An Improved Algorithm for Simulating the Surface Flow Dynamics based on the FlowPath Network Model
 ^{1}School of Environment and Energy Engineering, Anhui Jianzhu University, Hefei, 230601, China
 ^{2}School of Resource and Environment Science, Wuhan University, Wuhan, 430079, China
 ^{3}Institute of Remote Sensing and Geographic Information Systems, Anhui Jianzhu University, Hefei, 230601, China
 ^{4}School of Architecture and Urban Planning, Anhui Jianzhu University, Hefei, 230601, China
 ^{5}School of Civil Engineering, Anhui Jianzhu University, Hefei, 230601, China
 ^{1}School of Environment and Energy Engineering, Anhui Jianzhu University, Hefei, 230601, China
 ^{2}School of Resource and Environment Science, Wuhan University, Wuhan, 430079, China
 ^{3}Institute of Remote Sensing and Geographic Information Systems, Anhui Jianzhu University, Hefei, 230601, China
 ^{4}School of Architecture and Urban Planning, Anhui Jianzhu University, Hefei, 230601, China
 ^{5}School of Civil Engineering, Anhui Jianzhu University, Hefei, 230601, China
Abstract. This paper proposes an improved algorithm for simulating the surface flow dynamics based on the flowpath network model. This algorithm utilizes the parallelmultipoint method to extract the critical points and the D8 algorithm to retrieve the drainage networks from the regulargrid digital elevation model (DEM) for constructing a drainageconstrained triangulated irregular network (TIN). Then, it combines the flow directions of triangular facets over TIN with resampled flow source points to track flow lines to generate the flow path network (FPN) based on the flowpath network model. On this basis, the proposed algorithm employs three terrain parameters (slope length factor, topographic wetness index and flow path curvature) to improve the classical Manning equation based on the analytic hierarchy process (AHP) to enhance the accuracy of the flow velocity calculation. The topographic wetness index and flow path curvature are derived by the flowpathnetworktriangularfacetnetwork (FPN_TFN) algorithm, a new flowpathnetworktopographicwetnessindex (FPN_TWI) algorithm and the flowpathnetworkflowpathcurvature (FPN_C) algorithm, respectively. Finally, the velocity estimation function and surface flow discharge simulation function are parallelized by the Compute Unified Device Architecture (CUDA) to enhance its computational efficiency. The outcomes are compared with the algorithm before improvement (TIN_based algorithm) and the SWAT model. The results demonstrate that the speedup ratio reaches 15.7 compared to the TIN_based algorithm. The Nash coefficient increases by 6.49 %, the correlation coefficient decreases slightly, and the balance coefficient increases by 19.08 %. Compared with the SWAT model, the Nash coefficient and correlation coefficient increase by 97.56 % and 4.60 %, respectively. The balance coefficient is close to 1 and outperforms the compared algorithms.
Qianjiao Wu et al.
Status: final response (author comments only)

CEC1: 'Comment on gmd202292', Juan Antonio Añel, 16 Jun 2022
Dear authors,
After checking your manuscript, it has come to our attention that the "Code and Data Availability" section presents several problems.
First, the section reads: "The code still needs to be improved and will be updates when it's perfect". First, it does not exist such a thing as the perfect code, so such a statement does not make sense. Secondly, the role of such section and repository is not to promote your preferred webpage, the web of a project or link to the newest version of a model but to assure the replicability of your work. To be clear, nobody cares here about an improved and better version of your software but the one you have used for your work and mentioned in the manuscript. Therefore, please, remove this statement and include the DOI of the current Zenodo repository in any reviewed version of your manuscript.
Secondly, the Readme file in the Zenodo repository instructs the user to get code from a GitHub repository. We can not accept this. GitHub is not a suitable repository and instructs authors to use other alternatives for longterm archival and publishing. I guess you refer to the Zenodo repository, so instead of the GitHub repository, use the one of Zenodo.
Third, the Readme file mentions the need to use several proprietary technologies, such as Visual Studio and Cuda 8.0. It is a shame that the replicability of your work is compromised by using nonlibre software. Also, you include several binary files .exe, so verifying their code is impossible. This makes me guess that your software could only run on specific (also nonfree) operative systems, such as Windows. However, there is no information about OS requirements in your work. You must clarify all these details in the manuscript.
Finally, although the Zenodo repository states that the software license is "Other (Open)" in the files contained, there is no license file that identifies it. If you do not include a license, the code continues to be your property and can not be used by others, despite any statement on being free to use. Therefore, when uploading the model's code to the repository, you could want to choose a free software/opensource (FLOSS) license. We recommend the GPLv3. You only need to include the file 'https://www.gnu.org/licenses/gpl3.0.txt' as LICENSE.txt with your code. Also, you can choose other options that Zenodo provides: GPLv2, Apache License, MIT License, etc.
Please reply as soon as possible to this comment with the link for it so that it is available for peerreview, as it should be.
Be aware that failing to comply with this request could result in the rejection of your manuscript for publication.Best regards,
Juan A. Añel
Geosci. Model Dev. Exec. Editor
AC1: 'Reply on CEC1', Qianjiao Wu, 23 Jun 2022
Dear Editor,
Thanks for all of the comments and suggestions for our submission GMD202292. We have carefully examined the comment in the interactive discussion of its preprint, and revised the manuscript accordingly. Detailed correction is listed below point by point.
Specific comments:
First, the section reads: "The code still needs to be improved and will be updates when it's perfect". First, it does not exist such a thing as the perfect code, so such a statement does not make sense. Secondly, the role of such section and repository is not to promote your preferred webpage, the web of a project or link to the newest version of a model but to assure the replicability of your work. To be clear, nobody cares here about an improved and better version of your software but the one you have used for your work and mentioned in the manuscript. Therefore, please, remove this statement and include the DOI of the current Zenodo repository in any reviewed version of your manuscript.
Response: Thanks for the comments. According to the comments, we have removed the statement (“The code still needs to be improved and will be updates when it's perfec”) and included the DOI of the current Zenodo repository. In the revised manuscript, we have changed the section of Code Availability (P25, L480).
Secondly, the Readme file in the Zenodo repository instructs the user to get code from a GitHub repository. We can not accept this. GitHub is not a suitable repository and instructs authors to use other alternatives for longterm archival and publishing. I guess you refer to the Zenodo repository, so instead of the GitHub repository, use the one of Zenodo.
Response: Thanks for the comments. According to the comments, we have revised the Readme file in the Zenodo repository which refers to the Zenodo repository instead of the GitHub repository. In addition, the DOI will be acquired after the code had been archived into the Zenodo repository. So, we have only provided the method to download the code in the Readme file instead of its DOI which have been updated in the revised manuscript.
Third, the Readme file mentions the need to use several proprietary technologies, such as Visual Studio and Cuda 8.0. It is a shame that the replicability of your work is compromised by using nonlibre software. Also, you include several binary files .exe, so verifying their code is impossible. This makes me guess that your software could only run on specific (also nonfree) operative systems, such as Windows. However, there is no information about OS requirements in your work. You must clarify all these details in the manuscript.
Response: Thanks for the comments. Our software can only run on the Windows operate system which have supplemented in the revises manuscript.
Finally, although the Zenodo repository states that the software license is "Other (Open)" in the files contained, there is no license file that identifies it. If you do not include a license, the code continues to be your property and can not be used by others, despite any statement on being free to use. Therefore, when uploading the model's code to the repository, you could want to choose a free software/opensource (FLOSS) license. We recommend the GPLv3. You only need to include the file 'https://www.gnu.org/licenses/gpl3.0.txt' as LICENSE.txt with your code. Also, you can choose other options that Zenodo provides: GPLv2, Apache License, MIT License, etc.
Response: Thanks for the comments. We have uploaded a LICENSE.txt with the code into the Zenodo repository according to the GPLv3.

AC1: 'Reply on CEC1', Qianjiao Wu, 23 Jun 2022

RC1: 'Comment on gmd202292', Anonymous Referee #1, 29 Jul 2022
GENERAL COMMENTS
This manuscript describes a new algorithm for surface flow dynamics simulation, which is an improvement to the existing TINbased method by Chen et al. (2014). Both of them divide a raster DEM into TIN, generate flow path network (FPN) over the TIN, and track the flow along the FPN. The main difference to the TINbased method, if I understand the text correctly, is that the algorithm proposed in this study adopts an improved Manning equation to calculate the flow velocity, as well as the parallel computing to improve the efficiency. The new Manning equation takes into account slope length factor, topographic wetness index and flow path curvature, while a new method is introduced for topographic wetness index calculation with the TFN network. Although it is odd to introduce new parameters into the Manning equation, the results show the behavior to be effective.
Overall, I find this may be a useful paper, and it may propose an effective improvement to the classical Manning equation.
However, I think this manuscript is not readerfriendly especially for people who know less about this field. Firstly, the section Methodology lacks some important figures for illustration. For example, are the triangular facets of FPN (e.g., L136) and TFN (e.g., 169) the same? Secondly, some abbreviations and letters appear in multiple equations and have different definition. For example, S denotes slope in Eq. 1&6, and denotes specific catchment area in Eq. 4. Thirdly, the flow path is simulated over triangular facets (Section 2.1), and the parameters are calculated for DEM grids (Section 2.2), so how to combine the triangular facets and grids when simulating the surface flow dynamics?
I have major issue with the improved Manning equation. The authors explain that the slope length factor, topographic wetness index and flow path curvature should be normalized for Eq. 6, but I find no information about the method for normalization. Does this step rely on any parameter in the DEM? If so, a point may be assigned with different flow velocities when different basins or subbasins containing this point are adopted. In addition, the results show that the improved Manning equation combining four parameters outperforms the classical Manning equation only considering the slope. More assessments may be valuable to show whether all the four parameters are acting, or a better result may happen when only two or three important parameters are adopted.
Finally, the authors may add more descriptions about their methods and assessments such as whether they consider the baseflow like Chen et al. (2014) when assessing the algorithms. More discussions are need to explain why they ignored some conditions, such as the infiltration and water depth (Nilsson et al., 2022).
SPECIFIC COMMENTS
P2 L41&54 The statements here are contradictory that "regulargrid DEMs can better describe continuous terrain surfaces" in L41 and TIN is "better expression of complex and changeable surface" in L54.
P3 L6778 The authors described that the method of Shen et al. (1995) can "simulate runoff and surface flow discharge at any position and time" in L6768. However, they stated that the introduced methods including Shen et al. (1995) "can only simulate the surface flow dynamics of a limited number of points" (L7576), and it is difficult to simulate "at any location" (L78). The statements above are contradictory.
P5 L118137 The authors may want to add a figure to Section 2.1 to show the processes of FPN generation clearly.
P6 L147 The definitions of letters in Eq. (1) were not introduced.
P7 L173 The reference of TFN by Zhou et al. (2011) seems to be missed. The authors may explain why they accepted the method of Zhou et al. (2011) for the flow accumulation but used a new method rather than the one of Zhou et al. (2011) for aspect. Can it improve the accuracy?
P7 L183 "n denotes the nth triangular facet"? The "n" may be the number of the triangular facets treating the cell as the vertex. In addition, it is different for the readers to understand the triangular facet mode of TFN because there is no figure and the triangular facets decided by FPN in Figure 2 may mistake them.
P7 L186188 For Eq. (4), A should denote the number of flow lines passing the cell over the TFN (Zhou et al., 2011).
P8 L194 tanβ denotes the slope (m/m).
P8 L204 How did the authors normalize the slope length factor, topographic wetness index, and flow path curvature?
P8 L214 The analytic hierarchy process (AHP) may be effective according to the results. But authors may explain more about why they decided the relative importance between the parameters like Matrix 1. A reference is required because the method of AHP is existing.
P11 L262 The resolution of original DEM was 5 m. Why only the resolutions ranging from 10 m to 30 m were adopted for subsequent analysis?
P12 L276283 This paragraph should be improved because multiple thresholds with different uses are confusing. Is the filter threshold used to avoid narrow facets as described in L127128? Are the same values of drainage network threshold (2000 m2) and the filter threshold (8 m) adopted by the DEMs with coarser resolutions (i.e., 1030 m) used below? If so, the distance between two points over a10m resolution DEM is always longer than 8 m, is this threshold necessary?
P12 L282 A table can be added to list the numbers of critical points and facets over DEMs with different resolutions.
P12 L285288 There are six resolutions but five flow line numbers. So is the resolution of 5 m ignored?
P13 L293 Which step requires the threshold to cut the flow line?
P14 L298 Table 3 contains land use data, climate data, and soil data, but the caption only mentions the land use data, while only the land use data was used in this study.
P17 L322 Why was only the resolution of 30 m adopted for comparison between SWAT and the improved algorithm?
P19 L348 The terms "scale" and "resolution" seem to be mixed up in this manuscript.
TECHNICAL CORRECTIONS
P2 L50 The full name of the abbreviation "BGIS" should be "Basin Geomorphic Information System" rather than "Geomorphic Information System". And the reference "Tachikawa (1994)" may be false because this reviewer found the article published in 1992 and another journal according to the DOI.
P3 L6869 The full name of the abbreviation "SCS" and "HRU" were missed.
P21 L374 There are two lines labeled as scale = 5 m.
References
Chen, Y., Zhou, Q., Li, S., Meng, F., Bi, X., Wilson, J. P., Xing, Z., Qi, J., Li, Q. and Zhang, C.: The simulation of surface flow dynamics using a flowpath network model, Int. J. Geogr. Inf. Sci., 28(11), 22422260, https://doi.org/10.1080/13658816.2014.917312, 2014.
Nilsson, H., Pilesjö, P., Hasan, A., & Persson, A. (2021). Dynamic spatiotemporal
flow modeling with raster DEMs. Transactions in GIS, 26, 15721588. https://doi.org/10.1111/tgis.1287
Shen, X., Wang, L. and Xie, S.: A dynamic precipitationrunoff model for a watershed based on grid data, Acta Geographica Sinica, 50(3), 264271, https://doi.org/10.11821/xb199503009, 1995.
Tachikawa, Y., Shiiba, M. and Takasao, T.: Development of a basin geomorphic information system using a TINDEM data structure, Water Resour. Bull. Am. Water Resour. Assoc., 30(1), 917, https://doi.org/10.2208/prohe.36.677, 1994.
Zhou, Q., P. Pilesjö, and Y. Chen (2011), Estimating surface flow paths on a digital elevation model using a triangular facet network, Water Resour. Res., 47, W07522, doi:10.1029/2010WR009961.

CC1: 'Reply on RC1', Qianjiao Wu, 05 Aug 2022
Thanks for all of the comments and suggestions for our submission GMD202292. We have carefully examined the comment in the interactive discussion of its preprint, and revised the manuscript accordingly. Detailed correction is listed below point by point.
General comments:
This manuscript describes a new algorithm for surface flow dynamics simulation, which is an improvement to the existing TINbased method by Chen et al. (2014). Both of them divide a raster DEM into TIN, generate flow path network (FPN) over the TIN, and track the flow along the FPN. The main difference to the TINbased method, if I understand the text correctly, is that the algorithm proposed in this study adopts an improved Manning equation to calculate the flow velocity, as well as the parallel computing to improve the efficiency. The new Manning equation takes into account slope length factor, topographic wetness index and flow path curvature, while a new method is introduced for topographic wetness index calculation with the TFN network. Although it is odd to introduce new parameters into the Manning equation, the results show the behavior to be effective.
Overall, I find this may be a useful paper, and it may propose an effective improvement to the classical Manning equation.
Response: Thanks for the comments.However, I think this manuscript is not readerfriendly especially for people who know less about this field. Firstly, the section Methodology lacks some important figures for illustration. For example, are the triangular facets of FPN (e.g., L136) and TFN (e.g., 169) the same? Secondly, some abbreviations and letters appear in multiple equations and have different definition. For example, S denotes slope in Eq. 1&6, and denotes specific catchment area in Eq. 4. Thirdly, the flow path is simulated over triangular facets (Section 2.1), and the parameters are calculated for DEM grids (Section 2.2), so how to combine the triangular facets and grids when simulating the surface flow dynamics?
Response: Thanks for the comments. 1) The triangular facets of FPN (e.g., L136) and TFN (e.g., 169) is not the same. We have added the related figure (P8, Line 184). 2) The letters of all of the equations have been rearranges and corrected in the revised manuscript. 3) The flow path is simulated over triangular facets (Section 2.1), and the parameters are calculated for DEM grids (Section 2.2). When simulating the surface flow dynamics, we assigned the value of parameters at its corresponding position to the flow source points to combine the triangular facets and grids.I have major issue with the improved Manning equation. The authors explain that the slope length factor, topographic wetness index and flow path curvature should be normalized for Eq. 6, but I find no information about the method for normalization. Does this step rely on any parameter in the DEM? If so, a point may be assigned with different flow velocities when different basins or subbasins containing this point are adopted. In addition, the results show that the improved Manning equation combining four parameters outperforms the classical Manning equation only considering the slope. More assessments may be valuable to show whether all the four parameters are acting, or a better result may happen when only two or three important parameters are adopted.
Response: Thanks for the comments. In order to avoid large fluctuation of flow velocity before simulating the surface flow dynamics, we tried to normalize the three parameters and the normalization algorithm has been added in the revised manuscript (P10, L218221). And this step not rely on any parameter in the DEM. We first tried to combine three parameters with the classical Manning equation and found that the behavior is effective. We are trying to value whether all the four parameters are acting or a better result may happen when only two or three important parameters are adopted.Finally, the authors may add more descriptions about their methods and assessments such as whether they consider the baseflow like Chen et al. (2014) when assessing the algorithms. More discussions are need to explain why they ignored some conditions, such as the infiltration and water depth (Nilsson et al., 2022).
Response: Thanks for the comments. Daily observed daily flow discharge at the outlet of the BBW in 2001 are measured data provided by the BBW Watershed Monitoring Station. The observed daily flow discharge is combined surface runoff discharge with the baseflow discharge. The improved algorithm also only simulated the surface runoff discharge which is added to the baseflow discharge for getting the daily flow discharge. The baseflow discharge is calculated using the method proposed by Zhang et al. (2012). For the comparison, the same procedure was used for the SWAT simulates the daily flow discharge. Thus, we no need to consider the other conditions. We have supplemented it in the revised manuscript (P13, L289294).SPECIFIC COMMENTS:
(1) P2 L41&54 The statements here are contradictory that "regulargrid DEMs can better describe continuous terrain surfaces" in L41 and TIN is "better expression of complex and changeable surface" in L54.
Response: Thanks for the comments. The regulargrid DEMs can better describe the continuity of topography. TIN can better express the complexity and fluctuation of the terrain surface. We have corrected it in the revised manuscript.(2) P3 L6778 The authors described that the method of Shen et al. (1995) can "simulate runoff and surface flow discharge at any position and time" in L6768. However, they stated that the introduced methods including Shen et al. (1995) "can only simulate the surface flow dynamics of a limited number of points" (L7576), and it is difficult to simulate "at any location" (L78). The statements above are contradictory.
Response: Thanks for the comments. Shen et al. (1995) explored the water balance equation and Muskingum method to simulate runoff and surface flow discharge at any grid cell and time. The algorithm simulated the surface flow discharge based on the grid cell acquired by splitting the watershed and simulated the runoff of all of the grid cell. We have corrected it in the revised manuscript (P3, L6668).(3) P5 L118137 The authors may want to add a figure to Section 2.1 to show the processes of FPN generation clearly.
Response: Thanks for the comments. The processes of FPN generation have been illustrated in Figure 1. The specific tracking algorithm have been described in detail by Chen et al. (2014) and we have referenced the paper in Section 2.1.
(4) P6 L147 The definitions of letters in Eq. (1) were not introduced.
Response: Thanks for the comments. We have added the definitions of letters in Eq. (1) in the revised manuscript (P6, L146147).(5) P7 L173 The reference of TFN by Zhou et al. (2011) seems to be missed. The authors may explain why they accepted the method of Zhou et al. (2011) for the flow accumulation but used a new method rather than the one of Zhou et al. (2011) for aspect. Can it improve the accuracy?
Response: Thanks for the comments. Consider the constant slopes and aspects of the triangular facets, we tried to obtain the slope and aspect from the TFN constructed from the nodepression DEM by the TFN algorithm (Zhou et al., 2011). The accuracy of the surface flow dynamics demonstrates that the behavior is not bad. We hope to get the required parameter from the vector TFN or FPN for the further integration.(6) P7 L183 "n denotes the nth triangular facet"? The "n" may be the number of the triangular facets treating the cell as the vertex. In addition, it is different for the readers to understand the triangular facet mode of TFN because there is no figure and the triangular facets decided by FPN in Figure 2 may mistake them.
Response: Thanks for the comments. The "n" denotes the number of the triangular facets treating the cell as the vertex and we have corrected it in the revised manuscript (P7, L182182). In addition, we added a figure to understand the triangular facet mode of TFN in the revised manuscript (P8, L179180).(7) P7 L186188 For Eq. (4), A should denote the number of flow lines passing the cell over the TFN (Zhou et al., 2011).
Response: Thanks for the comments. We have corrected it in the revised manuscript (P7, L185186).(8) P8 L194 tanβ denotes the slope (m/m).
Response: Thanks for the comments. We have corrected it in the revised manuscript (P8, L193).(9) P8 L204 How did the authors normalize the slope length factor, topographic wetness index, and flow path curvature?
Response: Thanks for the comments. The minmax normalization method was utilized to normalize the three parameters in this study. We have supplemented it in the revised manuscript and added the related reference in the paper (P8, L203204).(10) P8 L214 The analytic hierarchy process (AHP) may be effective according to the results. But authors may explain more about why they decided the relative importance between the parameters like Matrix 1. A reference is required because the method of AHP is existing.
Response: Thanks for the comments. We tried to give the relative importance between the parameters like Matrix 1 and the matrix is deemed to pass the consistency test. So, we used the elements of the eigenvector corresponding to the maximum eigenvalue of the Matrix 1 as the weights. We had added the reference about the method of AHP in the revised manuscript (P8, L205).(11) P11 L262 The resolution of original DEM was 5 m. Why only the resolutions ranging from 10 m to 30 m were adopted for subsequent analysis?
Response: Thanks for the comments. We retrieved the critical points from the 5 m DEM with different thresholds of 0.5, 1.0, 1.5, 2.0 and 2.5 m to construct the TIN with different scales. The flow source points were obtained from the DEM with the resolution of 10, 15, 20, 25 and 30 m which are resampled from the 5 m DEM. Then the TIN was combined with the flow source points to generate the FPN for the surface flow dynamics simulation. The resolutions of flow source points ranging from 10 m to 30 m were adopted for subsequent analysis.(12) P12 L276283 This paragraph should be improved because multiple thresholds with different uses are confusing. Is the filter threshold used to avoid narrow facets as described in L127128? Are the same values of drainage network threshold (2000 m2) and the filter threshold (8 m) adopted by the DEMs with coarser resolutions (i.e., 1030 m) used below? If so, the distance between two points over a10m resolution DEM is always longer than 8 m, is this threshold necessary?
Response: Thanks for the comments. We retrieved the critical points from the 5 m DEM with different thresholds and not retrieved the critical points from DEM with different resolutions. Because the RMSE of drainageconstrained TIN slightly increases when the threshold of extracting the drainage networks is greater than 2000 m2 and the threshold of 8 m was used to filter the critical points because the greater threshold value basically keeps the RMSE of drainageconstrained TIN unchanged. Thus, in order to reduce the narrow facets, we selected the threshold of 2000 m2 to extract the drainage networks and the threshold of 8 m to filter the retrieved critical points with different thresholds of 0.5, 1.0, 1.5, 2.0 and 2.5 m.(13) P12 L282 A table can be added to list the numbers of critical points and facets over DEMs with different resolutions.
Response: Thanks for the comments. We list the numbers of critical points and triangular facets with different thresholds in Table 8. Here, we only illustrated the numbers of critical points and triangular facets with the threshold of 0.5 m and so we not list a table.(14) P12 L285288 There are six resolutions but five flow line numbers. So is the resolution of 5 m ignored?
Response: Thanks for the comments. The 5 m DEM is not ignored. The flow source points were obtained from the DEM with the resolution of 10, 15, 20, 25 and 30 m which are resampled from the 5 m DEM. The drainageconstrained TINs were constructed by the critical points extracted from the 5 m DEM.(15) P13 L293 Which step requires the threshold to cut the flow line?
Response: Thanks for the comments. The FPN_C algorithm was described in the paper “Wu, Q., Chen, Y., Zhou, H., Chen, S. and Wang, H.: A new algorithm for calculating the flow path curvature (C) from the squaregrid digital elevation model (DEM), ISPRS Int. J. GeoInf., 9(9), 32–34”. The cubic Bspine interpolation algorithm was used to smooth flow line over the flow path network in the FPN_C algorithm. To reduce the likelihood of overfitting, the flow line was cut up by a threshold.(16) P14 L298 Table 3 contains land use data, climate data, and soil data, but the caption only mentions the land use data, while only the land use data was used in this study.
Response: Thanks for the comments. We have replaced the caption of Table 3 as Summary of input data used for the simulations in the BBW region. The Manning’s roughness coefficient is determined according to the landuse types of the BBW region in Table 3 and the values proposed by Thompson (1999). Other data were used for the baseflow discharge simulation.(17) P17 L322 Why was only the resolution of 30 m adopted for comparison between SWAT and the improved algorithm?
Response: Thanks for the comments. We only have 30 m resolution of data required by the SWAT model currently and only compared their results under the resolution of 30 m. But we will compare their accuracy under other resolutions in the further research.(18) P19 L348 The terms "scale" and "resolution" seem to be mixed up in this manuscript.
Response: Thanks for the comments. We have corrected all of the confusing uses in the revised manuscript.TECHNICAL CORRECTIONS
(1) P2 L50 The full name of the abbreviation "BGIS" should be "Basin Geomorphic Information System" rather than "Geomorphic Information System". And the reference "Tachikawa (1994)" may be false because this reviewer found the article published in 1992 and another journal according to the DOI.
Response: Thanks for the comments. We have corrected it in the revised manuscript. (P2, L49)(2) P3 L6869 The full name of the abbreviation "SCS" and "HRU" were missed.
Response: Thanks for the comments. We have added their full name in the revised manuscript. (P3, L6768)(3) P21 L374 There are two lines labeled as scale = 5 m.
Response: Thanks for the comments. The three labels have been corrected in the revised manuscript. (P21, L369)References
(1) Chen, Y., Zhou, Q., Li, S., Meng, F., Bi, X., Wilson, J. P., Xing, Z., Qi, J., Li, Q. and Zhang, C.: The simulation of surface flow dynamics using a flowpath network model, Int. J. Geogr. Inf. Sci., 28(11), 22422260, https://doi.org/10.1080/13658816.2014.917312, 2014.
Response: Thanks for the comments. We have corrected it in the revised manuscript. (P26, L504506)(2) Nilsson, H., Pilesjö, P., Hasan, A., & Persson, A. (2021). Dynamic spatiotemporal flow modeling with raster DEMs. Transactions in GIS, 26, 15721588. https://doi.org/10.1111/tgis.1287
Response: Thanks for the comments. We have added it in the revised manuscript. (P27, L537538)(3) Shen, X., Wang, L. and Xie, S.: A dynamic precipitationrunoff model for a watershed based on grid data, Acta Geographica Sinica, 50(3), 264271, https://doi.org/10.11821/xb199503009, 1995.
Response: Thanks for the comments. We have corrected it in the revised manuscript. (P27, L547548)(4) Tachikawa, Y., Shiiba, M. and Takasao, T.: Development of a basin geomorphic information system using a TINDEM data structure, Water Resour. Bull. Am. Water Resour. Assoc., 30(1), 917, https://doi.org/10.2208/prohe.36.677, 1994.
Response: Thanks for the comments. We have corrected it in the revised manuscript. (P28, L557558)(5) Zhou, Q., P. Pilesjö, and Y. Chen (2011), Estimating surface flow paths on a digital elevation model using a triangular facet network, Water Resour. Res., 47, W07522, doi:10.1029/2010WR009961.
Response: Thanks for the comments. We have corrected it in the revised manuscript. (P28, L588589)
RC3: 'Reply on CC1', Anonymous Referee #1, 20 Aug 2022
Dear Authors,
Thank you for your detailed reply. Although I cannot find the revised version for the moment, I think you have addressed most of the concerns I raised. However, I am still worry about the normalization method used for Eq. (6) in your manuscript, so I add this comment.
According to your reply, the minmax normalization method was adopted. For a target cell, the points with the maximum or the minimum value of the parameters in the basin may not be located at the upstream area of this cell. So the flow velocity of a cell by Eq. (6) may be affected by the cells which do not drain flow to it. This is very odd because they are unrelated.
In addition, I attached a PDF document to show that a cell can be assigned with different normalized parameter value when basins with different scales (such as a large basin and its subbasin) are used for simulation, so its flow velocity by Eq. (6) can vary. This phenomenon shows that the results of the new algorithm are unstable, and the good performance for the Black Brook Watershed may be a lucky result caused by the weights decided by the subjective analytic hierarchy process (AHP). But these subjective weights may not be suitable for other basins.

AC3: 'Reply on RC3', Qianjiao Wu, 26 Aug 2022
Dear Researcher,
Thanks for all of the comments and suggestions for our submission GMD202292. For your worry about the problem (For a target cell, the points with the maximum or the minimum value of the parameters in the basin may not be located at the upstream area of this cell). From Figure 7 “The slope length factor, topographic wetness index and flow path curvature obtained from the 10 m DEM.”, we can see that the points with the maximum value of the parameters in the basin are located at the upstream area of a target cell along the flow path.In addition, we regard the large basin as the study region and simulate the flow dynamics for the region based on all of the flow paths from the flow source points resampled from the DEMs with different resolutions. Thus, the minimum and the maximum values of three terrain parameters will be changed when the study region is changed from the large basin. And it is worth discussing the influence of this change on the final simulation results further. Thank you for your comments again.

AC3: 'Reply on RC3', Qianjiao Wu, 26 Aug 2022

RC3: 'Reply on CC1', Anonymous Referee #1, 20 Aug 2022

CC1: 'Reply on RC1', Qianjiao Wu, 05 Aug 2022

RC2: 'Comment on gmd202292', Anonymous Referee #2, 08 Aug 2022
General comments:
The manuscript authored by Wu et al. presents an improved algorithm to simulate the surface flows. To increase the simulation accuracy and calculation efficiency, a flowpath network model by constructing the drainageconstrained TIN and refining the Manning formula using three terrain parameters. The improved algorithm was conducted and evaluated in the case study area, the Black Brook Watershed in northwestern New Brunswick, Canada. Overall, the paper is presented in a clear logic. However, several aspects of issues regarding the algorithm design and accuracy evaluation prevent the recommendation to be accepted in its present form.
(1) In the study, modifying Manning’s equation by combining the FPN and three terrain parameters (slope length factor, topographic wetness index (TWI), and flow path curvature) is the key step of the improved algorithm and one of the main contributions of this method. However, why the three terrain parameters were chosen and the roles of the different parameters on improving the simulation were not elucidated explicitly and evidenced powerfully. How about only using one or two parameters or add other terrain parameters???
Actually, the slope used in the classic Manning’s equation represents the situation in pixel scale, while the parameters, e.g., the slope length factor and TWI, are calculated in hilly slope (regional) scale. How to handle the merging of parameters in different spatial scales? In addition, the three parameters have strong selfcorrelation.
(2) A critical step to modify Manning’s equation is integration of three added terrain parameters. In this study, the three parameters are weighted by the analytic hierarchy process (AHP) method. However, as presented in Table 1 and Section 2.2.2, the determination of the importance of one factor to another factor and the weights is subjective. The weighting scheme needs to be validated more.
(3) The good performance of the improved algorithm was validated by comparing with the results derived from the SWAT model. Why was it compared with that derived from the conventional Manning’s equation? Besides, the performance of SWAT model simulation largely depends on the parameter calibration upon the sufficient insitu data. However, the information on the SWAT modeling is not given in detail.
Specific comments:
Line 92: A punctuation is missing after the bracket?
Line 138: The section title is too wordy. The content within the bracket is suggested to be deleted.
Line 143: The same to the advice above.
Line 147: What do the variable symbols mean? Please specify the descriptions for these variables of the formula, albeit the Manning’s equation is well known already.
Line 159: Here the abbreviation TWI is not presented first.
Line 160: The punctuation is missing in the paragraph end.
Line 163: The citation is not formatted correctly.
Line 179: What is the new point? Is it reliable?
Line 270: The geographic coordinates should be added in the insert map of Figure 3. The legend for the insert map is suggested. What is the mean of grey line (state boundary)? What does the red rectangle in the main map refer to?
Line 325: The line thickness and format of Figure 8 may be modified to enhance the clarity, especially for the highlight of the “improved algorithm” line.
Line 375: Similarly, the line thickness and format of Figure 11 should be adjusted.
Line 459: The TWI was calculated by a new algorithm? As presented in Section 2.2.1, the TWI is estimated by the definition reported by Beven and Kirkby (1979).

CC2: 'Reply on RC2', Qianjiao Wu, 17 Aug 2022
Dear Researcher,
Thanks for all of the comments and suggestions for our submission GMD202292. We have carefully examined the comment in the interactive discussion of its preprint and revised the manuscript accordingly. Detailed correction is listed below point by point.
General comments:
The manuscript authored by Wu et al. presents an improved algorithm to simulate the surface flows. To increase the simulation accuracy and calculation efficiency, a flowpath network model by constructing the drainageconstrained TIN and refining the Manning formula using three terrain parameters. The improved algorithm was conducted and evaluated in the case study area, the Black Brook Watershed in northwestern New Brunswick, Canada. Overall, the paper is presented in a clear logic.
Response: Thanks for the comments.However, several aspects of issues regarding the algorithm design and accuracy evaluation prevent the recommendation to be accepted in its present form.
(1) In the study, modifying Manning’s equation by combining the FPN and three terrain parameters (slope length factor, topographic wetness index (TWI), and flow path curvature) is the key step of the improved algorithm and one of the main contributions of this method. However, why the three terrain parameters were chosen and the roles of the different parameters on improving the simulation were not elucidated explicitly and evidenced powerfully. How about only using one or two parameters or add other terrain parameters???
Actually, the slope used in the classic Manning’s equation represents the situation in pixel scale, while the parameters, e.g., the slope length factor and TWI, are calculated in hilly slope (regional) scale. How to handle the merging of parameters in different spatial scales? In addition, the three parameters have strong selfcorrelation.Response: Thanks for the comments. 1) There are several terrain parameters (such as slope length factor, topographic wetness index, flow path curvature, upslope slope, and upslope area) have an influence on the flow velocity. In this paper, we tried to choose the slope length factor, topographic wetness index and flow path curvature to improve the simulation and found that this behavior has some effectiveness and we are exploring the use of only one or two parameters or other terrain parameters whether a better result may happen. 2) The slope used in the classic Manning’s equation represents the situation in pixel scale. The constraineddrainage TIN is constructed in a regional scale.
And the parameters, e.g., the slope length factor and TWI, are also calculated in pixel scale. The flow path is simulated over triangular facets over the constraineddrainage TIN (Section 2.1), and the parameters are calculated for DEM grids (Section 2.2). When simulating the surface flow dynamics, we assigned the value of parameters at their corresponding position to the flow source points to combine the triangular facets and grids. 3) The three parameters have strong selfcorrelation and we will try to improve the proposed algorithm in further to get a better result by reducing the selfcorrelation.(2) A critical step to modify Manning’s equation is integration of three added terrain parameters. In this study, the three parameters are weighted by the analytic hierarchy process (AHP) method. However, as presented in Table 1 and Section 2.2.2, the determination of the importance of one factor to another factor and the weights is subjective. The weighting scheme needs to be validated more.
Response: Thanks for the comments. The subjectivity of the determination of the importance of one factor to another factor and the weights is a shortage and we will validate the weighting scheme for a better result furtherly.
(3) The good performance of the improved algorithm was validated by comparing with the results derived from the SWAT model. Why was it compared with that derived from the conventional Manning’s equation? Besides, the performance of SWAT model simulation largely depends on the parameter calibration upon the sufficient insitu data. However, the information on the SWAT modeling is not given in detail.
Response: Thanks for the comments. 1) The good performance of the improved algorithm was not only validated by comparing with the results derived from the SWAT model, but also compared with that derived from the conventional Manning’s equation. In addition, the improved algorithm consists of parallelization for enhancing the computational effectiveness. And we also compare the results before and after the parallelization. 2) The experiment uses the daily runoff discharge of BBW in 2001 to simulate the daily surface flow discharge. The daily runoff discharge is simulated by the SWAT model according to the daily rainfall, and the data have a high accuracy (Chen et al., 2014). Daily observed daily flow discharge at the outlet of the BBW in 2001 is measured data provided by the BBW Watershed Monitoring Station. The observed daily flow discharge is a combined surface runoff discharge with the baseflow discharge. The improved algorithm also only simulated the surface runoff discharge which is added to the baseflow discharge for getting the daily flow discharge. The baseflow discharge is calculated using the method proposed by Zhang et al. (2012). For the comparison, the same procedure was used for the SWAT to simulate the daily flow discharge. We have supplemented these in the revised manuscript (P13, Line285292).
SPECIFIC COMMENTS:
(1) Line 92: A punctuation is missing after the bracket?
Response: Thanks for the comments. We have added the punctuation in the revised manuscript (P3, L93).(2) Line 138: The section title is too wordy. The content within the bracket is suggested to be deleted.
Response: Thanks for the comments. We have deleted the content within the bracket (P6, L138).(3) Line 143: The same to the advice above.
Response: Thanks for the comments. We have deleted the content within the bracket (P6, L143).(4) Line 147: What do the variable symbols mean? Please specify the descriptions for these variables of the formula, albeit the Manning’s equation is well known already.
Response: Thanks for the comments. We have added the definitions of letters in Eq. (1) in the revised manuscript (P6, L148149).(5) Line 159: Here the abbreviation TWI is not presented first.
Response: Thanks for the comments. We have corrected it and the abbreviation TWI is presented in P4 Line 11 first.(6) Line 160: The punctuation is missing in the paragraph end.
Response: Thanks for the comments. We have supplemented the punctuation in the revised manuscript (P7, L163).(7) Line 163: The citation is not formatted correctly.
Response: Thanks for the comments. We have modified “(Wu et al., 2020)” as “Wu et al. (2020)” in the revised manuscript (P7, L165).(8) Line 179: What is the new point? Is it reliable?
Response: Thanks for the comments. Considering the constant slopes and aspects of the triangular facets, we tried to obtain the slope and aspect from the TFN constructed from the nodepression DEM by the TFN algorithm (Zhou et al., 2011). The accuracy of the surface flow dynamics demonstrates that the behavior is not bad. We hope to get the required parameter from the vector TFN or FPN for further integration. In addition, we added a figure to understand the triangular facet mode of TFN in the revised manuscript (P8, L179180).(9) Line 270: The geographic coordinates should be added in the insert map of Figure 3. The legend for the insert map is suggested. What is the mean of grey line (state boundary)? What does refer to?
Response: Thanks for the comments. We have added the geographic coordinates in the main and insert map. The legend for the insert map has been added to the revised manuscript. The mean of grey line is the province or territory boundary of Canada. The red rectangle in the main map was used for some illustration of the subregion in the next two Figures and we have added some states in the caption of the Figure (P13, Line284).(10) Line 325: The line thickness and format of Figure 8 may be modified to enhance the clarity, especially for the highlight of the “improved algorithm” line.
Response: Thanks for the comments. We have modified the color of the “improved algorithm” line in the Figure to green (P18, L339).(11) Line 375: Similarly, the line thickness and format of Figure 11 should be adjusted.
Response: Thanks for the comments. The line thickness and format of Figure 11 have been corrected in the revised manuscript (P21, L369).(12) Line 459: The TWI was calculated by a new algorithm? As presented in Section 2.2.1, the TWI is estimated by the definition reported by Beven and Kirkby (1979).
Response: Thanks for the comments. The TWI is estimated by the definition reported by Beven and Kirkby (1979), but the slope and SCA in their definition are calculated by the new algorithm. It has been described in Section 2.2.1.

CC2: 'Reply on RC2', Qianjiao Wu, 17 Aug 2022
Qianjiao Wu et al.
Qianjiao Wu et al.
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