Applications of estimation theory to inverse problems in meteorology

Modern multivariate estimation theory has important potential applications in meteorological inverse problems involving weather assessment and prediction. This is especially true with the advent of sensitive satellite-borne passive spectrometers. which offer 24 hour global coverage. These applications include estimation of: (1) vertical temperature profiles, (2) cloud content, type, height and thickness, (3) atmospheric water vapor and liquid water columns, (4) surface parameters such as sea surface wind speed, sea ice, snow and soil, and (5) minor constituents such as O3. Typically, only a few noisy measurements are available and the problem is underdetermined. However, apriori information is available from climatology or forecast fields which can be combined with the data to yield filtered solutions. These problems are typically characterized by highly nonlinear measurements, necessitating approximate nonlinear filtering solutions. Several applications are presented. The extended Kalman filter (EKF) is utilized for recursive temperature profile retrievals using remote microwave soundings from a single scanning instrument. Horizontal and vertical spatio-temporal correlations are accounted for in the model. Numerical results indicate a 10-30% reduction in rms error when compared with standard regression techniques. Another application involves recovery of cloud and surface parameters from microwave data. The iterated extended Kalman filter(IEKF) is used to estimate cloud height, thickness and integrated liquid water, and surface wind speed. Analytical measurement models, which are highly nonlinear, are found using nonlinear regression in conjunction with sophisticated radiative transfer simulations. Numerical results are presented for the IEKF, EKF and regression solutions and these are compared with the Cramer-Rao bound. The IEKF offers the best inversion method of those tested.