{"id":"163dd6f8-5587-4abf-844d-ccbf59757b2d","arxiv_id":"2601.18182","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Using mrCOSTS, the authors separate sub-inertial (period >10 days, scale >100 km) sea-surface height from SWOT one-day-repeat orbit into a global geostrophic velocity product, with Rossby numbers mostly below unity and drifter agreement comparable to the standard AVISO product.","lead":"Satellite measurements of sea-surface height mix ocean currents with tides and waves; this paper uses a data-driven mode-decomposition method to extract what it calls the strictly geostrophic (current-dominated) part from three months of SWOT satellite data. The result is a publicly planned global dataset of geostrophic surface velocities at scales larger than about 100 km and slower than about 10 days, which the authors check against drifters in the Mediterranean.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Validation confounds spatial smoothing with temporal DMD filtering: Rossby-number improvement over L3HYCOM may be entirely due to the 6-km Gaussian pre-filter, leaving the 'strictly geostrophic' claim unsupported.","rationale":"The reader identified residual internal-tide contamination from the HYCOM correction as the weakest premise. I find a more fundamental and directly testable confound: the comparison in Section 3.2 does not control for spatial smoothing. The mrCOSTS pipeline includes a 6-km Gaussian filter before DMD, while the L3HYCOM baseline is unfiltered raw data. Since vorticity and strain are dominated by small scales, the improved Rossby-number PDFs are expected from spatial filtering alone and cannot be used to credit the temporal decomposition. This does not mean the product is wrong, but the 'strictly geostrophic' and 'overcomes spectral leakage' claims are not supported by the presented evidence. The proposed control experiment is straightforward using existing code and data. This is an addressable revision concern, consistent with a conditional verdict; the manuscript should not be rejected outright because the data product may still be useful and the frequency-band argument is physically plausible.","tokens_in":15528,"tokens_out":3710,"duration_ms":42790,"concrete_test":"Apply the same isotropic Gaussian spatial filter (σ≈6 km, step 3) to the L3HYCOM fields, compute geostrophic velocities and ζ/|f|, |α|/|f| joint PDFs using the same Tranchant et al. (2025) prescription, and compare to the mrCOSTS PDFs in Fig. 3d,i,o,t. If the filtered-L3HYCOM PDFs are statistically indistinguishable from mrCOSTS, the temporal DMD provides no added balance improvement and the 'strictly geostrophic' claim reduces to spatial filtering.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim is that mrCOSTS extracts a 'strictly geostrophic' component by temporal sub-inertial filtering (Section 2.1, steps 5–6), overcoming temporal aliasing. But the evidence for dynamical viability in Section 3.2 compares joint PDFs of vorticity and strain from mrCOSTS ηg against 'L3HYCOM, i.e., the raw SWOT data de-tided by the HYCOM forecast' (Fig. 3 caption). L3HYCOM is not subjected to the Gaussian spatial filter of step 3 (σ≈6 km). Since vorticity and strain amplify small-scale gradients, the reduced tails in the mrCOSTS PDFs could be produced entirely by this spatial low-pass filtering, with no contribution from temporal DMD. The paper explicitly says the spatial smoothing is 'not used to extract the geostrophic component but rather to a priori remove signals that should definitively not be in geostrophic balance,' yet the only head-to-head diagnostic shown does not isolate the temporal filter. Thus the claim that mrCOSTS 'overcomes spectral leakage' and yields dynamically viable modes is not established; a simpler spatial-filter product might perform identically in the metrics shown.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper applies the multi-resolution coherent spatio-temporal scale separation (mrCOSTS) dynamic mode decomposition to the global SWOT fast-sampling phase (March 29–July 11, 2023) Level-3 sea-surface height anomalies. The authors replace the default HRET internal-tide correction with a HYCOM forecast correction, then define a 'strictly geostrophic' component ηg as the sum of mrCOSTS modes with frequency <0.1 cpd (periods >10 days). They process every SWOT pass, promise public distribution of the global product, and evaluate it via frequency–wavenumber spectra at four cross-over regions, joint PDFs of vorticity and strain, and a comparison to SVP drifters in the western Mediterranean Sea. The main claims are that mrCOSTS overcomes spectral leakage due to temporal aliasing, that ηg has Rossby numbers mostly below unity, and that its velocity estimates agree with drifters at least as well as the default L3HRET product while reducing speed bias.","tokens_in":15860,"tokens_out":5333,"duration_ms":57815,"significance":"If fully supported, the paper would provide a practical, global method for exploiting the temporal dimension of the 1-day-repeat SWOT orbit to separate balanced motions from internal tides and ageostrophic eddies, avoiding the arbitrary spatial-filter choices common in SWOT analyses. The pipeline is clearly documented, the code is available, the HYCOM-based IT correction is state-of-the-art, and the authors are transparent about residual limitations (e.g., missing cyclonic skewness, short Cal/Val record, limited drifter sample). A publicly distributed global geostrophic product would be a valuable community resource. However, the validation as presented does not isolate the DMD temporal filter from the Gaussian spatial pre-filter, and the drifter comparison lacks a quantitative skill metric. Thus the central claims are defensible but not yet fully supported.","major_comments":[{"comment":"The head-to-head comparison of ζg/|f| and |αg|/|f| between mrCOSTS ηg and L3HYCOM confounds the temporal DMD filtering (Steps 5–6) with the Gaussian spatial filter of Step 3, which is applied only to mrCOSTS. Vorticity and strain amplify small-scale gradients, so the reduced tails in the mrCOSTS PDFs could be produced entirely by the ~6 km spatial smoothing. The text states the spatial smoothing is 'not used to extract the geostrophic component,' but no control product is shown. Please add a comparison of L3HYCOM after the same Gaussian filter, and ideally after a simple temporal low-pass filter, to isolate the DMD contribution. Without such a control, the central claim that mrCOSTS 'overcomes spectral leakage' is not established.","section":"§3.2, Fig. 3"},{"comment":"The sharp spectral cutoff at 10 days in the ω–k spectra of ηg is partly circular: ηg is defined as the sum of modes with frequency <0.1 cpd, so the observed cutoff restates the construction. The statement in §3.1 that 'there is a clear cutoff of power at time scales shorter than 10 days' acknowledges this, but it does not validate geostrophic character. Independent evidence must come from the drifter comparison or from a quantitative skill metric; the Rossby-number contrast is confounded per the preceding comment. Please provide a non-circular diagnostic, for example the fraction of spectral energy of ηg at periods just below and above 10 days, or a comparison to a model balanced component.","section":"§2.1, Step 6; §3.1, Fig. 2"},{"comment":"The drifter validation is qualitative and geographically narrow. The paper itself notes that L3HRET is 'slightly better aligned' (smaller angular spread) than mrCOSTS, while mrCOSTS reduces speed bias, but the claim 'at least as good as if not better' is not backed by a statistical measure. Please provide quantitative error statistics (e.g., complex correlation, median and interquartile range of the ratio, circular standard deviation) with uncertainty estimates. Consider extending the analysis to more than one Mediterranean pass or to other regions with available in situ data, or explicitly frame the results as a single-region case study.","section":"§3.3, Fig. 4"},{"comment":"The entire product rests on the assumption that the HYCOM forecast internal-tide correction removes essentially all incoherent IT energy after 'add back HRET, subtract HYCOM.' Any residual IT variance would be classified as geostrophic by the <0.1 cpd cutoff. The paper provides no independent check of residual tidal variance in ηg (e.g., spectral energy at M2/K1 frequencies or comparison to tide-gauge/current-meter data). If Yadidya et al. (2025) contains such validation, cite the specific evidence; otherwise add a diagnostic to the manuscript.","section":"§2.1, Step 1"},{"comment":"The mrCOSTS hyperparameters (window lengths [9,10,30,60] days, SVD ranks [4,4,10,12]) and the 0.1 cpd geostrophic-frequency cutoff are set by hand with no sensitivity analysis. DMD/mrCOSTS modes can depend nontrivially on windowing and rank truncation. A sensitivity test (e.g., varying the cutoff between 0.08 and 0.12 cpd, adjusting window/rank choices) is needed to show that the main conclusions—PDFs, spectra, drifter agreement—are robust. This is especially important because the 'strictly geostrophic' claim is the paper's central contribution.","section":"§2.1, Step 5"}],"minor_comments":[{"comment":"The author affiliation contains repeated/odd characters in the Chinese transliteration ('内 内 内田 田 田貴 貴 貴也 也 也'), likely a LaTeX artifact; please fix.","section":"Author list"},{"comment":"The Gaussian filter is described as having standard deviation 'of three grid points (~6km).' Please specify the nominal grid spacing and whether the filter is isotropic in both along-track and cross-track directions.","section":"§2.1, Step 3"},{"comment":"The text states that the geostrophic spectra 'peaks at scales larger than 100 km and slower than 20 days,' which is inconsistent with the 10-day cutoff in Fig. 2 and Step 6. Should read '10 days' unless a different frequency range is intended.","section":"§3.1"},{"comment":"The caption of Fig. 3 uses 'mrCOASTS' in one panel label; should be 'mrCOSTS' for consistency. Also, the sentence in §3.2 'the joint PDFs are documenting that geostrophic balance was applied to SSHa signals in L3HYCOM that were in fact not in balance' could be rephrased more concisely.","section":"§3.2, Fig. 3"},{"comment":"The polar-histogram labels in Fig. 4 use 'Drifter / L3' and 'Drifter / mrCOSTS' but the text refers to the L3HRET product; please harmonize notation. The rotary-spectra caption would benefit from explicitly describing which curves correspond to the 25-hr and 48-hr filters.","section":"§3.3, Fig. 4"}],"recommendation":"major_revision","confidential_remarks":"The central approach is plausible and the product would be a useful community asset, but the validation currently confounds the temporal DMD filter with the spatial pre-filter, and the drifter comparison lacks quantitative metrics. These are fixable within the manuscript's scope via a control experiment and additional diagnostics. I recommend major revision rather than reject, as the core methodology is sound and the authors appear aware of several limitations."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis is a useful data-product paper, not a conceptual breakthrough. The new bit is global: mrCOSTS applied to every SWOT one-day-repeat pass, with HYCOM-based internal-tide removal replacing HRET, and a Mediterranean drifter comparison. Uchida et al. (2025) had shown the method worked in the Gulf Stream; this paper industrializes it. The spectra and PDFs are clearly presented, and the public distribution of the product is a real service.\n\nThat said, the central claim—that mrCOSTS 'overcomes spectral leakage' and yields 'strictly geostrophic' velocities—is not fully established. Three issues:\n\n1. The vorticity-strain PDF comparison against L3HYCOM is confounded. L3HYCOM is the raw SWOT data after HYCOM de-tiding, with no spatial filter. The mrCOSTS field went through both the 6-km Gaussian pre-filter and the DMD temporal decomposition. Since vorticity and strain amplify small-scale gradients, the tighter PDF tails could come entirely from the spatial filter. A proper control would be L3HYCOM processed through step 3 only. Without that, the improvement over L3HYCOM doesn't isolate the temporal filtering, which is the paper's whole point. This is not a minor quibble; it's the load-bearing evidence for 'strictly geostrophic.'\n\n2. The 10-day cutoff in the ω-k spectra is circular. ηg is defined as modes with frequency <0.1 cpd, so spectral power dropping below 10 days restates the construction. The external grounding comes from the drifters, but that comparison is limited to one Mediterranean pass, covers only ~12,700 collocations, and the authors report that L3HRET actually aligns slightly better in phase, with mrCOSTS mainly reducing speed bias. No quantitative skill metric is given.\n\n3. The HYCOM IT subtraction is assumed accurate. Yadidya et al. (2025) support it, but residual incoherent ITs leaking into the sub-inertial band would be classified as geostrophic. There is no independent check of residual tidal variance in ηg.\n\nThe paper is honest about its own limitations—it acknowledges the lack of cyclonic skewness and the imperfect drifter agreement. The hyperparameters (window lengths, SVD ranks, cutoff) are hand-picked with no sensitivity analysis, which as a reviewer I'd want to see. These are addressable. The product itself, once public, will be useful for KE-cascade and QG vertical-velocity studies. I would send it out for review if I were the editor; I'd insist on a spatial-filter-only control, sensitivity tests, and a residual-tide check before accepting.\n\nCheers","headline":"A useful global extension of an existing DMD decomposition to all SWOT fast-sampling passes, but the 'strictly geostrophic' claim is stronger than the evidence supports because the key validation conflates spatial smoothing with temporal filtering.","tokens_in":16344,"tokens_out":2441,"would_cite":true,"duration_ms":25594,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A frequency-domain decomposition of SWOT's daily repeat orbit isolates a strictly geostrophic sea-surface height field, resolving the ambiguity of spatial filtering and matching drifters at least as well as the default product.","keywords":["SWOT","geostrophy","dynamic mode decomposition","mrCOSTS","internal tides","sea-surface height","vorticity-strain statistics","altimetry"],"falsifier":"Run the same mrCOSTS pipeline on synthetic SWOT-like observations generated from a model with known geostrophic and ageostrophic fields and compare the extracted sub-0.1-cycles-per-day height to the known truth; alternatively, check the released product for residual variance at diurnal and semidiurnal frequencies. If residual tidal variance is significant or the reconstructed geostrophic field deviates from truth beyond sampling error, the strict-geostrophy claim fails.","tokens_in":15449,"feed_emoji":"🌊","tokens_out":8444,"duration_ms":74092,"temperature":0.7,"pith_summary":"The paper sets out to remove the ambiguity in applying geostrophic balance to SWOT altimetry: instead of choosing a spatial filter and calling the result geostrophic, it uses the temporal dimension of the one-day-repeat orbit to keep only sea-surface height variability slow enough to be in geostrophic balance. The tool is a recursive dynamic mode decomposition, applied after replacing the default empirical internal-tide correction with an ocean-forecast-model tidal field. Summing modes with frequency below 0.1 cycles per day defines the geostrophic component; the paper claims this component has vorticity and strain mostly below the local Coriolis frequency, meaning small Rossby numbers, and that its velocities agree with drifters at least as well as the standard product with a reduced speed bias. A global public dataset of these strictly geostrophic velocities is the resulting deliverable, offering a baseline for diagnosing energy cascades and quasi-geostrophic vertical velocities.","feed_headline":"Frequency filter isolates geostrophic flow in daily SWOT data","feed_subtitle":"The sub-inertial height fields pass the Rossby-number test and match drifters at least as well as the standard product.","key_machinery":"mrCOSTS — multi-resolution COherent Spatio-Temporal scale Separation, a recursive dynamic-mode-decomposition variant that assigns each spatial pattern a temporal frequency without requiring periodic boundaries. It is applied over four levels with window lengths of 9, 10, 30 and 60 days, and the geostrophic component is the sum of modes with frequency below 0.1 cycles per day. The companion mechanism is internal-tide preprocessing: the default empirical tide product is added back, then internal-tide sea-surface signals from an ocean forecast model are subtracted, so that remaining variability is mostly free of both coherent and incoherent internal tides before the frequency split.","core_discovery":"The central claim is that geostrophy is a low-frequency balance, and that temporal information from SWOT's fast-sampling orbit can be used to enforce it, rather than relying on spatial scale alone. The geostrophic sea-surface height field, ηg, is constructed by summing mrCOSTS modes with frequencies below 0.1 cycles per day, after a two-step internal-tide removal. The resulting fields evolve on scales slower than about ten days and larger than about one hundred kilometres. The paper shows that vorticity and strain normalized by the inertial frequency are mostly smaller than order one in the mrCOSTS product, whereas applying geostrophy directly to the de-tided SWOT field gives fatter tails ab","pith_inferences":["A sensitivity test varying the 0.1 cycles-per-day cutoff and the SVD ranks would show how much of the improvement in vorticity and strain statistics is a consequence of the filter choice rather than an intrinsic property of the ocean signal.","If the frequency-based separation is as clean as claimed, the same machinery could be applied to other altimetry data with irregular temporal sampling once enough repeat observations accumulate, rather than waiting for a dedicated fast-sampling orbit.","The Mediterranean drifter comparison is the only direct velocity validation; a natural next test is to validate the global product against drifters or current meters in the energetic Agulhas and Gulf Stream regions examined in the paper, where the vorticity-strain diagnostics are strongest.","The paper attributes the missing cyclonic skewness in the vorticity distribution to the short three-month record; as SWOT data accumulate, one can test whether longer records restore the expected skewness or whether the frequency filter itself suppresses it."],"forward_implications":["Spatial filtering alone is insufficient: applying geostrophic balance directly to the de-tided SWOT field produces vorticity and strain values above the small-Rossby-number threshold, so the standard approach is shown to contain ageostrophic contamination.","The released global geostrophic fields enable geostrophic kinetic-energy cascade estimates and quasi-geostrophic omega-equation vertical velocity reconstructions without the high-frequency, high-wavenumber noise present in the residual ageostrophic component.","The frequency cutoff at 0.1 cycles per day makes the temporal definition of geostrophy explicit: only signals with periods longer than ten days and wavelengths above roughly 100 km are treated as balanced.","The fast-sampling orbit's daily repeats are sufficient for the method, while the science orbit's sparse repeats — about 50 per pass — are not yet enough, so the product's scope is tied to the duration and repeat rate of the calibration/validation phase."],"fun_headline_variants":["Time filter extracts geostrophic currents from SWOT daily orbit","SWOT sub-inertial modes give geostrophic sea-surface heights","Geostrophy from SWOT: use frequency, not spatial scale","Sub-inertial filtering produces geostrophic SSH from SWOT daily data","Public sub-inertial geostrophic product from SWOT fast phase"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The decomposition rests on the assumption that the ocean forecast model's internal-tide correction removes essentially all internal-tide sea-surface height, so that any residual tidal energy is not mistaken for low-frequency geostrophic motion.","fun_headline_variants_meta":{"raw":{"variants":["Time filter extracts geostrophic currents from SWOT daily orbit","SWOT sub-inertial modes give geostrophic sea-surface heights","Geostrophy from SWOT: use frequency, not spatial scale","Sub-inertial filtering produces geostrophic SSH from SWOT daily data","Public sub-inertial geostrophic product from SWOT fast phase"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000575,"raw_usage":{"total_tokens":2540,"prompt_tokens":722,"completion_tokens":1818,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":466,"completion_tokens_details":{"reasoning_tokens":1728}},"tokens_in":466,"tokens_out":1818,"duration_ms":18320,"temperature":1.0,"reasoning_tokens":1728,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T08:02:47.661371+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same mrCOSTS pipeline on synthetic SWOT-like observations generated from a model with known geostrophic and ageostrophic fields and compare the extracted sub-0.1-cycles-per-day height to the known truth; alternatively, check the released product for residual variance at diurnal and semidiurnal frequencies. If residual tidal variance is significant or the reconstructed geostrophic field deviates from truth beyond sampling error, the strict-geostrophy claim fails.","supporting_citations":[],"review_version":1}