A Covariance Conversion Approach of Gamma Random Field Simulation

Jun-Jih Liou 1, Yuan-Fong Su 1, Jie-Lun Chiang 2 and Ke-Sheng Cheng1+ 
1 Department of Bioenvironmental Systems Engineering, National Taiwan University, Taiwan
2 Dept. of Soil and Water Conservation, National Pingtung University of Science and Technology, Taiwan

Abstract. In studies involving environmental risk assessment, random field generators such as the sequential Gaussian simulation are often used to yield realizations of a Gaussian random field, and then realizations of the non-Gaussian target random field are obtained by an inverse-normal transformation. Such simulation requires a set of observed data for estimation of the empirical cumulative distribution function and covariance function of the random field under investigation. However, such observed-data-based simulation will not work if no observed data are available and realizations of a non-Gaussian random field with specific probability density and covariance function are needed. In this paper we present details of a gamma random field simulation approach which does not require a set of observed data. A key element of the approach lies on the theoretical relationship between the covariance functions of a gamma random field and its corresponding standard normal random field. The proposed gamma random field simulation technique is composed of three sequential components: (1) covariance function conversion between a gamma random field and a corresponding Gaussian random field, (2) generating realizations of a Gaussian random field with standard normal density and the desired covariance function, and (3) transforming Gaussian realizations to corresponding gamma realizations. Through a set of devised simulation scenarios, the proposed technique is shown to be capable of generating realizations of the given gamma random fields. The approximation function of the gamma-Gaussian covariance conversion works well for coefficient of skewness of the gamma density not exceeding 3.0. 

Keywords: stochastic simulation, gamma distribution, geostatistics, random field simulation

In: Wan, Y. et al. (eds) Proceeding of the 8th international symposium on spatial accuracy assessment in natural resources and environmental sciences, World Academic Union (Press).

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