the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 26 Jun 2025
Deriving hourly diagnostic surface velocity fields considering inertia and an application in the Yellow Sea
Abstract. Surface currents play an important role in the transport of floating materials in the Yellow Sea, a region strongly influenced by tidal forcing and seasonal wind variability driven by the East Asian monsoon. While diagnostic models have been widely used to estimate surface currents, due to their steady-state assumption, high frequency variations such as tides and inertial oscillations cannot be resolved. To address this limitation, a time-dependent diagnostic model incorporating inertial terms into the governing equations is proposed. The performance of the proposed method is evaluated using buoy and drifter observations from 2015 to 2023. The time-dependent model in this study captures not only low frequency components (geostrophic and Ekman currents) but also high frequency variability (inertial oscillations and tides). Compared to the traditional model assuming steady-state, it shows significant improvement, achieving a correlation of 0.76 and Root-Mean-Square Error of 0.18 m s-1 (compared to -0.08 and 0.43 m s⁻¹ for the steady model, that caused by wrong governing equation ignoring inertia to describe tides) because of successful consideration of high frequency variability. The decay rate of inertial oscillations is analytically derived, providing insight into the time scale for past signals in surface currents to dissipate. We expect that this study offers a practical framework for surface current estimation considering both high and low frequency signals and can be applied for quick assessments of material transport in other coastal oceans.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2025-2748', Anonymous Referee #1, 25 Aug 2025
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AC1: 'Reply on RC1', Young-Heon Jo, 05 Sep 2025
Reviewer Comment #1:
This manuscript employs a diagnostic model to derive the surface velocity fields in the Yellow Sea. It presents many comparisons between the steady state Ekman model and the time-dependent Ekman model, showing that the time-dependent Ekman model has a great improvement. This seems to be quite simple since we must use the time-dependent one when considering the velocity of higher frequencies, such as tide and inertial. And the same feeling for including the inertial term, which is absolutely important at the period of strong wind change as it generates significant near-inertial currents. And including the time-dependent and inertial parts is easy, and not new. Overall, there are little novel insight in this work, and its scientific significance is low.
Author Response #1:
We appreciate the reviewer’s comments and efforts for our study. As the reviewer mentioned, inertial term is essential for resolving high-frequency processes such as tides and near-inertial oscillations and previous studies have already addressed this importance of inertia term, that was acknowledged in our manuscript (Line 48 in original manuscript).
Nevertheless, it has not been considered in previous studies on diagnostic velocity fields (Bonjean and Lagerloef, 2002; Rio et al., 2014; Dohan, 2017; Choi et al., 2023; cited in the manuscript). It is worth noting that OSCAR and GlobCurrent (currently provided by the most famous agencies, NASA and CMEMS) are still based on steady-state formulations ignoring the inertial term. To the best of our knowledge, our study is the first study applying the time-dependent Ekman theory to the diagnostic surface current reconstruction, which represents the novel contribution of our work. We kindly argue that, even though the theory and dynamics are not new, the application testing its surface current reconstruction ability is new and scientifically significant.
Furthermore, we generalized the analytical solution used in the theory to account for the pressure gradient, which may be regarded as progress in theory, and it enables the diagnostic velocity field to resolve tidal component. The fact that method is easy is what we intended, so many other researchers can easily adopt the method proposed in this study for their study areas and own dataset.
Reviewer Comment #4:
Line 25: ‘coastal oceans’ is not propriate.
Author Response #4:
We have revised the wording to “marginal sea” to more accurately describe the Yellow Sea.
Reviewer Comment #5:
Line 155: The time range of drifter data should be noted, as the comparison probably has a seasonal difference.
Author Response #5:
In the revised manuscript, the explicit time range of the drifter dataset have been added in the Data section. We appreciate this valuable suggestion about the seasonal comparison. Unfortunately, as we mentioned in manuscript, drifter observations are not available in winter, so we examined buoy observation for both summer and winter. Please refer to Figure S1 in the attached file for details. There are not significant differences between summer and winter in terms of skill scores. The seasonality of the surface current system of the study area, governed by low-frequency Ekman-geostrophic balances, were well discussed by Choi et al. (2023). In this study, we would like to focus on high frequency dynamics.
Reviewer Comment #6:
Line 216: How to obtain the velocity from drifters should have more detail. The buoy movement is affected not only by the surface current, but also by the direct wind push through a drag coefficient and the Stoke drift induced by the surface wave. Do you consider them?
Author Response #6:
Thank you for this helpful comment. We obtained drifter velocities from the observed positions (latitude and longitude) by calculating successive positions over next timestep, that is added in the manuscript.
The direct wind pushing (e.g., leeway drift) and Stoke drift are not considered in this study, similarly with the other diagnostic velocity field did (Bonjean and Lagerloef, 2002; Rio et al., 2014; Choi et al., 2023; cited in the manuscript). In this study, we focus on the merit of the diagnostic velocity field in considering the inertia term. We expect that the incorporating the velocity components (leeway and Stoke drifts) will enhance the diagnostic velocity field, but the results in this study (e.g., Fig. 3) elucidate that most variations in the in-situ observation can be explained by the four terms (inertial, Coriolis, pressure gradient, and vertical eddy viscosity).
Reviewer Comment #7:
Line 280: It is not clear what the variance ellipse stands for
Author Response #7:
Following the reviewer’s comment, we have added a statement explaining the variance ellipse in the revised manuscript. The following sentences will be added in Section 5.1 of the revised manuscript:
Variance ellipse represents current variability: the orientation indicates the dominant direction of variability, the length of major and minor axis corresponds to the variances in the direction, respectively.
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AC1: 'Reply on RC1', Young-Heon Jo, 05 Sep 2025
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RC2: 'Comment on egusphere-2025-2748', Anonymous Referee #2, 08 Sep 2025
In this study, the authors implement a diagnostic model for surface flows in the Yellow Sea, using a time-dependent model that includes both low-frequency geostrophic and Ekman velocities, and high frequency flows such as tides and inertial oscillations. The model in this setting, appears to substantially improve on earlier work using a steady Ekman model.
The authors do a good job demonstrating the advantage of incorporating the inertial terms in the diagnostic velocity field and comparing it to the steady Ekman theory model.
I would recommend accepting the manuscript with minor revisions:
My main reservation is about the geostrophic component obtained from altimetry, and I believe the authors would improve the manuscript by attempting to address some of these concerns:
(1) What kind of geostrophic circulation features are recurring in the Yellow Sea? It may be mentioned in past studies, but it would help to add a figure or two in the introduction or in section 3.2.1, documenting mesoscale motions and their variability.
(2) What is the contribution of the geostrophic component for the surface velocities in the Yellow Sea, with respect to the tidal and Ekman velocities?
(3) More specifically regarding the altimetry product: how close is the altimetry-derived geostrophic component to the in-situ velocities? Are the (CMEMS) velocity field errors (due to spatiotemporal interpolations, and quite shallow depth of the Yellow Sea) distinct from the high frequency motion errors, which are the main focus of this study? For instance, if you were to remove the geostrophic component in the diagnostic model, how much would it affect the correlations and RMS errors?
- Typos:
line 43: "(Choi et al., 2023). Choi et al. (2023)"
line 64: "trajectories of drifter"
line 179: "..which, as a result,.."?
line 248-249 (rephrase?) " This explains that the reason the steady Ekman theory.." to "this explains why the steady Ekman theory.."
line 393: "not sufficiently" -> "not sufficient"
Citation: https://doi.org/10.5194/egusphere-2025-2748-RC2
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This manuscript employs a diagnostic model to derive the surface velocity fields in the Yellow Sea. It presents many comparisons between the steady state Ekman model and the time-dependent Ekman model, showing that the time-dependent Ekman model has a great improvement. This seems to be quite simple since we must use the time-dependent one when considering the velocity of higher frequencies, such as tide and inertial. And the same feeling for including the inertial term, which is absolutely important at the period of strong wind change as it generates significant near-inertial currents. And including the time-dependent and inertial parts is easy, and not new. Overall, there are little novel insight in this work, and its scientific significance is low.
Other comments:
Line 25: ‘coastal oceans’ is not propriate.
Line 155: The time range of drifter data should be noted, as the comparison probably has a seasonal difference.
Line 216: How to obtain the velocity from drifters should have more detail. The buoy movement is affected not only by the surface current, but also by the direct wind push through a drag coefficient and the Stoke drift induced by the surface wave. Do you consider them?
Line 280: It is not clear what the variance ellipse stands for.