# Units

The units used in atmospheric science are the Standard International (SI) units. These are essentially the MKS units familiar from introductory physics and chemistry courses. The unit of length is the meter, abbreviated m; that for mass is the kilogram, abbreviated kg; and for time the unit is the second, abbreviated s. The units for velocity then are m s-1. The unit of force is the newton (1 kg m s-2, abbreviated N). Tables 1.1-1.2 show the SI units for some basic physical quantities commonly used in atmospheric science.

The unit of pressure, the pascal (1 Nm-2 = 1 Pa), is of special importance in meteorology. In particular, atmospheric scientists like the millibar (abbreviated mb), but in keeping with SI units more and more meteorologists use the hectopascal (abbreviated hPa, 100 Pa = 1 mb). The kilopascal (1 kPa = 10 hPa) is the formal SI unit and some authors prefer it. One atmosphere (abbreviated 1 atm) of pressure is

1 atm = 1.013 bar = 1013.25 mb = 1013.25 hPa = 101.325 kPa = 101325 Pa

and 1mb = 1 hectopascal = 100 Pa. In some operational contexts and often in the popular media one still encounters pressure in inches of mercury (in Hg) or millimeters of mercury (mmHg); 1 atm = 760.000 mm Hg = 29.9213 in Hg.

The dimensions of a quantity such as density, p, can be constructed from the fundamental dimensions of length, mass, time and temperature, denoted by L, M, T, Temp respectively. The dimensions of density, indicated with square brackets [p], are M L-3. In the SI system the units are kg m-3. Many quantities are pure numbers and have no dimension; examples include arguments of functions such as sine or log. The radian is a ratio of lengths and is considered here to be dimensionless.

Temperature in SI units is expressed in degrees Celsius, e.g. 20 °C; or Kelvin, e.g. 285 K. We say " 285 kelvins" and omit writing the superscript "°" when

1.2 Earth, weight and mass Table 1.1 Useful numerical values

Universal gravitational constant universal gas constant (R*)

Boltzmann's constant (£B)

proton rest mass electron rest mass

Planck's constant speed of light in vacuum

Planet Earth equatorial radius polar radius mass of Earth rotation period (24 h)

acceleration of gravity (at about 45°N)

solar constant

Dry air gas constant (Rd)

molecular weight (Md)

speed of sound at 0 °C, 1000 hPa density at 0 ° C and 1000 hPa specific heat at constant pressure (cp)

specific heat at constant volume (cv)

Water substance molecular weight (Mw)

gas constant for water vapor (Rw)

density of liquid water at 0 °C

standard enthalpy of vaporization at 0 °C

standard enthalpy of fusion at 0 °C

specific heat of liquid water

6.673x10-11Nm2 kg-2 8.3145 JK-1 mol-1 6.022 x1023 molecules mol-1 1.381 x10 -23 J K-1 molecule-1 1.673 x10-27 kg 9.109 x10-31 kg 6.626 x10-34 Js 3.00 x 108ms-1

6378 km 6357 km 5.983 x 1024kg 8.640 x 104 s 9.8067 ms-2 1370 Wm-2

287.0 JK-1kg-1 28.97 g mol-1 331.3ms-1 1.276 kg m-3 1004 J K-1 kg-1 717JK-1 kg-1

18.015 g mol-1

461.5 JK-1kg-1

1.000 x 103 kgm-3

2.500x106 Jkg-1

T = 273.16K, p = 1013.25hPa using degrees kelvin. In operational meteorology we sometimes find temperature expressed in degrees Fahrenheit, e.g. 70 °F.

Each side of an equation must have the same dimensions. This principle can often be used to find errors in a problem solution. The argument of functions such as the exponential has to be dimensionless.