Parameter Estimation in River Transport Models With Immobile Phase Exchange Using Dimensional Analysis and Reduced-Order Models

Abstract

We propose a framework for parameter estimation in river transport models using breakthrough curve data, which we refer to as Dimensionless Synthetic Transport Estimation (DSTE). We utilize this framework to parameterize the one-dimensional advection-dispersion equation model, incorporating immobile phase exchange through a memory function. We solve the governing equation analytically in the Laplace domain and numerically invert it to generate synthetic breakthrough curves for different memory functions and boundary conditions. A dimensionless formulation enables decoupling the estimation of advection velocity from other parameters, significantly reducing the number of required forward solutions. To improve computational efficiency, we apply a Karhunen-Loeve (KL) expansion to transform the synthetic dataset into a reduced-order space. Given a measured breakthrough curve, we estimate the advection velocity by minimizing the distance from the measurement to the synthetic data in KL space, and infer the remaining dimensionless parameters by Projected Barycentric Interpolation (PBI). We benchmark our method against several alternatives, including Laplace domain fitting, moment matching, global random optimization, and variations of the DSTE framework using nearest-neighbor interpolation and neural network-based estimation. Applied to 295 breakthrough curves from 54 tracer tests in 25 rivers, DSTE delivers accurate parameter estimates. The resulting labeled dataset allows researchers to link transport parameters with hydraulic conditions, site characteristics, and measured concentrations. The synthetic dataset can be leveraged for the analysis of new breakthrough curves, eliminating the need for additional forward simulations.