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
The Dead Sea is nearly 10x as salty as the ocean, and has a density of about 1.240
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 has a mass of about 5.3 × 1018 kg = 5.3 × 106 Gt = 5.3 million Gt, so one ppmm (part-per-million by mass) weighs 5.3 Gt.
However, atmospheric gas concentrations are customarily expressed in ppmv (parts-per-million by volume,
or molar fraction),
so to calculate the mass of one ppmv requires scaling according to the molecular weight of the gas in question.
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.
400 ppmv CO2† has mass 400 × 8.053 Gt/ppmv = 3221 Gt
Methane:
1 ppmv CH4 (molecular wt 16.044) has mass ~(16/29) × 5.3 Gt = 2.9356 Gt
1.8 ppmv CH4† has mass 1.8 × 2.9356 Gt/ppmv = 5.284 Gt
Meltwater & sea-level:
The oceans cover about 3.618 × 108 km2 (sq-km) = 3.618 × 1014 m2.
A one mm 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.
Calculated another way, 361.8 Gt/mm-SLR × 0.262 mi3/Gt = 94.8 cubic miles per millimeter of sea-level rise.
Melting ~95 cubic miles of grounded ice (= 362 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.
-Dave Burton 3/28/2014, 8/18/2014
†which are the approximate current average atmospheric concentrations of the two gasses: 400 ppmv CO2 and 1.8 ppmv CH4