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Appendix 1: Symbols
a - average radius of the Earth (constant): 6.37 x 106m
 - acceleration
vector
A - area (also unit area, also wave amplitude, also coefficient
or constant of integration to be solved for per boundary conditions in
Ekman layer theory)
b - constant in Teten’s formula: = 17.27 K-1
B - coefficient (constant of integration) to be solved for per
boundary conditions in, e.g., Ekman layer theory
c - phase speed
C - circulation
Cabsolute - absolute circulation, including contributions
from planetary rotation and from other sources of rotation relative to
the surface of the planet
CAPE - convective available potential energy
CD - drag coefficient
Cearth - circulation resulting from Earth rotation
CFtotal - total centrifugal “force”
cgx - zonal group velocity
cgy - meridional group velocity
cgz - vertical group velocity
cp - specific heat at constant pressure (constant):
1004 J kg-1 K-1 (for dry air)
1952 J kg-1 K-1 (for water vapor)
Cp - phase speed, or speed of propagation, of ocean
waves
Crelative - circulation due to sources of rotary motion
relative to the surface of a planet
cv - specific heat at constant volume (constant):
717 J kg-1 K-1 (for dry air); 1463 J kg-1
K-1 (for water vapor)
cx - zonal phase speed component
 - intrinsic
zonal wave propagation speed
cy - meridional phase speed component
cz - vertical phase speed component
d - channel width
DC - wind directional constancy
 - Eulerian derivative
with respect to variable
 - Lagrangian,
substantial, or material derivative with respect to variable 
 - partial derivative
with respect to variable
Dg/D
- geostrophic Lagrangian derivative with respect to variable
Dh/D
- horizontal Lagrangian derivative with respect to variable
e - vapor pressure
EL - equilibrium level
es – saturation vapor pressure
esi – saturation vapor pressure over ice
f – Coriolis parameter, defined as 
 - force vector
fo - midlatitude reference Coriolis parameter, defined
as 2Ωsin45o
FCoriolis - Coriolis force
Fr - nondimensional Froude number
 - viscous force
vector
g - effective gravity (gravitational acceleration plus centrifugal
effect) (constant): 9.81ms-2 at sea level at equator
g* - gravitation vector
g*o - average gravitational acceleration at sea level
(constant): 9.85 ms-2
G - gravitation constant: 6.673 x 10-11 Nm2kg-2
h - lower boundary height as a function of location (x,y); frontal height
as a function of distance, x; constant in Ekman layer theory  ;
moist static energy
H - scale height  ;
high pressure center; vertical length scale
hm - barrier height
 - unit x-direction
vector in a Cartesian coordinate system
 - unit x-direction
in a rotated Cartesian coordinate system
I - moment of intertia
 - unit y-direction
vector in a Cartesian coordinate system
 - unit y-direction
in a rotated Cartesian coordinate system
 - unit z-direction
vector in a Cartesian coordinate system; wavenumber vector
 - unit z-direction
in a rotated Cartesian coordinate system
k - zonal wavenumber
Km - eddy viscosity
s
- stationary wavenumber
L - length scale; low pressure center
l – meridional wavenumber; ocean wave length
l2 - Scorer parameter
LCL - lifting condensation level
LFC - level of free convection
m - mass; vertical wavenumber
M - mass of the Earth (constant): 5.9742 x 1024 kg;
molecular mass
Mair - mass of a volume of air
Md - average molecular mass for dry air (constant):
28.966g mol-1
Mv - average molecular mass for water vapor (constant):
18.016 g mol-1
n - normally oriented coordinate in a natural coordinate system
N - 
or buoyancy frequency
p - pressure
P - Ertel’s potential vorticity
pd - perturbation, or dynamic, pressure
 - pressure
gradient force vector
pn - pressure of the nth gas in a mixture
po - surface pressure; reference pressure
pz - pressure at height z
q - specific humidity
Q - heat energy
r - mixing ratio; radius of curvature
R - gas constant for a particular gas; radius of curvature
R* - universal gas constant: 8.314 J mol-1 K-1
Rd - gas constant for dry air: R*/Md
= 287 J kg-1 K-1
Re - Reynolds non-dimensional number
RH - relative humidity
Rn - gas constant for the nth gas in a mixture
Ro - Rossby non-dimensional number
rR - Rossby radius of deformation
rs - saturation mixing ratio
Rv - gas constant for water vapor: 461 J kg-1
K-1
 - radial distance
from rotation axis to surface of the Earth at a given latitude
s - tangentially oriented coordinate in a natural coordinate system
 - vector describing
a smooth curve
t - time
T - temperature; time scale; period of oscillation
T1 - constant in Teten’s formula: 273.16 K
T2 - constant in Teten’s formula: 35.86 K
TA - temperature of parcel A
Td - dew point temperature
Tenv - temperature of the environment
To - reference temperature, most commonly a function of z
Too - constant reference temperature
Tparcel - temperature of a parcel
Tparcel, z - temperature of a parcel at height z
Tv - virtual temperature
Tw - wet bulb temperature
Tz - temperature at height z
u - zonal wind component
U - horizontal velocity scale
 - velocity
vector
 - zonal velocity
amplitude
 - velocity
vector in a rotated coordinate system
a
- ageostrophic wind vector
ua - zonal ageostrophic wind component
uearth - velocity vector attributable to motion due
to the rotation of the Earth
ui - velocity at a reference level i
g - geostrophic
velocity vector
h - horizontal
velocity vector
uo - reference zonal velocity component
 - equatorial
zonal velocity amplitude
ux - x-directed component of the velocity
vector
v - meridional wind component
V - wind speed in natural coordinates; volume
 - wind vector
in a natural coordinate system = 
va - meridional ageostrophic wind component
Vg - geostrophic wind in a natural coordinate system
vi - velocity at a reference level i
w - vertical wind component
W - vertical velocity scale
WD - wind direction
wo - amplitude of vertical velocity perturbation
WS - wind speed
x - -directed
Cartesian coordinate value
xo - reference -directed
Cartesian coordinate value
y - -directed Cartesian coordinate
value
yo - reference -directed
Cartesian coordinate value
z - -directed Cartesian coordinate
value; height; vertical coordinate in a natural coordinate system
Z - geopotential height
zo - reference -directed
Cartesian coordinate value
 - angle; specific volume; phase constant
for simple harmonic motion
 - meridional gradient of Coriolis
parameter  ;
ocean wave phase speed constant of proportionality
 - perturbation
or variation
 - change or
difference
 - angle subtended
through a curve s,
the path taken in the tangential direction in the natural coordinate system
 - frontal slope
in Margules formula; ratio of molecular mass of dry air to molecular mass
of water vapor
 - latitude;
smooth differentiable scalar function; phase of a simple harmonic oscillator
 - geopotential
 - normal unit
vector in a natural coordinate system
 - wavelength
 - dynamic viscosity
 - kinematic viscosity:
1.5 x 10-5 m2s-1 (Earth atmosphere),
1.0 x 10-6 m2s-1 (Earth ocean); frequency
 - intrinsic
frequency of oscillation
π - pi (constant): 3.14159
 - potential
temperature; angle of rotation of a pendulum
o
- amplitude of angular rotation of pendulum
parcel,
z - potential temperature of a parcel at height z
w
- wet bulb potential temperature
z
- potential temperature of air at height z
 - density
o
- surface density; reference density, most commonly a function of z
oo
- constant reference density
i
- density at a reference level i
n
- density of nth gas in a mixture
parcel,
z - density of a parcel at height z
v
- density of water vapor contained in a volume of air
z
- density at height z
 - buoyancy force
 - stress vector;
tangentially directed axis in a natural coordinate system
 x
- x-directed stress vector component
y
- y-directed stress vector component
' - perturbed ,
where is any variable or operator
 - averaged ,
where is any variable or operator
L - variable or parameter
in a defined lower layer in a two layer model
U - variable or parameter
in a defined upper layer in a two layer model
 - angular velocity
Ω - angular velocity of the Earth’s rotation (constant): 7.292
x 10-5 s-1
 - deviation
angle of the wind from the terrain fall line
 - vorticity
earth
- vorticity due to the Earth's rotation, f
g
- geostrophic vorticity
go
- geostrophic vorticity at the surface
 - vorticity
on a constant potential temperature surface, isentropic vorticity
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