This paper describes the basis for techniques such as stochastic subdivision in the theory of random processes and estimation theory. The popular stochastic subdivision construction is then generalized to provide control of the autocorrelation and spectral properties of the synthesized random functions. The generalized construction is suitable for generating a variety of perceptually distinct high-quality random functions, including those with non-fractal spectra and directional or oscillatory characteristics. It is argued that a spectral modeling approach provides a more powerful and somewhat more intuitive perceptual characterization of random processes than does the fractal model. Synthetic textures and terrains are presented as a means of visually evaluating the generalized subdivision technique. Categories and Subject Descriptors: I.3.3 [Computer Graphics]: Picture/Image Generation; I.3.7 [Computer Graphics]: Three Dimensional Graphics and Realism -<F11.

. In this paper, we explore the theory of optical deformations due to continuous variations of the refractive index of the air, and present several efficient implementations. We introduce the basic equations from geometrical optics, outlining a general method of solution. Further, we model the fluctuations of the index of refraction both as a superposition of blobs and as a stochastic function. Using a well known perturbation technique from geometrical optics, we compute linear approximations to the deformed rays. We employ this approximation and the blob representation to efficiently ray trace non linear rays through multiple environments. In addition we present a stochastic model for the ray deviations derived from an empirical model of air turbulence. We use this stochastic model to precompute deformation maps. 1

This document is available to the public through the National Technical Information Service, Springfield, VA 22161This document is disseminated under the sponsorship of the Department of Transportation in the interest of information exchange. The United States Government assumes no liability for its contents or use thereof.- 2-List of Errors: pg.5 Definitions concerning equation {2) are incorrect. 7 (ratio of specific heats is written as "g". T is written as "t '. pg.6 Definitions concerning c9uation (~~) are incorrect. Units 011 Da are wrong. Air density p is written as "r '. pg.8 Equation (7) should read 1\1/2 instcad of D il The following sentence should rea.d "... comparing Eqs. (:3) and (5)... " rather than "...(3) and (4)...". U de is inversely proportional to V. The text states that fa is directly proportional to V 4 / 3 • In fact, it is (~/3 that is inversely proportional to V 4 / 3 • In the following paragraph, the text should read " whereas f)a l / 2 will be ratIler tI lan "...D 1/3 " a •.. • pg.22 Second paragraph: Text should read "(seeF'igure 2 and Table 4)", not "...

In a previous paper we discussed the spectral properties of the Earth's ozone layer, obtained using Empirical Orthogonal Function decomposition of the Total Ozone Mapping Spectrometer (TOMS) database. Here we present other aspects of the analysis, including the EOF method adapted for incomplete datasets, analysis of spatial structure and temporal variation of first several eigenfunctions, and an extended study of small-scale properties of ozone concentration fields. Geophysical datasets collected by satellite-based devices currently provide a wealth of information which needs to be assimilated and interpreted. In this paper we analyze the global ozone concentration fields measured by Total Mapping Ozone Spectrometer [1]. The interest in atmospheric ozone is due to both its environmental role (ozone hole phenomenon [2, 3]), and the fact that it can be regarded as a passive tracer, thus providing an additional insight in the properties of atmospheric circulation. This is an extended version of a previous paper [4], where the principal attention was paid to the spectral properties of the ozone concentration fields.