A Methodology for Forecasting Dissolved Oxygen in Urban Streams

1

1. Paper title: the “reliable” should be removed from the title, which can be changed into “A linear methodology for forecasting dissolved oxygen in urban streams”.

Thank you. The title has been revised.

1

2. Line 44-45: Apart from nitrification process, degradation of carbonaceous BOD (biological oxygen demand) is another very important process leading to low DO in rivers. Such literatures can be found in Huang et al. (2017, water).

Thank you. The text has been revised to include details regarding the degradation of carbonaceous BOD to low DO in rivers.

Line 44-46 was revised to:

“Refractory carbonaceous biological oxygen demand (CBOD) and the oxidation of ammonia to form nitrite and nitrate are one the most significant processes leading to low dissolved oxygen concentrations in a river [8].”

[8] Huang, J.; Yin, H.; Chapra, S.C.; Zhou, Q. Modelling Dissolved Oxygen Depression in an Urban River in China. Water 2017, 9, 520.

1

3. Line 208-209: Is your model based on the daily-averaged data? Can you predict the time-series or real-time DO concentrations in rivers?

Thank you. Figure 11 has been added which illustrates the link between average daily DO and the original DO data. This method outlined in this may be applied to predict daily minimum and maximum values, which can be used to reconstruct the sub-hourly time series by a applying a sinusoidal function. We also added a discussion on the importance of daily minimum DO values in regards to water quality metrics and that there is a strong linear relationship between daily average DO and daily minimum DO.

1

4. Figure 5: This figure shows the plot of DO data after eliminating seasonal fluctuations and non-seasonal correlations. Does this plot represent the DO trend in rivers, e.g., the process of DO in Fig.3? I am perplexed if this data can predict the DO trend in rivers.

Thank you. Figure 5 is the autocorrelation function plot of the pre-processed DO time series.  An autocorrelation plot shows the value of the autocorrelation function (ACF) and is designed to show whether the elements of a time series are positively correlated, negatively correlated, or independent of each other. This plot provides information on the presence and intensity of the deterministic terms in the historical data visually to some extents, which are used in the forecasting process.

One of information presented by this plot, is the trend in historical time series as homolaterl positive values decaying to zero in the assessing range (n/4 of data).

 However this shape is affected by presence of other deterministic terms like period term. In this case the plot will be sinusoidal and identifying the trend will be hard. Therefore,  the trend should be detected by Mann-Kendall test.

Moreover, by using this plot correlation of the lags with previous one can be identified which help in determining the orders of the model for forecasting the future steps based the previous correlations.

In the figure 5, the ACF plots of the pre-processed data are presented. These plots indicate that all correlations have been removed and the deterministic terms, which impact the modeling results, are properly damped. Therefore, by using the sole random variables a more precise stochastic modeling and forecast can be carried out.

1

5. Table 4: Do you present or summarize all of the 6×99=594 stochastic models in this table?

Thank you. The table presents the superior models for each scenario. The models are selected based on the adequacy and parsimony alongside the precision indices.

Initially the models with the most independent residuals are chosen, then compared based on the simplicity and error indices. Finally the superior models of the each scenario are presented in Table 4 to provide a better comparison.

1

6. Fig.8: This figure shoes the comparison between measured and modeled data. However, I didn’t find the comparison between time-series measured and modeled data. This goes back to the question, that, if the developed model is able to predict the real-time DO concentration in urban stream that affected by complex processes such as rainfall, biological-chemical degradation, and possible pollutant discharge, and so on.

Thank you. For a better presentation of the models performance Figure 11 is added to the manuscript. In this Figure, the modeled data vs. the observed test data is illustrated. It is obvious that dynamic stochastic modeling with the proposed methodology can provide acceptable results in the forecasting real-time DO concentration in urban stream.

Also we admit that there are many factors involving in DO fluctuations. But these factors have been in interactions with each other for a long time. Most of these factors follow predictable patterns that influence the DO factor. These pattern can be also observed in historical data of DO and always have impacted the DO fluctuations such as meteorological parameters or flow fluctuations that contain periodic patterns and trends. The use of time series eliminates the problems of multivariate models. For example, the series length may not be the same across inputs, which will shorten the modeling time period. Moreover, it is possible to provide models with the acceptable precision and minimum parameters. Another advantage of undertaking such approach is cutting costs and declining the errors that each extra input contain. Measuring any variable always is accompanied by machine or human errors. Therefore, lowering the number of inputs can solve this problem. Finally, by a proper time series structural investigations the impact of the mentioned factors can be predicated and added to the forecasts of the mere DO future steps and obtain a precise model.

1

7. Fig.10. It is not clear that this methodology was successful in modeling the mean, median, quartiles and even the approximate estimation of the extreme values for DO I station from this figure. In view of the above-mentioned, I didn’t recommend publication for this manuscript before a major revision is made.

Thank you, since the forecasts are very similar and the statistics are vey close ,distinguishing the best method is a little hard. Therefore, the Box plot is replaced with the Table 5 to present the descriptive statistics numerically. Please see Table 5 and section 3.2.

2

This paper presents a reliable linear methodology for forecasting dissolved oxygen in urban streams. The only suggestion I have is to include a higher resolution/bigger picture (Fig 2).

Thank you, a higher quality version of this figure has been included.

3

First of all the title has to be changed. "Reliable" is not a scientific term for describing the work that has been done here and "linear" also. Readers can understand that just linear equations are used to simulate the DO.

Thank you. The title is revised and the keywords “Reliable” and “linear” have been removed.

3

Abstract: has to improved. Sentence 1 and 2 has to be merged. habitats instead of habitat. sole normalization. what is "sole"??

Thank you.

·         Sentences 1 and 2 are merged.

·         “Habitat” was changed to “habitats”.

·         The keyword “sole” was removed.

3

habitats instead of habitat

• Thank you. “habitat” was changed to “habitats”.

3

Introduction

The paper has many typos and the authors have to double check the english. 

In the introduction the litereture review doesnt include more recent studeis of 2019 and 2020. There is not any recent research on the subject? You have to use more recent articles. for instance
Chemometrics and Intelligent Laboratory Systems Volume 200, 15 May 2020, Article number 103978
Artificial intelligence-based single and hybrid models for prediction of water quality in rivers: A review

Thank you. Recommended more recent 2019 and 2020 references were cited in the introduction and the paper was carefully proofread to correct any remaining grammatical or spelling errors.

3

Improve the following sentence "They reported that the decomposition 55 methods does not necessarily improve the results as decomposition did not improve the CC models 56 results, it enhanced the MLP’s. Sentas et al. [8] compared the ARIMA model with artificial neural 57 network (ANN) for modelling short daily DO. They"

The following sentence doesnt give any information "Their 65 results led to presenting a novel graph linking air temperature and DO parameter." Novel graph? this is not scientific..

Thank you.

·         The first sentence has been revised for clarity and focus.

·         The following sentence was revised.

·         “Novel graph” was removed.

3

Lines 79-80 

"All these problems can be overcome by adoption of a single time series modelling approach, a proper 79 analysis procedure and pre-processing method, careful selection of inputs or using simpler models."

this is the authors personnal opinion and not the reality, based on research evidences. please delete this.

Thank you. The sentence has been restructured to dismiss the personal opinion and instead highlight the future opportunities available. 

3

Please describe the objectives of the study in the introduction and how your objectives are connected with the literature review. what are you adding in the existing knowledge? which gap you are covering?

Thank you. Therefore, the main objective of this study is to compare preprocessing methods applied to the DO ARIMA models to develop the most accurate while still simple and practical forecast model, which to our knowledge has not been studied in-depth before. The ultimate goal of the study is to develop a users-friendly model for the practitioners to easily assess the health of urban streams and avoid the challenging problems associated with the application of more complex multi-parameter models.

3

You are running 2 scenarios. Why? how do you select them? it is not adequately described.

Thank you. The normality and more importantly the stationarity are the two initial premises in stochastic modeling. The idea is to propose a novel methodology based on the most traditional methods yet comprehensible enough to be widely used and obtain the preferred results.

The stochastic models and the described methods of pre-processing are the most well-known methods amongst scholars and even non-expert users. A non-stationary time series can be transformed into a stationary one by the first order or successive differencing operations as stated in (Cryer and Chan,  2008; Peña et al. 2001). Using the proper differencing method requires recognizing the structure of the time series as non-seasonal, seasonal, consecutive non-seasonal-seasonal and multiple order differencing methods exist. More importantly, this method is the simplest and the most effective method of stationarizing time series that exists as a built-in operator in ARIMA and SARIMA models to eliminate non-stationarity. Standardization is also the most conventional stationarizing method that is widely used in the both  AI and statistical modeling methods. this method not only stationarizes the data to some extent, but also it rescales and normalizes the time series. the spectral analysis is also a well-known stationarizing methods in eliminating periodic term. Though this method is limited to periodicity and it has less effect in reducing the impact of the other non-stationary factors.  As mentioned earlier, the purpose in this study is to provide the most accurate method and yet the simplest one. Thus the best way to utilize the characteristics of all the mentioned methods is the proposed scenario by which not only both stochastic methods’ assumptions are considered but also the stationarizing methods are compared in a equal condition.

Cryer, Jonathan D.; Chan, Kung-sik (2008): Time series analysis. With applications in R. 2nd ed. New York: Springer (Springer texts in statistics).

Peña, Daniel; Tiao, George C.; Tsay, Ruey S. (2001): A course in time series analysis. New York: Wiley (Wiley Series in Probability and Statistics).

3

Materials and Methods

"Water quality was monitored using a Hydrolab DS5X 195 multi-parameter sonde at each location."

What is sonde?

Was it possible to forecast hourly DO values? You use only daily average.

Thank you, “sonde” is a term used to describe an environmental probe, typically containing multiple sensors as well as a means of transmitting the data (either wireless or through cable). The term is commonly used to describe sensor packages designed for water quality monitoring in both freshwater and marine environments.

Figure 11 has been added which illustrates the link between average daily DO and the original DO data. This method outlined in this may be applied to predict daily minimum and maximum values, which can be used to reconstruct the sub-hourly timeseries by a applying a sinusoidal function. We also added a discussion on the importance of daily minimum DO values in regards to water quality metrics and that there is a strong linear relationship between daily average DO and daily minimum DO.  

3

Results

I see in DO time series 1 that you have outliers. You should remove these values due to the mistakes from the very beginning. You cant have zero DO. It is obvious it is a measuring mistake.

Thank you for this valuable comment. The original series had some missing point that were replaced by using interpolation method. Unfortunately the method was not able to calculate some of missing point for a total of 10 days. Therefore these values are removed form the series and the modeling procedure has been carried out again. The new results are added to the manuscript. Please see the Table 4 and following definitions in the manuscript.

3

Table 2 Period values (F*) for std are negative and very small. What that means? Jump has the same value. What that means?

Thank you. Fisher’s test is a test for identifying periodicity in time series based on the Fourier series expansion. This method transfers the time-domain data to frequency-domain data and identifies the peaks in the series and determines if they are significant or not.  According to (Kashyap and Rao 1976; Moeeni et al. 2017), the critical value in the F-distribution for this test  is 3.00 at the 5% significance level for large degrees of freedom in the denominator. Therefor, the values of the test lower than this values indicates the insignificance of the periodicity in the time series. As the test values for S_td methods are lower than 3 then the periodicity is not significant is the series.

However, the test is based on the Fourier expansion. Therefore it has some drawbacks. One is that it considers the peaks and it might neglect the periodicity with lower frequencies and it is linear. Therefore, the test should accompanied by another tests like ACF and PACF plots.

The Mann-Whitney test is none-parametric test that compares that two samples from a population have same distribution. This test in utilized in the Water Engineering and Hydrology to assess the Jump in the series by dividing the series to two parts and comparing their characteristics. For instance, All the observations from both groups are independent of each other, or under the null hypothesis H0, the distributions of both populations are equal. Accordingly, the test statistic is evaluated in 1 and 5% significance level, usually. In the manuscript, the test applied to the DO series are assessed in 1% significance level and the higher values than 1% means that the Jump in the series is no significant and vice versa.

Moeeni, H., Bonakdari, H., & Ebtehaj, I. (2017). Monthly reservoir inflow forecasting using a new hybrid SARIMA genetic programming approach. Journal of Earth System Science, 126(2), 18.

Kashyap R L and Rao A R 1976 Dynamic stochastic models

from empirical data; Mathematics in Science and Engineering, New York, USA.

3

Line 220-221 "The spectral analysis method was able to significantly reduce the frequency of the DO II series, while the results of all these three pre-processing approaches are close for DO I." Why the frequency for DO I is not reduced? Both time series should follow the same pattern.

Thank you. Spectral analysis is one the methods of stationarizing time series. This method transforms the data from time-domain to frequency domain to extract the periodical pattern in the time series and stationarized them. Accordingly, it the Fourier expansion to perform the operation.

One of the main reasons for using a frequency-domain representation of a problem is to simplify the mathematical analysis. For mathematical systems governed by linear differential equations, a very important class of systems with many real-world applications, converting the description of the system from the time domain to a frequency domain converts the differential equations to algebraic equations, which are much easier to solve.

However, this method has some drawbacks. One of the main drawbacks of spectral analysis is that it is a linear method. In other words, it considers DO time series as composed by a linear combination of the independent oscillatory components, where interactions between those components are neglected. There. This method may produce different results in different situations.

Moreover, though the both time series are the same nature, but they differ in some statistical characteristics, howbeit small.

Finally, a normalization transformation is performed prior to stationarization. The transformation parameters are different in both series.

3

Table 3. Why the values are so different . For instance jumb has increased to 82 and is not stable in comparison to stationary?

Thank you. The Augmented Dickey-Fuller test for a unit root assesses the null hypothesis of a unit root using the model. Dickey and Fuller decided to take as null hypothesis ϕ=1(a unit root is present in a time series sample) because it has an immediate operational impact: if the null hypothesis is not rejected, then, in order to be able to analyze the time series and if necessary to make predictions, it is necessary to transform the series, using differencing.

Therefore, the corresponding probability to the test statistic lower than 5% means that the series is stationary and alternatively, the values higher than 5% means non-stationarity.

On the other hand, for MK, SMK and MW tests, the probability values higher than 5% indicating the desirable situation and absence or low impact of the deterministic terms.

In the Table 2, all values of ADF test are higher than 5% and indicating non-stationary. Low values of other tests indicate presence of deterministic terms. while in the Table 3, all values of ADF test declined to less than 5% meaning that the series has become stationary and the impact of the deterministic terms reduced significantly, e.g., MW test for Jump from zero to ~82%

3

Figure 5. Why the first lags values have high range?

Thank you. To show correlations between lags ACF plots are the best way. The values and the patterns depicted in this plot provides useful information on the time series. If the series initially shows strong positive autocorrelation, as see in both DO time series with sinusoidal pattern, then a non-seasonal difference will reduce the autocorrelation. However, differencing tends to introduce negative correlation. Therefore, the values of the ACF plot tend to be negative in the first lags. These negative values also mean that the following values tend to zero and the series is stationary. In case of using high order differencing operator in the model, the autocorrelation more negative than -0.5 means that the series probably has been over-differenced. The alternating pattern in a negative autocorrelation insures that a series will be more likely to bracket the true mean.

Furthermore, the values of the ACF range from -1 to +1. In presenting the ACF plot, the ACF at lag 0, r0, equals 1 by default meaning, the correlation of a time series with itself and it’s plotted as a reference point. The standard plot is as follows:

As you can see the values are much lower than -0.5 and all are bounded in the in confidence intervals. In the manuscript to better present the plots, they were magnified to range of

 -0.15:0.15

3

Table 4, check the units. for instance RMSE is not %. Ui and UII are high. why?

Thank you; please see revised Tables 4 with the units for the RMSE and MAE values that are in (mg/L) as indicated in the note below the table.

3

Figure 7. Please explain better this graph. It is not very clear the explanation.

The more explanation is added to the manuscript prior to Figure 7.

“Figure 7 graphically shows the results of the Ljung-Box test, which is used to check the independence of the residuals. The values of the test higher than 5% indicates the independence of the sample. Residuals independence is one of the post-modeling assumptions in stochastic modeling. This evaluation is performed to assess the adequacy of the stochastic models. In case of having significant correlations in the residuals, the modeling process should be reviewed. In this figure, the results of the independence test for both stations’ data are presented. Using the daily data time series, the first 365 primary non-seasonal lags or the first primary seasonal lag of the residuals from the ARIMA models were evaluated by lbq test. Since the results of the three methods for each station are very close, the corresponding lbq test results are overlapped. For station II (DO II) model residuals, a total independence for the residuals is observed. In the second station, however, some negligible correlations is seen in the first lags for all three methods. This correlations might be due to periodicity in the DO I time series. Consequently, as the lbq values for the correlated lags are close to significant 5% line, the correlations are removed immediately after few lags and the rest of the residual series are independent, it can be concluded that the models are adequate for DO I time series as well.”

3

Figure 9. The diagramm doesnt bring any new information. just describe in the text. also the symbols are not clear.

In general, with Taylor graph we can select the best model, however, in this case the obtained results are very close in this diagram for this reason we added Table 5.

3

Please in the conclusion explain why this method is better than other. It is not working well for the 1st time sereis in comparison to the second. Why to adapt this method. What do you improve?

Thank you, the conclusion has been updated to be clearer. As mentioned in the discussion the minor differences between the performance of the DO I model, and the DO II model is related to the periodicity of the residuals. There may be a variety of factors which may be causing this difference including land use, shading, different geomorphology, etc which is out of the scope of this paper. However, from the results this difference does not greatly impact the accuracy, which can be seen in Table 4. We improved our understanding of the sensitivity of preprocessing methods when applying the ARIMA model to DO time series, and demonstrated that daily min DO can be predicted via a simple linear relationship from daily average DO.