Applying a Graphical Method in Evaluation of Empirical Methods for Estimating Time of Concentration in an Arid Region

Round 1

Reviewer 1 Report

This study compares graphical method to empirical for evaluating their performance in estimating the concentration-time.  The authors found that three methods were most appropriate for estimating Tc.  Furthermore, the models suitable for local conditions were modified to predict with more accuracy Tc. Although the results of this paper can provide guidance for local hydrological study, it seems just an exercise for calculating Tc and selecting the better one and the obtained correction parameters are not widely applicable to other regions due to specific test conditions. You selected as a reference method the graphical one, but are we sure it is the more correct? Moreover, the main issue I found is that no on-field tests were conducted to measure the effective Tc. Using a hyetograph and a hydrograph (obtained from measurements) is correct but you compared the empirical methods with a graphical method which is not exactly scientific. Another element that fed my uncertainty is the extreme proximity of rainfall and runoff stations. in addition in some basins such as Shaghrud and Chahchakur , the rainfall variability of such large basins can not be evaluated by only one rainfall station.

 

minor comments

• the introduction lack of work hypothesis and possible implication of the research for stakeholders and researchers
• in the background you compare two definitions but it sounds strange. Please, change the approach comparing calculation or analysis method
• in the M&M the characteristics of the basin are lacking in important parameters ( drainage density, channel network length, and the linear and areal properties). However, a more accurate statistical analysis and statements is needed.
• the maps are without a grid
• results: you state "to minimize the bias coefficients and exponent were adjusted". Please support this technique with astrong references because it seems arbitrary .
• in the conclusion the figure 4 is inappropriat

Please, check the MS fr minor oversights

 

Author Response

Please see the Word attachment. Thanks for your assistance.

 

 

Author Response File: Author Response.docx

Reviewer 2 Report

The authors present an interesting analysis to find the best method and maximize the efficiency of empirical equations to estimate the Tc of some Iranian rural watersheds. These results could be also useful for engineers operating in those areas.

Even though the analysis is completed I would like to see a better organization of the paper’s content. Thus, I recommend moving forward after a major revision.

Comments and recommendations are written as follows:

• Line 9: add an institutional mail, instead of the personal one;
• 1. : please try to make the draft more fluent, instead of providing information like a list;
• Line 108: Rainfall intensity in the area is high -> please provide some data of what you consider high intensity;
• Lines 136-137: the concept is repeated and it is already mentioned in lines 86-88;
• 3.3 : please add equations and a graph (like figure 3 but generic) to better explain the method;
• Line 170: Km² instead of km2;
• Table 3: add the mean Tc for each sub-catchment;
• Line 232: probably you want to refer to Figure 4, isn’t it?
• Please consider moving figure 4 in supplementary materials to make the overall paper more readable;
• 4. : please enhance the discussions, I see the results but the critical analysis among them is lacking;
• 5. : please add some recommendations for further research work.

I suggest checking the formatting all over the paper, sometimes there are too many or missing spaces.

Regads

 

Author Response

Thanks for your insightful comments. Please follow the attachment.

Author Response File: Author Response.docx

Reviewer 3 Report

This manuscript deals with the determination of the time of concentration of arid catchments. Time of concentration is an old but useful concept in hydrology, and a source of debates. It could be the opportunity of an interesting contribution. However, I have several concerns with this manuscript, which, in my opinion, cannot be published in Water in the present version. A major revision could be viewed

Section Background

The authors give seven definitions of the time of concentration. There is only one correct definition : “the time needed for water to travel from the hydraulically furthermost point to the watershed outlet”.  Hydrologists have proposed various “characteristic times” to summarize the response of catchments to rainfall forcing.  These various times have most often different meanings , but are sometimes redundant. I encourage the authors to read the recent paper by Beven (2020) in HESS “A history of the concept of time of concentration” in open access.

Paragraph 3.3 Graphical method

I understand that the graphical method that the authors use as reference method is not based on the correct definition of the time of concentration. From that point, I consider that the evaluation presented by the authors is not valid while the used reference is not correct. Consequently, the manuscript can not be published in this version.

The authors test 15 empirical expressions of the time of concentration. They should explain the reasons of this choice. I suppose that most of these methods have been calibrated on catchments very different from arid catchments. The proximity of the test conditions with arid conditions could be a criterion to select a method.

It is well known that the numerous empirical relationships used to estimate the time of concentration lead to very different results and that their accuracy/representativity is questionable. Instead of comparing many existing methods and applying a correction to adapt them to the data, I would suggest that the authors proceed in a different way: 1) reflection on the specificities of arid catchments, 2) selection of tentative explicative variables adapted to these specificities, 3) development of an empirical relation adapted to their context, 4) validation of this relation. Point 1 could be the opportunity of an original contribution. For a very rigorous validation, the validation sample should be different from the calibration sample, But I am afraid that there is too few data for that.

Author Response

Thank you very much for your constructive comments. Please follow the attachment.

Author Response File: Author Response.docx

Reviewer 4 Report

This paper selected the top three empirical methods from 15 methods for estimating the time of concentration, and further improved their accuracy by modifying the coefficients using curve fitting technique. This was conducted for four sub-watersheds in the Hormozgan province. The justifications for the events used and approaches used in the paper (e.g., the ranking approach) are required. In addition, the results were reported, but without in-depth discussion. More importantly, according to the results reported in this manuscript, it appears that this paper lacks novelty.  

 

• Lines 30-31: argues the importance of Tc for developing flood hydrographs in ungauged watersheds. However, this paper appears to not be relevant to the ungauged watersheds.
• Lines 86-88: Justification of the selected graphical method is desired.
• Line 93: The use of the word of “true”.
• Lines 101-102: There is only one rain gauge located in each sub-watershed. Three out of four stations are situated on the boundary of the sub-watersheds. How representative of the rainfall measured at the gauge stations is for the entire sub-watersheds?
• Lines 109 and 110: How do the numerous stormwater management systems in the sub-watersheds affect the Tc? Were the management systems taken into consideration when estimating the Tc using the empirical methods?
• Lines 130-132: The restrictions of the use of empirical methods should be taken into consideration when selecting the empirical methods.
• Line 191: How the inflection point is determined?
• Table 4: The characteristics of rainfall events need to be reported in the paper. The events used in the study (for each sub-watershed) range over more than 10 years. Are there any changes in land use and the stormwater management systems in the watersheds? What are the criteria used to select the events for the analysis?
• Line 214: Sum of the rankings - The rationale behind this ranking method should be provided. When using this approach to select the method, the results might be different when considering different goodness-of-fit measures. Thus, the selection of the goodness-of-fit measures used in this approach should be justified. Among the goodness-of-fit measures used in this work, 4 out 5 are in fact the measures for error.
• Line 222: In the section 4.4, the top three models were modified. What would the results look like if all models are modified using the same approach?
• Table 6: Are the goodness-of-fit measures derived for all four sub-watersheds? Table 5 reported the differences for each sub-watershed. The ranks of the models would be different for different sub-watersheds.
• Curve fitting: The models were modified using the curve fitting approach (to minimize the bias), thus, overfitting could occur. The validation of the modified model can be performed to avoid/mitigate the overfitting issue.
• Fig. 4: The numbers of the data points in the plots (left and right panels) appear to be different.
• Lacking in-depth discussion.

Author Response

Thank you so much for your constructive comments. I highly appreciate your time and effort. Please follow the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The manuscript was properly improved

Author Response

Thank you so much for your insightful comments.

Reviewer 3 Report

The time of concentration is a very old hydrological concept, defined in different ways, and computed by numerous empirical equations, may be as many equations as hydrologists who addressed this subject.  This subject is not original even if the concentration time may be useful.

I did review the initial version of this manuscript, which did not convinced me. But I considered that it could be resubmitted, due its focus on arid basins.

I was disappointed when I read the revised version for the following reasons:

The revised manuscript is very long, about twice than the initial one, too much for a subject that could result in a technical note. The significant lengthening of the manuscript makes it more difficult to read and degrades the clarity of the objective and of the approach.

There is nothing in the manuscript regarding the specificity of arid basins concerning the determination of the time of concentration, which would have been interesting and which should be an element of originality, as announced in the manuscript title.

Several aspects of the manuscript are questionable:

• Figure 2 illustrates various definitions of characterisitc times of basin response, all introduced as time of concentration. Unfortunately some of these characteristic time :  time to peak, response time, and others are very different from the classical time of concentration and have not the same meaning. It is a source of confusion foe the reader
• The comparison of the said “graphical method” with the 15 tested methods is of weak interest, and questionable because it is likely that the tested empirical methods concern the classical definition of the time of concentration which can not be compared to the one used by the authors
• I am very surprised by the very weak variability of the values of Tc for the various flood events of a given basin while the maximum rainfall and the peak flow are very different
• The discussion page 17 to 21 is very long and not easy to follow for the reader.
• Figure 4 : It is not clear to me, why the authors have 12 or 13 comparison points for 4 basins, and why there is so many residual points.

Finally, the manuscript has not been improved by the its revision. I am sorry, but I can not recommend its publication

Author Response

Please see the attachment.

 

Thanks

Author Response File: Author Response.docx

Reviewer 4 Report

Thank the authors for addressing my comments in the revised manuscript. Improvements have been made in many aspects, but I still have three key questions (the first three comments) and a few minor comments that the authors might consider addressing in the next version.

• The sum of ranking for selecting the top models: As stated by the authors that “we used the mean absolute percentage of errors (MAPE) as a relative error measure, the mean absolute error (MAE), the root mean sum of squared errors (RMSE) as absolute (square) measures” and “The evaluation by MAE, RMSE, and MAPE had similar results.”, the ranks according to the similar metrics are similar. Although this method has been used in a previous work (in 2011) and is intuitive, there is big concern about the use of this approach to select the top models. To implement this approach, the selection of the goodness-of-fit measures is a key, as the results are expected to be very sensitive to what metrics are used in this approach. Definitely, the use of similar metrics (e.g., MAE and RMSE) should be avoided.
• The criteria used to select the events are still not clear. As shown in Fig. 6, there is only one flow peak. If there are more than one flow peak, how to measure TC in the graphical approach? Thus, criteria used need to be clearly stated.
• The justification for selecting definition (ii) for Tc appears invalid (Lines 143-145). The rainfall depth of the 33 events ranges from 5 mm to 99 mm. In arid region, the watersheds are not likely saturated at the end of rainfall excess, in particular in small and medium sizes of rain events.
• Regarding to the 7 definitions on Tc, definition (v) is the lag time; while for definition (vii), how to determine the start of the total runoff (when there is baseflow)?
• When selecting the top models from 15 empirical models, it might be okay to ignore the assumptions and limitations of these models. After determining the top three empirical models, the discussion on their assumptions and limitations, which should be linked to the geophysical characteristics of the watersheds, is desired.
• Regarding to the inflection point, it is determined by “drawing trend lines”. In the sample hydrograph (Fig. 6), the line is pretty smooth. If the line (hydrograph) is not smooth, how to draw the trend lines? In another word, the approach is “qualitative” not “quantitative”.
• In Fig. 7, provide the label for x-axis on the plot (right panel).
• 5 (daily rainfall) is not necessary.
• The improvements made by using the modified equations (compared to the estimates before modification) appear to be different among the sub-watersheds. Thus, the discussion in this regard, which is related to the geophysical characteristics of the watersheds, is desired.
• The manuscript is not concise. For instance, the phi-index is a method commonly used. The detailed description on the process is not necessary. In addition, improvement in writing is still needed.

Author Response

Please see the attachment

Many thanks

Author Response File: Author Response.docx

Round 3

Reviewer 3 Report

I have already spent a lot of time on that manuscript and I can't spend any more time on it. Altought I am not convinced, it can be published.

 

Author Response

Thank you for spending your time and effort in reviewing the manuscript.

 

 

Reviewer 4 Report

Point 1: The use of the sum of ranks to select the top models - As shown in the authors’ response, although using the different combinations of the metrics, same three top models were selected. However, as shown in the response, the use of the different selection metrics lead to different ranks among these three top models. In the literature, it has been well acknowledged that the use of different evaluation metrics can lead to select different models. Researchers have used different metrics for the model selection. Of course, there are several of them have been commonly used in the literature. When applying the approach to other sites (study regions), it could lead to select different top three models if using different metrics. Thus, the authors need to discuss the limitation of this approach adopted in the manuscript.

Point 2: The term “well-defined hydrograph” is ambiguous. It would better to use “single peak hydrograph”. A hydrograph of a rain event can have more than one flow peak.  

Point 3: Selection definition for Tc - The justification appears to be contradictory. Does the statement of “The rainfall depth in Shaghrud sub-watershed in 26 Feb 2017 is 5 mm but during the previous 10 days this sub-watershed received 118 mm of rain but runoff was not observed in the watershed’s outlet.” suggest that the watershed is not saturated before receiving 118 mm rain, as no runoff was generated?

The distribution or percentage of “alluvial fans” in the study watersheds should be reported. More detailed information on the alluvial fans is desired to be included.

Point 6: According to authors’ response, it seems that the inflection point was considered when selecting events for analysis. If it is true, the criteria should be added.

Author Response

Please follow the attachment. Thanks a lot for your insightful comments.

Author Response File: Author Response.docx