A segmented-breakpoint sea-surface-temperature upwelling index for the Benguela Upwelling System

Smit, Albertus Jacobus; Sweijd, Neville

doi:10.5194/egusphere-2026-3017

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https://doi.org/10.5194/egusphere-2026-3017

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23 Jun 2026

| 23 Jun 2026

Status: this preprint is open for discussion and under review for Ocean Science (OS).

A segmented-breakpoint sea-surface-temperature upwelling index for the Benguela Upwelling System

Albertus Jacobus Smit and Neville Sweijd

Abstract. Satellite sea-surface-temperature (SST) upwelling indices usually contrast coastal temperature with a fixed offshore reference, although the offshore extent of the surface cool tongue varies across cells and days. We replace the fixed reference with a daily fitted thermal breakpoint from a continuous two-segment regression on cross-shore SST profiles, accepted only when model-evidence, slope-ratio, offshore-baseline, edge-buffer, and residual-autocorrelation criteria are met. We apply the method to five Benguela upwelling cells (UCs) from 2015 to 2025 using two fine-resolution Level-4 SST products, namely the Operational Sea Surface Temperature and Ice Analysis and the Geo-Polar Blended analysis from the US National Oceanic and Atmospheric Administration; coarser Advanced Very High Resolution Radiometer and microwave optimum interpolation products serve as resolution comparisons. Median fitted breakpoints span 114 to 270 km across UCs, so 50 to 100 km reference points usually sample inside the fitted inshore segment rather than offshore water. In the Operational Sea Surface Temperature and Ice Analysis product, the daily correlation between inshore-segment SST drawdown and the conventional fixed-distance contrast rises from r = 0.06 at 50 km to r = 0.93 at 500 km, showing that reference distance changes the diagnostic itself. The Lüderitz annual r₅₀ point estimate is negative (-0.16), but its block-bootstrap interval includes zero. A paired comparison with a Bakun-type offshore-Ekman-transport flag shows that southern Benguela cells retain SST structure without the local wind flag on ca. one fifth of matched days. The method therefore positions fixed-reference SST indices as structural surface-temperature indicators whose interpretation depends on cell-scale geometry and SST-wind co-activity.

Received: 26 May 2026 – Discussion started: 23 Jun 2026

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Albertus Jacobus Smit and Neville Sweijd

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RC1:
'Comment on egusphere-2026-3017', Anonymous Referee #1, 17 Jul 2026 reply

Summary
The authors have developed a novel methodology for detecting cross-shore SST gradients (running along-shore the west coast of southern Africa) in any given SST data product and posit that this addresses one of the largest methodological issues that has persisted in the field of upwelling identification and quantification. Namely the use of static distances for defining/orienting the break-point analysis of temperatures along a transect. The methodology they have developed is able to be contained within the SST itself, not relying on wind data, as many upwelling index (UI) methods do.

The authors also utilise an interesting methods to draw non-overlapping shore-normal transects for the extraction of gridded satellite data for a number of products.

The method developed here is tested against two other established methods: 1) fixed distance and 2) wind based. By comparing these methodologies, it is clear that the fixed distance methodology is sub-optimal for the task at hand. The more malleable breakpoint transects developed here are clearly able to adapt according to the spatial SST anomaly on the given day. The matchups against the wind based method works very well for Lüderitz specifically, but much less so for the others. This is itself an interesting finding and opens the question for using this gap to aid in the understanding of the difference in the physical processes responsible for upwelling between the different Ucs. This is particularly evident in different groups of seasons per UC (e.g. Walvis Bay in JJA).

The manuscript is very compact and to the point. With little in the way of explanation for the statistics used. There is quite a lot of unexplained statistical jargon, and try as I might, following along with why certain statistical tests were chosen, or certain test values were used to validate the results, was not clear. It would have required that I read quite a lot of referenced literature to do so, which is outside of the scope of a reviewers duties. I recommend that the authors spend a few additional sentences to ensure all tests and values are explained so the reader can understand and follow along without needing to read additional literature.

That being said, after some re-reading it was clear what the authors had developed, and how it worked, from a higher level point of view. The method itself seems very sound to me and I see no point from which it should be improved. Though I wouldn’t necessarily be able to considering the density of information surrounding it.

The only substantive suggestion I have to add to the manuscript would be a multiple panel figure that walks the reader through exactly how a single day breakpoint is calculated. Being able to visualise that should help in understand the exact technical workflow of the methodology.

Otherwise the writing is solid (if not too dense) and the figures as they are now are acceptable. I particularly liked Figure 4. This manuscript could be accepted for publication now with very few edits (see below). Though I do think that adding that methodology illustrating figure would improve the communication.

Title
- No comment

Abstract
- ln. 6: Depending on how strict the editorial style is for acronyms in abstracts, I think it is generally better to use the product acronyms for satellites rather than the full name (i.e. OSTIA). This is because these products are always referred to by their acronym, almost never by their full name. With the famous exception of the Polar Orbiting Environmental Satellite.
- ln. 8: The 50 to 100 km reference for current methodologies could be mentioned in the first sentence to preface more clearly the current technical problem this study aims to address.
- ln 10-15: I am not able to understand these results from reading the abstract alone. What is an r_50 point estimate? A one fifth match to an established methodology sounds sub-optimal, but I’m not able to infer the rest of the meaning of this sentence. The concluding sentence seems to be a criticism of the established methodology, rather than an explanation of the benefits of the new methodology, but I’m not certain.
(Of course, after reading the full manuscript all of this information becomes clear.)

1. Introduction
- ln 36: UC was introduced in the abstract, but not the Intro before this use. It should therefore be given in full first on this line.

2. Methods
- ln 60: I think the authors should reference a publication that developed these Laplace and Dirichlet conditions. I’ve not seen this value used in physical oceanography publications before.
- ln. 93: ‘worse’ → ‘worst’
- ln. 131: ‘austral seasons’ Because there is no reference to any specific season, it is not necessary to specify that this is in the southern hemisphere.
- ln. 160: Are three consecutive days required to first begin the detection, or if there is one positive day, then a one day gap, then another positive day, this will flag as an event?

3. Results
- ln. 284: “austral-summer” As the authors prefer, but there is no reference to the northern hemisphere in the text (that I noticed) so specifying a season as austral seems unnecessary to me.
- ln 285: Generally as a writing style it is preferable not to refer to a figure directly in the text. But to make a statement about the results, which then requires that the figure be referred to within parentheses.

4. Discussion
- No comments.

5. Conclusions
- Good concluding point on the practical importance of the methodology developed in this study.

Supplement
There is quite a lot in the supplement. I see that the authors chose to keep the main text short and bunchy and to put all of the sensitivity analyses, of which there are many, into the supplement. One general comment is that the text size for the tables seem to vary quite a bit with no clear reason why.

Table 1
There is no need to explain the units in the caption if they are also shown in the column headers.

Figure 1
Very cool looking transects. I like the colour palette for the UCs.

Figure 2
The legend is plotted over the facet wrap text and should be bumped up a bit. There are commas and back slashes in the facet wrap text that I don’t think should be there (e.g. d_0 = 50\,km). Perhaps a failed escape character? The Cape Frio points are effectively completely over plotted and not visible. I see that the authors are already using alpha for the points, so there doesn’t appear much that can be done for this.

Figure S3
I understand why the x-axis is allowed to go from 0.0 to 1.0, even though this introduces a lot of dead space. But why does the y-axis go up to 0.35?

Reply

Citation: https://doi.org/10.5194/egusphere-2026-3017-RC1
- AC1:
  'Reply on RC1', Albertus Smit, 28 Jul 2026 reply
  
  We attach the supporting material for our reply to Referee 1 on our manuscript. The referee's main criticism was that the statistical passages in the Methods cannot be followed without referring to the cited literature, which is valid. Rather than describe our intention to revise, we give the rewritten passages in full as they would appear in the revised manuscript, with the corresponding submitted text quoted beneath each so that the two can be compared directly (see the attachment). Seven passages are edited, namely what counts as an observation, the four acceptance criteria, the treatment of the fitted breakpoint as a free parameter, the effective sample size under residual autocorrelation, the rule that groups days into events, the agreement statistics used to compare the SST and wind detectors, and the correlation interval together with the multiple-testing correction.
  The document also contains the walk-through figure the referee asked for, a five-panel schematic that follows one transect, on one day, at one cell, from the temperature field through the breakpoint search to the classification of the day, with its proposed caption. We close with point-by-point replies to the sixteen specific comments on the abstract, introduction, Methods, Results, Supplement, tables, and figures, including a fully revised abstract and the four new references we propose to add in reply to the comment at line 60. We accept almost all of the comments, and where we propose something different, we say so and give our reasoning.
  One caveat should be stated. Explaining a procedure on the page adds words, so the replacement passages are perhaps longer than the text they replace. We have written for clarity first and treated length as a separate problem, and when the revision is assembled, we will bring the manuscript within the length that Ocean Science permits.
  
  Reply
  
  Citation: https://doi.org/10.5194/egusphere-2026-3017-AC1
  - RC4: 'Reply on AC1', Anonymous Referee #1, 03 Aug 2026 reply
    
    I am happy with the range of changes proposed by the authors.
    I think that the manuscript should be ready for acceptance after the changes have been made.
    I find that the abstract in particular reads much better now.
    The change to the writing style to allow for more supported explanations of the statistics helps with their understanding. As does the new schematic that walks through the process visually.
    As for Figure S3, I see no need to expand the y-axis to the fully possible -1 to 1 range. The way the authors have it now is fine.
    
    Reply
    
    Citation: https://doi.org/10.5194/egusphere-2026-3017-RC4
RC2:
'Comment on egusphere-2026-3017', Anonymous Referee #2, 21 Jul 2026 reply

Dear Editor, Dear Authors,
to begin with, I am not a native English speaker. Hence, it may have happened that I misunderstood parts of the paper or overlooked an important piece of information. The language used in the paper is very dense but never exactly to the point. A lot of semantically ambiguous sentences require double reading and sometimes I could understand the ideas of the authors much later when continuing with the text. Sometimes I could not. To be fair to the paper, I am a physicist but I am not familiar with some of the statistical methods used here. So I will not try to review the statistical methods in detail, but will keep the focus on their usage in the general workflow.
The paper addresses the important topic of deriving a robust index for upwelling valid across the upwelling cells in the Southern and Northern Benguela Upwelling System. The method should be generally applicable, especially to other major upwelling systems and may contribute to comparison and further understanding of those ecosystems. System analysis based on remote sensing data has growing importance. So the method developed here and the analysis done should be published.
The paper is written around a new specific method to evaluate the structure of SST pattern. Especially the temperature gradients as a possible indicator for upwelling is investigated in detail. The authors project the horizontal pattern onto cross shore lines. After producing the grid lines perpendicularly to the coast by solving a Poisson equation, SST data from several SST products are mapped onto the new grid. For each grid line it is tested, if the SST shape along the grid line can be described by a model made up by 2 line segments with different linear slope connected at some "breakpoint". One intercept, slopes of the two segments as well as the position of this breakpoint are the model variables determined by this fit. Although such a fit in principle exists for all profiles, the validity of the two linear segment model is evaluated by several statistical criteria and only part of the segments are accepted for further analysis. Finally, the line parameters and the break point position are used to calculate a specific temperature difference between a coastal and an off-shore temperature that may characterize upwelling. In the further course of the paper, this newly defined index is compared with another temperature difference based indices and a wind bases index as well. The sound differences are not surprising. The major message seems to be that an index considering a temperature difference between the coast an the open ocean may suffer from a to small distance of the open ocean reference point from the coast. Another finding is that upwelling indices based on a simplistic version of the Ekman theory and temperature gradient (difference) based indices may show a considerably different time evolution of the status of an upwelling cell. It confirms that wind driven upwelling and SST pattern produced previously by upwelling may not coincide.
The strength of the paper is the sophisticated statistical treatment of the SST-data. Its limitation is the complete lack of any physical background - as said by the authors themselves. The only justification to have upwelling in the title is the generally accepted fact that cross-shore temperature gradients usually stem from colder water upwelled near the coast. Also, there is no discussion, why upwelling situations should correspond best to a model with 2 linear segments separated by some breakpoint. Is it granted somehow that rejected cross-shore profiles do not correspond to upwelling? The strong discrepancy between upwelling detected from the wind pattern and the SST profiles near Walvis Bay is astonishing. Here the benefit gained from the new approach does not become clear at all. May be, old papers like that of de Szoeke and Richman (1984) or similar analytical models can help to make progress here with a more physical justification of the method.
The authors reduce the complexity of the two-segment piece wise-linear regression on selected grid lines. This includes sampling and loss of information. Rejected profiles imply a further loss of information that cannot be controlled or quantified. Other methods that are shortly cited in the introduction use integrals over areas defined by selected isotherms. This does not imply a similar loss of information. The paper needs a discussion, why the two-segment piece wise-linear regression should be superior anyway.
In the paper the location of the upwelling cells is prescribed. I would expect that the location of the upwelling cells should emerge from the analysis itself. This should be discussed with some sentences, when the basic concept of the new method is introduced.
The analysis is based on L4 SST products. Hence, gaps are filled in space and time. However, highly resolving SST must use some information from the visible band and is usually incomplete from clouds. Infrared or microwave derived SST is less contaminated by clouds, but has also less horizontal resolution. In any case the gap filling algorithm needs some thoughts. I did not check this for the SST-products used in this paper, but in former years gap filling was not only done by horizontal interpolation or extrapolation but also by assuming persisting temperature pattern over time spans without any SST information. In rare cases with clouds persisting long, some areas got the same SST value assigned over the period with cloud covered skies. Especially the Northern Benguela System is a candidate for long lasting cloud coverage. When comparing a wind derived upwelling index with a SST derived upwelling index this needs consideration. Also, ERA-5 is a reanalysis product (or forecast) and may be not consistent with observations from different sources.
Another limitation of the paper is that the reader does not find enough details eventually to repeat the statistical tests to accept or reject a profile. No formula is provided. For sure there are citations for several mathematical objects, but the direct correspondence to the quantities used in this paper is not obvious.
I must confess that my statistical knowledge is limited and not all statistical concepts became clear for me. However, the text uses a lot of statistics slang and deserves a more thorough language. It does not become clear, why block-bootstrapping is needed. I see that the mapping onto the new grid is "sampling" and the question is clear, if the sample represents the ensemble. But I did not understand the essence of Section 2.8. May be, the problem is on my side, but rewriting this section should be considered.
The authors (or the apparent intelligence (AI) they are using) invent terms and concepts that are unusual. There is no way around some examples:
- What are "Lamont years".
- What is a "Bakun offshore-Ekman-transport detector"?
- In Fig.4 I read: "... is computed from ERA5 10 m winds rotated to the local equatorward unit vector following the convention of Lamont et al. (2018)". This paper is not a convention but an analysis based on a theory for wind driven ocean currents. The winds do not have to be rotated. They are projected onto a local coordinate system with a long-shore and a cross-shore component. One may call this a rotated coordinate system, but the winds are not rotated. The long-shore component drives coastal upwelling. The wind stress curl drives another contribution to upwelling. The curl calculation does not require a specific coordinate system. In the case of this paper the wind should be projected into the coordinates defined by the grid derived from the Poisson equation. They are perpendicularly to the coast.
- Line 184: "rotated to the local coast-normal direction following Lamont et al. (2018), drives net offshore Ekman transport " This is simply not true. It is the long-shore wind component that drives off-shore directed Ekman transport, for sure a little bit away from the coast. I wonder, what the authors scripts do here. They should be designed with help of the same AI and the formulation rises serious doubts on this part of the paper. The github link gives 404. I hope, this example is an AI generated piece of text and the authors just overlooked that it does not have any physical meaning. A correction by humans should be straightforward.
"The daily binary wind detector, which informs the paired classifier of Section 2.7 and the NUD / NUE comparison, ...". If the "binary wind detector" is a mathematical object, how should it "inform" another mathematical object and the "NUD / NUE comparison" as well? How the number of upwelling days and number of upwelling events should be compared?
- "3.3. Per-day SST-structure classification and the SST–wind agreement": One may guess the meaning. But please find a wording that says directly what is meant. This applies also to other section titles.
Generally, the paper exhibits many of such sentences with questionable and floating wording and semantics. A human reader should take the time to turn this back into human communication conventions.
The final conclusions are reasonable. Contrary, the second part of the Abstract cannot be understood without studying the paper in detail. This is not reasonable for an Abstract. Please start the first sentence of the Abstrakt with "Some". I could not find the acknowledged scripts, github returns 404.
In summary, the results are interesting for the scientific community and may be stimulating and helpful for future work. Especially it may push forward the still outstanding investigation of an upwelling index based on the results of a highly resolving ocean circulation model. Such models are mature and the results are available from servers like the remote sensing data are. However, in the present form the paper is difficult to read, contains unclear topics and sentences. It needs definitely human work. The lack of physical justification of the used methods cannot be compensated by any well sophisticated statistics.
Detailed Questions:
150: If both the indices are different quantities just showing an instance of the coastal temperature drop - what is the purpose of scatter plots like Fig. 2?
272: "... are Benjamini–Hochberg (not defined) adjusted to control the false discovery rate (FDR) ... The FDR-controlled negative ... " What controls what in detail? I am lost.
Fig. 3: what is a data-emergent value of a variable?
Readability, Figure quality, Font size:
Generally check size of labels and captions in Figures.
Fig. 2 and 4: overlap of headline and color definition
Some tables have a tiny font and are not readable without additional zoom.
Fig. S5: It is good to have this figure. However, the plots remain tiny even with large zoom. In the Cape Frio plot, I cannot see how the inshore and offshore segments meet in some breakpoint. Also not in other figures. It is also more or less impossible to identify the original pattern and the related fits. For the rejected pattern it is clear that they do not show the typical 2 segments. Are they rejected because of the coastal edge buffer? However, there is still the typical coastal temperature drop. If there is curl driven upwelling and not coastal upwelling, why should be the inshore slope steepest? This recalls the question after a justification of the two segment model.
408: Who would detect changes in the surface heat content or so on climate relevant time scale based on a time series produced from different UI? So, is this final statement really needed?
de Szoeke, R. A. and Richman, R.: On wind-driven mixed layers with strong horizontal gradients – A theory with application to coastal upwelling, J. Phys. Oceanogr., 14, 364–377, 1984.

Kind regards

Reply

Citation: https://doi.org/10.5194/egusphere-2026-3017-RC2
- AC2:
  'Reply on RC2', Albertus Smit, 28 Jul 2026 reply
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-3017/egusphere-2026-3017-AC2-supplement.pdf
  Reply
  
  Citation: https://doi.org/10.5194/egusphere-2026-3017-AC2
  - RC3: 'Reply on AC2', Anonymous Referee #2, 03 Aug 2026 reply
    
    I will be away for the next 3 weeks. So I will add a short reply only.
    The authors had worked successfully to answer my questions and added thoughts about my remarks. I am convinced that the new version is written in a differently structured language without semantic shortcuts and so on. Form this point I am satisfied and would like to give the paper a go.
    One caveat is the idea to introduce new names in oceanography. I am sure, the topic of the paper is not suitable to do this.
    In detail: Vagn Ekman had success to close a disturbing gap between oceanography and physics. Older theories (Zöppritz) could not derive ocean currents from basic principles of hydrodynamics already well established in physics. The key of Ekmans success was an appropriate representation of turbulence and Coriolis force. So he could show that one flow component is a mean transport perpendicularly to the surface wind stress. His theory brought oceanography home to physics and it is pretty fair to give it the name "Ekman". Hence, we know today the "Ekman theory" and "Ekman transport".
    Andy Bakun was using the Ekman theory to analyze the flow within upwelling systems. But it is still the Ekman transport he is analyzing and not the "Bakun Ekman transport". Bakun was also rising a hypothesis on changes within upwelling systems related to climate change. This is called often Bakun hypothesis, but this is not subject of the paper discussed here. Bakun did not find a new theory of wind driven currents, that is still the Ekman theory.
    Tarron Lamont was analyzing upwelling in the Benguela System within a specific time span. I like this paper, but I do not see a reason to call the analyzed time span Lamont period or so.
    If someone discovers a new path, this path may get a name. Sometimes the discovery is very important and this is honored by giving the path an appropriate name. But not any event that some important person has important thoughts on this path justifies to rename it or to extend the paths name. So please check carefully throughout the paper, whether or not the names for theories or objects are correctly chosen and please do not introduce other or new names without a very strong justification. This justification should be added to the Acknowledgement section.
    The second caveat: The title of the paper contains "upwelling". The wording "upwelling index" is used several times. Within the paper the authors see fishermen and biologists as possible readers. I think it is not fair to expect from them to recognize that the paper is not on upwelling but offers a statistically view on a specific SST pattern within the Benguela system. For sure it is clear that a main element of the flow field generating this pattern is wind driven upwelling. But in turn it is shown within this paper that the considered specific structure does not appear often in all upwelling cells. This leaves it open, how the specific considered structure is related to upwelling. I am not convinced that the numbers derived with the "segmented-breakpoint" method should be called "upwelling index" at all, but consider it as a misleading framing of the results presented here. The contradiction between the introduction of the results as "upwelling index" on the one hand side and the unclear relation to upwelling especially in the Walvis Bay cell on the other hand pile up as a serious obstacle for direct publication of the paper as it is.
    I would understand any anger of the authors that I was not that stringent in the first review and must say sorry. I thought a lot on the paper during the last days and ended up with this statement: this contradiction cannot be resolved just by reformulating some phrases.
    Nevertheless - to be positive - the authors propose a new measure to quantify some specific SST structure and its time development throughout the upwelling cells. This is interesting. Avoiding the framing as "upwelling index" and with a revised title these results may be published just as a different view on the Benguela system, even if the physical background and the relation to upwelling is neither obvious nor clear. The results may or may not help to understand the structuring and time development of the ecosystem. For me as a reviewer it is not clear in which direction this could go, but this is up to the authors and possibly up to later readers and other scientists. Explaining the reason for considering the dichotomy of the segment-breakpont profiles and other profiles may develop a new frame to publish the result. The sections on other upwelling indicators may be kept, but as caveat that the new measure does not simply stand for a however defined upwelling strength.
    I hope my comments help to disentangle the situation and to proceed with the publication of the results.
    
    Reply
    
    Citation: https://doi.org/10.5194/egusphere-2026-3017-RC3

Albertus Jacobus Smit and Neville Sweijd

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Albertus Jacobus Smit and Neville Sweijd

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Short summary

We fit a daily breakpoint to cross-shore sea-surface-temperature profiles in five Benguela upwelling cells. Conventional 50 to 100 kilometre offshore references usually sample inside the fitted cool tongue, which can weaken or reverse fixed-distance contrasts. The method clarifies how index definition shapes cell-scale comparisons and sea-surface-temperature and wind agreement.


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