GroMoPo Metadata for Noord-Brabant model

Numerical models are often used for simulating ground water flow. Written in state space form, the dimension of these models is of the order of the number of model cells and can be very high (> million). As a result, these models are computationally very demanding, especially if many different scenarios has to be simulated. Therefore we introduce in this paper a model reduction approach to develop an approximate model with a significantly reduced dimension. The reduction method is based upon several simulations of the large-scale numerical model. By computing the covariance matrix of the model results, we obtain insight into the variability of the model behavior. Moreover, selecting the leading eigenvector of this covariance matrix, we obtain the spatial patterns that represent the directions in state space where the model variability is dominant. These patterns are also called Emperical Orthogonal Functions (EOFs). The original numerical model can now be projected onto the reduced space spanned by the dominant spatial patterns. The result is a low dimensional model that is still able to reproduce the dominant model behavior. In this paper we introduce the reduction approach and describe a real life application of the appraoch to a large-scale numerical ground water flow model.数值模型常被用于模拟地下水流。若以状态空间形式表示，此类模型的维度与模型网格单元数量相当，通常极高（可达百万量级）。因此这类模型的计算成本极高，尤其当需要模拟大量不同场景时。为此，本文提出一种模型降阶方法，以构建维度显著降低的近似模型。该降阶方法基于对大规模数值模型的多次模拟：通过计算模型输出结果的协方差矩阵，可深入理解模型行为的变化特性；进一步对该协方差矩阵求解主特征向量，可得到表征模型变化主导方向的空间模态，此类空间模态亦被称为经验正交函数（Empirical Orthogonal Functions，EOFs）。原数值模型可投影至由主导空间模态张成的降维空间中，最终得到的低维模型仍可复现原模型的主导行为特性。本文将详细介绍该降阶方法，并展示其在某大规模地下水流数值模型中的实际应用案例。