Assessing Wet and Dry Periods Using Standardized Precipitation Index Fractal (SPIF) and Polygons: A Novel Approach

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Reviewer Report:

Standardized precipitation index fractal (SPIF) wet and dry polygons by Zekâi Şen

(Major Revision)

This manuscript tries to develop a new index for drought. The new index -- Standardized precipitation index fractal (SPIF) is based on an effective fractal geometric forecasting approach. The proposed index was applied on monthly rainfall records on the European side of the Istanbul Florya meteorological station in Turkey, and related results were presented. The manuscript is clear in the structure and easy to follow. However, there are some comments that should be addressed before the manuscript could be accepted.

1.     Line 20-21: provide “additional information”…, the author needs to summary the addition information as exactly what they are and explain in detail the “additional information” in the text.

2.     In the Introduction part: in this part, the author needs to explain clearly what is the disadvantages of the SPI, the motivation of the current research, the authors did mention SPI didn’t show patterns across different climate descriptions, did the SPIF solve this issue?

3.     For part 2: standard precipitation index probabilistic basis. This part should be shortened. I suggest combine Part 2 & 3 as “Method”

4.     Please provide a comparison between SPI and SPIF for the same record on the European side of the Istanbul Florya meteorological station in Turkey.

5.     The hydroclimate implications behind the new index should be discussed rather than present the method alone

Comments on the Quality of English Language

The manuscript is clear in the structure and easy to follow. 

Author Response

Reviewer #1

Thank you very much for your suggestions

(Major Revision)

This manuscript tries to develop a new index for drought. The new index -- Standardized precipitation index fractal (SPIF) is based on an effective fractal geometric forecasting approach. The proposed index was applied on monthly rainfall records on the European side of the Istanbul Florya meteorological station in Turkey, and related results were presented. The manuscript is clear in the structure and easy to follow. However, there are some comments that should be addressed before the manuscript could be accepted.

1. Line 20-21: provide “additional information”…, the author needs to summary the addition information as exactly what they are and explain in detail the “additional information” in the text. The sentence is expanded as “This methodology is referred to as SPI fractal (SPIF), and the classic SPI classification is converted into SPIF wet and dry polygons, which provide additional information about the drought period number within a valid polygonal area than the classic SPI results.”
2. In the Introduction part: in this part, the author needs to explain clearly what is the disadvantages of the SPI, the motivation of the current research, the authors did mention SPI didn’t show patterns across different climate descriptions, did the SPIF solve this issue? The proposal of these authors is further developed by the fractal SPIF methodology, which provides a number of different wet and dry period forecasts and thus allows drought risk calculations to be made objectively.

 

3. For part 2: standard precipitation index probabilistic basis. This part should be shortened. I suggest combine Part 2 & 3 as “Method” These two sections are combined under the section “2. SPI and SPIF methodologies”
4. Please provide a comparison between SPI and SPIF for the same record on the European side of the Istanbul Florya meteorological station in Turkey. This point is explained in the revised version at the end of section 2.
5. The hydroclimate implications behind the new index should be discussed rather than present the method alone. The discussion is enlarged in revised version.

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript provides an overview of a study proposing a new approach, referred to as SPI fractal (SPIF), for forecasting wet and dry periods based on historical records. The proposed methodology involves using a fractal geometric approach to analyze non-overlapping monthly duration dry periods in the standard precipitation index (SPI) classification. The results are presented as SPIF wet and dry polygons, which are suggested to offer additional information compared to the classic SPI results. The application of this methodology is demonstrated using monthly rainfall records from a specific meteorological station in Turkey.

 

Comments:

 

1.         Methodology Clarification:

What steps are involved in the proposed SPI fractal (SPIF) methodology for forecasting wet and dry periods?

2.         Fractal Geometry Explanation:

How does the utilization of fractal geometry enhance the understanding of wet and dry period formations in the context of SPI classification?

3.         Numerical Representation:

How does the proposed SPIF methodology address the numerical limitations in assessing the categorizations of wet and dry periods compared to the standard precipitation index (SPI)?

4.         Empirical Observations:

Could you elaborate on the observed relationship between the plotted periods on the double logarithmic paper and the power function in the SPIF methodology?

5.         Extension of Straight Line Significance:

What implications or insights are derived from extending the empirically derived straight line to forecast the number of periods that may occur over a range of SPI levels?

6.         Comparison with Classic SPI:

How do the SPIF wet and dry polygons provide additional information compared to the classic SPI results, and what aspects of wet and dry period features do they capture?

7.         SPIF Application:

Could you explain the rationale behind selecting the European side of the Istanbul Florya meteorological station in Turkey for applying the SPIF methodology?

8.         Data Considerations:

What types of historical records and data are utilized in applying the SPIF methodology, and how might variations in data affect the results?

9.         Practical Implications:

How can the SPIF wet and dry polygons generated through this methodology be practically applied in hydro-meteorological analyses or decision-making processes?

10.      Generalization of Results:

To what extent can the findings from applying the SPIF methodology in the Istanbul Florya meteorological station be generalized to other regions or meteorological stations?

 

 

Comments on the Quality of English Language

 Minor editing of English language required.

Author Response

Responses to reviewer 2

Reviewer#2

Thank you very much for constructive suggestions.

Comments and Suggestions for Authors

The manuscript provides an overview of a study proposing a new approach, referred to as SPI fractal (SPIF), for forecasting wet and dry periods based on historical records. The proposed methodology involves using a fractal geometric approach to analyze non-overlapping monthly duration dry periods in the standard precipitation index (SPI) classification. The results are presented as SPIF wet and dry polygons, which are suggested to offer additional information compared to the classic SPI results. The application of this methodology is demonstrated using monthly rainfall records from a specific meteorological station in Turkey.

 

Comments:

 

1. Methodology Clarification:

What steps are involved in the proposed SPI fractal (SPIF) methodology for forecasting wet and dry periods? As suggested by another reviewer, Sections 2 and 3 are combined under a new section with caption as “ SPI and SPIF methodologies” and the calculation steps for SPI and proposed SPIF are presented in Figure 1 and Figure 3, respectively

2. Fractal Geometry Explanation:

How does the utilization of fractal geometry enhance the understanding of wet and dry period formations in the context of SPI classification? SPI provides time series variation of wet and dry period classification after conversion of the original data probability distribution function (PDF) to standardized normal PDF with zero mean and unit standard deviation. SPIF gives the actual number of wet and dry spells without any classification but its change by period. Additionally, SPIF provides opportunities for future predictions by helping to determine the number of wet and dry periods over periods longer than the number of data points. Please see the end of Section “2 SPI and SPIF methodologies”

3. Numerical Representation:

How does the proposed SPIF methodology address the numerical limitations in assessing the categorizations of wet and dry periods compared to the standard precipitation index (SPI)? As described, SPI provides wet and dry spell classification based on the magnitude of the standardized normal (Gaussian) PDF, whereas SPIF, rather than classification, provides actual counts of possible wet and dry spell durations.

4. Empirical Observations:

Could you elaborate on the observed relationship between the plotted periods on the double logarithmic paper and the power function in the SPIF methodology? The power function is the general mathematical representation of a straight line on a double logarithmic paper graph.

5. Extension of Straight Line Significance:

What implications or insights are derived from extending the empirically derived straight line to forecast the number of periods that may occur over a range of SPI levels? The main meaning of an empirically derived straight line on a double logarithmic sheet is that the estimate of the number of wet and dry spells is spread over future periods. Please see below Figure 4 in the revised version.

6. Comparison with Classic SPI:

How do the SPIF wet and dry polygons provide additional information compared to the classic SPI results, and what aspects of wet and dry period features do they capture? There is no polygonal representation in the SPI approach, where only numerical values are categorized into a set of classes, as noted in Table 1. The polygonal SPIF representation provides the valid 2D relationship between the numbers of wet and dry periods and these periods, which cannot be obtained with the classic SIP method. Please see at the end of Section 4 in the revised version of the article.

7. SPIF Application:

Could you explain the rationale behind selecting the European side of the Istanbul Florya meteorological station in Turkey for applying the SPIF methodology? The application of the SPIF methodology to the Istanbul/Florya meteorological station provides an answer to the future wet and dry precipitation occurrences in different periods, which cannot be obtained with the classical SPI approach.

8. Data Considerations:

What types of historical records and data are utilized in applying the SPIF methodology, and how might variations in data affect the results? In the SPIF method application, monthly rainfall records are used as historical data. Changes in the data are highlighted fractally by double logarithmic (mathematical power function) calculations according to Eqs. (2) and (3). Please see the  “3. Applications” section

9. Practical Implications:

How can the SPIF wet and dry polygons generated through this methodology be practically applied in hydro-meteorological analyses or decision-making processes?  The generation of polygons in Figure 8 is based on numerical values in graphs of Figure 7 and they are collected in Table 3 and hence the plot of wet and dry period durations against the number of occurrences of these periods.

10. Generalization of Results:

To what extent can the findings from applying the SPIF methodology in the Istanbul Florya meteorological station be generalized to other regions or meteorological stations? This is explained in the text

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Overall, the paper is well-structured and informative. These suggestions aim to enhance clarity, provide a smoother flow, and emphasize key points throughout the abstract, introduction methodology, discussion and conclusion.

Title: 

The title "Standardized Precipitation Index Fractal (SPIF) Wet and Dry Polygons" is clear in its focus on SPIF and wet/dry polygons. However, you may want to consider making it more explicit or slightly more descriptive. For instance:

"Assessing Wet and Dry Periods Using Standardized Precipitation Index Fractal (SPIF) and Polygons: A Novel Approach"

This alternative title explicitly mentions the assessment of wet and dry periods, the use of SPIF, and highlights the novelty of the approach. Adjust it according to the specific emphasis of your study.

Abstract:

Clarify the novelty and significance of the SPIF methodology earlier in the abstract, emphasizing how it addresses the shortcomings of existing approaches.

Explicitly mention how the SPIF wet and dry polygons provide additional information compared to traditional SPI results. Briefly touch upon the real-world applications and benefits of this methodology.

Provide a concise overview of the results obtained from applying the methodology to monthly rainfall records in Istanbul. This can serve as a teaser for readers, prompting them to delve deeper into the paper.

Introduction:

Condense the introductory paragraphs for a more concise presentation of the background and motivation.

Smoothly transition from the general discussion on global warming and climate change to the specific focus on the Standard Precipitation Index (SPI) basis.

When introducing the SPIF version, provide a brief explanation or definition, ensuring that readers can easily grasp its essence.

Clearly convey the relevance of multifractal SPI and its connection to the current study. This will help readers understand the broader context of your research.

Clarity in Methodology Presentation:

Ensure a step-by-step explanation of the methodology is provided, especially in the calculation procedures. Break down complex procedures into smaller, digestible steps. This will enhance the reader's understanding and facilitate the reproducibility of your work.

For example, in Section 2 (Standard precipitation index probabilistic basis), you might consider:

- Clearly outlining the steps involved in calculating SPI.

- Provide additional explanations or examples where necessary to make the process more accessible to readers.

For Section 3 (Standard precipitation index fractal):

- Clarify the transition from SPI to SPI fractal. Clearly articulate how the SPI time series is prepared for fractal analysis.

- In Figure 3 and subsequent figures, provide clear annotations or labels for each step in the process. This will help readers follow the flow of the methodology.

Consistent Terminology:

Maintain consistency in the use of terminology. For instance, if you introduce SPIF (Standard Precipitation Index Fractal), ensure that this term is consistently used throughout the paper. This consistency aids in reader comprehension.

Visual Clarity:

Ensure figures and graphs are adequately labeled and explained. Figures 2 and 3 provide a visual representation of wet and dry periods and the SPI calculation flow chart, respectively. Adding clear labels and captions can enhance their interpretability.

Highlight Novelty:

In Section 3, emphasize the novelty of your approach. Clearly articulate how SPIF introduces a new perspective compared to classical SPI, and what advantages it brings to the analysis of wet and dry periods.

Discussion Section (Section 7):

   - Clearly articulate the advantages of the SPIF approach over the classical SPI. How does it enhance our understanding of wet and dry periods? Highlight the key differences and innovations.

   - Given the importance of graphical representations in your methodology, consider providing more detailed explanations or insights into the visual results. This could include specific observations from the graphs that support your discussion points.

   - Discuss the generalization of your findings. How applicable is the SPIF approach to other regions or climatic conditions? Address any limitations or constraints associated with the proposed method.

   - If applicable, discuss how the SPIF approach compares to other existing methods for assessing wet and dry periods. This could strengthen the argument for the novelty and effectiveness of your proposed method.

   - Discuss potential future research directions or applications that could build upon your work. Are there specific areas where the SPIF approach could be extended or modified for additional insights?

Conclusions Section (Section 8):

   - Provide a concise summary of the main findings of your study. Highlight the key contributions and insights gained through the SPIF approach.

   - Discuss the practical implications of your findings. How could the SPIF method be utilized in real-world scenarios, especially in the context of water resource management or meteorological applications?

   - Offer recommendations or suggestions for future researchers who might be interested in applying or further developing the SPIF approach. What aspects could be refined or expanded upon?

   - Ensure your concluding statements are clear and directly tied to the objectives and outcomes of your study. Reinforce the importance of your findings in the broader context of precipitation index research.

Comments on the Quality of English Language

Good!

Author Response

Responses to reviewer 3

Reviewer #3

Thank you very much for your detailed and constructive suggestions

Comments and Suggestions for Authors

Overall, the paper is well-structured and informative. These suggestions aim to enhance clarity, provide a smoother flow, and emphasize key points throughout the abstract, introduction methodology, discussion and conclusion.

Title: 

The title "Standardized Precipitation Index Fractal (SPIF) Wet and Dry Polygons" is clear in its focus on SPIF and wet/dry polygons. However, you may want to consider making it more explicit or slightly more descriptive. For instance:

"Assessing Wet and Dry Periods Using Standardized Precipitation Index Fractal (SPIF) and Polygons: A Novel Approach"

Thank you for such a proposal. The suggestion of the reviewer is taken into consideration and the new title is adopted as he suggested.

This alternative title explicitly mentions the assessment of wet and dry periods, the use of SPIF, and highlights the novelty of the approach. Adjust it according to the specific emphasis of your study.

Abstract:

Clarify the novelty and significance of the SPIF methodology earlier in the abstract, emphasizing how it addresses the shortcomings of existing approaches.

Explicitly mention how the SPIF wet and dry polygons provide additional information compared to traditional SPI results. Briefly touch upon the real-world applications and benefits of this methodology. IN the abstract the sentence is augmented as “This methodology is referred to as SPI fractal (SPIF), and the classic SPI classification is converted into SPIF wet and dry polygons, which provide additional information about the drought period number within a valid polygonal area than the classic SPI results.”

Provide a concise overview of the results obtained from applying the methodology to monthly rainfall records in Istanbul. This can serve as a teaser for readers, prompting them to delve deeper into the paper.

Introduction:

Condense the introductory paragraphs for a more concise presentation of the background and motivation.

Smoothly transition from the general discussion on global warming and climate change to the specific focus on the Standard Precipitation Index (SPI) basis.

When introducing the SPIF version, provide a brief explanation or definition, ensuring that readers can easily grasp its essence.

Clearly convey the relevance of multifractal SPI and its connection to the current study. This will help readers understand the broader context of your research.

Clarity in Methodology Presentation:

Ensure a step-by-step explanation of the methodology is provided, especially in the calculation procedures. Break down complex procedures into smaller, digestible steps. This will enhance the reader's understanding and facilitate the reproducibility of your work.

For example, in Section 2 (Standard precipitation index probabilistic basis), you might consider:

- Clearly outlining the steps involved in calculating SPI. In Figure 1 step by step calculations are given in a flow chart.

- Provide additional explanations or examples where necessary to make the process more accessible to readers.

For Section 3 (Standard precipitation index fractal):

- Clarify the transition from SPI to SPI fractal. Clearly articulate how the SPI time series is prepared for fractal analysis.

Sections 2 and 3 are combined as the suggestion of another reviewer and thus the step by step calculation is provided in “Figure 1 SPI calculation flow chart” Also “Figure 3. SPIF calculation steps” explains step by step SPIF methodology calculation

- In Figure 3 and subsequent figures, provide clear annotations or labels for each step in the process. This will help readers follow the flow of the methodology.

Consistent Terminology:

Maintain consistency in the use of terminology. For instance, if you introduce SPIF (Standard Precipitation Index Fractal), ensure that this term is consistently used throughout the paper. This consistency aids in reader comprehension. This terminology is mentioned consistently throughout the text.

Visual Clarity:

Ensure figures and graphs are adequately labeled and explained. Figures 2 and 3 provide a visual representation of wet and dry periods and the SPI calculation flow chart, respectively. Adding clear labels and captions can enhance their interpretability. All the labels are clearly explained in the text.

Highlight Novelty:

In Section 3, emphasize the novelty of your approach. Clearly articulate how SPIF introduces a new perspective compared to classical SPI, and what advantages it brings to the analysis of wet and dry periods. At the suggestion of one of the reviewers, sections 2 and 3 have been combined, resulting in a better explanation of the comparison of classical SPI and innovative SPIF.

Discussion Section (Section 7):

   - Clearly articulate the advantages of the SPIF approach over the classical SPI. How does it enhance our understanding of wet and dry periods? Highlight the key differences and innovations. The key differences are highlighted also in the application section

   - Given the importance of graphical representations in your methodology, consider providing more detailed explanations or insights into the visual results. This could include specific observations from the graphs that support your discussion points. The graphs are explained adequately in the text.

   - Discuss the generalization of your findings. How applicable is the SPIF approach to other regions or climatic conditions? Address any limitations or constraints associated with the proposed method. These points are discussed in different parts of the sections in the text.

   - If applicable, discuss how the SPIF approach compares to other existing methods for assessing wet and dry periods. This could strengthen the argument for the novelty and effectiveness of your proposed method. This point is also explained in the text.

   - Discuss potential future research directions or applications that could build upon your work. Are there specific areas where the SPIF approach could be extended or modified for additional insights? Potential research proposals are provided in the conclusion section.

Conclusions Section (Section 8):

   - Provide a concise summary of the main findings of your study. Highlight the key contributions and insights gained through the SPIF approach. The insight gained from the SPIF methodology is to estimate the actual number of wet and dry spell forecasts for a set of periods based on the fractal conceptual methodology. While the classical SPI approach helps in classifying wet and dry spells, the proposed SPIF methodology provides variation of actual numbers based on past monthly rainfall records and helps in predicting future numbers of wet and dry spells through a straight line as representation of fractals on double logarithmic. paper.

   - Discuss the practical implications of your findings. How could the SPIF method be utilized in real-world scenarios, especially in the context of water resource management or meteorological applications? The SPIF methodology can be used for water balance studies between wet and dry periods in real-world scenarios in the context of water resources management and for meteorological drought analysis in the context of meteorological applications.

   - Offer recommendations or suggestions for future researchers who might be interested in applying or further developing the SPIF approach. What aspects could be refined or expanded upon? As for future research, the SPIF methodology can be extended not only to the number of wet and dry spells but also to their length, drought magnitude and intensity concepts.

   - Ensure your concluding statements are clear and directly tied to the objectives and outcomes of your study. Reinforce the importance of your findings in the broader context of precipitation index research. In classical drought analysis studies, digital prime numbers are taken as basis, regardless of the importance of fractal features in studies of drought quantities such as length (period), size and severity. However, the SPIF method relies on fractal features for a precise prediction approach.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have addressed my comments; this manuscript is acceptable for publication in its present form.