METR 2413 3 March 2004 Thermodynamics IV Review First law of thermodynamics: conservation of energy du = dq dw dq = cv T + p = cp T - p = cp T p/ Adiabatic process, dq = 0, no external energy input to parcel Diabatic process, radiation or latent heating Adiabatic lapse rate dT g dz cp

Entropy dS = dQ/T remains constant or increases Adiabatic temperature variations Consider an adiabatic process again dq = 0 = cp dT dp / Then cp dT = R T dp / p Divide by cp T gives So using ideal gas law dT R dp T cp p R d (ln T ) d (ln p ) cp

Integrating from initial level pi to final level pf gives R Tf R p f p f cp ln ln ln Ti c p pi pi Adiabatic temperature variations So Tf pf Ti pi

R cp pf pi with = R/cp = 0.286 Given an initial pressure and temperature, we can calculate the final temperature Tf at pressure pf for adiabatic motion. pf T f Ti pi

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 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. p0 1000 T T p p

The potential temperature of an air parcel is constant for adiabatic motion. This is one of the most important concepts in meteorology! Atmospheric stability T hermo Diagram Dry Adiabats 10 Potential temperature constant corresponds to a dry adiabatic lapse rate and a neutrally stable layer. P in kPa A stable layer has the temperature decrease with height smaller than d and increasing with height. An unstable layer has the temperature decrease with height

0 20 40 60 80 greater than-40d and-20 decreasing with height. 100 -60 -40 -20 0 20

T or T_d in C Dry adiabats are lines of constant potential temperature 40 60 in C Atmospheric T hermostability Diagram Moist Adiabats Potential temperature constant corresponds to a dry adiabatic lapse rate and a neutrally stable layer. 10

P in kPa A stable layer has the temperature decrease with height smaller than d and increasing with height. 80 An unstable layer has the temperature decrease with height 0 20 40 60 greater than-40d and -20decreasing with height. 100 -60 -40 -20

0 20 40 L in C 60 or T_d in C Moist adiabats show the temperature Tvariations 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 constant corresponds to a dry adiabatic lapse rate dT g and a neutrally stable layer.

d dz cp A stable layer has the temperature decrease with height smaller than d and increasing with height. dT d d , 0 dz dz An unstable layer has the temperature decrease with height greater than d and decreasing with height. dT d d , 0 dz dz

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): CAPE value

Convective 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. 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 0 50 51 199 200 + Cap Strength weak moderate strong CINH will be reduced by: 1) Daytime heating 2) Synoptic upward forcing 3) Low level convergence 4) 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