Columnar density ρ ρ A is closely related to the vertically averaged volumetric density ρ ρ ¯ ¯ as ρ ρ ¯ ¯ = ρ ρ A Δ Δ z , where Δ Δ z = ∫ ∫ 1 d z ; ρ ρ ¯ ¯ , ρ ρ A , and Δ Δ z have units of, for example, grams per cubic metre, grams per square metre, and metres, respectively.