the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 01 Jun 2026
Local dissipation efficiency of internal tides at key topographic features in the South China Sea
Abstract. The local dissipation efficiency of internal tides, q, is a critical parameter in tidal mixing parameterizations. However, the conventionally adopted constant value (q ≈ 0.3) in large-scale ocean models neglects its significant spatiotemporal variability. Based on the MITgcm LLC4320 simulation, the internal tidal energy budgets at the Luzon Strait (a source region, LS) and the Nansha Islands (a sink region, Nansha) in the South China Sea (SCS) are analyzed. Results indicate that the barotropic-to-baroclinic energy conversion in the LS reaches approximately 45 GW, with semidiurnal constituents accounting for roughly 60 %, due to the resonance over the double-ridge topography. The value of q in the LS fluctuates between 0.3 and 0.7, primarily modulated by the high-mode local dissipation. Local internal tide generation around the Nansha Islands is less than 1.5 GW; however, this region experiences significant convergence of internal tidal energy flux, which elevates the value of q to generally greater than 1 and occasionally exceeding 2.5. Modal analysis confirms that the intensified dissipation over the Nansha Islands originates predominantly from topographic scattering and breaking of mode-1 internal tides from the far field. Parameterizations for q are developed based on both physical factors and data-driven algorithms, both of which successfully capture the macroscopic clustering of q. In the LS, q is modulated by near-field factors such as the barotropic tidal forcing and the local dissipation of high-mode internal tides. Conversely, q around the Nansha Islands is primarily contributed by mode-1 internal tidal energy coming from the far field, highlighting the jointly modulation of local extreme dissipation by far-field beam interference and nonlinear topographic scattering.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2026-2713', Anonymous Referee #1, 25 Jul 2026
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AC1: 'Reply on RC1', Qingxuan Yang, 07 Aug 2026
We sincerely appreciate the reviewer’s valuable comments on our manuscript. Here, we provide our responses to the reviewer's concerns, and hope these responses can satisfy the reviewer. Please refer to the attached PDF for the detailed responses.
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AC2: 'Reply on RC1', Qingxuan Yang, 23 Aug 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-2713/egusphere-2026-2713-AC2-supplement.pdf
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AC1: 'Reply on RC1', Qingxuan Yang, 07 Aug 2026
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RC2: 'Comment on egusphere-2026-2713', Anonymous Referee #2, 10 Aug 2026
General comment:
This manuscript uses hourly LLC4320 output to compare internal-tide energetics in the Luzon Strait, a strong generation region, and the Nansha Islands, a remote energy-sink region. The source-to-sink comparison, separation of diurnal and semidiurnal bands, modal analysis, and attempt to connect the diagnosed energy ratios with both a physics-based regression and XGBoost are useful. In particular, the contrast between strong local conversion in the Luzon Strait and substantial far-field energy import around the Nansha Islands is very interesting for relevant researchers.
The manuscript is generally well organized, and the main results appear publishable. I recommend minor revision, mainly about clarifying q>1, distinguishing energy-budget residuals, testing robustness of modal analysis etc. These issues can largely be addressed using the existing output without redesigning the study.
Specific comments:
1. The conventional local dissipation efficiency q is a fraction of locally generated internal-tide energy and is therefore normally interpreted between zero and one. In the Nansha area, the reported quantity exceeds one because dissipation is normalized only by local conversion while the domain also imports energy. This is informative, but it is no longer an efficiency in the usual fractional sense. Maybe consider renaming it throughout as " local dissipation ratio" ? Or for the Nansha region, you could report dissipation normalized by the total available energy supply, e.g., positive local conversion plus net incoming baroclinic flux? This would have a clearer interpretation as an efficiency.Â
2. The present dissipation estimate is obtained as a residual of the energy budget and should therefore be interpreted as an inferred dissipation. Have you compared this estimate with directly diagnosed dissipation from the model, using the available velocity/density gradients and vertical mixing coefficients? previous studies have reported difference between the two methods, or at least relevant discussions on this point should be included.Â
3. The four lower panels in Fig. 5 appear identical to the corresponding Luzon Strait panels in Fig. 3. Their magnitudes and curves also contradict lines 205-213, which state that the Nansha modal energy terms are much smaller and that mode-1 q>2, reaching approximately 5. Please recheck these panels, and verify numerical statement that depends on them.
4. The paper attributes local dissipation to "high modes," yet only modes 1-5 are retained. Could you please compare the sum of modes 1-5 with the undecomposed modes to see the fraction for higher modes (>5).Â
5. L30-36 The introduction would benefit from distinguishing radiation, loss of phase coherence, scattering, and irreversible dissipation. Alford et al. (2019) provide an independent estimate of basin-scale mode-1 attenuation and emphasize that apparent flux decay can include both true energy loss and loss of stationarity. This is relevant to the manuscript's nonlocal framing.7. Lines 40-46 define higher q as stronger near-field dissipation at a generation site. This interpretation cannot be transferred directly to Nansha, where q>1 arises from imported energy.
8. L69-71, here the introduction identifies background-flow shear as a possible control on q. Wang and Legg (2023, 2025) examined how baroclinic eddy shear affects internal-tide refraction, modal energy transfer, and dissipation, and therefore directly connect vertical shear to dissipation of internal tides.Â
9. L199-203, Kelly et al. (2013) is a relevant independent reference for the redistribution of incident mode-1 energy among reflection, transmission, and scattering to higher modes at large topographic features. It would also help the authors distinguish scattering from final irreversible dissipation.
10. Abstract: Please distinguish total-band q, constituent-specific q, and modal q. The abstract reports total q occasionally exceeding 2.5, whereas the text later reports mode-1 values approaching 5.Â
11. Table 1. revise caption. The caption promises "associated errors," but no coefficient errors or confidence intervals are shown.Â
12. Figure 8. Only D2 results are shown, although performance claims are made for both bands.
13. Please discuss uncertainty associated with approximately 2-km horizontal resolution, unresolved wave breaking, numerical mixing, and the residual method.
14. Equations and notation. Please define all symbols upon first use and ensure consistent notation, signs. Also clarify the sign conventions for Conv, ( div F), and (DIS_bc).
Â
Â
Â
Citation: https://doi.org/10.5194/egusphere-2026-2713-RC2 -
AC3: 'Reply on RC2', Qingxuan Yang, 23 Aug 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-2713/egusphere-2026-2713-AC3-supplement.pdf
-
AC3: 'Reply on RC2', Qingxuan Yang, 23 Aug 2026
Peer review completion
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2026-2713', Anonymous Referee #1, 25 Jul 2026
The study investigates the regional differences (q) in the local dissipation efficiency of internal tides between the Luzon Strait and the Nansha Islands based on the LLC4320 simulation outputs. A physically-based empirical formulation and an XGBoost model are subsequently developed to parameterize q . This study contributes much to improving the understanding and parameterization of internal tide dissipation in the SCS. However, the manuscript still has some shortcomings, and the following points should be addressed further by the authors before publication. 1. fig 1: Since q is calculated from area-integrated conversion and dissipation, its magnitude may be sensitive to the choice of regional boundaries. Could the authors clarify the criteria used to determine the boundaries of the Luzon Strait and the Nansha Islands?
2. Lines 100–108: The manuscript only retains the first five baroclinic modes in the modal decomposition. Please state why five modes are sufficient for the analysis presented in this study? Given that high-mode internal tides are significant and important over steep and rough topography, it would be helpful to either provide the proportion of total baroclinic kinetic energy captured by modes 1–5, or discuss the potential influence of unresolved higher modes on the diagnosed local dissipation.
3. Lines 40–44 and 122–125: w is defined as the fraction of locally dissipated internal tidal energy relative to locally generated internal tidal energy, which would conventionally be expected to fall between 0 and 1. However, subsequent results presented in the manuscript report q > 1 in the Nansha Islands and negative q values for some individual modes in the Luzon Strait. Please provide the definition and sign convention of q, and explicitly explain the physical meanings of q > 1 and q < 0 in the present energy-budget framework?
4. Lines 90–92and 125–127: The LLC4320 simulation outputs used in this study only span approximately 14 months, from September 2011 to November 2012. In the analysis, January and August are used to represent winter and summer, respectively. As a result, the summer-winter differences reported in this manuscript are based on a single annual cycle rather than a multiyear climatology. Could the authors point out this limitation explicitly and avoid interpreting these differences as climatological seasonal variations?
5. Figs 2–5: Since the first and final months of the dataset are incomplete, could the authors specify how the monthly mean valuesof q for these two months were treated in the time-series plots? If these mean values were calculated from incomplete monthly records, this should be stated clearly; alternatively, the corresponding data points can be removed or marked separately.
6. Regarding Fig. 5j–m: These panels appear identical to Fig. 3j–m. Additionally, they are seeminglyinconsistent with the results described in Lines 205–213, such as the reduced magnitude of energy-budget terms and the relatively large mode-1 q Could the authors examine whether the proper data for the Nansha Islands have been plotted?
Citation: https://doi.org/10.5194/egusphere-2026-2713-RC1 -
AC1: 'Reply on RC1', Qingxuan Yang, 07 Aug 2026
We sincerely appreciate the reviewer’s valuable comments on our manuscript. Here, we provide our responses to the reviewer's concerns, and hope these responses can satisfy the reviewer. Please refer to the attached PDF for the detailed responses.
-
AC2: 'Reply on RC1', Qingxuan Yang, 23 Aug 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-2713/egusphere-2026-2713-AC2-supplement.pdf
-
AC1: 'Reply on RC1', Qingxuan Yang, 07 Aug 2026
-
RC2: 'Comment on egusphere-2026-2713', Anonymous Referee #2, 10 Aug 2026
General comment:
This manuscript uses hourly LLC4320 output to compare internal-tide energetics in the Luzon Strait, a strong generation region, and the Nansha Islands, a remote energy-sink region. The source-to-sink comparison, separation of diurnal and semidiurnal bands, modal analysis, and attempt to connect the diagnosed energy ratios with both a physics-based regression and XGBoost are useful. In particular, the contrast between strong local conversion in the Luzon Strait and substantial far-field energy import around the Nansha Islands is very interesting for relevant researchers.
The manuscript is generally well organized, and the main results appear publishable. I recommend minor revision, mainly about clarifying q>1, distinguishing energy-budget residuals, testing robustness of modal analysis etc. These issues can largely be addressed using the existing output without redesigning the study.
Specific comments:
1. The conventional local dissipation efficiency q is a fraction of locally generated internal-tide energy and is therefore normally interpreted between zero and one. In the Nansha area, the reported quantity exceeds one because dissipation is normalized only by local conversion while the domain also imports energy. This is informative, but it is no longer an efficiency in the usual fractional sense. Maybe consider renaming it throughout as " local dissipation ratio" ? Or for the Nansha region, you could report dissipation normalized by the total available energy supply, e.g., positive local conversion plus net incoming baroclinic flux? This would have a clearer interpretation as an efficiency.Â
2. The present dissipation estimate is obtained as a residual of the energy budget and should therefore be interpreted as an inferred dissipation. Have you compared this estimate with directly diagnosed dissipation from the model, using the available velocity/density gradients and vertical mixing coefficients? previous studies have reported difference between the two methods, or at least relevant discussions on this point should be included.Â
3. The four lower panels in Fig. 5 appear identical to the corresponding Luzon Strait panels in Fig. 3. Their magnitudes and curves also contradict lines 205-213, which state that the Nansha modal energy terms are much smaller and that mode-1 q>2, reaching approximately 5. Please recheck these panels, and verify numerical statement that depends on them.
4. The paper attributes local dissipation to "high modes," yet only modes 1-5 are retained. Could you please compare the sum of modes 1-5 with the undecomposed modes to see the fraction for higher modes (>5).Â
5. L30-36 The introduction would benefit from distinguishing radiation, loss of phase coherence, scattering, and irreversible dissipation. Alford et al. (2019) provide an independent estimate of basin-scale mode-1 attenuation and emphasize that apparent flux decay can include both true energy loss and loss of stationarity. This is relevant to the manuscript's nonlocal framing.7. Lines 40-46 define higher q as stronger near-field dissipation at a generation site. This interpretation cannot be transferred directly to Nansha, where q>1 arises from imported energy.
8. L69-71, here the introduction identifies background-flow shear as a possible control on q. Wang and Legg (2023, 2025) examined how baroclinic eddy shear affects internal-tide refraction, modal energy transfer, and dissipation, and therefore directly connect vertical shear to dissipation of internal tides.Â
9. L199-203, Kelly et al. (2013) is a relevant independent reference for the redistribution of incident mode-1 energy among reflection, transmission, and scattering to higher modes at large topographic features. It would also help the authors distinguish scattering from final irreversible dissipation.
10. Abstract: Please distinguish total-band q, constituent-specific q, and modal q. The abstract reports total q occasionally exceeding 2.5, whereas the text later reports mode-1 values approaching 5.Â
11. Table 1. revise caption. The caption promises "associated errors," but no coefficient errors or confidence intervals are shown.Â
12. Figure 8. Only D2 results are shown, although performance claims are made for both bands.
13. Please discuss uncertainty associated with approximately 2-km horizontal resolution, unresolved wave breaking, numerical mixing, and the residual method.
14. Equations and notation. Please define all symbols upon first use and ensure consistent notation, signs. Also clarify the sign conventions for Conv, ( div F), and (DIS_bc).
Â
Â
Â
Citation: https://doi.org/10.5194/egusphere-2026-2713-RC2 -
AC3: 'Reply on RC2', Qingxuan Yang, 23 Aug 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-2713/egusphere-2026-2713-AC3-supplement.pdf
-
AC3: 'Reply on RC2', Qingxuan Yang, 23 Aug 2026
Peer review completion
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Zuqing Yuan
Fenyuan Han
Jianing Li
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(7510 KB) - Metadata XML
The study investigates the regional differences (q) in the local dissipation efficiency of internal tides between the Luzon Strait and the Nansha Islands based on the LLC4320 simulation outputs. A physically-based empirical formulation and an XGBoost model are subsequently developed to parameterize q . This study contributes much to improving the understanding and parameterization of internal tide dissipation in the SCS. However, the manuscript still has some shortcomings, and the following points should be addressed further by the authors before publication. 1. fig 1: Since q is calculated from area-integrated conversion and dissipation, its magnitude may be sensitive to the choice of regional boundaries. Could the authors clarify the criteria used to determine the boundaries of the Luzon Strait and the Nansha Islands?
2. Lines 100–108: The manuscript only retains the first five baroclinic modes in the modal decomposition. Please state why five modes are sufficient for the analysis presented in this study? Given that high-mode internal tides are significant and important over steep and rough topography, it would be helpful to either provide the proportion of total baroclinic kinetic energy captured by modes 1–5, or discuss the potential influence of unresolved higher modes on the diagnosed local dissipation.
3. Lines 40–44 and 122–125: w is defined as the fraction of locally dissipated internal tidal energy relative to locally generated internal tidal energy, which would conventionally be expected to fall between 0 and 1. However, subsequent results presented in the manuscript report q > 1 in the Nansha Islands and negative q values for some individual modes in the Luzon Strait. Please provide the definition and sign convention of q, and explicitly explain the physical meanings of q > 1 and q < 0 in the present energy-budget framework?
4. Lines 90–92and 125–127: The LLC4320 simulation outputs used in this study only span approximately 14 months, from September 2011 to November 2012. In the analysis, January and August are used to represent winter and summer, respectively. As a result, the summer-winter differences reported in this manuscript are based on a single annual cycle rather than a multiyear climatology. Could the authors point out this limitation explicitly and avoid interpreting these differences as climatological seasonal variations?
5. Figs 2–5: Since the first and final months of the dataset are incomplete, could the authors specify how the monthly mean valuesof q for these two months were treated in the time-series plots? If these mean values were calculated from incomplete monthly records, this should be stated clearly; alternatively, the corresponding data points can be removed or marked separately.
6. Regarding Fig. 5j–m: These panels appear identical to Fig. 3j–m. Additionally, they are seeminglyinconsistent with the results described in Lines 205–213, such as the reduced magnitude of energy-budget terms and the relatively large mode-1 q Could the authors examine whether the proper data for the Nansha Islands have been plotted?