Miazza et al. (2026) Technical note: Transit times of reactive tracers under time-variable hydrologic conditions

Identification

• Journal: Hydrology and earth system sciences
• Year: 2026
• Date: 2026-03-03
• Authors: Raphaël Miazza, Paolo Benettin
• DOI: 10.5194/hess-30-1247-2026

Research Groups

• Institute of Earth Surface Dynamics, Faculty of Geoscience and the Environment, Université de Lausanne, Lausanne, Switzerland

Short Summary

This study derives and explores novel analytical solutions for the transit time distributions (TTDs) of reactive tracers in randomly sampled hydrological systems, demonstrating how processes like sorption, degradation, and evapotranspiration, along with input patterns, cause tracer TTDs to differ significantly from water TTDs.

Objective

• Derive new analytical solutions for the time-variable transit time distributions (TTDs) of reactive tracers in randomly sampled hydrological systems.
• Investigate how linear processes of sorption, degradation, and evapoconcentration influence tracer transit times and their partitioning to different pathways.

Study Configuration

• Spatial Scale: Catchment scale, conceptualized as a single randomly sampled (well-mixed) hydrological system, serving as a building block for lumped and distributed transport models.
• Temporal Scale: Hourly time steps for numerical simulations, considering seasonal and annual hydrological cycles, with analysis of long-term mean transit times.

Methodology and Data

• Models used:
  • Analytical solutions for first-order partial differential equations describing water and tracer age balances in randomly sampled systems.
  • Numerical implementation using a fourth-order Runge-Kutta method for solving the tracer mass balance.
• Data sources:
  • Hydrologic time series (rainfall, streamflow, evapotranspiration) from Duchemin et al. (2025), based on hourly rainfall data from Basel, Switzerland (MeteoSwiss) and simulated output fluxes from a three-compartment hydrological model.
  • Synthetic sine wave input for tracer mass flux with annual frequency.

Main Results

• Sorption, quantified by the retardation factor (R ≥ 1), delays tracer transport, effectively acting as a magnifier of water storage and leading to longer tracer transit times.
• Evapotranspiration's effect on tracer transit times depends on the evapoconcentration factor (α): α < 1 (evapoconcentration) increases transit times, while α > 1 (net tracer extraction) decreases them.
• Degradation, characterized by a decay constant (k) or half-life (DT50), consistently shortens tracer transit times by acting as an additional output flux.
• Even perfectly passive tracers (R=1, α=1, k=0) exhibit different age distributions from water when their input patterns differ (e.g., seasonal tracer input vs. less seasonal water input).
• Tracer characteristics significantly influence the partitioning of tracer mass among streamflow, evapotranspiration, and degradation pathways, with strong sorption and degradation favoring decay, and prominent evapoconcentration reducing mass partitioned to evapotranspiration.

Contributions

• Developed novel analytical solutions for time-variable transit time distributions (TTDs) of reactive tracers in randomly sampled hydrological systems, extending existing water TTD frameworks.
• Provided a quantitative understanding of how linear processes (sorption, degradation, evapoconcentration) and input patterns cause tracer TTDs to diverge from water TTDs.
• Offers a theoretical foundation for interpreting multi-tracer experiments and improving the characterization of solute transport and water quality dynamics at the catchment scale.

Funding

• Faculty of Geoscience and the Environment of the University of Lausanne

Citation

@article{Miazza2026Technical,
  author = {Miazza, Raphaël and Benettin, Paolo},
  title = {Technical note: Transit times of reactive tracers under time-variable hydrologic conditions},
  journal = {Hydrology and earth system sciences},
  year = {2026},
  doi = {10.5194/hess-30-1247-2026},
  url = {https://doi.org/10.5194/hess-30-1247-2026}
}