the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 13 Mar 2023
Estimating response times, flow velocities and roughness coefficients of Canadian Prairie basins
Abstract. The hydrology and hydrography of the Canadian Prairies are complex and difficult to represent in hydrological models. Recent studies suggest that runoff velocities in the Canadian Prairies may be much smaller than are generally assumed.
Times to peak, basin-scale flow velocities and roughnesses were derived from hourly streamflow hydrographs from 23 basins in the central Alberta Prairies. The estimated velocities were much smaller than would be estimated from most commonly used empirical equations suggesting that many existing methods are not suitable for estimating time to peak or lag times in these basins. Basin area was found to be a poor predictor of basin-scale rainfall-runoff flow velocity. Estimated velocities generally increased with basin scale, indicating that slow basin response at small scales could be related to predominance of overland and/or shallow subsurface flow over the very level topography.
Basin-scale Manning’s roughness parameters, commonly used in hydrological models, were found to be orders of magnitude greater than values commonly used for streams in other parts of the world. The very large values of roughness call into question whether the Manning equation should be used for modelling runoff on the Prairies. These results have important implications for modelling rainfall-runoff in this region since using widely published values of roughness will result in poor model performance. It is likely that the Darcy-Weisbach equation, which is applicable to all flow regimes, may perform better in hydrological models of this region. Further modelling and field research will be required to determine the physical causes of these very small basin-scale velocities.
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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
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AC1: 'Reply on RC1', Kevin Shook, 28 Sep 2023
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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.
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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 tp 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 tp and tc and tl are 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 Lc 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 tcK and tlW were much smaller than the observed tp 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
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
-
AC1: 'Reply on RC1', Kevin Shook, 28 Sep 2023
-
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.
-
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 tp 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 tp and tc and tl are 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 Lc 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 tcK and tlW were much smaller than the observed tp 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
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