Hyporheic exchange in streams is critical to ecosystem functions such as nutrient cycling along river corridors, especially for slowly moving or small stream systems. The transient storage model (TSM) has been widely used for modeling of hyporheic exchange. TSM calibration, for hyporheic exchange, is typically used to estimate four parameters, including the mass exchange rate coefficient, the dispersion coefficient, stream cross-sectional area, and hyporheic zone cross-sectional area. Prior studies have raised concerns regarding the non-uniqueness of the inverse problem for the TSM, that is, the occurrence of different parameter vectors resulting in TSM solution that reproduces the observed in-stream tracer break through curve (BTC) with the same error. This leads to practical non-identifiability in determining the unknown parameter vector values even when global-optimal values exist, and the parameter optimization becomes practically non-unique. To address this problem, we applied the simulated annealing method to calibrate the TSM to BTCs, because it is less susceptible to local minima-induced non-identifiability. A hypothetical (or synthetic) tracer test data set with known parameters was developed to demonstrate the capability of the simulated annealing method to find the global minimum parameter vector, and it identified the “hypothetically-true” global minimum parameter vector even with input data that were modified with up to 10% noise without increasing the number of iterations required for convergence. The simulated annealing TSM was then calibrated using two in-stream tracer tests conducted in East Fork Poplar Creek, Tennessee. Simulated annealing was determined to be appropriate for quantifying the TSM parameter vector because of its search capability for the global minimum parameter vector.

中文翻译：

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使用模拟退火方法优化瞬态存储模型参数

溪流中的低流交换对生态系统功能至关重要，例如沿河流走廊的养分循环，特别是对于缓慢移动或小溪流系统。瞬态存储模型 (TSM) 已被广泛用于海流交换的建模。TSM 校准，用于低流交换，通常用于估计四个参数，包括质量交换率系数、分散系数、流横截面积和低流区横截面积。先前的研究提出了对 TSM 逆问题的非唯一性的担忧，即不同参数向量的出现导致 TSM 解决方案再现了观察到的流内示踪剂突破曲线 (BTC) 具有相同的误差。即使存在全局最优值，这也会导致在确定未知参数向量值时实际不可识别，并且参数优化实际上变得不唯一。为了解决这个问题，我们应用模拟退火方法将 TSM 校准到 BTC，因为它不太容易受到局部最小值引起的不可识别性的影响。开发了具有已知参数的假设（或合成）示踪剂测试数据集，以证明模拟退火方法找到全局最小参数向量的能力，即使输入数据为在不增加收敛所需的迭代次数的情况下，用高达 10% 的噪声进行了修改。然后使用在田纳西州 East Fork Poplar Creek 进行的两个流内示踪剂测试对模拟退火 TSM 进行校准。模拟退火被确定为适合量化 TSM 参数向量，因为它具有搜索全局最小参数向量的能力。