Long Memory Characteristics of Global Temperature Anomalies (1850–2025)

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

please see the attached word file

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The global oceans, which absorb >90% of anthropogenic heat in the Earth system, have been experiencing a persistent warming trend. However, this warming shows significant spatial variations. This study analyzes sea surface temperature records from polar, tropical, subtropical, and hemispheric regions from 1850 to 2025, using fractionally integrated time-series methods, aiming to quantify long-range dependence (long-term memory, parameter 𝑑) and persistent warming. The results show that all regions exhibit statistically significant long memory, but the degree of persistence varies. The tropical and subtropical basins exhibit higher persistence, whereas the polar regions show lower persistence. In most regions, statistically significant linear trends are found, especially in the Arctic. However, I consider this paper to offer little explanation of the physical mechanisms underlying the long memory of sea surface temperatures in these regions, and its scientific novelty is limited. Therefore, I do not recommend its publication in its current form. The specific reasons are as follows:

• Previous studies have demonstrated the long memory of the ocean using fractional integration methods. The authors’ own prior studies also documented the long memory in the Arctic, as well as in the northern and southern hemispheres. However, the manuscript fails to clarify what new findings or scientific contributions it offers beyond the existing literature. Therefore, this study lacks scientific novelty. The authors should clearly state the specific scientific question this study aims to address—that is, questions that previous research has not answered.
• This manuscript primarily presents the memory parameter values obtained using fractional integration methods; however, it fails to sufficiently link these statistical results to the associated physical processes of ocean and climate dynamics. For example, the study notes that the memory parameter values are higher in the Atlantic MDR region and the eastern North Pacific, but attributes this only vaguely to “strong ocean-atmosphere coupling, large-scale circulation patterns, and the progressive accumulation of anthropogenic heat”. Similarly, although the polar regions show less persistence, the Arctic has higher memory parameter values than those in the Antarctic. This is attributed to “polar amplification in the northern hemisphere, while the stabilizing role of the Southern Ocean and its circumpolar circulation in the southern hemisphere”. Such explanations are insufficient. It is recommended that the authors establish connections between the statistical results and known climate modes, ocean-atmosphere coupling processes, oceanic dynamic processes, or existing theoretical frameworks to provide a reasonable physical explanation.
• This study neither specifies the geographical domain of the selected regions nor explains the rationale for selecting them. Why were these specific regions chosen? In what ways are they representative?

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Summary: The manuscript presents an analysis of sea-surface temperature time series with respect to their persistent statistical characteristics. Time series may exhibit short-term, autoregressive behaviour. characteristics or long-memory parameter, with longer persistence. These characteristics are important to determine, for instance, the significance of deterministic trends in the presence of long-memory residuals.

 

Recommendation: Although from the technical standpoint I do not have concerns, I struggle to see the justification for the study and its implications, as I explain below. I think that the manuscript could benefit from a revision of the introduction and the conclusions section, making them more focused.

 

Main points

 

1) The introduction goes at length explaining the relevance of sea-surface temperatures for sea-level or for the CO2 budget, but those are aspects that are only indirectly important for the present study. In contrast, the introduction leaves the reader wondering why it is important to determine the long-term memory characteristics of sea-surface temperature. For instance, climate models do not incorporate that information, and it is unclear how it can be used for planning purposes.

I can think of other applications that are mentioned in the manuscript. For instance, as I wrote before, maybe that information may affect the statistical significance of deterministic trends, or the for the increase in the frequency of extremes, o other statistical aspects.

 

2) The conclusion and discussions section is not really based on the results of the study, and contains rather speculate assertions, which i do not think are all true. For instance, the long persistence of the tripodal oceans is explained by the strong coupling to the atmosphere. Well, the atmosphere has a short memory, so one would expect that coupling with a shorter-memory system would lower persistence rather than increase it. Also, the short persistence of the polar oceans is explained by the 'polar amplification', i.e. the higher sensitivity of high latitudes to greenhouse gas forcing, but the determination of the d parameters was also conducted after linearly determining the temperature data, so that effect should not play a role. Other than those aspects, this section contains only very general comments that could fit in many other manuscripts.

 

3) These limitations can be clearly seen in the lack of relevant references cited in the manuscript. There are many previous studies on long-memory of climatological time series, even of sea-surface temperatures, that are not cited here, and I would recommend that the author conduct a Google search. For instance, authors such as Bunde, Percival, Fraederik, Lennard, Rypdal, and others have published a long list of studies that would be relevant to cite here and could also help justify the present study.

 

Particular points

 

4) Not all equations are numbered

 

5) Which method was used to estimate the parameter d ? The text does not mention this at all.

 

 

6) Table 2. For me, it is a bit surprising that linear detrending does not seem to have a significant effect on the estimation of the parameter d. My guess is that the detrended residuals should display lower values of d, as part of the memory is filtered out. Is this correct? This would warrant a discussion.

 

Author Response

See attached file.

Author Response File: Author Response.docx

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

This version addresses some of my comments on the original submission, but not all of them:

1) I pointed out that the manuscript did not present the previous relevant literature on long-term memory of climate time series, and indicated some authors who had published important contributions in the field. This version still misses some important papers by some of these authors, for instance, Rybski, D., Bunde, A., & Von Storch, H. (2008). Long‐term memory in 1000‐year simulated temperature records. Journal of Geophysical Research: Atmospheres, 113(D2). https://doi.org/10.1029/2007JD008568). This study, in particular, has the same objective as the present manuscript but uses the output of long simulations with a General Circulation Model rather than observations. There might be differences in the results, as model data are not observations; however, this long simulation allows for a more accurate estimation of the d parameters. In my opinion, it should be discussed, as many results are comparable to the present study

2) The description of the estimation method is now included, but the author could have been a bit more specific. They write that the estimation method is based on the likelihood function, but this sentence could also imply a Bayesian approach, which is not the case. Also, it is not clear why the uncertainties are estimated (Table 2), unless I missed it. This is an important point, as they are part of the results and are discussed as such. The manuscript cites Robinson (1994), but the article is rather old and behind a paywall. So the reader would need here a more detailed description

Author Response

Please refer to the attachment

Author Response File: Author Response.pdf