Question

What difference in UV energy in units of W/m² made it to the surface of Antarctica in September 2018 vs January 2018?

The average amount of ozone above Antarctica was ~300 DU for January and ~100 DU for September that year.

Please assume the average energy at 200-300 nm from the sunlight in the stratosphere is ~10 W/m² and the molecular cross section of ozone over this range is 1.10 x 10^-18 cm²/molecule.

Please give your answer in W/m² (but do not write W/m²).

Answer 1

1 DU (Dobson unit) is equal to 2.687 x 10²⁰ molecules/m²

so, 100 DU = 2.687 x 10²² molecules/m²

300 DU = 8.061 x 10²² molecules/m²

now, molecular cross section of ozone is: 1.10 x 10^-18 cm²/molecule = 1.10 x 10^-22 m²/molecule

Absorption of the radiation will follow the exponential trend,

where x is the thickness of the Ozone layer

here, for 100 DU =

I_o = 10 W/m²

so, I = 10e^-2.9557 = 0.5204 W/m²

this is the energy received per second per m² in September.

For 300 DU (January),

so, I' = 10e^-8.867 = 0.001409 W/m²

therefore, the difference in energy received between September and January is: I - I' = 0.5190 W/m².