A two-look TIR radiometer views the same point on the Earth€™s surface at nadir and at 60 degrees from nadir. The brightness temperature of the detected radiation is T₁and T₂respectively. By assuming that the surface is a black body of temperature T_b, the atmosphere has a uniform temperature T₁, and that the Rayleigh€“Jeans approximation is valid, show that

and hence calculate T_b if T₁ = 274.0 K,T₂ = 269.0 K and T₀ = 265.0 K. Ignore any effects arising from the Earth€™s curvature.

(i) Calculate the sensitivity of your answer to the assumed value of T₀ and to the measured value of T₁.

(ii) Comment on the reasonableness or otherwise of the simplifying assumptions that have been made in deriving your answer.

(T, To) - +To