If the atmospheric microwave absorption coefficient Icirc sup3 varies with height z as Icirc sup3 Iuml Icirc sup2 exp ( Icirc sup2 z), Iuml being the optical thickness of the entire atmosphere, show that the brightness temperature measured by a passive microwave radiometer looking vertically down t...

First plot the points W M and F corresponding to water firstyear and multiyear ice and connect these ...

If the atmospheric microwave absorption coefficient Î³ varies with height z as Î³ = Ï Î²exp (-Î²z),

Question:

If the atmospheric microwave absorption coefficient Î³ varies with height z as Î³ = Ï„ Î²exp (-Î²z), Ï„ being the optical thickness of the entire atmosphere, show that the brightness temperature measured by a passive microwave radiometer looking vertically down through the atmosphere is given by

| a(2)T(2)dz, T(0)exp(-t)+

where the weighting function a(z) is given by

al) — Рехp(-B-)eхp(- теxp(-B-)

Show that a(z) takes its maximum value at (ln Ï„)/Î², and that, for a fixed value of Î², the only effect of changing Ï„ is to shift a(z) along the z-axis without change of scale. Interpret this result.