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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

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METR 2413

3 March 2004

Thermodynamics

IV


Review

First law of thermodynamics: conservation of energy

du = dq – dw

dq = cvΔT + p Δα = cpΔT - αΔp = cpΔT – Δp/ρ

Adiabatic process, dq = 0, no external energy input to parcel

Diabatic process, radiation or latent heating

Adiabatic lapse rate

Entropy dS = dQ/T remains constant or increases


Adiabatic temperature variations

Consider an adiabatic process again

dq = 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


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).


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!


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.


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.

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


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.


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.


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 pressure

Find sounding temperature 150 mb above the surface

From the temperature 150 mb above surface, follow the dry adiabat down to the surface


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 light

Temperatures 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


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.


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.


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):

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


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


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


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).


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 convection

  • The 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


  • CINH

    • Like CAPE, units of CINH are Joules/kilogram

    CINH Value Cap Strength

    0 – 50 weak

    51 – 199 moderate

    200 + strong

    • CINH will be reduced by:

    • Daytime heating

    • Synoptic upward forcing

    • Low level convergence

    • Low level warm air advection

    • CINH index is only relevant to the lower planetary boundary layer convection

    • If there is no CAPE, CINH index is meaningless


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