Long Memory Cointegration in the Analysis of Maximum, Minimum and Range Temperatures in Africa: Implications for Climate Change

Round 1

Reviewer 1 Report (Previous Reviewer 1)

Thanks to the authors for their efforts in responding to reviewers’ comments. The article has been much improved. However, there are a number of issues that still need to be carefully addressed, as outlined below, to provide the article with its maximum impact.

 

1. Section 4: I still find these big tables very confusing. Displaying results only in tabular form is not perfect and intuitive. I highly recommend adding more figures to visualize the results, because I want to know the spatial distribution of the results.

2. Adding a comparison with previous results can help to emphasizes the reliability of the results and uniqueness of this manuscript, and to enrich the content of the paper.

3. Figure 1: I suggest that the equator be changed to a dotted line, and that the north arrow, scale and elevation be added.

4. Figure 2: The words in Figure 2 are incomplete, need to be modified.

5. I still insist that the quality of data is the first prerequisite for this work. The authors should make it clear whether the datasets from the World Bank Climate Change Knowledge Portal have undergone a quality control process. Otherwise, extreme phenomena caused by outliers are very unconvincing.

6. There's an extra dot in the title, such 1. . Introduction, 4. . Conclusion.

English need to be further improved.

Author Response

Comments to Reviewer # 1

 

We thank this reviewer for all his (her) interesting comments. The reviewer is in favour of the publication of the manuscript, and he/she only reports six minor comments:

 

1.)        “Section 4: I still find these big tables very confusing. Displaying results only in tabular form is not perfect and intuitive. I highly recommend adding more figures to visualize the results, because I want to know the spatial distribution of the results.”

Reply:             The results in the tables in Section 4 cannot be adequately displayed in figures. We believe that the readers would be able to understand the results presented. We have really thought on this further, and we have included instead an African map in the introduction, see new Figure 1, and another Figure (n. 2) displaying min and max temperature values of six African countries.

 

2.)        “Adding a comparison with previous results can help to emphasizes the reliability of the results and uniqueness of this manuscript, and to enrich the content of the paper.”

Reply:             The most related research to our work is Carcel and Gil-Alana (2015), which has been reviewed in the literature review part. In that work the authors found a significant temperature rise, 30 years before 2015 in the case of Kenya, while no trends were found for South Africa and Cote d’Ivoire.  They used the fractional integration approach but no cointegration was employed.

We have also included the following sentence in the conclusion:

 “ … Few papers along this line are those of Gil-Alana, Yaya and Fagbamigbe, (2019), and Gil-Alana (2003, 2008, 2012), among others. …”.

 

3.)         “Figure 1: I suggest that the equator be changed to a dotted line, and that the north arrow, scale and elevation be added.”

Reply:             We have included the following African map:

Source: authors simulated it using R programming.     

 

4.)        “Figure 2: The words in Figure 2 are incomplete, need to be modified”

Reply:             As far as we can see, the words in Figure 2 are complete. We could not identify any incomplete word.

 

5.)         “I still insist that the quality of data is the first prerequisite for this work. The authors should make it clear whether the datasets from the World Bank Climate Change Knowledge Portal have undergone a quality control process. Otherwise, extreme phenomena caused by outliers are very unconvincing.”

Reply:            See below as curled from the World Bank Climate Change Knowledge Portal:

“ … The CRU TS version 4.04 gridded historical dataset is derived from observational data and provides quality controlled temperature and rainfall values from thousands of weather stations worldwide, as well as derivative products including monthly climatologies and long term historical climatologies. The dataset is produced by the Climatic Research Unit (CRU) of the University of East Anglia (UEA) CRU- (Gridded Product). …”.

Also,

“ … In order to present historical climate conditions, the World Bank Group’s Climate Change Knowledge Portal (CCKP) uses the globally available observational datasets derived from CRU. These datasets are widely accepted as reference for the baseline in climate research. The historical trend information presented in the CCKP Portal uses CRU data to quantify changes in mean annual temperature and mean annual precipitation, for the period: 1901 to 2019.2 To test the ability of the models to represent the historical climate, simulations of that historical past (for the same period as the data available for CRU) are compared against CRU. To evaluate projected temperature and precipitation, the model’s representation of the seasonal cycle (monthly values for key variables) is additionally evaluated with respect to historic values. The same thresholds and assumptions to categorize the observed changes have been used as for the projected changes. …”.

Source: CCKP_Metadata_Final_January2021.pdf (worldbank.org)

 

6.)        “There's an extra dot in the title, such 1. . Introduction, 4. . Conclusion.”

Reply:             Thanks for catching these. These have been corrected in the new version of the manuscript.

 

7.)        “English need to be further improved”

Reply:             Thanks for the comment. This have been improved in the new version of the manuscript.

 

 

Reviewer 2 Report (Previous Reviewer 2)

The authors have made the amendments according the reviewer's comments, and the relevant replies are also reasonable. The suggestion is to publish the revised version. 

Author Response

Comments to Reviewer # 2

 

We thank this reviewer for all his (her) interesting comments and recognition of the impact of this research. The reviewer is in favour of the publication of the manuscript with no further comment.

 

Reviewer 3 Report (Previous Reviewer 3)

This version is an slight improvement over the previous one, but I still miss the theoretical grounding of the study (including some maps of Africa and updating the CC report does not count as a theoretical support). This is a well performed fractional cointegration analysis technically speaking, but the specification (two endogenous variables, max and min) comes from out of the blue. Temperature dynamics are more complex than this. 

No comments, It is good enough.

Author Response

Comments to Reviewer # 3

 

We thank this reviewer for all his (her) interesting comments and recognition of the impact of this research. The reviewer recognizes the improvement in the revised manuscript but believe still that improvement is required:

 

 

Comment.

“This version is an slight improvement over the previous one, but I still miss the theoretical grounding of the study (including some maps of Africa and updating the CC report does not count as a theoretical support). This is a well performed fractional cointegration analysis technically speaking, but the specification (two endogenous variables, max and min) comes from out of the blue. Temperature dynamics are more complex than this.” 

Reply:            Many thanks for these comments. We agree with the reviewer that the paper may improve with a theoretical model behind. However, this is an empirical paper using econometric techniques to analyze climatic variables. We hope that if the paper is accepted in Atmosphere, it will gain readerships of climate scientists and will serve as a source to cite.

 

Pardon us for the data limitations but this paper must be seen as an eye opener to future similar papers to be published in Atmosphere.

 

Reviewer 4 Report (Previous Reviewer 4)

The authors have addressed most of my earlier comments, and the quality of the manuscript is improved. Additional minor comments can be found below.

 

Line 150: What is CC? Climate change? Did you define the acronym?

Line 167: “distribution” to “time series”.

Lines 170-171: delete the sentence “In each case, both the maximum and minimum temperatures are plotted on the left vertical axis as shown in Figure 1.”

Line 185: Delete “sample”.

Line 188: Delete “trend”. No trend analysis has been done until now.

Line 209: “dependenc” to “dependence”

Line 221-222: What do you mean by “we will LRD or shift or shift in mean state”?

Line 245: “in annual temperature series” to “is annual temperature series”?

Author Response

Comments to Reviewer # 4

 

We thank this reviewer for all his (her) interesting comments and recognition of the impact of this research. The reviewer recognizes the improvement in the revised manuscript and provide minor comments:

 

1).        “Line 150: What is CC? Climate change? Did you define the acronym?”

 

This has been updated.

 

2).        “Line 167: “distribution” to “time series”.”

 

This has been updated.

 

3).        “Lines 170-171: delete the sentence “In each case, both the maximum and minimum temperatures are plotted on the left vertical axis as shown in Figure 1.”

 

This has been updated.

 

4).        “Line 185: Delete “sample”.”

 

This has been updated.

 

 

5).        “Line 188: Delete “trend”. No trend analysis has been done until now.”

 

This has been updated.

 

 

6)         “Line 209: “dependenc” to “dependence”.”

 

This has been updated.

 

 

7).        “Line 221-222: What do you mean by “we will LRD or shift or shift in mean state”?”

 

Words were omitted here. This has been addressed.

 

 

8).        “Line 245: “in annual temperature series” to “is annual temperature series”?”

 

This has been updated.

 

 

 

Other minor changes

1.)       When listing a group of papers they have been ordered chronologically.

2.)       Comments from the Editor and four anonymous reviewers are gratefully acknowledged.

3.)       All changes in the manuscript have been marked in red.

 

Round 2

Reviewer 1 Report (Previous Reviewer 1)

The authors have replied my comments well. No other comments are given.  I suggest the manuscript can be published in Atmosphere.

The English is now relatively good. 

Reviewer 3 Report (Previous Reviewer 3)

I understand the argument in the author´s last reply. I don´t fully agree with it, but it is my understanding that the other 3 referees are satisfied with the contents of the manuscript. It would be nice if, in future papers, a theoretical grounding is provided.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comment:

This paper investigates persistence and linear trends in the maximum and minimum annual average temperatures in 36 African countries. It is an important topic that allows for proper understanding of historical temperature patterns in Africa, which is crucial for predicting and mitigating the impacts of climate change. Moreover, it helps in studying the large-scale climate patterns that influence African’s climate in its different regions. While there have been previous studies of African temperature, the use of a long memory model based on fractional integration and cointegration is relatively novel and the authors do demonstrate that their method has utility for studies of African temperature. The paper is certainly suitable for publication in atmosphere, but I have some concerns about the results and its presentation, and how the results relate to previous studies of African climate variability, that need to be addressed before the paper is suitable for publication.

1. I strongly recommend reframing the article, putting data before methods, and adding a study area map. It is not perfect and intuitive to display the result only in the form of table. It is recommended to add more figures to visualize the result. This entire section could be extended because it's an important part of the manuscript. The discussion and conclusion can be placed in one section, adding the comparison with previous results, in order to emphasizes the reliability of the results and uniqueness and of this manuscript.

2. Section 2 describes the statistical methods used in the paper, testing for fractional integration and cointegration are difficult to follow, due to using highly technical and specialized language. We consider that at this point, the methodology is not explained clearly enough or in sufficient detail so that the paper's scientific conclusions could be tested by others. My (strong) recommendation is that this section should be rewritten.

3. Section 2. It really missing an introductory sentence or two as to how you are going to be using this method before you describe it. Else, the reader is in the dark until we get to the results section.

4. What about the quality of data used in this paper? Can the data be trusted? The influence of outliers on the calculation of maximum, minimum and range temperatures is very large.

5. It is suggested to anomaly the data to reduce the influence of outliers, and to make the variability of maximum and minimum temperature values in Figure 1 more obvious. Moreover, the words in Figure 1 are incomplete, need to be modified.

6. Introduction should be rephrased because none of these findings are new. For example, IPCC,2014 can be replaced with IPCC AR6. It is recommended to add the latest research results.

7. It is recommended to indicate the URL link of the data source. For example, the World Bank Climate Change Knowledge Portal.

8. It is recommended to retain two decimal places in the whole text.

9. Many of the references are out of alphabetical order. And please check the citation format of references.

10. Abstract should be further condensed to reflect the innovation and academic value of this paper.

Minor editing of English language required

Reviewer 2 Report

1)Africa is one of the most sensitive regions to global climate change. The study on the time-varying characteristics of temperature in Africa will help to improve the understanding of the implact of gloal warming on Africa.

2)The approach used in this manuscript checking trend and future predictions based on fractional integration is innovative and rarely adopted in climatological studies. 

3）For the results such as show in table 2 and 3, it is recommended that to add some figures to present appropriately on a map, to increase the readability of the full text.

 

 

Reviewer 3 Report

The manuscript employs a dataset of 36 African nations (maximum, minimum, and its difference, range of temperature). Then, the authors estimate the fractional integration order of each series, test whether the maximum and minimum series (fractionally) cointegrate in a linear trend model, estimated via the narrow band frequency domain least squares technique (Nielsen, 2015). This studied is carried out on a country basis (this is, there are 36 estimates). The authors find evidence of cointegration and fractional cointegration for only 19 countries and consider that this retrieval implies that the exposure to climatic change of these 19 countries is higher than in the remaining 17 countries.  

 

Main comment: I fail to grasp the interest of this study. The authors find evidence of rising temperatures for all countries except Liberia and Sierra Leone) through a fairly simple deterministic trend model (this is, an eq. with a constant term and a linear trend) and then look for evidence of a long term relationship between the max and a minimum temperature. They make the claim that failing to find it (this is the evidence of cointegration) implies that the country is at higher CC risk. Why? It may be intuitive, but the lack of a geophysical interpretation makes the argument rather weak. What is this relationship supposed to be, according to physics? Moreover, the study spans a large period (121 years, using annual data). I see two potential pitfalls in this: First, the quality of temperature measurements over a Century. Second The last century was a particularly convulse era of humankind; heterogeneity (changes in the variance) and stability (structural breaks) in the data because of this should at least be controlled.

This econometric analysis is correct and well done, but there is no underlying model and therefore, the interpretation of the results is compromised. This manuscript seems to present a fairly simple econometric exercise that lacks theoretical grounding.

It is well known that it is difficult to stablish causal links in time-series analysis; nonetheless, a theoretical model that justifies the econometric specification (at least partially) would greatly benefit this research.

No comments. The quality of English  Language is ok. 

Reviewer 4 Report

The study applied the concept of cointegration to investigate the trends of maximum and minimum temperatures and the diurnal temperature range in Africa. Cointegration is widely used in econometrics. It is exciting and encouraging to apply statistical methods from other principles in climate science. However, the organization and scientific interpretation of the statistical results could be clearer. The manuscript cannot be published in its current form.

 

Major comments:

1). The description of the statistical methods needs significant improvement. The authors just listed several equations which needed to be explained. I hope the authors explain how they applied the statistical techniques to the temperature datasets and how to interpret the statistical results.

2). Cointegration is stricter than linear regression, which is widely used in atmospheric and climate sciences. Is it necessary to use cointegration in temperature trends? When we talk about climatological trends, it does allow “large” perturbations, which will break a cointegration relationship since climate indicates weather conditions over a long period. It would be better if the author could clarify the motivation for using cointegration in climate analysis in more detail in the introduction.

3). Section 3 is full of pure statistical results and lacks detailed interpretations of the statistical results. How are the statistical results connected to temperature trends?

 

Minor comments:

Lines 28-30: I don’t understand why no evidence of cointegration indicates a very high risk of climate change.

Lines 40-41: What does “global warming is 1.0°C higher than pre-industrial temperatures” mean? I understand what you want to say, but please rewrite this sentence.

Line 50: highest warmest?

Lines 67 and 72: “equation” to “equator”?

Lines 83-86: Can temperature rise and GHG increase be considered two independent variables? According to your previous description in Lines 51-53, GHG increases induce temperature rising.

Lines 93-100: Are these studies related to DTR? Otherwise, please reorganize the paragraph.

Lines 124-126: Climate change is not limited to the frequency or intensity of extreme temperatures.

 

Line 166: Where did you define I(0) process?