{"id":"1447667e-fd98-4c24-a7f7-3527c0b6d19a","arxiv_id":"2608.07761","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A mostly review chapter adds an idealized model showing that surface ember transport can explain why some fires grow linearly in area while others grow quadratically.","lead":"This book chapter reviews how embers and firebrands spread wildfires and combines that review with simulations of a simple 2D fire model. The model suggests that near-ground 'ember wash' can push fire area growth from linear to quadratic in time, depending on ember flight time and ignition probability.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central scaling transition in Section 5.4 depends on a kinematic 2D wind model that excludes momentum feedbacks; if the fire-induced flow feedbacks are misrepresented, the linear-to-quadratic ember-driven growth regimes may be artifacts.","rationale":"The reader identified the same weakest assumption: the adequacy of the kinematic 2D wind model for fire-induced flow feedbacks. The central claim about growth-rate scaling is plausible but rests on this reduced flow representation, and the paper itself acknowledges the wind model is not a full momentum set. The regime transition is demonstrated with hand-picked parameters and single realizations, without error bars or ensemble statistics, so the claim is not yet established at the level of certainty required for acceptance. The paper is not internally inconsistent, and the mathematical derivations in Sections 4.2-4.3 are sound, so REJECT would be too strong. A CONDITIONAL verdict is appropriate: the claim could be confirmed by the proposed numerical sensitivity tests, which would either support the physical robustness of the ember-driven scaling transition or reveal that it is an artifact of the kinematic flow parameterization.","tokens_in":24615,"tokens_out":1444,"duration_ms":15263,"concrete_test":"Re-run the Section 5.4 simulations with the same ember wash and ignition parameters but with the fire-induced wind component (pyrogenic potential and vorticity) disabled, leaving only uniform background wind. If the A(t)~t^1.5 or A(t)~t^2 regimes weaken or disappear, the transition depends critically on the kinematic feedbacks. To further settle the concern, run the same ember wash parameterization in a dynamically coupled model such as WRF-Fire or CM1 with identical ember flight-time and ignition parameters, and check whether the same scaling exponents appear.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim is that ember wash, through feedbacks between ember combustion, ignition probability, and fire-induced wind, transitions area growth from A(t)~t to A(t)~t^1.5 and A(t)~t^2 (Section 5.4, Fig. 15). The load-bearing assumption is that the 2D idealized wind model in Section 5.1 adequately represents near-surface fire-induced flow. The model solves only a Poisson equation for a pyrogenic potential plus vorticity, and the text explicitly states it is kinematic and 'not a full set of momentum equations.' Ember transport in Section 5.3 is directed by this kinematic total wind (background + fire-induced). If the fire-induced flow is incorrectly represented, the stagnation points, flow reversals, and residence-time feedbacks that help produce the accelerated growth (Section 5.3, Fig. 13) could be artifacts of the kinematic parameterization rather than robust physical feedbacks. This is not an internal inconsistency, but a correctness risk for the central regime claim. The paper does not provide a sensitivity test with the fire-induced flow component disabled, nor a comparison with a dynamically consistent 2D or 3D wind field for the same ember parameters.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript, written as a book chapter, reviews the physics and statistics of ember transport in wildland fire and presents a hierarchy of models: a stochastic jump SDE, a Fokker-Planck advection-diffusion-decay model, a survival-function model of ember travel distance, and a coupled idealized 2D cellular-automaton fire model with a kinematic wind field representing background flow, a pyrogenic potential, and vorticity. The central new result is in Section 5.4: in the coupled model, surface ember transport (\"ember wash\") changes burned-area growth from linear A(t)~t to A(t)~t^1.5 and A(t)~t^2 as the mean ember flight time and ignition probability increase (Fig. 15). The authors connect these regimes to observed linear and quadratic growth in western US fires (Section 2.4) and argue that ember wash is a first-order control on the growth dichotomy.","tokens_in":24795,"tokens_out":6385,"duration_ms":58129,"significance":"If the central claim holds, the paper identifies a physically motivated mechanism for the observed linear-to-quadratic growth transition in wildfire area, which would have implications for operational models that currently omit near-surface ember transport. The manuscript has notable strengths: the derivations in Sections 4.2 and 4.3 are transparent and correct (the exponential survival law follows exactly from a constant hazard, and the Fokker-Planck steady-state solution is standard); the authors are explicit about the kinematic nature of the wind model in Section 5.1; and the scaling regimes are grounded in a specific observational dataset of 22 fires (Fig. 4). However, the central claim rests on stochastic simulations presented without error bars or a stated number of realizations, and on a kinematic wind field whose feedbacks are not tested against a dynamically consistent model. These gaps currently limit the robustness of the claimed growth-regime transition.","major_comments":[{"comment":"The central scaling transitions are displayed as single curves without any measure of stochastic variability. The model includes multiple stochastic elements (exponential flight times, Bernoulli ignition, random launch threshold, and turbulent diffusion in Section 5.1), so individual realizations will fluctuate; the paper does not state the number of realizations per parameter setting, nor provide error bars, shaded confidence bands, or a fitted-slope distribution. The claim that the model transitions from A(t)~t to A(t)~t^1.5 and A(t)~t^2 is therefore not yet supported with statistical confidence. Please add ensemble statistics (e.g., 20-50 realizations, median and interquartile range of A(t), and a distribution of fitted exponents) for at least the parameter sets in Fig. 15.","section":"Section 5.4, Fig. 15"},{"comment":"The wind field in the coupled model is kinematic: it solves a Poisson equation for a pyrogenic potential plus vorticity and is explicitly described as \"not a full set of momentum equations\" in Section 5.1. The hypothesized feedback in Sections 5.3-5.4 is that ember-wash-generated fires modify the flow, create stagnation points, and increase local ember residence time, which in turn accelerates area growth. If the fire-induced flow is not dynamically consistent, these stagnation points and flow reversals may be artifacts of the reduced representation. To make the central claim robust, the paper should include a sensitivity test with the fire-induced component disabled (or with its strength varied), and ideally a comparison with a dynamically consistent 2D or 3D simulation (e.g., the CM1 LES of Section 3.2) for the same ember parameters, to show that the growth-regime transition survives in a more physical flow.","section":"Section 5.1"},{"comment":"The exponential survival law S(r)=exp(-kr) is an input assumption, not a derived consequence of the dynamics: the text states that \"a constant spatial hazard uniquely leads to the exponential survival law (20).\" The model therefore cannot be said to \"recover\" exponential landing statistics; rather, it prescribes them. While the paper connects the exponential law to observations (e.g., Page et al. [51], Storey et al. [65]), the area-growth scaling results in Section 5.4 inherit this assumption. The paper should clarify, either in Section 4.3 or in the discussion of Section 5.4, that the growth regimes are conditional on the exponential landing distribution, and should state what observable quantity (e.g., the hazard k or the mean flight time mu) would be needed to falsify this input.","section":"Section 4.3"}],"minor_comments":[{"comment":"The vertical drag term in Eq. (8c) is written as (We - Ww)^2, which is always non-negative and would incorrectly oppose settling in both directions; it should use a signed relative velocity, e.g., (We - Ww)|We - Ww|.","section":"Section 3.1, Eq. (8c)"},{"comment":"The text states that \"the ember trajectories are determined by the background wind\" for lofted spotting, but this simplification is introduced without noting that the same plot (Fig. 12) shows streamlines of the total wind; the distinction between the wind used for ember advection and the wind shown in the figures should be clarified.","section":"Section 5.2, p. 18"},{"comment":"The figure caption refers to \"first arrival time\" maps but does not define the color scale or the units of time; adding a color bar and time units would improve interpretability.","section":"Figure 11 caption"},{"comment":"The ember launch threshold of 0.2 m/s is described as causing either all combusting cells to launch embers or none, but no sensitivity analysis is provided; a brief statement of how the results depend on this threshold would help the reader assess the role of this parameter.","section":"Section 5.3, p. 19"},{"comment":"The chapter title in the footer (\"Models of Ember Transport\") differs from the title on the first page (\"Models of Wildland Fire and Ember Spread\"); please reconcile these.","section":"Footer, p. 26"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is explicitly a book chapter, which explains its review-like structure and the presence of several expository sections. The novel contribution is the ember-wash model and its scaling regimes in Section 5.4. The most serious gap is the absence of ensemble statistics for the stochastic simulations; if the authors can add those, along with a sensitivity test of the kinematic wind assumption, the chapter would be much stronger. I would also ask the editor to ensure that the sign error in Eq. (8c) is corrected before publication, as it is a physical equation that readers may quote."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThis is a review-heavy book chapter whose only genuinely new piece is an idealized simulation showing that near-surface ember transport can shift fire area growth from linear to t^1.5 and t^2. The claim is plausible and clearly stated, but it is not established. As a journal submission it would deserve a conditional accept; as a book chapter it lays out a useful research program.\n\nWhat is good: the chapter compiles a hierarchy of models, from SDE and Fokker-Planck treatments through a 3D LES to a cellular automaton with embers. The derivations in Section 4 are correct and clearly explained. The authors are honest about what is idealized—the 2D wind is kinematic, explicitly not a full momentum set, and they say the real test needs more realistic models. The Section 5.4 sweep is a nice illustration of how mean ember flight time and ignition probability might control growth regime, and it frames ember wash as a plausible missing ingredient in operational models.\n\nSoft spots, in order of weight. First, the central figure has no error bars, no stated number of realizations, and the parameter values are chosen to produce the slopes. The step from scanning parameters until you see slope 2 to explaining observed quadratic growth is qualitative. Second, the positive feedback that powers superlinear growth comes from fire-induced wind altering ember trajectories and creating stagnation zones. That feedback lives entirely inside a kinematic Poisson-based wind field. If the real momentum response of the fire-induced flow differs, the regime transition could be an artifact. A sensitivity run with the pyrogenic term disabled would have been cheap and would help. Third, the exponential landing distribution is an input assumption (constant hazard), not a result recovered from data. That is a legitimate modeling choice, but it means the chapter is not testing the exponential law, only using it.\n\nThe observational basis is a small selected set: 15 fires that grow linearly, 7 that grow quadratically, chosen from 500+ GIS records. It is suggestive, not a discriminating test.\n\nWho this is for: someone new to ember transport wanting a readable map of the modeling landscape, or a researcher looking for a testable hypothesis. It is not a definitive answer. I would send it to review if it were a journal submission—the hypothesis deserves referee time—but I would push for ensemble statistics and at least one check with a dynamically consistent wind field.","headline":"A review-heavy book chapter whose one genuinely new piece—an idealized simulation linking ember wash to linear, t^1.5, and t^2 fire area growth—is plausible but not established; worth engaging, not yet convincing.","tokens_in":25428,"tokens_out":2904,"would_cite":false,"duration_ms":30189,"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":"Near-surface embers can switch wildfire growth from linear to quadratic in a coupled model.","keywords":["wildland fire","ember transport","firebrands","ember wash","spotting","rate of spread","area growth scaling","statistical survival model"],"falsifier":"Run the same ember parameterization inside a full-momentum boundary-layer model on the same domain and compare the burned-area growth exponent over the same nondimensional time; if the exponent no longer moves from 1 through 1.5 to 2 as mean flight time and ignition probability increase, the scaling transition is an artifact of the simplified wind. Field data provide another check: any documented fire with heavy spotting that nevertheless maintains linear area growth over many days would contradict the proposed mechanism.","tokens_in":24297,"feed_emoji":"🔥","tokens_out":8293,"duration_ms":76475,"temperature":0.7,"pith_summary":"This chapter argues that near-surface ember transport, which it calls ember wash, can be the controlling process behind the observed dichotomy between linear and quadratic wildfire area growth. In the authors' idealized coupled model, a fire that would otherwise burn a linearly growing area switches to $A(t)\\sim t^{3/2}$ and then $A(t)\\sim t^2$ as the mean ember flight time and the ignition probability increase. The transition is governed by two parameters: the mean time an ember stays aloft and the probability that a landed ember ignites the fuel. This matters because fire-area growth is the metric used to judge operational fire models, and most of those models do not include ember wash. If the claim holds, ember wash is not an occasional side effect of extreme fires but a first-order engine of their growth.","feed_headline":"Embers flip wildfire growth from linear to quadratic","feed_subtitle":"A coupled fire-ember model ties the switch to mean flight time and ignition probability.","key_machinery":"The load-bearing object is a coupled two-dimensional cellular automaton, a grid of cells that are unburnt, burning, or burnt. Its near-surface wind is the sum of a constant background flow, a pyrogenic potential (a divergent term representing the buoyant plume's inflow), and a vorticity field, computed by solving a Poisson equation at each step. Ember wash is added through an exponential survival model: each ember travels downwind along a line-drawing ignition path for a flight time drawn from an exponential distribution with mean $\\mu$, and on landing it ignites its cell with probability $p_{ig}$. The fire modifies the wind, the wind redirects the embers, and the embers create new fire, and that closed loop is what produces the growth-scaling result.","core_discovery":"The central claim, made most directly in Section 5.4, is that the feedback loop formed by ember combustion, flight, landing, ignition, and fire-modified wind is sufficient to reproduce the observed range of wildfire area-growth scalings. In simulations with a line ignition parallel to the wind and no embers, burned area grows linearly in time; as the mean ember flight time increases, growth becomes $A(t)\\sim t^{3/2}$ at ignition probability $p_{ig}=0.1$, and at $p_{ig}=0.5$ it reaches $A(t)\\sim t^2$. The authors present this as evidence that the linear-to-quadratic growth dichotomy seen in western US fire perimeters can be explained by ember wash rather than by an unexplained geometric or kinematic rate of spread. At higher ember flux the same mechanism produces a mass-ignition regime in which gaps between separate fires are filled and the fire can no longer be described as a single moving front.","pith_inferences":["If this mechanism transfers to real fires, high-temporal-resolution perimeter data should show the area-growth exponent rising shortly after conditions that generate many embers, and flattening when fuels stop igniting.","A direct laboratory test would release embers with different mean flight times into a fixed wind and measure the burned-area exponent; the model implies a monotone rise from 1 toward 2 as $\\mu$ grows at fixed $p_{ig}$.","The same constant-hazard survival logic could be applied to post-landing rolling and trapping in built environments, so ember risk in the wildland-urban interface may depend on how building layouts interrupt the spatial memory of transport.","Because the wind model carries no momentum dynamics, the cleanest check is to run the same ember parameterization in a full three-dimensional boundary-layer model; if the scaling transition disappears, it is an artifact of the reduced wind."],"forward_implications":["If the claim is correct, the absence of ember wash in operational spread models is a structural gap rather than a refinement.","The observed split between linear and quadratic growth in real fires can be read as a difference in mean ember flight time and ignition probability, not only a difference in wind speed or fuel geometry.","Fires with abundant spotting should show accelerating burned-area growth even when the main front moves at a steady rate.","The exponential survival law turns the problem into a measurable parameterization: infer mean ember flight time and ignition probability, and the area-growth exponent follows."],"supporting_citations":[{"why":"Supplies the baseline idealized fire-atmosphere cellular automaton to which ember wash is added.","marker":"[55]"},{"why":"Provides the exponential survival model of ember travel distance that the coupled model uses for ember wash.","marker":"[56]"},{"why":"Supplies the observational scaling dA/dt ~ A^beta that motivates the linear-to-quadratic growth question.","marker":"[34]"},{"why":"Documents exponential short-range spotting distances in Rocky Mountain fires, the near-front behavior ember wash is meant to reproduce.","marker":"[51]"},{"why":"Documents short-range spotting distributions in Australian fires used to support the surface-mode exponential transport statistics.","marker":"[67]"},{"why":"Supplies the stochastic ember lifetime distribution used to model lofted spotting flight times.","marker":"[73]"},{"why":"Introduces the pyrogenic potential used to compute the fire-induced divergent wind component.","marker":"[32]"},{"why":"Provides the overview of ember generation and spotting processes that frames the source and transport parameter choices.","marker":"[36]"}],"fun_headline_variants":["Embers flip wildfire growth to quadratic","Ember feedback switches fire growth from linear to t^2","Why embers make wildfires spread quadratically","Ember flight time controls wildfire growth law","Coupled ember model explains wildfire area scaling"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole scaling result rests on the assumption that the simplified near-surface wind, built from a background flow plus a fire-driven inflow and spin without solving the full momentum equations, carries embers the way the real boundary layer would.","fun_headline_variants_meta":{"raw":{"variants":["Embers flip wildfire growth to quadratic","Ember feedback switches fire growth from linear to t^2","Why embers make wildfires spread quadratically","Ember flight time controls wildfire growth law","Coupled ember model explains wildfire area scaling"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000173,"raw_usage":{"total_tokens":1235,"prompt_tokens":856,"completion_tokens":379,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":472,"completion_tokens_details":{"reasoning_tokens":308}},"tokens_in":472,"tokens_out":379,"duration_ms":4875,"temperature":1.0,"reasoning_tokens":308,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T00:23:42.850132+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same ember parameterization inside a full-momentum boundary-layer model on the same domain and compare the burned-area growth exponent over the same nondimensional time; if the exponent no longer moves from 1 through 1.5 to 2 as mean flight time and ignition probability increase, the scaling transition is an artifact of the simplified wind. Field data provide another check: any documented fire with heavy spotting that nevertheless maintains linear area growth over many days would contradict the proposed mechanism.","supporting_citations":[{"cited_title":"A Simple Model for Wildland Fire Vortex–Sink Interactions","cited_arxiv_id":null,"evidence_quote":"Supplies the baseline idealized fire-atmosphere cellular automaton to which ember wash is added."},{"cited_title":"Statistical Models of Ember Wash and Their Impact on Wildfire Area Growth.arxiv, 2603.28222, 2026","cited_arxiv_id":null,"evidence_quote":"Provides the exponential survival model of ember travel distance that the coupled model uses for ember wash."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the observational scaling dA/dt ~ A^beta that motivates the linear-to-quadratic growth question."},{"cited_title":"An analysis of spotting distances during the 2017 fire season in the northern rockies, usa.Canadian Journal of Forest Research, 49(3):317–325, 2019","cited_arxiv_id":null,"evidence_quote":"Documents exponential short-range spotting distances in Rocky Mountain fires, the near-front behavior ember wash is meant to reproduce."},{"cited_title":"Experiments on the influence of spot fire and topography interaction on fire rate of spread.Plos one, 16(1):e0245132, 2021","cited_arxiv_id":null,"evidence_quote":"Documents short-range spotting distributions in Australian fires used to support the surface-mode exponential transport statistics."},{"cited_title":"Stochastic modeling of firebrand shower scenarios.Fire Safety Journal, 91:91–102, 2017","cited_arxiv_id":null,"evidence_quote":"Supplies the stochastic ember lifetime distribution used to model lofted spotting flight times."},{"cited_title":"Hilton, A.L","cited_arxiv_id":null,"evidence_quote":"Introduces the pyrogenic potential used to compute the fire-induced divergent wind component."},{"cited_title":"Woycheese","cited_arxiv_id":null,"evidence_quote":"Provides the overview of ember generation and spotting processes that frames the source and transport parameter choices."}],"review_version":2}