Assessing lateral flows and solute transport during floods in a conduit-flow-dominated karst system using the inverse problem for the advection–diffusion equation

Cholet, Cybèle; Charlier, Jean-Baptiste; Moussa, Roger; Steinmann, Marc; Denimal, Sophie

doi:https://doi.org/10.5194/hess-21-3635-2017

Articles | Volume 21, issue 7

https://doi.org/10.5194/hess-21-3635-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/hess-21-3635-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 21, issue 7

Research article

|

18 Jul 2017

Research article |

| 18 Jul 2017

Assessing lateral flows and solute transport during floods in a conduit-flow-dominated karst system using the inverse problem for the advection–diffusion equation

Cybèle Cholet, Jean-Baptiste Charlier, Roger Moussa, Marc Steinmann, and Sophie Denimal

Download

Final revised paper (published on 18 Jul 2017)
Preprint (discussion started on 11 Nov 2016)
Supplement to the preprint

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

- Printer-friendly version

- Supplement

RC1: 'Reviewer comments', Anonymous Referee #1, 09 Dec 2016
RC2: 'The referee’s comments for the Editor of Hydrology and Earth System Sciences on the paper entitled FRAMEWORK FOR ASSESSING LATERAL FLOWS DURING FLOODS IN A CONDUIT-FLOW DOMINATED KARST SYSTEM USING AN INVERSE DIFFUSIVE MODEL by Cybèle Cholet, Jean-Ba', Anonymous Referee #2, 11 Dec 2016
RC3: 'Review of "Framework for assessing lateral flows and fluxes during floods in a conduit-flow dominated karst system using an inverse diffusive model" by Cholet et al.', Anonymous Referee #3, 20 Dec 2016
RC4: 'Comments to Framework for assessing lateral flows and fluxes during floods in a conduit-flow dominated karst system using an inverse diffusive model', Anonymous Referee #4, 27 Dec 2016
AC1: 'Authors responses', Cybèle Cholet, 10 Jan 2017

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

ED: Reconsider after major revisions (further review by Editor and Referees) (25 Jan 2017) by Mauro Giudici

AR by Cybèle Cholet on behalf of the Authors (02 Mar 2017) Author's response Manuscript

ED: Referee Nomination & Report Request started (05 Mar 2017) by Mauro Giudici

RR by Anonymous Referee #3 (02 Apr 2017)

RR by Anonymous Referee #2 (18 Apr 2017)

Suggestions for revision or reasons for rejection

I would like to find out that practically all my critical remarks presented previously were taken into account and respective comments and corrections were introduced by the Authors into the revised version of submitted manuscript.
However, although in the same review I tried to pay the Authors’ attention that the subject of their manuscript in fact deals with solution of the inverse problem, in many places of the considered text, including even its title, they use still the term “inverse model”. To my mind the term “model” simply means the equation or the system of equations describing the analyzed phenomenon. In the considered case both models are constituted by the partial differential equations of parabolic type: the advection – diffusion equations. If in assumed region of solution and for the auxiliary conditions imposed at its limits these equations are solved then it is said that their direct solutions was performed. In the case when knowing the solution we are looking for some auxiliary conditions or for the parameters describing the considered process then it is said that the inverse problem is solved. In my opinion this is the case considered by the Authors because they consider lateral inflow/outflow as unknown. Therefore, instead of the term “inverse model” they should rather use the term “inverse problem for the advection - diffusion equations” as in the mathematical physics the terms “direct models” and “inverse models” do not exist. The Authors should not introduce new nomenclature if it is not necessary (page 3, lines 15-20).
My second remark is dealing with Eq. (4). In explanation given below this equation it is stated that dT is “the time step of integration”. In definition of integral “the step of integration” does not exist and dT has another interpretation (please see definition of integral in any book). The time step of integration will occur when the convolution integral (4) is replaced using the respective approximating formula.

Hide

ED: Publish subject to minor revisions (further review by Editor) (28 Apr 2017) by Mauro Giudici

AR by Cybèle Cholet on behalf of the Authors (03 May 2017) Author's response Manuscript

ED: Publish subject to minor revisions (further review by Editor) (24 May 2017) by Mauro Giudici

AR by Cybèle Cholet on behalf of the Authors (01 Jun 2017) Author's response Manuscript

ED: Publish subject to technical corrections (02 Jun 2017) by Mauro Giudici

AR by Cybèle Cholet on behalf of the Authors (08 Jun 2017) Author's response Manuscript

Short summary

This paper aims to improve the understanding of transport processes in karst aquifers, which remains a great challenge due to its complex nature. A framework is proposed to identify and quantify the spatio-temporal variability of lateral exchanges along a karst conduit network during flood events, for both flow and solute transport. An inverse problem approach is used on discharge and water mineralization data sets and gives new insights into the hydrogeological behavior of such complex systems.