Estimating response times, flow velocities, and roughness coefficients of Canadian Prairie basins

Shook, Kevin R.; Whitfield, Paul H.; Spence, Christopher; Pomeroy, John W.

doi:https://doi.org/10.5194/hess-28-5173-2024

Articles | Volume 28, issue 23

https://doi.org/10.5194/hess-28-5173-2024

© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/hess-28-5173-2024

© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 28, issue 23

Research article

|

02 Dec 2024

Research article |

| 02 Dec 2024

Estimating response times, flow velocities, and roughness coefficients of Canadian Prairie basins

Kevin R. Shook, Paul H. Whitfield, Christopher Spence, and John W. Pomeroy

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Final revised paper (published on 02 Dec 2024)
Preprint (discussion started on 13 Mar 2023)

Interactive discussion

Status: closed

RC1:
'Comment on hess-2023-51', Anonymous Referee #1, 25 Apr 2023

I have reviewed the manuscript by Shook et al., in which they estimated response times, flow velocities and roughness coefficients for basins in the Canadian prairies. They claim that the velocities found are much smaller than previously thought, and that Manning's n values were higher than expected, and this has relevant implications in the parametrization of models for this region. If the paper only provided estimation of response times, flow velocities and roughness coefficients for a given region, this would have been a very simplistic manuscript. However, I believe this is a relevant contribution because it highlights previous misconceptions about the Canadian prairies. The authors try to relate the velocities or Manning's n values to basin's characteristics, but no strong correlations were found. However, the discussion is rich and it provides hypothesis on why the correlations with basin's characteristics was not significant. From reading the discussion, it's clear that the authors have good knowledge about the hydrology of the study area (the Canadian prairies), and this paper provides important insights about the hydrological processes of the region. I therefore recommend that the paper should be accepted, but some concerns are presented as follows.
The manuscript is overall straight-forward, but I believe that there are some missing references. I think there could be more references about other studies that show the variability in estimating Manning's n values or the time of concentration, for instance (e.g., Grimaldi et al., 2010; https://doi.org/10.1080/02626667.2011.644244).
I think the structure of the paper could be revised. For instance, there is a sub-section "darcy-weisbach roughness coefficient f", and it looks like the remaining of the text is within this sub-section, because the next sub-section is already "summary and conclusions". Moreover, the "Summary and conclusions" section should be a wrap-up about the manuscript and not cite new references (L516-517).
Other specific major concerns are:
L 89: "the basins are dominated by agriculture" - are there any effects of water use for irrigation then? Because if yes, then this should be discussed. Moreover, are there any controls by dams in the region? If not, then please state this. This is relevant because later in the manuscript, you discuss about the effects of roads, so other factors such as water use for irrigation or impact by dams should be presented.
L 294-295, 298: Isn’t the celerity calculated as Lc divided by tp? In the manuscript, it is stated that celerity is calculated by dividing tp by Lc.
L 544 "All data, R code, and calculation results used in this research will be published online at zenodo.org": ideally as a reviewer I would like to have access to these calculations, so I would be able to double-check some results. The link to the data should have been submitted in conjunction with the manuscript.
Minor concerns:
L 25-26: "region's cold region"
L 70: "general feature of the region" -> please specify which region, Canadian prairies?
L 74: "the the response times"
L 77 and 78: why is "study area" within "data" ?
L 82: "other factors believed to influence" - too vague. please cite these factors
L 87-88: "If small velocities are documented in the study basins.." - I am sorry, I didn't really understand this sentence. Is this a hypothesis?
L 92: no comma between subject and verb ("equations for basin response times are listed in Table 1")
L 110: why May 24?
L 116: unfortunately, an unpublished work is a weak reference. is it under review?
Figure 3: the colors of blue and green are very similar. maybe for the badland and montane graphs the gauging station code could be written on top of the graph?
For equations, please make sure that units are presented (e.g., unit of tcK in equation 1, is it hours?)
L 240, 241, 242, 270, 271 (...): please adjust the formatting so that the variables are defined within the text (as they were defined in the previous equations), and not as items.
Equation 3: not ideal to have a variable with two letters (HT). It could be interpreted as H times T.
Equation 5: same problem of a variable defined by two letters. Also, previously, the authors used A for drainage area. Please be consistent with variables and abbreviations.
L 362: the section should be called "Results and Discussion", because the results are presented and already discussed.
L 375: why is table 3 presented before table 2?
L 383-384: "the points are coloured according to the basin topographic type" - this is more appropriate to be written in the figure's caption
L 410: use comma instead of point
L 424-425: "The values of f for basins ... in Figure 10" could be described in the figure's caption instead.

Citation: https://doi.org/10.5194/hess-2023-51-RC1
- AC1:
  'Reply on RC1', Kevin Shook, 28 Sep 2023
  Comment
  I have reviewed the manuscript by Shook et al., in which they estimated response times, flow velocities and roughness coefficients for basins in the Canadian prairies. They claim that the velocities found are much smaller than previously thought, and that Manning's n values were higher than expected, and this has relevant implications in the parametrization of models for this region. If the paper only provided estimation of response times, flow velocities and roughness coefficients for a given region, this would have been a very simplistic manuscript. However, I believe this is a relevant contribution because it highlights previous misconceptions about the Canadian prairies. The authors try to relate the velocities or Manning's n values to basin's characteristics, but no strong correlations were found. However, the discussion is rich and it provides hypothesis on why the correlations with basin's characteristics was not significant. From reading the discussion, it's clear that the authors have good knowledge about the hydrology of the study area (the Canadian prairies), and this paper provides important insights about the hydrological processes of the region. I therefore recommend that the paper should be accepted, but some concerns are presented as follows.
  
  The manuscript is overall straight-forward, but I believe that there are some missing references. I think there could be more references about other studies that show the variability in estimating Manning's n values or the time of concentration, for instance (e.g., Grimaldi et al., 2010; https://doi.org/10.1080/02626667.2011.644244).
  
  Response
  Thanks. The reference has been added.
  
  Comment
  I think the structure of the paper could be revised. For instance, there is a sub-section "darcy-weisbach roughness coefficient f", and it looks like the remaining of the text is within this sub-section, because the next sub-section is already "summary and conclusions". Moreover, the "Summary and conclusions" section should be a wrap-up about the manuscript and not cite new references (L516-517).
  
  Response
  Unfortunately, the heading “Discussion” was accidentally deleted. It has been restored.
  The section from lines 515-524 has been moved to the discussion.
  
  Comment
  Other specific major concerns are:
  L 89: "the basins are dominated by agriculture" - are there any effects of water use for irrigation then? Because if yes, then this should be discussed. Moreover, are there any controls by dams in the region? If not, then please state this. This is relevant because later in the manuscript, you discuss about the effects of roads, so other factors such as water use for irrigation or impact by dams should be presented.
  
  Response
  None of the streams are affected by damming or irrigation diversions. It is stated on line 78 that all the streams examined are unregulated, meaning that no dams or irrigation diversions exist.
  Added the sentence:
  “This region is under dryland farming, i.e. without irrigation.”
  
  Comment
  L 294-295, 298: Isn’t the celerity calculated as Lc divided by tp? In the manuscript, it is stated that celerity is calculated by dividing tp by Lc.
  
  Response
  Oops! You are quite right. It has been fixed. The error is only in the text; the calculations are correct.
  
  Comment
  L 544 "All data, R code, and calculation results used in this research will be published online at zenodo.org": ideally as a reviewer I would like to have access to these calculations, so I would be able to double-check some results. The link to the data should have been submitted in conjunction with the manuscript.
  
  Response
  Agreed. It has now been added.
  
  Comment
  Minor concerns:
  L 25-26: "region's cold region"
  
  Response
  Thank you. We have fixed this rather awkward phrasing.
  
  Comment
  L 70: "general feature of the region" -> please specify which region, Canadian prairies?
  
  Response
  Yes. This has been clarified. The sentence now reads:
  “The objectives of this research are to determine a) if small runoff flow velocities are a general feature of the study area and therefore of the Canadian Prairies
  
  Comment
  L 74: "the the response times"
  
  Response
  Thanks. Fixed.
  
  Comment
  L 77 and 78: why is "study area" within "data" ?
  
  Response
  Thanks, the heading has been changes to “Study Area and Data”
  
  Comment
  L 82: "other factors believed to influence" - too vague. please cite these factors
  
  Response
  Agreed.
  
  Changed to
  “factors (stream lengths, surface geologies, and depressional storages) believed
  to influence”
  
  Comment
  L 87-88: "If small velocities are documented in the study basins.." - I am sorry, I didn't really understand this sentence. Is this a hypothesis?
  
  Response
  This statement is related to the objective stated in line 70:
  “The objectives of this research are to determine a) if small runoff flow velocities are a general feature of the region,”
  Changed to
  “If small velocities are documented in the study basins, then in concert with the data for Steppler and St. Denis, it may be concluded that they are a feature of the Canadian Prairie landscape.”
  
  Comment
  L 92: no comma between subject and verb ("equations for basin response times are listed in Table 1")
  
  Response
  Thank you. It’s been removed.
  
  Comment
  L 110: why May 24?
  
  Response
  On the Canadian Prairies, the spring melt of the accumulated snow pack generally occurs in the months of March and April, although it can occasionally extend into early May. Using the end of May is a very conservative assumption. May 24, which happens to coincide with a national holiday, is generally considered to be the beginning of summer in the Canadian Prairies. It is traditionally the date when people plant their gardens as the soils are warmed and the risk of frost is low.
  
  The text now reads:
  Manual gauging values obtained between May 24 and September 1 (which very conservatively approximate the frost-free period) in the Canadian Prairies)
  
  Comment
  L 116: unfortunately, an unpublished work is a weak reference. is it under review?
  
  Response
  No. The text is changed to
  “Many of the selected basins responded to large-scale rain events in the summer of 2011 (not shown here).”
  
  Comment
  Figure 3: the colors of blue and green are very similar. maybe for the badland and montane graphs the gauging station code could be written on top of the graph?
  
  Response
  The figures have been re-plotted, separately listing the gauging stations directly for the badland and montane graphs.
  
  Comment
  For equations, please make sure that units are presented (e.g., unit of tcK in equation 1, is it hours?)
  
  Response
  Thank you. The units have been added.
  
  Comment
  L 240, 241, 242, 270, 271 (...): please adjust the formatting so that the variables are defined within the text (as they were defined in the previous equations), and not as items.
  
  Response
  Done
  
  Comment
  Equation 3: not ideal to have a variable with two letters (HT). It could be interpreted as H times T.
  
  Response
  Agreed. However, as was stated on line 204: “Note that the equations given below are as they are taken from the literature, so the symbols used, and their units, vary.”
  
  We have kept the original nomenclature because:
  It is consistent with the original work,
  
  As was stated, the units may vary among the authors. Note that the area is sometimes in km² and sometimes in ha. Changing to a common symbol might imply that the units are also common.
  
  The methods by which the values were obtained may also vary, and in many cases are not known by us. Therefore, we are not exactly sure of their actual meaning.
  
  We have also made sure each was in italics and that there are spaces between elements so H T differs from HT
  
  Equation 5: same problem of a variable defined by two letters. Also, previously, the authors used A for drainage area. Please be consistent with variables and abbreviations.
  
  Response
  See above response.
  
  Comment
  L 362: the section should be called "Results and Discussion", because the results are presented and already discussed.
  
  Response
  Done
  
  Comment
  L 375: why is table 3 presented before table 2?
  
  Response
  It has been moved.
  
  Comment
  L 383-384: "the points are coloured according to the basin topographic type" - this is more appropriate to be written in the figure's caption
  
  Response
  Agreed. Done.
  
  Comment
  L 410: use comma instead of point
  
  Response
  Thank you
  
  Comment
  L 424-425: "The values of f for basins ... in Figure 10" could be described in the figure's caption instead.
  
  Response
  The reason for including the description within the text, rather than the caption, is that it gives the context needed for the next sentence: “The agreement between the observed points and the published values is remarkable ...”. This applies particularly for the specified stations.
  
  Citation: https://doi.org/10.5194/hess-2023-51-AC1
RC2:
'Comment on hess-2023-51', Anonymous Referee #2, 01 Sep 2023
Please see detailed comments in the attached pdf.
The paper generally gives an important contribution about the usefulness empirical formulas about time of concentration, time to peak and lag time in different sized catchments in Canadian Prairie basins. The evaluation of these formulas matters because many hydrologists use them without a critical understanding of their premises. Wrong estimation of response times leads to wrong shapes and peaks of the resulting hydrographs.
However, the analysis is not performed very well.
My main concerns are (please consider also the comments in the attached pdf):
Time of concentration, lag time and time to peak have different meanings and physical backgrounds. Please clarify the differences between them and how it effects rainfall-runoff-simulations.

The distinction between stream flow velocities and overland flow velocities is important and not sufficiently discussed.

Empirical equations are only valid within the limits of the based experiments. This should be discussed in order to evaluate the empirical equations.

The discussion shows some of the shortcuts in the analysis very clearly. Why didn’t the authors try to divide the catchments into more homogenous subcatchments?

The paper should be improved by discussing (and applying) hydrodynamic approaches (Only Costa et al. is mentioned as an 2D hydrodynamic application).

It makes no sense to calibrate the Darcy-Weisbach f roughness parameter. Whereas Manning’s n could be treated as an empirical parameter (However, it has also physical constraints), the parameter f is determined by the Moody diagram. It has a pure physical meaning and is dependent on the Reynolds number, the hydraulic radius and the absolute (Nikuradse) roughness. Therefore, we have an ideal basis to calibrate hydrodynamic models with this approach. However, the authors treat f as an empirical parameter like Mannig’s n. I do not see any advantage when using f in this way.

A scientific benefit of the paper would be in the comparison / connection of hydrological and hydrodynamic approaches to estimate the time of concentration.
Citation: https://doi.org/10.5194/hess-2023-51-RC2
- AC2:
  'Reply on RC2', Kevin Shook, 28 Sep 2023
  Comment
  Please see detailed comments in the attached pdf.
  The paper generally gives an important contribution about the usefulness empirical formulas about time of concentration, time to peak and lag time in different sized catchments in Canadian Prairie basins. The evaluation of these formulas matters because many hydrologists use them without a critical understanding of their premises. Wrong estimation of response times leads to wrong shapes and peaks of the resulting hydrographs.
  Response
  We thank the reviewer for this comment as it aligns completely with the intention of our paper.
  
  Comment
  However, the analysis is not performed very well.
  My main concerns are (please consider also the comments in the attached pdf):
  Time of concentration, lag time and time to peak have different meanings and physical backgrounds. Please clarify the differences between them and how it effects rainfall-runoff-simulations.
  
  Response
  We provided this in detail in the original manuscript, and emphasized it in in the section “Observed basin response times”. It was also addressed in “Response times from existing empirical equations”. It is our opinion that the reviewer’s point regarding clarifying the differences between these terms was fully covered. The second part “how it effects [sic “affects”] rainfall-runoff-simulations [sic]” is outside the scope of our paper. We noted the importance to simulations in lines 25-34. Our paper does not include rainfall-runoff simulations so this part of the comment seems to fall outside of the scope of our paper.
  
  Comment
  The distinction between stream flow velocities and overland flow velocities is important and not sufficiently discussed.
  
  Response
  Note that we do not use the term overland flow velocities to describe the basin responses, as we cannot distinguish among overland flow, and sub-surface flows. However, the difference between basin velocity and stream velocity was addressed in several places. For example:
  Line 397
  “It is important to note that these values are basin-scale averages; they do not represent the velocity of flow at the outlet, or at any other point.”
  Line 433
  “This indicates that the cause(s) of the exceptionally small [basin] velocities are related to the presence of overland and/or shallow subsurface flows, as channel flows will dominate at large scales.”
  The word “basin” is inserted before “velocities” in Line 433 to make this clearer.
  
  Comment
  Empirical equations are only valid within the limits of the based experiments. This should be discussed in order to evaluate the empirical equations.
  
  Response
  Agreed. This is addressed in the section “Response times from existing empirical equations” where the limitations of each empirical equation, i.e. how its originating data set differs from the conditions within the research basins, are discussed.
  Unfortunately, many empirical equations in the literature either do not specify the experimental limits of the source, or the original limits have become lost over time. In a more perfect world empirical equations would have meta information about original limits, and limit extensions that have been determined in wider application.
  
  Comment
  The discussion shows some of the shortcuts in the analysis very clearly. Why didn’t the authors try to divide the catchments into more homogenous subcatchments?
  
  Response
  The study basins are defined by the gauges which exist within the region, and that streamflow data used to test/validate the empirical equations. There are no further gauges available by which to divide the basins into more homogeneous sub-basins. Note that the study basins were classified by their topographic type in order to see if this consistently affected the basin responses (it did not).
  It may be possible for a modelling study to sub-divide the catchments, but modeling approaches remain outside the scope of our paper.
  
  Comment
  The paper should be improved by discussing (and applying) hydrodynamic approaches (Only Costa et al. is mentioned as an 2D hydrodynamic application).
  
  Response
  Our paper presents an investigation into the observed characteristics of some basins to determine how they can affect modelling.
  The objectives of the paper are stated in line 69-71:
  
  “The objectives of this research are to determine a) if small runoff flow velocities are a general feature of the Canadian Prairies, b) if the velocities can be related to any obvious basin-scale parameters, and c) the effects of the flow velocities on basin-scale roughness parameters used in hydrological modelling.”
  The reviewer’s comment seems to be based on an expectation that rainfall-runoff models are included in the study. They are not.
  
  Comment
  It makes no sense to calibrate the Darcy-Weisbach f roughness parameter. Whereas Manning’s n could be treated as an empirical parameter (However, it has also physical constraints), the parameter f is determined by the Moody diagram. It has a pure physical meaning and is dependent on the Reynolds number, the hydraulic radius and the absolute (Nikuradse) roughness. Therefore, we have an ideal basis to calibrate hydrodynamic models with this approach. However, the authors treat f as an empirical parameter like Mannig’s n. I do not see any advantage when using f in this way.
  
  Response
  We disagree, the Darcy-Weisbach f roughness parameter values were estimated from the actual flow data. f was not calibrated as might be done in a modelling exercise.
  The Manning equation obviously did not work at basin scales in many locations. This indicates that it is not suitable for modelling flows which may have an overland component. Could the Darcy-Weisbach equation be a more practical method of modelling roughness in the Canadian Prairies? This was stated clearly in the paper in lines 346-348:
  “Darcy-Weisbach values were calculated and compared to values derived from the literature to determine if the roughness coefficient f (dimensionless) could be used as a robust routing variable in hydrological models in gentle agricultural basins.”The last part of the sentence was reworded to make this clearer as
  “gently-sloping agricultural basins”.
  
  Comment
  A scientific benefit of the paper would be in the comparison / connection of hydrological and hydrodynamic approaches to estimate the time of concentration
  
  Response
  Thank you. This is an interesting suggestion, but outside the scope of the paper. Such as study might be a valid follow-on. Our intention was to document the very low flow rates and relate them to the physics and characteristics of these basins and compare to the existing literature upon which modelling in the future might be based.
  
  Detailed comments from the PDF
  Line 40
  Comment
  More of hydrodynamic is missing in the paper!
  
  Response
  We do not understand this statement. Our paper is unrelated to hydrodynamic modelling so we are unable to determine what the reviewer expects to be added.
  
  Line 50
  Comment
  Please provide more details of this catchment.
  
  Response
  We do not agree that more detail is required. We have already stated the location, the area, and the topography, and that the basin is described in detail in Brannen et al. (2015). Lines 35-38
  “An example of a very slow Prairie event is shown in Figure 1, where a flood wave took about 39 hours to travel approximately 1.8 km from the inlet to the outlet of a small (gross area ≈ 1.2 km2) hummocky sub-basin near St. Denis, Saskatchewan, Canada, within the St. Denis Research Basin (SDRB). SDRB is a small (22.1 km2), relatively hummocky, endorheic basin which has been studied for more than 50 years. The basin is described in detail in Brannen et al. (2015).”
  
  Figure 2
  Comment
  Where is the catchment of figure 1 located?
  
  Response
  Thank you. We have added the locations of the St. Denis and Stettler catchments in the overview map and include details in the caption.
  
  Line 93
  Comment
  How do you get this data? Not from SRTM, correct?
  
  Response
  Yes, the main channel slope is derived from SRTM. The resolution of SRTM is adequate for determining the basin attributes used in this study. See the following references for confirmation on this point:
  Annand, H. J., H. S. Wheater and J. W. Pomeroy (2023). "The influence of roads on depressional storage capacity estimates from high-resolution LiDAR DEMs in a Canadian Prairie agricultural basin." Canadian Water Resources Journal/Revue canadienne des ressources hydriques: 1-20
  Datta, S., S. Karmakar, S. Mezbahuddin, M. M. Hossain, B. S. Chaudhary, M. Hoque, M. M. Abdullah-Al-Mamun and T. K. Baul (2022). "The limits of watershed delineation: implications of different DEMs, DEM resolutions, and area threshold values." Hydrology Research
  Nazari-Sharabian, M., M. Karakouzian and S. Ahmad (2019). "Effect of DEM Resolution on Runoff Yield, and Sensitivity of Parameters Contributing to Runoff in a Watershed." Preprint http://dx.doi.org/10.20944/preprints201901.0192.v1
  Yang, J. and X. Chu (2013). "Effects of DEM resolution on surface depression properties and hydrologic connectivity." Journal of Hydrologic Engineering 18: 1157-1169
  
  Line 95
  Comment
  Why 2 years return period?
  
  Response
  The 2-year return period was used by Godwin and Martin (1975), who did the delineation for the Prairie Farm Rehabilitation Administration. The return-period length was presumably used as it gives the median peak flow, which is useful in characterizing the highly skewed discharges in the region.
  Line 133
  Comment
  The accuracy of SRTM is not sufficient for basin cannel estimation.
  
  Response
  We agree that the SRTM data are coarse and this limits their use. However, we used SRTM to estimate the length of the main channel, and the elevation difference between the divide and the outlet. We did not do any form of drainage network delineation, or channel width delineation, using it. As noted above, a higher resolution dem would not affect the area, the length of the main channel nor the highest and lowest elevations on this nearly flat landscape.
  Line 155
  Comment
  definition of response time (see below) is missing.
  
  Response
  Altered the sentence at line 151:
  “As is described in the next section, there are many existing empirical equations for basin response times.”
  
  Line 164
  Comment
  Please analyse the differences and the consequences!
  
  Response
  The differences among the varying definitions are detailed and discussed. Again, modelled consequences are outside the scope of the paper.
  
  Line 170
  Comment
  That is fine. However, describe the implications for the further analysis.
  
  Response
  We do not quite understand what the reviewer is requesting. We state the meaning of each method of defining the response time, including the fact that the time of concentration cannot be measured empirically.
  To address this, we have added a summary paragraph at the beginning of this section
  “Modelling based on these empirical relationships requires caution and understanding of the assumptions of any chosen for use. The empirical relationships are based on quite limited sets for observations and extrapolation to different landscapes can be challenging. As will be seen, most available empirical equations fail on the landscapes in this study so modelling based on those relationships is likely to be unsuccessful.”
  
  Line 203
  Comment
  What means "some differences"? Be precise.
  
  Response
  The differences were explained above. However, the sentence will be clarified. Line 203 now reads:
  “The definitions of these response times are similar enough that they can be compared with the observed t_p values, despite the differences described above.”
  
  Line 295
  Comment
  The other way round!
  
  Response
  Thank you. As we said in response to reviewer #1, the typo in lines 295 and 298 will be fixed.
  
  Line 335
  Comment
  That is not so important (common sense).
  
  Response
  The reviewer’s comment may be true. But the intent here (line 336-345) is to clearly document the simple way in which we estimated the hydraulic radius at the scale of these basins and not make the reader guess.
  
  Line 357
  Comment
  f is a function of Reynolds number and Nicuradse roughness. There is physic behind it! You treat it like an emperical equation..
  
  Response
  That is not what we are doing. We are trying to see if Darcy-Weisbach could be used at large (i.e. basin) scales, where the Manning equation evidently cannot. As stated in the text, Manning requires fully turbulent flow, while Darcy-Weisbach works in all flow regimes. If Darcy-Weisbach works, then some of the issues with using Manning in these basins may be related to the flow regime, as is discussed.
  See also comment regarding this matter above line 84 to 106.
  
  Line 383
  Comment
  tp and tc and tl are different parameters!
  
  Response
  These are different ways of conceptualizing the response of a basin as described in lines 162 to 361. The values t_p and _tc and t_lare not parameters.
  
  Line 388
  Comment
  All equations cannot be applied in a meaningful way (= are useless). The mean ratio says nothing.
  
  Response
  We are not sure we entirely understand this statement. The mean ratio is a simple test to demonstrate approximately how well each empirical equation did in representing the response times of the basins. Equations where the mean ratio is near 1 did a better job than the those equations where the ratio is very small as they grossly underestimate the basin response times.
  
  Table 3
  Comment
  Add Lc
  Response
  The value of L_c is given in Table 1, which lists the basin parameters. Table 3 lists the responses of the basins, so putting a basin parameter in Table 3 would be redundant.
  Comment
  Why do you apply the ratio 3/5 here? This is not valid here.
  Response
  We assume that the reviewer is referring to the 5/3 ratio between celerity and velocity as in equation 7. This is how we are estimating basin-scale velocity from the celerity. We are not aware of any invalidity in its use here.
  
  Line 417
  Comment
  and too small!!
  
  Response
  Possibly, however the smallest computed basin-scale Manning’s n values are greater than that for a clear straight channel.
  
  Figure 9
  Comment
  This is the n for channel and surface. You should introduce two Manning's n seperately for surface and channel.
  
  Response
  The reviewer has misunderstood the figure. All the points are for basin-scale estimates of n. The dashed line is simply to put the points into context, by allowing the user to compare the values to a value that they might be familiar with, i.e. that of a straight stream, as taken from the literature.
  
  Line 429
  Comment
  Therefore, f is also not plausible. n and f are closely related (see eq. 8 and 12).
  
  Response
  We show that f values that we have estimated are quite plausible for the smallest basins, unlike the n values. Furthermore, as we have stated, n and f are only related when the flow is fully turbulent, which may not be the case.
  
  Figure 10
  Comment
  These Darcy Weisbach values do not match with the Moody diagram. Which sense do they have?
  
  Response
  We do not understand what the reviewer means by this. We are not talking about flows through pipes or in channels, but very complex flows through vegetation, through culverts and depressions. The Darcy-Weisbach values are not expected to match with values from a Moody diagram. We do not mention Moody diagrams in the manuscript, and we do not make this comparison.
  
  Line 431
  Comment
  Therefore, we have to distinguish between channel flow and overland flow!
  
  Response
  Yes, that is one of the points of this paper.
  
  Line 444
  Comment
  That is okay because you compare tp with tp within the same slope range. All empirical formulas are only valid within their experimental boundaries.
  
  Response
  That is correct for some, but not all of the empirical equations. That of Watt and Chow did not work well:
  Line 441
  “...but the values of t_cK and _tlW were much smaller than the observed t_p values. Watt and Chow (1985) also incorporate the slope; the slopes of the basins studied here lie within the range of those used to derive their relationship and at least three of the Alberta basins lie within the range of the areas of the basins that they used.”
  So, slope alone cannot explain the results.
  
  Line 471
  Comment
  Therefoe, you cannot model it in a lumped version. It must be divided into subbasins.
  
  Response
  We are not modelling or including rainfall-runoff models in this study.
  
  Line 480
  Check the effective area calculation. Is this equivalent to depression storage?
  
  Response
  The effective area fraction is the fraction of the basin which responds to flow at least 1 year in 2. It is the fraction of the basin that is not much affected by depressional storage. It was calculated by dividing the effective area (which was determined by Godwin and Martin (1975)) by the basin area. There is no error in this calculation.
  However, the effective area fraction is related to the depressional storage, in that basins with very large effective fractions will tend to have small depths of depressional storage and vice-versa.
  
  Line 487
  Comment
  Correct!!
  Response
  Thank you.
  
  Line 491
  Comment
  This is a further argument for hydrdynamic approaches.
  Response
  Yes, but that is not what we are trying to do with this paper. Rainfall-runoff models are not included in the study.
  
  Line 497
  Comment
  good discussion.
  Response
  Thank you.
  
  Line 518
  Comment
  good!
  Response
  Thank you.
  
  Line 522
  Comment
  Exactly, therefore hydrodynamic modelling is needed!
  
  Response
  Possibly true. However, it’s not what we are doing. The reviewer’s comment seems to be based on an expectation that rainfall-runoff models are included in the study. They are not.
  
  Line 532
  Comment
  Good!
  
  Response
  Thank you
  
  Citation: https://doi.org/10.5194/hess-2023-51-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

ED: Reconsider after major revisions (further review by editor and referees) (10 Oct 2023) by Erwin Zehe

Dear Mr. Shook

I have read your manuscript, the two reviews and your responses with great interest. I concur with both reviewers, that your study can potentially add important insights to our understanding of rainfall-runoff processes in the Canadian Prairie and the hydraulics of overland and stream flow.

While I am generally happy with your responses to the reviews and the outlined changes therein, I think reviewer II made a few important points that deserve further attention in a round of major revisions.

I absolutely agree with you, that your data do not allow distinguishing between overland flow and stream flow. Yet the option that shallow overland flow is a limiting /explaining factor for the slow catchment response is worth to be discussed, also in the light of choosing 5/3 for beta. Manning’s equation assumes fully turbulent flow and a flow depth that is much larger than the lengths scale of roughness element. This won’t be the case for overland flow on agricultural land, where roughness depends also on the growth status of the crops and surface preparation. While, I think that to using depth dependent Mannings coefficients is a quick fix, it clearly indicates the limitations of the Gauckler-Manning-Strickler equation ...

By choosing beta equal to 5/3 you assume fully turbulent conditions for the catchment average. Recent work from my own group (Schroers 2022 HESS) revealed that Reynolds numbers of shallow overland flow were not necessary in the turbulent range. I think this choice needs to be discussed, even if there is no better alternative at hand.

You calculated the Darcy-Weisbach roughness coefficient f, by solving the Darcy Weisbach equation for f and using the estimated empirical velocities. However, in open channel hydraulics the f coefficient is determined by the Moody diagram, as function of the Reynolds number and the relative roughness (Nikuradse roughness/ hydraulic radius Rh). Wouldn’t it be interesting to either compare both values?

Is there any data evidence about the areas contribution to rainfall - runoff generation, beyond the assumption that it is the entire catchment?

Maybe I missed it, but it seems that there is a mismatch in the temporal resolution of discharge (hours) and rainfall (days). How does this mismatch affect the calculation of centroids and the related ratios?

Looking forward to receive the revised manuscript,

Erwin Zehe

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AR by Kevin Shook on behalf of the Authors (17 Nov 2023) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (22 Nov 2023) by Erwin Zehe

RR by Anonymous Referee #2 (04 Dec 2023)

RR by Anonymous Referee #1 (02 Jan 2024)

Suggestions for revision or reasons for rejection

I have reviewed the manuscript "Estimating response times, flow velocities and roughness coefficients of Canadian Prairie basins" for the second time. It is a valuable contribution to the field of hydrology, as it questions assumptions which are usually taken without much attention (e.g., estimating response times or Manning's n coefficients for hydrological modeling). They reported that, for the Canadian praries, these assumptions are usually not valid. The text was well written from the beginning, but now the authors have improved the formatting, making it clearer. They have made the codes and spreadsheets used for calculations avaialable for download. I would consider the manuscript ready for publication, except for the fact that I was not able to retrieve the values that they reported. I apologize if this is my mistake. I tried to retrieve the values of the following equations: Kirpich, Watt & Chow, Capece and Sheridan. None of them resulted in the same values reported in "table2" (zenodo -> output -> table2.csv) nor in "basin_responses" (zenodo -> output -> basin_responses.csv).
The values for Kirpich, Capece and Sheridan are at least in the same order or magnitude. However, the values for Watt & Chow are in a completely different order of magnitude.
For instance, for catchment 05CC001, here is the comparison between the values reported by the authors, and the values I retrieved, respectively:
Kirpich - 13.9335; 34.3315
Watt & Chow - 18.4379; 0.19856
Capece - 7.36392; 9.0854
Sheridan - 91.6754; 169.4879 (the value of 169.4879 is actually reported in "basin_responses" under "Sheridan_area_tc" column, but it is not the value reported in "table2 > sheridan_tc".

These values are not reported as numbers in the main manuscript. They are only plotted in Fig 6. This is why the values in the same order of magnitude are not a big problem, however the fact that I was not able to retrieve the same values raised questions as to whether the calculations are correct, particularly for the Watt & Chow equation, which do differ in orders of magnitude. I applied the equations following the values provided in Table 1 (for instance, for catchment 05CC001, L = 125.9km and S = 0.0014 (-)). I tried to be careful about the units, following how the units are described in the tables and in the text (for instance, L in km and S dimensionless).
Here's one of my attempts to calculate the Watt & Chow equation, which resulted in 0.19 instead of the reported 18.43:
https://www.wolframalpha.com/input?i2d=true&i=0.000326*Power%5B%5C%2840%29Divide%5B+125.9%2CSqrt%5B0.0014%5D%5D%5C%2841%29%2C0.79%5D

My suggestion is that the authors review these calculations. If they are correct and this was my mistake, I apologize for the inconvenience. If these are not correct, I suggest that the authors review all the calculations in the manuscript.

Moreover, there is one sentence that can be improved in the manuscript: "Artificial drainage channels are much narrower for a given depth, and also be straighter and shorter, than natural channels which will result in deeper and faster flows than in natural channels." - I think the correct way would be to say that the "Artificial drainage channels are much narrower for a given depth, and are also straighter and shorter, than (...)"

I hope my comments are useful. Thank you for improving the manuscript and for taking my comments into consideration.

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RR by Anonymous Referee #3 (15 Feb 2024)

Suggestions for revision or reasons for rejection

I have read the manuscript „Estimating response times, flow velocities and roughness coefficients of Canadian Prairie basins“ by Shook et al. with great interest. The authors analyzed a big dataset of Canadian prairie basins and show that their observed tp does not fit good to most of the compared empirical equations. Furthermore, they calculate basin wide velocities and resistance coefficients. They also show in the chapter discussion that they have a great understanding of the hydrology and the hydraulic processes in the surveyed catchments and conclude that more research needs to be done.

Major Comments:
The authors explain the meaning and differences between Time of Concentration, lag time and time to peak very well. Nevertheless, they state that “The definitions of these response times, as described above, they are similar enough that they can be compared with the observed tp values, despite the differences described above.“ and eventually compare them to their observed tp. I get that in this case there is no rainfall data available to specify tc and tl. But by comparing them there should be given an idea about the relationship and sensitivity of these values in contrast to tp and also followed up on that in chapt. 4.2.

As I understood there were velocity measurements carried out for different discharges at the streams. Based on these there was an extrapolation of a velocity-discharge-curve to determine flow velocities for the observed peak flows. Based on the known cross-sections at the gauging stations you could calculate the mean velocity for the streamflow directly from the discharge which seems to be more accurate? Usually you should have also Q-h curves or similar for all the gauging stations which are used in the first place to calculate the discharges? Streamflow velocities for peak flow velocity could also be given in Tab. 3 and also be compared to the cited values of Bjerklie (2007). Also, here manning/DW coefficients for the channel could be calculated for comparison reasons to the basin wide values and a discussion of the differences could follow as another point why a more detailed analyses (differentiation between overland flow, channel flow, retentional areas …) is needed.

One could learn a lot from a deeper analysis of individual basins. “Hydrographs demonstrate that the observed times to peak varied widely amongst, and within, basins” E.g. Basin 05CG006 looks like it has a very big spread in observed tp. This shows that there can be already a natural spread of tp for one basin which seems to be independent from the parameters used in the tested equations. This could also lead to a better understanding of the processes and shows also the uncertainties using approaches for calculating tp (even when the observed data is already so diverse) based on these really simple eq. How should a simple approach fit to those data if the data itself has already such a big spread?

“The Darcy-Weisbach equation, (…), has the advantage of being applicable across all flow regimes, from laminar to fully turbulent.” This sentence is correct in relation to hydrodynamics and has the (physic based) advantages to calculate friction factors for pipes and channels based on the Reynolds number and potentially superposition them with drag coefficients. The authors however are looking at the entire basin and by doing so they mix up all the (hydraulic) processes (fill and spill, routing, vegetation, overland flow, channel flow …) and calculate a synthetic basin velocity leading to an abstract empirical friction factor. This should be properly discussed in the manuscript and also kept in mind by comparing the basin wide values to values based on experiments. Also, one could think about using mbasin und fbasin for these empirical values.

Therefore, there should be no advantage about using DW over Manning besides that the coefficient is dimensionless. The comparison between DW and Manning coefficients with literature is also lacking some depth. Please keep in mind that the calculated abstract manning and DW coefficients by the authors are for the whole basin therefore it´s highly depended on the diversity of flow processes. It´s not suprising that some of the values are fitting better to mannings for channel hydraulics (Schneider and Arcement), some are better fitting for overland (Weltz et al.) and some are even more rough and could be affected by other effects which could be also of geometrical nature (routing, retention areas …). DW values look better in this case due to the used log-scale in contrast to Manning values but a lot of them are much bigger than the comparative values. The DW-values which are fitting to the experiments from very small experimental plots are also partly fitting to those manning coefficents of Weltz.

If approaches are needed to estimate tp in Canadian prairie basin, an approach that includes the retention/depressions in the effective area might be useful? On the other hand one can also ask oneself whether such a blanket approach is still appropriate today. In times where we have access to a lot of remote sensing data / land use data and high computational power. Which could lead to the use of hydrodynamic models - or simplified models of the basins based on sub-basins and channel flow – or the use of machine learning approaches.

Referee Report: PDF

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ED: Publish subject to revisions (further review by editor and referees) (26 Feb 2024) by Erwin Zehe

AR by Kevin Shook on behalf of the Authors (22 May 2024) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (05 Jun 2024) by Erwin Zehe

RR by Anonymous Referee #3 (03 Jul 2024)

Suggestions for revision or reasons for rejection

Thanks for your last reply, it gave me some more insight. I would like to follow up on the DW roughness coefficient:

In the abstract you still have the sentence: “It is likely that the Darcy-Weisbach equation, which is applicable to all flow regimes, may perform better for hydrological prediction in this region.” (similar statement in conclusion). You stated in your last response that you are working with basin-scale averages (velocities). Thus, the friction factors are also empirically basin-scale averages. Therefore, there should be no advantage of using the DW over Manning.
You can also use Manning eq. for non-primarily turbulent flow (just not the recommended values for river hydraulics, but Manning values especially for this condition). For overland flow there is eg. a table from Engman 1986: ROUGHNESS COEFFICIENTS FOR ROUTINGSURFACE RUNOFF. Or you could also use water-depth dependent manning values… Or in your case you could also convert the DW friction factors which fitted to your data to manning values and you would get the same result like with using DW. So, it´s from my point of view not likely that DW eq. will perform better for hydrological predictions in this region. It just depends on the understanding of the system and choosing (or empirically calculating) “correct” roughness values and either way DW or Manning should perform equally.

Following on that I think the conclusion regarding this topic should be more into the direction that the processes are very complex (sometimes dominant channel hydraulics, sometimes dominant overland flow and sometimes other effects like routing or depressions which influence DW and Manning roughness on a basin scale immensely) as you already stated. And thus, by comparing basin-scale-roughness-values with empirical roughness values it shows: 1. It´s not useful to use roughness values (DW and Manning) from channel hydraulics as basin-scale-roughness-values. 2. for some catchment’s roughness values empirically determined for overland flow (DW and Manning) have been somehow correct and 3. for most of the catchments the roughness values from the examined literature examined weren´t satisfactory at all. So, it might be questionable if one can find a correct parameter set for the Canadian prairie which is also an open question in the end? (some of this you have already written but it still is not completely clear to the reader).

Please have also again a look into my comments (in pdf file) from my last review. There were also some technical aspect which haven´t been addressed. hess-2023-51-referee-report.pdf Most are just suggestions or questions. But some should be fixed eg. Fig.9 minus is missing in manning unit.

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ED: Publish subject to minor revisions (review by editor) (05 Jul 2024) by Erwin Zehe

AR by Kevin Shook on behalf of the Authors (16 Aug 2024) Author's response Author's tracked changes Manuscript

ED: Publish as is (09 Sep 2024) by Erwin Zehe

AR by Kevin Shook on behalf of the Authors (15 Sep 2024)

Short summary

Recent studies suggest that the velocities of water running off landscapes in the Canadian Prairies may be much smaller than generally assumed. Analyses of historical flows for 23 basins in central Alberta show that many of the rivers responded more slowly and that the flows are much slower than would be estimated from equations developed elsewhere. The effects of slow flow velocities on the development of hydrological models of the region are discussed, as are the possible causes.