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Analysis of Karst Aquifer Spring Flows with a Gray System Decomposition Model

机译：灰色系统分解模型分析岩溶含水层泉水

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摘要

There are ～470,000 km~2 of karst aquifers that feed many large springs in North China. Turbulent flow often exists in these karst aquifers, which means that the classical ground water model based on Darcy's law cannot be applied here. Ground water data are rare for these aquifers. As a consequence, it is difficult to quantitatively investigate ground water flow in these karst systems. The purpose of this study is to develop a parsimonious model that predicts karst spring discharge using gray system theory. In this theory, a white color denotes a system that is completely characterized and a black color represents a system that is totally unknown. A gray system thus describes a complex system whose characteristics are only partially known or known with uncertainty. Using this theory, we investigated the karst spring discharge time series over different time scales. First, we identified three specific components of spring discharge: the long-term trend, periodic variation, and random fluctuation. We then used the gray system model to simulate the long-term trend and obtain periodic variation and random fluctuation components. Subsequently, we developed a predictive model for karst spring discharge. Application of the model to Liulin Springs, a representative example of karst springs in northern China, shows that the model performs well. The predicted results suggest that the Liulin Springs discharge will likely decrease over time, with small fluctuations.
机译：华北地区约有470,000 km〜2的岩溶含水层，可为许多大型泉水提供食物。这些岩溶含水层中经常存在湍流，这意味着基于达西定律的经典地下水模型不能在此应用。这些含水层的地下水数据很少。结果，很难定量研究这些岩溶系统中的地下水流量。这项研究的目的是建立一个使用灰色系统理论预测岩溶泉水排放量的简约模型。在该理论中，白色表示已完全表征的系统，而黑色则表示完全未知的系统。因此，灰色系统描述了一个复杂的系统，其特征仅是部分已知或具有不确定性。利用这一理论，我们研究了不同时间尺度上的岩溶泉水排放时间序列。首先，我们确定了弹簧卸荷的三个特定组成部分：长期趋势，周期性变化和随机波动。然后，我们使用灰色系统模型来模拟长期趋势，并获得周期性变化和随机波动分量。随后，我们开发了岩溶泉水排放的预测模型。该模型在柳林泉（中国北方岩溶泉的典型例子）中的应用表明，该模型表现良好。预测结果表明，柳林泉水流量可能会随着时间的推移而减少，且波动很小。

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