Constants & Conversions for Atmospheric Science

typical density of air at sea level	$\rho_0$	=	1.25 kg m-3
density of water	$\rho_{water}$	=	$10^{3} \, kg \, m^{-3}$
acceleration due to gravity at sea level	g	=	9.81 N kg-1
molecular mass for H2O	Mw	=	18.016 kg kmol-1
effective molecular mass for dry air	Md	=	28.97 kg kmol-1
molecular weight ratio of H2O to dry air	$\varepsilon$	=	Mv / Md = 0.622
universal gas constant in SI units	R*	=	8.3143 J K-1 mol-1
universal gas constant in chemical units	(Rc)*	=	0.0821 L atm K-1 mol-1
gas constant for dry air	Rd	=	287 J K-1 kg-1
gas constant for water vapor	Rv	=	461 J K-1 kg-1
Boltzmann's constant	k	=	$1.38 \times 10^{-23}$ J K-1 molecule-1
Avogadro's number	NA	=	$6.022 \times 10^{23}$ molecules mol-1
specific heat of dry air, constant pressure	cpd	=	1004 J K-1 kg-1
specific heat of dry air, constant volume	cvd	=	717 J K-1 kg-1
specific heat of water vapor	cw	=	4218 J K-1 kg-1
latent heat of vaporization (H2O)	lvo	=	$2.5 \times 10^6$ J kg-1
latent heat of sublimation (H2O)	lso	=	$2.8345 \times 10^6$ J kg-1
latent heat of fusion (H2O)	lfo	=	$3.34 \times 10^5$ J kg-1
mass of the earth	$m_{\oplus}$	=	$5.97 \times 10^{24}$ kg
mass of the earth's atmosphere	me	=	$5.3 \times 10^{18}$ kg
radius of the earth	$r_{\oplus}$	=	$6.37 \times 10^6$ m
mass of an atmospheric column	ma	=	$1.017 \times 10^{4}$ kg m-2
rotation rate of earth	$\Omega$	=	$7.292 \times 10^{-5} s^{-1}$
mass of the sun	$m_{\odot}$	=	$1.99 \times 10^{30}$ kg
radius of the sun	$r_{\odot}$	=	$6.96 \times 10^8$ m
mean earth-sun distance	$R_{\oplus\odot}$	=	$1.50 \times 10^{11}$ m = 1.00 AU
solar constant (solar flux at $R_{\oplus\odot}$)	$F_{\oplus\odot}$	=	1368 W m-2
total luminosity of the sun	$L_{\odot}$	=	$3.85 \times 10^{26}$ W
Average Intensity of the sun	Isun	=	2 $\times$ 107 Wm-2sr-1
Planck's constant	h	=	$6.626 \times 10^{-34}$ J s
universal gravitational constant	G	=	$6.67 \times 10^{-11}$ N m2 kg-2
Stefan-Boltzmann constant	$\sigma$	=	$5.67 \times 10^{-8}$ J s-1 m-2 K-4
Wien's displacement law	$\lambda_{max} T$	=	$2.897 \times 10^{-3}$ m K
Loschmidt number	L	=	$2.69 \times 10^{25}$ molecules m-3
column-integrated terrestrial carbon	510 gigatons (GTC)	=	1 kg m-2
fahrenheit-celsius conversion	TC	=	$\frac{5}{9}\left( T_F - 32 \right)$
Kelvin-celsius conversion	K	=	$^{\circ}C + 273.15$
Dobson unit	1 DU	=	$2.6 \times 10^{16}$ molecules O3 cm-2
	Rd / cp	=	0.286
	g / cp	=	$9.8 \times 10^{-3}$ km-1
	1 m3	=	1000 L
	1 Å	=	10-10 m
	1 day	=	86,400 seconds
	1 atm	=	$1.01325 \times 10^5$ Pa
	1 cal	=	4.1855 J
	$0^{\circ}$C	=	273 K
	$1^{\circ}$ lat	=	60 nautical miles = 111 km = 69 statute miles
	$1^{\circ}$ lon	=	111 km $\times \cos(\mbox{latitude})$
	1 knot	=	1 nautical mph = 1.15 statute mph
	1 m s-1	=	1.9426 knots
	1 mb	=	103 dynes cm-2
	1 sV (Sverdrup)	=	106 m3 s-1
	1 eV	=	96489 Jmol-1

 

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