Numerical Weather Prediction Moist Thermodynamics ECMWF Training Course May 2001 Numerical Weather Prediction Moist Thermodynamics Peter Bechtold and Adrian Tompkins Clouds 3

Can we represent clouds in a GCM ie Can we represent clouds in a GCM ie. Moisture transport and phase changes ? e.g. T799 36h forecast from 20080525 Meteosat 9 versus forecasted satellite image What is the annual global mean cloud cover ?

The same for GOES12 versus IFS! Tropical Cyclone (Gustaf), Tropical continental convection Stratocumulus , Cirrus

Overview of Clouds/Convection ECMWF Training Course May 2001 Overview of Clouds/Convection Introduction Moist thermodynamics Parametrization of moist convection (4 lectures, Peter), Theory of moist convection Common approaches to parametrization including the ECMWF scheme Cloud Resolving Models (1 lecture - Richard) Their development and use as parametrization tools Parametrization of clouds (4 lectures - Richard) Basic microphysics of clouds The ECMWF cloud scheme and problem of representing cloud cover Issues concerning validation Planetary boundary-layer (4 lectures – Martin+Anton) -- Surface fluxes, turbulence, mixing and clouds Exercise Classes (1 afternoon, Peter and Richard) Clouds 3

Moist Thermodynamics Textbooks The great Belgian tradition: “Thermodynamique de l’atmosphere” Dufour and v. Mieghem (1975) Most recent: Maarten Ambaum (2010) “Thermal physics of the atmosphere” For simplified Overview: Rogers and Yau (1989) “A short course in cloud physics” Thermodynamics and Kinematics: K. A. Emanuel (1994) “Atmospheric Convection”

The First and Second Law ----- The First Law of Thermodynamics: Heat is work and work is heat. Heat is work and work is heat Very good! The Second Law of Thermodynamics: Heat cannot of itself pass from one body to a hotter body, Heat cannot of itself pass from one body to a hotter body Heat won't pass from a cooler to a hotter, Heat won't pass from a cooler to a hotter You can try it if you like but you'd far better notter, You can try it if you like but you'd far better notter 'Cos the cold in the cooler will get hotter as a ruler, 'Cos the cold in the cooler will get hotter as a ruler 'Cos the hotter body's heat will pass to the cooler, 'Cos the hotter body's heat will pass to the cooler Good, First Law: Heat is work and work is heat and work is heat and heat is work Heat will pass by conduction, Heat will pass by conduction And heat will pass by convection, Heat will pass by convection And heat will pass by radiation, Heat will pass by radiation And that's a physical law. Heat is work and work's a curse, And all the heat in the universe, Is gonna cooooool down 'Cos it can't increase, Then there'll be no more work And there'll be perfect peace Really? Yeah, that's entropy, maan!

The First and Second Law And its all because of the Second Law of Thermodynamics, which lays down: That you can't pass heat from a cooler to a hotter, Try it if you like but you far better notter, 'Cos the cold in the cooler will get hotter as a ruler, 'Cos the hotter body's heat will pass to the cooler. Oh you can't pass heat, cooler to a hotter, Try it if you like but you'll only look a fooler 'Cos the cold in the cooler will get hotter as a ruler And that's a physical Law! Oh, I'm hot! Hot? That's because you've been working! Oh, Beatles - nothing! That's the First and Second Law of Thermodynamics! Authors: M. Flanders (1922-1975) & D. Swann (1923-1994) From "At the Drop of Another Hat“

Moist Thermodynamics Ideal Gas Law What is definition of ideal gas? Assume that “moist air” can be treated as mixture of two ideal gases: “dry air” + vapour Density Dry air equation of state: Temperature Gas Constant for dry air = 287 J Kg-1 K-1 Pressure Water Vapour equation of state: Vapour pressure vapour density Gas constant for Vapour = 461 J Kg-1 K-1 0.622

Pressure, partial pressures and gas law for moist air Partial pressures add if both gases occupy same volume V. Nx are the mol masses

First law of thermodynamics ECMWF Training Course May 2001 First law of thermodynamics Energy conservation and Heat All quantities are per unit mass (specific) dQ is not a perfect differential, but ds (change in entropie is !) Change in internal Energy Heat supplied by diabatic process Work done by Gas Specific Heat at constant volume Can write as Clouds 3

First law of thermodynamics: Enthalpy and Legendre transformation ECMWF Training Course May 2001 First law of thermodynamics: Enthalpy and Legendre transformation Changing variables Special processes: “Adiabatic Process” dQ=0 or better ds=0 Special significance since many atmospheric motions can be approximated as adiabatic Clouds 3

Enthalpy and flow process ECMWF Training Course May 2001 Enthalpy and flow process velocity In isentropic (adiabatic) flow Clouds 3

Summary :Potentials and Maxwell relations ECMWF Training Course May 2001 Summary :Potentials and Maxwell relations Internal Energy Enthalpy Helmholtz free Energy Gibbs free Energy Clouds 3

ECMWF Training Course May 2001 Conserved Variables Using enthalpy equation and integrating, obtain Poisson’s equation What is the speed of sound? Setting reference pressure to 1000hPa gives the definition of potential temperature for dry air Conserved in dry adiabatic motions, e.g. boundary layer turbulence Clouds 3

ECMWF Training Course May 2001 Humidity variables There are a number of common ways to describe vapour content etc e 1. Vapour Pressure 2. Absolute humidity 3. Specific humidity Mass of water vapour per unit moist air 4. Mixing ratio Mass of water vapour per unit dry air 5. Relative humidity 6. Specific liquid water content 7. Total water content Clouds 3

ECMWF Training Course May 2001 Humidity variables How to define “moist quantities” and how to switch from mixing ratio to specific humidity. For any intensive quantity we have Clouds 3

Virtual temperature Tv It describes the temperature required for dry air, in order to have at the same pressure the same density as a sample of moist air Another way to describe the vapour content is the virtual temperature , an artificial temperature. Definition: By extension, we define the virtual potential temperature, which is a conserved variable in unsaturated ascent, and related to density

The Clausius-Clapeyron equation ECMWF Training Course May 2001 The Clausius-Clapeyron equation water air+water vapour Consider this closed system in equilibrium: T equal for water & air, no net evaporation or condensation Air is said to be saturated For the phase change between water and water vapour the equilibrium pressure (often called saturation water vapour pressure) is a function of temperature only with av >> aw, and the ideal gas law av=RvT/es Clouds 3

The Clausius-Clapeyron equation - Integration ECMWF Training Course May 2001 The Clausius-Clapeyron equation - Integration The problem of integrating the Clausius-Clapeyron equation lies in the temperature dependence of Lv. Fortunately this dependence is only weak, so that approximate formulae can be derived. Nonlinearity has consequences for mixing in convection es0 = 6.11 hPa at T0=273 K Clouds 3

Meteorological energy diagrams Total heat added in cyclic process: rotate to have pressure (almost) horizontal Thus diagram with ordinates T versus ln q will have the properties of “equal areas”=“equal energy” Called a TEPHIGRAM Pressure T Dry adiabatic motion q

Tephigram (II) T q r Saturation specific humidity Saturation mixing ratio pressure Function of temperature and pressure only – tephigrams have isopleths of rs

plot a atmospheric sounding Using a Tephigram At a pressure of 950 hPa Measure T=20 oC r=10 gkg-1 plot a atmospheric sounding

Enthalpy and phase change ECMWF Training Course May 2001 Enthalpy and phase change Have we been a bit negligeant ? Yes, more precisely Divide by md (or md+mv) and assume adiabatic process Clouds 3

Ways of reaching saturation Several ways to reach saturation: Diabatic Cooling (e.g. Radiation) Evaporation (e.g. of precipitation) Expansion (e.g. ascent/descent) All of these are important cloud processes!!! Cooling: Dew point temperature Td Temperature to which air must be cooled to reach saturation, with p and r held constant Evaporation: Wet-bulb temperature Tw Temperature to which air may be cooled by evaporation of water into it until saturation is reached, at constant p Will show how to determine graphically from tephigram

Ways of reaching saturation: Expansion: (Pseudo) Adiabatic Processes As (unsaturated) moist air expands (e.g. through vertical motion), cools adiabatically conserving q. Eventually saturation pressure is reached, T,p are known as the “isentropic condensation temperature and pressure”, respectively. The level is also known as the “Lifting Condensation Level”. If expansion continues, condensation will occur (assuming that liquid water condenses efficiently and no super saturation can persist), thus the temperature will decrease at a slower rate.

Ways of reaching saturation: Expansion: (Pseudo) Adiabatic Processes Have to make a decision concerning the condensed water. Does it falls out instantly or does it remain in the parcel? If it remains, the heat capacity should be accounted for, and it will have an effect on parcel buoyancy Once the freezing point is reached, are ice processes taken into account? (complex) These are issues concerning microphysics, and dynamics. The air parcel history will depend on the situation. We take the simplest case: all condensate instantly lost as precipitation, known as “Pseudo adiabatic process” Pseudo adiabatic process

Remember: Involves an arbitrary “cloud model” Tephigram (III) T q r Pseudoadiabat (or moist adiabat) Remember: Involves an arbitrary “cloud model” pressure

parcel mixing ratio=5g/kg Expansion, (adiabatic process) gives condensation temperature Cooling: (Isobaric process) gives dew point temperature

Moist Adiabat Wet Bulb Temperature

qe Equivalent Potential temperature Te (=315K) Raise parcel pseudoadiabatically until all humidity condenses and then descend dry adiabatically to reference pressure Equivalent Potential temperature conserved in adiabatic motions Parcel at 850 hPa, T=12.5oC r=6 g/kg Te qe (=315K)

Summary: Conserved Variables ECMWF Training Course May 2001 Summary: Conserved Variables Dry adiabatic processes Moist adiabatic processes potential temperature equivalent potential temperature In HYDROSTATIC ATMOSPHERE: dry static energy moist static energy Specific humidity total water specific humidity Clouds 3

Last not least: how to compute numerically saturation (adjustment) ECMWF Training Course May 2001 Last not least: how to compute numerically saturation (adjustment) T,qv T*,qvs(T*) qv given T, q check if q > qs(T) then solve for adjusted T*,q* so that q* = qs(T*) ql = q-qs(T*) using cp dT = -Lv dqs either numerically through iteration or with the aid of a linearisation of qs(T*) (see Excercises !!) Clouds 3

ECMWF Training Course May 2001 A few Unofficial Social Tips… see also www.reading-guide.co.uk For Music listings: pick up “Bla Bla” Gulshan Indian Restaurant Jazz club – live music on Thurs £7 (incl 2 drinks) “Thai corner” Purple Turtle, open until 3am Station If the Weather is nice, don’t forget to take a walk by Thames, off the top of this map, or take a train to Pangbourne or Goring nearby and see the Thames there For London theatre, check out OFFICIAL half-price ticket booth in Leicester Square ARTS cinema at Reading University, Tues/Thurs, see readingfilmtheatre.co.uk “Beijing noodle house” Abbey Ruins, Reading’s (only) historical part! Revolution Iguana: Coffee+cocktails (upstairs) Zero Degrees:Best Pizza and brewery “Sweenie and Todds” Pie Pub Mango Wagamamas (Oracle by canal), Asian noodle Chain Gospoda-Polish Pub, Oxford Street Karaoke on Thursdays “RISK”: Salsa 19.30 lessons £5/9, free dancing after 21:30 Tuesday (upstairs) International drinks Clouds 3