Direct Sequential Co-simulation with Joint Probability Distributions

Abstract

The practice of stochastic simulation for different environmental and earth sciences applications creates new theoretical problems that motivate the improvement of existing algorithms. In this context, we present the implementation of a new version of the direct sequential co-simulation (Co-DSS) algorithm. This new approach, titled Co-DSS with joint probability distributions, intends to solve the problem of mismatch between co-simulation results and experimental data, i.e. when the final biplot of simulated values does not respect the experimental relation known for the original data values. This situation occurs mostly in the beginning of the simulation process. To solve this issue, the new co-simulation algorithm, applied to a pair of covariates Z ₁(x) and Z ₂(x), proposes to resample Z ₂(x) from the joint distribution F(z ₁,z ₂) or, more precisely, from the conditional distribution of Z ₂(x ₀), at a location x ₀, given the previously simulated value $z_{1}^{(l)}(x_{0})$ ($F(Z_{2}|Z_{1}=z_{1}^{(l)}(x_{0})$ ). The work developed demonstrates that Co-DSS with joint probability distributions reproduces the experimental bivariate cdf and, consequently, the conditional distributions, even when the correlation coefficient between the covariates is low.