# Common conversion factors for water, ice, sea-level, air, etc.

Pure (fresh) liquid water has a density of about 1.000 kg/liter, or equivalently 1.000 g/cm3, or 1000 kg/m3 (1.000 metric tonnes), at 4.3°C and 1 atm pressure.

The units are often omitted, so the density of liquid H2O may be stated as simply "1.000".

Ice has a density of about 0.9167

Seawater has a density of about 1.027, and an average salinity of about 35 pptm = 35,000 ppmm = 3.5% by mass.

First year sea-ice has salinity of only about 4-6 pptm, because about 85% of the salt ie expelled when seawater freezes. The Dead Sea has a density of about 1.240 because it is nearly 10× as salty as seawater.

The density of water varies only slightly with temperature & pressure, but if you need more precision various online tables and calculators can give you nearly exact water densities for specific temperatures, pressures & salinities.

1 km = 0.621371 mile,
so 1 km3 (cubic kilometer, or cu-km) = 0.239913 mi3

```1 GT = 1 gigaton = one billion tons
= 109 tons (U.S. tons or "short tons," each 907.185 kg or 2000 lbs)

1 Gt = 1 gigatonne
= 1 Pg = 1 petagram = 1015 grams
= 1000 Tg = 1000 teragrams
= 109 tonnes (metric tons, each 1000 kg or 2204.62 lbs)
= 1012 kg
= 1.1023 GT
= the mass of 1 cubic kilometer of fresh water
= the mass of 1.091 cubic km of ice
= the mass of 0.240 cubic miles of fresh water
= the mass of 0.262 cubic miles of ice

1 cubic mile of ice weighs 1/0.262 = 3.82 Gt
```

The Earth's atmosphere is variously estimated to have a mass of 5.1 to 5.3 × 1018 kg = 5.3 × 106 Gt = 5.3 million Gt, so (using the “5.3” estimate) one ppmm (part-per-million by mass) weighs about 5.3 Gt.

However, atmospheric gas concentrations are customarily expressed in ppmv (parts-per-million by volume, a/k/a molar fraction, µ mol/mol), so to calculate the mass of one ppmv requires scaling according to the molecular weight of the gas in question. (Note: if water vapor is ignored this is properly called the dry molar fraction.)

The average molecular weight of the Earth's atmosphere is 28.966 g/mole (≈29). So, for example:

Carbon Dioxide:
1 ppmv CO2 (molecular wt 44.01) has mass ≈(44/29) × 5.3 Gt = 8.053 Gt, of which 12/44-ths or 2.196 Gt is carbon.
1 Pg = 1 Gt, so 1 PgC (“petagrams carbon”) is contained in (44/12) = 3.667 Gt CO2, and is equivalent to 3.667/8.053 = 0.4553 ppmv CO2 in the atmosphere.
416 ppmv CO2 has mass 416 × 8.053 Gt/ppmv = 3350 Gt.
That much CO2 contains (12/44)×3350 = 914 PgC.

Methane:
1 ppmv CH4 (molecular wt 16.044) has mass ≈(16/29) × 5.3 Gt = 2.9356 Gt.
1.9 ppmv CH4 has mass 1.9 × 2.9356 Gt/ppmv = 5.578 Gt.

Meltwater & sea-level:
The oceans cover about 3.618 × 108 km2 (sq-km) = 3.618 × 1014 m2. A one millimeter global average increase in sea-level requires 1/1000-th of a cubic meter of water for each square meter of ocean surface: 10-3 m3 × (3.618 × 1014) = 3.618 × 1011 m3 of water.
(Note: sea ice is frozen nearly-fresh water, not saltwater, because most of the salt is expelled when seawater freezes.)
A cubic meter of fresh water weighs 1000 kg, so (disregarding the minor salinity/density effects of mixing fresh meltwater with seawater) a one mm increase in sea-level requires about 3.618 × 1014 kg = 361.8 Gt of meltwater.
Ice has a density of about 0.9167, so 361.8 Gt = 394.7 km3, which is 94.7 cubic miles.
Melting ≈95 cubic miles of grounded ice (= ≈361.8 Gt = ≈395 km3) into ≈87 cubic miles of fresh water and adding it to the oceans would raise globally averaged sea-level by ≈1 mm.

Ocean heat content (OHC):
OHC is estimated from temperature measurements by Argo Floats, starting around 2005. The units are usually “zettajoules” (abbreviated ZJ). One ZJ = 1021 joules.
The volume of water in the oceans is about:
1,338,000,000 cubic-km = 1.338 × 109 km3 = 1.338E9 km3
Seawater has an average density of about 1.029 (a bit less near the surface) so 1.338E9 km3 (all the Earth's seawater) masses:
(1.029 × 1.338) × 109 Gt = 1.377E9 Gt = 1.377E21 kg
To calculate how much energy it would take to heat that much water by 1°C, note that the specific heat of seawater at average salinity (35) and temperature (5°C) is about 3992.5 J/kg, meaning that it takes 3992.5 J to warm one kg of seawater by 1°C. So:
It would take (1.377E21 kg) × (3992.5 J/kg) = 5.498E24 Joules = 5498 ZJ to raise the average temperature of the Earth's oceans by 1°C.

-Dave Burton  3/28/2014, 8/18/2014, 5/10/2015, 12/9/2015, 12/13/2016, 2/3/2017, 6/25/2018, 12/23/2018, 1/23/2022, 3/18/2022

IPCC AR5 WGI uses a slightly different figure: 2.12 PgC per ppmv (Prather et al, 2012).

which are the approximate current (2022) average atmospheric concentrations of the two gasses: 416 ppmv CO2 and 1.90 ppmv CH4.

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