Probabilistic Forecast for Real-Time Control of Rainwater Pollutant Loads in Urban Environments

Round 1

Reviewer 1 Report (New Reviewer)

Comments and Suggestions for Authors

The manuscript deals with a modelling technique for the “probabilistic” forecast of the total suspended solids, accounting for the uncertainty. The Model Conditional Processor (MCP) is used to forecast the complete predictive probability density of total suspended solids conditional on one or multiple deterministic predictions.

The manuscript is an original contribution. It addresses the aims of the special issue “Understanding, Forecasting and Control of Flooding and Pollution in the Urban Environment: The 10th Anniversary of Hydrology”. The topic is of interest for the readership of the Journal. The analysis on a real case study strengthens the research; the implementation of the MCP approach is applied to observations of a real urban stormwater drainage system in southeastern Virginia acquired from a large long-term stormwater monitoring initiative conducted by the USGS.

English language is clear, and the presentation is good; anyway, I have detected some criticisms in the text that should be properly addressed.

The Authors can benefit from the comments below to improve their paper. These have to be accomplished before manuscript acceptance.

 

 

Abstract

The abstract is concise and reflects the content of the article. It summarizes the main outcomes of the study.

 

 

Keywords

The provided keywords are informative and useful for indexing purposes.

 

 

Introduction

The Section is well arranged. Aims of the study are properly clarified and relevant references are included.

Authors are recommended to replace “wastewater” with “wet-weather flow” at lines 65 and 70 since the joint contribution of wastewater and stormwater flow activates the flow divider/regulator.

Lines 74-82: It should be specified that it is mandatory to ensure that the flow rate is delivered to the treatment plant in compliance with the regulatory constraints.

 

 

Materials and Methods

This section is clear and adequately detailed.

The provided figures and table are effective and necessary for the presentation.

Lines 148-150: In addition to the initial traditional sampling phase required to calibrate the conversion models, it is important to specify in the introductory discussion that periodic calibrations of the multiparametric probes are necessary to obtain reliable measurements.

Authors are advised to emphasize the fact that peak TSS load does not necessarily coincide with peak TSS concentration.

Lines 205-212: Some results may be included on the trial-and-error tests on different combinations of available surrogate parameters.

Line 314: Check the number of figure. It seems that “Figure 1” should be replaced with “Figure 2”.

Line 464: In the graphs of Figure 2 comma must be replaced with point as decimal separator.

Line 494: The indicated number of equations is not correct and should be checked.

 

 

The case study

This section is presented in a logical sequence. It is quite clear even if some improvement is recommended. The title of this session could be improved as it reports the results of applying the methodology to a real urban stormwater drainage system.

Line 525: Does streamflow centroid mean the hydrograph centroid at the outlet of the Lucas Creek urban catchment?

It is clarified that the available TSS concentration data in stormwater flow are not temporally continuous. In this regard, some specifications are recommended on the characteristics of available individual water samples.

Lines 560-563: 129 data of TSS load and the corresponding TB and Q of the previous time step, correspond to a total of n.3x129 data. It is not clear the reason why a total of n.4x129 data are indicated. Is it because the TSS load is the product of the TSS concentration and the flow rate?

Lines 565-571: the choice of the TSS polluting load threshold of 42 𝑔/𝑠 should be better motivated.

Lines 608 and 638: It is not clear the meaning of symbol “=” in table 2 and table 3.

Since figure 7 include the information of figure 2, figure 2 can be omitted.

Line 661: In the graphs of Figure 6 comma must be replaced with point as decimal separator.

Line 696: In the graphs of Figure 8 comma must be replaced with point as decimal separator.

Lines 701-704: Since tables 4 and 5 provide the same results as figure 8 in tabular form, they can be omitted.

 

 

Conclusions

Conclusions seem reasonable and supported by the results.

The limitations of the study should be appropriately indicated in the concluding remarks.

 

 

References

Several relevant references are included in the paper. Based on my knowledge, no important reference is missing.

Author Response

Comment 1:

Authors are recommended to replace “wastewater” with “wet-weather flow” at lines 65 and 70 since the joint contribution of wastewater and stormwater flow activates the flow divider/regulator.

Reply 1:

Done

Comment 2:

Lines 74-82: It should be specified that it is mandatory to ensure that the flow rate is delivered to the treatment plant in compliance with the regulatory constraints.

Reply 2:

We have introduced the following sentence:

“It is, in fact, mandatory to guarantee that the flow rate is delivered to the treatment plant in accordance with the regulatory constraints, which include the regulatory threshold values for the concentrations of pollutants in discharges into water bodies and for the inflow rates of treatment plants.”

Comment 3:

Materials and Methods

This section is clear and adequately detailed.

The provided figures and table are effective and necessary for the presentation.

Lines 148-150: In addition to the initial traditional sampling phase required to calibrate the conversion models, it is important to specify in the introductory discussion that periodic calibrations of the multiparametric probes are necessary to obtain reliable measurements.

Reply 3:

We have introduced the following sentences:

“Rather than recalibrations, the surrogate parameter monitoring system requires periodic interventions and cleaning of the probes submerged in the wastewater flow. This is to keep the measurement from being influenced by the formation of a biological membrane, which would lead to its interpretation as a traditional pollution parameter. In fact, the latter's measurement undergoes a complete transformation upon the formation of the biological film, making recalibration unnecessary.

 

Comment 4:

Authors are advised to emphasize the fact that peak TSS load does not necessarily coincide with peak TSS concentration.

Reply 4:

We have changed the sentence:

“Therefore, TSS represents an important water quality parameter, extensively used in this research field [27].”

into:

“Therefore, although peak TSS volume does not coincide with its peak concentration, it represents an important water quality parameter, extensively used in this research field [27].”

Comment 5:

Lines 205-212: Some results may be included on the trial-and-error tests on different combinations of available surrogate parameters.

Reply 5:

We concur in principle; however, the manuscript is already excessively lengthy, and we have decided to omit this information, which appeared to be unnecessary for the comprehension of the concepts and methodologies described.

Comment 6:

Line 314: Check the number of figure. It seems that “Figure 1” should be replaced with “Figure 2”.

Reply 6:

Done.

Comment 7:

Line 464: In the graphs of Figure 2 comma must be replaced with point as decimal separator.

 Reply 7:

Done.

Comment 8:

Line 494: The indicated number of equations is not correct and should be checked.

 Reply 8:

Done.

We really appreciate your attentive reading and your bringing all these errors to our attention.

Comment 9:

The case study

This section is presented in a logical sequence. It is quite clear even if some improvement is recommended.

 The title of this session could be improved as it reports the results of applying the methodology to a real urban stormwater drainage system.

Reply 9:

The title has been modified in “Application to a real urban stormwater drainage system“

Comment 10:

Line 525: Does streamflow centroid mean the hydrograph centroid at the outlet of the Lucas Creek urban catchment?

Reply 10:

Yes. To clarify this, we have rewritten the sentence:

“Depending on the amount of rainfall and the initial conditions, the lag time between the hyetograph centroid and the hydrograph centroid at the Lukas Creek urban catchment's outlet usually varies between 25 and 1 hour [63], while the hydrograph's estimated time to peak is approximately 45 minutes.” 

Comment 11:

It is clarified that the available TSS concentration data in stormwater flow are not temporally continuous. In this regard, some specifications are recommended on the characteristics of available individual water samples.

Reply 11:

We have introduced the following sentence:

“The automated samplers are set to trigger (i.e., collect a sample) each time the water level in the storm drain exceeds the water level threshold, which is a unique height for each site. The sampler algorithm also checks when the last sample was taken—the time from the previous sample must exceed 15
minutes; this way we space out our samples across the storm hydrograph (Porter, personal communication).”

Comment 12:

Lines 560-563: 129 data of TSS load and the corresponding TB and Q of the previous time step, correspond to a total of n.3x129 data. It is not clear the reason why a total of n.4x129 data are indicated. Is it because the TSS load is the product of the TSS concentration and the flow rate?

Reply 12:

The reviewer is right. We have rewritten the sentence as:

“Therefore, 129 data of TSS load and the corresponding turbidity (T) and flow (Q) values of the four previous 5 minutes time steps were used in the model calibration process, and 84 data of TSS load and corresponding turbidity (T) and flow (Q) values of the four previous 5 minutes time steps were used for their validation.”  

Comment 13:

Lines 565-571: the choice of the TSS polluting load threshold of 42 ?/? should be better motivated.

Reply 13:

We have rewritten the sentence:

“In this study, a TSS polluting load threshold of  was used (about ), a value supported by the analysis of historical data. In fact, it was possible to verify that once this load value is exceeded, the TSS concentration values frequently exceed the common regulatory thresholds (e.g. it was observed when the TSS load was equal to , the TSS concentration reached , exceeding the threshold value according to the Italian law - D.Lgs. n.152/2006).”

as:

“In this study, a TSS polluting load threshold of  was used (about ), a value supported by the analysis of historical data. In fact, it was noted that already when the concentration is 42 g/s, the TSS concentration frequently exceeds the Italian regulatory limit of 35 mg/l. It should be noted that the threshold value for pollutant loads is case-specific, as it is contingent upon the sewer channel being analyzed and expresses the safety margins that decision makers wish to adopt.

Anyway, given that the scope of this work is to demonstrate the superiority of the probabilistic approach against the deterministic one, the choice of a specific value, such as , does not prevent generalizing results.”

Comment 14:

Lines 608 and 638: It is not clear the meaning of symbol “=” in table 2 and table 3.

Reply 14:

The tables have been modified to eliminate the symbol “=”.

Comment 15:

Since figure 7 include the information of figure 2, figure 2 can be omitted.

Reply 15:

We do not entirely concur with the reviewer. Figure 7 definitely contains the information of the joint and conditional distributions; however, its purpose is to demonstrate the decision-making process. In contrast, Figure 2 is employed to elucidate the concepts and representation of the joint and conditional distributions, which could not be accomplished using Figure 7. The caption of Figure 7 has been modified to reflect the concepts that were discussed in section 2.2 and illustrated in Figure 2.

Comment 16:

Line 661: In the graphs of Figure 6 comma must be replaced with point as decimal separator.

Reply 16:

Done

Comment 17:

Line 696: In the graphs of Figure 8 comma must be replaced with point as decimal separator.

Reply 17:

Done

Comment 18:

Lines 701-704: Since tables 4 and 5 provide the same results as figure 8 in tabular form, they can be omitted.

Reply 18:

In principle, we concur with the reviewer; however, in this instance, we would prefer to preserve them. This is due to the fact that the probabilistic approach generates an estimated gain that is supported by numerical data in the tables but cannot be substantiated solely by the figures. 

Comment 19:

Conclusions

Conclusions seem reasonable and supported by the results.

The limitations of the study should be appropriately indicated in the concluding remarks.

Reply 19:

We have introduced the following sentences in the conclusions:

“The validity of the case study under investigation can be questioned in several respects, including the use of total suspended solids volume as a decision variable, which is problematic due to the discrepancy between the volume of total suspended solids and their concentration. In order to obtain more comprehensive indications, it would also be desirable to apply the deterministic modeling approach to a broader range of cases in the future, as the morphometric characteristics of the basin are believed to significantly influence the hydrograph and the pollution graph, as well as the functional relationship between classical and surrogate pollution parameters. Nevertheless, the significance of this work and its results, which were obtained under the same conditions for deterministic and probabilistic forecasts, is not compromised by these factors. The implementation of more representative and high-performing forecasting models will not only result in improved deterministic forecasts but also in the enhancement of the probabilistic forecasts that are conditional on the deterministic ones.”

 

Reviewer 2 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

Mitigating water-pollution hazards from urban drainage demands more sophisticated wastewater-management systems. Traditional deterministic forecasting cannot support robust decisions under uncertainty; therefore, the manuscript forecast the complete probability density of TSS given one or multiple deterministic predictions. The article is rich in content and clearly expressed. However, there are still some issues that need to be revised.

1、Please provide a graphic abstract to summarize the full text

2、The conclusion is not mentioned in the Abstract. It is recommended to add

3、Conclusions is not concise enough, please revise it further

4、The article format needs to be further improved, such as equation numbers, chapter titles, and citation superscripts

5、The last part of the Introduction should state the limitations of the current study and your new findings.

Comments on the Quality of English Language

The language expression can be further improved and made more academic

Author Response

Comment 1:

Please provide a graphic abstract to summarize the full text

Reply 1:

We have prepared a Graphical Abstract

Comment 2:

The conclusion is not mentioned in the Abstract. It is recommended to add

Reply 2:

Done

Comment 3:

Conclusions is not concise enough, please revise it further

Reply 3:

We have revised the conclusions as requested.

Comment 4:

The article format needs to be further improved, such as equation numbers, chapter titles, and citation superscripts

Reply 4:

We have corrected the wrong equation numbers and the comma instead of the point as the decimal separator in three figures. We have modified the title of section 3 to better reflect the application to a real-world case, as requested by reviewer #1

Comment 5:

The last part of the Introduction should state the limitations of the current study and your new findings.

Reply 5:

Instead of in the introduction, we decided to include the limitations in the conclusions of the work, as suggested by reviewer #1. Accordingly, we introduced the following sentences:

“The validity of the case study under investigation can be questioned in several respects, including the use of total suspended solids volume as a decision variable, which is problematic due to the discrepancy between the volume of total suspended solids and their concentration. In order to obtain more comprehensive indications, it would also be desirable to apply the deterministic modeling approach to a broader range of cases in the future, as the morphometric characteristics of the basin are believed to significantly influence the hydrograph and the pollution graph, as well as the functional relationship between classical and surrogate pollution parameters. Nevertheless, the significance of this work and its results, which were obtained under the same conditions for deterministic and probabilistic forecasts, is not compromised by these factors. The implementation of more representative and high-performing forecasting models will not only result in improved deterministic forecasts but also in the enhancement of the probabilistic forecasts that are conditional on the deterministic ones.”

Comment 6:

Comments on the Quality of English Language

The language expression can be further improved and made more academic

Reply 6:

We have rewritten several parts of the document to make it more formal/academic as requested.

Round 2

Reviewer 1 Report (New Reviewer)

Comments and Suggestions for Authors

The manuscript has been significantly improved following the recommendations of the Reviewers; all my concerns have been addressed and convincingly justified.

Author Response

Comment 1

The manuscript has been significantly improved following the recommendations of the Reviewers; all my concerns have been addressed and convincingly justified.

Reply 1

We are grateful to the reviewer, whose comments were greatly appreciated and helped to improve the previous version of the manuscript.

Reviewer 2 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

The author responded positively to my comments and revised the manuscript. In my opinion, the author needs to make some necessary optimizations to the standardization of the paper, such as the resolution of the figures, the mathematical formulas in P372-P396, etc. Besides this, I have no other comments.

Author Response

Comment 1

The author responded positively to my comments and revised the manuscript. In my opinion, the author needs to make some necessary optimizations to the standardization of the paper, such as the resolution of the figures, the mathematical formulas in P372-P396, etc. Besides this, I have no other comments.

Reply 1

We are grateful to the reviewer, whose comments helped us improve the previous version of the manuscript.

The figures and equations will be modified on the galley proofs in collaboration with the editorial team in accordance with the Hydrology journal's guidelines.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The proposed method of Probabilistic Quality Surrogate Forecasting (PQSF) for stormwater quality assessment in urban catchments offers an innovative approach to real-time control of pollutant loads. The combination of deterministic models (such as Multivariate Regression and Artificial Neural Networks) and probabilistic decision-making frameworks, including Bayesian approaches, represents a significant advancement in improving the accuracy and reliability of stormwater quality predictions. Overall, the proposed methodology presents a promising solution for urban drainage system operators to make more informed decisions regarding the capture of first flush waters and pollution event management.

 

Here are some comments:

12. The description in the methodology section is not sufficiently clear. I suggest that the authors revise and refine the language to improve clarity and precision.
13. When assuming a normal distribution, the authors should justify the rationale behind this assumption and provide the reasons for its validity.
14. In the Artificial Neural Networks (ANN) section, the authors should explain the process of selecting the network’s width and depth, as this is critical for understanding the model’s configuration.
15. Please adhere to proper terminology. In Table 1, the correct term should be "confusion matrix" instead of its current designation.
16. In Section 3.2, it is recommended that the authors first perform descriptive statistics on the dataset to provide a better understanding of the data characteristics.
17. There are some typographical errors: In Equation 18, there are two equal signs, which should be corrected. Additionally, Table 2 lacks a bottom border, and line 262 does not include the variable "k." I advise the authors to carefully review the entire manuscript.
18. Please clarify whether the real data follow a normal distribution. Additionally, it would be useful to assess whether the data meet normality assumptions after transformations, which can be illustrated using a QQ plot.
19. The resolution of Figure 5 should be improved for better clarity.
20. In Figure 8, the authors should use black instead of gray for better contrast and visibility.
21. Regarding notation, Equation 1 should represent the fitting of the transformed variables y and x. In Equation 6, it seems the determinant should be used instead of the norm. Please provide the correct definition and ensure consistent notation throughout the manuscript.
22. In Figure 8, is the covariance matrix the same as the correlation matrix? This seems unlikely, as although eta comes from a normal distribution, the estimated eta (hat eta) does not guarantee that the variance is one. This point requires further clarification.
23. It is recommended that the authors include more comparisons with other methods to further highlight the superiority of the proposed approach.

Author Response

The proposed method of Probabilistic Quality Surrogate Forecasting (PQSF) for stormwater quality assessment in urban catchments offers an innovative approach to real-time control of pollutant loads. The combination of deterministic models (such as Multivariate Regression and Artificial Neural Networks) and probabilistic decision-making frameworks, including Bayesian approaches, represents a significant advancement in improving the accuracy and reliability of stormwater quality predictions.

Overall, the proposed methodology presents a promising solution for urban drainage system operators to make more informed decisions regarding the capture of first flush waters and pollution event management.

Here are some comments:

We are grateful to the Reviewer who, having precisely grasped the purpose of the manuscript, highlighted some of the manuscript's shortcomings. Below are our specific replies to the observations of the Reviewer, which are reflected in the new version of the manuscript.

 

12. The description in the methodology section is not sufficiently clear. I suggest that the authors revise and refine the language to improve clarity and precision.

In the new version, the English (American) language of the entire manuscript, including the Materials and Methods section, has been improved.

 

13. When assuming a normal distribution, the authors should justify the rationale behind this assumption and provide the reasons for its validity.

We thank the reviewer for pointing out that the description of the methodology is not sufficiently clear. We improved it, and from the revised text the reviewer will notice that there is no reason for assuming that the distribution is Normal, because we have transformed all the observations and deterministic forecasts in their images in a Gaussian multivariate space in which all the variables are standard Normally N(0,1) distributed. These images are obtained via probability matching, either using the well-known Normal Quantile Approach or by fitting a parametric probability distribution function to the observations and the forecasts.

The reason for transforming all the variables into the Gaussian space is to develop a simple and easy way to obtain their joint and, successively, their conditional probability distribution. Obtaining the joint and the conditional distribution with variables that are not Normally distributed is frequently impossible. To get them, one would need to use the copula approaches, which work well when the dimensions are limited to 2-3 but have problems when dealing with higher dimensionalities. The proposed approach could be defined as the Gaussian copula, although it is not commonly used as such. In the Gaussian space, one can obtain analytically the joint and the various conditional distributions, as shown by Mardia et al. [Mardia, K. V., Kent, J. T., & Bibby, J. M. Multivariate Analysis. Probability and Mathematical Statistics, 1979, London: Academic Press.]

We have added a couple of comments in the revised version to clarify this point.

 

14. In the Artificial Neural Networks (ANN) section, the authors should explain the process of selecting the network’s width and depth, as this is critical for understanding the model’s configuration.

In the new version of the manuscript, section 4.2. The ANN models has been significantly expanded, also reporting the information requested by the Reviewer.

 

15. Please adhere to proper terminology. In Table 1, the correct term should be "confusion matrix" instead of its current designation.

Both terms ("contingency matrix" and "confusion matrix") are valid to describe the indices in Table 1, but we would like to retain the definition "contingency matrix" as it is more consistent with the statistical literature.

 

16. In Section 3.2, it is recommended that the authors first perform descriptive statistics on the dataset to provide a better understanding of the data characteristics.

To preserve the conciseness of the article, additional descriptive statistics were not included. Detailed information about the dataset can be found in the original source, (see the USGS website linked in Appendix A).

 

17. There are some typographical errors: In Equation 18, there are two equal signs, which should be corrected. Additionally, Table 2 lacks a bottom border, and line 262 does not include the variable "k." I advise the authors to carefully review the entire manuscript.

The highlighted corrections have been implemented. The double equals sign in equation 18 reflects an international mathematical convention (the equals sign must be repeated when the relationship string is interrupted by the equals sign to continue on the next row) and has therefore been retained.

 

18. Please clarify whether the real data follow a normal distribution. Additionally, it would be useful to assess whether the data meet normality assumptions after transformations, which can be illustrated using a QQ plot.

Neither the real data nor the forecasts follow a normal distribution. This is why we need to transform them into their images in the Gaussian space, where all the variables become N(0,1). The transformation of the variables in the Normal space was performed by probability matching. In other words, we produce the Normal image by utilizing the N(0,1) variable, which possesses the same probability distribution as the order statistics of the original variable. This approach allows preserving the Spearman’s rank correlation of the ones in the original space. By transforming the probability distribution of variables, it is not possible to preserve the Pearson product-moment correlation, which, by the way, is only fully meaningful for Gaussian-distributed variables.

The conditional distribution of the forecasted image value in the Gaussian space is then reconverted back into the real space by probability matching with the reverse process used in the first step.

 

19. The resolution of Figure 5 should be improved for better clarity.

The resolution of Figure 5 has been improved.

 

20. In Figure 8, the authors should use black instead of gray for better contrast and visibility.

The colour in Figure 8 has been changed to black.

 

21. Regarding notation, Equation 1 should represent the fitting of the transformed variables y and x. In Equation 6, it seems the determinant should be used instead of the norm. Please provide the correct definition and ensure consistent notation throughout the manuscript.

We appreciate the observation of the Reviewer, which revealed a non-sequential order of equations causing confusion. Therefore, the equations have been reordered to clarify and improve the manuscript.

 

22. In Figure 8, is the covariance matrix the same as the correlation matrix? This seems unlikely, as although eta comes from a normal distribution, the estimated eta (hat eta) does not guarantee that the variance is one. This point requires further clarification.

We presume you meant Equation 8.

The reason for the coincidence of the covariance matrix with the correlation matrix is not an error. It descends from the fact that, as we described in the reply to comment 13, all the variables that were transformed in the Gaussian space are N(0,1) by construction.

We clarified it more explicitly in the revised version.

 

23. It is recommended that the authors include more comparisons with other methods to further highlight the superiority of the proposed approach.

In the Introduction section, we have augmented the bibliographic references, thereby demonstrating that the comparison of the proposed approach with the technical literature underscores the superior performance of the PQSF.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

After reading the article, I have made the following remark.

1. The introduction must be restructured to clarify what has already been done, the drawbacks of previous approaches, and the novelty of this approach. 
2. The last section in the Introduction must be removed.
3. Artificial Neural Networks are not deterministic models because they are likely to obtain different results when run many times!
4. Please mind the typos. 'Forecated' must be 'Forecasted', for example.
5. The assertion ''...it is possible to transform them into normally distributed variables'' is not correct. There are many situations when such a transformation is not possible.
6. The parameters settings in ANN are not presented. The ratio between the training and test sets was set to 70:30. If it is 80:20 or 90:10 waht happen? The sensitivity analysis for the output is not presented here. Moreover, I insist that given that ANN is not a determininstic approach as you pretend, how did you treat the results after running the algorithm 100 times, for example? This aspect should be clarified before going forward with the models.
7. I don't see any test of significance for the coefficients and the regression model as a whole. Moreover, the multicollinearity test is absent.  
8.  What do you mean by 10 distinct ANNs, and how did you '' average'' them? What is the difference between them?
9. No mention of the stop criteria, training algorithm, etc., for the ANN is provided, and no goodness of fit index for the results can be found. Clarifying these aspects before continuing to review the rest of the article is essential. The results of these phases are extremely important because they are the input in the algorithm in the second stage.

Author Response

The insightful remarks of the Reviewer have enabled us to improve the latest version of the manuscript. Where the suggestion was not taken up, we have provided arguments. We would like to thank the Reviewer for his valuable suggestions.

 

1. The introduction must be restructured to clarify what has already been done, the drawbacks of previous approaches, and the novelty of this approach.

The introduction section has been improved and expanded according to the suggestions of the Reviewer.

 

2. The last section in the Introduction must be removed.

The final section of the Introduction does not enhance the explanation of the proposed approach; nonetheless, we contend that outlining the manuscript's structure aids the reader. For this reason we have considered it useful to keep the last section.

 

3. Artificial Neural Networks are not deterministic models because they are likely to obtain different results when run many times!

The reviewer noted that artificial neural networks possess a stochastic nature due to factors like weight initialization during training. Nonetheless, post-training, the model yields outcomes akin to those of a deterministic model; thus, it has been discussed in this manner within the paper. These clarifications have been included in the manuscript.

 

4. Please mind the typos. 'Forecated' must be 'Forecasted', for example.

Corrections have been made.

 

5. The assertion ''...it is possible to transform them into normally distributed variables'' is not correct. There are many situations when such a transformation is not possible.

The reviewer’s observation is relevant; however, this holds true only when the random variable is discrete, which occurs in specific and limited cases (e.g., binary variables). In the application domain investigated in this study, the variables are always defined as continuous.

 

6. The parameters settings in ANN are not presented. The ratio between the training and test sets was set to 70:30. If it is 80:20 or 90:10 waht happen? The sensitivity analysis for the output is not presented here. Moreover, I insist that given that ANN is not a determininstic approach as you pretend, how did you treat the results after running the algorithm 100 times, for example? This aspect should be clarified before going forward with the models.

To address the reviewer’s concerns, Section 4.2 The ANN models has been revised to better cover elements that were previously not fully addressed.

 

7. I don't see any test of significance for the coefficients and the regression model as a whole. Moreover, the multicollinearity test is absent.

If the Reviewer is referring to the results of these tests, they are provided here for completeness. However, including further details about the regression analysis in the manuscript would be excessively burdensome, considering its already considerable length.

 

Regression Statistics
R	0.950956
R Square	0.904317
Adjusted R Square	0.897939
Standard Error	0.310375
Observations	129
VARIANCE ANALYSIS
	df (Degrees of Freedom)	SS (Sum of Squares)	MS (Mean Square)	F	Significance F
Regression	8	109.2554	13.65693	141.7682	2.09E-57
Residual	120	11.55993	0.096333
Total	128	120.8153
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0.009994	0.027332	0.365658	0.715264	-0.04412	0.06411
QShift1	1.292571	0.097934	13.19839	4.03E-25	1.098668	1.486473
QShift2	-0.57445	0.159326	-3.6055	0.000455	-0.8899	-0.25899
QShift3	-0.03543	0.165777	-0.21371	0.831135	-0.36366	0.292799
QShift4	0.013421	0.12905	0.104002	0.917342	-0.24209	0.268932
TBShift1	0.282552	0.064516	4.379574	2.56E-05	0.154815	0.410289
TBShift2	0.072068	0.068896	1.046036	0.297647	-0.06434	0.208478
TBShift3	0.08166	0.068183	1.197665	0.233408	-0.05334	0.216657
TBShift4	-0.14226	0.068476	-2.07744	0.039894	-0.27783	-0.00668

 

8. What do you mean by 10 distinct ANNs, and how did you '' average'' them? What is the difference between them?

To address the reviewer’s concerns, Section 4.2 The ANN models has been revised to better cover elements that were previously not fully addressed.

 

9. No mention of the stop criteria, training algorithm, etc., for the ANN is provided, and no goodness of fit index for the results can be found. Clarifying these aspects before continuing to review the rest of the article is essential. The results of these phases are extremely important because they are the input in the algorithm in the second stage.

To address the reviewer’s concerns, Section 4.2 The ANN models has been revised to better cover elements that were previously not fully addressed.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This is a good article that should be improved as follows:
Provide a schematic of a research approach
State whether the results are transferable to other study areas or specific to the case study. Provide an adequate explanation.
Give an example of how the achievement can be used in practice.

Author Response

This is a good article that should be improved as follows: Provide a schematic of a research approach State whether the results are transferable to other study areas or specific to the case study. Provide an adequate explanation.

Give an example of how the achievement can be used in practice.

We thank the Reviewer for the overall positive evaluation and for the improvement suggestions.

The suggestions of the Reviewer leaded us in integrating especially the sections: Introduction (see rows 51-58 and 82-86); Conclusions (see rows 686-691)

 

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

This manuscript provides a new forecasting approach (called Probability Quality Surrogate Forecasting) for urban stormwater quality assessment - both deterministic and probabilistic approaches were tested. Real time turbidity and flow data were used to calibrate and validate the two approaches.

While the forecasting approach is generic, specific data for each system will need to be collected to calibrate the equations for use.

The manuscript is well structured with the deterministic and probabilistic approaches well explained, and the comparison between the two approaches tested using a real data set from the USGS

I recommend the manuscript be published after the authors address the following minor comments.

Introduction - provide a good introduction to previous work on turbidity/flow and TSS loads to assist decision making regarding urban stormwater management.

The aim of this study is provided in the abstract but not in the introduction - I suggest the authors provide a succinct statement of the aim of the study as theist paragraph of the Introduction 

I have not checked in any detail the mathematics in the manuscript

The following need attention"

1. Figure 1 - define the terms
2. line 231-233 - sentence needs to be modified to make it understandable
3. line 237-238 - meaning is unclear
4. line 412-417 - was it possible to calculate regression between turbidity and TSS?
5. line 453 - how was the TSS load threshold obtained?
6. Table 3 and elsewhere in the manuscript - the number of significant figures quoted (not decimal points) need to be addressed - e.g., figure 95.57 implied the 4th figure is significant (values in not 95.56 or 95.58) which is an accuracy of 1/9557 or 100/9557 or around 0.001% accurate - I very much doubt that this level oof accuracy in the figures can be justified (perhaps 96 or around 1% accuracy can be justified) 

 

Comments on the Quality of English Language

The manuscript needs some work on the English

Author Response

This manuscript provides a new forecasting approach (called Probability Quality Surrogate Forecasting) for urban stormwater quality assessment - both deterministic and probabilistic approaches were tested. Real time turbidity and flow data were used to calibrate and validate the two approaches.

While the forecasting approach is generic, specific data for each system will need to be collected to calibrate the equations for use.

The manuscript is well structured with the deterministic and probabilistic approaches well explained, and the comparison between the two approaches tested using a real data set from the USGS

I recommend the manuscript be published after the authors address the following minor comments.

We thank the Reviewer for the overall positive evaluation and for the improvement suggestions.

 

Introduction provide a good introduction to previous work on turbidity/flow and TSS loads to assist decision making regarding urban stormwater management.

The aim of this study is provided in the abstract but not in the introduction - I suggest the authors provide a succinct statement of the aim of the study as theist paragraph of the Introduction I have not checked in any detail the mathematics in the manuscript

To better describe the aims of the study in a situated manner, the paragraph in the Introduction has also been expanded with the rows 82-87.

 

The following need attention"

1. Figure 1 - define the terms

The terms of the flowchart in Fig.1 are described in the section 2. In addition, at the end of the manuscript the section “Abbreviation” was integrated with the symbols and terms.

 

2. line 231-233 - sentence needs to be modified to make it understandable

The sentence has been improved (see rows 256-257)

 

3. line 237-238 - meaning is unclear

It was preferred to eliminate the sentence since the content did not provide a concrete contribution to the description of the objectives of the paragraph.

 

4. line 412-417 - was it possible to calculate regression between turbidity and TSS?

We investigated the correlation between turbidity and TSS, but we preferred the regression TSS = f(turbidity, flow) (as Eq.(18)), because the relationship fit better the observed data. In addition, Eq.(18) is consistent with the proposed relationship of USGS [42-44].

 

5. line 453 - how was the TSS load threshold obtained?

The choice of the threshold for TSS load was based on qualitative assessments, since the aim was only to demonstrate the predictive effectiveness of the proposed approach.

However, for the case study it was verified that when threshold values of the load equal to 42 mg/s occurred, the TSS concentrations of stormwater flows were close to the maximum value admissible according to the Italian technical regulation (35 mg/l).

It is worth noting that the load pollution threshold value depends on the flow rates, therefore it is site-specific. For this reason, the TSS load 42 mg/s must be understood as value example of a threshold

 

6. Table 3 and elsewhere in the manuscript - the number of significant figures quoted (not decimal points) need to be addressed - e.g., figure 95.57 implied the 4th figure is significant (values in not 95.56 or 95.58) which is an accuracy of 1/9557 or 100/9557 or around 0.001% accurate - I very much doubt that this level oof accuracy in the figures can be justified (perhaps 96 or around 1% accuracy can be justified)

We agree with the observation of the Reviewer. Therefore, the high precision of the values (fourth decimal place) depended on the need to facilitate comparison between the indices, where these are numerically similar. However, in the new manuscript we followed the Reviewer's suggestion, so we scaled down the degree of precision of the indices to the third decimal place.

Author Response File: Author Response.pdf

Reviewer 5 Report

Comments and Suggestions for Authors

The authors in the current study investigated a probabilistic approach for forecasting TSS loads during storm events in urban drainage systems. They developed a method that combines surrogate sensor data (turbidity and flow) with data driven models (linear regression and neural networks) to produce short-term TSS load forecasts. These forecasts are then passed through the  MCP model to generate probability distributions. This allows stormwater managers to trigger real time control actions based on the probability that pollutant concentration will exceed a critical probability threshold.  The method was tested on five years of data from the Lucas Creek catchment and showed strong performance in detecting high-pollution events with reduced false alarms.

This study presents a practical method for improving real-time stormwater quality management using probabilistic analysis which is  based on sensor data. It has potential to improve the decision regarding urban water pollution and thusly it is recommended for publication in Hydrology.

Suggestions:

• The authors should expand the introduction and compare their approach to existing probabilistic and real-time control methods. Are there any other models similar to MCP for decision making regarding TSS forecast?
• Lines 22-23: “… forgetting, that while … real occurrence.” Probably the phrase “by the” is missing between “affected” and “virtual representation”. Fix the typo.
• Lines 116-117. Extended here what are the range of times, which are not compatible with the short time forecasts required by the decision making operations.
• Lines 174-178: “This research was conducted …for prediction.” Here the authors should expand their discussion what methods did they use to find the minimal number of combinations to predict the TSS values. Did they employ machine learning approaches like feature importance?
• The authors should state if the table 1 is the classical confusion matrix seen in machine learning literature. If yes, they should identify it as
• Lines 453-454: ”In the case…of historical data.” How this value of 42 g/s was decided? What analysis was carried out? Else a reference is needed here.
• Lines 527-528: Extend the discussion regarding the PC, POD, CSI and FAR metrics. Shortly what these indicators represent? This would greatly help in interpreting the results of the analysis that follows.

Author Response

The authors in the current study investigated a probabilistic approach for forecasting TSS loads during storm events in urban drainage systems. They developed a method that combines surrogate sensor data (turbidity and flow) with data driven models (linear regression and neural networks) to produce short- term TSS load forecasts. These forecasts are then passed through the MCP model to generate probability distributions.

This allows stormwater managers to trigger real time control actions based on the probability that pollutant concentration will exceed a critical probability threshold. The method was tested on five years of data from the Lucas Creek catchment and showed strong performance in detecting high-pollution events with reduced false alarms.

This study presents a practical method for improving real-time stormwater quality management using probabilistic analysis which is  based on sensor data. It has potential to improve the decision regarding urban water pollution and thusly it is recommended for publication in Hydrology.

We are grateful to the reviewer for his appreciation and suggestions, which allowed us to improve the new version of the manuscript.

 

Suggestions:

The authors should expand the introduction and compare their approach to existing probabilistic and real-time control methods.

The introduction has been expanded by increasing the bibliographic study (see rows 51-58), but in the technical literature, we are not aware of specific probabilistic approaches for the forecast of polluting loads in urban drainage systems when stormwaters occur.

It should be noted that the proposed method is also innovative since it starts from the measurement of surrogate parameters to arrive at a prediction of a classic pollution parameter, such as the TSS.

 

Are there any other models similar to MCP for decision making regarding TSS forecast?

We are not aware of any probabilistic approaches of the MCP type for the prediction of the quality of stormwater in urban drainage systems. We know of applications of the MCP model only in other hydrological settings, as reported in the manuscript (see References of the manuscript).

 

Lines 22-23: “… forgetting, that while … real occurrence.” Probably the phrase “by the” is missing between “affected” and “virtual representation”. Fix the typo.

We are sorry, but we didn't detect the typo

 

Lines 116-117. Extended here what are the range of times, which are not compatible with the short time forecasts required by the decision making operations.

The time range is declared in the last version of the manuscript (see row 139)

 

Lines 174-178: “This research was conducted …for prediction.” Here the authors should expand their discussion what methods did they use to find the minimal number of combinations to predict the TSS values. Did they employ machine learning approaches like feature importance?

The combinations of surrogate indices were investigated by means of a heuristic approach. In this way, the combination of turbidity and flow rate was identified, a conclusion that Porter had already reached [48-49].

Furthermore, it is highlighted that some surrogate parameters detected by the multiparametric probe immediately proved to be not very effective (e.g. temperature and conductance), hence the number of combinations to be investigated was significantly reduced.

These considerations are reported in section 3.2. The available dataset.

 

The authors should state if the table 1 is the classical confusion matrix seen in machine learning literature. If yes, they should identify it as Lines 453-454: ”In the case…of historical data.” How this value of 42 g/s was decided? What analysis was carried out? Else a reference is needed here.

The choice of the threshold for TSS load was based on qualitative assessments, since the aim was only to demonstrate the predictive effectiveness of the proposed approach. However, for the case study it was verified that when threshold values of the load equal to 42 mg/s occurred, the TSS concentrations of stormwater flows were close to the maximum value admissible according to the Italian technical regulation (35 mg/l).

It is worth noting that the load pollution threshold value depends on the flow rates, therefore it is site-specific. For this reason, the TSS load 42 mg/s must be understood as value example of a threshold.

 

Lines 527-528: Extend the discussion regarding the PC, POD, CSI and FAR metrics. Shortly what these indicators represent?

This would greatly help in interpreting the results of the analysis that follows.

Expanding the description of the APC, POD, CSI and FAR metrics provided in section 2.4. Evaluation of performances would make the article much longer.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

1. Check the format and font of Figure 3

2. The conclusion section should be further refined based on the full revision and improvement of the results and discussion sections.

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors,

I am sorry you do not understand the difference between the deterministic and stochastic approaches. I am also sad that you insist that all variables—continuous or discrete—can be transformed into Gaussian. If this were true, there would be no need to develop the theory for other kinds of distributions. 

Going to the formal aspects, there is still a discrepancy between the journal template and the format of your article.