Exploring the influence of wind stress and ocean stratification on sea surface temperature variability in the central tropical Pacific

Eusebi Borzelli, Gian Luca; Carniel, Cosimo Enrico; Carniel, Sandro; Sclavo, Mauro

doi:10.5194/egusphere-2026-2393

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https://doi.org/10.5194/egusphere-2026-2393

Preprints

28 May 2026

| 28 May 2026

Exploring the influence of wind stress and ocean stratification on sea surface temperature variability in the central tropical Pacific

Gian Luca Eusebi Borzelli, Cosimo Enrico Carniel, Sandro Carniel, and Mauro Sclavo

Abstract. The El Niño-Southern Oscillation (ENSO) is a climate oscillation in the tropical Pacific sustained by a positive feedback between sea surface temperature (SST) gradient and the Walker circulation, known as the Bjerknes feedback. This results in an oscillation in the SST anomaly between warm (El Niño) and cold (La Niña) phases. In traditional ENSO theories, the Bjerknes feedback amplifies an initial disturbance to produce a full El Niño or La Niña, while the Sverdrup transport, caused by off-equatorial wind stress (WS) curl, determines the slow charging of the equatorial Pacific through deepening of the thermocline. However, recent research has emphasized the role played by the WS divergence in generating Kelvin waves that initiate El Niño. To account for changes in the action of the WS over a varying ocean stratification, we introduce a dimensionless WS (DWS) and use the Helmholtz decomposition to break it down into an irrotational (curl-free) and solenoidal (divergence-free) component to study ENSO variability over the interannual-to-interdecadal time scale. We show that the irrotational component of the DWS drives the thermocline dynamics on interannual time-scales, while the solenoidal component, which drives Sverdrup transport, determines off-equatorial internal waves, referred to as q-waves, that induce changes in the thermocline depth over longer time-scales. Furthermore, we develop an integral relation that links the variability of the thermocline depth anomaly across the tropical Pacific to the Niño-3.4 index variability. We conclude that the DWS irrotational component determines the Niño-3.4 index interannual variability, while the solenoidal component determines its long-term variability.

Received: 26 Apr 2026 – Discussion started: 28 May 2026

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Gian Luca Eusebi Borzelli, Cosimo Enrico Carniel, Sandro Carniel, and Mauro Sclavo

Status: final response (author comments only)

RC1:
'Comment on egusphere-2026-2393', Anonymous Referee #1, 23 Jun 2026
This manuscript evaluates the impact of slowly varying components of wind stress and ocean stratification on the Niño3.4 index for sea surface temperature in the central tropical Pacific. The analysis offers an interesting analysis approach for evaluating processes governing central Pacific variability. However, I have reservations about the study in its present form.
Major concerns:
The study makes use of Copernicus data extending from 1960 through 2020. The record therefore begins prior to the start of the satellite era, and it is not clear that the data used for the analysis are consistent or realistic for the duration of the record. The authors do not seem to comment on questions about data validation or appropriateness for the analysis.

Figure 5 has an unexpected structure and needs to be checked carefully, and if it does not reflect a coding bug, then it needs to be explained. The most concerning aspect is the step-like monotonic increase in PC1 in Figure 5b. Since Figure 5d does not contain step changes, the year-by-year step changes in Figure 5b look like they could be the result of an erroneous signal fed into the EOF that is somehow dominating the mode 1 solution. For an ENSO-related signal, there is little or no reason to expect anything to show a steady monotonic increase over a 60-year period. I looked at the author’s code to try to gain clarity on this and was unable to identify the Matlab program responsible for the plots in Figure 5.

In section 4, the manuscript switches from discussion Z_15 to h. The term h is defined as the departure of the interface layer from D, but it is not linked to Z_15, and it’s unclear how the derivation in section 4 relates to the derivation in the previous section.

Setting h_eq and phi: At line 260, the authors note that -nabla^2 h_eq = nabla^2 phi, and use this as a justification to set -h_eq = phi. This doesn’t strictly need to be true, since h_eq and phi could differ by a gradient plus a constant, so the authors should clarify the logic that allows them to define phi. Subsequently, at line 293, the authors assume partial h_eq/partial t = 0. Taken together, these arguments seem to assume that phi is time invariant. The assumptions underlying these approximations should be justified more carefully.

The methods presented in section 3 are described without citations, as if this is brand-new material. In reality, the approach appears to be a fairly textbook approach to least-squares fitting and to empirical orthogonal functions. The work should be described in the context of previously published literature. I’ll also note that the presentation would probably be easier for readers to understand if the equations used matrix notation.

Figure labels and legends are too small to be read. As a courtesy to readers, authors should assume that readers might have printed out the manuscript on paper and need to be able to read it without hunting for a magnifying glass.

Other concerns
The first few lines of the introduction (lines 45-51) provide a general introduction to El Niño that would be appropriate for a popular science article but seems out of place in this analysis. I think the authors can start with their concerns about the Bjkerknes feedback and the Walker circulation.

Lines 171-172. Formally the drag coefficient should probably be a constant for very high wind speeds---in typhoon conditions, a foam layer is established at the ocean surface, which is thought to limit further growth of the draft coefficient. That detail is probably not important for this study. However, the authors should be aware that there has been further research on drag coefficients since 1981.

Lines 230-231. Note that the sign of the transfer function is arbitrary and depends only on the sign assigned to the EOF. To avoid confusing readers, it might be worth emphasizing that the sign applies to the figure but does not convey specific information about the solution.

Lines 241-242. “solenoidal (i.e. divergence-free) and irrotational (curl-free) vector field”. These words seem to be in reverse order relative to the terms in Equation (7), which is likely to confuse readers.

Line 242. Morse and Feshbach, 1953. While Morse and Feshbach might be the definitive reference for this material, there have been extensive publications in the last 10-20 years, and readers would likely be helped if they had pointers to the more recent literature as well.

Line 258. Why is the equation in the text set equal to zero. It seems to be the righthand side of Equation (8), but I do not see a clear justification for assuming that the lefthand side should be zero in a hydrostatic state. Maybe the authors mean a word other than “hydrostatic”?

Style and grammar

Line 74. “is described” -> “are described”

Line 97. “in to” -> “into”

Line 154. “as a” -> “to be a” [You might not think that the subjunctive exists in English, but it does….]

Line 179. “data includes” -> “data include”

Line 194. “is `optimal’” -> “be `optimal’”

Line 195. “(RMS) between” -> “(RMS) difference between”

Line 195. “is minimum” -> “be a minimum”

Line 196. “the bra-ket symbol”. This could be worded more succinctly (and more consistently with the oceanographic literature) as “the angular brackets”.

Line 243. Since the sentence following equation (7) defines the terms in the equation, it should probably not start a new paragraph. No indent.

Line 254. “seek for” -> “seek “ or “look for”

Line 257. “to as quasi-equilibrium layer” -> “as the quasi-equilibrium layer”

Line 293. “in to” -> “into”

Line 370. “by the equilibrium dynamics, which encapsulates” -> “by equilibrium dynamics, which encapsulate”

Line 507, 687. “Wusch” -> “Wunsch”

Line 514. Need a line break. The title for Appendix C seems to have been run into the
Citation: https://doi.org/10.5194/egusphere-2026-2393-RC1
- AC1: 'Reply on RC1', Gian Luca Eusebi Borzelli, 30 Jun 2026
  
  Dear Reviewer, please find attached our reply to your comments. Thanks for the time and effort devoted to evaluating our work.
  
  Citation: https://doi.org/10.5194/egusphere-2026-2393-AC1
RC2:
'Comment on egusphere-2026-2393', Anonymous Referee #2, 27 Aug 2026

Major comments:
The assumptions underlying h_eq and q do not satisfy current standards in the literature: h_eq is derived under the assumption of no motion, while the formulation of q excludes the region near the equator. The layer-thickness subcomponents associated with the rotational and divergent wind stress can be readily obtained by running the shallow-water model. The diagnostic expressions for the layer-thickness subcomponents should be discussed after their dynamical responses have been obtained from the shallow-water model.
The relative contributions of h_eq and q to the reconstructed Niño-3.4 variability are not quantified. In particular, since the manuscript attributes the long-term variability primarily to q, it would be useful to quantify and compare the low-frequency contributions from h_eq and q.
Technical Comments:
Figure 1a: Why does the Niño-3.4 index shown in Fig. 1a appear to have a substantial positive bias, with the La Niña events being systematically weaker? Compared with the Niño-3.4 index provided by the Copernicus Marine Service, the blue curve in Fig. 1a appears to be biased toward positive values. Please clarify the data source and processing used to obtain the Niño-3.4 index.
Figure 1a, 2b and 3: The ticks on the horizontal axis are difficult to read.
Figure 2b: The ticks on the vertical axis are difficult to read.
Line 192: It is unclear whether Z represents the interannual variability after removing the monthly climatology, or the raw (unprocessed) Z field.
Line 201: Please clarify whether the climatological and interannual components are treated together or separately in the analysis.
Line 202, 388: A conventional alternative would be to perform an EOF analysis of the Z_15field (or SSH, SST) and examine the correlations between Niño-3.4 and the leading PCs (PC1, PC2, etc.). What are the advantages of the method adopted in this study compared with this conventional approach?
Line 255: Defining h_eq by considering a stationary state may be useful as a second choice. This assumption effectively excludes the dynamical contribution of propagating waves, such as equatorial Kelvin waves. The manuscript initially appears to examine the dynamics of Z_15, but the subsequent analysis bypasses the mathematical symmetry of rotational and divergent contributions. The authors should clarify this point and its physical implications.
Line 265: The terminology used in the main text, the figure title, and the figure caption is inconsistent, which is confusing for the reader. In addition, the potential anomaly and h_eq should have opposite signs according to the definition given in the manuscript. Please make the terminology and sign convention consistent throughout the text and figures.
Eqs. (5) and (6): The notation c_n and c_m can easily be confused with c_1in Eq. (7). Please use distinct notation to avoid this ambiguity.
Eq. (7): It is unclear whether τ represents the interannual variability after removing the monthly climatology, or the raw (unprocessed) τ field.
Line 244: It would be useful to mention here that previous studies have suggested that the second baroclinic mode is more closely associated with Niño-3 variability.
Eq. (10): Its present form permits Rossby waves to propagate only westward and cannot capture the equatorward bending of wave rays associated with beta dispersion. A further concern is that Eq. (10) cannot account for the excitation of Rossby waves by equatorial and coastal Kelvin waves that propagate around the eastern boundary of the Pacific. Thus, the present formulation does not capture all wind-driven themocline variations associated with the rotational or divergent components of the wind stress.
Line 325: The quantity q will be obtained by time-integrating Eq. (8) with ϕ=0.

Citation: https://doi.org/10.5194/egusphere-2026-2393-RC2
- AC2: 'Reply on RC2', Gian Luca Eusebi Borzelli, 31 Aug 2026
  
  Dear Reviewer, please find attached our reply to your comments. Thanks for the significant suggestions and efforts devoted to evaluating our work.
  
  Citation: https://doi.org/10.5194/egusphere-2026-2393-AC2

Gian Luca Eusebi Borzelli, Cosimo Enrico Carniel, Sandro Carniel, and Mauro Sclavo

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Short summary

We study the central tropical Pacific sea surface temperature (SST) variability. Wind stress divergence drives thermocline fluctuations that trigger interannual SST variability. Mass redistribution due to wind stress curl, generates internal, off-equatorial Rossby-like waves. These waves have different propagation properties compared to ordinary Rossby waves, as they evolve alongside ocean stratification. The evolving propagation properties of these waves dictates the long-term SST variability.


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