A nadir-viewing instrument on a satellite is used to measure IR radiances in thr

Question

A nadir-viewing instrument on a satellite is used to measure IR radiances in three channels within the 15 nm band of CO 2 with weighting functions that can be approximated by (see figure) W 1(z)= 0.1 km -1 5 km le z le 15 km W 1(z)= 0.1 km -1 15 km le z le 25 km W 1(z)= 0.1 km -1 25 km le z le 35 km and W1=W2=W3=0 elsewhere. The three measured radiances are L 1=53, L 2=39, and L 3=49 mW m-2 sr-1 (cm-1)-1 and the mean frequency of the channels is 700 cm -1. The altitude variation of the Planck function at this mean frequency can be represented by B(z)=b 1F 1(z) + b 2F2(z) + b3F3(z) with basis functions F1(z)=1, F2(z)=z, and F3(z)=z2. Calculate the temperature of the atmosphere at an altitude of 40 km.

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