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/cm^{^3}, or 1000 kg/m^{^3} (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 35,000 ppmm = 3.5% by mass.

First year sea-ice has salinity of only about 0.4% to 0.6% by mass, 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 and 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 km^{^3} (cubic kilometer, or cu-km) = 0.239913 mi^{^3}

1 GT = 1 gigaton = one billion tons
     = 10^9 tons (U.S. tons or "short tons," each 907.185 kg or 2000 lbs)

1 Gt = 1 gigatonne = one billion metric tonnes
     = 1 Pg = 1 petagram = 10^15 grams
     = 1000 Tg = 1000 teragrams
     = 10^9 tonnes (metric tons, each 1000 kg or 2204.62 lbs)
     = 10^12 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

Begin revised section... (old version is here)

The Earth's atmosphere has a total dry mass of (5.1352 ±0.0003) × 10^{^18} kg, so one ppmm (part-per-million by mass) weighs about 5.1352 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, as is usually the case, this is more precisely called the dry molar fraction.)
 
The average molecular weight of the Earth's dry atmosphere is 28.966 g/mol (ref). So, for example: ↑

Carbon Dioxide:
1 ppmv CO₂ (molecular wt 44.00940 ±0.00174) has mass ≈(44.0094/28.966) × 5.1352 Gt = 7.8022 Gt, of which (12.01/44.01)^ths or 2.1294 Gt^† is carbon.
1 Pg = 1 Gt, so 1 PgC (“petagrams carbon”) is contained in (44.01/12.01) = 3.6642 Gt CO₂^‡ which is equivalent to 3.6642/7.8022 = 0.46964 ppmv CO₂ in the atmosphere.
430 ppmv CO₂^⹋ has mass 430 × 7.8022 Gt/ppmv = 3355 Gt.
That much CO₂ contains (12.01/44.01)×3355 = 916 PgC. ↑

(Note: for details & confidence intervals see:  https://sealevel.info/PgC_vs_Gt_CO2.html)

Methane:
1 ppmv CH4 (molecular wt 16.044) has mass (16.044/28.966) × 5.1352 Gt = 2.8444 Gt.
1.95 ppmv CH₄^⹋ has mass 1.95 × 2.8444 Gt/ppmv = 5.5465 Gt. ↑

End revised section.
 

Meltwater & sea-level:
The oceans cover about 3.618 × 10^{^8} km^{^2} (sq-km) = 3.618 × 10^{^14} m^{^2}. 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} m^{^3} × (3.618 × 10^{^14}) = 3.618 × 10^{^11} m^{^3} 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 × 10^{^14} kg = 361.8 Gt of meltwater.
Ice has a density of about 0.9167, so 361.8 Gt = 394.7 km^{^3}, which is 94.7 cubic miles.
Melting ≈95 cubic miles of grounded ice (= ≈361.8 Gt = ≈395 km^{^3}) 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 = 10^{^21} joules.
The volume of water in the oceans is about:
1,338,000,000 cubic-km = 1.338 × 10^{^9} km^{^3} = 1.338E9 km^{^3}
Seawater has an average density of about 1.029 (a bit less near the surface) so 1.338E9 km^{^3} (all the Earth's seawater) masses:
(1.029 × 1.338) × 10^{^9} 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, 8/24/2026, 9/1/2026

 

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

^‡ The GCB rounds this to 3.664 Gt CO₂ per PgC.

^⹋ The approximate current (2026) average atmospheric concentrations of the two gasses are 430 ppmv CO₂ and 1.95 ppmv CH₄.

 

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