Review Reports

Round 1

Reviewer 1 Report

The paper title "Bathymetry development and flow analyses using two-dimensional numerical modeling approach for Lake Victoria" proposed two scientific questions:

1. "How are the systematic methods developed for lake bathymetry relevant for lake numerical and hydrodynamic modelling?"

2. "How did we develop the lake bathymetry model and flow model in CM?"

Both question are very interesting and can provide an useful insight for Lake Victoria and their importance in the "East African Rift System". The paper does an interesting introduction and motivation to the study of shallow water flow in Lake Victoria, it then introduces "Materials and Methods" in section 3, explaining in detail the source of the data available for the bathymetry. Within section 3, mention "Interpolation by Kriging", "Delaunay triangulization and interpolation" and "Merging the iso-curve data with the NAFIRRI data", which I think are related to the scientific question 1. This is a bit puzzle since question 1 mentions a systematic development and it would have been interesting to observe more methods or at least obtained perturbed outputs from those models. What it is analyzed is important and interesting, but too limited.

Later in section 4, "Governing Equations, boundary conditions and mesh geometry", they authors provide an overview of the SWE and also include different type of boundary conditions. The section finished with the subsection "Comsol model setup".

Section 5, "Results and Discussion", show several numerical experiments, including short and long period of time simulations. They main analysis seems to forget the scientific question 1 (SQ1). However, scientific question 2 (SQ2) does seems to be consider completely.

Finally, for the "Conclusions", they claim a new systematic method was developed for lake bathymetry and that also predicted water levels reasonably, among others.

So, I strongly recommend the authors to highlight more the importance of SQ1 and analyze the effect of the bathymetry for this case, since it seems to be critical for time-invariant flows.

Author Response

Dear Reviewer,

Thank you very much for all your detailed and constructive comments.

Please see the annotated version of the manuscript for detailed replies and actions. We now present DACE toolbox with Delaunay (using iso-depth curve) that produced 3D grid-based interpolation for lake bathymetry; the model simulations are presented by Matlab and COMSOL. We have bit elaborated all of the sections to make clear and understandable of the Manuscript and re-structured some sections. We have improved the English text, and we have tried to follow all suggestions and comments. Please find out the attached file where we have listed all of your comments as well as our reply and action.

Best Regards,

Seema Paul (Author)

Author Response File: Author Response.pdf

Reviewer 2 Report

This manuscript seeks to improve upon existing bathymetry data developments for the Lake Victoria water basin by bias-correcting coarse resolution contour data with new sounding depth-data obtained  from the NaFIRRI data set. They use a shallow water modelling framework, powered by Comsol Multiphysics (CM) finite element software suite, to validate their newly constructed bathymetry map and coastline geometry against historical data for mean water level.

I enjoyed reading this manuscript, but I feel that the authors may have missed an opportunity to provide further details and insights into their bias-correction methodology for obtaining the improved bathymetry map used in the simulations. Furthermore, the introduction section appears to be missing some other relevant modelling literature with respect to Lake Victoria. See for instance, Nyamweya et al., PlosONE (2016). There are also some open questions surrounding the finite element validation methodology the authors have adopted. I will address these questions in logical order below in my suggestions for the manuscript.

I would recommend major revisions before considering this manuscript for general publication, see below for details.

Corrections/Suggestions:

line 58: "Unfortunately, the details [of the] bathymetry survey..." (words are missing). line 65: You mention that lake inflow/outflow as well as precipitation and evaporation are important in the lake dynamics, but what about other common transport-driving limnic driving factors, e.g., inundation, wind stress, tides, vertical transport, Coriolis force? Are these factors unimportant for Lake Victoria or are they simply just not mentioned here? Please clarify. line 70: You've made a choice to adopt CM to carry out your simulations, but you haven't stated why. What other tools were considered? Why choose CM over an open-source tool like PetSc or GeoClaw? line 98: I would not simply state that numerical modelling is "an option", it is perhaps the best tool available for the task at hand given that analytical methods are theoretically impossible for sophisticated geometries. lines 107-109 (first sentence): Incorrect grammar here. It is not clear what you are trying to say. line 134: "It should be noted that this is only a test..." The use of "this" here leads to ambiguity; consider clarifying. e.g., "this validation approach..." line 140: ‘celerity’ is the wave speed, not the wave height. line 176. Please provide a reference and a proper complete citation for the "old maps"/data. Reference [14] (line 512). line 184: "...from giving [given?] depth data points" Section 3.2.5 (general comment): You mention that you are using the Delaunay triangulation plus interpolation to construct a cartesian DEM. It seems like this could be done using the Matlab intrinsic 'griddata' function, which already implements this procedure for you. Was this considered? Line 228: Can you provide the details on this bilinear transformation? e.g., what is its functional form and how are weights/control points chosen? Explaining these details to the reader would help with this novel bathymetry reconstruction approach. line 229: "...best overall fit as judged by the eye." I find it troubling that a quantitative measure was not used to determine the best fit. Please explain why not. line 242: Provide a citation for the emergence of shocks/hydraulic jumps (perhaps LeVeque finite volume book) line 246: "... with the vertical component". Do you mean 'poleward (northing) component'? Line 249: One usually only sees viscosity terms in the momentum equations in depth-averaged equations. Please explain why a diffusion-like term appears in the conservation of mass equation here. Lines 263-265: Please provide a citation for the statement that different Froude number regimes amount to a different number of required boundary conditions. This is not well-known, at least not to me, anyways. Lines 313-316: Can you give a sentence to indicate what typical run-times were for CM and on what type of processor?

General comments/questions for the authors: 

Since your focus is on long time simulations, implicit time-stepping appears to be a reasonable choice, but it effectively filters out the effects of the short time-scale surface gravity waves. Why not consider a simpler set of equations that neglects the gravity waves if this is the case? e.g., barotropic vorticity equation if inertial effects are important, or a ‘diffusion-wave’ type equation if frictional effects are dominant.

Though quite well-resolved, the finite element mesh used in the simulations uses linear shape functions along the boundary which are known to result in spurious/singular vorticity production at re-entrant corners (see Steinmoeller et al., Ocean Modelling, 2016). Are such singular corners a problem for the presented simulations, why or why not?

I realize that CM is something of a black box, but it would serve the numerically-minded reader to have some further details on its finite element internals. For instance, it is quite well-known that continuous elements are not ideal for hyperbolic equation sets (such as the shallow water system used here). What stabilization approach does Comsol adopt for such types of equations, e.g., when nonlinear advection is important and shocks may form.

The authors say that the equations are written in conservation form which is necessary in the case of shocks, then proceed to say their simulations are nearly fully linear which appears to contradict their choice in the methods section. The authors make little or no mention of inundation effects, which are certainly as (maybe more?) important than hydraulic jumps in this case. The shallow water / Saint-Venant system chosen here can model coastal inundation, usually under some light numerical adjustments, but this does not appear to have been done, so why not? Some further thought should be put into what the physical modelling regime is vs. what types of equations and terms are being used in the model.

Author Response

Dear Reviewer,

Thank you very much for all your detailed and constructive comments.

Please see the annotated version of the manuscript for detailed replies and actions. We now present DACE toolbox with Delaunay (using iso-depth curve) that produced 3D grid-based interpolation for lake bathymetry; the model simulations are presented by Matlab and COMSOL. We have bit elaborated all of the sections to make clear and understandable of the Manuscript and re-structured some sections. We have improved the English text, and we have tried to follow all suggestions and comments. Please find out the attached file where we have listed all of your comments as well as our reply and action.

Best Regards,

Seema Paul (Author)

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Dear Authors,

Thanks for including the suggestions. The manuscript has improved a lot. However, I still have some minor suggestions about the format, which may be related to the PDF file I received with the highlighted green. The issue is that some equations look strange, for instance:

1.- Equation (16) has a "Precip" where "Pr" seems to have a different format from "ecip". Same in (18).

2.- Equation (19) has a s.t. at the end, is the constraint missing?

Thanks.

Author Response

Dear Reviewer,

Thank you for your response, present minor revisions have been made following your comments and suggestions.

Best Regards,

Seema Paul

Author Response File: Author Response.docx

Reviewer 2 Report

I appreciate the work the authors have put into this revised form of the manuscript. I feel that with the expanded methods section, that they are now capitalizing on the key pieces of novelty within the scope of this work.

While I still have my concerns about the choices made in numerical modelling with respect to the relevant physics at these length and time scales, I feel that since the majority of the modelling work is already completed and it would be a monumental task to re-do, I won't push on this further since the end-results indeed quite a good fit to the historical data and are therefore convincing to the reader.

In any case, I would make the following comments and suggestions as a follow-up, and recommend an amendment to Section 3 as follows:

In their rebuttal, the authors say that switching elements on or off as an inundation model is "downright impossible", but provide examples of Galerkin-based models that do just this, so I suspect what the authors really mean is that it is impossible to carry out this task within the COMSOL framework. Which leads me back to my original question, which is whether COMSOL is really the best tool for the job.

Therefore, I would suggest that in the methods section (perhaps a new subsection at the end of section 3), the authors at least give mention and citation to some other academic/open-source models capable of modelling shallow water flow for Lake Victoria (e.g, the Delft model, GeoClaw, POM, ELCOM, etc.). They can then lead into an explanation of why they chose COMSOL (e.g., perhaps Comsol is easy to setup/use? less or no custom code to write; less configuration?), then this prepares the reader for the explanation of model equations and boundary conditions used in COMSOL, as done in Section 4.

There is no reason to give the reader the impression that COMSOL is the best and/or the only choice of modelling software for the physics considered in this study.

Author Response

Dear Reviewer,

Thank you for your response, present minor revisions have been made following your comments and suggestions.

Best Regards,

Seema Paul

Author Response File: Author Response.docx