Mathematical aspects of the meteorological interpretation of satellite hyperspectral infrared measurements part I: statement of the inverse problem for estimation of the cloud absorption vertical profile

Abstract

ABSTRACTSatellite high spectral resolution infrared measurements provide information for cloud vertical characterization when optically semi-transparent clouds at high altitude cover cloud layers at lower altitudes. It is an important issue because such atmospheric conditions are common and clouds are characterized by large-scale vertical development. An approximation radiative transfer model for a cloudy atmosphere is introduced. Cloud particle absorption of infrared (IR) radiation depends on the spectral frequency. So, the effective cloud parameters such as amount (absorption) and height, derived from IR spectral measurements, will be spectral functions as well. The degree of uncertainty in the determination of effective cloud parameters cannot be eliminated by increasing the number of spectral measurements. A cloud model should have extra degrees of freedom to address the spectral and spatial (vertical) variability of cloud absorption. A semi-discrete multilevel cloud model is used to describe the perturbation of the outgoing IR thermal radiation caused by cloudiness in the field of view of a satellite instrument. The model delineates cloudiness in a number of layers at fixed heights. Each layer (level) is characterized by the effective cloud absorption. An inverse problem of cloud absorption vertical profile (CAVP) estimation is described. The estimate of an effective cloud absorption profile is considered as predictor for identification of cloud presence at specific atmospheric layers. The problem is numerically examined for real satellite IR spectral measurements and solution estimates are compared with lidar measurements. Results show that the resulting estimate of CAVPs provides a realistic characterization of cloud top and cloud vertical scale.