Numerical Weather Prediction Moistly Thermodynamics

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Numerical Weather Prediction Mo(i)st(ly)
Thermodynamics

• Peter Bechtold and Adrian Tompkins

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Clouds - why are they important?
Clouds are a common atmospheric feature and cover
large parts of the globe
Cloud Cover from ISCCP 2000/2001
95 80 65 50 35 20 0
What is the mean coverage?
Latent heat release or consumption occur either
directly in clouds or in the precipitation
produced in them.
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Clouds in GCMs How to define the conserved
quantities during ascent/descent, mixing, and
compute phase changes
There is a huge variety of cloud types
stratocumulus
cirrus
cumulus/cumulonimbus
http//australiasevereweather.com/photography
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Yes we can ! Meteosat 9 versus forecasted
satellite image
e.g. T799 36h forecast from 20080525
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The same for GOES12 versus IFS!
Tropical Cyclone (Gustaf), Tropical continental
convection Stratocumulus ,
Cirrus
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Overview of Clouds/Convection

• Introduction
• Motivation, 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)
• -- Surface fluxes, turbulence, mixing and
  clouds
• Exercise Classes (1 afternoon, Peter and Richard)

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Moist Thermodynamics
Brief Overview of what we presume you are
familiar with, and an introduction to
thermodynamic charts The great Belgian
tradition Thermodynamique de latmosphere Dufou
r and v. Mieghem (1975) For simplified
Overview Rogers and Yau (1989) A short course
in cloud physics Thermodynamics and Kinematics
K. A. Emanuel (1994) Atmospheric Convection
And a Book to appear soon Maarten Anbaum (2009)
A short course in atmospheric physics
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Moist ThermodynamicsIdeal 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
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Pressure, partial pressures and gas law for moist
air
Partial pressures add if both gases occupy same
volume V. Nx are the mol masses
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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 !)
Heat supplied by diabatic process
Change in internal Energy
Work done by Gas
Specific Heat at constant volume
Can write as
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First law of thermodynamics Enthalpy and
Legendre transformation
Changing variables
Special processes Adiabatic Process dQ0 or
better ds0
Special significance since many atmospheric
motions can be approximated as adiabatic
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Enthalpy and flow process
velocity
In isentropic (adiabatic) flow
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Summary Potentials and Maxwell relations
Internal Energy
Enthalpy
Helmholtz free Energy Gibbs
free Energy
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Conserved Variables
Using enthalpy equation and integrating, obtain
Poissons equation
What is the speed of sound?
Conserved in dry adiabatic motions, e.g. boundary
layer turbulence
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Humidity variablesThere are a number of common
ways to describe vapour content etc
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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
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Humidity variablesHow to define moist
quantities and how to switch from mixing ratio
to specific humidity.
For any intensive quantity we have
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Virtual temperature Tv
It describes the temperature required for dry
air would 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
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The Clausius-Clapeyron equation

• with av gtgt aw, and the ideal gas law avRvT/es

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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 T0273 K
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Meteorological energy diagrams
Total heat added in cyclic process
Pressure
T
Dry adiabatic motion
q
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Tephigram (II)
Saturation specific humidity
Saturation mixing ratio
Function of temperature and pressure only
tephigrams have isopleths of rs
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Using a Tephigram
At a pressure of 950 hPa Measure T20 oC r10
gkg-1
plot a atmospheric sounding
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Enthalpy and phase change
Have we been a bit negligeant ? Yes, more
precisely
Divide by md (or mdmv) and assume adiabatic
process
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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!!!
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Ways of reaching saturationExpansion (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.
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Ways of reaching saturationExpansion (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
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Tephigram (III)
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parcel mixing ratio5g/kg
Expansion, (adiabatic process) gives condensation
temperature
Cooling (Isobaric process) gives dew point
temperature
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Moist Adiabat
Wet Bulb Temperature
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Raise parcel pseudoadiabatically until all
humidity condenses and then descend dry
adiabatically to reference pressure
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Summary Conserved Variables
In HYDROSTATIC ATMOSPHERE dry static energy
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Last not least how to compute numerically
saturation (adjustment)
given T, q if q gt 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 !!)
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great guest beers
Station
If the Weather is nice, dont forget to take a
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RISK Salsa 19.30 lessons 5/9, free dancing
after 2130 Tuesday (upstairs) International
drinks