Forecasting of SPI and Meteorological Drought Based on the Artificial Neural Network and M5P Model Tree

Round 1

Reviewer 1 Report

The authors conducted detailed verification using multiple models for drought prediction, which can be evaluated as important research.

However, it is recommended to add explanations because there are some points that are difficult for non-experts to understand, such as the characteristics of the data used and the evaluation method of the model.

I recommend adding or correcting the following descriptions.

[LINE 109]

SPI is used here as an abbreviation for soil moisture index, but isn't it an abbreviation for standardized precipitation index?

[LINE 132]

The terms SPI-3 and SPI-6 are used for the first time here, but it is better for understanding to explain their definitions.

[LINE 144]

Two observation points are plotted in the lower of Figure 1, but it is easier to see if the letters are larger.

[LINEs from 185 to 192]

In this section, it is explained that multiple models with different input/output and number of layers of the ANN model are adopted. I think it's easier to understand these models graphically.

[LINEs from 222 to 223]

The data processing procedure of the MP5 algorithm is explained, but I think it is easier to understand if these are illustrated.

[LINE 289]

Combinations from SPI-1 to SPI-12 are listed as variables in Table 1, but I think it is difficult to understand what these combinations mean. I think it would be better to add an explanation in the text about what these variable combinations mean.

[LINEs from 309 to 310]

The words from SPI(t-1) to SPI(t-11) appear here, but I couldn't find an explanation for the variable of "t". You should add an explanation.

[LINEs from 404 to 407]

It would be better to write a little more detail on how to interpret the Taylor diagram.

Author Response

Reviwer-1

The authors conducted detailed verification using multiple models for drought prediction, which can be evaluated as important research.

However, it is recommended to add explanations because there are some points that are difficult for non-experts to understand, such as the characteristics of the data used and the evaluation method of the model.

I recommend adding or correcting the following descriptions.

 Response; Thanks for suggestions to paper improvement and considering the paper to publication.

[LINE 109]

SPI is used here as an abbreviation for soil moisture index, but isn't it an abbreviation for standardized precipitation index?

Response: WE have changed the SPI full form as per your suggestions.

[LINE 132]

The terms SPI-3 and SPI-6 are used for the first time here, but it is better for understanding to explain their definitions.

 Response: We have added the SPI definition in the methodology section.

[LINE 144]

Two observation points are plotted in the lower of Figure 1, but it is easier to see if the letters are larger.

 Response: We have revised the Fig.1 as per your suggestions.

[LINEs from 185 to 192]

In this section, it is explained that multiple models with different input/output and number of layers of the ANN model are adopted. I think it's easier to understand these models graphically.

Response: Thanks for suggestions, in writing part is a better to understand and very clearly explained each and every about the models and all variables are arranged in the tables. I think so no need for figures.

 [LINEs from 222 to 223]

The data processing procedure of the MP5 algorithm is explained, but I think it is easier to understand if these are illustrated.

  Response: Thanks for suggestions, but it is no need for illustration.

[LINE 289]

Combinations from SPI-1 to SPI-12 are listed as variables in Table 1, but I think it is difficult to understand what these combinations mean. I think it would be better to add an explanation in the text about what these variable combinations mean.

 Response: Thanks for suggestions, we have added in the SPI-1 to SPI- 12 variables in the paper.

 [LINEs from 309 to 310]

The words from SPI(t-1) to SPI(t-11) appear here, but I couldn't find an explanation for the variable of "t". You should add an explanation.

Response: These variables have been explained below Table 1 A.

[LINEs from 404 to 407]

It would be better to write a little more detail on how to interpret the Taylor diagram.

Response: Thanks for suggestions, we have added how to interpret the Taylors diagram in the paper.

Reviewer 2 Report

This paper applied ANN and M5P methods in forecasting  SPI-3 & SPI-6 using  monthly rainfall data from 2000-2019 at two discrete meteorological stations in India and presented the results. M5P model is found to be the most accurate model for predicting SPI-3 and SPI-6 at both stations.

Some specific comments:

1. Indrduction should be enriched. The progress, effectiveness and problems in the field of drought forecasting espcecially using ML methods should be reviewed. 

Line 122-125: 'Although scientists and scholars have come up with many different models for modeling DIs, it's difficult to generalize or create a "perfect" model that can work for the tropical region': What are the specific reasons? Those privious researches on drought forecasting should be reviewed more specifically.

Line125：'the inappropriate combination of inputs of a model’s structure can lead to misguidance': What's the special combination used in this research?

2.The models used in this research, i.e. ANN, LWLR, M5T,  have already been used in previous SPI forecasting. What are the special findings obtained from this reasearch in terms of optimal mopdel selection? As been noted that the scale of SPI isn't linear, whats's the necessity to use LWLR?

3. Line 157-173: The scheme and Eqs to derived SPI should be described more clearly. Units should be provided for variables exept for dimensionless parameters. Vaiables in Eqs should be explained. What's the consideration of adopting two SPIs derived using Eq. 7 and 8? 

4. In section 2.2.2: As MATLAB software is used to explement the ML models, the general introduction of the model may be simlified. 

5. Section 3: The model input and output SPI-n  SPI-(t-n) should be explained for better understanding in section 3.1 and 3.2. The selection criteria is somewhat not clear. For example, in Line 295-297,  'best input combination 7 (SPI-1 / SPI-3 / SPI-4

/ SPI-5 / SPI-8 / SPI-9 / SPI-11) has the highest values of the R2 and Adjusted R2 of 0.758 and 750 and lowest values of MSE of 0.471 [Table 2 (A)]', but  R2 is not the highest.  

6. Section 4: Discussion should be enriched. The results are compared with Taylor diagram [50] at these 2 stations, however the training and testing data are not described clearly when comparison. What's the reason for the better performance? In application, what's the specific accuracy requirement for SPI forecasting. Does the results meet the requiement? Why the prediction error at some period is large? 

7. Some writing issues:

Line 109, 'soil moisture index (SPI)': Is SPI is the correct abbreviation? 

Line 123, 'DIs': First appearance of abbreviations without full expression.

In introduction L130-131, 'Three discrete ma131 chine learning models were developed, such as ANN, LWLR, and M5T' , while in section 2.2.2 M5P is used. 

Line 297： '750'

'determination coefficients (R2)' or 'determination coefficients (r2)'?

Author Response

Reviwer-2

This paper applied ANN and M5P methods in forecasting  SPI-3 & SPI-6 using  monthly rainfall data from 2000-2019 at two discrete meteorological stations in India and presented the results. M5P model is found to be the most accurate model for predicting SPI-3 and SPI-6 at both stations.

 Response; Thanks for some specific comments on the paper and also thanks for considering the paper to publication.

Some specific comments:

1. Introduction should be enriched. The progress, effectiveness and problems in the field of drought forecasting especially using ML methods should be reviewed. 

 Response: We have revised and added the ML methods in the introduction section also it is enriched the section.

Line 122-125: 'Although scientists and scholars have come up with many different models for modeling DIs, it's difficult to generalize or create a "perfect" model that can work for the tropical region': What are the specific reasons? Those previous researches on drought forecasting should be reviewed more specifically.

 Response: Tropical Regions is not corrected sir, this area is under in the semi –arid region, Thanks for suggestions, very few research and scientist worked on the drought forecasting in the India. Drought forecasting model creation is perfect but we have used large time series data should require for ML model, now a day so many datasets available in the platform. Previous researches have already explained in the paper one four or five peoples work on drought forecasting and as per suggestion we have added in current version of paper.

Line125：'the inappropriate combination of inputs of a model’s structure can lead to misguidance': What's the special combination used in this research?

Response: First, we have used 12 lag datasets as input variables to ML models then used the best subset regression model to select the best input variable combination as shown in Tables 1 and 2 for SPI 3 and 6. Second in each station, the best input combination was different due to climate change condition used for calculation of SPI 3 and 6. The best subset model select the best model without human intervention based on some statistical performance metrics as shown in Tables 3 and 4. 

2.The models used in this research, i.e. ANN, LWLR, M5T,  have already been used in previous SPI forecasting. What are the special findings obtained from this reasearch in terms of optimal mopdel selection? As been noted that the scale of SPI isn't linear, whats's the necessity to use LWLR?

Response: We have used these models in these stations because it considers the first work in these regions and will help water users for monitoring drought phenomena easily in the next decades. We have removed LWLR from this work.

3. Line 157-173: The scheme and Eqs to derived SPI should be described more clearly. Units should be provided for variables exept for dimensionless parameters. Vaiables in Eqs should be explained. What's the consideration of adopting two SPIs derived using Eq. 7 and 8? 

Response: Thanks for suggestions, units not required for the input variables because SPI estimated based on the rainfall, SPI is an index values, in this reason no unit available in the literature and past papers. we have defined the SPI as per suggestions.

4. In section 2.2.2: As MATLAB software is used to explement the ML models, the general introduction of the model may be simplified. 

Response: Done as per your great suggestion

5. Section 3: The model input and output SPI-n  SPI-(t-n) should be explained for better understanding in section 3.1 and 3.2. The selection criteria is somewhat not clear. For example, in Line 295-297,  'best input combination 7 (SPI-1 / SPI-3 / SPI-4/ SPI-5 / SPI-8 / SPI-9 / SPI-11) has the highest values of the R2 and Adjusted R2 of 0.758 and 750 and lowest values of MSE of 0.471 [Table 2 (A)]', but  R2 is not the highest.  

Response: These variables have been explained below Table 1 A. As we shown that in your previous comment related to the best subset regression model, the best input combination was different for each station due to climate change condition used for calculation of SPI 3 and 6. The best subset model select the best model without human intervention based on some statistical performance metrics as shown in Tables 3 and 4. 

6. Section 4: Discussion should be enriched. The results are compared with Taylor diagram [50] at these 2 stations, however the training and testing data are not described clearly when comparison. What's the reason for the better performance? In application, what's the specific accuracy requirement for SPI forecasting. Does the results meet the requirement? Why the prediction error at some period is large? 

Response: we have revised whole section as per your suggestion. Thanks for suggestion and paper improvement.

7. Some writing issues:

Line 109, 'soil moisture index (SPI)': Is SPI is the correct abbreviation? 

Response- We have corrected in revised version paper.

Line 123, 'DIs': First appearance of abbreviations without full expression.

Response: It means Drought Indices. We have illustrated it in paper

In introduction L130-131, 'Three discrete ma131 chine learning models were developed, such as ANN, LWLR, and M5T' , while in section 2.2.2 M5P is used. 

Response- We have corrected in revised version paper.

Line 297： '750'

'determination coefficients (R2)' or 'determination coefficients (r2)'?

Response: determination coefficients is R2, we have changed it in paper.

Round 2

Reviewer 2 Report

The manuscript has been revised accordingly.  Some descriptions need to be verified.

1. Line 270, 'SPI-1 to SPI-24 menas one to twelve months for standardized precipitation index', SPI-24 for twelve months?

2. As mentioned in the previous comment 5，the best input criterion is not clear enough. 'The criterion for the selection of best input grouping is based on the higher values of R2 and Adjusted R2 while lowest values of MSE, Mallows' Cp, Akaike's AIC and Amemiya's PC. ' However, for a certain site and SPI-n , these indices are not highest or lowest at the same time. What's the priority ?

Author Response

Reply to first comment: Thanks for your great comment, we have used 12 lag datasets (SPI-1 to 12) as inputs to ML models to predict SPI over the period 3 and 6 months in this work. There is no SPI-24 in this paper but SPI-24 means SPI- 3 months value of 24-days lag (t – 24). 

Reply to second comment: Best subsets regression is an exploratory model building regression analysis.  It compares all possible models that can be created based upon an identified set of predictors.  The results presented for best subsets, show the two best models for one predictor, two predictors, three predictors, and so on for the number of possible predictors that were entered into the best subsets regression.  The output presents R2, adjusted R2, Mallow’s Cp, and S.  To determine the best model, these model fit statistics will be used in conjunction with one another.  R2and adjusted R2measure the coefficient of multiple determination and are used to determine the amount of predictability of the criterion variable based upon the set of predictor variables. Mallow’s Cp is a measure of bias or prediction error.  Sis the square root of the mean square error (MSE).

So, as i showed before, we do not have human intervention to select another best model. If model selects lower values of R2 than the best value, it takes in account lowest value of Mallows' Cp and vice versa. This model compare the results of all combinations and select the best input combination directly based on the suitable correlation coefficient and optimal values of statistical metrics.