the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 07 Apr 2026
Near-Real-Time Assimilation of Satellite-Derived Ocean Surface Currents Using a Multi-Model Ensemble Kalman Filter
Abstract. Accurate near-real-time (NRT) estimation of ocean surface currents remains challenging due to sparse in-situ observations and structural model uncertainties. Most operational systems primarily assimilate altimeter-derived geostrophic currents, which omit ageostrophic contributions from wind forcing, coastal processes, and transient mesoscale dynamics. Direct assimilation of satellite-derived ocean surface currents therefore provides a pathway to improve the dynamical consistency of NRT surface current estimates, particularly in regions of highly variable circulation where accurate knowledge of the evolving ocean state is critical for marine operations. We present an end-to-end framework for direct assimilation of high-resolution satellite-derived surface current fields into a Multi-model Ensemble Kalman Filter (MEnKF). Surface currents are retrieved using an adaptive, constrained Maximum Cross-Correlation (MCC) algorithm applied to sequential AVHRR thermal imagery. The Earth Observation (EO)-derived currents are then integrated into a heterogeneous ensemble of global and regional forecasts to explicitly account for structural model uncertainty. Evaluation against coastal HF-Radar observations and regional reanalysis confirms statistically significant improvements over background forecasts. Under optimal observational conditions, the lowest RMSE (0.18 m/s) occurs when 9–12 EO-derived surface current products contribute to each assimilation cycle, accompanied by improved directional consistency relative to reanalysis data. Sensitivity analysis reveals that performance is driven by observational density and spatial representativeness, with maximum skill achieved at intermediate densities of 8–12 images per assimilation cycle. This framework provides a scalable, physically consistent pathway for improving NRT predictions in data-sparse regions.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-1683', Anonymous Referee #1, 18 May 2026
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RC2: 'Comment on egusphere-2026-1683', Anonymous Referee #2, 18 May 2026
Ocean velocity observations are presently not routinely assimilated in most ocean forecasting systems. This is largely due to the availability of NRT surface velocity observations which provided sufficient spatial coverage. This study looks at the impact of assimilating a novel surface velocity product into a multi model ensemble. Ocean surface velocities are derived from AVHRR SSTs using a maximum cross-correlation algorithm. The authors describe the methods used to process the data and outline the multi-model Ensemble Kalman filter used to assimilate the observations. I believe that this study is of interest to the community as it expands on the relatively limited field of ocean velocity assimilation. However, I feel the paper would benefit from significant revisions. In many places the explanations are unclear and in some places there are contradictions in the text. In addition, many of the results need a clearer benchmark to allow meaningful conclusions to be drawn.
Main general comments:
- The paper needs to have some context for the HF radar and renalaysis comparisons (in sections 4.2 and 4.3) by providing the statistics for the background multi model ensemble. In some places in the text these comparisons are alluded to (lines 499, 646, 818) but I can’t find any assessment of the background ensemble outside of section 4.1
- The paper requires a more thorough and clear description of the MEnKF method. The authors mention an iterative strategy, but this isn’t clearly defined in the text. Cycling aspects of the MEnKF are mentioned at times (e.g Figure 2) but it’s unclear if and how this is applied in this study.
- The paper would benefit from providing an example MCC EO image
- The observation errors for the HF radar should be provided
- More discussion/details on the handling of the different temporal windows for the observations is required. From my understanding, the temporal windows used to calculate the velocities can very from 1 hours to 24 hours. Are all these observations assumed to represent the 3 hourly mean currents? Are the handled in a different way during the data assimilation?
- In several places there authors claim that current magnitudes are underestimated in the MEnKF (lines 535, 536) but in other places they state that the current magnitudes are overestimated in MEnKF (lines 561,685-686, 743,749,767). Please make sure the results are consistently and correctly represented
- In general, the conclusions drawn from the results seem too strong. Please ensure that the results are not overstated.
- The discussion section would benefit from rationalisation. It is very long and not very coherent, in places it feels like statements are being repeated.
Specific comments:
Introduction
Line 60 “. They describe the instantaneous motion of surface features” – given that they are the displacement between 2 sequential features, I don’t think they can be considered instantaneous.
Line 99. These studies (Mirouze et al. 2024 and Waters et al. 2024) were assimilating synthetic data from a proposed satellite mission, real observation data of this type is not presently available. Please make sure this is clear in the text.
Line 114 “Despite these DA advances, only a limited fraction of available EO-derived ocean surface current observations” – This sentence is a bit misleading as in reality there are very limited NRT ocean surface currents available and the generally don’t provide the necessary spatial coverage for data assimilation.
Line 123 “Although EO satellite systems now provide near-global, high-temporal observations” – do you mean surface current velocities? I don’t think this is true.
Materials and methods
Line 159 – 161. “The selected period captures active mesoscale variability and evolving flow structures, offering a sufficiently complex dynamical regime for rigorous testing of ensemble behavior, covariance propagation, and incremental forecast skill.” – Do the authors have any evidence for this?
Line 161 “The objective at this stage is not climatological generalization” –Can the authors please clarify what they mean by this.
Line 170 – Was does “harmonized” mean in this context? It’s not defined or explained until later in the text.
Line 171 – What is the “associated climatology”? It hasn’t been defined yet.
Table1. – More information is needed about the forecasts used in this study. What forecast lead times are use? How often are the forecasts initialised? My impression from the table is that both a global and regional version of NEMO are used. These should be separated in the table for clarity.
Line 197 – “The suitability of reanalysis products for evaluating EO-derived surface currents is well established.” - can the reanalysis really be used to assess the ageostrophic currents? Since the reanalysis doesn’t assimilate velocity observations directly, it may largely be useful for assessing geostrophic currents.
Line 200- 204 – “More recently, Wang et al. (2023) reported high spatial correlations and relatively low RMSE between satellite-derived surface currents and CMEMS reanalysis fields, noting that residual discrepancies were often comparable to intrinsic model uncertainty rather than attributable solely to observational error.”- In general, this paragraph is arguing that a reanalysis is a useful product for assessing the currents, however, this sentence appears to be counter to that argument. It is fine to include this, but it needs to be clear that this is a counter-argument in the phrasing of this text.
Section 2.2.4 - I don’t think that at any point the authors explicity list the number of ensemble members in their multi-model ensemble. Please make sure this is provided.
Line 208 – In the text you refer to the “the CMEMS global analysis” but this isn’t included in Table 1. Please make sure the text and table are consistent. It is also perhaps a little confusing that both the renanalysis and NEMO forecast model are CMEMS products using NEMO. I believe the are produced by different centres (UK Met Office and Mercator). A clearer naming convention would be beneficial.
Line 208- 210 – It is unclear to me whether the ensemble is made up for forecast outputs, or analysis outputs from the these models. Please make this clear. If forecasts are used the forecast lead times should be provided.
Line 211 “All selected models provide surface current fields at spatial and temporal resolutions compatible with the underlying DA framework.” What is that temporal and spatial resolution of the DA framework?
Methodology
Line 217 – “Harmonization” is used again but it hasn’t yet been defined what this is.
Line 217 – It would be useful for the reader if the authors included a sentence here to clarify that these components will be described in more details later in this section.
Figure 2 - I was very unclear on how the cycling aspects on the MEnKF framework worked and whether any cycling of the MEnKF was used data assimilation framework was applied in this study. Please include a more detailed description of this Figure.
Line 228-231 “To mitigate data gaps and irregular acquisition timing inherent to NRT operations, a data-enrichment strategy was employed whereby all valid AVHRR image pairs acquired within a 24-hour window were systematically constructed. This enrichment strategy substantially increased the availability of short time-lag image pairs (ΔT < 3 hour), critical for NRT ocean currents estimation.” I found this difficult to understand, please rewrite. I found the explanation provided on lines 149-250 easier to understand.
Line 270 –Are missing vectors the same as missing pixels mentioned above? In figure 17, are the number of pixels therefore the number of "non fill-value" pixels? Please make this clear in the description of Figure 17.
Line 271 - I have some concerns about the choice to fill missing data with very low velocity information. The surface currents in this area could be very strong but the data may be missing because of cloud cover. Assimilating these calm-wind condition values will systematically underestimate the currents. While this is addressed in this discussion, something should be said about this here.
Line 290 – Need to state that this is Surface current velocity components.
Line 291 –“ extracted at matching lead times” – what is this lead time?
Line 292 – “forecasts were resampled onto the highest-resolution regional grid using bilinear interpolation” – It would be useful to state the resolution used explicitly here.
Line 309 – “and the resulting posterior ensemble was then advanced to initialize the subsequent forecast cycle. This approach ensures temporal consistency between asynchronous observations and forecast models.” - Please provide more explanation of this cycling aspect in the text.
Line 318 – “the global analysis field” – how is this defined?
318-320 – “The resulting analysis state was then used as the initial state for the next assimilation cycle if additional EO products remained available within the current time window, or otherwise adopted directly as the initial state for the forward forecast.” - were forward forecasts run in this study? Please make this clearer.
Line 364 – Is anything done to account for the different deltaT used in the AVHRR pairing? Please clarify the temporal interpolation aspect.
Line 387 -388 - “Following the analysis update, Xa and Pa serve as the prior for the subsequent assimilation cycle, with the final analysis state mapped back to the native model grid to initialize the next forecast.” – From my understanding this study is using historical forecasts from an archive, how can the analysis state be used to initialised the next forecast in this framework?
Line 423 – Please specify what the withheld observations are and how they are sampled.
Results
Line 443 “By effectively integrating dynamically relevant information from EO data into the MEnKF, the system significantly enhances the representation of mesoscale circulation features.” – which result demonstrates this?
Figure 6 – I assume these are the RMSE of the ensemble means? Please clearly define this. Same goes for line 450.
In section 4.1 does the sampling of the reference data also vary temporally? This may have an impact on the results.
In figure 7a, the RMSE is low at 03:00 despite a limited number of EO images. I don’t think this is discussed. Is there an explanation for this?
Line 492 – “RMSE values range from 0.15–0.17 m/s and MAE from 0.10 to 0.13 m/s” These values don’t seem to be entirely consistent with results in the tables provided with the Figures 8-10.
Line 493 – Where the paper mentions the small positive bias, does this mean in the current speed?
Line 499-501: “Nevertheless, these results indicate a moderate level of consistency between the MEnKF analysis and HFR observations, demonstrating the effectiveness of the assimilation in constraining surface circulation when direct velocity measurements are available.” - without providing the baseline of the background statistics, the results don’t clearly demonstrate that the EO assimilation is constraining the surface circulation. This comment also applies to lines 646-647 and line 818.
Line 532 – “observation – analysis” – since the results are comparing the reanalysis and MEnKF this needs clarification
Line 547 – state here what the RMSE, bias and SI are calculated relative to.
Line 583 - The persistent negative bias suggests a consistent tendency in the assimilation system of the observations themselves.” – this sentence isn’t clear
Section 4.3.1 – In figure 17 and 18 how much are the results impacted by the number of samples in each bin? The results may not very robust if there are only a small number of samples in some of the bin. This should be taken into account when the authors draw their conclusions from the data.
Discussion
Line 652 - (Wang et al., 2023; King et al., 2021; Vandenbulcke et al., 2017). – please check these references are being used correctly.
Line 666 – “The mean RMSE of ∼0.18 m/s against HFR measurements, ∼60% less than the internal misfit, confirms that the MEnKF achieves meaningful correction of the background ocean state” – What does the internal misfit mean? Where was this 60% shown?
Line 686 – “This is physically consistent with the known tendency of MCC-derived observations to capture energetic surface features, particularly in regions of strong thermal gradients” – this seems to contradict previous statements in the paper e.g line 512-513.
Line 730 – “The temporal stability throughout January 2021 (RMSE ∼0.6 m/s), maintaining stable performance across the variable winter time characteristics of the Galician shelf, including mesoscale eddy activity and intermittent poleward flow events” – This sentence isn’t clear.
Line 767 – would it be better to not assimilate the observations with low signal to noise (this would include the calm-weather values used to fill missing data)?
Conclusion
The authors mention the calm-weather fill values in the conclusion, but I’m not clear why it is necessary to fill these values. Data assimilation algorithms can deal with irregularly spaced observations already.
Reference
Vandenbulcke, L., Barth, A., and Beckers, J.-M.: Assimilation of High-Frequency Radar Surface Currents to Improve the Representation of 1055 Inertial Oscillations in a Coastal Ocean Model, Ocean Science, 13, 1–20, https://doi.org/10.5194/os-13-1-2017, 2017. – The DOI goes to a different paper.
Evensen, G.: The Ensemble Kalman Filter : theoretical formulation and practical implementation, Ocean Dynamics, pp. 343–367,https://doi.org/10.1007/s10236-003-0036-9, 2003 – This is provided in the references twice.
Citation: https://doi.org/10.5194/egusphere-2026-1683-RC2
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- 1
Review of “Near-Real-Time Assimilation of Satellite-Derived Ocean Surface Currents Using a Multi-Model Ensemble Kalman Filter”, by Baig et al.
This manuscript presents a technically sophisticated and timely framework for assimilating satellite-derived surface currents into a multi-model Ensemble Kalman Filter, addressing an important problem in ocean forecasting with clear potential operational relevance. The methodology is carefully constructed and supported by extensive sensitivity analyses. However, several aspects of the study raise substantive concerns that limit confidence in the results as currently presented. These include imprecise framing of the motivation, inconsistencies between the assimilated observations and the ensemble representation of the flow, the treatment of missing data, and the lack of independence in parts of the validation. In addition, the level of agreement with independent observations appears more moderate than implied, and the reported degradation of performance with increasing observational density, together with persistent biases, suggests that key assumptions underlying the data assimilation framework may not be satisfied in practice. For these reasons, significant clarification and revision are required before the manuscript can be considered for publication.
Detailed comments
A first issue relates to the motivation and the description of existing operational systems.
At L2, the manuscript states: “Most operational systems primarily assimilate altimeter-derived geostrophic currents.” I am not aware of operational ocean forecasting systems that directly assimilate surface geostrophic currents. In most cases, systems assimilate sea surface height and other scalar variables, from which geostrophic velocities may be inferred diagnostically, rather than assimilated explicitly.
A similar point arises at L35-37, where the manuscript again suggests that operational systems assimilate geostrophic velocities derived from sea surface height, citing Le Traon et al. (2019). That reference does not present examples of such assimilation, but rather notes parenthetically that geostrophic velocities can be derived from sea level. As currently written, this aspect of the manuscript risks giving a misleading impression of operational practice. This does not undermine the broader motivation of the study. The authors can make a strong argument that direct assimilation of observed or derived velocity fields may complement existing approaches by representing ageostrophic contributions. Reframing the motivation along these lines would strengthen the manuscript.
Related to this, the discussion of ageostrophic dynamics could be improved. At L40, the manuscript identifies “shelf seas and frontal zones” as regions where ageostrophic dynamics are significant. This is somewhat misleading. Ageostrophic contributions are important wherever the flow evolves in time, including much of the open ocean. In some frontal regions, geostrophic balance may in fact be particularly strong due to large density gradients. A more general and dynamically consistent description would be preferable.
The experimental design also raises some limitations that should be discussed more clearly. At L157, the study period is limited to one month (January 2021). The manuscript notes that the aim is not climatological generalisation but rather a controlled assessment of the method. Even so, the short duration limits the robustness of the conclusions, particularly given the strong dependence of the results on observational density and environmental variability. This limitation should be more clearly reflected in the interpretation of the results.
Another important issue concerns the independence of the validation. At L207, the CMEMS reanalysis product is used both as part of the ensemble (Section 2.2.4) and as a dataset for evaluation (Section 2.2.3). This means that the comparison with CMEMS is not independent. At best, it demonstrates that the system is internally consistent and does not introduce major technical errors. The inclusion of HF radar observations as an independent validation dataset is a strength of the study, but the role of the CMEMS comparison should be more carefully described.
A key methodological concern relates to the consistency between the observations being assimilated and the ensemble fields. The MCC-derived currents represent total surface velocity, and therefore include contributions from tides and other high-frequency processes. In contrast, none of the ensemble models appear to resolve tides. At the same time, assimilation is performed every three hours using an eight-hour time window, and the observations used in the assimilation seem to include tidal signals. This creates a fundamental inconsistency: the innovations being assimilated include processes that are not represented within the ensemble. It is not clear how this is reconciled within the framework, and this issue should be addressed explicitly.
The treatment of missing data is also a concern. At L269-276, missing values are assigned a near-zero velocity (0.001 m/s), justified as representing calm conditions. Although the authors provide a rationale for this approach, the assumption is problematic. Surface currents can remain strong in the absence of wind, for example in boundary currents or mesoscale eddies. More importantly, assigning artificial values to missing data alters the statistical structure of the observations and may influence covariance estimates in the assimilation. In a data assimilation framework, it is generally preferable to allow the model dynamics to fill observational gaps rather than imposing fixed values. This choice should be reconsidered or more carefully justified.
The temporal assumptions underlying the assimilation window also deserve clarification. At L305, the manuscript states that currents “remain approximately coherent over a period of up to three hours,” but the basis for this assumption is not clearly provided. Given the presence of tides, mesoscale variability, and rapidly evolving coastal processes, the validity of this assumption may vary significantly. Further justification would strengthen the methodological framework.
The description of the CMEMS reanalysis as a “physically consistent benchmark” at L193 and L198 also warrants clarification. While reanalyses represent state-of-the-art products, they are not strictly dynamically consistent in the sense of being free solutions of the governing equations. Sequential data assimilation introduces imbalances at each analysis step, followed by model adjustment. This does not invalidate their use as a reference, but the terminology could be refined.
At L210, the manuscript states that “a summary of these models and their key characteristics is provided in Table 1.” Table 1 lists spatial and temporal resolution, but does not include key information about the models themselves, such as their dynamical formulation, forcing, or data assimilation approaches. Expanding this description would improve clarity.
The quality of agreement between the MEnKF analysis and independent observations also deserves closer scrutiny. In the HFR comparisons (e.g., Figures 8-10), the reported RMSE values (~0.15-0.17 m/s) appear reasonable, but the visual comparisons suggest only moderate agreement in both magnitude and spatial structure. In particular, the vector fields and distribution plots indicate noticeable discrepancies in current strength and direction.
Similarly, the comparison with the CMEMS reanalysis (Figures 11-16) shows systematic underestimation of current magnitudes and only moderate correlation (mean complex correlation ~0.48). This level of agreement suggests that the assimilation captures some aspects of the flow but does not fully reproduce the observed or reanalysis structures. While the manuscript acknowledges some of these limitations, the overall interpretation tends to emphasise success more strongly than the results appear to support. A more balanced discussion of the strengths and limitations of the method would improve the manuscript.
The behaviour of the bias in Figure 17 is somewhat unexpected and deserves further discussion. In an ensemble Kalman filter framework, both model and observation errors are typically assumed to be unbiased, such that the analysis should not exhibit large systematic biases if these assumptions hold. However, the manuscript reports persistent and sometimes relatively large biases across observational regimes.
This likely reflects the combined effects of several factors, including biases in the MCC-derived currents, the use of near-zero fill values over regions with missing data, and inconsistencies between the assimilated observations (which include high-frequency processes such as tides) and the ensemble models (which do not represent these processes). In addition, structural differences between the assimilated fields and the reanalysis used for comparison may contribute to the apparent bias.
These factors suggest that the unbiased-error assumption underlying the data assimilation framework is not satisfied in practice. A more explicit discussion of these issues, and their impact on the reported bias, would strengthen the interpretation of the results.
The discussion beginning at L697, where the authors note that both low and high observational densities degrade performance, is somewhat concerning and warrants further examination. While it is expected that insufficient observational coverage leads to poorer analyses, the degradation of performance at high observation densities is less intuitive and suggests more fundamental issues in the assimilation framework.
In a well-posed ensemble Kalman filter system, the addition of more independent and unbiased observations should not systematically degrade performance; at worst, one would expect diminishing returns. The behaviour reported here indicates that the effective information content of the observations is not increasing with observation count and may in fact be degrading the analysis.
The explanations provided – such as spatial clustering, temporal inconsistency, and ensemble limitations – are plausible contributing factors, but they point toward deeper issues, including correlated observation errors, inconsistency between observed and model-resolved dynamics (e.g., tides and high-frequency variability), and limitations in the representation of error covariance. The treatment of missing data may also play a role, as the introduction of artificial near-zero values could further reduce the effective quality of the assimilated observations at higher data volumes.
This behaviour deserves more careful analysis, as it suggests that the data assimilation system may not be optimally configured to handle the characteristics of the observational dataset. A more explicit examination of these mechanisms, or additional sensitivity tests, would strengthen the manuscript.
In summary, this manuscript presents an interesting and potentially valuable framework for assimilating satellite-derived surface currents into a multi-model ensemble system. The methodological approach and sensitivity analyses are strengths, and the study addresses an important problem in ocean forecasting. However, several aspects of the work require substantial clarification or revision. These include the framing of the motivation, the consistency between observations and ensemble fields, the handling of missing data, and the independence of the validation.
In addition, the level of agreement between the MEnKF analysis and independent datasets appears more moderate than implied by the overall narrative, with discrepancies in structure, magnitude, and correlation that warrant a more balanced interpretation. The presence of persistent bias and the reported degradation of performance at higher observational densities further suggest that key assumptions underlying the data assimilation framework – such as unbiased errors and consistent dynamical representation – may not be fully satisfied in practice. These behaviours point to potential structural limitations in the assimilation system that deserve more explicit examination.
Addressing these issues would significantly strengthen the manuscript and improve confidence in the reported results.
I recommend reconsideration after major revision.