the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Estimating flood discharge at river bridges using the entropy theory. Insights from Computational Fluid Dynamics flow fields
Abstract. Estimating the flow velocity and discharge in rivers is of particular interest for monitoring, modelling, and research purposes. Instruments for measuring water level and surface velocity are generally mounted on bridge decks, and this poses a challenge because the bridge structure (e.g., piers and abutments) can lead to perturbated flow fields. The current research aims to investigate the applicability of the entropy theory to estimate the velocity distribution and the discharge in the vicinity of river bridges. To this purpose, a Computational Fluid Dynamics (CFD) model is used to obtain threedimensional flow fields along a stretch of the Paglia River (central Italy), where a historical multiarch bridge strongly affects flood flows. The input data for the entropy model include the crosssectional bathymetry and the surface velocity provided by the numerical simulations. Different flow conditions and crosssections, either upstream and downstream of the bridge, are considered. It is found that the entropy model can be applied safely upstream of the bridge, also when forced with a single (i.e., the maximum) value of the surface velocity, with errors on total discharge below 13 % in the considered case. On the contrary, downstream the bridge, the wakes generated by the bridge piers strongly affect the velocity distribution, both in the spanwise and in the vertical directions, and for very long distances. Here, notwithstanding the complex and multimodal spanwise distribution of flow velocity, the entropy model estimates the discharge with error lower than 8 % if forced with the riverwide distribution of the surface velocity. The present study has important implications for the optimal positioning of sensors and suggest the potential of using CFD modelling and entropy theory jointly to foster the knowledge of river systems.
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RC1: 'Comment on hess2023253', Anonymous Referee #1, 10 Jan 2024
Review of “Estimating flood discharges at river bridges using the entropy theory. Insights from Computational Fluid Dynamics flow fields”
By Bahmanpouri, F. et al.
January 10th, 2024
The manuscript presents an application of entropy theory to determine the discharge at a river section from measurements of the surface velocity. The key features of the manuscript are (i) comparing the discharge estimates when a transverse profile of surface velocity is entirely known and when only a singlepoint value of surface velocity is known and (ii) considering sections where the flow distribution is significantly disturbed by interfering structures like bridges.
The manuscript is quite interesting but I feel that some revision could strengthen it and make the method more appealing for readers. I have some major concerns with this manuscript:
(1)
Section 2.5, entitled “Entropy theory”, provides some equations but no concept at all. Which is the grounding principle of this method? Which is the physical meaning of M and phi(M) or, in other words, what do these parameters parameterize? No need to rewrite referenced papers, obviously, but providing some conceptual ground would be needed to understand the description and interpret later findings (for example, at line 234 it is mentioned that the disturbance by the bridge reduces the entropy parameter; why? Which is the physical interpretation?).
(2)
The authors should better describe how they use data and to do what. My understanding is that they rely on surface velocity measurements by ADCP and on the results of the 3D simulations. The ADCP measurements are used to “validate the numerical models” (line 136), while the entropy theory is applied to the simulated flow fields. For the latter, the procedure is: (i) determining the entropy parameters phi(M) and M based on the simulated velocity distribution in a cross section (obtaining the values listed in Tab 2 and plotted in Fig 3); (ii) determining a velocity distribution in the cross section based on the surface velocity from the simulations (entire profile or singlepoint); (iii) integrating the obtained velocity distribution; and (iv) compare the discharge with that used as an upstream boundary condition in the simulations. Now, steps (i) and (ii) sound like creating a loop, more or less like when the same data are used for calibration/training and validation. It is not completely so, since a bulk estimate of an entropy parameter is later used to determine a velocity profile at every vertical, but some selfdependence should be present. Can the authors comment on this issue? Or, I may have misunderstood the procedure, that would need more explanation.
(3)
It is not clear to me how this method could be applied at a section where the entropy parameter is not known, starting just from a profile of surface velocity. My impression is that, in such a case, a tentative value of the entropy parameter should be used. How estimated? Expert judgement leading to sound values, as we normally do for roughness? I note that also the iterative procedure described at lines 192 and following “can be applied for sites with a given phi(M)”.
Related to this issue, I note that an estimated discharge sounds quite sensitive to the entropy parameter, as the two quantities are linearly dependent based on eq. (2).
The problem is the same that affects discharge determination based on largescale PIV (e.g., 10.1029/2008WR006950, 10.1016/j.jhydrol.2010.05.049) where a coefficient is used to pass from surface to depthaveraged velocity. The coefficient is not known, but most references use 0.85 as a suitable value. In the present context, one might use phi(M) = 0.72 for “undisturbed” flows (average of values for 50 and +200 in Tab 2), but it will be hard to have a robust indication for disturbed flows.
(4)
I would suggest to carefully reconsider the use of “at” river bridges in the title. My initial interpretation was that the focus of the paper would be on sections immediately upstream or downstream of the bridge, and I think that most hydraulicians would have done the same. Instead, the paper considers sections in the vicinity of the bridge but at some distance from it (some/several widths). This is quite important for applying the method using monitoring data since, as remarked by the authors, instrumentation is generally mounted on the bridge.
Several additional comments (listed by line)
16: I think that mentioning explicitly that 12 sample applications are considered (3 flow rates by 4 sections) would make the manuscript findings sound more robust.
17: not sure that the word “safely” is the appropriate one to state that the method is satisfactorily accurate.
5068: I find these lines a bit hard to follow, due to the lack of a clear purpose. To me, the point is that one would like to determine Q based on its definition, that is integral(v)dA. Since the crosssectional distribution of velocity is unknown, a method to infer the crosssectional velocity distribution from other data (that are in the end surface velocities) is sought. I would recommend to use this line of thought to revise these lines.
70: the method based on a ratio between surface and depthaveraged velocities could be mentioned as an alternative one (some references are found in major comment 3).
76: what is meant with “weak” gauging site?
107: if the river is characterized by high sediment transport, one can expect relevant morphologic changes. The simulations carried on in this work are with a fixed bed and always the same geometry; this is not a problem for the present manuscript but morphologic changes complicate the business in case of future application of the method. In the present version of the manuscript this is almost overlooked, apart from a quick mention at the end of the Conclusions. Few more lines on the issue would be an important addition.
168: the events could be better described in terms of (i) flow over the sediment bar, (ii) pressurized flow below the arches, and (iii) bridge overflow. Later in the manuscript the reader will understand that only for the strongest event there was incipient pressurization of flow below the arches. It would be probably better to add details here.
173: is it possible to give some value of return period for these events?
Tab 1: the discharge values come, I guess, from rating curves mentioned at line 133. Is it so?
Eq. (2) and (3): this is the first time M and phi(M) appear, but they are not given a name.
Tab 2: please indicate how the values of phi(M) and M were obtained. From (3) and (2), respectively?
236: I would say this is true also for the 2019 event.
294: I think that “accuracy” would be better than “precision” here. Same at line 366.
321: actually in Tab 4 the errors for elliptic are larger than those for parabolic.
354: like the one mounted on this bridge (I mean the radar sensor).
Citation: https://doi.org/10.5194/hess2023253RC1  AC1: 'Reply on RC1', Daniele P. Viero, 01 Mar 2024

RC2: 'Comment on hess2023253 RC2 Estimating flood discharge at river bridges using the entropy theory: Insights from Computational Fluid dynamics flow fields', Anonymous Referee #2, 18 Jan 2024
The comment was uploaded in the form of a supplement: https://hess.copernicus.org/preprints/hess2023253/hess2023253RC2supplement.pdf
 AC2: 'Reply on RC2', Daniele P. Viero, 01 Mar 2024
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