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Global Guide to Tropical Cyclone Forecasting:
Chapter 9: Ready Reckoner

9.7 DERIVED PARAMETERS

9.7.1 Definition of Terms

b empirical constant.
cg gravity wave phase speed.
cp specific heat of dry air at constant pressure.
c1, c2 empirical constants.
e base of natural logarithm.
f Coriolis parameter.
h,H atmospheric scale height.
I inertial frequency.
k unit vector perpendicular to the earth surface.
L latent heat of condensation.
Lr Rossby radius of deformation.
ln natural logarithm.
Ma absolute angular momentum.
N Brunt Vaisala frequency, total number in population sample.
p air pressure.
pc central (minimum) pressure of a tropical cyclone.
pn representative environmental pressure for a tropical cyclone.
q specific humidity.
R universal gas constant.
Rd gas constant for dry air.
Ro Rossby number.
r radius.
rm radius of maximum winds.
T temperature.
t time.
u wind component, either zonal or radial.
V velocity.
v wind component, either meridional or azimuthal.
vg geostrophic wind.
vm maximum wind speed.
x empirical parameter.
z height above the earth surface.
delta.gif (919 bytes) gradient operator.
theta2.gif (927 bytes) partial derivative.
over.gif (56 bytes) overbar denotes mean.
! factorial.
rvort.gif (880 bytes) relative vorticity.
oval.gif (939 bytes) potential temperature.
oval.gif (939 bytes)E equivalent potential temperature.
upy.gif (863 bytes) latitude, azimuthal angle.
airden.gif (893 bytes) air density.
sumcon.gif (907 bytes) summation convention.
theta.gif (70 bytes) standard deviation.
hshoe.gif (98 bytes) earth angular velocity.

 

9.7.2 Derived Parameters

Angular Momentum:

where f0 is evaluated at the cyclone centre (Holland, 1983).

Brunt Vaisala Frequency (Static Stability):

Coriolis Parameter:

Divergence:

Equation of State:

Equivalent Potential Temperature:

 

Inertial Frequency (Inertial Stability):

Mean:

Poisson Distribution: The discrete probability distribution

which has the properties of mean= upy.gif (863 bytes)and standard deviation,theta.gif (846 bytes) =upy.gif (863 bytes)½.

Potential Temperature:

Rossby Number:

Rossby Radius of Deformation:

Standard Deviation:

Thermal Wind:

Vorticity:

Wind Balance:

For cyclones, the positive (negative) root is used in the northern (southern) hemisphere.

Wind Profiles: (Holland, 1980)

Wind/Pressure Relationships (ms-1):

Note that the Fletcher (1955) formulation has an error in it and will overpredict wind speeds (Myers, 1957).

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