the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 24 Jan 2025
Determining the depth and pumping speed of the equatorial Ekman layer from surface drifter trajectories
Abstract. Trajectories of more than 500 drogued surface drifters launched since 1979 in the equatorial ocean are analyzed by employing the results of a new Lagrangian theory of wind-driven transport along the equator forced by the prevailing Trade winds. The analysis yields robust estimates of 45 meters for the Ekman layer’s depth and 1.0 meters/day for the upwelling speed of deep water into the layer.
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Status: closed
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RC1: 'Comment on egusphere-2025-89', Anonymous Referee #1, 20 Feb 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-89/egusphere-2025-89-RC1-supplement.pdf
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AC1: 'Reply on RC1', Nathan Paldor, 26 Mar 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-89/egusphere-2025-89-AC1-supplement.pdf
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AC1: 'Reply on RC1', Nathan Paldor, 26 Mar 2025
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RC2: 'Comment on egusphere-2025-89', Anonymous Referee #2, 21 Feb 2025
Review of Paldor and De-Leon “Determining the depth and pumping speed of the equatorial Ekman layer from surface drifter trajectories”.
Paldor and De-Leon investigate equatorial upwelling velocity by applying a recently developed Ekman theory for the equatorial beta plane to surface drifter data. By fitting the theory to Lagrangian trajectories, they derive an Ekman layer depth and an upwelling vertical velocity. This is a well-conceived and straightforward study that highlights new aspects of equatorial Ekman dynamics.
However, the authors should elaborate further on the underlying theory, the assumptions made, and, in particular, the applicability of drifters with drogues representing velocity at 15 m depth. Additionally, they should discuss the role of stratification. In the equatorial cold tongue regions of the Atlantic and Pacific, mixed layer depths are often extremely shallow (e.g., ~10 m). How would this affect the Ekman layer depth?
A primary concern is that the selection criteria for drifters could introduce a significant bias in the estimated Ekman layer depth and vertical velocity. The authors should also expand their literature review, acknowledging that different studies have reported varying vertical velocities depending on the meridional scale used in their analyses. I will provide a few examples, including Poulain (1993), which reports very high values for small meridional scales.
Overall, the manuscript is well written and suitable for publication after revision. Below are my specific comments:
L54: Minimum potential. More information would be helpful here to make this understandable without referring directly to Paldor (2024).
L101: Did you check for drifters that lost their drouges? Should be noted.
L103: Typically, there is substantial meridional wind, particularly in the equatorial Atlantic. How do you account for this effect? With the selection criteria used, a significant bias could be introduced, as only drifters associated with specific non-Ekman dynamics—such as tropical instability waves, Yanai waves, or meridional wind forcing—are considered. A way to test for such a bias would be to calculate the mean meridional drifter velocity as a function of latitude. It would be interesting to see how this quantity compares to the meridional velocities derived from Ekman theory.
L111: I do not understand this sentence. Please clarify. What does it mean? L is 2° or is L approaching y(0)? Or do you mean if y(0) approches L=2°? Is the erratic behavior a consequence of meridional wind forcing?
L113: Criterion for selection of drifters. Would it be a better criterion to consider the strength of the meridional wind, i.e., to only use drifters in cases of weak meridional wind? Additionally, what is the initial velocity of the drifters—for example, is it influenced by meridional wind forcing or, more importantly, by tropical instability waves, Yanai waves, etc.? Drifters could be deployed under different conditions.
L140: Result of the Ekman layer depth. There must be a strong bias in the mean since you specifically neglect drifters that do not flow in the expected direction or that cross the equator. As a result, you include all drifters that may be driven by other motions away from the equator but exclude those drifting toward it.
What would be the equatorial divergence if calculated from all drifters, i.e., the mean meridional velocity averaged along the equator at different latitudes (3°, 4°, 5°)? If there is a difference, how could it be explained?
L141: Can this be called oscillation free. How do you subtract the oscillation from the drifter velocity? To my understanding this would require the knowledge of the initial velocity.
L142: The derived velocity corresponds to the velocity at the depth of the drifters' drogue. What assumptions do you make about the vertical structure of the Ekman velocity? Would it be useful to also consider Argo drift velocities, which represent surface velocity, to calculate mean meridional velocities? This could provide an estimate of the vertical structure of the Ekman flow near the equator.
L147: I think one of the main results is the dependence of the derived vertical velocity on the meridional scale, which could also explain many previous estimates (see references below). This aspect should be given more emphasis.
References:
Bubnov, V. A., 1987: Vertical motions in the central equatorial Pacific. Oceanol. Acta, Spec.Vol. 6, 15–17.
Gouriou, Y., and G. Reverdin, 1992: Isopycnal and diapycnal circulation of the upper equatorial Atlantic Ocean in 1983–1984. J. Geophys. Res., 97(C3), 3543–3572.
Halpern, D., and H. P. Freitag, 1987: Vertical motion in the upper ocean of the equatorial eastern Pacific. Oceanol. Acta, Spec. Vol. 6, 19–26.
Halpern, D., R. A. Knox, D. S. Luther, S. G. H. Philander, 1989: Estimates of Equatorial Upwelling Between 140° and 110°W During 1984. J. Geophys. Res., 94, 8018-8020.
Hansen, D. V., and C. A. Paul, 1984: Genesis and effects of long waves in the equatorial Pacific, J. Geophys. Res., 89, 10,431–10,440.
Hansen, D. V., and C. A. Paul, 1987: Vertical motion in the eastern equatorial Pacific inferred from drifting buoys. Oceanol. Acta, Spec. Vol. 6, 27–32.
Poulain, P.-M., 1993: Estimates of Horizontal Divergence and Vertical Velocity in the Equatorial Pacific. J. Phys. Oceanogr., 23, 601–607.
Quay, P. D., M. Stuiver, and W. S. Broecker, 1983: Upwelling rates for the equatorial Pacific Ocean derived from the bomb 14C distribution. J. Mar. Res., 41, 769–792.
Citation: https://doi.org/10.5194/egusphere-2025-89-RC2 -
AC2: 'Reply on RC2', Nathan Paldor, 26 Mar 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-89/egusphere-2025-89-AC2-supplement.pdf
-
AC2: 'Reply on RC2', Nathan Paldor, 26 Mar 2025
Status: closed
-
RC1: 'Comment on egusphere-2025-89', Anonymous Referee #1, 20 Feb 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-89/egusphere-2025-89-RC1-supplement.pdf
-
AC1: 'Reply on RC1', Nathan Paldor, 26 Mar 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-89/egusphere-2025-89-AC1-supplement.pdf
-
AC1: 'Reply on RC1', Nathan Paldor, 26 Mar 2025
-
RC2: 'Comment on egusphere-2025-89', Anonymous Referee #2, 21 Feb 2025
Review of Paldor and De-Leon “Determining the depth and pumping speed of the equatorial Ekman layer from surface drifter trajectories”.
Paldor and De-Leon investigate equatorial upwelling velocity by applying a recently developed Ekman theory for the equatorial beta plane to surface drifter data. By fitting the theory to Lagrangian trajectories, they derive an Ekman layer depth and an upwelling vertical velocity. This is a well-conceived and straightforward study that highlights new aspects of equatorial Ekman dynamics.
However, the authors should elaborate further on the underlying theory, the assumptions made, and, in particular, the applicability of drifters with drogues representing velocity at 15 m depth. Additionally, they should discuss the role of stratification. In the equatorial cold tongue regions of the Atlantic and Pacific, mixed layer depths are often extremely shallow (e.g., ~10 m). How would this affect the Ekman layer depth?
A primary concern is that the selection criteria for drifters could introduce a significant bias in the estimated Ekman layer depth and vertical velocity. The authors should also expand their literature review, acknowledging that different studies have reported varying vertical velocities depending on the meridional scale used in their analyses. I will provide a few examples, including Poulain (1993), which reports very high values for small meridional scales.
Overall, the manuscript is well written and suitable for publication after revision. Below are my specific comments:
L54: Minimum potential. More information would be helpful here to make this understandable without referring directly to Paldor (2024).
L101: Did you check for drifters that lost their drouges? Should be noted.
L103: Typically, there is substantial meridional wind, particularly in the equatorial Atlantic. How do you account for this effect? With the selection criteria used, a significant bias could be introduced, as only drifters associated with specific non-Ekman dynamics—such as tropical instability waves, Yanai waves, or meridional wind forcing—are considered. A way to test for such a bias would be to calculate the mean meridional drifter velocity as a function of latitude. It would be interesting to see how this quantity compares to the meridional velocities derived from Ekman theory.
L111: I do not understand this sentence. Please clarify. What does it mean? L is 2° or is L approaching y(0)? Or do you mean if y(0) approches L=2°? Is the erratic behavior a consequence of meridional wind forcing?
L113: Criterion for selection of drifters. Would it be a better criterion to consider the strength of the meridional wind, i.e., to only use drifters in cases of weak meridional wind? Additionally, what is the initial velocity of the drifters—for example, is it influenced by meridional wind forcing or, more importantly, by tropical instability waves, Yanai waves, etc.? Drifters could be deployed under different conditions.
L140: Result of the Ekman layer depth. There must be a strong bias in the mean since you specifically neglect drifters that do not flow in the expected direction or that cross the equator. As a result, you include all drifters that may be driven by other motions away from the equator but exclude those drifting toward it.
What would be the equatorial divergence if calculated from all drifters, i.e., the mean meridional velocity averaged along the equator at different latitudes (3°, 4°, 5°)? If there is a difference, how could it be explained?
L141: Can this be called oscillation free. How do you subtract the oscillation from the drifter velocity? To my understanding this would require the knowledge of the initial velocity.
L142: The derived velocity corresponds to the velocity at the depth of the drifters' drogue. What assumptions do you make about the vertical structure of the Ekman velocity? Would it be useful to also consider Argo drift velocities, which represent surface velocity, to calculate mean meridional velocities? This could provide an estimate of the vertical structure of the Ekman flow near the equator.
L147: I think one of the main results is the dependence of the derived vertical velocity on the meridional scale, which could also explain many previous estimates (see references below). This aspect should be given more emphasis.
References:
Bubnov, V. A., 1987: Vertical motions in the central equatorial Pacific. Oceanol. Acta, Spec.Vol. 6, 15–17.
Gouriou, Y., and G. Reverdin, 1992: Isopycnal and diapycnal circulation of the upper equatorial Atlantic Ocean in 1983–1984. J. Geophys. Res., 97(C3), 3543–3572.
Halpern, D., and H. P. Freitag, 1987: Vertical motion in the upper ocean of the equatorial eastern Pacific. Oceanol. Acta, Spec. Vol. 6, 19–26.
Halpern, D., R. A. Knox, D. S. Luther, S. G. H. Philander, 1989: Estimates of Equatorial Upwelling Between 140° and 110°W During 1984. J. Geophys. Res., 94, 8018-8020.
Hansen, D. V., and C. A. Paul, 1984: Genesis and effects of long waves in the equatorial Pacific, J. Geophys. Res., 89, 10,431–10,440.
Hansen, D. V., and C. A. Paul, 1987: Vertical motion in the eastern equatorial Pacific inferred from drifting buoys. Oceanol. Acta, Spec. Vol. 6, 27–32.
Poulain, P.-M., 1993: Estimates of Horizontal Divergence and Vertical Velocity in the Equatorial Pacific. J. Phys. Oceanogr., 23, 601–607.
Quay, P. D., M. Stuiver, and W. S. Broecker, 1983: Upwelling rates for the equatorial Pacific Ocean derived from the bomb 14C distribution. J. Mar. Res., 41, 769–792.
Citation: https://doi.org/10.5194/egusphere-2025-89-RC2 -
AC2: 'Reply on RC2', Nathan Paldor, 26 Mar 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-89/egusphere-2025-89-AC2-supplement.pdf
-
AC2: 'Reply on RC2', Nathan Paldor, 26 Mar 2025
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