Question

The main source of water vapor to the atmosphere is evaporation. The main sink for water vapor is precipitation. If the total mass of water vapor in the atmosphere is 1.3x10¹⁶ kg, and global mean precipitation rate to the Earth’s surface is 0.2 cm/day. What is the mean lifetime of water vapor in the atmosphere? What does this imply for the lifetime of any highly soluble particles or gases in the atmosphere?

Answer 1

total surface area of earth = π x d²

d = diameter of earth = 12,742 km = 12742000m

area =  π x (12742000m)² = 5.1 x 10¹⁴ m²

volume per day precipitation = area x height = 5.1 x 10¹⁴ m² x 0.002 m = 1.02 x 10¹² m³/day

mass of this precipitate = density x volume = 1000 kg/m³ x 1.02 x 10¹² m³/day = 1.02 x 10¹⁵ kg/day

total vapour = 1.3 x 10¹⁶ kg

average lifetime = mass / precipitation rate = 1.3 x 10¹⁶ kg / 1.02 x 10¹⁵ kg/day = 12.75 days

average mean life time = 12.75 days

it implies that whatever the soluble particles are present in atmosphere will get dissolved in the vapour and will be precipitated with the water vapour and they can maximum stay for 12.75 days at an average