Water Level Forecasting in Tidal Rivers during Typhoon Periods through Ensemble Empirical Mode Decomposition

Round 1

Reviewer 1 Report

Review of the manuscript Water Stage Forecasting in Tidal Streams during High Water 3 using Ensemble Empirical Mode Decomposition, by Chen et al., for Hydrology

General comments

This manuscript introduces a new empirical method to forecast water levels at an estuarine tide gauge one hour in advance. The forecast is based on past data from the tide gauge itself and neighboring stations (both upstream and downstream. The method is then applied to data from an estuary in Taiwan. The method is calibrated, and the validation results are convincing.

While a good numerical model would probably do a better job, the proposed method is cheaper in terms of CPU and data. The downside is that the method can only be applied at a location where a tide gauge is installed.

Major comments

I find the descriptions often difficult to follow. The manuscript needs to be edited for correctness and clarity.

Minor comments

Line 49. The authors write “Both theoretical and empirical approaches are usually used”, then proceed to present two numerical approaches.  It is unclear whether the authors consider that the application of a numerical model is a theoretical or an empirical approach. In my opinion, it is neither.

Line 131. “The problem with the modes resolved using EMD is the appearance of mode mixing.” Please explain what “mode mixing” means.

Line 156. Please explain what is meant by “power” in this sentence.

Line 251. How was the frequency of each IMF calculated? How do you define that a given IMF is periodic?

Table 2. Please include the units of the frequency. Same for Table 3.

Figure 10. Please eliminate the last sentence in the figure caption.

Author Response

Major comments

1. I find the descriptions often difficult to follow. The manuscript needs to be edited for correctness and clarity.

Ans:

        Your commends are very valuable and helpful for the modification that grammatical and writing style errors in the original version is corrected by my colleague who is a native English speaker.

Minor comments

1. Line 49. The authors write “Both theoretical and empirical approaches are usually used”, then proceed to present two numerical approaches. It is unclear whether the authors consider that the application of a numerical model is a theoretical or an empirical approach. In my opinion, it is neither.

Ans:

        I apologize that it is not unclear for the readers. The numerical methods are mathematical tools to solve a problem which often has no analytical solution. They are usually used in hydraulic and oceanic engineering. Therefore a paragraph is added. It is “These hydraulic and hydrological models usually apply numerical method to obtain the results.”

2. Line 131. “The problem with the modes resolved using EMD is the appearance of mode mixing.” Please explain what “mode mixing” means.

Ans:

Thanks for the review’s comment.

The mode mixing in EMD is the situation when an IMF resulting from EMD de-composition has components of different frequencies. The problem of mode mixing is caused by the intermittency signals and noises.

3. Line 156. Please explain what is meant by “power” in this sentence.

Ans:

        The power of the IMF is not used in this study. In order not to confuse the readers, “power” is eliminated.

4. Line 251. How was the frequency of each IMF calculated? How do you define that a given IMF is periodic?

Ans:

        To calculate frequency, divide the number of times the event occurs by the length of time. The periodicity is the IMF with a repeating pattern made up of cycles that repeat some interval.

5. Table 2. Please include the units of the frequency. Same for Table 3.

Ans:

        The units of tide frequency is hr^-1 and shown on Tables 2 and 3.

6. Figure 10. Please eliminate the last sentence in the figure caption.

Ans:

It is our mistake. And the last sentence in the caption of the Figure 10 is deleted.

Reviewer 2 Report

I review the article “Water Stage Forecasting in Tidal Streams during High Water using Ensemble Empirical Mode Decomposition”. The article is interesting dealing with an up-to dated topic.

Present the research gap in the introduction and highlight the novel points of this research.

Figure 3. add a base map (backround) for better representation of the results.

Add some directions for future research arise from the currents findings.

Remove the word summary from the last chapter. Provide an extent conclusion based on the results.

Author Response

1. Present the research gap in the introduction and highlight the novel points of this research.

Ans:

        Thanks for your suggestion. We write a paragraph to address the research gap in the section of introduction as “The hydrological processes in a tidal river is unique and the water level is contin-ually changing under the interaction of riverine and marine processes. The most obvi-ous factors having a profound influence on the water level that include shape of the tidal river, astronomical tide, wind, salinity, temperature, sediment, flood, storm surge, and others are too complex to model directly. Consequently, the hydrodynamic pro-cesses of tidal rivers are manifestly complex, nonstationary and notoriously nonlinear [15]. Many of the concepts or principles derived from other watercourses have been applied to forecast water level in tidal rivers. The theoretical approach is based on the following pair of differential equations. One of the major disadvantages of using these methods is that the parameters are usually difficult to determine form the observed data, especially discharge [17]. Additionally, it is time consuming and costly to pro-gram and execute those sophisticated models.”

The highlight of this paper is “The most advantage of the proposed model is the data used is only water levels. Compared with the other sophisticated models, the model using EEMD to forecast water levels in tidal rivers is simple, accurate, and reliable.”

2. Figure 3. add a base map (backround) for better representation of the results.

Ans:

        The gaging stations that are not used in this study are removed. Thus the readers can easily see the locations of the gaging stations in the study area.

3. Add some directions for future research arise from the currents findings.

Ans:

        A paragraph in conclusions is added to show the directions for future research. It is “If more data in tidal rivers can be obtained, it is possible to decompose the water level into more groups, not only ocean and stream components. It will help to establish a more reliable and accurate model to forecast water levels in tidal rivers.”

4. Remove the word summary from the last chapter. Provide an extent conclusion based on the results.

Ans:

        We rewrite the conclusions as: “Owing to too many factors affecting the hydrological processes and too little data can be obtained in estuaries, forecasting of water level in tidal rivers is never an easy task. The proposed model based on EEMD is simple when comparing with those hy-drological and hydraulic models. When applying EEMD for water level forecasting in tidal rivers, there is no need to input numerous uncertain parameters as required by other flooding simulation algorithms, such as the Manning’s coefficient, channel bed elevation, energy slope, and cross-sectional area, etc. The only data needed for the proposed model is only water levels that is easy to obtain. No complicated theories and computing work is needed when this simple model is applied to forecast water levels in tidal rivers. It is only composed of EEMD and stepwise regression. The EEMD is used to decompose the water level into two components as the regressors. The two most in-fluential factors for water level of tidal rivers are tides and river flow. By using EEMD, the water level can be decomposed into the ocean component affected by tides and the stream component dependent on the river flows. The forecasting of the estuarine water level can be achieved by adding the ocean and stream component calculated from the regression models. The stepwise regression is used to determine the parameters for forecasting the water levels.

A successful implementation of the methodology is demonstrated on the case study of the Tanshui River which is a tidal river. A water level forecasting model is constructed to forecast one hour ahead water level at the Taipei Bridge. The results show promising performance of water level forecasting during high water in tidal riv-ers by using the EEMD. Both RMSE and correlation coefficient indicate the model can forecast water level accurately. It also shows the proposed model is a simple, and reli-able conceptual model.

If more data in tidal rivers can be obtained, it is possible to decompose the water level into more groups, not only ocean and stream components. It will help to establish a more reliable and accurate model to forecast water levels in tidal rivers.”

Reviewer 3 Report

This paper discussed the prediction of water levels in tidal rives. The topic of this paper fit within the stated scope of Hydrology and this paper is basically well-organized. However, it seems that this paper does not have novelty and the authors lack knowledge on river-tide interactions. Therefore, my recommendation is reject (I think I am too rigorous). The main questions I encountered when reading the manuscript are as follows:

Major technical concerns:

1、The application of EEMD method to analyze river tides is not new. See the paper ‘Application of the EMD Method to River Tides’ (DOI: 10.1175/JTECH-D-17-0185.1) published at 2018 in JAOT, and the paper ‘Application of the Variational Mode Decomposition (VMD) method to river tides’ (DOI: 10.1016/j.ecss.2021.107570) published at 2021 in ECSS. The last paper compared the performance of EMD, EEMD, VMD as well as physical-based NS_TIDE in tidal rivers and found that VMD is superior than EEMD/EMD. Thus, the authors may use VMD method to replace EEMD. Other references: 'Ensemble Empirical Mode Decomposition on Storm Surge Separation from Sea Level Data' by Wu et al. or 'Estimation of extreme sea levels along the Bangladesh coast due to storm surge and sea level rise using EEMD and EVA' by Lee et al.

2、The authors do not know too much about tide-river interplay in tidal rivers. Thus, their understanding on the results of EEMD is misleading (refer the paper I list above for more details). Tides have been modified by river flow, thus, you cannot simply divided IMFs into two groups.

3、I encourage the authors upload their codes and data to the web to let reviewers and readers can examine and test your method. For example, the code and data of the VMD paper I list above can be downloaded from the following website:

https://www.researchgate.net/publication/354370526_Data_and_code_of_paper_'_Application_of_the_Variational_Mode_Decomposition_VMD_method_to_river_tides''

Major editorial concerns:

1、Title is not accurate. The authors can use new title like ‘Water level forecasting in tidal rivers during periods of typhoon using Ensemble Empirical Mode Decomposition’

2、The introduction is not well-written and in a mess. The authors do not clearly indicate the problem of previous studies (even not cite some vital studies). I suggest the authors state their motivation more clearly based on the defects of previous studies.

3、In section 2, there is no need to introduce EEMD method in details because EEMD is well-known. Just introduce EEMD briefly or move the details to the appendix.

4、Display study area and data before methodology. Also, language can be further improved.

Minor concerns (only a small part is listed):

L12, it is suggested that to change ‘water stage’ to ‘water level’, change ‘tidal stream’ to ‘tidal river’

L32, delete ‘constantly’

L33, awkward sentence, please revise.

L73, change ‘tidal stream water stage’ to ‘water levels in tidal rivers’.

L103, ‘(b)’ appears twice.

L158, I do not agree with the authors, tides in tidal rivers are influenced by river flow, thus, EEMD cannot simply classify IMFs into two groups.

L182, please provide the website to download water levels you use.

Author Response

Major technical concerns:

1. The application of EEMD method to analyze river tides is not new. See the paper ‘Application of the EMD Method to River Tides’ (DOI: 10.1175/JTECH-D-17-0185.1) published at 2018 in JAOT, and the paper ‘Application of the Variational Mode Decomposition (VMD) method to river tides’ (DOI: 10.1016/j.ecss.2021.107570) published at 2021 in ECSS. The last paper compared the performance of EMD, EEMD, VMD as well as physical-based NS_TIDE in tidal rivers and found that VMD is superior than EEMD/EMD. Thus, the authors may use VMD method to replace EEMD. Other references: 'Ensemble Empirical Mode Decomposition on Storm Surge Separation from Sea Level Data' by Wu et al. or 'Estimation of extreme sea levels along the Bangladesh coast due to storm surge and sea level rise using EEMD and EVA' by Lee et al.

Ans:

        Thanks for the reviewer to share his experience with me. The references you mentioned are important for us and are cited in section of introduction.

2. The authors do not know too much about tide-river interplay in tidal rivers. Thus, their understanding on the results of EEMD is misleading (refer the paper I list above for more details). Tides have been modified by river flow, thus, you cannot simply divided IMFs into two groups.

Ans:

        Yes, the water level in tidal river are affected by many factors such as tide, topography, friction, and river flow. It is quite complex. However it is impossible for us to obtain the data used to develop a sophisticated model. The only data that can be used is water level. By using EEMD, the IMFs can be obtained. Owing to the shortage of data, it is impossible to know the factor affecting the IMF. Therefore we have to simplify the model and divided IMFs into two groups. The results also show the proposed model works.

3. I encourage the authors upload their codes and data to the web to let reviewers and readers can examine and test your method. For example, the code and data of the VMD paper I list above can be downloaded from the following website: https://www.researchgate.net/publication/354370526_Data_and_code_of_paper_'_Application_of_the_Variational_Mode_Decomposition_VMD_method_to_river_tides''

Ans:

        Thanks for your suggestion. We do not develop our program to obtain the IFMs. The program we used is Visual Signal that is a commercial software (http://www.ancad.com.tw/pro_visual_signal_01.htm). It is quite easy to obtain the IMFs by using Visual Signal without coding. The data we use can be obtained from the Water Resources Agency of Taiwan.

Major editorial concerns:

1. Title is not accurate. The authors can use new title like ‘Water level forecasting in tidal rivers during periods of typhoon using Ensemble Empirical Mode Decomposition’

Ans:

        Thank. It is a good suggestion. We change the title as “Water level forecasting in tidal rivers during periods of typhoon using Ensemble Empirical Mode Decomposition

2. The introduction is not well-written and in a mess. The authors do not clearly indicate the problem of previous studies (even not cite some vital studies). I suggest the authors state their motivation more clearly based on the defects of previous studies.

Ans:

        One paragraph is added to let the readers clearly know why we do not take advantage of the sophisticated models to forecast the water level in the tidal rivers.

The hydrological systems in a tidal river is unique and the water-level is continually changing under the interaction of riverine and marine processes.  The most obvious factors having a profound influence on the water-level that include shape of the tidal river, astronomical tide, wind, salinity, temperature, sediment, flood, storm surge, and others are too complex to model directly. Consequently, the hydrodynamic processes of tidal rivers are manifestly complex, nonstationary and notoriously nonlinear [15]. Many of the concepts or principles derived from other watercourses have been applied to forecast water level in tidal rivers. The theoretical approach is based on the following pair of differential equations. One of the major disadvantages of using these methods is that the parameters are usually difficult to determine form the observed data, especially discharge [17]. Additionally, it is time consuming to program and execute those sophisticated models

3. In section 2, there is no need to introduce EEMD method in details because EEMD is well-known. Just introduce EEMD briefly or move the details to the appendix.

Ans:

        EEMD is the key of the proposed model. Also EEMD is well-known, but it is still very unfamiliar to many readers. The introduction and detail of the EEMD is very important for the readers to obtain the IMFs that is shown in the results. It is better to keep the detail and theory of EEMD in section 2.

4. Display study area and data before methodology. Also, language can be further improved.

Ans:

        This study is try to propose a new model to forecast the water level in tidal rivers. It can be applied in any tidal river. Therefore the methodology is important than the study. We try to show the proposed model can be used in the study area. Therefore it is better not to move the section of study before the section of detail of EEMD.

Minor concerns (only a small part is listed):

1. L12, it is suggested that to change ‘water stage’ to ‘water level’, change ‘tidal stream’ to ‘tidal river’

Ans:

        Ok! All of them are changed.

2. L32, delete ‘constantly’

Ans:

        Ok! It is deleted.

3. L33, awkward sentence, please revise.

Ans:

        It is revise as “Resulting from the rotation of the earth and the varying strength of the gravitational pull from the Moon and the Sun the water level varies quasi periodically with 12.25 hours or twice every lunar day.”.

4. L73, change ‘tidal stream water stage’ to ‘water levels in tidal rivers’.

Ans:

        Thanks for your help and it is changed.

5. L103, ‘(b)’ appears twice.

Ans:

        It is our mistake and (b) is deleted.

6. L158, I do not agree with the authors, tides in tidal rivers are influenced by river flow, thus, EEMD cannot simply classify IMFs into two groups.

Ans:

We try to find the most important factors affecting water level in the tidal river. One is affected by ocean and the other is affected by flood. If an IMF exhibits periodicity, we can say it is influenced by tides. Therefore, it is possible to classify the IMFs from water stage into two groups: one affected by the ocean and one by the flood. By adding all IMFs affected by the ocean, the ocean component is obtained, and the same for the stream component by summing all IMFs not affected by the ocean to obtain stream component.

7. L182, please provide the website to download water levels you use.

Ans:

        The Water Resources Agency of Taiwan release real-time water stage data. Submit a request through the Water Resources Agency to obtain the water level data is necessary. The website of Water Resources Agency is www.wra.gov.tw.

Round 2

Reviewer 1 Report

Review of the revised manuscript Water Level Forecasting in Tidal Rivers during Periods of Typhoon Using Ensemble Empirical Mode Decomposition, by Chen et al., for Hydrology

In my previous evaluation, I indicated that the manuscript needed to be edited for correctness and clarity. This was not done. The manuscript is poorly written: it is wordy, sometimes colloquial, and has grammar errors. This makes it difficult to follow. Below are some examples from the abstract and introduction. Also, many statements are incorrect. Most sentences need to be rewritten before the paper can be published.

Line 11. “The most advantage of the proposed model is the data needed is only water level.” -> The main advantage of the proposed model is that the only required data are water levels

Line 28. I suggest replacing “tidal river” by “estuary”

Line 39. Circulating -> circulation

Line 43. “Considering all the factors mentioned above, we can see it is not easy to account for all physical processes in tidal rivers.” This is too colloquial for a scientific paper. Besides, numerical models that account for all the mentioned processes are routinely used worldwide. Hence, I dispute the sentence: it is easy to account for all the physical processes.

Line 58. “The theoretical approach is based on the following pair of differential equations.” Which pair? I was expecting a specification of the pair following this sentence.

Line 59. “One of the major disadvantages of using these methods is that the parameters are usually difficult to determine from the observed data, especially discharge”. Discharge is not a parameter.

Line 61. “Additionally, it is time-consuming and costly to program and executes those sophisticated models”. There are lots of open-source models available for free. The cost of coding them is not an argument not to use them.

Line 62. “Some hydraulic models applying energy and momentum principles”. You mean conservation principles. But, in general, these models use mass – not energy – conservation principles.

Line 85. “during the period of the flood is proposed, as shown in Figure 1” -> “during flood is proposed (Figure 1)”

Author Response

In my previous evaluation, I indicated that the manuscript needed to be edited for correctness and clarity. This was not done. The manuscript is poorly written: it is wordy, sometimes colloquial, and has grammar errors. This makes it difficult to follow. Below are some examples from the abstract and introduction. Also, many statements are incorrect. Most sentences need to be rewritten before the paper can be published.

        Ans:

       The manuscript is checked by a paid editing service to reflect the English level.

Line 11. “The most advantage of the proposed model is the data needed is only water level.” -> The main advantage of the proposed model is that the only required data are water levels

        Ans:

       Thanks! It is replaced as you suggestion.

Line 28. I suggest replacing “tidal river” by “estuary”

        Ans:

       Thanks for you suggestion. It is replaced by “estuary”.

Line 39. Circulating -> circulation

        Ans:

       Circulating is replaced by circulation.

Line 43. “Considering all the factors mentioned above, we can see it is not easy to account for all physical processes in tidal rivers.” This is too colloquial for a scientific paper. Besides, numerical models that account for all the mentioned processes are routinely used worldwide. Hence, I dispute the sentence: it is easy to account for all the physical processes.

        Ans:

       I agree with you. It is replaced by “It is not easy to develop a model which can deal with all hydrological processes in tidal rivers.”

Line 58. “The theoretical approach is based on the following pair of differential equations.” Which pair? I was expecting a specification of the pair following this sentence.

        Ans:

       It is replaced as “The theoretical approach is based on continuity, momentum and energy equations.”

Line 59. “One of the major disadvantages of using these methods is that the parameters are usually difficult to determine from the observed data, especially discharge”. Discharge is not a parameter.

        Ans:

       It is replaced as “However, a major disadvantages of theoretical methods is that the required parameters are usually difficult to determine from the observed data; in particular, the dis-charge is challenging to measure”

Line 61. “Additionally, it is time-consuming and costly to program and executes those sophisticated models”. There are lots of open-source models available for free. The cost of coding them is not an argument not to use them.

        Ans:

       The sentence is replaced as “Although there are lots of open-source models available for free, programming and executing a new developed model is time-consuming and costly.”

Line 62. “Some hydraulic models applying energy and momentum principles”. You mean conservation principles. But, in general, these models use mass – not energy – conservation principles.

        Ans:

       The energy is replaced by mass conservation.

Line 85. “during the period of the flood is proposed, as shown in Figure 1” -> “during flood is proposed (Figure 1)”

        Ans:

        Thanks! It is replaced as “In this study, a conceptual model was developed for forecasting tidal river water levels during a flood period (Figure 1)”.

Reviewer 3 Report

 I am satisfied with most revisions. Here, only minor revisions are needed.

First,  pictures should be plotted with color for better visualization

Second, I think the results of EEMD should be compared to those of VMD.  This is not difficult to realize.

At last, language can be further improved. For example, L31, 'the tides from the ocean' can be replaced by 'ocean tides'

Author Response

I am satisfied with most revisions. Here, only minor revisions are needed. First, pictures should be plotted with color for better visualization. Second, I think the results of EEMD should be compared to those of VMD. This is not difficult to realize. At last, language can be further improved. For example, L31, 'the tides from the ocean' can be replaced by 'ocean tides'

Ans:

        Thanks for your help to improve our paper. The manuscript is checked by a paid editing service to reflect the English level.

        Figures 1, 3, 5, 6, 7 and 8 are plotted with color to make sure the readers can read them clearly.

        There is no time for us to get the results from VMD to compare with our model. Therefore we suggest the future work should include the comparison of VMD and EEMD.

        “the tides from the ocean” in Line 31 is replaced by “ocean tides’.