Simulation of strongly non-Gaussian processes using Karhunen–Loeve expansion

The non-Gaussian Karhunen–Loeve (K–L) expansion is very attractive because it can be extended readily to non-stationary and multi-dimensional fields in a unified way. However, for strongly non-Gaussian processes, the original procedure is unable to match the distribution tails well. This paper proposes an effective solution to this tail mismatch problem using a modified orthogonalization technique that reduces the degree of shuffling within columns containing empirical realizations of the K–L random variables. Numerical examples demonstrate that the present algorithm is capable of matching highly non-Gaussian marginal distributions and stationary/non-stationary covariance functions simultaneously to a very accurate degree. The ability to converge correctly to an abrupt lower bound in the target marginal distributions studied is noteworthy.