In this paper, to develop novel methods for satellite optical remote sensing of severe storms, chaotic time-series analysis is carried out and the time delay embedding technique is used for phase space reconstruction, which is relied strongly on a choice of good time delay and the embedding dimension. A new approach for calculations of the mutual information for the choice of time delay for a time series with any probability distribution is proposed. To confirm the validity of the approach developed, the tests using simulated nonlinear time series for some famous chaotic attractors are performed. Then, application of the approach in the time series of GMS-5 11μm IR channel brightness temperature observations of rainstorm occurred in Wuhan area in China on 21-27 July 1998 is discussed. The results show that the new method proposed is a good tool for the best choice of time delay in time series analysis.
To develop a new and modern satellite retrieval method to study the severe storm process, satellite remote sensing is combined with nonlinear chaos dynamics. In this paper, the choice of time delay for the phase space reconstruction for nonlinear time series analyses is carried out. The method based on the information generation is employed. A new algorithm for calculations of the mutual information for the choice of time delay for phase space reconstruction for any probability distribution is developed. To confirm the validity of the algorithm proposed, the tests using simulated time series for some famous chaotic attractors and other nonlinear processes are performed. Finally application of the algorithm in the time series of GMS-5 11μm IR channel brightness temperature observations of rainstorm occurred in Wuhan area in China on 21-27 July 1998 is discussed. The results show that the new algorithm proposed is a good tool for the best choice of time delay in time series.
Two issues relevant to the best choice of time delay for phase space reconstruction are further studied by using the time series of GMS-5 11μm IR channel brightness temperature observations of rainstorm processes occurred in Wuhan area in China in July and in August of 1998. Periodic components existing in the satellite signals are investigated, first. The results demonstrate that the periodic components have noticeable influence on the choice of the optimum time delay. A new algorithm - the derivative method - is then developed for the extraction of possible periodic components from the time series. The advantages of this method and its importance are discussed.
A quantity called the mutual information dimension is proposed based on the concepts of the information theory and fractal theory. The application of the mutual information dimension in the time series of GMS-5 11μm IR channel brightness temperature observations of the severe rainstorm process occurred in Wuhan area in China on 21-27 July 1998 is carried out. Its application in the simulated time series of the attractor of Henon map is also performed. Furthermore, the key characteristics of the mutual information dimension are discussed. The study indicates that the new quantity is suitable for applications in nonlinear time series analysis.
Based on the analyses of nonlinear time series of satellite observations, some critical issues relevant to the choice of time delay for phase space reconstruction, i.e., them utual information calculations, and the effects of the possible periodic components on the choice of the best time delay and their extraction formthe satellite signals, are studied. Some important results are obtained.
KEYWORDS: LIDAR, Multiple scattering, Clouds, Scattering, Signal attenuation, Photons, Monte Carlo methods, Receivers, Mass attenuation coefficient, Distance measurement
The return of a spaceborne lidar system contains essential contributions form multiple scattering. Hence, methods for the retrieval of cloud parameters from such returns must be based on equations which take into account such multiple scattering. The more precisely this is done the more complicated these equations will be and the less changes are to be able to retrieve the parameters. At least this is true for retrieval procedures which are based on solving integro- differential equations. Hence, in such a case it is necessary to use simplified equations to describe such returns. Such simplified equations may be equations which introduce a correction term into the classical (single scattering) lidar equation or which take into account one or two orders of multiple scattering only or which have the for of some sophisticated exponential series including knowledge of depolarization. Of course, it is necessary to check the validity of such approximative multiple scattering lidar equations. We show simulations of lidar returns from different clouds. These simulations are obtained by variance reduction Monte Carlo methods which are based on an exact multiple scattering lidar equation obtained within the framework of a stochastic model from the transport of polarized light through the atmosphere. These simulations demonstrate the great importance of the contributions from multiple scattering to the return signal, the diffusion of the laser beam in the cloud seen from the receiver, the difficulty of determining the type and the location of the particles contributing to the return, and the need of careful analysis of returns of spaceborne lidar systems. We show simulations of such returns from clouds of aerosols (randomly oriented oblate and prolate spheroids) and a sensitivity analysis for such returns from water clouds with varying extinction coefficient and droplet size distribution. The simulations and the sensitivity analysis clearly show that the validity of retrieval procedures based on approximative multiple scattering lidar equations has to be examined with care.
For good visibility lidar return signals may be analyzed using the classical lidar equation which describes the single scattering contribution only. Here the range, from which a contribution to the return signal comes, is proportional to the time difference between emission and reception. For dense cloud sensing with a ground-based lidar or for a spaceborne lidar system, the return signal contains also essential contributions from higher orders of multiple scattering. In this case the physical range or the distance along the emitted beam, from which the contribution comes, is no longer proportional to the time elapsed since emission. The elapsed time is only proportional to the photon path-length. Thus making the analysis of the return signal much more difficult. Which part of the return signal comes from what range and, hence, from which type of scatterers? The diffusion process of multiple scattering of light in the atmosphere is non-isotropic and extremely complicated. The key to the solution of the problem is the simulation of multiple scattering lidar returns where the separate orders of scattering are tracked. Such information about the diffusion of the laser beam is needed to give a better understanding of the extend of contribution from the type of scatterers to the return signal. In this paper, we offer such a non-trivial analysis of the diffusion of the laser beam in the cloud modeled by two kinds of atmospheric particles, i.e., aerosols and ice crystals, by using a multi-dimensional contribution distribution for different orders of scattering. This is done by conditioning the probability of return e.g. by the time elapsed, the order of scattering, the distance from the axis of the direction of emission, and the distance of the projection of the point of contribution on this axis to the emitter. This gives a fairly complete information about the diffusion process as it is seen from the receiver.
Scattering properties, i.e., the integral photometric characteristics, of polydisperse, randomly oriented small ice crystals modeled by finite circular cylinders at some infrared (IR) wavelengths are calculated by using the exact T-matrix approach. The effects caused by various aspect ratios and effective variances of size distributions are investigated. The results further show that scattering properties of small ice cylinders in the IR region depend strongly on wavelengths, particle size distributions with different x and ve and aspect ratios. Both the 25micrometers and 3.979micrometers together have some potential applications for remote sensing of cirrus and other ice clouds.
Light scattering characteristics by small ice particles modeled by polydisperse, randomly oriented, finite circular cylinders at both the visible, and near-infrared 1.38 micrometers wavelengths are investigated. The effects caused by an increase in aspect ratio and by changes in effective variance of particle size distributions are addressed. Comparison of our results with those calculated by Zakharova and Mishchenko (2000) shows that light scattering properties of small ice particles modeled by finite circular cylinders are different from those modeled by spheroids having the same aspect ratio. The results are significant in optical modeling and applications in remote sensing.
In the modeling study, the characteristics, of the wavelengths ranging from the visible, near IR, and entire thermal IR spectra up to 40 μm have been investigated systematically. We find that the wavelengths of 1.38 μm and 25.0 μm located, respectively, in the near- and far-IR water vapor bands are superior to the other IR channels and have potential possibility of remote sensing of microphysical and optical properties of cirrus clouds.
The scattering phase function angular characteristics, including the effects of particle nonsphericity on the phase function and the uncertainties using the Henyey-Greenstein approximation for hexagonal ice crystals are investigated systematically. Some new and significant facts are obtained.
From the standpoint of remote sensing, the scattering and radiative transfer properties of model cirrus clouds with hexagonal columns and plates in visible, near-IR, and IR spectra have been investigated by using the improved ray-optics theory and adding/doubling method. The radiative properties for eight types of water clouds are also studied. It is shown that the single scattering and multiple scattering properties of clouds depend strongly on the cloud macro- and micro- physics, and wavelengths. The analysis of brightness temperatures (BT) indicate that measurements of BT at 2.16, 2.7, and 3.1 micrometers from space may be used to distinguish cirrus clouds from water clouds. Furthermore, a technique for detecting clear skies and cirrus clouds is developed by analyzing the BT difference in both IR windows, i.e., 11.2 and 13.34 micrometers .
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