000 J/kg expect isolated regions of very heavy rain, perhaps accompanied by strong downdrafts

CAPE > 2000 J/kg will typically produce storms with intense lightning

Caveats:Storms will only form if low level capping inversion is broken

CAPE magnitude can rise or fall very rapidly

Page 16: METR 2413 3 March 2004

CINH

Convective Inhibition (CINH) – basically anti-CAPE

CINH is defined as the amount of energy beyond the normal work of expansion need to lift a parcel from the surface to the Level of Free Convection (LFC).

Increasing amounts of CINH indicate more energy is needed to lift the parcel

Page 17: METR 2413 3 March 2004

CINH

On a skew-T diagram, the CINH is the area bounded by the temperature sounding on the right and the Dry/Saturated adiabats on the left (dry if below the LCL, wet if above the LCL).

Page 18: METR 2413 3 March 2004

CINH

CINH area is generally called the "negative energy region“ the more CINH in the sounding, the greater the atmospheric stability and the less chance of vigorous convectionThe top of the CINH area is the Level of Free Convection (LFC), which is the first level in the atmosphere where the parcel can continue to rise on it's own, without any outside energy contribution.

CINH may also be referred to as a “capping layer” – must be broken before a parcel can move into a region of CAPE and develop into deep convection

Page 19: METR 2413 3 March 2004

CINH

Like CAPE, units of CINH are Joules/kilogram

CINH will be reduced by:1) Daytime heating2) Synoptic upward forcing3) Low level convergence4) Low level warm air advection

CINH index is only relevant to the lower planetary boundary layer convectionIf there is no CAPE, CINH index is meaningless

CINH Value Cap Strength0 – 50 weak51 – 199 moderate200 + strong