Technical note: Transit times of reactive tracers under  time-variable hydrologic conditions

Miazza, Raphaël; Benettin, Paolo

doi:10.5194/hess-30-1247-2026

Articles | Volume 30, issue 4

https://doi.org/10.5194/hess-30-1247-2026

© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/hess-30-1247-2026

© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 30, issue 4

Technical note

|

03 Mar 2026

Technical note |

| 03 Mar 2026

Technical note: Transit times of reactive tracers under time-variable hydrologic conditions

Raphaël Miazza and Paolo Benettin

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Final revised paper (published on 03 Mar 2026)
Preprint (discussion started on 09 Sep 2025)

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-3554', Anonymous Referee #1, 25 Nov 2025

The paper addresses the non-stationary theory of transit time distribution under simplified assumptions, derives analytical solutions for a simplified case, explains them, and presents some conceptual applications. Overall, I believe the paper has merit. The concepts developed, while not entirely novel, have not yet broken through to the broader hydrological community's consciousness. However, the applications require clarification of several aspects to be truly useful. I find value in the paper, but for the sake of reproducibility, I recommend that the authors more clearly specify the conditions under which the simulations were conducted. I recommend minor revisions.
Detailed Comments
Page 8 - Equation (17): Is the so-called "mass-normalized breakthrough curve" not simply the discharge at time T+t_i generated by the input at time t_i? Additionally, how can one determine the partition coefficient at any finite time? More practically, how can this be approximated given that the partition is not known in advance? This concern extends to systems with multiple partition coefficients. It would also be valuable to understand the seasonal variation of these coefficients, as I assume ET, for instance, varies seasonally. Furthermore, how was ET determined?
Page 9 - Line 233: The information that the models were implemented in Python is not essential. More relevant would be information about code availability and licensing. I consider code availability an important step toward understanding implementation details, which can be technically challenging.
Page 9 - Line 239: The authors state they use the Kirchner 2016b model as a foundation. I would therefore expect the overall TTD model to address convolutions of two reservoirs, not just one. Have the authors done this? This point remains unclear and requires clarification. A treatment of this specific subject can be found, for instance, in Rigon and Bancheri (2021). That said, there is nothing inherently wrong with addressing a simpler system.
Reference Rigon, Riccardo, and Marialaura Bancheri. 2021. "On the Relations between the Hydrological Dynamical Systems of Water Budget, Travel Time, Response Time and Tracer Concentrations." Hydrological Processes 35 (1). https://doi.org/10.1002/hyp.14007.

Citation: https://doi.org/10.5194/egusphere-2025-3554-RC1
- AC1: 'Reply on RC1', Raphaël Miazza, 18 Dec 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-3554/egusphere-2025-3554-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-3554-AC1
RC2:
'Comment on egusphere-2025-3554', Ype van der Velde, 28 Nov 2025

Review of: “Technical note: Transit times of reactive tracers under time-variable hydrologic conditions” by Raphael Miazza and Paolo Benettin
This technical note describes how the transit time approach developed for tracking water ages through catchments can be extended to yield transit times of reactive tracers. I find this paper a well written and valuable addition to the theory development around transit time distributions of water and solutes. This study applies the theory of transittime distributions for water to solutes and combines it with assumptions from advective-diffusion solute transport modelling (Retardation: constant equilibrium between dissolved and sorbed concentration, linear decay, fractionation). As such it is a novel contribution. In the attach I list a couple of suggestions that in my opinion could improve the manuscript.

Citation: https://doi.org/10.5194/egusphere-2025-3554-RC2
- AC2: 'Reply on RC2', Raphaël Miazza, 18 Dec 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-3554/egusphere-2025-3554-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2025-3554-AC2

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

ED: Publish subject to minor revisions (further review by editor) (25 Jan 2026) by Laurent Pfister

AR by Raphaël Miazza on behalf of the Authors (03 Feb 2026) Author's response Author's tracked changes Manuscript

ED: Publish subject to technical corrections (25 Feb 2026) by Laurent Pfister

AR by Raphaël Miazza on behalf of the Authors (26 Feb 2026) Manuscript

Short summary

We studied the time it takes for solutes like pollutants to travel through the landscape and reach streams compared to water. Although water and solutes travel together, they can take different paths and exit at different times due to different processes like sorption, decay, or uptake by plants. Using a simple modeling approach, we identified the conditions under which these travel time differences occur. This helps improve how we understand and predict water quality in natural environments.