On the synthesis of random field sampling from the spectrum: An application to the generation of hydrologic spatial processes

A procedure for the synthesis of processes exhibiting temporal and spatial variability is presented. The method involves the addition of harmonics of random frequencies that are sampled from the spectral density function or the radial spectral density function. The process obtained is asymptotically Gaussian and ergodic. An estimate of the error in time or space averages due to the nonergodicity of the process as a function of the number of harmonics is also included.