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Atmospheric Radiation – Lecture 14 PHY2505 - Lecture 14 IR temperature retrieval 1 Atmospheric Radiation – Lecture 14 Line shape – altitude dependence Emission Re-absorption Z n 2 Atmospheric Radiation – Lecture 14 15um CO2 band and temperature of Mars 1 2 3 1 3 2 3 Atmospheric Radiation – Lecture 14 Retrieval methods Even under cloud free conditions, with a noise free radiometer that measures all l, a unique solution for T(z) is not guaranteed With instrument noise and a limited number of l, an infinite numbers of solutions is possible. We want to find a temperature profile that satisfies the RTE and approximates the true profile as closely as possible 4 Atmospheric Radiation – Lecture 14 Three classes of methods Physical methods: Chahine’s method – uses RTE & weighting functions & non-linear iteration (Liou 7.4.3.1) Statistical methods: no RTE (no physics!), regression between radiances and training set of temperature profile solutions - (Liou 7.4.3.2) Hybrid retrievals: – uses RTE and weighting functions and linearisation of the RTE to allow use of matrix inversion ( Liou 7.4.3.2) 5 Atmospheric Radiation – Lecture 14 Physical methods 6 Atmospheric Radiation – Lecture 14 Physical methods: Chahine’s method (Liou 7.4.3.1) Ii Ti(pi) Iterate the relaxation equation 7 Atmospheric Radiation – Lecture 14 Chahine’s method – relaxation equation derivation (Liou 7.4.3.1) Liou equation 7.4.25a Approximate the observed radiance using the mean value theorem Dividing expected by observed: as low dependence on temperature Can approximate by relaxation equation 8 Atmospheric Radiation – Lecture 14 Chahine’s method outline– (Liou 7.4.3.1) 9 Atmospheric Radiation – Lecture 14 Chahine’s method outline– how good is it? 10 Atmospheric Radiation – Lecture 14 Statistical methods – (Liou 7.4.3.2) First operational measurements 11 Atmospheric Radiation – Lecture 14 Hybrid methods – (Liou 7.4.3.2) 12