Why Are the High Frequency Structures of the Sea Surface Temperature in the Brazil–Malvinas Confluence Area Difficult to Predict? An Explanation Based on Multiscale Imagery and Fractal Geometry
Round 1
Reviewer 1 Report
The paper by Alonso et al. Employed the multiscale ultrahigh resolution Sea Surface Temperature imagery data and the fractal geometry model and explored the possible factors related to the low predictability of the Brazil-Malvinas Confluence Zone (BMC). In their work, a quasi-annual wave and a quasi-semiannual wave with periods about 420 and 210 days respectively has been confirmed. The authors have computed the three firsts order Rényi dimensions and found that the BMC area can be regarded as a monofractal object.
In my view, this work has a high implication for understanding the low predictability of the BMC area. In general, the manuscript is well organized and written. I would like to recommend it for possible publication on JMSE. Note that the quality of most figures needs further improvement. For example, figures 4-6 have too small coordinate labels to be recognized.
Author Response
Review 1
The paper by Alonso et al. Employed the multiscale ultrahigh resolution Sea Surface Temperature imagery data and the fractal geometry model and explored the possible factors related to the low predictability of the Brazil-Malvinas Confluence Zone (BMC). In their work, a quasi-annual wave and a quasi-semiannual wave with periods about 420 and 210 days respectively has been confirmed. The authors have computed the three firsts order Rényi dimensions and found that the BMC area can be regarded as a monofractal object.
In my view, this work has a high implication for understanding the low predictability of the BMC area. In general, the manuscript is well organized and written. I would like to recommend it for possible publication on JMSE. Note that the quality of most figures needs further improvement. For example, figures 4-6 have too small coordinate labels to be recognized.
Dear Reviewer
Thank you for your comments.
We have done again the figures improving their quality and the legibility of the legends.
Thank you again.
- Alonso
Reviewer 2 Report
This paper uses multiscale ultrahigh resolution sea surface temperature image data and fractal geometry method to discuss the reasons why the current in the Brazil Malvinas Conflict area is difficult to accurately predict. The research results mainly point out two reasons. The first is the low harmonicity and the low harmonic predictability, and the second is that the fractal structure of SST is too complex to achieve prediction. The paper has a certain degree of innovation, but many key issues are not clearly stated, such as: What is the study object? Why can SST represent a flow? What is the relationship between the fractal features and the current predictability? For example, the paper adopts the perspective of SST to study ocean currents, rather than directly analyzing them. This method has good innovation, but it also raises the issue of the rationality of such treatment. These problems are fundamental logical issues, and if not solved, they directly affect the scientific validity of the entire research. Therefore, the entire paper needs sufficient revisions before consideration for publication. I think the following issues require special attention when the authors rewrite the paper.
(1) The definition of the object studied in this paper has not been clearly stated. The statement of the Title is very vague because it does not explain what variable is difficult to predict. From the text, this paper should focus on ocean currents, so I understand that the author is trying to say that the current is difficult to predict. In addition, it is still unclear whether Brazil Malvinas Conflict is difficult to predict, or the current in the Brazil Malvinas Conflict area is difficult to predict. I guess that it may be the latter, as there may be currents of different components within a certain area. Moreover, as mentioned in the paper, quasi-annual and quasi-semiannual waves with periods are verified. Does this mean that the interannual or semi-annual variability of the Brazil Malvinas Conflict flow is well predictable? The conclusion also points out that the periodicity of the interannual and semi-annual changes of that current is strong, making it easier to predict interannual and semi-annual changes. So, the authors may intend to discuss the difficulty in predicting relatively high-frequency changes in ocean currents. Therefore, this paper focuses on high-frequency changes in the currents in the Brazilian Malvinas Conflict area, which are approximately daily (or even more high-frequency) changes. However, the authors seem to have not stated this fundamental issue about the study object throughout the entire paper. So, I strongly suspect that there may be serious errors in the description or understanding of certain issues in the paper.
(2) Why SST can represent flow? The objective of this study is to illustrate the difficulty of ocean current forecasting, but the relationship between SST and current is not clearly defined, and the process of calculation and inversion of their relationship is not described. There may be a general relationship between temperature and ocean currents, mostly when water temperature responds significantly to upwelling, eddies, etc. As seen in Figure 1, the currents are all horizontal currents. Is it related to the actions of cold and warm eddies? Therefore, additional work should be done to demonstrate that the seawater temperature in the study area does characterize ocean currents.
(3) Why use fractal structures for forecasting? Understandably, fractal structures are difficult to predict if they are complex. However, the actual relationship between fractal characteristics and predictability is not clearly defined. The fractal characteristics of SST may not be related to the flow of Brazil-Malvinas Confluence at large- or mesoscale. The complex fractal structures may only lead to the poor prediction of small-scale current characteristics and will not affect the overall flow forecast. This issue involves the ambiguity of the study subjects mentioned above. Are your studies concerned only with very small-scale ocean processes?
(4) What factors determine the harmonicity of SST? Generally, harmonicity refers to tides and trends. The harmonization of the tidal current is good because the harmonization of the tide is good. But the current of Brazil-Malvinas Confluence is not dominated by tides, and thus poor harmonicity is reasonable. Many currents are not tidal-dominated and can be predicted. So, I think the fact that this flow is easy to predict has nothing to do with how well harmonicity can be predicted.
(5) The Title raises a question and draws the readers’ attention. So the authors must give a very clear answer. However, neither in the Abstract nor in the Conclusion section can I find a very clear explanation about "why is the Brazil-Malvinas Confluence area so difficult to predict?" This may be due to the authors’ unclear understanding of the study objects. The logic of some of the key questions may not be clear enough to give a concise and powerful answer. If I were to answer, as I understand the content of the paper (of course, may be wrong), it can be concluded that: Due to the weak periodicity of the SST time-varying process and the complexity of the spatial fractal characteristics, it is difficult to predict the small-scale and high-frequency changes of the current in Brazil-Malvinas Confluence area through periodicity or fractal characteristics.
(6) The first six paragraphs of the introduction are all about Figure 1, emphasizing the complexity of the flow system in the region. However, did the first 14 references cited in the six paragraphs mention that currents in this area are difficult to predict? Did they explore the reason for the difficulty of forecasting?
(7) Paragraph 7 describes the observation and simulation studies for Brazil-Malvinas Confluence. However, it is not clear whether there are already some results about the difficulty of predicting the dynamic process of Brazil-Malvinas Confluence. If no previous authors thought that Brazil-Malvinas Confluence was unpredictable, the focus of this paper could be shifted to focusing on the unpredictable phenomenon of Brazil-Malvinas Confluence rather than on the reason for its unpredictability.
(8) What is the bright yellow noise in Figure 2? I suspect they are incorrect data. If they are correct and SST can characterize ocean currents, then these noise points should represent very small but very strong ocean currents, right? So I always feel that the authors’ research object is the ocean currents with very small spatial scales and high frequency of variation. If so, the authors should explain this clearly.
(9) In line 20, “The observed correlation” refers to the correlation between what and what?
(10) In Figure 1, what is SASW?
(11) In Figure 3, "the non-linear fit" refers to the fitting of what variables?
(12) Figure 4: Celsius degrees should be the unit of a wave.
The language is fluent and easy to understand.
Author Response
Review 2
This paper uses multiscale ultrahigh resolution sea surface temperature image data and fractal geometry method to discuss the reasons why the current in the Brazil Malvinas Conflict area is difficult to accurately predict. The research results mainly point out two reasons. The first is the low harmonicity and the low harmonic predictability, and the second is that the fractal structure of SST is too complex to achieve prediction. The paper has a certain degree of innovation, but many key issues are not clearly stated, such as: What is the study object? Why can SST represent a flow? What is the relationship between the fractal features and the current predictability? For example, the paper adopts the perspective of SST to study ocean currents, rather than directly analyzing them. This method has good innovation, but it also raises the issue of the rationality of such treatment. These problems are fundamental logical issues, and if not solved, they directly affect the scientific validity of the entire research. Therefore, the entire paper needs sufficient revisions before consideration for publication. I think the following issues require special attention when the authors rewrite the paper.
- The definition of the object studied in this paper has not been clearly stated. The statement of the Title is very vague because it does not explain what variable is difficult to predict. From the text, this paper should focus on ocean currents, so I understand that the author is trying to say that the current is difficult to predict. In addition, it is still unclear whether Brazil Malvinas Conflict is difficult to predict, or the current in the Brazil Malvinas Conflict area is difficult to predict. I guess that it may be the latter, as there may be currents of different components within a certain area. Moreover, as mentioned in the paper, quasi-annual and quasi-semiannual waves with periods are verified. Does this mean that the interannual or semi-annual variability of the Brazil Malvinas Conflict flow is well predictable? The conclusion also points out that the periodicity of the interannual and semi-annual changes of that current is strong, making it easier to predict interannual and semi-annual changes. So, the authors may intend to discuss the difficulty in predicting relatively high-frequency changes in ocean currents. Therefore, this paper focuses on high-frequency changes in the currents in the Brazilian Malvinas Conflict area, which are approximately daily (or even more high-frequency) changes. However, the authors seem to have not stated this fundamental issue about the study object throughout the entire paper. So, I strongly suspect that there may be serious errors in the description or understanding of certain issues in the paper.
Thank you for your comments. They have been very valuable to thinking again in the approach we have carried out.
As we know, the SST is a good tracer of the dynamic of the upper layer of the ocean. So, the object of our study is the dynamic of the Brazil-Malvinas Confluence from the point of view of the SST, used as a tracer.
As you have pointed out, we use two approaches. The first one consists of recognizing that our planet is a thermic machine. In this sense, some periodicities arise naturally as the annual and semiannual. But when we try to make a harmonic regression point by point by building up a time series for each one, we find coefficients of determination of 0.7, meaning a correlation of 0.5, very low for the usual standards in Physical Oceanography. In a couple of works from some time ago, the harmonicity of a time series was checked against the fractal dimension through the contractor operator on very good quality long time series from earth tides. The second ones came from the Geometrical Theory of Measurements, substantiated in what is known as fractals. Now, two different approaches. The Renyi dimensions (or fractal, information and correlation dimensions) leaded to the concept of monofractal, and the strongest approach is computing the contraction factor as if a linear fractal interpolation was carried out. The values point to high energy dynamical structures.
Hence, although the two periods (annual and semiannual) be the strongest signals, the SST field cannot be predicted accurately (correlation of 0.5).
However, the mean behavior of the BMC is properly modeled by numerical models (copernicus) but the fine structures not. The time scale we are talking about is longer than 1 day because the MUR imagery is daily.
- Why SST can represent flow? The objective of this study is to illustrate the difficulty of ocean current forecasting, but the relationship between SST and current is not clearly defined, and the process of calculation and inversion of their relationship is not described. There may be a general relationship between temperature and ocean currents, mostly when water temperature responds significantly to upwelling, eddies, etc. As seen in Figure 1, the currents are all horizontal currents. Is it related to the actions of cold and warm eddies? Therefore, additional work should be done to demonstrate that the seawater temperature in the study area does characterize ocean currents.
Thank you for the question. As it is well known, the SST is a very good tracer for the dynamic of the most upper layer of the ocean. Of course, we have not inverted the hydrodynamic equations for a rotating Earth, we use directly the SST signal as the tracer as usual in many works of Satellite Oceanography.
About Figure 1. Yes, the 2D representation is the general scheme of the current in the area and no information is given in the vertical dimension, it is impossible. However, the descriptions of the area in all the references in the work detail the scheme of the currents
- Why use fractal structures for forecasting? Understandably, fractal structures are difficult to predict if they are complex. However, the actual relationship between fractal characteristics and predictability is not clearly defined. The fractal characteristics of SST may not be related to the flow of Brazil-Malvinas Confluence at large- or mesoscale. The complex fractal structures may only lead to the poor prediction of small-scale current characteristics and will not affect the overall flow forecast. This issue involves the ambiguity of the study subjects mentioned above. Are your studies concerned only with very small-scale ocean processes?
We are very sorry, we have not been able to explain clearly this point in the work. We are not using fractal structures to predict. We compute some fractal parameters for the time series of each point (the three Renyi dimensions and the coefficients of the linear fractal interpolation, mainly the contraction coefficient) to quantify the high level of order-disorder, say noise, chaos, no-determinism, unpredictability, un-harmonicity ….,
- What factors determine the harmonicity of SST? Generally, harmonicity refers to tides and trends. The harmonization of the tidal current is good because the harmonization of the tide is good. But the current of Brazil-Malvinas Confluence is not dominated by tides, and thus poor harmonicity is reasonable. Many currents are not tidal-dominated and can be predicted. So, I think the fact that this flow is easy to predict has nothing to do with how well harmonicity can be predicted.
Thank you very much for this question. This is a really interesting question. In some previous works by Alonso, harmonicity, predictability and fractal dimension were related in the frame of high quality very long time series of Earth Tides and in two low quality time series of ocean tides. Alonso found that harmonic time series, with a high predictability, had low fractal dimension (earth tides records from the observatories of Brussels and Black Forest), while low quality time series, more difficult to predict harmonically, had higher fractal dimension (for the tidal stations of Ceuta and Algeciras at the Strait of Gibraltar).
Now, just suppose that a geophysical signal, say the temperature, is driven by the sun. Then, some clear periods arise as diurnal, a small contribution in the three months period, the semiannual and the annual. What happens in the BMC is that the mouth of Rio de la Plata is very close, incrementing the uncertainty, the unpredictability, the un-harmonicity, of the SST signal in the area. The fractal tools allow to get into the deepest geometrical structures of the time series. In this case, the SST time series of each point of the domain under study in the BMC.
- The Title raises a question and draws the readers’ attention. So the authors must give a very clear answer. However, neither in the Abstract nor in the Conclusion section can I find a very clear explanation about "why is the Brazil-Malvinas Confluence area so difficult to predict?" This may be due to the authors’ unclear understanding of the study objects. The logic of some of the key questions may not be clear enough to give a concise and powerful answer. If I were to answer, as I understand the content of the paper (of course, may be wrong), it can be concluded that: Due to the weak periodicity of the SST time-varying process and the complexity of the spatial fractal characteristics, it is difficult to predict the small-scale and high-frequency changes of the current in Brazil-Malvinas Confluence area through periodicity or fractal characteristics.
The title has been modified in order to clarify the object of the work.
- The first six paragraphs of the introduction are all about Figure 1, emphasizing the complexity of the flow system in the region. However, did the first 14 references cited in the six paragraphs mention that currents in this area are difficult to predict? Did they explore the reason for the difficulty of forecasting?
No. Those references are devoted to explain the complexity of the area and the complexity of the temporal evolution of its different parts. Under our point of view, this is the first very important point in any work in Physical Oceanography. Because the BMC is a very complex area and many studies have been carried out, the first references must be very descriptive. The next references (Piola et al, Pierini et al, etc) discuss the difficulty of prediction. In this sense, because the area is so complex, it is essential a very good presentation. Even more, Pierini et al is the only reference in the same address, working with the Fisher-Shannon theory. So, we are given away the more classical techniques but justifying the new ones with the previous and well-established results.
(7) Paragraph 7 describes the observation and simulation studies for Brazil-Malvinas Confluence. However, it is not clear whether there are already some results about the difficulty of predicting the dynamic process of Brazil-Malvinas Confluence. If no previous authors thought that Brazil-Malvinas Confluence was unpredictable, the focus of this paper could be shifted to focusing on the unpredictable phenomenon of Brazil-Malvinas Confluence rather than on the reason for its unpredictability.
The only reference to a similar work is Pierini et al (2016). As you know, in the Fisher-Shannon analysis, the Fisher’s part is close to the fractal analysis while the Shannon’s one computes the so-called Shannon entropy. Our conclusions point out to those in Pierini et al (2016), and their values support our results.
We have modified the title of the work. In fact, the main dynamic features are well predicted (see Copernicus), but the small scale or high frequency not.
(8) What is the bright yellow noise in Figure 2? I suspect they are incorrect data. If they are correct and SST can characterize ocean currents, then these noise points should represent very small but very strong ocean currents, right? So I always feel that the authors’ research object is the ocean currents with very small spatial scales and high frequency of variation. If so, the authors should explain this clearly.
Thank you for your question. We have revised the data and we have found some incorrect values in except just in front of the mouth of Rio de La Plata.
(9) In line 20, “The observed correlation” refers to the correlation between what and what?
Corrected.
(10) In Figure 1, what is SASW?
We have added explanations in the text.
(11) In Figure 3, "the non-linear fit" refers to the fitting of what variables?
The harmonic model of Eq 14 consider the frequencies as parameters to be fit. So, it is a non-linear model (very hard to fit and very sensitive to errors). Figure 3 shows the correlation in each point between the data and the model of Eq 14. We have added (Eq 14) in the legend of Figure 3.
(12) Figure 4: Celsius degrees should be the unit of a wave.
Thank you for the suggestion. It is more correct to say “component” instead “wave”. This has been corrected in the text.
Reviewer 3 Report
Review of the MS ‘Why is the Brazil-Malvinas Confluence area so difficult to predict? An explanation from Multiscale Ultrahigh Resolution Sea Surface Temperature imagery and Fractal Geometry’
My general concern is that the MS is poorly written and it is difficult to understand what information or conclusions the authors wish to convey to a reader. The title is misleading. The dynamics of the BMC is difficult to predict if only using such basic tools as decomposition into annual and semi-annual waves – the method that is applied by the authors. Even though the authors do not explain what the difficulty is. Modern ocean models such as Global Ocean Physics Analysis and Forecast (https://data.marine.copernicus.eu/product/GLOBAL_ANALYSISFORECAST_PHY_001_024/description) are able to provide reasonable prediction of the global ocean circulation including the BMC area. No referencing or analysis of such prediction is made in the MS.
The periods of the annual and semi-annual variability found by the author are of interest. However the time period used in the analysis (three years and nine month ) may be too short to give an accurate estimate of annual variability. The authors should use a longer period of observation, eg from 1981 to 2022 availble at (https://data.marine.copernicus.eu/product/SST_GLO_SST_L4_REP_OBSERVATIONS_010_024/description).
The fractal analysis is an interesting approach to study the structure of the BMC, but it should be presented in a better way. The conclusion that ‘the dynamics of the BMC is complex’ is obvious and insufficient. The input data and the resulting maps contain a large number of outliers which should be removed.
The MS requires a major revision before it can be considered for publication in JMSE.
The language requires a major improvement throughout the text, some examples are below
Line 26-27 The phrase ‘implying the no good enough oceanic prediction in the area’ requires rewording
Line 34 ‘Although the region oscillates’ probably means ‘ the location of BMC oscillates in latitudinal direction’
Line 46. ‘conforms the South Atlantic subtropical gyre’ -> constitute the South Atlantic subtropical gyre
Line 59 ‘only the privileged observation platforms, the artificial satellites, have given a more complete view’ –please rephrase
Line 67 ‘high hydrodynamical regime’ – please re-phrase
Lines 71-72 ‘The BMC has been studied by means of classical oceanographic surveys [3][4], by satellite altimetry [5] and by satellite sea surface imagery [15][13]’. Satellite altimetry is part of satellite sea surface imagery. Please rephrase
Other specific comments
Fig.1. Abbreviation ‘SASW’ requires explanation in the caption. ‘ Fakland current’ probably means ‘Falkland current’
Line 62 A the Cleopatra and Antony eddies permanent or intermittent features of the confluence zone?
Line 79 ‘time series of SST point-by-point’ – what is this?
Lines 96-103. The authors should specify which of the GHRSST-MUR products they use. Is it a Level 3 or Level 4 product?
Lines 104-107. The authors should specify the geographical area of study, eg by giving the coordinates of the corners.
Line 107 . What is ‘standard error’? Is it the same as standard deviation? Or is it the error of observation declared by the data provider?
Lines 117-118. ‘the points with highest values are in the area of confluence of currents’ The tiny isolated areas with high ‘errors’ in Fig 2b do not look reasonable on the background nearly uniform ‘error’ field.
Section 2. The quasi-harmonic model must be described in the Section 2 ‘Data set and numerical methods’ before it is discussed in the Results section.
Section 3.1 The curve fitting using equation (14) is a simple exercise to obtain the unknown frequencies. The results of the curve fitting contain a large number of outliers covering small isolated areas as shown in Figs 4 and 5. These are probably linked to the ‘errors’ mentioned earlier and must be excluded from the analysis.
Line 330. The first main result is that the curve fitting gives the frequency of oscillation of 420 and 210 days. It is not clear that these frequencies are uniform across the area or vary significantly between the subdomains within and outside the BMC.
Line 336. The second result is quite vague and generally obvious from looking at the individual maps of SST or SSH
Line 346. The conclusion that ‘there are not multiple time scales’ contradicts to the previous statement that there are at least two time scales – 420 and 210 days.
The language requires a major improvement throughout the text, some examples are below
Author Response
Review 3
Review of the MS ‘Why is the Brazil-Malvinas Confluence area so difficult to predict? An explanation from Multiscale Ultrahigh Resolution Sea Surface Temperature imagery and Fractal Geometry’
My general concern is that the MS is poorly written and it is difficult to understand what information or conclusions the authors wish to convey to a reader. The title is misleading. The dynamics of the BMC is difficult to predict if only using such basic tools as decomposition into annual and semi-annual waves – the method that is applied by the authors. Even though the authors do not explain what the difficulty is. Modern ocean models such as Global Ocean Physics Analysis and Forecast (https://data.marine.copernicus.eu/product/GLOBAL_ANALYSISFORECAST_PHY_001_024/description) are able to provide reasonable prediction of the global ocean circulation including the BMC area. No referencing or analysis of such prediction is made in the MS.
The periods of the annual and semi-annual variability found by the author are of interest. However the time period used in the analysis (three years and nine month ) may be too short to give an accurate estimate of annual variability. The authors should use a longer period of observation, eg from 1981 to 2022 availble at (https://data.marine.copernicus.eu/product/SST_GLO_SST_L4_REP_OBSERVATIONS_010_024/description).
The fractal analysis is an interesting approach to study the structure of the BMC, but it should be presented in a better way. The conclusion that ‘the dynamics of the BMC is complex’ is obvious and insufficient. The input data and the resulting maps contain a large number of outliers which should be removed.
The MS requires a major revision before it can be considered for publication in JMSE.
The language requires a major improvement throughout the text, some examples are below
Line 26-27 The phrase ‘implying the no good enough oceanic prediction in the area’ requires rewording
Line 34 ‘Although the region oscillates’ probably means ‘ the location of BMC oscillates in latitudinal direction’
Line 46. ‘conforms the South Atlantic subtropical gyre’ -> constitute the South Atlantic subtropical gyre
Line 59 ‘only the privileged observation platforms, the artificial satellites, have given a more complete view’ –please rephrase
Line 67 ‘high hydrodynamical regime’ – please re-phrase
Lines 71-72 ‘The BMC has been studied by means of classical oceanographic surveys [3][4], by satellite altimetry [5] and by satellite sea surface imagery [15][13]’. Satellite altimetry is part of satellite sea surface imagery. Please rephrase
Thank you for your suggestions. We have revised the English but we asked MDPI for a language checking as well.
Other specific comments
Fig.1. Abbreviation ‘SASW’ requires explanation in the caption. ‘ Fakland current’ probably means ‘Falkland current’
Solved, thank you. The explanation has been included in the text, just before invoking the figure.
Line 62 A the Cleopatra and Antony eddies permanent or intermittent features of the confluence zone?
Both are due to the confluence of currents. So, they are so permanent as the currents are and they are so energetic as the currents meet.
Line 79 ‘time series of SST point-by-point’ – what is this?
Solved. This has been corrected in the text by “time series in each point of the domain”
Lines 96-103. The authors should specify which of the GHRSST-MUR products they use. Is it a Level 3 or Level 4 product?
L4, thank you. This has been included in the text.
Lines 104-107. The authors should specify the geographical area of study, eg by giving the coordinates of the corners.
Included. Thank you.
Line 107 . What is ‘standard error’? Is it the same as standard deviation? Or is it the error of observation declared by the data provider?
The “standard error in the estimation” is the error in the estimation of the mean value. It has been clarified in the text by adding “in its estimation”.
Lines 117-118. ‘the points with highest values are in the area of confluence of currents’ The tiny isolated areas with high ‘errors’ in Fig 2b do not look reasonable on the background nearly uniform ‘error’ field.
Thank you for the suggestion. We have revised all the work from the original data and there were errors. After their elimination, we have done new maps. Now, the errors are concentrated nearby the mouth of the Rio de la Plata. The remaining yellow structures are due to the smoothness of new the conditions on the data reliability.
Section 2. The quasi-harmonic model must be described in the Section 2 ‘Data set and numerical methods’ before it is discussed in the Results section.
A new subsection (2.2.3) has been added. Thank you.
Section 3.1 The curve fitting using equation (14) is a simple exercise to obtain the unknown frequencies. The results of the curve fitting contain a large number of outliers covering small isolated areas as shown in Figs 4 and 5. These are probably linked to the ‘errors’ mentioned earlier and must be excluded from the analysis.
Thank you. Right. However, the result is the same after the partial correction we have done. We read this from the high sensitivity of the non-linear fit and the geometrical computations.
Line 330. The first main result is that the curve fitting gives the frequency of oscillation of 420 and 210 days. It is not clear that these frequencies are uniform across the area or vary significantly between the subdomains within and outside the BMC.
Thank you for the observation. Yes, there is an interval where the frequency is contained and the subdomains coincide with those places with high energy (say where Cleopatra is located, along the SASW, the subtropical shelf front, etc). This can be read from two points of view. The first one is that there are exogenous bearings distorting the frequency. The second one seems more promissory: there are phase lag shifts. These are frequencies, distorting the nominal one of the components. We think that this is a future working line.
Line 336. The second result is quite vague and generally obvious from looking at the individual maps of SST or SSH
Thank you for the observation. We did not explain well enough. Assuming that a time series is the result of a dynamical system implies give way to those tools from the Geometrical Theory of the Measure can be used. So, this has been written again.
Line 346. The conclusion that ‘there are not multiple time scales’ contradicts to the previous statement that there are at least two time scales – 420 and 210 days.
Thank you for this interesting observation. The fractals theory is fully based in the self-similarity principle. This means invariance under the scale. You can see a Mandelbrot set, or a Julia set, a make zoom as many times you wish and the result is a similar set. This is not possible when working with physical entities. Following Alonso (1998), the self-similarity in tidal records is observed from the Fourier transform of the time series, obtaining smaller and smaller components when zooming, until a physical limit, fixed by the smallest side of the box to be used. This uses to be two or three times the sampling interval. So, the behavior as monofractal points out to the same results after rescaling under the self-similarity principle, just the same than when earth tide super-gravimeter time series.
Round 2
Reviewer 2 Report
The revised version is clearer in many respects than before. I support the publication of this paper if further improvements are made in both of the following areas.
(1) I finally realized that the authors were looking at sea surface temperature, not currents. In this case, the title can be further revised to: “Why the high-frequency structures of sea surface temperature in the Brazil-Malvinas Confluence area are difficult to predict? An explanation based on multiscale imagery and fractal geometry”. The relevant statements in the text should also be thoroughly checked and revised.
(2) The resolution of the figures is too low and must be replaced by high-resolution images.
The language is fluent and easy to understand.
Author Response
Dear Reviewer,
All your suggestions has been fulfilled. The title has been changed (thank you for this, it helps to understand the work) and the figures has been exported at 600ppp.
Thank you again,
J. Alonso
Reviewer 3 Report
The MS is improved. My minor comment is that all responses to the reviewers have to be reflected in the actual MS not just in the cover letter to the editor.
Minor corrections to English
Author Response
Dear Reviewer,
We are very sorry for our confusion, and at the same time we must say you that you for your comments.
J. Alonso
