Meteorological Variables 1. Local right-hand Cartesian coordinate 2. Polar coordinate x y U V W O O East North Up Dynamic variable: Wind

3. Conversion to speed and direction 4. Conversion to U and V

1. Atmospheric pressure P: Force F acting on unit area due to the weight of the atmosphere. 2. Temperature 3. Equation of state, gas law Thermodynamic variables

4. Water vapor pressure, e 5. Mixing ratio, r 6. Specific humidity, q 7. Saturation Saturated water vapor pressure, E

8. Clausius-Clapeyron equation 9. Relative humidity, h 10. Dew-point, the temperature to which air is cooled to become saturated at constant pressure.

The change of enthalpy is more useful in thermodynamics The first law of thermodynamics Work may be represented by Thus, For isobaric process Enthalpy U: internal energy (in joules), p: pressure of the system, (in pascals) V : volume, (in cubic meters) 10. Wet bulb temperature

Wet bulb temperature Since

12. Moist virtual effect Tv: the temperature that dry air would need to have at the given pressure in order to have the same density as moist air, assuming idea gas behavior. 13. Potential temperature Temperature is not conserved. Potential temperature is conserved during adiabatic processes 14. Specific heat at the constant pressure

Statistic representation of turbulence The average could be temporal, spatial, or ensemble average depending on specific dataset. 1. Mean and perturbation

2. Rule of average 3. Reynolds average

covariance variance Standard deviation Correlation coefficient

4. Turbulent kinetic energy (TKE) Mean kinetic energy TKE TKE measures turbulent intensity Convective boundary layer: dominates Shear driven boundary layer: dominates

It is through the boundary layer that a hurricane gets energy. Turbulence Warm ocean surface Heat Friction Water Vapor Momentum Turbulent transport Flux: the amount of flow passes through a unit area per unit time Heat flux, moisture flux, momentum flux

5. Sensible heat flux, Latent heat flux, buoyancy flux Sensible heat flux, SH Specific heat at constant pressure Kinematic sensible heat flux, sh Sensible heat flux, SH z T z T daytimenighttime

Latent heat z 1 2 Latent heat flux, LE Kinematic latent heat flux, le Latent heat flux, LE

Buoyancy flux, Bu Transport by dry turbulent atmosphere Sensible heat flux Transport by moist turbulent atmosphere Buoyancy heat flux

8. Reynolds stress U X Z Shear stress x y z Tensor 6. Frictional velocity

Project 1: (1) Calculating mean wind speed in local cartesian coordinate (u, v, w) at the time interval of 1, 5, 15 minutes. (2) Estimating the momentum fluxes ( ), turbulent intensity ( ), TKE, and frictional velocity at the same time intervals. Note that the first, second, and third rows of the dataset are the horizontal wind speed, wind direction in polar coordinate, and vertical velocity. The data is recorded at 10 Hz.