{"id":"71fe344e-f2fb-480f-9ca1-30268dbe55f1","arxiv_id":"2608.09584","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Rogue wave probabilities in unidirectional seas are approximated by the tail of a log-normal distribution fitted to the amplitudes of sparse soliton-like packets extracted from the wave field.","lead":"The authors show that a random, strongly nonlinear ocean wave field can be broken down into a sparse set of soliton-like wave packets whose amplitudes follow a log-normal distribution. They then use this distribution to predict the probability of extreme rogue waves and test the prediction in a wave flume.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Log-normal law of effective soliton amplitudes may be an artifact of the matching-pursuit selection rule; the missing linear-wave control is the single decisive test.","rationale":"The reader's weakest assumption identifies the non-uniqueness of the sparse decomposition as the main vulnerability. I agree and sharpen it: the specific algorithm, with its greedy 'largest residual packet' selection and sech template, may itself generate log-normal-looking amplitude products for almost any input envelope, including a linear Gaussian sea. The authors' assertion that linear conditions do not produce log-normality is the one observation that would break this artifact interpretation, but it is stated without data. This makes the missing linear-wave control the most load-bearing single test. The manual adjustment of µ and σ in two of the three validation sea states further weakens the parameter-free claim, but that is secondary to the algorithm-dependence question. If the linear control confirmed the absence of log-normality, the central claim would be substantially strengthened; if not, the framework would reduce to a fitting device. Therefore the appropriate verdict remains conditional: the paper's core prediction is plausible but not yet established as a physical law. The reader's CONDITIONAL verdict, with moderate confidence, is well calibrated, and my stress test does not move it.","tokens_in":9581,"tokens_out":5790,"duration_ms":65440,"concrete_test":"Generate a linear (Gaussian) random wave field with the same JONSWAP spectrum, Hs, and fp by superposing linear components with random phases. Apply the identical matching-pursuit algorithm (Eq. 7, same stopping rule and template). If the extracted A = aN again follows log-normal with similar sigma, the claimed log-normal law is not specific to nonlinear waves and the central prediction in Eq. (5) is an artifact. As a secondary check, re-decompose the experimental envelope using a Gaussian template instead of sech; if the tail changes substantially, the theory depends on the arbitrary template choice.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Equation (5) makes the exceedance probability equal to the survival function of the effective soliton amplitude A = aN, whose log-normal distribution (Eq. 6) comes entirely from the matching-pursuit extraction in the Supplemental Material. The algorithm greedily subtracts the largest sech-shaped packet until residual energy drops below 5%, and the text concedes the decomposition is 'inherently non-unique'. Nothing in the algorithm guarantees that the fitted A distribution is a physical property of the wave field rather than a consequence of repeatedly isolating the most energetic localized packet. The paper asserts that 'these statistical features are entirely absent under linear wave conditions', but provides no data or analysis supporting that control. If that assertion is false, the log-normal tail, the a-N correlation, and the resulting rogue-wave prediction are all algorithmic artifacts and the central physical mechanism (multiplicative cascade from modulational instability) is unsupported. Whether the concern lands is therefore testable by a single experiment: run the same decomposition on a linear Gaussian wave field with the same JONSWAP spectrum and significant wave height.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a sparse coherent structure decomposition of unidirectional laboratory wave fields: an iterative matching pursuit algorithm represents the complex envelope as a sum of sech-shaped soliton-like packets with effective amplitudes A = aN, phases φ, and arrival times t0. From extracted ensembles, the authors report log-normal A, uniform phases, and uniform arrival times, and derive an extreme-value formula P(>H) ≈ 1 − F_A(H) in the sparse limit ρ ≈ 1. The formula is validated against three JONSWAP sea states and compared with Rayleigh, Tayfun, and NLS simulation predictions.","tokens_in":9789,"tokens_out":13169,"duration_ms":124734,"significance":"If the result holds, the paper provides an analytically simple, closed-form estimate of rogue-wave exceedance probabilities from the tail of a log-normal coherent-structure amplitude distribution, without weakly nonlinear corrections. Strengths include the use of controlled flume experiments across multiple sea states, a quantified sparsity count (862 solitons in a 1000-peak-period record), and the inclusion of NLS simulation benchmarks. However, the central physical interpretation as a nonlinear cascade effect, the quantitative mapping from soliton amplitude to wave height, and the parameter-free character of the prediction all require scrutiny before the claim of a direct physics-based link is fully established.","major_comments":[{"comment":"The effective soliton amplitude A = aN is the envelope amplitude of the packet in Eq. (1), whose surface elevation η(t) = Re(ψ(t)e^{-iω_p t}) has a crest-to-trough height of approximately 2A for a narrowband soliton. Yet Eq. (6) evaluates F_A(H) directly at the wave height H plotted in Figure 3 against the Rayleigh and Tayfun wave-height distributions. If H is the crest-to-trough height, the correct argument should be H/2; if H is the crest height, the benchmark Rayleigh and Tayfun curves in Figure 3 would be wrong by several orders of magnitude. The authors must state explicitly which definition of H is used and correct the argument of F_A accordingly, or justify why A and H are the same quantity.","section":"Eq. (6) and Figure 3"},{"comment":"The assertion that 'these statistical features are entirely absent under linear wave conditions' is load-bearing because the log-normal law of A is the foundation of the prediction, and the matching pursuit is a nonlinear fitting procedure that could imprint such statistics on any input signal. No linear-wave control, either from experiments or from synthetically generated Gaussian sea states with the same JONSWAP spectrum, is provided in the paper or the Supplemental Material. The authors should either supply this control or remove and qualify the claim; without it, the physical mechanism (multiplicative cascade from modulational instability) remains unverified and the log-normal tail could be an artifact of the greedy decomposition algorithm.","section":"Page 3, paragraph on log-normal statistics"},{"comment":"The transition from Eq. (4), the exceedance probability of the maximum over an observation time T, to Eq. (5), interpreted as the exceedance probability of an individual randomly selected wave crest, is compressed. In the sparse limit with independent events, Pmax(>H) ≈ ρ P(>H) for small P(>H); setting ρ ≈ 1 equates the two only if the number of independent events equals the number of waves in the record, which is exactly the sparsity assumption being made. This reasoning should be stated explicitly and tested, and the validity of Eq. (5) should be restricted to the range where 1 − F_A(H) is small, as already noted in the text but not reflected in the figures.","section":"Eqs. (4) and (5)"},{"comment":"The per-sea-state adjustment of μ and σ, together with the systematic overprediction for H/H_s > 2 in panel (b), limits the predictive claim. The overprediction occurs in the rogue-wave range and is attributed to breaking, but no quantitative breaking correction is provided. Furthermore, panels (c) and (d) use μ and σ that are re-estimated or adjusted for each sea state, so the framework is not parameter-free but a two-parameter statistical fit per condition. The independent content is the log-normal form of A and the mapping A→H; this should be acknowledged, and the applicable range of the theory should be clearly stated.","section":"Figure 3(b)–(d)"}],"minor_comments":[{"comment":"The notation ρ = λT is introduced without defining λ and T in the main text; specify how these are computed from the experimental records and how the observed value ρ ≈ 1 is obtained.","section":"Text near Eq. (4)"},{"comment":"The continuous shape factor N_j is used in Eq. (1) before it is defined; introduce it explicitly in the main text rather than only in the Supplemental Material.","section":"Eq. (1)"},{"comment":"The phrase 'Hilbert-Huang transform' is unusual for envelope extraction; clarify whether the standard analytic signal via the Hilbert transform is meant, or a specific empirical-mode-decomposition procedure, and cite the method.","section":"Experimental methods"},{"comment":"The experimental exceedance probabilities are shown without error bars. Given the finite record length, add bootstrap or other uncertainty estimates so that the reported agreement can be assessed quantitatively.","section":"Figure 3"},{"comment":"In the figure captions, indicate the range of validity of the approximation in Eq. (5) (i.e., where 1 − F_A(H) is small), so that the curve is not read as an exact expression for all H.","section":"Eq. (5) and Figure 2(d)"},{"comment":"There are a few typographical issues, such as 'JONSW AP' in the experimental section and the repeated use of 'Hilbert-Huang transform' with inconsistent capitalization; these should be corrected.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The factor-of-2 ambiguity in the definition of H is the most serious technical issue and needs to be resolved in revision, as it affects every quantitative curve shown. The linear-wave control is the single most decisive test: if the same matching pursuit algorithm yields log-normal A for a Gaussian sea, the physical claim is not supported. The paper is potentially interesting and the experimental dataset appears valuable, but the current presentation overstates the predictive, parameter-free nature of the result."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this paper is worth a referee's time, but it currently overstates what is established. The genuinely new thing is the experimental observation that a greedy matching-pursuit decomposition of measured deep-water envelopes gives sech-like packets whose effective amplitudes are close to log-normal. That is a nice empirical result, and it is not something I have seen in the earlier IST/kurtosis literature. The extraction algorithm is described carefully enough to be reproduced, and the comparison against NLS simulations in Fig. 3 is a legitimate independent check. Credit where due: the authors are also upfront that the decomposition is non-unique and that sparsity limits the framework.\n\nWhere it gets soft: the step from Eq. (4) to Eq. (5) is not fully justified. The Poisson-maxima formula does not by itself become the marginal exceedance probability for a randomly selected crest; the rho = 1 approximation hides a change of interpretation. More important, the log-normal parameters are fitted to the same field whose tail is then 'predicted,' and in the two validation cases (c) and (d) the parameters are adjusted (mu from -4.4 to -4.5, sigma from 0.5 to 0.48). That makes the agreement in panels (b)-(d) less compelling than the text suggests. The overprediction at H/Hs > 2 in (b) may well be breaking, as the authors argue, but it could also be the model tail being too heavy.\n\nThe decisive missing check is the one the stress-tester flags: run the same decomposition on a linear Gaussian wave field with the same spectrum and Hs. The paper asserts that the log-normal features are 'entirely absent' there, but no data are shown. Without that control, the central mechanism claim—that these statistics come from nonlinear MI dynamics—is not actually supported. The log-normal law might simply be what a greedy sech-dictionary on any band-limited random signal produces.\n\nBottom line: as an empirical study of a particular decomposition, it is solid and interesting; as a predictive law for rogue-wave probabilities, it is not yet closed-form. I would send it to peer review because the observation deserves scrutiny and the field would benefit from the linear-wave test being done in revision. If the authors can show the log-normal law disappears under linear conditions, the paper becomes much stronger.\n\nReading group: maybe. I would assign it to a student working on extreme wave statistics. I would not cite it yet in my own work.","headline":"A clever empirical claim about sparse soliton-like decompositions, but the missing linear-wave control and parameter re-fitting keep it from being a closed-form prediction.","tokens_in":10344,"tokens_out":3042,"would_cite":false,"duration_ms":29599,"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":"This paper claims that in moderately to strongly nonlinear random seas, the probability of a rogue wave is governed by the upper tail of a log-normal distribution of sparse soliton-like packet amplitudes, and validates that claim with…","keywords":["rogue waves","soliton decomposition","matching pursuit","log-normal distribution","extreme value statistics","nonlinear water waves","JONSWAP spectrum","modulational instability"],"falsifier":"Run the same matching pursuit with a different soliton template (for example, a Gaussian envelope) or a different stopping criterion on the same flume records; if the extracted amplitudes no longer follow a log-normal distribution, or if the resulting P(>H) ≈ 1 − F_A(H) prediction departs from the measured exceedance curve, then the rogue-wave tail is an artifact of the chosen basis rather than a property of the wave field.","tokens_in":9318,"feed_emoji":"🌊","tokens_out":5739,"duration_ms":51542,"temperature":0.7,"pith_summary":"This paper claims that a strongly nonlinear random sea is not a dense jumble of linear waves but can be viewed as a sparse collection of soliton-like wave packets. After extracting those packets from laboratory wave flume data with an iterative matching pursuit algorithm, the packet amplitudes follow a log-normal distribution while phases and arrival times are uniform. The paper argues that once those two facts hold, the probability of an extreme wave is just the upper tail of the packet amplitude distribution, P(>H) ≈ 1 − F_A(H), with no further adjustable parameters. The prediction is checked against three JONSWAP sea states with different steepness and spectral width and agrees with the experimental exceedance probabilities, including in a saturated, strongly nonlinear regime with kurtosis near 4. If true, this gives a physics-based, analytically simple route to rogue wave statistics that does not rely on weak-nonlinearity corrections.","feed_headline":"Rogue wave odds follow one log-normal curve","feed_subtitle":"Laboratory seas with kurtosis near 4 confirm that exceedance probability is just the packet amplitude tail.","key_machinery":"The engine of the paper is the sparse soliton dictionary produced by iterative matching pursuit. Each element is a sech-shaped envelope soliton template with four parameters: amplitude a_j, continuous shape factor N_j, carrier phase φ_j, and emergence time t_0,j. The algorithm repeatedly finds the most energetic localized packet in the residual, subtracts it, and stops when residual energy is below 5%, yielding roughly one soliton per peak period. The statistics of this dictionary—log-normal amplitudes A = a·N, uniform phases, uniform arrival times—are then fed into the extreme value relation P(>H) = 1 − exp[−ρ(1 − F_A(H))], which, for sparse fields with ρ ≈ 1, collapses to P(>H) ≈ 1 − F_A(H) = 1 − Φ((ln H − μ)/σ). The log-normal cumulative distribution F_A is the piece that converts packet statistics into wave-height statistics.","core_discovery":"The central claim is that extreme wave heights in moderately to strongly nonlinear unidirectional seas are governed by the statistics of sparse coherent structures, not by a dense superposition of linear modes. Representing the measured complex envelope as a sum of sech-shaped soliton templates and extracting the parameters with an iterative matching pursuit algorithm (residual energy below 5%), the authors find that the effective soliton amplitudes A = a·N follow a log-normal distribution, while phases and peak emergence times are uniformly distributed. Combining this log-normal law with the observed sparsity (roughly one soliton per wave period, ρ ≈ 1) reduces the extreme value formula to a closed form: the exceedance probability is P(>H) ≈ 1 − Φ((ln H − μ)/σ), where μ and σ come from the packet amplitudes alone. This formula contains no adjustable parameters once the log-normal parameters are fixed, and it reproduces the experimental tails across three independent sea states, comparing favorably with Rayleigh, Tayfun, and NLS-based predictions in the ranges tested. The paper proposes that heavy tails are therefore an intrinsic consequence of the amplitude distribution of sparse coherent structures.","pith_inferences":["If the log-normal amplitude law is robust, wave-height hazard forecasts could be made from spectral shape alone by calibrating μ and σ against sea-state parameters, without running the full decomposition each time; this is an extension beyond the paper's stated results.","The non-uniqueness of the decomposition implies a testable robustness check: varying the template shape or the 5% stopping threshold should leave the tail prediction statistically unchanged, and if it does not, the log-normal tail is an artifact of the fitting procedure rather than a physical mechanism.","The cascade analogy suggests that the log-normal amplitudes may be a signature of multiplicative energy transfer through the modulational instability; a direct test would be to track individual packets between wave gauges and verify that their amplitudes evolve multiplicatively.","Directional seas and wave-breaking energy loss are natural next regimes; the paper already notes that breaking suppresses the tail, so a combined model that includes breaking should recover the observed deviation at H/H_s greater than about 2."],"forward_implications":["Rogue wave probability in a given sea state reduces to estimating two numbers, μ and σ, from the distribution of coherent structure amplitudes.","Heavy tails persist even when bulk spectral parameters are identical to Gaussian fields, because the log-normal amplitude law is the mechanism.","Reduced steepness and broader bandwidth enter the theory as one-parameter changes in μ or σ, giving physical interpretation to the two log-normal parameters.","The framework complements weakly nonlinear kurtosis corrections and may apply to any nonlinear dispersive system with sparse coherent structures, such as optics, cold gases, and plasmas."],"supporting_citations":[{"why":"Supplies the inverse scattering transform and soliton formalism used to motivate the coherent-structure representation and envelope extraction.","marker":"[15]"},{"why":"Establishes the weakly nonlinear kurtosis–Benjamin–Feir index scaling that the paper positions against as the conventional framework.","marker":"[17]"},{"why":"Provides the large-scale flume experiments showing Rayleigh underestimation at high BFI, the strong-nonlinearity evidence the new framework targets.","marker":"[18]"},{"why":"Defines the JONSWAP spectral shapes used to synthesize the experimental sea states.","marker":"[29]"},{"why":"Documents the wave flume and measurement setup from which the envelope data are taken.","marker":"[30]"},{"why":"Characterizes wave-breaking energy loss, used to interpret the tail deviation above H/H_s ≈ 2.","marker":"[33]"},{"why":"Provides fully nonlinear simulation results showing enhanced kurtosis relative to third-order models, motivating the strongly nonlinear regime studied here.","marker":"[26]"},{"why":"Shows NLS simulations may underestimate individual steep rogue wave amplitudes, cited as a limitation of the conventional framework.","marker":"[14]"}],"fun_headline_variants":["Sparse solitons set rogue wave odds","Rogue waves follow log-normal soliton tails","One log-normal tail predicts rogue wave risk","Soliton statistics pinpoint extreme wave chance","Log-normal packet law explains rogue wave odds"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The decomposition of the wave field into soliton-like packets is not unique, so the log-normal amplitude law, the uniform phases, and the resulting tail prediction all describe the particular dictionary produced by this algorithm rather than an independently defined physical ensemble.","fun_headline_variants_meta":{"raw":{"variants":["Sparse solitons set rogue wave odds","Rogue waves follow log-normal soliton tails","One log-normal tail predicts rogue wave risk","Soliton statistics pinpoint extreme wave chance","Log-normal packet law explains rogue wave odds"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000304,"raw_usage":{"total_tokens":1724,"prompt_tokens":903,"completion_tokens":821,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":519,"completion_tokens_details":{"reasoning_tokens":753}},"tokens_in":519,"tokens_out":821,"duration_ms":7942,"temperature":1.0,"reasoning_tokens":753,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T14:36:33.956213+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same matching pursuit with a different soliton template (for example, a Gaussian envelope) or a different stopping criterion on the same flume records; if the extracted amplitudes no longer follow a log-normal distribution, or if the resulting P(>H) ≈ 1 − F_A(H) prediction departs from the measured exceedance curve, then the rogue-wave tail is an artifact of the chosen basis rather than a property of the wave field.","supporting_citations":[{"cited_title":"Osborne,Nonlinear Ocean Waves and the Inverse Scattering Transform(Academic Press, 2010)","cited_arxiv_id":null,"evidence_quote":"Supplies the inverse scattering transform and soliton formalism used to motivate the coherent-structure representation and envelope extraction."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the weakly nonlinear kurtosis–Benjamin–Feir index scaling that the paper positions against as the conventional framework."},{"cited_title":"Onorato, A","cited_arxiv_id":null,"evidence_quote":"Provides the large-scale flume experiments showing Rayleigh underestimation at high BFI, the strong-nonlinearity evidence the new framework targets."},{"cited_title":"Hasselmann, T","cited_arxiv_id":null,"evidence_quote":"Defines the JONSWAP spectral shapes used to synthesize the experimental sea states."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Documents the wave flume and measurement setup from which the envelope data are taken."},{"cited_title":"Eeltink, H","cited_arxiv_id":null,"evidence_quote":"Characterizes wave-breaking energy loss, used to interpret the tail deviation above H/H_s ≈ 2."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides fully nonlinear simulation results showing enhanced kurtosis relative to third-order models, motivating the strongly nonlinear regime studied here."},{"cited_title":"Slunyaev, E","cited_arxiv_id":null,"evidence_quote":"Shows NLS simulations may underestimate individual steep rogue wave amplitudes, cited as a limitation of the conventional framework."}],"review_version":1}