06 Sep 2021

06 Sep 2021

Review status: this preprint is currently under review for the journal HESS.

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

Rong Mao1, Jiu Jimmy Jiao1, Xin Luo1, and Hailong Li2 Rong Mao et al.
  • 1Department of Earth Sciences, The University of Hong Kong, P. R. China
  • 2School of Environmental Science and Engineering, Southern University of Science and Technology, Shenzhen, P.R. China

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.

Rong Mao et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2021-430', Anonymous Referee #1, 06 Oct 2021
    • AC1: 'Reply on RC1', Rong Mao, 30 Nov 2021
  • RC2: 'Comment on hess-2021-430', Anonymous Referee #2, 16 Oct 2021
    • AC2: 'Reply on RC2', Rong Mao, 30 Nov 2021
  • RC3: 'Comment on hess-2021-430', Anonymous Referee #3, 31 Oct 2021
    • AC3: 'Reply on RC3', Rong Mao, 30 Nov 2021

Rong Mao et al.

Model code and software

Codes and dataset used in the manuscript entitled "Quantifying time-variant travel time distribution by multi-fidelity model in hillslope under nonstationary hydrologic conditions" Rong Mao

Rong Mao et al.


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Short summary
Travel time distribution provides fundamental information on water circulation and subsurface mixing in aquifers. This study develops a multi-fidelity model to overcome limitations of previous methods to estimate time-variant travel time distribution. The multi-fidelity model combines the efficiency of high-fidelity model and accuracy of low-fidelity model. In the model with a low Peclet number and large spatial scale, the multi-fidelity model is a better method than the other numerical methods.