# Definitions

## Leading dimensions

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 | \(\frac{kg m^2}{K s^2}\) | \(1.38064852\cdot10^{-23}\)
\(N_A\) | Avogadro constant | \(\frac{1}{mol}\) | \(6.022140857\cdot10^{23}\)
\(p_{0}\) | 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