pith. sign in

arxiv: 2507.09211 · v2 · submitted 2025-07-12 · 💻 cs.LG · physics.ao-ph· physics.data-an· physics.geo-ph· stat.ML

Capturing Unseen Spatial Heat Extremes Through Dependence-Aware Generative Modeling

Pith reviewed 2026-05-19 04:47 UTC · model grok-4.3

classification 💻 cs.LG physics.ao-phphysics.data-anphysics.geo-phstat.ML
keywords generative modelingclimate extremesspatial dependenceunseen eventsheat wavesrisk assessmentMiddle EastNorth Africa
0
0 comments X

The pith

DeepX-GAN captures spatial dependencies to generate statistically plausible unseen heat extremes that reveal hidden risks in the Middle East and North Africa.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops DeepX-GAN, a generative adversarial network that models the spatial structure of heat extremes to simulate events beyond the historical record. It distinguishes direct-hit and near-miss extremes and validates the outputs against climate model ensembles. Application to the MENA region shows these unseen extremes threaten vulnerable countries more, with future warming creating persistent and new hotspots. Sympathetic readers would care because ignoring spatial dependence and unseen events leads to underestimating simultaneous multi-location hazards and false senses of security.

Core claim

DeepX-GAN explicitly captures the spatial structure of rare extremes through dependence-enhanced embedding, enabling zero-shot generation of statistically plausible direct-hit and near-miss heat extremes beyond observed records, as confirmed by comparison to long climate model large-ensemble simulations. When applied to the Middle East and North Africa, these unrealized events disproportionately threaten countries with high vulnerability and low socioeconomic readiness, while future warming is projected to expand and shift extremes into persistent hotspots in Northwest Africa and the Arabian Peninsula and new hotspots in Central Africa.

What carries the argument

DeepX-GAN, a deep generative model with dependence-enhanced embedding that captures the spatial dependence of physical extremes to enable simulation of unseen events.

If this is right

  • Unseen extremes can either prompt proactive adaptation measures or reinforce a false sense of resilience in affected regions.
  • Future warming will expand and shift heat extreme hotspots, necessitating spatially adaptive risk planning.
  • Countries with high vulnerability and low socioeconomic readiness face disproportionate threats from these unseen events.
  • Traditional observed records provide an incomplete view of risk by missing events that affect multiple locations simultaneously.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar generative approaches could be applied to other climate hazards like floods or droughts in different regions to uncover hidden spatial risks.
  • Integration with socioeconomic data might help prioritize adaptation investments in the most threatened areas.
  • Policy makers could use these simulations to test the robustness of current infrastructure designs against extreme scenarios.

Load-bearing premise

That a generative model trained on historical climate records can produce extremes beyond the observed record whose statistical properties match those from independent large-ensemble climate model simulations.

What would settle it

A mismatch between the spatial patterns, frequencies, or intensities of generated extremes and those found in long climate model large-ensemble simulations would falsify the model's ability to produce valid unseen events.

read the original abstract

Observed records of climate extremes provide an incomplete view of risk, missing "unseen" events beyond historical experience. Ignoring spatial dependence further underestimates hazards striking multiple locations simultaneously. We introduce DeepX-GAN (Dependence-Enhanced Embedding for Physical eXtremes - Generative Adversarial Network), a deep generative model that explicitly captures the spatial structure of rare extremes. Its zero-shot generalizability enables simulation of statistically plausible extremes beyond the observed record, validated against long climate model large-ensemble simulations. We define two unseen types: direct-hit extremes that affect the target and near-miss extremes that narrowly miss. These unrealized events reveal hidden risks and can either prompt proactive adaptation or reinforce a sense of false resilience. Applying DeepX-GAN to the Middle East and North Africa shows that unseen heat extremes disproportionately threaten countries with high vulnerability and low socioeconomic readiness. Future warming is projected to expand and shift these extremes, creating persistent hotspots in Northwest Africa and the Arabian Peninsula, and new hotspots in Central Africa, necessitating spatially adaptive risk planning.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces DeepX-GAN, a dependence-aware generative adversarial network that captures spatial structure in heat extremes. It claims zero-shot generation of statistically plausible 'unseen' direct-hit and near-miss extremes beyond the observational record, validates these outputs against long climate-model large-ensemble simulations, and applies the framework to the Middle East and North Africa to show disproportionate threats to high-vulnerability countries and the emergence of persistent and new hotspots under future warming.

Significance. If the central claim holds, the work offers a practical route to quantify compound spatial risks that are invisible in short observational records, with direct relevance to adaptation planning in vulnerable regions. The explicit separation of direct-hit versus near-miss events and the linkage to socioeconomic readiness indices are useful framing devices.

major comments (2)
  1. [Validation section] Validation section (implicitly §4–5): the claim that GAN outputs are 'statistically plausible' unseen extremes rests entirely on agreement with a single family of climate-model large ensembles. No independent check against reanalysis tail dependence or a structurally different model ensemble is reported, leaving open the possibility that shared biases in convective or land-surface schemes are being reproduced rather than validated against physical reality.
  2. [MENA application] Application results (MENA case study): the reported expansion of hotspots in Northwest Africa and the Arabian Peninsula and emergence in Central Africa under future warming is presented without quantitative uncertainty bounds on the GAN-generated tail probabilities or sensitivity tests to the choice of training hyperparameters listed in the free_parameters ledger.
minor comments (2)
  1. [Methods] Notation for 'direct-hit' and 'near-miss' extremes should be defined with explicit probability thresholds in the methods section rather than only in the abstract.
  2. [Figures] Figure captions for spatial maps should include the exact ensemble size and time period of the climate-model reference data used for validation.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive comments, which help clarify the scope and limitations of our validation and application sections. We respond point by point below.

read point-by-point responses
  1. Referee: [Validation section] Validation section (implicitly §4–5): the claim that GAN outputs are 'statistically plausible' unseen extremes rests entirely on agreement with a single family of climate-model large ensembles. No independent check against reanalysis tail dependence or a structurally different model ensemble is reported, leaving open the possibility that shared biases in convective or land-surface schemes are being reproduced rather than validated against physical reality.

    Authors: We selected large-ensemble simulations as the validation benchmark because they alone provide a sufficiently large sample of rare spatial extremes that are statistically inaccessible in the short observational record or in most reanalysis products. Reanalysis tail dependence estimates would be noisy or undefined for events rarer than those already observed. We acknowledge that agreement with one model family cannot fully exclude shared parameterization biases. In revision we will add an explicit discussion of this limitation together with any feasible tail-dependence diagnostics that can be computed from available reanalysis, but a full cross-model ensemble comparison lies outside the present computational scope. revision: partial

  2. Referee: [MENA application] Application results (MENA case study): the reported expansion of hotspots in Northwest Africa and the Arabian Peninsula and emergence in Central Africa under future warming is presented without quantitative uncertainty bounds on the GAN-generated tail probabilities or sensitivity tests to the choice of training hyperparameters listed in the free_parameters ledger.

    Authors: We agree that uncertainty quantification and hyperparameter sensitivity strengthen the MENA projections. In the revised manuscript we will report empirical uncertainty intervals obtained from repeated independent GAN generations and will add a dedicated sensitivity analysis for the principal hyperparameters listed in the ledger, confirming that the reported hotspot shifts remain qualitatively stable. revision: yes

standing simulated objections not resolved
  • A comprehensive validation against a structurally different climate-model large ensemble, which would require access to additional high-resolution ensemble output not currently available.

Circularity Check

0 steps flagged

No significant circularity; external climate-model validation anchors the claims

full rationale

The paper trains DeepX-GAN on historical observations to generate unseen spatial heat extremes and then validates statistical plausibility directly against independent large-ensemble climate-model simulations. This external benchmark lies outside the fitted parameters and observed record, so the central claim does not reduce to its inputs by construction. No self-citations, definitional loops, or fitted-input-renamed-as-prediction steps appear in the abstract or described derivation. The derivation chain therefore remains self-contained against an external reference rather than internally tautological.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete; the approach rests on the assumption that spatial dependence structures learned from limited observations can be extrapolated to unseen events without additional physical constraints.

free parameters (1)
  • GAN architecture and training hyperparameters
    Deep generative models require numerous fitted choices for layers, loss weights, and sampling that are not detailed in the abstract.
axioms (1)
  • domain assumption Spatial dependence patterns in historical extremes are sufficient to generate statistically plausible unseen events.
    This premise underpins the zero-shot generalizability claim and is invoked when defining direct-hit and near-miss extremes.

pith-pipeline@v0.9.0 · 5748 in / 1323 out tokens · 39895 ms · 2026-05-19T04:47:55.028706+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

78 extracted references · 78 canonical work pages

  1. [1]

    High risk of unprecedented UK rainfall in the current climate,

    V. Thompson, N. J. Dunstone, A. A. Scaife, D. M. Smith, J. M. Slingo, S. Brown, and S. E. Belcher, “High risk of unprecedented UK rainfall in the current climate,”Nature Communications, vol. 8, no. 1, p. 107, 2017

  2. [2]

    Chapter 3 - changes in climate extremes in observa- tions and climate model simulations. from the past to the future,

    M. G. Donat, J. Sillmann, and E. M. Fischer, “Chapter 3 - changes in climate extremes in observa- tions and climate model simulations. from the past to the future,” inClimate Extremes and Their Implications for Impact and Risk Assessment(J. Sillmann, S. Sippel, and S. Russo, eds.), pp. 31–57, Elsevier, 2020

  3. [3]

    Coles,An Introduction to Statistical Modeling of Extreme Values

    S. Coles,An Introduction to Statistical Modeling of Extreme Values. Springer Series in Statistics, London: Springer London, 2001

  4. [4]

    Interpreting extreme climate impacts from large ensemble simulations—are they unseen or unrealistic?,

    T. Kelder, N. Wanders, K. Van Der Wiel, T. I. Marjoribanks, L. J. Slater, R. L. Wilby, and C. Prud- homme, “Interpreting extreme climate impacts from large ensemble simulations—are they unseen or unrealistic?,”Environmental Research Letters, vol. 17, no. 4, p. 044052, 2022

  5. [5]

    Increasingprobabilityofrecord-shatteringclimateextremes,

    E.M.Fischer, S.Sippel, andR.Knutti, “Increasingprobabilityofrecord-shatteringclimateextremes,” vol. 11, no. 8, pp. 689–695

  6. [6]

    Storylines for unprecedented heatwaves based on ensemble boosting,

    E. M. Fischer, U. Beyerle, L. Bloin-Wibe, C. Gessner, V. Humphrey, F. Lehner, A. G. Pendergrass, S. Sippel, J. Zeder, and R. Knutti, “Storylines for unprecedented heatwaves based on ensemble boosting,”Nature Communications, vol. 14, no. 1, p. 4643, 2023

  7. [7]

    Very rare heat extremes: Quantifying and understanding using ensemble reinitialization,

    C. Gessner, E. M. Fischer, U. Beyerle, and R. Knutti, “Very rare heat extremes: Quantifying and understanding using ensemble reinitialization,”Journal of Climate, vol. 34, no. 16, pp. 6619–6634, 2021

  8. [8]

    The most at-risk regions in the world for high-impact heatwaves,

    V. Thompson, D. Mitchell, G. C. Hegerl, M. Collins, N. J. Leach, and J. M. Slingo, “The most at-risk regions in the world for high-impact heatwaves,”Nature Communications, vol. 14, no. 1, p. 2152, 2023

  9. [9]

    The unprecedented Pacific northwest heatwave of June 2021,

    R. H. White, S. Anderson, J. F. Booth, G. Braich, C. Draeger, C. Fei, C. D. G. Harley, S. B. Hen- derson, M. Jakob, C.-A. Lau, L. Mareshet Admasu, V. Narinesingh, C. Rodell, E. Roocroft, K. R. Weinberger, and G. West, “The unprecedented Pacific northwest heatwave of June 2021,”Nature Communications, vol. 14, no. 1, p. 727, 2023

  10. [10]

    Has the impact of heat waves on mortality changed in france since the european heat wave of summer 2003? A study of the 2006 heat wave,

    A. Fouillet, G. Rey, V. Wagner, K. Laaidi, P. Empereur-Bissonnet, A. Le Tertre, P. Frayssinet, P. Besse- moulin, F. Laurent, P. De Crouy-Chanel, E. Jougla, and D. Hémon, “Has the impact of heat waves on mortality changed in france since the european heat wave of summer 2003? A study of the 2006 heat wave,”International Journal of Epidemiology, vol. 37, no...

  11. [11]

    Past hydroclimate extremes in Europe driven by Atlantic jet stream and recurrent weather patterns,

    S. Brönnimann, J. Franke, V. Valler, R. Hand, E. Samakinwa, E. Lundstad, A.-M. Burgdorf, L. Lipfert, L. Pfister, N. Imfeld, and M. Rohrer, “Past hydroclimate extremes in Europe driven by Atlantic jet stream and recurrent weather patterns,”Nature Geoscience, vol. 18, no. 3, pp. 246–253, 2025

  12. [12]

    Sketching the spatial disparities in heatwave trends by changing atmospheric teleconnections in the northern hemisphere,

    F. Cai, C. Liu, D. Gerten, S. Yang, T. Zhang, K. Li, and J. Kurths, “Sketching the spatial disparities in heatwave trends by changing atmospheric teleconnections in the northern hemisphere,”Nature Communications, vol. 15, no. 1, p. 8012, 2024

  13. [13]

    Heatwave location changes in relation to Rossby wave phase speed,

    W. Wicker, N. Harnik, M. Pyrina, and D. I. V. Domeisen, “Heatwave location changes in relation to Rossby wave phase speed,”Geophysical Research Letters, vol. 51, no. 14, p. e2024GL108159, 2024. 48 Capturing Unseen Spatial Extremes Through Knowledge-Informed Generative Modeling

  14. [14]

    S. Duan, K. McKinnon, and I. R. Simpson, “Quantifying the impact of atmospheric circulation and soil preconditioning with large ensembles of simulation under constrained circulation: A case study of the 2021 Pacific Northwest heatwave,”Authorea Preprints, 2025

  15. [15]

    Letdowns, wake-upcalls, andconstructed preferences: People’s responses to fuel and wildfire risks,

    J.Arvai, R.Gregory, D.Ohlson, B.Blackwell, andR.Gray, “Letdowns, wake-upcalls, andconstructed preferences: People’s responses to fuel and wildfire risks,”Journal of Forestry, vol. 104, no. 4, pp. 173–181, 2006

  16. [16]

    How near-misses influence decision making under risk: A missed opportunity for learning,

    R. L. Dillon and C. H. Tinsley, “How near-misses influence decision making under risk: A missed opportunity for learning,”Management Science, vol. 54, no. 8, pp. 1425–1440, 2008

  17. [17]

    Near-miss events, risk messages, and decision making,

    R. L. Dillon and C. H. Tinsley, “Near-miss events, risk messages, and decision making,”Environment Systems and Decisions, vol. 36, no. 1, pp. 34–44, 2016

  18. [18]

    Learning from hurricane Laura’s near miss: Evacuation decision-making under uncertainty,

    D. Retchless and R. Ashley, “Learning from hurricane Laura’s near miss: Evacuation decision-making under uncertainty,” Report Report 4, 2022

  19. [19]

    Near-misses and future disaster preparedness,

    R. L. Dillon, C. H. Tinsley, and W. J. Burns, “Near-misses and future disaster preparedness,”Risk Analysis, vol. 34, no. 10, pp. 1907–1922, 2014

  20. [20]

    Tropical cyclone report, hurricane Wilma,

    R. J. Pasch, E. S. Blake, H. D. Cobb Iii, and D. P. Roberts, “Tropical cyclone report, hurricane Wilma,” report, NOAA/NWS/Tropical Prediction Center/National Hurricane Center, 2006

  21. [21]

    Asymmetric response of global drought and pluvial detection to the length of climate epoch,

    B. Long, B. Zhang, and X. He, “Asymmetric response of global drought and pluvial detection to the length of climate epoch,”Journal of Hydrology, p. 130078, 2023

  22. [22]

    Multivariate copula analysis toolbox (mvcat): De- scribing dependence and underlying uncertainty using a Bayesian framework,

    M. Sadegh, E. Ragno, and A. AghaKouchak, “Multivariate copula analysis toolbox (mvcat): De- scribing dependence and underlying uncertainty using a Bayesian framework,”Water Resources Research, vol. 53, no. 6, pp. 5166–5183, 2017

  23. [23]

    Salvadori, C

    G. Salvadori, C. D. Michele, N. T. Kottegoda, and R. Rosso,Extremes in Nature: An Approach Using Copulas. Water Science and Technology Library, Dordrecht: Springer Netherlands, 2007

  24. [24]

    A global drought and flood catalogue from 1950 to 2016,

    X. He, M. Pan, Z. Wei, E. F. Wood, and J. Sheffield, “A global drought and flood catalogue from 1950 to 2016,”Bulletin of the American Meteorological Society, vol. 101, no. 5, pp. E508 – E535, 2020

  25. [25]

    Leveraging extremal dependence to better characterize the 2021 Pacific northwest heatwave,

    L. Zhang, M. D. Risser, M. F. Wehner, and T. A. O’Brien, “Leveraging extremal dependence to better characterize the 2021 Pacific northwest heatwave,”Journal of Agricultural, Biological and Environmental Statistics, 2024

  26. [26]

    The 2021 western North America heat wave among the most extreme events ever recorded globally,

    V. Thompson, A. T. Kennedy-Asser, E. Vosper, Y. T. E. Lo, C. Huntingford, O. Andrews, M. Collins, G. C. Hegerl, and D. Mitchell, “The 2021 western North America heat wave among the most extreme events ever recorded globally,”Science Advances, vol. 8, no. 18, p. eabm6860, 2022

  27. [27]

    Large ensemble climate model simulations: Introduc- tion, overview, and future prospects for utilising multiple types of large ensemble,

    N. Maher, S. Milinski, and R. Ludwig, “Large ensemble climate model simulations: Introduc- tion, overview, and future prospects for utilising multiple types of large ensemble,”Earth System Dynamics, vol. 12, no. 2, pp. 401–418, 2021

  28. [28]

    Ad- vancing research on compound weather and climate events via large ensemble model simulations,

    E. Bevacqua, L. Suarez-Gutierrez, A. Jézéquel, F. Lehner, M. Vrac, P. Yiou, and J. Zscheischler, “Ad- vancing research on compound weather and climate events via large ensemble model simulations,” Nature Communications, vol. 14, no. 1, p. 2145, 2023

  29. [29]

    Developing low-likelihood climate storylines for extreme precipitation over central Europe,

    C. Gessner, E. M. Fischer, U. Beyerle, and R. Knutti, “Developing low-likelihood climate storylines for extreme precipitation over central Europe,”Earth’s Future, vol. 11, no. 9, p. e2023EF003628, 2023. 49 Capturing Unseen Spatial Extremes Through Knowledge-Informed Generative Modeling

  30. [30]

    Risk and dynamics of unprecedented hot months in South East China,

    V. Thompson, N. J. Dunstone, A. A. Scaife, D. M. Smith, S. C. Hardiman, H.-L. Ren, B. Lu, and S. E. Belcher, “Risk and dynamics of unprecedented hot months in South East China,”Climate Dynamics, vol. 52, no. 5, pp. 2585–2596, 2019

  31. [31]

    Using unseen trends to detect decadal changes in 100-year precipitation extremes,

    T. Kelder, M. Müller, L. J. Slater, T. I. Marjoribanks, R. L. Wilby, C. Prudhomme, P. Bohlinger, L. Ferranti, and T. Nipen, “Using unseen trends to detect decadal changes in 100-year precipitation extremes,”npj Climate and Atmospheric Science, vol. 3, no. 1, pp. 1–13, 2020

  32. [32]

    AI firms will soon exhaust most of the internet’s data,

    “AI firms will soon exhaust most of the internet’s data,”The Economist, 2024

  33. [33]

    Modeling extreme events in time series prediction,

    D. Ding, M. Zhang, X. Pan, M. Yang, and X. He, “Modeling extreme events in time series prediction,” Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 2019

  34. [34]

    Enhancing time series predictors with generalized extreme value loss,

    M. Zhang, D. Ding, X. Pan, and M. Yang, “Enhancing time series predictors with generalized extreme value loss,”IEEE Transactions on Knowledge and Data Engineering, pp. 1–1, 2021

  35. [35]

    Deep learning for improving numerical weather prediction of heavy rainfall,

    P. Hess and N. Boers, “Deep learning for improving numerical weather prediction of heavy rainfall,” Journal of Advances in Modeling Earth Systems, vol. 14, no. 3, p. e2021MS002765, 2022

  36. [36]

    Pareto GAN: Extending the representational power of GANs to heavy-tailed distributions,

    T. Huster, J. E. J. Cohen, Z. Lin, K. Chan, C. Kamhoua, N. Leslie, C.-Y. J. Chiang, and V. Sekar, “Pareto GAN: Extending the representational power of GANs to heavy-tailed distributions,”arXiv e-prints, p. arXiv:2101.09113, 2021

  37. [37]

    Modeling and simulat- ing spatial extremes by combining extreme value theory with generative adversarial networks,

    Y. Boulaguiem, J. Zscheischler, E. Vignotto, K. v. d. Wiel, and S. Engelke, “Modeling and simulat- ing spatial extremes by combining extreme value theory with generative adversarial networks,” Environmental Data Science, vol. 1, p. e5, 2022

  38. [38]

    ExGAN: Adversarial generation of extreme samples,

    S. Bhatia, A. Jain, and B. Hooi, “ExGAN: Adversarial generation of extreme samples,”Proceedings of the AAAI Conference on Artificial Intelligence, vol. 35, no. 8, pp. 6750–6758, 2021

  39. [39]

    Generative adversarial networks,

    I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, “Generative adversarial networks,” 2014

  40. [40]

    J. M. Tomczak,Deep Generative Modeling. Cham: Springer International Publishing, 2022

  41. [41]

    C. M. Bishop and H. Bishop,Generative Adversarial Networks, pp. 533–545. Cham: Springer International Publishing, 2024

  42. [42]

    Notre Dame Global Adaptation Initiative’s (ND-GAIN) Country Index,

    University of Notre Dame, “Notre Dame Global Adaptation Initiative’s (ND-GAIN) Country Index,” 2023

  43. [43]

    Forecasting fierce floods with transferable AI in data-scarce regions,

    H.-M. Wang, X. Peng, and X. He, “Forecasting fierce floods with transferable AI in data-scarce regions,”The Innovation, vol. 5, no. 4, 2024

  44. [44]

    Origin, importance, and predictive limits of internal climate variability,

    F. Lehner and C. Deser, “Origin, importance, and predictive limits of internal climate variability,” Environmental Research: Climate, vol. 2, no. 2, p. 023001, 2023

  45. [45]

    Deterministic nonperiodic flow,

    E. N. Lorenz, “Deterministic nonperiodic flow,”Journal of the Atmospheric Sciences, vol. 20, pp. 130– 141, 1963

  46. [46]

    Global warming has increased global economic inequality,

    N. S. Diffenbaugh and M. Burke, “Global warming has increased global economic inequality,” Proceedings of the National Academy of Sciences, vol. 116, no. 20, pp. 9808–9813, 2019

  47. [47]

    Climate inequality report 2023,

    L. Chancel, P. Bothe, and T. Voituriez, “Climate inequality report 2023,” report, World Inequality Lab Study 2023/1, 2023. 50 Capturing Unseen Spatial Extremes Through Knowledge-Informed Generative Modeling

  48. [48]

    Global risk of deadly heat,

    C. Mora, B. Dousset, I. R. Caldwell, F. E. Powell, R. C. Geronimo, C. R. Bielecki, C. W. W. Counsell, B. S. Dietrich, E. T. Johnston, L. V. Louis, M. P. Lucas, M. M. McKenzie, A. G. Shea, H. Tseng, T. W. Giambelluca, L. R. Leon, E. Hawkins, and C. Trauernicht, “Global risk of deadly heat,”Nature Climate Change, vol. 7, no. 7, pp. 501–506, 2017

  49. [49]

    Geostatistics of extremes,

    A. C. Davison and M. M. Gholamrezaee, “Geostatistics of extremes,”Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 468, no. 2138, pp. 581–608, 2012

  50. [50]

    AghaKouchak, S

    A. AghaKouchak, S. Sellars, and S. Sorooshian,Methods of Tail Dependence Estimation, pp. 163–179. Dordrecht: Springer Netherlands, 2013

  51. [51]

    Climate stress testing,

    V. V. Acharya, R. Berner, R. Engle, H. Jung, J. Stroebel, X. Zeng, and Y. Zhao, “Climate stress testing,” tech. rep., Federal Reserve Bank of New York, 2023

  52. [52]

    Quantitative stress test of compound coastal-fluvial floods in China’s Pearl River Delta,

    J. Qiu, B. Liu, F. Yang, X. Wang, and X. He, “Quantitative stress test of compound coastal-fluvial floods in China’s Pearl River Delta,”Earth’s Future, vol. 10, no. 5, p. e2021EF002638, 2022

  53. [53]

    A framework to diagnose barriers to climate change adaptation,

    S. C. Moser and J. A. Ekstrom, “A framework to diagnose barriers to climate change adaptation,” Proceedings of the National Academy of Sciences, vol. 107, no. 51, pp. 22026–22031, 2010. doi: 10.1073/pnas.1007887107

  54. [54]

    Adaptation and transformation,

    M. Pelling, K. O’Brien, and D. Matyas, “Adaptation and transformation,”Climatic Change, vol. 133, no. 1, pp. 113–127, 2015

  55. [55]

    Reconceptualising adaptation to climate change as part of pathways of change and response,

    R. M. Wise, I. Fazey, M. Stafford Smith, S. E. Park, H. C. Eakin, E. R. M. Archer Van Garderen, and B. Campbell, “Reconceptualising adaptation to climate change as part of pathways of change and response,”Global Environmental Change, vol. 28, pp. 325–336, 2014

  56. [56]

    Fueling injustice: Globalization, ecologically unequal exchange and climate change,

    T. J. Roberts and B. C. Parks, “Fueling injustice: Globalization, ecologically unequal exchange and climate change,”Globalizations, vol. 4, no. 2, pp. 193–210, 2007

  57. [57]

    Double exposure: Assessing the impacts of climate change within the context of economic globalization,

    K. L. O’Brien and R. M. Leichenko, “Double exposure: Assessing the impacts of climate change within the context of economic globalization,”Global Environmental Change, vol. 10, no. 3, pp. 221– 232, 2000

  58. [58]

    Reckoning climate apartheid,

    J. Long, “Reckoning climate apartheid,”Political Geography, vol. 112, p. 103117, 2024

  59. [59]

    Identifying the policy space for climate loss and damage,

    R. Mechler and T. Schinko, “Identifying the policy space for climate loss and damage,”Science, vol. 354, no. 6310, pp. 290–292, 2016

  60. [60]

    Loss and damage finance should apply to biodiversity loss,

    D. Roe, E. Holland, N. Nisi, T. Mitchell, and T. Tasnim, “Loss and damage finance should apply to biodiversity loss,”Nature Ecology & Evolution, vol. 7, no. 9, pp. 1336–1338, 2023

  61. [61]

    Characterizing loss and damage from climate change,

    R. James, F. Otto, H. Parker, E. Boyd, R. Cornforth, D. Mitchell, and M. Allen, “Characterizing loss and damage from climate change,”Nature Climate Change, vol. 4, no. 11, pp. 938–939, 2014

  62. [62]

    A typology of loss and damage perspectives,

    E. Boyd, R. A. James, R. G. Jones, H. R. Young, and F. E. L. Otto, “A typology of loss and damage perspectives,”Nature Climate Change, vol. 7, no. 10, pp. 723–729, 2017

  63. [63]

    SPATE-GAN: Improved generative modeling of dynamic spatio-temporal patterns with an autoregressive embedding loss,

    K. Klemmer, T. Xu, B. Acciaio, and D. B. Neill, “SPATE-GAN: Improved generative modeling of dynamic spatio-temporal patterns with an autoregressive embedding loss,”Proceedings of the AAAI Conference on Artificial Intelligence, vol. 36, no. 4, pp. 4523–4531, 2022

  64. [64]

    Progressive growing of GANs for improved quality, stability, and variation,

    T. Karras, T. Aila, S. Laine, and J. Lehtinen, “Progressive growing of GANs for improved quality, stability, and variation,”arXiv, 2018. 51 Capturing Unseen Spatial Extremes Through Knowledge-Informed Generative Modeling

  65. [65]

    Geological facies modeling based on progressive growing of generative adversarial networks (GANs),

    S. Song, T. Mukerji, and J. Hou, “Geological facies modeling based on progressive growing of generative adversarial networks (GANs),”Computational Geosciences, vol. 25, no. 3, pp. 1251–1273, 2021

  66. [66]

    Integrating structured biological data by kernel maximum mean discrepancy,

    K. M. Borgwardt, A. Gretton, M. J. Rasch, H.-P. Kriegel, B. Schölkopf, and A. J. Smola, “Integrating structured biological data by kernel maximum mean discrepancy,”Bioinformatics, vol. 22, no. 14, pp. e49–e57, 2006

  67. [67]

    On the effects of batch and weight normalization in generative adversarial networks,

    S. Xiang and H. Li, “On the effects of batch and weight normalization in generative adversarial networks,”arXiv, 2017

  68. [68]

    Bayesian computation for Log-Gaussian Cox Processes: A comparative analysis of methods,

    M. Teng, F. S. Nathoo, and T. D. Johnson, “Bayesian computation for Log-Gaussian Cox Processes: A comparative analysis of methods,”Journal of Statistical Computation and Simulation, vol. 87, no. 11, pp. 2227–2252, 2017

  69. [69]

    Log gaussian cox processes,

    J. Møller, A. R. Syversveen, and R. P. Waagepetersen, “Log gaussian cox processes,”Scandinavian Journal of Statistics, vol. 25, no. 3, pp. 451–482, 1998

  70. [70]

    Møller and R

    J. Møller and R. Waagepetersen,Statistical Inference and Simulation for Spatial Point Process, vol. 100. Chapman and Hall/CRC, 2003

  71. [71]

    IPCC, Climate Change 2022: Impacts, Adaptation and Vulnerability. 2022

  72. [72]

    NCEP-DOE AMIP-II Reanalysis (R-2),

    M.Kanamitsu,W.Ebisuzaki,J.Woollen,S.-K.Yang,J.Hnilo,M.Fiorino,andG.L.Potter,“NCEP-DOE AMIP-II Reanalysis (R-2),” 2002

  73. [73]

    CMIP6 simulations with the CMCC earth system model (CMCC-ESM2),

    T. Lovato, D. Peano, M. Butenschön, S. Materia, D. Iovino, E. Scoccimarro, P. G. Fogli, A. Cherchi, A. Bellucci, S. Gualdi, S. Masina, and A. Navarra, “CMIP6 simulations with the CMCC earth system model (CMCC-ESM2),”Journal of Advances in Modeling Earth Systems, vol. 14, no. 3, p. e2021MS002814, 2022

  74. [74]

    Global mean climate and main patterns of variability in the CMCC-CM2 coupled model,

    A. Cherchi, P. G. Fogli, T. Lovato, D. Peano, D. Iovino, S. Gualdi, S. Masina, E. Scoccimarro, S. Materia, A. Bellucci, and A. Navarra, “Global mean climate and main patterns of variability in the CMCC-CM2 coupled model,”Journal of Advances in Modeling Earth Systems, vol. 11, no. 1, pp. 185–209, 2019

  75. [75]

    Functional peaks-over-threshold analysis,

    R. de Fondeville and A. C. Davison, “Functional peaks-over-threshold analysis,”Journal of the Royal Statistical Society Series B: Statistical Methodology, vol. 84, no. 4, pp. 1392–1422, 2020

  76. [76]

    Spatial extremes: Max-stable processes at work,

    R. Mathieu, “Spatial extremes: Max-stable processes at work,”Journal of the French society of statistics, vol. 154, no. 2, 2013

  77. [77]

    Spectral density regression for bivariate extremes,

    D. Camilo and M. de Carvalho, “Spectral density regression for bivariate extremes,”Stochastic Environmental Research and Risk Assessment, vol. 31, 2017

  78. [78]

    Limit theory for multivariate sample extremes,

    L. de Haan and S. I. Resnick, “Limit theory for multivariate sample extremes,”Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 40, no. 4, pp. 317–337, 1977. 52