Modelling the Water & Solute Transit Time Distributions in a Groundwater System

Groundwater transport of legacy contaminants (e.g., excess nutrients in agricultural watersheds) into streams and rivers is a likely contributor to the lag in surface water quality improvement. This lag being linked to the distribution of groundwater transit times, ample study of groundwater transit times becomes critical. Catchments are spatially complex and subsurface flow is invisible, so one can only infer the movement and mixing of waters from the chemical and isotopic tracer signatures that they carry.(JW Kirchner, X Feng, C Neal - Nature, 2000*). Thus, building a code that can explain the movement of inert tracers (like nitrogen) can reveal a lot of information.

To model TTDs in a catchment, conceptual lumped parameter models are most commonly used, which include long-established conventional models like piston flow, exponential, gamma & dispersion models, & recent ones like TRANSEP, ETNA etc—mostly claiming parsimony. But real-world catchments are not only heterogeneous, they are also nonstationary: their travel-time distributions shift with changes in their flow regimes, due to shifts in the relative water fluxes and flow speeds of different flow paths.

The distributed models (which mostly use Finite Element analysis to solve intricate PDEs) despite being more accurate are also quite complicated—with complex assembly processes, & often needless fineness in discretization, thereby rendering equifinality & overparameterization.

We follow a unique semi-distributed 1d modelling approach in determining TTDs -- our entire groundwater catchment is discretized into a bunch of interconnected Continuous Stirred Tank Reactors (CSTRs)—which best captures the geometry, heterogeneity, temporal assortation & varying flow conditions of the domain—in short, it performs as well as a distributed model, only with lesser parameters. The approach is often used by chemical engineers but is yet alien to hydrology. It’s a black-box with a simple GUI & a simple assembly process--just the solution of a bundle of 1^st order linear ODEs furnish us with a robust description of the processes going on within the system—for example, it can explain water balance issues in nested watersheds with layered heterogeneity.

We are now using the model to perform simple benchmark tests on the Kerbernez Site of South-Western French Brittany (which belongs to the observatory of research on environment AgrHys) to simulate the measured baseflow & stream nitrate concentration patterns at seasonal & inter-annual time scales.

 

Reference:

*Kirchner, James W., Xiahong Feng, and Colin Neal. "Fractal stream chemistry and its implications for contaminant transport in catchments." Nature 403.6769 (2000): 524.