9/26/20121ESPM 129 BiometeorologyTemperature and Thermodynamics, Part II• Topics to be Covered– Profiles of Temperature in the Boundary Layer– Potential temperature– Adiabatic Lapse Rate– Thermal StratificationWhy are We Interested in Thermal Stratification of the Atmosphere?• Compare Temperatures measured at Different Heights and Altitudes• Creates or Suppresses Turbulence and Diffusion• Adiabatic Lifting can Cause Cooling– It can cause water to change phases– Condensation Promotes the Formation of Clouds and Rain• Adiabatic Compression can Cause Heating– Downslope Santa Ana winds, Hot and Dry• Microclimate Modification– Wind machines Break the Nocturnal Inversion Layer and Prevent FrostESPM 129 Biometeorology9/26/20122ESPM 129 BiometeorologyPressure, kPa65 70 75 80 85 90 95 100 105Height, m050010001500200025003000Air Density, kg m-30.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20Height, m050010001500200025003000Changes in Air Pressure and Density with Height, Ideal ConditionsadP g dz()aamPeRTAir Parcel Lifted Expands and Becomes Less Dense because Surrounding Pressure is Less, ConsequentlyIts Temperature Drops as the Parcel ExpendsESPM 129 BiometeorologyTemperature Profiles in the Boundary Layer:Adiabatic Lapse RateTair, K265 270 275 280 285 290 295 300 305Height, m05001000150020002500300019.8Kkm9/26/20123ESPM 129 BiometeorologyPotential Temperature, TPPRmcp()/( )0 TPPRCp()/0T, Temperature (K)R, Universal Gas Constant, 8.314P, Pressure, kPaP0, reference pressure, eg 101.3 kPaCp, Heat Capacity of air at constant pressurecp, specific heat capacity of air at constant pressureThe Temperature a Parcel of Air would have if it were Expanded or Compressed, Adiabatically, from its Existing Temperature and Pressure to a Standard, near sea level (P=101.3 kPa): Wallace and Hobbs, 1977 ESPM 129 BiometeorologyTair, K265 270 275 280 285 290 295 300 305Height, m050010001500200025003000Potential Temperature, K296 298 300 302 304Pressure, kPa707580859095100Temperature Profiles in the Boundary Layer:Adiabatic Lapse Rate and Potential Temperature9/26/20124ESPM 129 BiometeorologyJune 1, 1999, 1800 UTOak Ridge, TN280 290 300 310 320Pressure, mb7007508008509009501000Virtual Potential TemperatureDry Bulb TemperatureunstableneutralStableProfiles of Air and Potential TemperatureESPM 129 BiometeorologyHeight,mzTunstablethermalstratifiation0zHeight,mHeight,mstablethermalstratificationzT0zHeight,m0zHeight,mHeight,mnear neutralstabilityzTTparcel > TairTparcel < TairFundamentals of Thermal Stratification9/26/20125ESPM 129 BiometeorologyThermal stratification causes the atmosphere to be either buoyant or stable• The atmosphere is neutrally stratified if: • The atmosphere is unstably stratified if: • The atmosphere is stably stratified if:vz0Tzvvz0Tzvvz0TzvUpcoming Features• Describe Adiabatic Processes and Potential Temperature• Start with 1stLaw of Thermodynamics• Normalize 1stLaw by Mass, yielding ‘Specific’ Equation• Substitute Terms with Gas Laws, converting Equation from a function of Cv to Cp• Rearrange Equation so T is on one side and P is on the other• Integrate both sides, yielding equations Ln(T) and Ln(P)• Take anti-log and solve for potential temperatureESPM 129 Biometeorology9/26/20126ESPM 129 BiometeorologyAdiabatic ProcessAn air parcel changes its physical state (either its pressure, volume or temperature) without heat being added or withdrawn from the surrounding environment dQ0. ESPM 129 BiometeorologyNo Heat is Exchanged, But Temperature Can ChangedQ C dT PdVV0CdT PdVVChange in Internal Energy Equals Change in Work Done on the ParcelUnderstanding Adiabatic Compression and Expansion, And its Impact on Temperature Profiles With the First Law of ThermodynamicsChange in internal EnergyChange in Work9/26/20127ESPM 129 BiometeorologyUnderstanding Adiabatic Processes in the Atmosphere by considering Parcels of Air per unit Mass (m), Specific quantitiesqQmwWmuUmcCmcCmvvppdVmdd()1Change in Volume per unit Mass isEquivalent to the change of the inverse in density, ESPM 129 BiometeorologyThe Specific Form of the 1stLaw of Thermodynamicsdq c dT Pd c dT Pdvv ()19/26/20128ESPM 129 BiometeorologydP dP PdmdRTmRdT() ()   11Pd adPRmdT Algebraic Tricks to Express dq as f(T, P) and solve for PdRTPmRTPmESPM 129 BiometeorologyPd adPRmdT dq cRmdT dPv ()Algebraic Tricks to Express dq as f(T, P), things we can measurevdq c dT Pd9/26/20129ESPM 129 Biometeorology()vRdq c dT dPm pvRccmpdq c dT dPChange in Specific Heat, dq, is a function of the Specific Heat Capacity, cp, times a change in Temperature, minusA change in pressure, dP….terms we can MEASUREESPM 129 BiometeorologydqdTcRmcpv p| dq cRmdT dPv ()Isobaric case, dP equals 0Define specific heat capacity at constant P9/26/201210ESPM 129 BiometeorologyAdiabatic Process, dq=00pdq c dT dPpdPcdT dPESPM 129 BiometeorologypdPcdT dPpRTdPcdTmPpdT R dPcTmPmPRTP: PressureV: volumen: number of molesR: Universal Gas Constantm: mass per mole T: absolute air temperature: air density9/26/201211ESPM 129 BiometeorologyppdT R dP R dPTmcPCPdTTRmcdPPTpPPzz0ln lnTRmcPPp0ESPM 129 Biometeorologyln lnTRmcPPp00pRmcTPP0exp(ln ) exp( ln )pTRPmc P9/26/201212ESPM 129 BiometeorologyPotential TemperatureTPPRmcp()/( )0 TPPRCp()/0ESPM 129 BiometeorologyAdiabatic lapse rate, How Temperature Changes with Height0pcdT dPpcdT dPdPdzgHydrostatic EquationChange in Pressure with height is a function of the density ofAir times the acceleration due to gravity, g9/26/201213ESPM 129 BiometeorologyThe dry adiabatic lapse rate, 9.8 K km-1|adiabaticpdT gdz cpdT dPcgdz dzDry Adiabatic Lapse RateESPM 129 BiometeorologyMoist Adiabatic|moist moistspdT gdedzcdT water vapor condenses and latent heat of condensation is released. is the latent heat of vaporization des/dT is the slope of the saturation vapor pressure-temperature curve.9/26/201214Key Points• Define Thermal