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.

模型仿真已成为情景分析、风险评估和环境模型校准的不可或缺的工具。特别令人感兴趣的是动态仿真——来自随时间变化的输入或过程的模型输出的近似值。本文提出了一种高维模型输出的数据驱动动态仿真方法，该方法克服了传统多元统计中关于输出协方差的假设所带来的逻辑挑战。在该方法中，输出经过主成分分析，并沿新的正交轴拟合高斯随机场以适应空间异质性和序列相关性。该技术在墨西哥城大都市的区域地下水模型上进行了演示，它成功地模拟了两种管理方案导致的地面沉降和含水层水位波动的时空动态。在此过程中，我们引入了仿真技术的方法论进步，这有助于在计算成本高的规划和优化应用程序中使用具有高维输出的模型。