Enhancing Drought Forecast Accuracy Through Informer Model Optimization

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript evaluates 4 methods to forecast the drought index SPEI. The authors conclude that the hybrid model of VMD-JAYA-Informer outperforms the other three ones. Here are some comments for author to consider:

Line 3-5, It is confusing, you assessed Informer, but not mentioned in here.

Line 6, what does VMD-JATA stand for?

Line 12, NSE?  …other evaluation indices?  Be specific.

The abstract needs to be more specific and summarized, current is a bit messy in terms of logic.

Line 52- 53, why did you choose SPEI? Like other drought index, e.g., SPI also considered time dependence.

Line 54, these modeling? Be specific.

Line 60, 0.09 or 0.33?

Line 94-115, this paragraph can be moved before the literature review of drought modeling using varied methods.

Line 124, VMD-JAYA-LATM? Typo?

Line 128, Since you have not started your storyline, this is inappropriate to indicate any conclusive information.

Line 139-147, how many climate stations were used to train these modes? Particularly, attention models are extensive data needed.

Line 306-337, There sentences are repetitive and less informative, please consider revising them. By the way, Are you able to visualize the contribution of the each IFM, which would beneficial the reading.

Line 386-388, There are lots of optimization packages available, why are you able to argument this conclusion? Clarifying it.

Please pay attention when you are writing a manuscript, there are lots of grammar errors and typos!

 

 

 

 

 

 

Comments on the Quality of English Language

n/a

Author Response

Dear Reviewer,

Thank you for your careful review and the insightful comments on our manuscript titled "Enhancing Drought Forecast Accuracy through Informer Model Optimization". Your detailed comments and insightful critiques are not only appreciated but have been instrumental in highlighting areas that required improvement and in guiding our efforts to enhance the quality of our work. Each point you raised was carefully considered and served as a valuable compass in our revision process.We recognize the extensive expertise each reviewer brings to the table, and it is clear from your comments that you have engaged deeply with our text, offering both challenging questions and constructive feedback. This kind of detailed review process is essential for the advancement of knowledge within our field.

We have carefully considered all your suggestions and have made comprehensive revisions to our manuscript. Below, I have detailed our responses to each of your comments, indicating how we have addressed them in the revised submission.

 

 

Comments 1:Line 3-5, It is confusing, you assessed Informer, but not mentioned in here.

Response 1: I mentioned Informer model. ” This paper employed the Informer model to forecast drought and conducted a comparative analysis with the Autoregressive Integrated Moving Average (ARIMA), Long Short-Term Memory (LSTM), and Convolutional Neural Network (CNN) models. The findings indicate that the Informer model outperforms the other three models in terms of drought forecasting accuracy across all time scales. Nevertheless, the predictive capacity of the Informer model remains suboptimal when it comes to short-term intervals.”
Comments 2:what does VMD-JATA stand for?

Response 2: In the abstract, I changed “This work suggests a drought forecasting system called VMD-JAYA-Informer to enhance the accuracy of predicting droughts on short time scales.” to “Aiming at the problem of drought forecasting accuracy in short time scale, this study proposed a drought forecasting model named VMD-JAYA-Informer based on Variational Mode Decomposition (VMD) and JAVA optimization algorithm to improve Informer.”

Comments 3:Line 12, NSE?  …other evaluation indices?  Be specific.

Response 3: I changed “The performance of these models was evaluated using NSE and other evaluation indexes.” to “The performance of these models was evaluated using Root Mean Square Error(RMSE),Nash-Sutcliffe efficiency coefficient(NSE) and Mean Absolute Error(MAE)”

Comments 4:Line 52- 53, why did you choose SPEI? Like other drought index, e.g., SPI also considered time dependence.

Response 4: In the introduction, we analyzed the strength and weaknesses of several drought indices and explained why SPEI should be used, in line98-line12.

In previous research, the precise measurement of regional drought is typically achieved by utilizing a drought index. This index is widely employed for the purpose of monitoring and evaluating drought conditions or spatiotemporal characteristics . Commonly utilized drought metrics in studies encompass the Z index ,Meteorological Drought Composite Index (CI), Palmer Drought Severity Index (PDSI), Standardized Precipitation Index (SPI), Standardized Precipitation Evapotranspiration Index (SPEI), and others. The Palmer Drought Severity Index (PDSI) is a meteorological drought measure introduced by Palmer in 1965. It is used to analyze regional water balance by distinguishing between dry and wet periods. Nevertheless, the PDSI calculation heavily relies on meteorological station data at a specific location, which greatly hampers its capacity to evaluate drought conditions across different areas. As a result, the index falls short in regionalizing drought and is not highly effective in monitoring short-term drought or in diverse climate regions. SPI utilizes long-term monthly precipitation data within a specific range and incorporates various time scales to measure the excess or deficiency of precipitation. This allows for the identification of drought and wet periods, as well as the determination of drought severity and duration in a particular region. SPI is determined by analyzing long-term precipitation data for a specific location. The calculation process is straightforward and can be applied to various climate conditions. However, it does not take into account the impact of temperature, wind speed, and other meteorological factors on evapotranspiration. Therefore, it is not suitable for analyzing the impact of climate change on evapotranspiration. SPEI, a novel drought index introduced by Vicente-Serrano et al. in 2010, aims to overcome the constraints of the aforementioned drought indices and the SPEI data consists of time-series data that exhibits multiple time scales. Hence, the drought index employed in this study is the SPEI.

Comments 5:Line 54, these modeling? Be specific.

Response 5:We replaced “these models” to “Drought forecasting”.

Comments 6:Line 60, 0.09 or 0.33?

Response 6:Sorry this is a problem due to latex compilation issues.Actually, it is 0.09 - 0.33.

Comments 7:Line 94-115, this paragraph can be moved before the literature review of drought modeling using varied methods.

Response 7:This paragraph have been moved before the literature review of drought modeling using varied methods in line 53 .

Comments 8:Line 124, VMD-JAYA-LATM? Typo?

Response 8:This is our mistake, it should be VMD-JAYA-LSTM here.

Comments 9:Line 128, Since you have not started your storyline, this is inappropriate to indicate any conclusive information.

Response 9:We have deleted “The research showed that VMD-JAYA-Informer is suitable for forecasting drought across many time scales.”

Comments 10:Line 139-147, how many climate stations were used to train these modes? Particularly, attention models are extensive data needed.

Response 10:We used 100 stations data to train these models.

Comments 11:Line 306-337, There sentences are repetitive and less informative, please consider revising them. By the way, Are you able to visualize the contribution of the each IFM, which would beneficial the reading.

Response 11: We have made changes and added the content about VMD decomposition and related charts in line315-line340, the additions are as follows.

“Constructing the VMD algorithm typically requires determining four parameters, namely, Number of Modes(K), Penalization Factor(α), Noise Tolerance(τ) and Convergence Criterion Tolerance(ε). Compared to K, α, τ and ε have less impact on the decomposition effect of SPEI sequences and are usually using their default values. When the K value is smaller, the VMD algorithm is in an under-decomposition state, and the main frequency signal contained in the SPEI series cannot be fully decomposed. Nevertheless, selecting a substantial value for K results in the central frequencies of neighboring modal components being closer together, potentially resulting in modal repetition or increased noise generation. Tang et al. calculated the IMFs central frequencies obtained for a given range of K values, which resulted in appropriate K values. This paper uses SPEI1 data as an example, and Table 3 shows the IMFs central frequencies generated by the K values within the established range.

From Table 3, when K=7, the central frequencies of IMF6 and IMF7 are similar, indicating that the decomposition of SPEI data by VMD might be in an over-decomposed state. Therefore, k is set to 6. In this paper, the default values are used for the other parameters of the VMD algorithm.

The results of the SPEI decomposition at 1, 3, 6, 9, 12, and 24-month time scales are presented in Figures 8 to 13. The figures demonstrate that the VMD algorithm decomposes the SPEI sequence across multiple time scales into six components with distinct frequencies. VMD, as an adaptive frequency decomposition method, decomposes the SPEI time series data into six SPEI components. This decomposition enhances comprehension of the frequency characteristics and periodic variations in SPEI data, facilitating the identification of notable frequency components and cycles across various temporal scales. The resulting sequences not only eliminate the noise interference but also more accurately capture the periodic oscillation trends in SPEI.

”.

Comments 12:There are lots of optimization packages available, why are you able to argument this conclusion? Clarifying it.

Response 12:We added in line342 - line348 about JAYA parameter optimization.

Comments 13:Please pay attention when you are writing a manuscript, there are lots of grammar errors and typos!

Response 13:Thank you very much for your valuable suggestions. We have further optimized and polished the entire document.

We've also done a full English touch-up of the entire paper.

Thank you once again for your time and thoughtful review. We hope that the revisions we have made address your concerns, and that the revised manuscript meets your approval.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Overall, the paper presents an interesting contribution to the field. However, several significant issues need to be addressed before the manuscript can be considered for publication. I recommend rejection at this stage, with encouragement for the authors to make the following major revisions:

(1) The paper contains many abbreviations/acronyms that are not defined or introduced (e.g., CEEMD, CNN, RNN, LSTM, ARIMA, and several others). This makes it more challenging to ascertain the paper's intended meaning. Please check the whole manuscript regarding this issue. Abbreviations should be defined at first mention and used consistently after that.

(2) A specific table or subsection detailing the parameters used for CNN, VMD, JAYA, and others used, along with the initialization values, the tuning process during the experiments, and the justification for the chosen values (whether based on literature or experimentation).

(3) The results lack clarity. Providing details on how the parameters were tuned adds credibility to the findings, especially for complex models like Informer.

(4) The paper mentions that JAYA optimizes the hyperparameters of the Informer model but does not provide details about the stopping criteria or the search space, including the upper and lower bounds for the optimizable parameters (e.g., learning rate ranging from 0.001 to 0.1).

(5) The authors should specify which hyperparameters were optimized and present the results of the optimization, including the final values determined by JAYA.

(6) How was the dataset divided between training, validation, and testing?

(7) Were the splits based on a temporal strategy (e.g., older data for training and newer data for testing), or was a random split used? What percentage of the data was allocated to each set?

(8) For example, how much data was assigned to training, validation, and testing (e.g., 80% training, 10% validation, 10% testing)? Was cross-validation employed, or was a fixed split of training and testing sets used?

(9) If cross-validation was used, what method was employed (e.g., k-fold, leave-one-out)? If a fixed split was used, how was it ensured that the testing set was independent and representative?

(10) Finally, I believe it would be beneficial to present the results obtained using the test dataset rather than the corresponding training data. This will provide a more accurate assessment of the model's generalization capability and performance on unseen data.

Author Response

Dear Reviewer,

Thank you for your careful review and the insightful comments on our manuscript titled "Enhancing Drought Forecast Accuracy through Informer Model Optimization". Your detailed comments and insightful critiques are not only appreciated but have been instrumental in highlighting areas that required improvement and in guiding our efforts to enhance the quality of our work. Each point you raised was carefully considered and served as a valuable compass in our revision process.We recognize the extensive expertise each reviewer brings to the table, and it is clear from your comments that you have engaged deeply with our text, offering both challenging questions and constructive feedback. This kind of detailed review process is essential for the advancement of knowledge within our field.

We have carefully considered all your suggestions and have made comprehensive revisions to our manuscript. Below, I have detailed our responses to each of your comments, indicating how we have addressed them in the revised submission.

 

Comments 1:The paper contains many abbreviations/acronyms that are not defined or introduced (e.g., CEEMD, CNN, RNN, LSTM, ARIMA, and several others). This makes it more challenging to ascertain the paper's intended meaning. Please check the whole manuscript regarding this issue. Abbreviations should be defined at first mention and used consistently after that.

Response 1:We have carefully checked. Abbreviations have been defined at first mention .

Comments 2:A specific table or subsection detailing the parameters used for CNN, VMD, JAYA, and others used, along with the initialization values, the tuning process during the experiments, and the justification for the chosen values (whether based on literature or experimentation).

Response 2: We provide a detailed explanation for the chosen values in lines 279 to 282, and list the parameters for CNN, LSTM, ARIMA, and Informer in Table 2.

In line315-line340, we added the parameter selection of VMD and the content of experimental results, and added Table 3 and Figure 8-13. The additions are as follows.

“Constructing the VMD algorithm typically requires determining four parameters, namely, Number of Modes(K), Penalization Factor(α), Noise Tolerance(τ) and Convergence Criterion Tolerance(ε). Compared to K, α, τ and ε have less impact on the decomposition effect of SPEI sequences and are usually using their default values. When the K value is smaller, the VMD algorithm is in an under-decomposition state, and the main frequency signal contained in the SPEI series cannot be fully decomposed. Nevertheless, selecting a substantial value for K results in the central frequencies of neighboring modal components being closer together, potentially resulting in modal repetition or increased noise generation. Tang et al. calculated the IMFs central frequencies obtained for a given range of K values, which resulted in appropriate K values. This paper uses SPEI1 data as an example, and Table 3 shows the IMFs central frequencies generated by the K values within the established range.

From Table 3, when K=7, the central frequencies of IMF6 and IMF7 are similar, indicating that the decomposition of SPEI data by VMD might be in an over-decomposed state. Therefore, k is set to 6. In this paper, the default values are used for the other parameters of the VMD algorithm.

The results of the SPEI decomposition at 1, 3, 6, 9, 12, and 24-month time scales are presented in Figures 8 to 13. The figures demonstrate that the VMD algorithm decomposes the SPEI sequence across multiple time scales into six components with distinct frequencies. VMD, as an adaptive frequency decomposition method, decomposes the SPEI time series data into six SPEI components. This decomposition enhances comprehension of the frequency characteristics and periodic variations in SPEI data, facilitating the identification of notable frequency components and cycles across various temporal scales. The resulting sequences not only eliminate the noise interference but also more accurately capture the periodic oscillation trends in SPEI.

”.

A salient characteristic of the JAYA algorithm is its parameter-free nature, indicating that in its standard implementation, there is no requirement to establish conventional parameters (such as crossover rate, mutation rate, etc.). The fundamental idea of the JAYA algorithm is to directly guide the search process towards an optimal solution, adjusting the search direction based on the performance of the individuals.

Comments 3:The results lack clarity. Providing details on how the parameters were tuned adds credibility to the findings, especially for complex models like Informer.

Response 3:For the model before improvement, the main parameters involved in the model and their values are shown in Table 2. The parameter values are predominantly established according to existing literature[ 24-26 ,28 , 30] and experimental results, whereas other parameters utilize the default values.We chose to adjust the parameters manually to ensure that the model achieves optimal performance.”

Comments 4: The paper mentions that JAYA optimizes the hyperparameters of the Informer model but does not provide details about the stopping criteria or the search space, including the upper and lower bounds for the optimizable parameters (e.g., learning rate ranging from 0.001 to 0.1).

Response 4: In line341-line348,we added Table 4, which describes the parameters that were optimized by JAYA for several models, the parameter optimization search space, and the parameter values obtained after optimization.

We added the content”In this study, we employed the JAYA algorithm to optimize key parameters of the LSTM, ARIMA, CNN, and Informer models. The JAYA algorithm is a parameter-free optimization technique that updates parameter values by identifying the differences between the current solution and both the best and worst solutions to achieve global optimality. To ensure optimal performance of the model, the key parameters optimized, their search spaces, and the optimal parameter values determined using the JAYA algorithm are presented in Table4.”.

Comments 5:The authors should specify which hyperparameters were optimized and present the results of the optimization, including the final values determined by JAYA.

Response 5: In line341-line348,we added Table 4, which describes the parameters that were optimized by JAYA for several models, the parameter optimization search space, and the parameter values obtained after optimization.

We added the content”In this study, we employed the JAYA algorithm to optimize key parameters of the LSTM, ARIMA, CNN, and Informer models. The JAYA algorithm is a parameter-free optimization technique that updates parameter values by identifying the differences between the current solution and both the best and worst solutions to achieve global optimality. To ensure optimal performance of the model, the key parameters optimized, their search spaces, and the optimal parameter values determined using the JAYA algorithm are presented in Table4.”.

Comments 6: How was the dataset divided between training, validation, and testing?

Response 6: In the experiment, the dataset is divided as follows: training set 70%,validation set 10%, testing set 20%.

Comments 7:Were the splits based on a temporal strategy (e.g., older data for training and newer data for testing), or was a random split used? What percentage of the data was allocated to each set?

Response 7: The dataset is segmented based on time series.In the experiment, the dataset is divided as follows: training set 70%,validation set 10%, testing set 20%.

Comments 8: For example, how much data was assigned to training, validation, and testing (e.g., 80% training, 10% validation, 10% testing)? Was cross-validation employed, or was a fixed split of training and testing sets used?

Response 8:In the experiment, the dataset is divided as follows: training set 70%,validation set 10%, testing set 20%. We was not employed cross-validation. We used fixed split of training and testing sets.

Comments 9:If cross-validation was used, what method was employed (e.g., k-fold, leave-one-out)? If a fixed split was used, how was it ensured that the testing set was independent and representative?

Response 9: We was not employed cross-validation. We used fixed split of training and testing sets. For fixed splitting, we ensure that the validation and test sets maintain temporal continuity and do not overlap with the training set in terms of time. Additionally, we validate the stability and consistency of the model by conducting multiple independent tests across different time periods during the model development phase.

Comments 10: Finally, I believe it would be beneficial to present the results obtained using the test dataset rather than the corresponding training data. This will provide a more accurate assessment of the model's generalization capability and performance on unseen data.

Response 10: Our study originally utilizes the test dataset to present the results.

Thank you once again for your time and thoughtful review. We hope that the revisions we have made address your concerns, and that the revised manuscript meets your approval.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The revised version of the manuscript satisfactorily addresses most of my concerns. It has been improved in readability and focuses more on the research goal. This manuscript is suitable for publication.

Therefore, I have no further comments.