A Simple Stochastic Model for Generating Broken Cloud Optical Depth and Top Height Fields

A simple and fast algorithm for generating two correlated stochastic twodimensional (2D) cloud fields is described. The algorithm is illustrated with two broken cumulus cloud fields: cloud optical depth and cloud top height retrieved from Moderate Resolution Imaging Spectrometer (MODIS). Only two 2D fields are required as an input. The algorithm output is statistical realizations of these two fields with approximately the same correlation and joint distribution functions as the original ones. The major assumption of the algorithm is statistical isotropy of the fields. In contrast to fractals and the Fourier filtering methods frequently used for stochastic cloud modeling, the proposed method is based on spectral models of homogeneous random fields. For keeping the same probability density function as the (first) original field, the method of inverse distribution function is used. When the spatial distribution of the first field has been generated, a realization of the correlated second field is simulated using a conditional distribution matrix. This paper is served as a theoretical justification to the publicly available software that has been recently released by the authors and can be freely downloaded from http://i3rc.gsfc.nasa.gov/Public codes clouds.htm. Though 2D rather than full 3D, stochastic realizations of two correlated cloud fields that mimic statistics of given fields have proved to be very useful to study 3D radiative transfer features of broken cumulus clouds for better understanding of shortwave radiation and interpretation of the remote sensing retrievals

Exact and Fast Numerical Algorithms for the Stochastic Wave Equation

On the basis of integral representations we propose fast numerical methods to solve the Cauchy problem for the stochastic wave equation without boundaries and with the Dirichlet boundary conditions. The algorithms are exact in a probabilistic sense

on the basis of thresholds of

binary random field

Geophysics, Siberian Branch of Russian Academy of Sciences ‡

of two numerical methods t

and Mathematical Geophysics ‡

We propose a new approach for model selection in mathematical statistics that is based not on the probability but on the ‘waiting time ’ of a sample. By waiting time of a sample we understand the average time of the first appearance of the sample in a sequence of independent identically distributed random variables. In the paper we consider a few simple examples to illustrate the main idea and further mathematical problems related to the new approach. Key words: mathematical statistics, sample, model selection

Geophysics, Siberian Branch of Russian Academy of Sciences ‡

of two numerical methods t

Imitation of binary random textures on the basis of Gaussian numerical models

We present a method for binary texture synthesis based on thresholds of Gaussian random fields. The method enables us to reproduce the average value and correlation function of the observed texture. The method is comparatively simple, and it seems to be effective for a wide class of random binary textures. In the paper we discuss properties of the method and illustrate its performance in the statistically homogeneous and isotropic case. Key words: texture analysis and synthesis, binary texture simulation, numerical modeling of random fields, Gaussian threshold models