Enabling dynamic emulation of high-dimensional model outputs: Demonstration for Mexico City groundwater management

Model emulation has become an integral tool in scenario analysis, risk assessment, and calibration of environmental models. Of particular interest is dynamic emulation - the approximation of model outputs from inputs or processes that vary in time. This paper presents a method for data-driven dynamic emulation of high-dimensional model outputs that overcomes the logistical challenges from assumptions in traditional multivariate statistics concerning output covariance. In this method, outputs are subjected to principal component analysis, and Gaussian random fields are fit along new orthogonal axes to accommodate spatial heterogeneity and serial correlation. The technique is demonstrated on a regional groundwater model of metropolitan Mexico City, where it successfully emulates spatial and temporal dynamics of land subsidence and aquifer level fluctuation resulting from two management scenarios. In doing so, we introduce methodological advances to emulation techniques, which facilitate the use of models with high-dimensional outputs in computationally expensive planning and optimization applications.