Computation of Time of Concentration Based on Two-Dimensional Hydraulic Simulation

Round 1

Reviewer 1 Report

I carefully read the manuscript. It is a very interesting topic for hydrologists, however, it is required to be improved considering the following comments to be addressed and prepare the revised version.

- what was the accuracy of the EC meter used in field measurements?, more details should be added

what future works do you propose to continue your study?, it better be added in the end of the conclusion section

- explain the limitations of your study., it would be great to add these limitations at the end of the results and discussion section

- update the references according to the latest studies and double-check the reference formatting

- how was the model stabilized?, it would be great to add this detail in the methodology section

- it will be great to pay more attention to improving the quality of the figures and tables, for example, Table 2 and Figure 3

Author Response

Comment 1:

What was the accuracy of the EC meter used in the field measurement? More details should be added

Response:

Thanks for your comment. The EC meter accuracy was in Micro Siemens per centimeter (µs/cm). Any changes in Electrical Conductivity were measured by the device. Lines 213-214.

Comment 2:

What future works do you propose to continue your study? It better be added in the end of the conclusion section

Response:

Thanks for your suggestions. The comment is addressed in the conclusion section. Lines 602-608.

1-It is recommended to consider graphical method (rainfall-runoff) as an alternative of salt solution tracing in a gauged basin as a benchmark to compare 2D simulation output.

2-In this study, to introduce the bathymetry into the model, the DEM file with the resolution of 12.5m from Advanced Land Observation Satellite (ALOS) was employed. It is recommended to apply higher resolution satellites or other methods such as using drone to survey map of the area or bathymetry with high resolution in order to investigate the map resolution effect on TC.

Comment 3:

Explain the limitations of your study. It would be great to add these limitations at the end of the results and discussion section.

Response:

Thanks for your comment. To represent underlying terrain, maps with different resolution can be applied. Therefore, map with less special resolution, for instance, more than 30 meters, cannot represent rivers with the width of 15 meters. Therefore, this limitation should be taken into account. In addition, to run a fast 2D simulation, users need at least 3.4 GHz or higher CPU processor, otherwise, the simulation would be time consuming. Lines 558-563.

Comment 4:

Update the references according to the latest studies and double check the reference formatting.

Response:

The new and latest studies are added in the reference section. In addition, the reference section is checked about formatting. The new references are as follows:

González-Álvarez, Á.; Molina-Pérez, J.; Meza-Zúñiga, B.; Viloria-Marimón, O.M.; Tesfagiorgis, K.; Mouthón-Bello, J.A. Assessing the Performance of Different Time of Concentration Equations in Urban Ungauged Watersheds: Case Study of Cartagena de Indias, Colombia. Hydrology 2020, 7, 47. doi: 10.3390/hydrology7030047. Lines 662-665.

Comment 5:

How was the model stabilized? It would be great to add this detail in the methodology section.

Response:

Thanks for your comments. To stabilize the model, selecting appropriate time step is crucial. Selecting appropriate time step is function of both cell size and the velocity of flow passing through cells. As a result, we used trial and error method considering following relation:

 with the max C=5

In which C is Courant Number and V is the wave velocity,  is time step and  is cell size. After determining cell size in early steps, users try different time steps to gain stable results. Fortunately, HEC-RAS 5 has an option which enables the user to select a desired bound for Courant number in which the model picks the best time step in each cell to stabilize the simulation. This option decreases the instability issues and accelerate the required time for running the model. Accordingly, Courant number bounded between 0.5 to 4. It confirms that estimation is not affected by both cell size and time steps. Line 251-261.

Comment 6:

It will be great to pay more attention to improving the quality of the figures and tables, for example, table 2 and figure 3.

Response:

Thanks for your suggestion. Table 2 is removed and its data is added to the table 2-6 in the new version of the manuscript. Figure 3 is changed and modified and is shown as Figure 2 in the new version of the manuscript as well.

Author Response File: Author Response.docx

Reviewer 2 Report

General comments

This paper developed a 2-dimensional HEC-RAS model to calculated the time of concentration (TC) of a given watershed, and compared the HEC-RAS simulated TC to TC results from 31 empirical equations. Sensitivity analysis of parameters of the 31 empirical equations are also conducted. While the research topic of comparing performances of empirical equations and hydraulic models is plausible, some questions about experimental procedure and result discussion needs to be further discussed.

Firstly, the empirical models used for comparison needs to be more carefully selected. It’s not appropriate to include calculation results form empirical equations that are clearly not suitable based on watershed area.

Secondly, the purpose and conclusion of sensitivity test need to be more clearly stated. Since there are adequate literatures stating the importance of selected parameters, and that sensitivity is not necessarily directly related to accuracy, the significance of section 3.1.1 is low.

The paper can be better organized if HEC-RAS results are put in front of empirical equations, as HEC-RAS is the actual important content.

Detailed points

Section 1 Introduction

1.TC and Tc are both used to represent time of concentration in the text, and are separately defined in section 1. However I don't see the differences between them. Use only use abbreviation if they are one, or define more different abbreviations for different parameters.

2. Paragraphs starting line 79 and line 97 can be more clear if they lead to a conclusion. For example, empirical equations are site specific and it’s hard to decide their accuracy for an area of interest. Also, it’s not clear why Bennis and Crobeddu (2017) and Sadatinejad (2012) should be in another paragraph.

Section 2 Methodology

1. Please provide citation for rainfall, temperature, evaporation, and Curve Number data if they are published online, or cite the methodology used to get CN (line 160-175).

2. Line 200-203. Is the measured travel time averaged?  What do you mean by ‘measurement were started as close as possible to the basin’s border to minimize the overland flow duration’? 

Section 3 Results and Discussion

1. Tables 3-7 and Figure 2. As there are 31 empirical equations, it’s hard for readers to remember the equation when they read about the equation names. It would be clearer if table 2 can be combined with tables 3-7, or at least equations are included in Tables 3-7. Also, readers can interpret the results better if the numbers in Figure 2 are listed in Tables 3-7.

2. Line 308-317. I am not understanding what can explain that Haktanir and Sezen equation has the best results, and why Sheridan equation has the worst. You do a much better job in the next paragraph, which clearly points out that coverage area is the reason for different accuracy of equations. For lines 308-317, your conclusions are a bit more vague.

 3. For this section, why did you choose to categorize equations according to the ‘dominant factors’? Are equations in one of the five categories more accurate than others? If you believe so, you should state your conclusions following Figure 2. Otherwise, it seems that whether the simulated watershed has area and slope within the recommended ranges are more influential to equation accuracy.

It makes perfect sense that sensitivity analysis is down according to parameters used. However for this section, I would suggest you to categorize equations according to ranges of suitable watershed areas, and then compare the new radar charts. Also among the equations which has suitable watershed area range for your study site, you can observe which one is more accurate, and as you stated in line 373-380, some of the additional factors might be the reason for higher accuracy. Your conclusions can be more convincing this way.

Also, the phrase ‘dominant factors’ is a little confusing since there’s not yet sensitivity test results for empirical equations, stating that certain factors ‘dominate’ the calculation results. ‘Distinctive factors’ or ‘special factors’ can be better choices of world.  

4. It need to be clear what exactly you what to analyze through sensitivity test, and state it in line 397-400. It seems like you what to know which parameters are less important, but you just stated in line 394 that ‘some parameters, namely equivalent circle diameter, distance…, are less important.’ So it’s not clear why we need section 3.1.1. Plus, you don’t have 3.1.2 so you need to fix this section number.

Accuracy is not necessarily the same with sensitivity to (errors of ) input values. This should also be clear when you try to reorganize the section.

Author Response

This paper developed a 2-dimensional HEC-RAS model to calculated the time of concentration (TC) of a given watershed, and compared the HEC-RAS simulated TC to TC results from 31 empirical equations. Sensitivity analysis of parameters of the 31 empirical equations are also conducted. While the research topic of comparing performances of empirical equations and hydraulic models is plausible, some questions about experimental procedure and result discussion needs to be further discussed.

Comment:

Firstly, the empirical models used for comparison needs to be more carefully selected. It’s not appropriate to include calculation results from empirical equations that are clearly not suitable based on watershed area.

Response:

Thanks for your comments. You rightfully noticed in regard to empirical equations. An initial filtering was performed to remove completely irrelevant equations like those that are developed for urban basins and the study was conducted on the remained equations. However, we believe that many researchers and engineers consider equations that meet the study area properties, yet result in unrealistic values. On the other hand, some equations that do not meet the basin’s characteristics well, result in more accurate results. Besides, some scientists or practitioners consider equations regardless of their limitations. We aimed to show the importance of considering each relation’s limitations by demonstrating the outcomes.   For example, we considered both “Sheridan” and “Breansby-Williams” equations. Our study area satisfies their coverage area limitations (2.62<A<334 Km² for “Sheridan”, and A<129.5 Km²for “Bransby-Williams”), however “Sheridan” is proposed for flatland area and Bransby-Williams for rural districts. “Sheridan” resulted one of the worst estimations and in contrast, “Bransby-Williams” resulted one of the best estimations showing the importance of accurate selection of empirical relations. on the other hand, “Temes” relation is appropriate for natural basins in “Spain”, and we applied it and resulted limited relative error. Therefore, that’s why we used various equations in order to show that researchers should pay attention to the limitations of the relations, yet this does not guarantee accurate results. In addition, the same procedure-applying various formulas that some of which do not match the watersheds’ characteristics- was adopted by other researchers including Salimi et al. 2017, Azizian 2018 and Grimaldi et al. 2012.

Taghvaye Salimi, E. Nohegar, A. Malekian, A. Hoseini, M. Holisaz, A Estimating time of concentration in large watersheds. J International Society of Poddy and Water Environmental Engineering, 2017, 15(1):123-132. DOI 10.1007/s10333-016-0534-2

Grimaldi, S., Petroselli, A., Tauro, F., & Porfiri, M. Time of concentration: a paradox in modern hydrology. Hydrological Sciences Journal, 2012, 57(2), 217–228. https://doi.org/10.1080/02626667.2011.644244

Azizian, A. Uncertainty Analysis of Time of Concentration Equations based on First-Order-Analysis (FOA) Method. American Journal of Engineering and Applied Sciences, 2018, 11(1), 327–341. https://doi.org/10.3844/ajeassp.2018.327.341

Comment:

Secondly, the purpose and conclusion of sensitivity test need to be more clearly stated. Since there are adequate literatures stating the importance of selected parameters, and that sensitivity is not necessarily directly related to accuracy, the significance of section 3.1.1 is low.

Response:

It is absolutely true that sensitivity analysis does not imply the accuracy of the models. However, as indicated in the text added (lines 409-419) a model being highly sensitive to an imprecise input might give far inaccurate estimations, arisen by a small over/under approximation of that input. Therefore, a sensitivity analysis is performed to investigate the variability of each model estimation to its inputs.

Comment:

The paper can be better organized if HEC-RAS results are put in front of empirical equations, as HEC-RAS is the actual important content.

Response:

Thanks for your suggestion. The HEC-RAS results are added to the tables 2-6 and modifications are made.

Detailed points

Section 1 Introduction

Comment:

1.TC and Tc are both used to represent time of concentration in the text, and are separately defined in section 1. However, I don't see the differences between them. Use only use abbreviation if they are one, or define more different abbreviations for different parameters.

Response:

Thanks for your comment. Both TC and Tc are the same and it is modified in allover the text. “TC” is considered in the revised version of the manuscript.

Comment:

2. Paragraphs starting line 79 and line 97 can be more clear if they lead to a conclusion. For example, empirical equations are site specific and it’s hard to decide their accuracy for an area of interest. Also, it’s not clear why Bennis and Crobeddu (2017) and Sadatinejad (2012) should be in another paragraph.

Response:

Thanks for your suggestions. In these paragraphs, the conclusions are added at the end of each paragraph. Lines 82-84 and Lines 96-98.

About Bennis and Crobeddu (2017) and Sadatinejad (2012), they are merged with a relevant paragraph. In the new version of manuscript, the paragraphs focused on evaluating empirical formulas are changed as one paragraph.

Section 2 Methodology

Comment:

1. Please provide citation for rainfall, temperature, evaporation, and Curve Number data if they are published online, or cite the methodology used to get CN (line 160-175).

Response:

Thanks for your comment. required descriptions are mentioned in line 183-185. They are gathered from Local Natural Resources Organization. 

In regard to methodology used to get CN, the procedure is detailed as follow, however, the summary of the procedure is stated in lines 193-198

To determine Curve Number (CN), the Natural Resource Organization have done following steps, and then CN was calculated based on SCS recommendation.

• Preparing information

-Providing aerial photograph with scale of 1/40000 and topographic maps with scale of 1/25000 from National Mapping Agency of Iran.

-Providing watershed characteristics including physiography, meteorology, geology, geomorphology, vegetation (forests and pastures) and land use.

-Preparing three-dimensional image of the area by assembling FCC image (False Color Composite) and DEM image

-Preparing the resulting image of assembling geological maps on the three-dimensional image of the area

• Assessment of land resources

-separation of physiographic types using Mahler recommendation based on interpretation of aerial images.

-field observation and soil sampling to separate land types into land units based on soil and land characteristics.

-drilling profile and sampling soils in each of the land units and sending to soil laboratories for physicochemical analysis. In this case, to determine soil features, pattern and structures, not only the amount of sand, silt and clay were determined, but also very small particles ranging from 0.05 to 0.1 mm were evaluated.

These data were captured and evaluated to determine soil classification which is included:

• Determining soil classification using soil Taxonomy 2006.
• Determination of soil hydrological groups based on SCS classification and providing the map of soil hydrological group.

Accordingly, the map of soil hydrological groups and land use was provided. It should be mentioned that this procedure was applied in a larger region where the study area is a part of it.

Comment:

2. Line 200-203. Is the measured travel time averaged?  What do you mean by ‘measurement were started as close as possible to the basin’s border to minimize the overland flow duration’?

Response:

Yes. The mean value of the measured ones was considered as a reference point; however, it is noteworthy that the nearly close values were obtained in the measurements.  

In regard to what is our intension of stating ‘measurements were started as close as possible to the basin’s border to minimize the overland flow duration’: we know that overland flow, which occurs near watershed divides, is responsible for a part of TC duration. that is why salt solution tracing was started as close as possible to the watershed divides where the flow emerges. This enables us to take the whole length of the main river into consideration as much as it possible and minimize errors.

Section 3 Results and Discussion

1. Tables 3-7 and Figure 2. As there are 31 empirical equations, it’s hard for readers to remember the equation when they read about the equation names. It would be clearer if table 2 can be combined with tables 3-7, or at least equations are included in Tables 3-7. Also, readers can interpret the results better if the numbers in Figure 2 are listed in Tables 3-7.

Response:

Thanks for your suggestions. Table 2 is removed and All the equations are added in the tables 2-6 in the new version of the manuscript.

In regard to figure 2, based on modifications done in the manuscript, this figure was eliminated. This figure was found confusing because it shows the residual values despite tables which show relative errors.

Comment:

2. Line 308-317. I am not understanding what can explain that Haktanir and Sezen equation has the best results, and why Sheridan equation has the worst. You do a much better job in the next paragraph, which clearly points out that coverage area is the reason for different accuracy of equations. For lines 308-317, your conclusions are a bit more vague.

Response:

Thanks for your comment. The paragraph is modified and rephrased as follow: Lines 319-331.

In category I, Haktanir and Sezen (1990) yields the best results among others. Haktanir and Sezen (1990) developed synthetic unit hydrographs for ten different watersheds in Turkey by means of probability density function. A regression equation was developed for peak discharge and lag time of the mentioned unit hydrographs. Haktanir and Sezen (1990) claimed that they selected ten basins based on reliable measured data. Basins apparently differ in runoff characteristics with a wide range of sudden and late peaking hydrographs. Therefore, the equation can be applied for watersheds with different climatic characteristics including runoff, area, length. Besides, Fang et al. (2008) showed that this equation produces reliable estimations for TC. These explains why this equation resulted the best estimation in category I. In the same category, Sheridan yields the worst results, since Sheridan focused his study on flatland basins and developed an equation which TC is only dependent on the main river length. Our study area is a mountainous watershed completely different with those studied by Sheridan. Therefore, this method yields the lowest accuracy among others in category I.

Comment:

3. For this section, why did you choose to categorize equations according to the ‘dominant factors’? Are equations in one of the five categories more accurate than others? If you believe so, you should state your conclusions following Figure 2. Otherwise, it seems that whether the simulated watershed has area and slope within the recommended ranges are more influential to equation accuracy.

Response:

Thanks for arising questions. In regard to why we categorized equations according to the ‘dominant factors’, since sensitivity analysis is done based on dominant factors, we adopted the same procedure to run the sensitivity analysis.

In regard to second part of the question, it is noteworthy that sensitivity analysis does not imply the accuracy of the models. However, due to the experimental nature of the used models, of which many parameters (such as Manning's roughness coefficient, curve number and runoff coefficient, etc.) cannot be precisely measured, one has to rely on the estimated values based on his field experiences for such inputs. Therefore, it is admissible that poor performances of some models can be caused by the approximative nature of the input values and not necessarily the accuracy of the models. Obviously, the more sensitive a model is to these parameters, the more its accuracy might be affected by the certitude of such inputs. Therefore, performing a sensitivity analysis in this study was not for the purpose of comparing the models’ accuracy, but because of having a view of their sensitivity to different inputs. Lines 409-419

Comment:

It makes perfect sense that sensitivity analysis is down according to parameters used. However for this section, I would suggest you to categorize equations according to ranges of suitable watershed areas, and then compare the new radar charts. Also among the equations which has suitable watershed area range for your study site, you can observe which one is more accurate, and as you stated in line 373-380, some of the additional factors might be the reason for higher accuracy. Your conclusions can be more convincing this way.

Response:

Area range is only one of the various factors defining Tc. Since this study includes one specific watershed, the results cannot be generalized to other areas only based on the similarity between the area ranges nor the equations with suitable watershed area range, cannot be considered as an indicator for the models accuracy comparison. The radar charts, on the hand, were omitted from the manuscript, due to the changes made to the tables and suggested by the reviewers.

Comment:

Also, the phrase ‘dominant factors’ is a little confusing since there’s not yet sensitivity test results for empirical equations, stating that certain factors ‘dominate’ the calculation results. ‘Distinctive factors’ or ‘special factors’ can be better choices of world.  

Response:

Thanks for your suggestion. Required modifications are made based on this suggestion.

Comment:

4. It need to be clear what exactly you what to analyze through sensitivity test, and state it in line 397-400. It seems like you what to know which parameters are less important, but you just stated in line 394 that ‘some parameters, namely equivalent circle diameter, distance…, are less important.’ So it’s not clear why we need section 3.1.1. Plus, you don’t have 3.1.2 so you need to fix this section number.

Response:

Thank you for your comments. Required descriptions are added and the argumentation sensitivity test is added to the text, lines 409-419.

Comment:

Accuracy is not necessarily the same with sensitivity to (errors of ) input values. This should also be clear when you try to reorganize the section

Response:

Thank you for mentioning this point. As noted in lines 409-419., performing a sensitivity analysis in this study was not for the purpose of comparing the models accuracy, but because of having a view of their sensitivity to different inputs.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Thanks for your response to each of the comments. You have answered all  of my questions and justified your modifications. 

The only thing is about lines 188-190 and 195-200 in the revised manuscript. Here, you've provided sufficient information for the dataset and CN generating methodology. If the data is published online, it would be nice to cite a link to the websites. (is the organization named as 'Local Resources Organization'?) Just because the data provider should have their credits. As for CN values, the methodology can be better justified if it has been used in other publications. 

As you did not add any citations I would assume the dataset is not published, or the citation is hard to find. If that's the case, I would suggest that you use published dataset for future research, so that your results are replicable and more convincing.

Good job on this manuscript, and best of luck for your future research!