Beyond Water Surface Profiles: A New Iterative Methodology for 2D Model Calibration in Rivers Using Velocity Data from Multiple Cross-Sections

1. Summary

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions highlighted in red in the resubmitted files.

Point-by-point response to Comments and Suggestions for Authors

Comments 1: [I hesitate about the words "Beyond longitudinal profiles" in the title, because the water surface data considered in the paper are still 1D profiles. When accepting to review this paper, these words made me expect a solution to the problem that water level gauges usually don't provide 2D water surface topography information. Water levels at river banks may deviate from values at centre-lines due to, for instance, bends (transverse water level slopes due to centrifugal forces) and braided configurations (gauges located along inactive channels). The first sentence of the abstract ("Observed longitudinal water surface profiles are commonly used ..") reinforces this expectation. I therefore recommend replacing "Beyond longitudinal profiles" by "Beyond water surface profiles". That more accurately describes the contents of the paper and avoids creating wrong expectations.]

Response 1: Thank you for pointing this out. We agree with this comment. Therefore, we have changed the title to: BEYOND WATER SURFACE PROFILES: A NEW METHODOLOGY FOR 2D MODEL CALIBRATION IN RIVERS.

Comments 2: [The introduction explains the contents of the paper from line 115 onwards, but it does not state an objective. The objective appears as late as in line 609, almost at the end of the paper. I recommend to be more clear about this in the introduction too.]

Response 2: Agree. We have modified the introduction to emphasize this point. We add the following paragraph (lines 55-62). “The present study develops and validates a novel methodology for calibrating two-dimensional hydrodynamic models using high-resolution field data from ADCP and MBES. The approach enhances simulations' accuracy by addressing the limitations of traditional calibration methods, which often rely solely on longitudinal water surface profiles and/or individual cross section velocity data, thereby neglecting the spatial variability of velocity fields. By introducing an iterative, systematic alignment of bathymetric and hydrodynamic data and employing robust statistical metrics, the proposed Matlab-based methodology provides a more comprehensive and reproducible framework for evaluating model performance”.

Comments 3: [The authors generally make a correct distinction between "bed morphology" (= map of bed elevations with respect to a horizontal datum) and "bathymetry" (= map of water depths below a water surface). MBES instruments do produce bathymetry data in bathymetric surveys, but those are subsequently converted into bed elevation data. The distinction goes wrong, however, in the legend of Figure 7 panel c which displays the term "bathymetry" for bed elevations in metres above sea level (masl). As it is not always clear in the text whether bed morphology or bathymetry is intended, I recommend verifying this throughout the paper and correcting whenever necessary.]

Response 3: Agree. We have revised all text and replaced the term in correspondence with the clarification. Particularly in Figure 7 and its captions, we use elevation for clarity since the map incorporates both channel bed and floodplain elevations.

Comments 4: [Lines 108-110: Remove subjective qualification "very" (twice). Same in line 478.]

Response 4: Agree. We removed the qualification in lines 108, 110, and 477.

Comments 5: [Line 318, "overly steep slopes might suggest insufficient energy dissipation": I don't understand this sentence. Steeper slopes correspond to more energy dissipation per unit of long-stream distance, not less energy dissipation. Please explain or correct.]

Response 5: Agree. We have modified the paragraph for clarity (lines 327-332) as: For example, if the measured WSL has steeper slopes than the simulation, it might suggest insufficient energy dissipation (requiring increased roughness within the model). Alternatively, if the measured WSL has lower slopes than the model, it could indicate the need for refinements to the  in the model. Careful evaluation of these factors helps ensure that both local and domain-wide calibration objectives are met.

Comments 6: [Line 344: The unit of flow velocity is meter per second, not kilohertz. Accordingly, "ms-1" (= inverse of milliseconds) must be written as "m.s-1" or "m s-1", like the correct notation in line 401 and Figure 10.]

Response 6: Agree. We modified the units as  m s^-1.

Comments 7: [Does "EO" on page 10 refer to observational error (lines 358, 360, 371)? If not, please explain. If it does, then why is it not spelled "OE" like on page 9 (lines 337, 340, 344)?.]

Response 7: Agree. We have, changed "EO" on page 10 to refer to observational error (lines 366 - 382) by “OE”

Comments 8: [The Manning n roughness is not a dimensionless number, so it requires specification of the corresponding unit throughout the paper (e.g. lines 432-435, line 490, Table 3, line 525, line 561, line 576, Figure 11).

Response 8: Agree. We have added the units for the n Manning in the correspondent lines and Table 3   

Comments 9: [The "n" of the Manning n roughness needs to be written in italics. This has been done correctly in line 434 but not in line 432. Please verify this for the entire paper.]

Response 9: Agree. We revised all paper and modified the n format where necessary

Comments 10: [Caption of Table 2: Please specify the co-ordinate system (State Plane Coordinate System?) and the unit (metres?) used for values of easting and northing.]

Response 10: Agree. We added in the caption of Table 2 the cartesian coordinates and added the units [m] in columns 4 and 5 from Table 2.

Comments 11: [Line 476: "spatially, fairly even" => "spatially fairly even".]

Response 11: Agree. We have done the suggestion line 499.

Comments 12: [Figure 11: Explain the numbers 0 to 38 around the circles in the figure caption.]

Response 12: Agree. We modified the figure 11 caption (line 580) and added the suggestion.  

1. Summary

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions highlighted in red in the resubmitted files.

Point-by-point response to Comments and Suggestions for Authors

Comments 1: [The Authors used as numerical model the Telemac2D. Despite it is a well known software some explanation on the equations should be presented.]

Response 1: Thank you for pointing this out. We added the next paragraph to explain the main characteristics of Telemac2D, and we added a reference [29] (lines 403-412). "Telemac2D is a widely used hydraulic simulation software that models free-surface flow in rivers, estuaries, and coastal environments [29]. It solves shallow water equations (Saint-Venant equations) using finite element or finite volume methods, allowing flexible mesh configurations to capture complex geometries. These equations consist of continuity and momentum conservation principles that account for variations in water depth and flow velocities over time and space. Telemac2D incorporates advanced numerical schemes to ensure stability and accuracy, even in strong gradients like hydraulic jumps or steep slopes. Additionally, it can handle complex boundary conditions, multi-dimensional interactions, and sediment transport, making it a robust tool for hydrodynamic modeling".

Comments 2: [A crucial point of the proposed methodology is the number of measurements required for a good calibration of the numerical model. Authors should better investigate such point, evaluating the minimum data set needed for a reasonable model calibration.]

Response 2:  We appreciate the observation and understand the importance of evaluating the minimum data required to calibrate hydrodynamic models. However, we want to clarify that the main objective of this work is not to determine the number of measurements needed for proper calibration but rather to propose an innovative methodology for robustly integrating spatial measurements and hydrodynamic simulations into the calibration of two-dimensional models. Additionally, as our presented data were collected from only one field site, adequately addressing the minimum amount of data needed is not possible, as this will vary between field sites depending on the hydrodynamic complexity being investigated. We have added a paragraph with relevant references that provide guidance and considerations on the selection and amount of data required (lines 620-627). Although a critical aspect of hydrodynamic modeling is determining the appropriate amount and distribution of calibration data, this study does not aim to establish the minimum data requirements for effective calibration. Still, we acknowledge the relevance of this topic. Works as [32] highlight that data density and geomorphological alignment improve model accuracy. Similarly, [33] emphasizes carefully selecting calibration data and conducting sensitivity analyses to minimize input uncertainties. These references provide context for future research, though this study focuses on proposing a robust calibration methodology rather than data thresholds, which will depend to some extent on the hydrodynamic complexity of the system being modeled.

Comments 3: [Alignment of bed profiles reported in Figure 8 does not seem very important. This point should be stressed by the Authors.]

Response 3: We appreciate the observation regarding the importance of the bed profile alignment shown in Figure 8. We disagree with this comment and the statement here. One of the leading drivers for this calibration method is to ensure that the two datasets are consistent. In many modeling cases, the elevational mesh is created using the MBES data, and then separately evaluated using the ADCP velocity data. However, there is often very little consideration for how well the ADCP bed profiles match with the MBES or model mesh, and misalignments in those profiles could lead to discrepancies between the measured and simulated velocities.

Comments 4: [If migrating bed forms are in the stream, is the procedure applicable? This point should be stressed by the Authors.]

Response 4: Thank you for your observation. We acknowledge the relevance of considering migrating bed forms in hydrodynamic analyses. However, the present study assumes minimal bed adjustments and does not account for the movement of bedforms. The methodology proposed was explicitly designed for scenarios where the hydrologic conditions remain steady (non-temporally varying). In most cases, careful consideration is given to ensure that ADCP and MBES measurements in the field can be conducted in a time period where the discharge is relatively constant. Under these conditions, it is unlikely that the bedform geometries will vary considerably (e.g., increasing or decreasing dune height). Thus while bedforms may be migrating, the overall effect on the 2D flow field should be minimal, and the approach presented valid. We have added a paragraph addressing these considerations for application of this approach to (lines 659-670) as: Finally, the hydrodynamic conditions of the system should always be carefully considered whenever field measurements are acquired, particularly if those measurements are intended for use in calibrating numerical models. Since acquisition of ADCP data along multiple cross-sections within a study area does require some amount of time, it is important to ensure that the discharge remains relatively constant during the measurement period. Similarly, if MBES data are to be coupled with the ADCP measurements, the discharge should remain relatively constant for the entire field campaign to ensure similar bed morphology. Bedforms are known to adjust their size with varying discharge conditions (Nelson et al., 2011), resulting in non-neglible variations to the flow roughness that can alter patterns and magnitudes of 2D flow fields (Simons and Richardson, 1966). While bedforms can migrate during conditions of steady flow, these fluctuations in local bed elevation will not have a considerable effect on the time-averaged 2D flow field.

Comments 5:  One example is not enough for demonstrating the reliability of the proposed procedure. At least another application should be presented.]

Response 5: We appreciate the suggestion to include an additional example to demonstrate the reliability of the proposed procedure further, however we respectfully disagree. The primary objective of this study is to illustrate the methodology and its application through a detailed example. Adding another case would unnecessarily extend the article without providing significant additional insight into the methodology. Instead, we recommend applying the proposed methodology following the guidance provided in (24), which can be downloaded as supplementary material. This guide outlines a systematic approach for implementing and testing the methodology in other scenarios.

Comments 6: [Page 2 row 53: it is Figure 1, not Figure 2.]

Response 6: We reorder the paragraph for clarity (lines 55 – 62) thus, the number is correct: Figure 2

Comments 7: [and rows 61-69: Figure 1 not Figure 2. Figures 2(c) and 2(d) do not exist.]

Response 7: We reorder the paragraph for clarity (lines 100 – 121) thus, the numbers are corrects

Comments 8: [In general pay attention to the figures and their numeration.).

Response 8: We reviewed the numeration   

1. Summary

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions highlighted in red in the resubmitted files.

Point-by-point response to Comments and Suggestions for Authors

Comments 1: [ Authors state that they used all the data measured by different methods for the calibration. But there is no discussion on the error of the measurements. If one technique allows one to obtain data of much higher quality (with much less measurement error) compared to the second one, then the alignment effectiveness might be poor. ]

Response 1: Thank you for pointing this out. It is important to note that our study was not focused on analyzing the measurement errors intrinsic to each piece of equipment. Instead, one objective was precisely the challenge of aligning measurements obtained with different equipment, particularly focusing on the difference in resolution between the ADCP and MBES. The MBES provides high-resolution bathymetric data, while the ADCP offers hydrodynamic data with lower resolution. Recognizing this disparity, one of the main contributions of the article is the development of a novel cross-correlation methodology to align the lower-resolution ADCP measurements with the higher-resolution MBES data.

Comments 2: [ I have not found any quantitative comparison of the proposed methodology and regular approaches that sustain the advantages of the new methodology. The conclusion section also does not contain any references to figs. which could support the statements made by the authors.]

Response 2:  Thank you for pointing this out. The lack of a direct quantitative comparison between the proposed methodology and traditional approaches arises because the objectives of the two methodologies differ significantly. Traditional calibration methods primarily rely on reproducing water surface profiles, which are one-dimensional and do not account for the spatial variability of velocity distributions within the river. While this approach can provide a general agreement for water levels, it does not capture the complex two-dimensional (2D) flow dynamics that occur in natural river systems. In contrast, the proposed methodology not only reproduces the water surface profile, as traditional methods do, but also includes a second calibration step that incorporates the distribution of velocities within cross-sections. By aligning ADCP and MBES data and calibrating the simulated depth-averaged velocity fields, the methodology captures measured flow effects in the river more accurately. This dual calibration ensures a better representation of the hydrodynamics, particularly for 2D phenomena.

We disagree with the last part about the conclusion. We don’t add any reference to figs or tables to keep it succinct.

Comments 3: [Why HydroAPP almost not described in the manuscript? Even the name is not mentioned.]

Response 3: The manuscript briefly mentions the HydroAPP tool as part of the methodology for spatial alignment and evaluation of 2D hydrodynamic simulations but does not elaborate on its specifics. This is because the detailed description and implementation of HydroAPP are provided as supplementary material in Reference 24. The reference includes the MATLAB© script, a user guide, and complementary data necessary for its application. It allows the manuscript to focus on presenting the broader methodology and case study results while leaving the technical and operational details of the tool for interested readers to explore in the supplementary material. By separating these elements, the authors ensure that the primary document remains concise and focused on the scientific contribution while still making the technical details accessible for replication and further use

Comments 4: [At least a brief description of the numerical model used in the study is required. What settings were implemented in TELEMAC-2D?.]

Response 4: Thank you for pointing this out. We added the next paragraph to explain the main characteristics of Telemac2D, and we added a reference [29] (lines 403-412). "Telemac2D is a widely used hydraulic simulation software that models free-surface flow in rivers, estuaries, and coastal environments [29]. It solves shallow water equations (Saint-Venant equations) using finite element or finite volume methods, allowing flexible mesh configurations to capture complex geometries. These equations consist of continuity and momentum conservation principles that account for variations in water depth and flow velocities over time and space. Telemac2D incorporates advanced numerical schemes to ensure stability and accuracy, even in strong gradients like hydraulic jumps or steep slopes. Additionally, it can handle complex boundary conditions, multi-dimensional interactions, and sediment transport, making it a robust tool for hydrodynamic modeling".

Comments 5:  Line 91. In my opinion, reference in a paragraph beginning should be avoided.]

Response 5: We appreciate the suggestion; we rewrite the sentence (line 79) as: Previous work has adapted statistical methods used in meteorological sciences for the performance evaluation of hydrodynamic models.  [15] studied estuarine hydrodynamics and classified the agreement between measured and simulated velocities based on the relative error.   

Comments 6: [Figure 1 (a) contains a test with too small font. At least a more detailed description in the caption is required. ]

Response 6: We add a more detail description in the caption of Figure 1 as: Figure 1.  Field data for hydrodynamic modeling: (a) Streamwise velocity field measured with an ADCP, showing velocity magnitudes in color (red: high, blue: low) and transverse flow vectors, with the riverbed profile (gray line); (b) High-resolution bathymetry captured with a MBES, illustrating detailed channel morphology, including meander bends and sedimentary features.

Comments 7: [The importance of the sentence “we understand that uncertainties in input data exist, such as bathymetric measurements, boundary conditions, and flow and water level measurements, and these uncertainties can affect the simulation results” is unclear (line 590). In my opinion, this is too obvious statement. ]

Response 7: We delete the sentence (lines 614).

Comments 8: [The following sentence is difficult to understand: “This process also yielded an observed channel centerline water surface profile with associated uncertainty information” (line 631). What is “an observed channel centerline”.)

Response 8: We delete the entire sentence