{"id":"b60758d0-22e2-4906-883b-6f1630ffb011","arxiv_id":"1908.02844","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":9,"one_line_summary":"Damage allowances, the protection heights that hold expected annual flood damage constant under sea-level rise, are larger than traditional hazard allowances and depend strongly on assumptions about Antarctic ice loss after mid-century.","lead":"This paper presents a framework for calculating how high coastal flood defenses must be built to keep expected annual flood damage constant as sea levels rise. It applies the framework to Manhattan and shows that assumptions about uncertain Antarctic ice loss can change the required levee height by more than a meter by 2100.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Sec. A.4 depth-damage cubics are used beyond their 0-3 m fitted range and become negative above ~6.3 m of flood depth, so D(z) in Eq. 2 can decline with ESL; the reported damage allowances may be artifacts of an extrapolated damage function.","rationale":"I read the paper in good faith: the conservation-of-damage idea in Eq. 2 is coherent, the extension from hazard allowances to damage allowances is a genuine contribution, and the p-box treatment of deep uncertainty is defensible as an illustrative multi-prior approach. However, the single most load-bearing weakness is not the arbitrary AISmax truncation, which the authors explicitly acknowledge and parameterize over; it is the unacknowledged use of the depth-damage polynomials far outside their fitted range. The cubics in Sec. A.4 are calibrated to USACE observations only up to 3 m of inundation depth, yet the manuscript applies them for arbitrarily deep floods and never clips them. As written, φ_hrise becomes negative above ~6.3 m, so the cumulative damage function D(z) can decrease at high ESLs. Since the central quantitative claims are the damage allowances—including the 1.70 m versus 0.86 m comparison and all Table 1-2 values—an artifact in D(z) propagates directly into every headline number. This is not a matter of disagreement with external consensus; it is an internal inconsistency between the stated formulas and the physically intended damage function. The reader's p-box concern is valid, but it is a modeling-choice limitation the authors flag; the damage-function extrapolation is a technical defect that is not flagged and that would require either correction or explicit domain restriction. Because the framework itself is sound and the issue is fixable, I do not recommend changing the conditional verdict, but the condition should now explicitly include validating or clipping the depth-damage functions before any tabulated allowance is used.","tokens_in":49718,"tokens_out":9186,"duration_ms":110570,"concrete_test":"Recompute D(z) from Eq. A.3 over z=0–8 m using exactly the published φ_hrise and φ_res polynomials and the stated p(e) distribution, and check whether D(z) is nonnegative and monotonic. Then recompute the RCP8.5 2100 levee damage allowance (Table 1, βc=1, AISmax=1.75) after capping φ at its value at 3 m flood depth (or at the maximum of the observed depth-damage table) for all x>3 m. If D(z) turns negative or the allowance shifts by more than ~0.2 m, the reported damage allowances are contaminated by extrapolation of the depth-damage fits and need to be revised or explicitly restricted to the valid range.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Equation A.3 defines D(z) = ∫ p(e)·φ(z−e) de, and the aggregate depth-damage function is φ = 0.95·φ_hrise + 0.05·φ_res. The published polynomials, e.g. φ_hrise(x) = 0.142 + 0.0541x − 0.00368x² − 0.00133x³, are fit to observed points only over roughly x∈[0,3] m (SI Tables A.3/A.4), but are then applied for all flood depths with no stated clip or renormalization. φ_hrise peaks near 3 m and becomes negative once x exceeds about 6.3 m (φ_res behaves similarly above ~6.7 m), so the aggregate φ also turns negative at high flood depths. Because Eq. 2 integrates z to infinity and the 2100 SLR p-box extends to ~3 m, future ESLs can easily produce flood depths in this regime. The consequence is that D(z) is not a physically valid damage function: total damage can decrease with increasing water height, and the AAL balance used to solve for the damage allowance A can be satisfied by an extrapolation artifact rather than by a meaningful design height. The paper's own Fig. 1B plots D(z) as monotonically increasing to $12B at 7 m, but the stated formulas do not guarantee monotonicity; no clipping condition is given anywhere in Sec. A.3 or A.4. This affects every numerical allowance in Tables 1-2 and the headline comparison (1.70 m levee vs 0.86 m hazard allowance), independently of any choice of AISmax or βc. The p-box truncation flagged by the reader is acknowledged in Sec. A.8; this damage-function issue is unacknowledged and more directly internal to the calculation.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a 'damage allowance' framework for sizing coastal protection under uncertain sea-level rise: the design height A is the vertical adjustment that keeps the annual average flood loss (AAL) at a chosen target, most often the current AAL, when the full distribution of future sea-level rise is considered. The central balance is Eq. (2), equating the current AAL to the AAL under future sea level with a strategy-modified damage function. Strategy-specific damage functions are given for elevation, levee, storm surge barrier, and coastal retreat in Secs. 2.1.1–2.1.3. Deep uncertainty in Antarctic ice-sheet behavior is represented by a p-box whose edges are the Kopp et al. (2014) and Kopp et al. (2017) local projections, combined by a user-specified weight βc and an upper truncation AISmax (Sec. 2.2, Eq. A.6). The framework is applied to Manhattan, with results including a 2070 levee allowance of 1.70 m versus a hazard allowance of 0.86 m (Sec. 3.1) and 2100 levee allowances of 1.8–3.4 m across AIS assumptions (Table 1).","tokens_in":50216,"tokens_out":5769,"duration_ms":60986,"significance":"If the numerical results are robust, the paper makes a useful contribution by extending hazard allowances to financial risk and by making the decision-maker's subjective AIS assumptions explicit. The strengths include the transparent conservation-of-damage equation, the clear strategy-specific damage functions, the use of published probabilistic SLR projections, an open-source code base, and an honest statement of the p-box truncation's acknowledged limitations. The framework is a reasonable reduced-form input to benefit-cost or cost-effectiveness analysis, which is the paper's stated aim.","major_comments":[{"comment":"The depth-damage polynomials φ_hrise and φ_res are least-squares fits to USACE data over roughly x ∈ [0,3] m (Figs. A.3 and A.4), but they are used without any clip or renormalization for all flood depths in Eq. (A.3) and hence in Eq. (2). Since φ_hrise(x) = 0.142 + 0.0541x − 0.00368x² − 0.00133x³ becomes negative for x above about 6.3 m (and φ_res turns negative above about 6.7 m), the aggregate damage function D(z) is not guaranteed to be non-negative or monotone, and with the 2100 p-box extending to roughly 3 m of SLR, the z-integration in Eq. (2) samples this invalid regime. The reported allowances in Tables 1–2 and Fig. 5, including the headline 1.70 m levee versus 0.86 m hazard allowance, may therefore be affected by an extrapolation artifact. Please re-estimate or clip the depth-damage functions to a physically valid range and re-run the allowance calculations, or demonstrate numerically that the results are insensitive to this choice.","section":"Sec. A.4 (also Eq. 2, Tables 1-2)"},{"comment":"The effective SLR distribution P̃(βc, AISmax, t) = βc·Phigh + (1−βc)·Plow is built on an arbitrarily truncated AIS contribution, and the paper acknowledges in Sec. A.8 that this truncation 'could impact results in a significant way, but is not investigated here.' Because Tables 1–2 and the associated figures condition every headline allowance on AISmax, this acknowledged limitation is load-bearing for the main numerical claims. A simple sensitivity sweep over AISmax values does not substitute for an analysis of the truncation's effect, since the reported spread across AISmax in Table 1 is itself the quantity being used to communicate deep uncertainty. Please provide a quantitative statement of how the allowance ranges change if the truncation is removed or replaced with a defined-tail distribution, or clearly re-label the results as illustrative of the method rather than as design recommendations.","section":"Sec. A.8, Eq. A.6"},{"comment":"The headline allowance tables report point estimates only, although the underlying calculations include GPD parameter uncertainty (Sec. A.2, with 1000 Latin hypercube samples) and SLR projection uncertainty (Table B.1). For a decision-support tool whose purpose is to communicate uncertainty, the absence of any interval or sensitivity measure for the allowances makes it difficult to know whether differences across AISmax and βc, such as the 1.8 m versus 3.4 m levee allowances in Table 1, are larger than the numerical uncertainty in the calculation. Please report at least a 5–95% range or an indication of the parameter-uncertainty contribution for the main allowance values, or state explicitly why they are omitted.","section":"Tables 1-2 and Sec. 3.3"}],"minor_comments":[{"comment":"The notation for the Antarctic ice-sheet limit is inconsistent: the text uses AISmax, AIS max, and AIS_max (e.g., Secs. 2.2, 3.2, and A.8); please choose one symbol and define it once.","section":"Notation throughout"},{"comment":"Eq. (4) defines the levee-protected damage function with the failure probability p_f, but the caption of Fig. 2B states that the levee curve assumes 'zero probability of structural failure and no freeboard'; please clarify whether that curve is the limit p_f→0 or a different construct.","section":"Sec. 2.1.2 and Fig. 2B"},{"comment":"The phrase 'average flood damage in a given year' is a bit loose; the paper actually uses annual average loss, which is an expectation over all events, so consider using 'expected annual flood damage' consistently.","section":"Abstract and Sec. 2"},{"comment":"The lower limit of integration e_min in Eq. (A.3) is not defined precisely; please specify the lowest first-floor elevation in the data or set e_min = 0 for clarity.","section":"Eq. A.3"},{"comment":"When reporting that 0.5 m of SLR increases the AAL from roughly $0.1 billion/yr to roughly $0.7 billion/yr, please state the rounding convention and confirm that all values are in 2017 USD.","section":"Sec. 3.1"},{"comment":"The acknowledgments contain the placeholder text '[ADD OTHERS]'; please complete the data and code availability statement before publication.","section":"Acknowledgments"}],"recommendation":"major_revision","confidential_remarks":"The p-box inputs are drawn from Kopp et al. (2014) and Kopp et al. (2017), on which two co-authors appear, but the weights and truncation are user choices rather than fitted parameters, so I do not see a circularity problem. The main risk is the unexamined depth-damage extrapolation described in Major Comment 1. The journal may wish to verify that the released code matches the tables after the requested re-analysis."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a real contribution, worth a serious referee, but treat the Manhattan numbers as conditional illustrations until a few loose ends are tightened. The damage-allowance concept - design heights that hold annual average loss constant rather than event frequency - is not in the earlier hazard-allowance literature, and the four-strategy treatment is a genuine extension. Equation 2 is algebraically sound given its stated assumptions, and the strategy-specific damage functions are clearly laid out. The authors also deserve credit for acknowledging several caveats in the discussion, including the arbitrary AISmax truncation and the limitation of a frozen city. The soft spots are three. First, the AISmax truncation is admittedly arbitrary and can significantly affect the late-century spread; the paper says this, but the headline tables lean on it heavily. Second, the reported allowances are point values with no propagated uncertainty, even though GPD parameter uncertainty and SLR projection uncertainty are both sampled elsewhere in the chain; that makes the 0.1 m precision in Tables 1 and 2 look stronger than the inputs support. Third, the depth-damage cubics in Sec. A.4 are fit over roughly 0-3 m of inundation depth, and the stated polynomials turn negative above about 6.3 m. No clipping or renormalization is given. This is a real defect in the written formulation, and it should be fixed and quantified. That said, the stress-test claim that all reported allowances are artifacts is too strong: Fig. 1B shows a monotone D(z) to 7 m, so the practical effect of the unclipped tail is probably small, but the authors need to confirm it rather than leave it implicit. The circularity concern from the reader does not land. The SLR inputs come from published Kopp et al. projections, beta_c is a user input, and nothing is fitted to reproduce the allowances. Self-citation appears because two authors are on the projection papers, but that is not a flaw here. The code release is incomplete, with a placeholder in the acknowledgments and no versioned workflow; that should be fixed. Bottom line: the framework is coherent and the central idea holds up. I would send this to peer review, asking for a clipped or reformulated damage function with a monotonicity check, uncertainty propagation or an explicit statement that the tables are best-estimate illustrations, and a complete code archive. It is a decision-support template worth engaging with, not a final design manual.","headline":"A useful and genuine extension of hazard allowances to damage-based design heights, with a sound core equation and some unvalidated choices that make the headline numbers illustrative rather than definitive.","tokens_in":784,"tokens_out":3181,"would_cite":true,"duration_ms":91337,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"To hold annual flood losses steady under sea-level rise, coastal defenses may need to be nearly twice as high as hazard-based allowances suggest.","keywords":["sea-level rise","coastal flood protection","damage allowance","annual average loss","deep uncertainty","Antarctic ice sheet","extreme sea level","benefit-cost analysis"],"falsifier":"Run the damage-allowance calculation on synthetic flood records drawn from a known sea-level distribution whose upper tail is longer than the chosen AISmax cutoff; if Eq. (2) fails to hold simulated annual losses at the target, the arbitrary truncation is load-bearing. Alternatively, track the Battery tide gauge over the coming decades: if realized sea level repeatedly falls outside the p-box bounds, allowances conditional on those bounds are biased.","tokens_in":49512,"feed_emoji":"🌊","tokens_out":6351,"duration_ms":68642,"temperature":0.7,"pith_summary":"This paper proposes that the design height of coastal flood protection should be set by the financial damage it prevents, not just by the water level it blocks. It defines a 'damage allowance' as the height needed to keep the annual average flood loss at a chosen target, traditionally today's loss, under uncertain future sea-level rise. Using Manhattan as a test case, it shows the damage allowance can be about twice the conventional hazard allowance: a 1.70 m levee in 2070 versus a 0.86 m hazard allowance, because damages are nonlinear and protection structures can fail. The framework also shows that after mid-century under high emissions, the required height depends strongly on what one believes about Antarctic ice-sheet collapse, with 2100 levee allowances spanning roughly 1.8 to 3.4 m.","feed_headline":"Flood defenses may need double the height of sea-level allowances","feed_subtitle":"A damage-based levee for Manhattan reaches 1.7 m by 2070, while a hazard-only allowance stops at 0.86 m.","key_machinery":"The load-bearing object is the damage allowance A defined by Eq. (2), which balances the protected expected annual loss under sea-level rise against the current annual average loss. The protected damage functions encode strategy-specific behavior: levees and surge barriers fail with an exponential fragility curve; surge barriers leave gates open below a closure threshold; coastal retreat removes assets below A with a compliance parameter; elevation shifts the damage function upward. Uncertainty in sea-level rise is represented by an 'effective' distribution formed as a weighted average of two bounding cumulative distributions (a probability box), with weight $\\beta_c$ reflecting belief in Antarctic ice-sheet collapse and with the upper tail truncated at a chosen AISmax. The allowance is the height that balances the two sides of the conservation equation.","core_discovery":"The central claim is that holding flood risk constant in financial terms requires solving a conservation-of-damage equation: the expected annual loss under future sea-level rise, after adding protection of height A, must equal the current annual average loss. The paper constructs protected damage functions for four strategies—elevation, levee, storm surge barrier, and coastal retreat—each with its own failure or compliance behavior, and solves Eq. (2) for A. For Manhattan's 2070 conditions with a levee, the resulting damage allowance is 1.70 m, nearly twice the 0.86 m hazard allowance that only keeps the frequency of extreme sea levels constant; by 2100 under RCP8.5 the levee allowance ranges from 1.8 m to 3.4 m depending on assumptions about Antarctic melt and collapse likelihood. The authors argue this makes the damage allowance a direct input to benefit-cost and cost-effectiveness analysis, because it quantifies avoided damages in dollars.","pith_inferences":["The relative gap between damage and hazard allowances is likely to vary by city: places with steep depth-damage curves or concentrated assets just above the waterline would need proportionally taller defenses, a testable extension of the Manhattan result.","The p-box weighting could be interpreted as a set of priors; combining the resulting allowance ranges with robust decision rules, such as minimax regret over the allowance set, would avoid committing to a single $\\beta_c$.","The 'frozen city' assumption may understate allowances where protection encourages development behind the levee; re-running the model with endogenous asset growth would test the size of this levee effect."],"forward_implications":["Hazard-based allowances understate the vertical protection needed when the goal is to stabilize dollar losses, because damage grows faster than water level and defenses can fail.","Design heights should be reported as ranges over Antarctic ice-sheet assumptions rather than as single values; under RCP8.5 the 2100 levee allowance spans 1.8 to 3.4 m.","Strong emissions reductions make allowances far less sensitive to ice-sheet beliefs: under RCP2.6 the spread across assumptions is at most about 0.6 m.","The allowance can be used directly as the benefit side of a benefit-cost or cost-effectiveness analysis, because it specifies the avoided annual loss.","Different strategies imply different allowances: coastal retreat needs less height than a levee because it removes assets rather than defending them, while a surge barrier needs more than a levee because gates remain open up to the closure threshold."],"supporting_citations":[{"why":"Defines the hazard allowance and the log-linear relationship between extreme sea level frequency and water height that the damage allowance extends.","marker":"Buchanan et al., 2016"},{"why":"Provides the simple allowance technique for uncertain sea-level rise on which the hazard allowance side of the framework builds.","marker":"Hunter, 2012"},{"why":"Supplies the lower-bound sea-level projection set with slower Antarctic ice-sheet mass loss used in the probability box.","marker":"Kopp et al., 2014"},{"why":"Supplies the upper-bound projection set with fast Antarctic ice-sheet mass loss used in the probability box.","marker":"Kopp et al., 2017"},{"why":"Provides the rapid ice-sheet loss mechanisms embedded in the upper sea-level projections.","marker":"Deconto and Pollard, 2016"},{"why":"Provides the expert elicitation of ice-sheet mass loss used in the lower projection set.","marker":"Bamber and Aspinall, 2013"},{"why":"Gives the method for constructing the aggregate flood damage function from property values and depth-damage relationships.","marker":"Diaz, 2016"}],"fun_headline_variants":["Damage-based flood risk doubles Manhattan levee height","Coastal defense height set by financial risk, not flood odds","Manhattan levee needs 1.7m to hold flood damage constant","Flood protection sized by damage, not sea-level extremes","Risk-based allowances for sea-level rise double defense height"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The framework's headline numbers rest on an 'effective' sea-level distribution built by averaging two bounding projections with a subjective weight and cutting the upper tail at an arbitrary maximum Antarctic melt; the paper concedes that this truncation could change results significantly and is not tested.","fun_headline_variants_meta":{"raw":{"variants":["Damage-based flood risk doubles Manhattan levee height","Coastal defense height set by financial risk, not flood odds","Manhattan levee needs 1.7m to hold flood damage constant","Flood protection sized by damage, not sea-level extremes","Risk-based allowances for sea-level rise double defense height"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00023,"raw_usage":{"total_tokens":1539,"prompt_tokens":1056,"completion_tokens":483,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":672,"completion_tokens_details":{"reasoning_tokens":400}},"tokens_in":672,"tokens_out":483,"duration_ms":5074,"temperature":1.0,"reasoning_tokens":400,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:34:37.248774+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the damage-allowance calculation on synthetic flood records drawn from a known sea-level distribution whose upper tail is longer than the chosen AISmax cutoff; if Eq. (2) fails to hold simulated annual losses at the target, the arbitrary truncation is load-bearing. Alternatively, track the Battery tide gauge over the coming decades: if realized sea level repeatedly falls outside the p-box bounds, allowances conditional on those bounds are biased.","supporting_citations":[{"cited_title":", Kopp , R E","cited_arxiv_id":null,"evidence_quote":"Defines the hazard allowance and the log-linear relationship between extreme sea level frequency and water height that the damage allowance extends."},{"cited_title":"APACrefauthors \\ 2012","cited_arxiv_id":null,"evidence_quote":"Provides the simple allowance technique for uncertain sea-level rise on which the hazard allowance side of the framework builds."},{"cited_title":", DeConto, R M","cited_arxiv_id":null,"evidence_quote":"Supplies the upper-bound projection set with fast Antarctic ice-sheet mass loss used in the probability box."},{"cited_title":"\\ Pollard, D","cited_arxiv_id":null,"evidence_quote":"Provides the rapid ice-sheet loss mechanisms embedded in the upper sea-level projections."},{"cited_title":"\\ Aspinall, W P","cited_arxiv_id":null,"evidence_quote":"Provides the expert elicitation of ice-sheet mass loss used in the lower projection set."},{"cited_title":"APACrefauthors \\ 2016","cited_arxiv_id":null,"evidence_quote":"Gives the method for constructing the aggregate flood damage function from property values and depth-damage relationships."}],"review_version":1}