Quantifying Time-Variant Travel Time Distribution and Internal Mixing by Multi-Fidelity Model under Nonstationary Hydrologic Conditions

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 highfidelity model and the computational efficiency of low-fidelity model. Moreover, in groundwater and solute transport model with low P & eacute;clet 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.