the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 16 Jan 2025
Comparing an idealized deterministic-stochastic model (SUP model, version 1) of the tide-and-wind driven sea surface currents in the Gulf of Trieste to HF Radar observations
Abstract. In the Gulf of Trieste the sea surface currents are observed by High Frequency Radar for almost two years (2021–2022) at a temporal resolution of 30 min. We developed a hierarchy of idealized models to simulate the observed sea surface currents, combining a deterministic and a stochastic approach, in order to reproduce the externally forced motion and the internal variability, which is characterized by a fat-tailed statistics. The deterministic signal includes tidal and Ekman forcing and resolves the slowly varying part of the flow, while the stochastic signal represents the fast-varying small-scale dynamics, characterized by Gaussian or fat-tailed statistics, depending on the statistical used. This is done using Langevin equations and modified Langevin equations with a Gamma distributed variance parameter. The models were adapted to resolve the dynamics under nine tidal and wind Forcing Protocols in order to best fit the observed forced motion and internal variability Probability Density Function (PDF). The stochastic signal requires 2 stochastic degrees of freedom when the averaged tidal forcing is adopted, while it needs 1/2 stochastic degree of freedom when the complete tidal forcing is used. Despite its idealization, the deterministic-stochastic model with stochastic fat-tailed statistics captures the essential dynamics and permits to mimic the observed PDF. Moreover, a Fluctuation Response Relation is valid when the stochastic signal is perturbed, showing that the response to an external perturbation can be obtained by considering the fluctuations of the unperturbed system.
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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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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2024-3391', Anonymous Referee #1, 06 Mar 2025
The paper introduces a hierarchy of idealized models to simulate surface current observations from an HFR site in northern Adriatic. They show that stochastic part of the signal (ie. residual current after tide and Ekman removal) obeys fat-tailed statistics with extremes occuring more often than expected from a Gaussian distribution. They employ deterministic, Gaussian and superstatistical stochastic models under several forcing protocols and observe the reproduction of statistical moments of each combination. The paper is interesting and might be of interest after some clarifications.Â
Perhaps i am missing something but in my opinion it would be interesting to take an existing hourly predictions from the CMEMS MFS model (or another full physics numerical model at your disposal, perhaps one with higher (r,t) resolution) as a baseline to compare your models to. They are hourly resolution but still it would be interesting to see what kind of statistics remains in the stochastic component from that full physics model.
Specific remarks:
L156: you mention $\gamma_u$ is "adjusted to obtain the observed decay function"Â - how is it adjusted, through what method?
Eq 4: \nu should be defined already here, not later in the text
L 168: please introduce Langevin equation and Ornstein-Uhlenbeck process in broad terms or refer readers to the appendix. You describe Ekman and Coriolis effects in more detail while perhaps it should be the other way around.
L176: what would be a physical interpretation of $\nu=1/2$?
L190: unknow = typo
L191: how is \beta increased empirically? What does this mean?
L219: why is M=131?Â
L238-9: the way they are defined, are \chi and \epsilon correlated or not?
L243: i am having trouble understanding exactly how this is done in the model? What do the forcing files look like for example? HOW do you impose this forcing? And furthermore, how exactly is FP1 forcing enforced?Â
L269; when you write the DET model is "trivial", do you mean zero?
I think the entire paper would benefit from considering CMEMS MFS, for example showing it on Figure 3.Â
As for Figure 3: you mention that DET simulation is missing the negative peak on April 3rd, which is clearly visible in HFR obs. But i don't see the negative peak in GAU or SUP simulations either. Am I missing something? What should I be paying attention to? Please explain this to the readers.Â
Figure 5: again, is it possible to add a PDF from CMEMS MFS stochastic residual current to this otherwise interesting plot?
P32: typo in the first line
Figure A1 is unreadable...
Â
Citation: https://doi.org/10.5194/egusphere-2024-3391-RC1 -
RC2: 'Comment on egusphere-2024-3391', Anonymous Referee #2, 10 Apr 2025
In this manuscript, the authors develop deterministic and stochastic parameterizations to represent the tide- and wind-driven sea surface currents in the Gulf of Trieste. A hierarchy of idealized models is introduced, where deterministic components account for tidal and Ekman forcing, while stochastic components, based on Langevin and superstatistical formulations, simulate unresolved small-scale variability. The model coefficients are calibrated to reproduce the Probability Density Functions (PDFs) of observed High Frequency Radar (HFR) velocity increments. The proposed models are evaluated under various wind and tidal forcing protocols and validated against observed statistics. The authors show that the full stochastic model (SUP) accurately reproduces the observed fat-tailed PDFs, captures extreme events, and improves the temporal autocorrelations. Furthermore, they demonstrate that when the complete tidal and wind forcing is used, the stochastic component requires fewer degrees of freedom, as more of the dynamics are captured deterministically.
This paper is well written, clearly structured, and presents compelling results. Overall, I recommend it for publication after minor revisions. Below I provide several comments aimed at further improving the manuscript.
- The conclusion section would benefit from being more concise. In its current form, it is overly long and technical, which may obscure the key takeaways of the study. The authors are encouraged to focus on the most important messages that readers should retain from the results presented. Detailed discussions and technical aspects would be more appropriately placed in Section 4, if not already covered there. Alternatively, the authors could consider summarizing the main findings at the end of each subsection in Section 4 to enhance clarity.
- In the context of the stochastic models GAU and SUP, is there a specific justification for assuming that the components x and y are uncorrelated, as indicated by the diagonal covariance matrix in equation (2)? Could this assumption be relaxed to allow for a correlation between the two components of the stochastic velocity in (4)? A more thorough clarification of this choice and its potential implications for the model would be appreciated. Â
- Line 298: The authors mention that data assimilation methods are adopted, but it is unclear which specific techniques are employed. Are they using 4DVar, EnKF, nudging, or another method? If this has already been addressed and I have overlooked it, I apologize. Otherwise, I would appreciate a clarification.
- The calculations presented in the appendices could be streamlined. In particular, several equations—such as (A4), (A13), (A16), (A19), (A20), (A22–A24), (A27), (A31), (B8), (C5–C7), (D4), and (D7)—include intermediate steps that could be omitted, especially where the variables involved have already been introduced earlier in the manuscript. To enhance clarity and conciseness, the authors are encouraged to reduce unnecessary multi-line derivations and express equations in a single line where feasible.
Typos:
- Line 69: Lorentz models -> Lorenz system
- Line 70: hierachy -> hierarchy
- Line 118: paramerterized -> parameterizedÂ
- Line 175: the bracket notation <Q> should be introduced here not later in Line 215
- Line 288: currrents -> currents
- Line 293: istantaneous -> instantaneous
- Lines 318, 347: occurrance -> occurrence
- Line 418: normailzed -> normalized
- Line 424: correspondance -> correspondence
- Line 646: respect -> with respect to, semplicity -> simplicity
- Line 659: indipendent -> independent
- Table 4 caption: (Flora et al., 2023) -> Flora et al. (2023)
Â
Suggestions:
- Line 74: Our modelization -> Our modelling approach
- Line 78: wind-and-tide-driven circulation -> wind- and tide-driven circulation
- Table 4: The authors may consider adding brief descriptions of the listed parameters to enhance clarity and understanding—for example, water density \rho. More importantly, it would be helpful for the model-specific parameters.
- Line 325, 326: due probably to -> probably due to, deviate slightly -> slightly deviate
Citation: https://doi.org/10.5194/egusphere-2024-3391-RC2 -
AC1: 'Comment on egusphere-2024-3391', Sofia Flora, 07 May 2025
Dear Editor,
We are grateful to both reviewers for their corrections and comments as they have increased the quality of the paper.
Please find our detailed answers (written in blue) and corrections to both reviewers comments (reproduced in black) in the attachment.
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2024-3391', Anonymous Referee #1, 06 Mar 2025
The paper introduces a hierarchy of idealized models to simulate surface current observations from an HFR site in northern Adriatic. They show that stochastic part of the signal (ie. residual current after tide and Ekman removal) obeys fat-tailed statistics with extremes occuring more often than expected from a Gaussian distribution. They employ deterministic, Gaussian and superstatistical stochastic models under several forcing protocols and observe the reproduction of statistical moments of each combination. The paper is interesting and might be of interest after some clarifications.Â
Perhaps i am missing something but in my opinion it would be interesting to take an existing hourly predictions from the CMEMS MFS model (or another full physics numerical model at your disposal, perhaps one with higher (r,t) resolution) as a baseline to compare your models to. They are hourly resolution but still it would be interesting to see what kind of statistics remains in the stochastic component from that full physics model.
Specific remarks:
L156: you mention $\gamma_u$ is "adjusted to obtain the observed decay function"Â - how is it adjusted, through what method?
Eq 4: \nu should be defined already here, not later in the text
L 168: please introduce Langevin equation and Ornstein-Uhlenbeck process in broad terms or refer readers to the appendix. You describe Ekman and Coriolis effects in more detail while perhaps it should be the other way around.
L176: what would be a physical interpretation of $\nu=1/2$?
L190: unknow = typo
L191: how is \beta increased empirically? What does this mean?
L219: why is M=131?Â
L238-9: the way they are defined, are \chi and \epsilon correlated or not?
L243: i am having trouble understanding exactly how this is done in the model? What do the forcing files look like for example? HOW do you impose this forcing? And furthermore, how exactly is FP1 forcing enforced?Â
L269; when you write the DET model is "trivial", do you mean zero?
I think the entire paper would benefit from considering CMEMS MFS, for example showing it on Figure 3.Â
As for Figure 3: you mention that DET simulation is missing the negative peak on April 3rd, which is clearly visible in HFR obs. But i don't see the negative peak in GAU or SUP simulations either. Am I missing something? What should I be paying attention to? Please explain this to the readers.Â
Figure 5: again, is it possible to add a PDF from CMEMS MFS stochastic residual current to this otherwise interesting plot?
P32: typo in the first line
Figure A1 is unreadable...
Â
Citation: https://doi.org/10.5194/egusphere-2024-3391-RC1 -
RC2: 'Comment on egusphere-2024-3391', Anonymous Referee #2, 10 Apr 2025
In this manuscript, the authors develop deterministic and stochastic parameterizations to represent the tide- and wind-driven sea surface currents in the Gulf of Trieste. A hierarchy of idealized models is introduced, where deterministic components account for tidal and Ekman forcing, while stochastic components, based on Langevin and superstatistical formulations, simulate unresolved small-scale variability. The model coefficients are calibrated to reproduce the Probability Density Functions (PDFs) of observed High Frequency Radar (HFR) velocity increments. The proposed models are evaluated under various wind and tidal forcing protocols and validated against observed statistics. The authors show that the full stochastic model (SUP) accurately reproduces the observed fat-tailed PDFs, captures extreme events, and improves the temporal autocorrelations. Furthermore, they demonstrate that when the complete tidal and wind forcing is used, the stochastic component requires fewer degrees of freedom, as more of the dynamics are captured deterministically.
This paper is well written, clearly structured, and presents compelling results. Overall, I recommend it for publication after minor revisions. Below I provide several comments aimed at further improving the manuscript.
- The conclusion section would benefit from being more concise. In its current form, it is overly long and technical, which may obscure the key takeaways of the study. The authors are encouraged to focus on the most important messages that readers should retain from the results presented. Detailed discussions and technical aspects would be more appropriately placed in Section 4, if not already covered there. Alternatively, the authors could consider summarizing the main findings at the end of each subsection in Section 4 to enhance clarity.
- In the context of the stochastic models GAU and SUP, is there a specific justification for assuming that the components x and y are uncorrelated, as indicated by the diagonal covariance matrix in equation (2)? Could this assumption be relaxed to allow for a correlation between the two components of the stochastic velocity in (4)? A more thorough clarification of this choice and its potential implications for the model would be appreciated. Â
- Line 298: The authors mention that data assimilation methods are adopted, but it is unclear which specific techniques are employed. Are they using 4DVar, EnKF, nudging, or another method? If this has already been addressed and I have overlooked it, I apologize. Otherwise, I would appreciate a clarification.
- The calculations presented in the appendices could be streamlined. In particular, several equations—such as (A4), (A13), (A16), (A19), (A20), (A22–A24), (A27), (A31), (B8), (C5–C7), (D4), and (D7)—include intermediate steps that could be omitted, especially where the variables involved have already been introduced earlier in the manuscript. To enhance clarity and conciseness, the authors are encouraged to reduce unnecessary multi-line derivations and express equations in a single line where feasible.
Typos:
- Line 69: Lorentz models -> Lorenz system
- Line 70: hierachy -> hierarchy
- Line 118: paramerterized -> parameterizedÂ
- Line 175: the bracket notation <Q> should be introduced here not later in Line 215
- Line 288: currrents -> currents
- Line 293: istantaneous -> instantaneous
- Lines 318, 347: occurrance -> occurrence
- Line 418: normailzed -> normalized
- Line 424: correspondance -> correspondence
- Line 646: respect -> with respect to, semplicity -> simplicity
- Line 659: indipendent -> independent
- Table 4 caption: (Flora et al., 2023) -> Flora et al. (2023)
Â
Suggestions:
- Line 74: Our modelization -> Our modelling approach
- Line 78: wind-and-tide-driven circulation -> wind- and tide-driven circulation
- Table 4: The authors may consider adding brief descriptions of the listed parameters to enhance clarity and understanding—for example, water density \rho. More importantly, it would be helpful for the model-specific parameters.
- Line 325, 326: due probably to -> probably due to, deviate slightly -> slightly deviate
Citation: https://doi.org/10.5194/egusphere-2024-3391-RC2 -
AC1: 'Comment on egusphere-2024-3391', Sofia Flora, 07 May 2025
Dear Editor,
We are grateful to both reviewers for their corrections and comments as they have increased the quality of the paper.
Please find our detailed answers (written in blue) and corrections to both reviewers comments (reproduced in black) in the attachment.
Peer review completion
Post-review adjustments
Journal article(s) based on this preprint
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Sofia Flora
Laura Ursella
Achim Wirth
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(10863 KB) - Metadata XML