Quantifying time-variant travel time distribution by multi-fidelity model in hillslope under nonstationary hydrologic conditions

Abstract

The travel time distribution (TTD) is a lumped representation of groundwater discharge and solute export responding to rainfall. It reflects the mixing process of water parcels and solute particles of different ages and characterizes reactive transport progress in hillslope aquifers. As a result of the mixing process, groundwater leaving the system at a certain time is an integration of multiple water parcels of different ages from different historical rainfall events. Under nonstationary rainfall input condition, the TTD varies with transit groundwater flow, leading to the time-variant TTD. Most methods for estimating time-variant TTD are constrained by requiring either the long-term continuous hydrogeochemical data or the intensive computations. This study introduces a multi-fidelity model to overcome these limitations and evaluate time-variant TTD numerically. 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 P'eclet 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. The correlation between high and low-fidelity models is demonstrated in a one dimensional pulse injection case. 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.