Showing papers by "Adolfo Comerón published in 1999"

Lidar inversion of atmospheric backscatter and extinction-to-backscatter ratios by use of a Kalman filter

Abstract: A first inversion of the backscatter profile and extinction-to-backscatter ratio from pulsed elastic-backscatter lidar returns is treated by means of an extended Kalman filter (EKF). The EKF approach enables one to overcome the intrinsic limitations of standard straightforward nonmemory procedures such as the slope method, exponential curve fitting, and the backward inversion algorithm. Whereas those procedures are inherently not adaptable because independent inversions are performed for each return signal and neither the statistics of the signals nor a priori uncertainties (e.g., boundary calibrations) are taken into account, in the case of the Kalman filter the filter updates itself because it is weighted by the imbalance between the a priori estimates of the optical parameters (i.e., past inversions) and the new estimates based on a minimum-variance criterion, as long as there are different lidar returns. Calibration errors and initialization uncertainties can be assimilated also. The study begins with the formulation of the inversion problem and an appropriate atmospheric stochastic model. Based on extensive simulation and realistic conditions, it is shown that the EKF approach enables one to retrieve the optical parameters as time-range-dependent functions and hence to track the atmospheric evolution; the performance of this approach is limited only by the quality and availability of the a priori information and the accuracy of the atmospheric model used. The study ends with an encouraging practical inversion of a live scene measured at the Nd:YAG elastic-backscatter lidar station at our premises at the Polytechnic University of Catalonia, Barcelona.

Error analysis for the lidar backward inversion algorithm

Abstract: Here we depart from the inhomogeneous solution of a lidar equation using the backward inversion algorithm that is nowadays generally referred to as the Klett method. In particular, we develop an error sensitivity study that relates errors in the user-input parameters boundary extinction and exponential term in the extinction-to-backscatter relationship to errors in the inverted extinction profile. The validity of the analysis presented is limited only by the validity of application of the inversion algorithm itself, its numerical performance having been tested for optical depths in the 0.01–10 range. Toward this end, we focus on an introductory background about how uncertainties in these two parameters can apply to a family of inverted extinction profiles rather than a single profile and on its range-dependent behavior as a function of the optical thickness of the lidar inversion range. Next, we performed a mathematical study to derive the error span of the inverted extinction profile that is due to uncertainties in the above-mentioned user calibration parameters. This takes the form of upper and lower range-dependent error bounds. Finally, appropriate inversion plots are presented as application examples of this study to a parameterized set of atmospheric scenes inverted from both synthesized elastic-backscatter lidar signals and a live signal.

Numerical simulation of long path spherical wave propagation in three-dimensional random media

Abstract: A new method to overcome some limitations in the simulation of the propagation of waves originating from a point source through a very long path in a turbulent medium is presented. Existing propagation simulation algorithms suffer from either windowing or lack of resolution when applied to long paths. If Cartesian coordinates are used, the limited size of the numerical mesh eventually leads to windowing errors. Casting the classical split-step Fourier algorithm in a spherically diverging coor- dinate system allows one to get around this problem. In this way an angular mesh matching the source and the propagation algorithm to the problem geometry is used. But for long-path propagation, this spherical divergent mesh causes a loss of resolution that can become a serious problem in the evaluation of the field statistical moments. The method discussed in this paper overcomes both the windowing effect associated with Cartesian coordinates and the loss of resolution accompanying spherical coordinates by using a spherical-coordinate algorithm and per- forming repeated interpolations of the numerically propagated field be- fore the mesh grows too large to sample the field accurately. Each time an interpolation is done, the angular window is decreased to maintain the matrix size. © 1999 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(99)00309-8)