Units and Constants Useful In Meteorology





Fundamental Units

Quantity

Name of unit

Abbreviation

Length
meter
m
Mass
kilogram
kg
Time
second
s
Electrical Current
ampere
A
Temperature
kelvin
K


Derived Units

Quantity

Name of unit

Symbol

SI Units

Force
newton
N

kg m s-2
Pressure
pascal
Pa

N m-2 = kg m-1 s-2
Energy
joule
J

kg m2 s-2
Power
watt
W

J s-1 = kg m2 s-3

Electrical Potential Difference

volt
V

W A-1 = kg m2 s-3 A-1

Electrical Charge

coulomb
C

A s

Electrical Resistance

ohm
W

V A-1 = kg m2 s-3 A-2

Electrical Capacitance

farad
F

A s V-1 = kg-1 m-2 s4 A2
Frequency
hertz
Hz

s-1
Sound Level
decibel
dB

10 log (p1/p2)

Celsius Temperature

degree
°C

K - 273.15

Temperature Interval

degree

deg or °

either K or °C



Useful Unit Convertions

Quantity

English

SI

Velocity

1 mph; 1 knot

0.45 m/s; 0.514 m/s

Temperature

°F

(°F - 32)(5/9) = °C

Length

39.4 in

1 m

Pressure

1 psi

6895 Pa

Mass

1 lb

0.45 kg

Energy

1 ft lb

1.36 J

Volume

1 gal

3.8 x 10-3 m3


Standard Atmosphere

1 atm

1013.25 mb; 760 mmHg; 29.921 inHg; 14.7 lb in-2


Other Units

Quantity

Name of unit

Symbol

Fundamental Units

Volume
liter
l

10-3 m3
Pressure
millibar

mbar or mb

102 Pa



Decimal Multiples of Units

Multiple

Prefix

Symbol

10-1
deci
d
10-2
centi
c
10-3
milli
m
10-6
micro
m
10-9
nano
n
10-12
pico
p
10-15
femto
f
10-18
atto
a
101
deca; deka
da
102
hecto
h
103
kilo
k
106
mega
M
109
giga
G
1012
tera
T


Useful Physical Constants

Name of the Constant

Abbreviation

Value and Units

Universal Gas Constant

R*

8.3143 x 103 J K-1 molecule-1

Boltzmann's Constant

k

1.381 x 10-23 J K-1 molecule-1

Avogadro's Number

NA

6.022 x 1023 mol-1

Stefan-Boltzmann Constant

s

5.6696 x 10-8 W m-2 K-4

Planck's Constant

h

6.6262 x 10-34 J s

Velocity of Light

c

2.998 x 108 m s-1

Permittivity of Vacuum

eo

8.85 x 10-12 C2 N-1 m-2

Average Radius of the Earth

RE

6.37 x 106 m

Mean Gravity at Earth's Surface

go , g

9.81 m s-2

Angular Velocity of Rotation of the Earth

W

7.292 x 10-5 rad s-1

Average Distance from the Center of the Sun to the Center of the Earth

d , do

1.50 x 1011 m

Solar Irradiance on a Perpendicular Plane at the mean Earth-Sun Distance

So

1.367 x 103 W m-2

Average Molecular Weight of Dry Air

Md

28.97

Gas Constant of Dry Air
Rd

287 J K-1 kg-2

Density of Dry Air at 0°C and 1000mb

rd

1.275 kg m-3

Specific Heat of Dry Air at Constant Pressure

cpd

1004 J K-1 kg-1

Specific Heat of Dry Air at Constant Volume

cvd

717 J K-1 kg-1

Thermal Conductivity of Dry Air at 0°C
k

2.40-2 J m-1 s-1 K-1

Molecular Weight of Water

Mw

18.016

Gas Constant for Water Vapor

Rv

461 J K-1 kg-1

Density of Liquid Water at 0°C

r w

1.00 x 103 kg m-3

Density of Ice at 0°

r i

0.917 x 103 kg m-3

Specific Heat of Water Vapor at Constant Pressure

cpv

1952 J K-1 kg-1

Specific Heat of Water Vapor at Constant Volume

cvv

1463 J K-1 kg-1

Specific Heat of Water Vapor at 0°C

cw

4218 J K-1 kg-1

Specific Heat of Ice at 0°C

ci

2106 J K-1 kg-1

Enthalpy (Latent Heat) of Vaporization of Water at 0°C

lv

2.50 x 106 J kg-1

Enthalpy (Latent Heat) of Vaporization of Water at 100°C

lv

2.25 x 106 J kg-1

Enthalpy (Latent Heat) of Fusion of Water at 0°C

lf

3.34 x 105 J kg-1

Enthalpy (Latent Heat) of Sublimation of Water at 0°C

ls

2.83 x 106 J kg-1


An asterisk (*) denotes other abbreviations. Click on them to see other common abreviations used.

List of Other Abbreviations

Abbreviation(s)

Meaning

a

Radius of the Earth; Acceleration

b

Buoyancy

c

Phase Speed of a Wave

cpd

Specific Heat of Dry Air at Constant Pressure

cpv

Specific Heat of Water Vapor at Constant Pressure

cvd

Specific Heat of Dry Air at Constant Volume

cw

Specific Heat of Liquid Water

e

Internal Energy Per Unit Mass or Vapor Pressure

es

Saturation Vapor Pressure

f

Coriolis Parameter (=2W sinf)

g

Mangnitude of Gravity; Antenna Gain

g (*)

Gravity Vector

g*

Effective Gravitational Acceleration

h

Specific Enthalpy; Effective Pulse Length

i

Square Root of Negative One

i (*)

Unit Vector Along the x-axis

j (*)

Unit Vector Along the y-axis

k (*)

Unit Vector Along the z-axis

k

Zonal Wave Number

l

Mixing Length; Meridional Wave Number

m

Mass; Vertical Wave Number; Planetary Wave Number

mv

Molecular Weight of Water

n

Distance in Direction Normal to a Parcel Trajectory; Meridional Index for Equatorial Waves; Refractive Index

n (*)

Unit Vector Normal to a Surface

p

Pressure

po; ps

Standard Constant Pressure; Surface Pressure in s Coordinates

pr

Received Power

pt

Transmitted Power

q

Specific Humidity; Quasi-geostrophic Potential Vorticity; Water Vapor Mixing Ratio

qs; ws

Saturation Mixing Ratio

r

Radial Distance in Spherical Coordinates; Range to Target

r (*)

A Position Vector

s

Generalized Vertical Coordinates; Distance Along a Parcel Trajectory; Specific Entropy; Dry Static Energy

t

Time

t (*)

Unit Vector Parallel to a Parcel Trajectory

u*

Friction Velocity

u

x-component of Velocity (Eastward); Specific Internal Energy

v

y-component of Velocity (Northward); Specific Volume (may also be written as a)

w

z-component of Velocity (Upward)

w*

Vertical Motion in Log-Pressure System

x

Eastward Distance

y

Northward Distance

z

Upward Distance (Usually From Surface Of The Earth)

z*

Vertical Coordinate in Log-Pressure System

A

Area

B

Magnetic Field; Convective Available Potential Energy (CAPE)

C

Circulation

Cd

Surface Drag Coefficient

DE

Depth of Ekman Layer

Di

Drop Diameter

E

Electric Field; Evaporation Rate

F

Irradiance

F (*)

Friction

G

Universal Gravitational Constant; Zonal Force

H

Scale Height; Enthalpy

J

Heating Rate Per Unit Volume

K

Total Horizontal Wave Number; Kinetic Energy

Km

Eddy Viscosity Coefficient

L

Radiance; Angular Momentum

M

Total Mass; Mass in Convergence in Ekman Layer; Absolute Zonal Momentum; Angular Momentum

Mv

Molecular Weight of Water

N

Buoyancy Frequency; Number Density; Refractivity

P

Available Potential Energy; Precipitation Rate; Ertel Potential Vorticity

Q (*)

Q Vector

Q

Heating Rate

R

Gas Constant for Dry Air; Distance From the Axis of Rotation of the Earth to a Point on the Surface of the Earth; Diabatic Energy Generation Rate

Rmax

Maximum Unambiguous Range

R (*)

Vector in the Equatorial Plane Directed from the Axis of Rotation

R*

Universal Gas Constant

S

Entropy

So

Solar Irradiance

Sp

-Tln T /p, Stability Parameter in Pressure Coordinates

T

Absolute Temperature

U

Horizontal Velocity Scale; Internal Energy

U (*)

Three Dimensional Velocity Vector

V

Speed in Natural Coordinates; Volume

Vr

Radial Velocity

Vmax

Maximum Unambiguous Velocity

V (*)

Horizontal Velocity Vector

W

Working Rate; Vertical Motion Scale

X

Zonal Turbulent Drag Force

Z

Geopotential Height; Radar Reflectivity

a

Specific Volume (may also be written as v); Albedo

b

Scattering Coefficient; df/dy, Variation of the Coriolis Parameter with Latitude; Angular Direction of the Wind

e

Efficiency; Rate of Frictional Dissipation; Thermal Expansion Coefficient of Water; Emissivity; Ratio of Molecular Weights

g

Cp/Cv, Ratio of Specific Heats; T/z, Environmental Lapse Rate

h

Vertical Component of Absolute Vorticity; Weight Function for Heating Profile

j

Latitude; Vertical Beam Width

k

Absorption Coefficient; R/Cp, Ratio of Gas Constant to Specific Heat at Constant Pressure; Rayleigh Friction Coefficient

l

Wavelength; Longitude, Positive Eastward

m

Dynamic Viscosity

n

Frequency; Angular Frequency; Kinematic Viscosity

q

Potential Temperature; Angle; Horizontal Beam Width

q'

Potential Temperature Deviation (may also be written as Q)

qe

Equivalent Potential Temperature

r

Density

s

-a ¶q/¶p, Stability Parameter In Isobaric Coordinates; -p/ps, Vertical Coordinate System in s System; Density in Isentropic Coordinates; Standard Deviation; Backscattering Cross-section; Spectrum Width; Surface Tension

sa

Absorption Cross-Section

ss

Scattering Cross-Section

t

Optical Depth; Optical Thickness; Optical Path Length; Pulse Duration

td

Diffusive Time Scale

tE

Eddy Stress

to

Surface Stress

w

Vertical Velocity (dp/dt) in Isobaric Coordinates; Angular Frequency

w (*)

Vorticity Vector

y

Horizontal Streamfunction

z

Vertical Component of Relative Vorticity

za

Vertical Component of Absolute Vorticity

C

Geopotential Tendency; Meridional Streamfunction

Ci

Ozone Mixing Ratio

G

-dT/dz, Lapse Rate of Temperature

Gd

g/Cp Dry Adiabatic Lapse Rate

Gs

Moist Adiabatic Lapse Rate

F

Geopotential

P

Exner Function

Q

Potential Temperature Deviation (may also be written as q')

W

Solid Angle; Angular Speed of Rotation of the Earth; Angular Speed of Rotation

Wrot (*)

Angular Velocity of the Earth





(*) = (You will also see all vectors written in the following notation. Where in this case the authors just used (A) for the example.)