Accurate modeling of dependencies between variables of interest is imperative for understanding biophysical processes and mechanisms relevant to Earth Science research. This study presents a methodology to model the temporal or spatial distributions of variables using copula-based cosimulation (CopCoSim). This technique models and simulates the joint distribution of multiple variables by capturing their dependencies and correlations. We compared CopCoSim with the traditional Sequential Gaussian CoSimulation (SGCoSim) technique through two applications relevant to Earth Science representing one (i.e., time) and two dimensions (i.e., space). We present an application for soil CO2 efflux, which is a major flux in the global carbon budget, using two case studies: (1) temporal distribution of soil CO2 efflux and temperature, and (2) spatial distribution of soil CO2 efflux and temperature across the conterminous United States (CONUS). The methodology involves three steps: data input, application of stochastic simulation methods, and comparison of simulation outputs. The results indicate that CopCoSim provides a better model with higher precision and accuracy for representing variables of interest. CopCoSim better reproduces the univariate probability distribution, temporal or spatial autocorrelation, and dependency relationship between the predictor and response variables. We propose that CopCoSim is useful for research in Earth Science, where variables of interest (e.g., soil CO2 efflux and temperature) are often interdependent and exhibit complex temporal or spatial patterns.