The travel time distribution (TTD) is a lumped representation of water leaving the system responding to external forces such as rainfall. It reveals the mixing of water parcels and solute particles of different ages from different historical rainfall events at the outlet of a system. Under nonstationary rainfall input condition, the TTD varies with transit groundwater flow, leading to the time-variant TTD. The exploration of internal control on time-variant TTD requires the flow information inside the system. Numerical simulation of water flow and age distribution inside the system provide a valuable insight. However, gaps exist when solving the 5-dimensional governing equation of groundwater age distribution. This study introduces a multi-fidelity model to overcome these limitations. In this multi-fidelity model, groundwater age distribution model is taken as the high-fidelity model, and particle tracking model without random walk is taken as the low-fidelity model. Non-parametric regression by non-linear Gaussian process is applied to correlate the two models and then build up the multi-fidelity model. The advantage of the multi-fidelity model is that it combines the accuracy of high-fidelity model and the computational efficiency of low-fidelity model. Moreover, in groundwater and solute transport model with low Péclet number, as the spatial scale of the model increases, the number of particles required for multi-fidelity model is reduced significantly compared to random walk particle tracking model. In a two-dimensional hypothetical model, convergence analysis indicates that the multi-fidelity model converges well when increasing the number of high-fidelity models. Error analysis also confirms the good performance of the multi-fidelity model. By reducing the random noise stemming from molecular diffusion and mechanical dispersion, the multi-fidelity model enables a more focused study on the internal control factors influencing the time-variant TTD.

中文翻译：

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非平稳水文条件下通过多保真度模型量化时变行程时间分布和内部混合

行程时间分布 (TTD) 是离开系统的水响应降雨等外力的集中表示。它揭示了系统出口处不同历史降雨事件中不同年龄的水团和溶质颗粒的混合。在非平稳降雨输入条件下，TTD随着过境地下水流量的变化而变化，导致TTD时变。时变TTD内部控制的探索需要系统内部的流动信息。系统内部水流和年龄分布的数值模拟提供了有价值的见解。然而，在求解地下水年龄分布的五维控制方程时存在空白。本研究引入了多保真度模型来克服这些限制。在该多保真模型中，采用地下水龄分布模型作为高保真模型，采用不带随机游走的粒子跟踪模型作为低保真模型。应用非线性高斯过程的非参数回归来关联两个模型，然后建立多保真度模型。多保真模型的优点在于它结合了高保真模型的准确性和低保真模型的计算效率。此外，在低佩克莱特数的地下水和溶质输运模型中，随着模型空间尺度的增加，多保真模型所需的粒子数量与随机游走粒子跟踪模型相比显着减少。在二维假设模型中，收敛分析表明，当增加高保真模型数量时，多保真模型收敛良好。误差分析也证实了多保真模型的良好性能。通过减少分子扩散和机械分散产生的随机噪声，多保真模型可以更集中地研究影响时变 TTD 的内部控制因素。