# Definitions

Many algorithms can be applied exactly the same to a variable even though it may have different dimension dependencies. For instance, a density conversion can be the same algorithm for either density {}, density {time}, density {latitude,longitude}, density {time,vertical}, etc. The algorithm is just applied element-wise for each element in the dimensions that density depends on. Such leading dimensions that can be handled element-wise are captured by a ‘:’ in the variable reference in the definitions below. Any dimensions that are significant for the conversion (for instance, the vertical dimension when integrating a vertical profile to a total column) will still be mentioned explicitly and will map to an index in the symbol used for the quantity (e.g. $$\nu(:,i)$$). If an algorithm has variables with a ‘:’ in the dimension specification then the algorithm will contain a description of which combination of dimensions are supported for ‘:’.

## Constants

symbol

name

unit

value

$$a$$

WGS84 semi-major axis

$$m$$

$$6378137.0$$

$$b$$

WGS84 semi-minor axis

$$m$$

$$6356752.314245$$

$$c$$

speed of light

$$\frac{m}{s}$$

$$2.99792458\cdot10^{8}$$

$$\frac{1}{f}$$

WGS84 inverse flatting

$$298.257223563$$

$$g_{0}$$

mean earth gravity

$$\frac{m}{s^2}$$

$$9.80665$$

$$g_{e}$$

earth gravity at equator

$$\frac{m}{s^2}$$

$$9.7803253359$$

$$g_{p}$$

earth gravity at poles

$$\frac{m}{s^2}$$

$$9.8321849378$$

$$GM$$

WGS84 earth’s gravitational constant

$$\frac{m^3}{s^2}$$

$$3986004.418\cdot10^{8}$$

$$k$$

Boltzmann constant

$$\frac{kg m^2}{K s^2}$$

$$1.38064852\cdot10^{-23}$$

$$N_A$$

$$\frac{1}{mol}$$

$$6.022140857\cdot10^{23}$$

$$p_{0}$$

standard pressure

$$Pa$$

$$101325$$

$$R$$

universal gas constant

$$\frac{kg m^2}{K mol s^2}$$

$$8.3144598$$

$$T_{0}$$

standard temperature

$$K$$

$$273.15$$

$$\omega$$

WGS84 earth angular velocity

$$rad/s$$

$$7292115.0\cdot10^{-11}$$

## Molar mass

The following table provides for each species the molar mass $$M_{x}$$ in $$\frac{g}{mol}$$.

See the documentation on the HARP data format for a description of all species.

name

molar mass

dry air

28.9644

BrO

95.9034

BrO2

111.9028

CCl2F2

120.9135

CCl3F

137.3681

CCl4

153.822

CF4

88.00431

CHClF2

86.4684

CH3Cl

50.48752

CH3CN

41.05192

CH3OH

32.04186

CH4

16.0425

CO

28.0101

COF2

66.0069

COS

60.0751

CO2

44.0095

C2H2

26.0373

C2H2O2

58.036163

C2H6

30.0690

C2H3NO5

121.04892

C3H8

44.09562

C5H8

68.11702

ClNO3

97.4579

ClO

51.4524

HCHO

30.026

HCOOH

46.0254

HCN

27.0253

HCl

36.4609

HF

20.006343

HNO2

47.013494

HNO3

63.0129

HNO4

79.0122

HOCl

52.4603

HO2

33.00674

H2O

18.0153

H2O_161

1.00782503207 + 15.99491461956 + 1.00782503207

H2O_162

1.00782503207 + 15.99491461956 + 2.0141017778

H2O_171

1.00782503207 + 16.99913170 + 1.00782503207

H2O_181

1.00782503207 + 17.9991610 + 1.00782503207

H2O2

34.01468

IO

142.903873

NH3

17.03056

NO

30.00610

NOCl

65.4591

NO2

46.00550

NO3

62.0049

N2

28.01340

N2O

44.0129

N2O5

108.0104

OClO

67.4518

OH

17.00734

O2

32.000

O3

47.99820

O3_666

15.99491461956 + 15.99491461956 + 15.99491461956

O3_667

15.99491461956 + 15.99491461956 + 16.99913170

O3_668

15.99491461956 + 15.99491461956 + 17.9991610

O3_686

15.99491461956 + 17.9991610 + 15.99491461956

O4

63.9976

SF6

146.0554

SO2

64.0638