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arxiv: 2604.21647 · v1 · submitted 2026-04-23 · 📊 stat.AP · stat.ME

Recognition: unknown

Exploring climate change effects on concurrent floods and concurrent droughts via statistical deep learning

A. Sasse, B. Poschlod, C. J. R. Murphy-Barltrop, J. Richards, J. Zscheischler

Pith reviewed 2026-05-08 13:24 UTC · model grok-4.3

classification 📊 stat.AP stat.ME
keywords compound extremesclimate changefloodsdroughtsdeep learningmultivariate dependenceDanube basinhydrology
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The pith

Concurrent floods and droughts become more likely in the Upper Danube by 2100 under high emissions.

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

The paper applies a statistical deep learning model to joint discharge records from four catchments in the Upper Danube basin. Large climate-model ensembles drive a hydrological simulation that supplies training data for both present and future periods. The model detects rising probabilities of simultaneous extreme high flows and simultaneous extreme low flows by the late 21st century. Most of the increase traces to strengthened dependence among the extremes rather than to changes in the separate catchments alone. This joint behavior is difficult to recover with conventional methods that treat dependence as fixed.

Core claim

The deep SPAR model reproduces the multivariate tail behavior of simulated discharge across the four catchments. When applied to high-emission scenario output, it shows that joint probabilities of concurrent floods and concurrent droughts rise toward 2100, with shifts in the dependence structure supplying a substantial fraction of the change.

What carries the argument

The deep SPAR framework, a statistical deep learning model that learns multivariate tail dependence directly from large samples of discharge data.

If this is right

  • Both compound flooding and simultaneous drought-like conditions grow more probable by 2100.
  • Dependence changes, not only marginal shifts, drive most of the detected increase.
  • Standard univariate or independence-based risk assessments would miss or understate the compound changes.
  • The approach enables flexible inference on compound extremes for other hydrological applications.

Where Pith is reading between the lines

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

  • The same modeling strategy could be transferred to other river basins to map global patterns of dependence-driven compound risk.
  • Water managers may need to revise planning assumptions that treat extremes in nearby catchments as independent.
  • Direct comparison with emerging real-world concurrent events in the coming decades would provide an out-of-sample test.
  • Linking the joint probabilities to impact models could translate the changes into concrete costs for infrastructure and ecosystems.

Load-bearing premise

The deep SPAR model correctly recovers the true dependence structure among extreme discharges in the climate-driven simulations.

What would settle it

Independent future discharge observations or a separate large ensemble of hydrological runs that show no increase in joint tail probabilities, or no change in cross-catchment dependence, would falsify the projected rise.

Figures

Figures reproduced from arXiv: 2604.21647 by A. Sasse, B. Poschlod, C. J. R. Murphy-Barltrop, J. Richards, J. Zscheischler.

Figure 1
Figure 1. Figure 1: Topography of the four neighbouring catchments under study. Elevation is view at source ↗
Figure 2
Figure 2. Figure 2: Visual illustration of the pre-processing and SPAR modelling procedures for view at source ↗
Figure 3
Figure 3. Figure 3: Flowchart illustrating our implementation of the deep SPAR modelling frame view at source ↗
Figure 4
Figure 4. Figure 4: GPD QQ plot for the 2010–2039 time window. Shading represents 95% confi view at source ↗
Figure 5
Figure 5. Figure 5: Model performance in the joint tail region view at source ↗
Figure 6
Figure 6. Figure 6: Return level plots in the lower (left) and upper (right) tails of each marginal view at source ↗
Figure 7
Figure 7. Figure 7: Model performance in the joint tail region view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of return level estimates and uncertainty intervals (shaded; point view at source ↗
Figure 9
Figure 9. Figure 9: Estimated tail probability return periods over each time period with 95% view at source ↗
read the original abstract

Concurrent floods and concurrent droughts in nearby catchments pose challenges to risk assessment and water management. Climate change is affecting extremely high and low discharge, but the complex interplay between changes in individual catchments and in the dependence across catchments make it difficult to provide accurate assessments of the occurrence probabilities of concurrent extremes. In this work, we use a contemporary statistical deep learning model (the deep SPAR framework) to capture concurrent river floods and droughts in four catchments in the Upper Danube basin, based on discharge simulated by a hydrological model driven with large ensemble climate model output. The statistical model is able to accurately capture the multivariate extremes of the simulated discharge, which we assess by making use of the large available sample size. We subsequently use our statistical model to study changes in joint tail behaviour of discharge over time, finding that both compound flooding and drought-like conditions are becoming increasingly likely towards the end of the 21st century under a high-emission scenario. In particular, our results highlight that changes in the dependence structure of extremes strongly contribute to the detected changes, an aspect that would be difficult to capture with traditional approaches. This work paves the way for highly flexible, general inference on compound extremes in hydrological applications, and demonstrates key advantages of using statistical deep learning in this setting.

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 applies the deep SPAR deep learning model to simulated discharge time series from four catchments in the Upper Danube basin, generated via a hydrological model forced by large climate ensembles. It claims the model accurately captures multivariate extremes due to the large sample size, and projects that concurrent floods and concurrent droughts become increasingly likely by the end of the 21st century under a high-emission scenario, with changes in the dependence structure of extremes contributing strongly to these increases—an aspect difficult to capture with traditional methods.

Significance. If the validation holds and the simulations faithfully reproduce real tail dependencies, the work would be significant for introducing a flexible deep learning approach to compound hydrological extremes and for highlighting the role of non-stationary dependence, which traditional copula or parametric methods often cannot easily accommodate. The use of large ensembles to sample rare events is a clear strength. However, the significance is currently limited by the absence of quantitative validation and explicit attribution details.

major comments (2)
  1. [Abstract and Methods] Abstract and Methods section: The assertion that the deep SPAR model 'accurately capture[s] the multivariate extremes of the simulated discharge' relies solely on the availability of a large sample size, but no quantitative validation metrics (such as estimated tail dependence coefficients, exceedance probabilities, or cross-validated scores) or comparisons to empirical estimates or traditional methods are supplied. This is load-bearing for the subsequent claim that dependence changes drive the projected increases.
  2. [Results and Discussion] Results and Discussion sections: The attribution that 'changes in the dependence structure of extremes strongly contribute' to increased concurrent probabilities is not supported by a decomposition, sensitivity test, or isolation procedure separating marginal shifts from dependence shifts. Without this, it is impossible to rule out that the detected changes partly reflect biases in the climate-hydrological simulation chain rather than independent physical signals.
minor comments (2)
  1. [Abstract] The abstract is dense; splitting the description of the model application and the projection findings would improve readability.
  2. [Methods] Notation for the deep SPAR framework parameters should be introduced with a brief reference to the original method paper or an equation in the main text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback on our manuscript. We address the major comments point by point below and will revise the paper accordingly to incorporate the suggested improvements.

read point-by-point responses

  1. Referee: [Abstract and Methods] Abstract and Methods section: The assertion that the deep SPAR model 'accurately capture[s] the multivariate extremes of the simulated discharge' relies solely on the availability of a large sample size, but no quantitative validation metrics (such as estimated tail dependence coefficients, exceedance probabilities, or cross-validated scores) or comparisons to empirical estimates or traditional methods are supplied. This is load-bearing for the subsequent claim that dependence changes drive the projected increases.

    Authors: We agree that explicit quantitative validation would strengthen the paper. The large sample size from the climate model ensembles does allow for robust empirical benchmarks, but we did not present direct comparisons in the submitted version. In the revised manuscript, we will include quantitative metrics, such as estimated tail dependence coefficients and joint exceedance probabilities from the deep SPAR model versus empirical estimates from the data, along with comparisons to traditional copula-based methods. These will be added to the Methods section to support the claim. revision: yes

  2. Referee: [Results and Discussion] Results and Discussion sections: The attribution that 'changes in the dependence structure of extremes strongly contribute' to increased concurrent probabilities is not supported by a decomposition, sensitivity test, or isolation procedure separating marginal shifts from dependence shifts. Without this, it is impossible to rule out that the detected changes partly reflect biases in the climate-hydrological simulation chain rather than independent physical signals.

    Authors: We acknowledge the need for a clearer separation of effects. Our deep SPAR model learns the joint distribution, so changes in concurrent probabilities reflect both marginal and dependence shifts. To address this, we will add a sensitivity analysis in the revised Results section: we will compare projections using the full model against a version where dependence parameters are held constant at present-day values (while allowing marginals to change). This will isolate the contribution of dependence changes. Regarding potential biases in the simulation chain, we note that the hydrological model and climate ensembles are standard tools in the field, but the added analysis will help attribute the signals within this framework. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper fits the deep SPAR model to large-ensemble simulated discharge series generated by a hydrological model forced by climate ensembles, validates capture of multivariate extremes on historical periods using the large sample size, and then applies the fitted model to examine joint-tail changes across future periods. The central finding—that dependence-structure changes contribute to rising concurrent flood and drought probabilities—is obtained by analyzing properties of the future simulations as processed by the statistical model, not by any equation or step that reduces the result to the fitting inputs by construction. No self-definitional relations, fitted parameters renamed as predictions, load-bearing self-citations, imported uniqueness theorems, or smuggled ansatzes appear in the provided text. The derivation remains self-contained within the analysis of the external simulation ensemble.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the fidelity of climate-driven hydrological simulations and the capacity of the deep learning model to learn and extrapolate dependence without bias; no new physical entities are postulated.

free parameters (1)
  • deep SPAR model parameters
    The neural network architecture contains numerous trainable parameters optimized to fit the joint distribution of discharge extremes from the simulated data.
axioms (1)
  • domain assumption Simulated discharge from the hydrological model driven by large-ensemble climate output accurately represents the statistical properties of future river flows under high-emission conditions.
    This assumption is required to train the model on historical simulations and to project changes in tail behavior to the end of the century.

pith-pipeline@v0.9.0 · 5548 in / 1373 out tokens · 87877 ms · 2026-05-08T13:24:43.078494+00:00 · methodology

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Reference graph

Works this paper leans on

92 extracted references · 86 canonical work pages · 2 internal anchors

  1. [1]

    1975,Ann

    Balkema1974 APACrefauthors Balkema, A A. \ de Haan , L. APACrefauthors \ 1974 . Residual Life Time at Great Age Residual Life Time at Great Age . The Annals of Probability 2 5 792--804 . APACrefDOI doi:10.1214/aop/1176996548 APACrefDOI

    work page doi:10.1214/aop/1176996548 1974

  2. [2]

    APACrefauthors \ 1976

    Barnett1976 APACrefauthors Barnett, V. APACrefauthors \ 1976 . The Ordering of Multivariate Data The Ordering of Multivariate Data . Journal of the Royal Statistical Society. Series A (General) 139 3 318--344 . APACrefDOI doi:10.2307/2344839 APACrefDOI

    work page doi:10.2307/2344839 1976

  3. [3]

    , Goegebeur, Y

    Beirlant2004 APACrefauthors Beirlant, J. , Goegebeur, Y. , Teugels, J. \ Segers, J. APACrefauthors \ 2004 . Statistics of Extremes Statistics of Extremes . Wiley . APACrefDOI doi:10.1002/0470012382 APACrefDOI

    work page doi:10.1002/0470012382 2004

  4. [4]

    , Allen, S T

    Berghuijs2019 APACrefauthors Berghuijs, W R. , Allen, S T. , Harrigan, S. \ Kirchner, J W. APACrefauthors \ 2019 . Growing Spatial Scales of Synchronous River Flooding in Europe Growing Spatial Scales of Synchronous River Flooding in Europe . Geophysical Research Letters 46 3 1423--1428 . APACrefDOI doi:10.1029/2018GL081883 APACrefDOI

    work page doi:10.1029/2018gl081883 2019

  5. [5]

    , Rakovec, O

    Bevacqua2024 APACrefauthors Bevacqua, E. , Rakovec, O. , Schumacher, D L. , Kumar, R. , Thober, S. , Samaniego, L. Zscheischler, J. APACrefauthors \ 2024 . Direct and lagged climate change effects intensified the 2022 European drought Direct and lagged climate change effects intensified the 2022 European drought . Nature Geoscience 17 11 1100--1107 . APAC...

    work page doi:10.1038/s41561-024-01559-2 2024

  6. [6]

    , Shepherd, T G

    Bevacqua2021 APACrefauthors Bevacqua, E. , Shepherd, T G. , Watson, P A. , Sparrow, S. , Wallom, D. \ Mitchell, D. APACrefauthors \ 2021 . Larger spatial footprint of wintertime total precipitation extremes in a warmer climate Larger spatial footprint of wintertime total precipitation extremes in a warmer climate . Geophysical Research Letters 48 8 e2020G...

    work page doi:10.1029/2020gl091990 2021

  7. [7]

    , Felsche, E

    bohnisch2025 APACrefauthors B \"o hnisch, A. , Felsche, E. , Mittermeier, M. , Poschlod, B. \ Ludwig, R. APACrefauthors \ 2025 . Future patterns of compound dry and hot summers and their link to soil moisture droughts in Europe Future patterns of compound dry and hot summers and their link to soil moisture droughts in Europe . Earth's Future 13 2 e2024EF0...

    work page doi:10.1029/2024ef004916 2025

  8. [8]

    , Zscheischler, J

    Boulaguiem2022 APACrefauthors Boulaguiem, Y. , Zscheischler, J. , Vignotto, E. , van der Wiel, K. \ Engelke, S. APACrefauthors \ 2022 . Modeling and simulating spatial extremes by combining extreme value theory with generative adversarial networks Modeling and simulating spatial extremes by combining extreme value theory with generative adversarial networ...

    work page doi:10.1017/eds.2022.4 2022

  9. [9]

    , Swain, D L

    brunner2021 APACrefauthors Brunner, M I. , Swain, D L. , Wood, R R. , Willkofer, F. , Done, J M. , Gilleland, E. \ Ludwig, R. APACrefauthors \ 2021 . An extremeness threshold determines the regional response of floods to changes in rainfall extremes An extremeness threshold determines the regional response of floods to changes in rainfall extremes . Commu...

    work page doi:10.1038/s43247-021-00248-x 2021

  10. [10]

    \ Davison, A C

    Chavez-Demoulin2005 APACrefauthors Chavez-Demoulin , V. \ Davison, A C. APACrefauthors \ 2005 . Generalized Additive Modelling of Sample Extremes Generalized additive modelling of sample extremes . Journal of the Royal Statistical Society: Series C (Applied Statistics) 54 1 207--222 . APACrefDOI doi:10.1111/J.1467-9876.2005.00479.X APACrefDOI

    work page doi:10.1111/j.1467-9876.2005.00479.x 2005

  11. [11]

    , Richards, J

    Cisneros2023 APACrefauthors Cisneros, D. , Richards, J. , Dahal, A. , Lombardo, L. \ Huser, R. APACrefauthors \ 2024 . Deep graphical regression for jointly moderate and extreme Australian wildfires Deep graphical regression for jointly moderate and extreme Australian wildfires . Spatial Statistics 59 100811 . APACrefDOI doi:10.1016/j.spasta.2024.100811 A...

    work page doi:10.1016/j.spasta.2024.100811 2024

  12. [12]

    Coles ,\ 10.1007/978-1-4471-3675-0 title An Introduction to Statistical Modeling of Extreme Values \ ( publisher Springer ,\ year 2001 ) NoStop

    Coles2001 APACrefauthors Coles, S. APACrefauthors \ 2001 . An Introduction to Statistical Modeling of Extreme Values An Introduction to Statistical Modeling of Extreme Values . London Springer London . APACrefDOI doi:10.1007/978-1-4471-3675-0 APACrefDOI

    work page doi:10.1007/978-1-4471-3675-0 2001

  13. [13]

    , Heffernan, J

    Coles1999 APACrefauthors Coles, S. , Heffernan, J. \ Tawn, J. APACrefauthors \ 1999 . Dependence Measures for Multivariate Extremes Dependence measures for multivariate extremes . Extremes 2 4 339--365 . APACrefDOI doi:10.1023/A:1009963131610 APACrefDOI

    work page doi:10.1023/a:1009963131610 1999

  14. [14]

    \ Thibaud, E

    Cooley2019a APACrefauthors Cooley, D. \ Thibaud, E. APACrefauthors \ 2019 . Decompositions of Dependence for High-Dimensional Extremes Decompositions of dependence for high-dimensional extremes . Biometrika 106 3 587--604 . APACrefDOI doi:10.1093/biomet/asz028 APACrefDOI

    work page doi:10.1093/biomet/asz028 2019

  15. [15]

    \ Huser, R

    Davison2015 APACrefauthors Davison, A C. \ Huser, R. APACrefauthors \ 2015 . Statistics of Extremes Statistics of extremes . Annual Review of Statistics and Its Application 2 1 203--235 . APACrefDOI doi:10.1146/annurev-statistics-010814-020133 APACrefDOI

    work page doi:10.1146/annurev-statistics-010814-020133 2015

  16. [16]

    \ Smith, R L

    Davison1990 APACrefauthors Davison, A C. \ Smith, R L. APACrefauthors \ 1990 . Models for Exceedances Over High Thresholds Models for Exceedances Over High Thresholds . Journal of the Royal Statistical Society. Series B: Statistical Methodology 52 3 393--425 . APACrefDOI doi:10.1111/j.2517-6161.1990.tb01796.x APACrefDOI

    work page doi:10.1111/j.2517-6161.1990.tb01796.x 1990

  17. [17]

    , Huser, R

    demonte2025generative APACrefauthors De Monte, L. , Huser, R. , Papastathopoulos, I. \ Richards, J. APACrefauthors \ 2025 . Generative modelling of multivariate geometric extremes using normalising flows Generative modelling of multivariate geometric extremes using normalising flows . arXiv 2505.02957

    work page arXiv 2025

  18. [18]

    , Tawn, J A

    Darcy2023a APACrefauthors D’Arcy, E. , Tawn, J A. , Joly, A. \ Sifnioti, D E. APACrefauthors \ 2023 . Accounting for seasonality in extreme sea-level estimation Accounting for seasonality in extreme sea-level estimation . The Annals of Applied Statistics 17 4 3500--3525 . APACrefDOI doi:10.1214/23-AOAS1773 APACrefDOI

    work page doi:10.1214/23-aoas1773 2023

  19. [19]

    Chapman and Hall/CRC, New York (1994)

    Efron1994 APACrefauthors Efron, B. \ Tibshirani, R. APACrefauthors \ 1994 . An Introduction to the Bootstrap - 1st Edition An Introduction to the Bootstrap - 1st Edition . Chapman and Hall/CRC . APACrefDOI doi:10.1201/9780429246593 APACrefDOI

    work page doi:10.1201/9780429246593 1994

  20. [20]

    APACrefauthors \ 2023

    copernicus_glo30 APACrefauthors European Space Agency (ESA) . APACrefauthors \ 2023 . Copernicus Digital Elevation Model GLO-30 . Copernicus digital elevation model GLO-30 . ESA Copernicus Data Space Ecosystem . Available at: https://dataspace.copernicus.eu/explore-data/data-collections/copernicus-contributing-missions/collections-description/COP-DEM APAC...

    work page doi:10.5270/esa-c5d3d65 2023

  21. [21]

    , Bevacqua, E

    Fang2024 APACrefauthors Fang, B. , Bevacqua, E. , Rakovec, O. \ Zscheischler, J. APACrefauthors \ 2024 . An increase in the spatial extent of European floods over the last 70 years An increase in the spatial extent of European floods over the last 70 years . Hydrology and Earth System Sciences 28 16 3755--3775 . APACrefDOI doi:10.5194/hess-28-3755-2024 APACrefDOI

    work page doi:10.5194/hess-28-3755-2024 2024

  22. [22]

    , Rakovec, O

    Fang2025 APACrefauthors Fang, B. , Rakovec, O. , Bevacqua, E. , Kumar, R. \ Zscheischler, J. APACrefauthors \ 2025 . Diverging trends in large floods across Europe in a warming climate Diverging trends in large floods across Europe in a warming climate . Communications Earth & Environment 6 1 717 . APACrefDOI doi:10.1038/s43247-025-02734-y APACrefDOI

    work page doi:10.1038/s43247-025-02734-y 2025

  23. [23]

    Econometrica , author =

    Farrell2021 APACrefauthors Farrell, M H. , Liang, T. \ Misra, S. APACrefauthors \ 2021 . Deep Neural Networks for Estimation and Inference Deep Neural Networks for Estimation and Inference . Econometrica 89 1 181--213 . APACrefDOI doi:10.3982/ECTA16901 APACrefDOI

    work page doi:10.3982/ecta16901 2021

  24. [24]

    , B \"o hnisch, A

    felsche2024 APACrefauthors Felsche, E. , B \"o hnisch, A. , Poschlod, B. \ Ludwig, R. APACrefauthors \ 2024 . European hot and dry summers are projected to become more frequent and expand northwards European hot and dry summers are projected to become more frequent and expand northwards . Communications Earth & Environment 5 1 410 . APACrefDOI doi:10.1038...

    work page doi:10.1038/s43247-024-01575-5 2024

  25. [25]

    , Derksen, C

    fyfe2017 APACrefauthors Fyfe, J C. , Derksen, C. , Mudryk, L. , Flato, G M. , Santer, B D. , Swart, N C. Jiao, Y. APACrefauthors \ 2017 . Large near-term projected snowpack loss over the western United States Large near-term projected snowpack loss over the western United States . Nature Communications 8 1 14996 . APACrefDOI doi:10.1038/ncomms14996 APACrefDOI

    work page doi:10.1038/ncomms14996 2017

  26. [26]

    , Bengio, Y

    Goodfellow2016 APACrefauthors Goodfellow, I. , Bengio, Y. \ Courville, A. APACrefauthors \ 2016 . Deep Learning Deep learning . Cambridge, Massachusetts The MIT Press

    2016

  27. [27]

    , Wyncoll, D

    Gouldby2017 APACrefauthors Gouldby, B. , Wyncoll, D. , Panzeri, M. , Franklin, M. , Hunt, T. , Hames, D. Pullen, T. APACrefauthors \ 2017 . Multivariate Extreme Value Modelling of Sea Conditions around the Coast of England Multivariate extreme value modelling of sea conditions around the coast of England . Proceedings of the Institution of Civil Engineers...

    work page doi:10.1680/jmaen.2016.16 2017

  28. [28]

    \ Tawn, J A

    Heffernan2004 APACrefauthors Heffernan, J E. \ Tawn, J A. APACrefauthors \ 2004 . A Conditional Approach for Multivariate Extreme Values A conditional approach for multivariate extreme values . Journal of the Royal Statistical Society. Series B: Statistical Methodology 66 3 497--546 . APACrefDOI doi:10.1111/j.1467-9868.2004.02050.x APACrefDOI

    work page doi:10.1111/j.1467-9868.2004.02050.x 2004

  29. [29]

    Multilayer feedforward networks are universal approximators , journal =

    Hornik1989 APACrefauthors Hornik, K. , Stinchcombe, M. \ White, H. APACrefauthors \ 1989 . Multilayer Feedforward Networks Are Universal Approximators Multilayer feedforward networks are universal approximators . Neural Networks 2 5 359--366 . APACrefDOI doi:10.1016/0893-6080(89)90020-8 APACrefDOI

    work page doi:10.1016/0893-6080(89)90020-8 1989

  30. [30]

    , Opitz, T

    Huser2025 APACrefauthors Huser, R. , Opitz, T. \ Wadsworth, J L. APACrefauthors \ 2025 . Modeling of Spatial Extremes in Environmental Data Science: Time to Move Away from Max-Stable Processes Modeling of spatial extremes in environmental data science: Time to move away from max-stable processes . Environmental Data Science 4 e3 . APACrefDOI doi:10.1017/e...

    work page doi:10.1017/eds.2024.54 2025

  31. [31]

    \ Wadsworth, J L

    Huser2019 APACrefauthors Huser, R. \ Wadsworth, J L. APACrefauthors \ 2019 . Modeling Spatial Processes with Unknown Extremal Dependence Class Modeling Spatial Processes with Unknown Extremal Dependence Class . Journal of the American Statistical Association 114 525 434--444 . APACrefDOI doi:10.1080/01621459.2017.1411813 APACrefDOI

    work page doi:10.1080/01621459.2017.1411813 2019

  32. [32]

    \ Nagavciuc, V

    Ionita2021 APACrefauthors Ionita, M. \ Nagavciuc, V. APACrefauthors \ 2021 . Changes in drought features at the European level over the last 120 years Changes in drought features at the European level over the last 120 years . Natural Hazards and Earth System Sciences 21 5 1685--1701 . APACrefDOI doi:10.5194/nhess-21-1685-2021 APACrefDOI

    work page doi:10.5194/nhess-21-1685-2021 2021

  33. [33]

    , Cadavid, L

    Jane2020 APACrefauthors Jane, R. , Cadavid, L. , Obeysekera, J. \ Wahl, T. APACrefauthors \ 2020 . Multivariate Statistical Modelling of the Drivers of Compound Flood Events in South Florida Multivariate statistical modelling of the drivers of compound flood events in south Florida . Natural Hazards and Earth System Sciences 20 10 2681--2699 . APACrefDOI ...

    work page doi:10.5194/nhess-20-2681-2020 2020

  34. [34]

    APACrefauthors \ 1997

    Joe1997 APACrefauthors Joe, H. APACrefauthors \ 1997 . Multivariate Models and Multivariate Dependence Concepts Multivariate Models and Multivariate Dependence Concepts . Chapman and Hall/CRC . APACrefDOI doi:10.1201/9780367803896 APACrefDOI

    work page doi:10.1201/9780367803896 1997

  35. [35]

    , Hochrainer-Stigler, S

    Jongman2014 APACrefauthors Jongman, B. , Hochrainer-Stigler, S. , Feyen, L. , Aerts, J C. , Mechler, R. , Botzen, W W. Ward, P J. APACrefauthors \ 2014 . Increasing stress on disaster-risk finance due to large floods Increasing stress on disaster-risk finance due to large floods . Nature Climate Change 4 4 264--268 . APACrefDOI doi:10.1038/nclimate2124 APACrefDOI

    work page doi:10.1038/nclimate2124 2014

  36. [36]

    , Simpson, E S

    Kakampakou2024 APACrefauthors Kakampakou, L. , Simpson, E S. \ Wadsworth, J L. APACrefauthors \ 2024 . Spatial Extremal Modelling: A Case Study on the Interplay between Margins and Dependence Spatial extremal modelling: A case study on the interplay between margins and dependence . Stat 13 4 . APACrefDOI doi:10.1002/sta4.70021 APACrefDOI

    work page doi:10.1002/sta4.70021 2024

  37. [37]

    \ Wadsworth, J L

    Kakampakou2025 APACrefauthors Kakampakou, L. \ Wadsworth, J L. APACrefauthors \ 2025 . Geometric Modelling of Spatial Extremes Geometric modelling of spatial extremes . arXiv 2511.08192

    work page arXiv 2025

  38. [38]

    , Tawn, J A

    Keef2013a APACrefauthors Keef, C. , Tawn, J A. \ Lamb, R. APACrefauthors \ 2013 . Estimating the Probability of Widespread Flood Events Estimating the probability of widespread flood events . Environmetrics 24 1 13--21 . APACrefDOI doi:10.1002/env.2190 APACrefDOI

    work page doi:10.1002/env.2190 2013

  39. [39]

    , Merz, B

    Kemter2020 APACrefauthors Kemter, M. , Merz, B. , Marwan, N. , Vorogushyn, S. \ Bl \"o schl, G. APACrefauthors \ 2020 . Joint trends in flood magnitudes and spatial extents across Europe Joint trends in flood magnitudes and spatial extents across Europe . Geophysical Research Letters 47 7 e2020GL087464 . APACrefDOI doi:10.1029/2020GL087464 APACrefDOI

    work page doi:10.1029/2020gl087464 2020

  40. [40]

    Kingma2017 APACrefauthors Kingma, D P. \ Ba, J. APACrefauthors \ 2017 . Adam: A Method for Stochastic Optimization Adam: A Method for Stochastic Optimization . arXiv 1412.6980

    work page internal anchor Pith review arXiv 2017

  41. [41]

    APACrefauthors \ 2017

    Koenker2017 APACrefauthors Koenker, R. APACrefauthors \ 2017 . Quantile Regression: 40 Years On Quantile regression: 40 years on . Annual Review of Economics 9 155--176 . APACrefDOI doi:10.1146/annurev-economics-063016-103651 APACrefDOI

    work page doi:10.1146/annurev-economics-063016-103651 2017

  42. [42]

    , Mailhot, A

    leduc2019 APACrefauthors Leduc, M. , Mailhot, A. , Frigon, A. , Martel, J L. , Ludwig, R. , Brietzke, G B. Scinocca, J. APACrefauthors \ 2019 . The ClimEx Project: A 50-Member Ensemble of Climate Change Projections at 12-km Resolution over Europe and Northeastern North America with the Canadian Regional Climate Model (CRCM5) The climex project: A 50-membe...

    work page doi:10.1175/jamc-d-18-0021.1 2019

  43. [43]

    , Rootz \'e n, H

    Lhaut2025 APACrefauthors Lhaut, S. , Rootz \'e n, H. \ Segers, J. APACrefauthors \ 2026 . Simulation of multivariate extremes: A Wasserstein--Aitchison GAN approach Simulation of multivariate extremes: A wasserstein--aitchison gan approach . Extremes 1--38

    2026

  44. [44]

    \ Jonathan, P

    Mackay2023 APACrefauthors Mackay, E. \ Jonathan, P. APACrefauthors \ 2023 . Modelling Multivariate Extremes through Angular-Radial Decomposition of the Density Function Modelling multivariate extremes through angular-radial decomposition of the density function . arXiv 2310.12711

    work page arXiv 2023

  45. [45]

    , Murphy-Barltrop, C J R

    Mackay2025 APACrefauthors Mackay, E. , Murphy-Barltrop, C J R. \ Jonathan, P. APACrefauthors \ 2025 . The SPAR Model: A New Paradigm for Multivariate Extremes: Application to Joint Distributions of Metocean Variables The SPAR model: A new paradigm for multivariate extremes: Application to joint distributions of metocean variables . Journal of Offshore Mec...

    work page doi:10.1115/1.4065968 2025

  46. [46]

    , Murphy-Barltrop, C J R

    Mackay2025b APACrefauthors Mackay, E. , Murphy-Barltrop, C J R. , Richards, J. \ Jonathan, P. APACrefauthors \ 2025 . Deep Learning Joint Extremes of Metocean Variables Using the SPAR Model Deep learning joint extremes of metocean variables using the SPAR model . Journal of Offshore Mechanics and Arctic Engineering 148 021201 . APACrefDOI doi:10.1115/1.40...

    work page doi:10.1115/1.4069999 2025

  47. [47]

    , Richards, J

    Mackay2026diags APACrefauthors Mackay, E. , Richards, J. \ Jonathan, P. APACrefauthors \ 2026 . Diagnostic Tools for Extreme Value Regression Models Diagnostic tools for extreme value regression models . arXiv

    2026

  48. [48]

    \ Richards, J

    Majumder2025 APACrefauthors Majumder, R. \ Richards, J. APACrefauthors \ 2025 04 . Semi-Parametric Bulk and Tail Regression Using Spline-Based Neural Networks Semi-parametric bulk and tail regression using spline-based neural networks . arXiv 2504.19994

    work page arXiv 2025

  49. [49]

    , Christensen, J H

    matte2022spatial APACrefauthors Matte, D. , Christensen, J H. \ Ozturk, T. APACrefauthors \ 2022 . Spatial extent of precipitation events: when big is getting bigger Spatial extent of precipitation events: when big is getting bigger . Climate Dynamics 58 5 1861--1875 . APACrefDOI doi:10.1007/s00382-021-05998-0 APACrefDOI

    work page doi:10.1007/s00382-021-05998-0 2022

  50. [50]

    Bernoulli , author =

    Minsker2015 APACrefauthors Minsker, S. APACrefauthors \ 2015 . Geometric Median and Robust Estimation in Banach Spaces Geometric median and robust estimation in Banach spaces . Bernoulli 21 4 2308--2335 . APACrefDOI doi:10.3150/14-BEJ645 APACrefDOI

    work page doi:10.3150/14-bej645 2015

  51. [51]

    and Chen, Kun , number =

    Murphy2024 APACrefauthors Murphy, C. , Tawn, J A. \ Varty, Z. APACrefauthors \ 2024 . Automated Threshold Selection and Associated Inference Uncertainty for Univariate Extremes Automated threshold selection and associated inference uncertainty for univariate extremes . Technometrics 67 2 1--10 . APACrefDOI doi:10.1080/00401706.2024.2421744 APACrefDOI

    work page doi:10.1080/00401706.2024.2421744 2024

  52. [52]

    , Mackay, E

    Murphy-Barltrop2024 APACrefauthors Murphy-Barltrop, C J R. , Mackay, E. \ Jonathan, P. APACrefauthors \ 2024 . Inference for Bivariate Extremes via a Semi-Parametric Angular-Radial Model Inference for bivariate extremes via a semi-parametric angular-radial model . Extremes 28 209–238 . APACrefDOI doi:10.1007/s10687-024-00492-2 APACrefDOI

    work page doi:10.1007/s10687-024-00492-2 2024

  53. [53]

    , Majumder, R

    Murphy-Barltrop2024c APACrefauthors Murphy-Barltrop, C J R. , Majumder, R. \ Richards, J. APACrefauthors \ 2024 . Deep Learning of Multivariate Extremes via a Geometric Representation Deep learning of multivariate extremes via a geometric representation . arXiv 2406.19936

    work page arXiv 2024

  54. [54]

    , Wadsworth, J L

    Murphy-Barltrop2023 APACrefauthors Murphy-Barltrop, C J R. , Wadsworth, J L. \ Eastoe, E F. APACrefauthors \ 2023 . New Estimation Methods for Extremal Bivariate Return Curves New estimation methods for extremal bivariate return curves . Environmetrics e2797 1--22 . APACrefDOI doi:10.1002/env.2797 APACrefDOI

    work page doi:10.1002/env.2797 2023

  55. [55]

    \ Wadsworth, J L

    Nolde2022 APACrefauthors Nolde, N. \ Wadsworth, J L. APACrefauthors \ 2022 . Linking Representations for Multivariate Extremes via a Limit Set Linking representations for multivariate extremes via a limit set . Advances in Applied Probability 54 3 688--717 . APACrefDOI doi:10.1017/APR.2021.51 APACrefDOI

    work page doi:10.1017/apr.2021.51 2022

  56. [56]

    APACrefauthors \ 2016

    Opitz2016 APACrefauthors Opitz, T. APACrefauthors \ 2016 . Modeling Asymptotically Independent Spatial Extremes Based on Laplace Random Fields Modeling asymptotically independent spatial extremes based on Laplace random fields . Spatial Statistics 16 1--18 . APACrefDOI doi:10.1016/j.spasta.2016.01.001 APACrefDOI

    work page doi:10.1016/j.spasta.2016.01.001 2016

  57. [57]

    , de Monte , L

    Papastathopoulos2025 APACrefauthors Papastathopoulos, I. , de Monte , L. , Campbell, R. \ Rue, H. APACrefauthors \ 2025 10 . Statistical Inference for Radially-Stable Generalized Pareto Distributions and Return Level-Sets in Geometric Extremes Statistical inference for radially-stable generalized Pareto distributions and return level-sets in geometric ext...

    work page arXiv 2025

  58. [58]

    \ Wadsworth, J

    Papastathopoulos2026 APACrefauthors Papastathopoulos, I. \ Wadsworth, J. APACrefauthors \ 2026 . Geometric Extremal Graphical Models and Coefficients of Extremal Dependence on Block Graphs Geometric extremal graphical models and coefficients of extremal dependence on block graphs . arXiv 2601.00239

    work page arXiv 2026

  59. [59]

    \ Engelke, S

    Pasche2024 APACrefauthors Pasche, O C. \ Engelke, S. APACrefauthors \ 2024 . Neural Networks for Extreme Quantile Regression with an Application to Forecasting of Flood Risk Neural networks for extreme quantile regression with an application to forecasting of flood risk . The Annals of Applied Statistics 18 4 1--27 . APACrefDOI doi:10.1214/24-AOAS1907 APACrefDOI

    work page doi:10.1214/24-aoas1907 2024

  60. [60]

    The Annals of Statistics , author =

    Pickands1975 APACrefauthors Pickands, J. APACrefauthors \ 1975 . Statistical Inference Using Extreme Order Statistics Statistical Inference Using Extreme Order Statistics . The Annals of Statistics 3 1 119--131 . APACrefDOI doi:10.1214/aos/1176343003 APACrefDOI

    work page doi:10.1214/aos/1176343003 1975

  61. [61]

    \ Ludwig, R

    poschlod2021internal APACrefauthors Poschlod, B. \ Ludwig, R. APACrefauthors \ 2021 . Internal variability and temperature scaling of future sub-daily rainfall return levels over Europe Internal variability and temperature scaling of future sub-daily rainfall return levels over europe . Environmental Research Letters 16 6 064097 . APACrefDOI doi:10.1088/1...

    work page doi:10.1088/1748-9326/ac0849 2021

  62. [62]

    , Sailer, L

    poschlod2026 APACrefauthors Poschlod, B. , Sailer, L. , Sasse, A. , Vogelbacher, A. \ Ludwig, R. APACrefauthors \ 2026 . Climate change effects on river droughts in Bavaria using a hydrological large ensemble Climate change effects on river droughts in Bavaria using a hydrological large ensemble . Hydrology and Earth System Sciences 30 4 1165--1188 . APAC...

    work page doi:10.5194/hess-30-1165-2026 2026

  63. [63]

    , Willkofer, F

    poschlod2020 APACrefauthors Poschlod, B. , Willkofer, F. \ Ludwig, R. APACrefauthors \ 2020 . Impact of climate change on the hydrological regimes in Bavaria Impact of climate change on the hydrological regimes in Bavaria . Water 12 6 1599 . APACrefDOI doi:10.3390/w12061599 APACrefDOI

    work page doi:10.3390/w12061599 2020

  64. [64]

    , Bates, P D

    Quinn2019 APACrefauthors Quinn, N. , Bates, P D. , Neal, J. , Smith, A. , Wing, O. , Sampson, C. Heffernan, J. APACrefauthors \ 2019 . The Spatial Dependence of Flood Hazard and Risk in the United States The Spatial Dependence of Flood Hazard and Risk in the United States . Water Resources Research 55 3 1890--1911 . APACrefDOI doi:10.1029/2018WR024205 APACrefDOI

    work page doi:10.1029/2018wr024205 2019

  65. [65]

    , Turnbull, K

    Randell2016 APACrefauthors Randell, D. , Turnbull, K. , Ewans, K. \ Jonathan, P. APACrefauthors \ 2016 . Bayesian Inference for Nonstationary Marginal Extremes Bayesian inference for nonstationary marginal extremes . Environmetrics 27 7 439--450 . APACrefDOI doi:10.1002/env.2403 APACrefDOI

    work page doi:10.1002/env.2403 2016

  66. [66]

    APACrefauthors \ 2002

    Resnick2002 APACrefauthors Resnick, S. APACrefauthors \ 2002 . Hidden Regular Variation , Second Order Regular Variation and Asymptotic Independence Hidden Regular Variation , Second Order Regular Variation and Asymptotic Independence . Extremes 5 4 303--336 . APACrefDOI doi:10.1023/A:1025148622954 APACrefDOI

    work page doi:10.1023/a:1025148622954 2002

  67. [67]

    \ Huser, R

    Richards2024 APACrefauthors Richards, J. \ Huser, R. APACrefauthors \ 2026 1 . Extreme Quantile Regression with Deep Learning Extreme Quantile Regression with Deep Learning . M. de Carvalho, R. Huser, P. Naveau \ B J. Reich\ ( ), Handbook of Statistics of Extremes . Handbook of Statistics of Extremes . Chapman & Hall / CRC

    2026

  68. [68]

    \ Huser, R

    Richards2022a APACrefauthors Richards, J. \ Huser, R. APACrefauthors \ 2026 2 . Regression modelling of spatiotemporal extreme US wildfires via partially-interpretable neural networks Regression modelling of spatiotemporal extreme US wildfires via partially-interpretable neural networks . Journal of Computational and Graphical Statistics . To appear

    2026

  69. [69]

    , Huser, R

    Richards2023a APACrefauthors Richards, J. , Huser, R. , Bevacqua, E. \ Zscheischler, J. APACrefauthors \ 2023 . Insights into the Drivers and Spatiotemporal Trends of Extreme Mediterranean Wildfires with Statistical Deep Learning Insights into the Drivers and Spatiotemporal Trends of Extreme Mediterranean Wildfires with Statistical Deep Learning . Artific...

    work page doi:10.1175/aies-d-22-0095.1 2023

  70. [70]

    \ Tawn, J A

    richards2022tail APACrefauthors Richards, J. \ Tawn, J A. APACrefauthors \ 2022 . On the tail behaviour of aggregated random variables On the tail behaviour of aggregated random variables . Journal of Multivariate Analysis 192 105065 . APACrefDOI doi:10.1016/j.jmva.2022.105065 APACrefDOI

    work page doi:10.1016/j.jmva.2022.105065 2022

  71. [71]

    , Feyen, L

    Rojas2011 APACrefauthors Rojas, R. , Feyen, L. , Dosio, A. \ Bavera, D. APACrefauthors \ 2011 . Improving Pan- European Hydrological Simulation of Extreme Events through Statistical Bias Correction of RCM-driven Climate Simulations Improving pan- European hydrological simulation of extreme events through statistical bias correction of RCM-driven climate s...

    work page doi:10.5194/hess-15-2599-2011 2011

  72. [72]

    \ Katz, R W

    Rootzen2013 APACrefauthors Rootz \'e n, H. \ Katz, R W. APACrefauthors \ 2013 . Design Life Level : Quantifying Risk in a Changing Climate Design Life Level : Quantifying risk in a changing climate . Water Resources Research 49 9 5964--5972 . APACrefDOI doi:10.1002/wrcr.20425 APACrefDOI

    work page doi:10.1002/wrcr.20425 2013

  73. [73]

    arXiv preprint arXiv:1903.00954 , year =

    Rothfuss2019 APACrefauthors Rothfuss, J. , Ferreira, F. , Walther, S. \ Ulrich, M. APACrefauthors \ 2019 03 . Conditional Density Estimation with Neural Networks: Best Practices and Benchmarks Conditional density estimation with neural networks: Best practices and benchmarks . arXiv 1903.00954

    work page arXiv 2019

  74. [74]

    An Overview of Multi-Task Learning in Deep Neural Networks

    Ruder2017 APACrefauthors Ruder, S. APACrefauthors \ 2017 . An Overview of Multi-Task Learning in Deep Neural Networks An Overview of Multi-Task Learning in Deep Neural Networks . arXiv 1706.05098

    work page internal anchor Pith review arXiv 2017

  75. [75]

    Nonparametric regression using deep neural networks with ReLU activation function , volume=

    Schmidt-Hieber2020 APACrefauthors Schmidt-Hieber , J. APACrefauthors \ 2020 08 . Nonparametric Regression Using Deep Neural Networks with ReLU Activation Function Nonparametric regression using deep neural networks with ReLU activation function . The Annals of Statistics 48 4 1875--1897 . APACrefDOI doi:10.1214/19-AOS1875 APACrefDOI

    work page doi:10.1214/19-aos1875 2020

  76. [76]

    APACrefauthors \ 2021

    schulla_wasim_2021 APACrefauthors Schulla, J. APACrefauthors \ 2021 . WaSiM (Water balance Simulation Model) M odel D escription Wasim (water balance simulation model) M odel D escription \ [ ]. Z \"u rich, Switzerland . Version of 2021. Available at: http://www.wasim.ch/downloads/doku/wasim/

    2021

  77. [77]

    \ Tawn, J A

    Simpson2024 APACrefauthors Simpson, E S. \ Tawn, J A. APACrefauthors \ 2024 . Inference for New Environmental Contours Using Extreme Value Analysis Inference for new environmental contours using extreme value analysis . Journal of Agricultural, Biological and Environmental Statistics 30 3 . APACrefDOI doi:10.1007/s13253-024-00612-2 APACrefDOI

    work page doi:10.1007/s13253-024-00612-2 2024

  78. [78]

    , Wadsworth, J L

    Simpson2020 APACrefauthors Simpson, E S. , Wadsworth, J L. \ Tawn, J A. APACrefauthors \ 2020 . Determining the Dependence Structure of Multivariate Extremes Determining the dependence structure of multivariate extremes . Biometrika 107 3 513--532 . APACrefDOI doi:10.1093/biomet/asaa018 APACrefDOI

    work page doi:10.1093/biomet/asaa018 2020

  79. [79]

    APACrefauthors \ 1985

    Smith1985 APACrefauthors Smith, R L. APACrefauthors \ 1985 . Maximum Likelihood Estimation in a Class of Nonregular Cases Maximum likelihood estimation in a class of nonregular cases . Biometrika 72 1 67--90 . APACrefDOI doi:10.1093/biomet/72.1.67 APACrefDOI

    work page doi:10.1093/biomet/72.1.67 1985

  80. [80]

    , Randell, D

    Towe2023 APACrefauthors Towe, R. , Randell, D. , Kensler, J. , Feld, G. \ Jonathan, P. APACrefauthors \ 2023 . Estimation of Associated Values from Conditional Extreme Value Models Estimation of associated values from conditional extreme value models . Ocean Engineering 272 113808 . APACrefDOI doi:10.1016/j.oceaneng.2023.113808 APACrefDOI

    work page doi:10.1016/j.oceaneng.2023.113808 2023

Showing first 80 references.