INTRODUCTION
TO PHYSICAL METEOROLOGY
ATMO
451/551
Course
Outline
I. Introduction and Basic Concepts
Composition - gases and particles
Gravitation - Newton's law, g, satellite orbits
Mass density, r
Barometers and the concept of pressure
Hydrostatic equation
Gas law
Scale heights
II. Gases
Major Species - N2, O2
Residence Time
Importance of Biosphere
CO2 and the carbon cycle
Water vapor - Physical properties of water
- Evaporation and condensation
- Saturation vapor density, pressure
- Clausius-Clapeyron relation
- Relative humidity
- Mixing ratios, etc.
Ice - Physical properties
- Ice saturation relative to water
- Electrical properties
Trace Gases - Basic chemistry
Photochemistry
2-body reactions
3-body reactions
Chemistry of trace constituents, O3 and NOx
Examples: Photochemical Smog - urban, natural
Ozone - interactions with UV, ozone hole, etc.
Temperature vs altitude, "spheres" and "pauses"
III. Kinetic Theory and Transport
Probability-basic ideas
Distribution functions
Solid angle
Basic assumptions
Ideal gas law
Temperature in kinetic theory
Internal energy
Boltzmann distribution
Thermal escape phenomena, exosphere
Free - path concepts
collision cross-section
collision frequency
Free - path distributions
mean free path
Transport coefficients
Diffusion
Thermal conduction
Dynamic viscosity
Fluxes of mass and heat
Random walk and diffusion
IV. Vector analysis - review
Operator - gradient, divergence, and curl
Vector identities
Flux integrals
Line integral
Divergence theorem
Example: Archimedes principle
Stokes theorem
Continuity equation for a fluid
Time-dependent diffusion equations - mass and heat
Steady-state solutions
Examples: Evaporation
Thermal diffusion cloud chamber
Drop growth equation
V. Atmospheric Aerosol
Sources and characteristics of atmospheric particles
Size distributions - linear and log (radius)
Cumulative distributions
Various integrals and examples
Inverse power (or Junge) distribution
Gaussian distribution
Short review of classical mechanics
Newton's laws of motion
Impulse - momentum theorem
Work - energy theorem
Small sphere falling in air
stopping distance terminal velocity
relaxation time mobility
Diffusion coefficient of particles
Langevin integral of equation of motion
Methods of measuring particle size distributions
Nuclepore filters
Electrical mobility analyzers
Particles in Curvilinear Flow
Equation of motion
Processes in filtration – diffusion and impaction
Collection efficiency
experimental data
Stokes number
Examples: aircraft icing
fog harvesting
Relative diffusion coefficient
Monodisperse coagulation equation
Polydisperse coagulation
Transport of mass through the size distribution
Removal processes
VI. Kinematics of Fluids
Tangential shear stress and the definition of a fluid
Position, velocity, and acceleration vectors
Eulerian and Lagrangian derivatives
Rotation and vorticity
Decomposition of general fluid motion
Irrotational flow - Laplaces equation
Example - motion of ideal fluid past a sphere
Forces on a fluid parcel - surface and body
General condition for hydrostatic equilibrium
VII. Dynamics of an Ideal Fluid
Equation of motion and boundary conditions
Cartesian coordinates
Curvilinear coordinates
Integrals of the equation of motion
Bernoulli's equation - incompressible fluid
- compressible fluid
Vorticity equation
VIII. Atmospheric Acoustics
Basic assumptions, adiabatic perturbation
Wave equation
Solutions of a wave equation, d'Alembert's method
One-dimension
Three-dimensions
Velocity of sound
Acoustic refraction and Snell's law
Acoustic trajectory equations
Acoustic anemometer/thermometer
IX. Real Fluids
Laminar vs. turbulent flow
Stresses and Newtonian hypothesis
Equation of motion
Vorticity equation
Similarity and modeling
Reynolds number
Examples - low Re flow
Poiseuille flow
Flow past a solid sphere
Stoke's law
Flow at high Re
Non-dimensional drag coefficient - low Re
- high Re
Prandtl boundary layer hypothesis
Solving problems at high Re.
X. Turbulent Fluids (Optional)
Examples of motion
Mean motion - averaging interval
Euler equation to form of Navier-Stokes
Reynolds stresses
Isotropic-approximation, eddy viscosity, etc.
XI. The Sun and the Earth's Radiation Budget
Structure of the sun
Radiant flux and intensity
Blackbody radiation
Stefan-Boltzmann law, Wien's law
Planck spectral distribution
Solar radiation
Radiation from the Earth and the atmosphere
Lines vs. continuum
Selective emission and absorption
Effective temperature of a planet
Earth's albedo
Radiation budget
XII. Radiative Transfer
Shortwave transport through a thin layer
Scattering and absorption
Extinction coefficient
Extinction cross-section and mean free path
Vertical optical depth
Integral of transport equation
Langley plot
Method of measurement
Analysis
Shortwave optical thickness
Ozone
Turbidity
Angstrom turbidity coefficient and size distribution
Scattering - basics
Extinction plus re-radiation
Scattering plane, scattering angle
Angular distribution, phase function
Size parameter
Rayleigh and Mie scattering
The aerosol and climate
Optical properties of a thin layer
Effect of layer on radiation budget
Equation of transfer with scattering and emission
Integral of equation of transfer
XIII. Scattering from a Single Target
Rayleigh scattering - dimensional analysis
Electromagnetic radiation
Polarizability
Radiation fields
Poynting vector
Polarization - single scattering, skylight
Unpolarized Rayleigh phase function
Refractive index of a gas and molecular polarizability
Rayleigh scattering cross-sections
Rayleigh optical depths
Refractive index of a liquid or solid
Rayleigh scattering from water drops
Radar scattering and absorption cross-sections
Radar back-scattering cross-section
Radar meteorology and applications
Reflectivity factor
Estimates of rainfall
Dual polarization radars
Doppler radars
XIV. Multiple Scattering
Scattering and absorption at large size parameters
Computation of Mie coefficients
Cloud layers
Extinction cross-sections
Photon mean free path
Optical thickness
Single-scattering albedo
Asymmetry factor
Optical properties of deep layers
Two-stream approximation
Scaled optical thickness and scaling relations
XV. Cloud Physics
Vertical stability and convection
Humidity of parcel in an updraft
Condition for an increase in RH
RH vs time for parcel in an updraft with condensation
Drop growth equation-again
Surface tension
Gibbs-Thomson equation
Effects of solute
Köhler curves
Critical supersaturation
Critical radius
Effects of latent heat
Nucleation and growth in an updraft
Rain formation by stochastic coagulation
Bergerson-Findeisen process
Entrainment
XVI. Lightning and Atmospheric Electricity
Overview of the global electric circuit
Fair weather electric fields and conductivity
Thunderstorms as electrical generators
Charge structure of a thunderstorm
Mechanisms of electrification
Inductive
Non-inductive
Lightning
Types and frequency
Flash densities and strike probabilities
Luminous phenomena
Physical properties of return strokes
Mechanisms of damage
Protection
(8/2003)