ABSTRACT

Fractal analysis of a time series provides information on how the series varies across all (possible) temporal scales with respect to a given statistical measure. Dynamic hydrological models are typically optimized/calibrated using performance criteria defined in the time domain; however, the performance of models in simulating the fluctuation structure of a time series is seldom investigated. We use a multi-objective pattern search algorithm to calibrate a combined 15-minute resolution recharge–groundwater flow model. The non-dominated simulations of the model are then analysed in the fractal domain using robust detrended fluctuation analysis. The results show that some non-dominated simulations can be eliminated based on poor performance in the fractal domain, hence ensuring that the fluctuation structure of the optimized simulations is captured; this was named fractal-domain-refinement. Furthermore, some recharge parameters are sensitive to fractal-domain-refinement. This gives insights into which parameters are sensitive to the fractal behaviour of the simulated variable.

摘要

时间序列的分形分析提供了关于序列如何在所有（可能的）时间尺度上相对于给定统计测量变化的信息。动态水文模型通常使用时域中定义的性能标准进行优化/校准；然而，很少研究模型在模拟时间序列波动结构方面的性能。我们使用多目标模式搜索算法来校准组合的 15 分钟分辨率补给-地下水流模型。然后使用稳健的去趋势波动分析在分形域中分析模型的非支配模拟。结果表明，由于分形域的性能较差，可以消除一些非支配模拟，从而确保捕获优化模拟的波动结构；这被命名为分形域细化。此外，一些补给参数对分形域细化很敏感。这可以深入了解哪些参数对模拟变量的分形行为敏感。