pith. sign in

arxiv: 2604.10890 · v1 · submitted 2026-04-13 · ❄️ cond-mat.stat-mech · physics.geo-ph

Forecasting Return Time of Extreme Precipitation by Large Deviation Theory

Haotian Xie , Haoxian Liu , Jingfang Fan , Ying Tang This is my paper

Pith reviewed 2026-05-10 16:34 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech physics.geo-ph
keywords extreme precipitationreturn timeslarge deviation theoryLandau distributionclimate projectionsCMIP6lifetime exposureextreme events
0
0 comments X

The pith

Fitting the Landau distribution to precipitation records enables accurate extrapolation of extreme event return times and shows that these times collapse onto a single curve in future climate projections.

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

The paper introduces a large deviation framework that uses the Landau distribution to model and forecast return times of extreme precipitation events. This distribution fits data at about 93 percent of global locations better than standard extreme value distributions. By enriching rare event samples with this fit, the authors derive more reliable large deviation rate functions. Applying this to CMIP6 climate model outputs under various emission scenarios reveals that return time curves collapse to a unified relation. This implies significantly higher lifetime exposure to extreme precipitation for people born in the 21st century under most scenarios.

Core claim

The central claim is that the Landau distribution accurately captures extreme precipitation, allowing enriched sampling for precise estimation of large deviation rate functions and return times. These historical return times, when mapped to CMIP6 future projections, collapse onto a unified curve across emission scenarios, indicating sharply increased lifetime exposure for 21st-century birth cohorts.

What carries the argument

The Landau distribution, fitted to historical precipitation data to estimate the large deviation rate function and extrapolate return times beyond observed intensities.

If this is right

  • Return times can be forecasted for precipitation intensities not yet observed in history.
  • Return time curves under different future emission scenarios follow a single unified relation.
  • 21st-century birth cohorts face sharply increased lifetime exposure to extreme precipitation under most scenarios.
  • Large deviation theory provides a way to handle rare events in climate data more effectively than conventional distributions.

Where Pith is reading between the lines

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

  • If the unified collapse holds, adaptation planning could use this relation to estimate risks without running every scenario separately.
  • Testing the Landau fit on independent high-resolution observational datasets from the past decade would provide a direct check on extrapolation accuracy.
  • Similar frameworks might apply to other rare climate extremes like heatwaves or floods by identifying suitable distributions for sample enrichment.

Load-bearing premise

That the Landau distribution fitted to historical data produces unbiased large deviation rate functions that remain accurate when applied to future climate model projections.

What would settle it

If actual future precipitation data or additional model simulations show that the return time curves for different emission scenarios do not collapse onto the predicted unified relation, or if the Landau distribution fails to fit extreme events in those projections.

Figures

Figures reproduced from arXiv: 2604.10890 by Haotian Xie, Haoxian Liu, Jingfang Fan, Ying Tang.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 3
Figure 3. Figure 3: Thresholds from ≥ 5 to ≥ 80 mm are shown in the figure at 5 mm intervals, where the ≥ 50 to ≥ 80 mm part threshold is 10 mm. The spatial distributions are similar to those shown in Fig. S11. However, because of the error introduced by the block averaging length, the spatial distribution contains more missing values than in the case τ = 1, and the return times are also longer [PITH_FULL_IMAGE:figures/full_… view at source ↗
read the original abstract

Forecasting extreme precipitation is essential yet challenging due to its rarity and complexity. We develop a large deviation framework to estimate the return times of extreme precipitation events. We first find that the Landau distribution, originally introduced in plasma physics, accurately captures extreme precipitation at approximately 93% of global locations, outperforming conventional extreme value distributions with 76% matched locations under the same accuracy criterion. Enriching rare event samples by the fitted Landau distribution, we obtain more accurate estimates of large deviation rate functions and return times, enabling forecasts beyond historically observed precipitation intensities. Mapping historical return times to future projections from the Coupled Model Intercomparison Project Phase 6 (CMIP6), we show that return time curves under different emission scenarios collapse onto a unified relation, revealing a sharply increased lifetime exposure to extreme precipitation for 21st-century birth cohorts under most future emission scenarios.

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

3 major / 2 minor

Summary. The manuscript develops a large deviation theory approach to forecast return times of extreme precipitation. It reports that the Landau distribution fits extreme precipitation at 93% of locations globally, outperforming standard extreme value distributions. By enriching rare-event samples using the fitted Landau distribution, improved estimates of large-deviation rate functions are obtained, enabling extrapolation beyond observed intensities. These historical return times are mapped onto CMIP6 projections, demonstrating that return-time curves under various emission scenarios collapse onto a single relation, implying substantially higher lifetime exposure to extreme precipitation for cohorts born in the 21st century.

Significance. If the methodological concerns are addressed, the results would offer a statistically grounded method for projecting extreme precipitation risks under climate change, with the observed collapse across scenarios providing a simplified framework for risk assessment. The application of large deviation theory to enrich rare-event statistics could advance forecasting for extremes, though the significance hinges on demonstrating that the enrichment procedure yields unbiased extrapolations.

major comments (3)
  1. [Large deviation framework and sample enrichment] The procedure of fitting the Landau distribution to historical data and then enriching rare-event samples from this same distribution to estimate large-deviation rate functions (as described in the large deviation framework section) introduces a risk of circularity. The rate functions and subsequent return-time forecasts may be partially determined by the fitted parameters rather than by independent observations, which directly affects the reliability of extrapolations to CMIP6 future climates.
  2. [CMIP6 projections and return time collapse] The claim that return time curves collapse onto a unified relation across emission scenarios (in the CMIP6 mapping results) relies on the accuracy of the enriched rate-function estimates. Without reported cross-validation, error propagation, or out-of-sample testing of the extrapolated return times, the support for this collapse and the derived lifetime-exposure projections is limited.
  3. [Validation and extrapolation discussion] The assumption that the Landau distribution's tail shape and the large-deviation principle remain valid under altered climate statistics in CMIP6 runs (e.g., potential shifts in moisture convergence or convective regimes) is not sufficiently tested. If the tail behavior changes with warming, the enriched estimates become biased, undermining the central forecasting claims.
minor comments (2)
  1. [Abstract and results] The percentages '93% of global locations' and '76% matched locations' in the abstract and results should be accompanied by the precise accuracy criterion and statistical test used for the comparison to allow assessment of the claimed improvement.
  2. [Figures] Figures illustrating the return-time curve collapse should include uncertainty quantification (e.g., confidence bands from the enrichment procedure) to convey the robustness of the unified relation.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. These have prompted us to clarify methodological details, strengthen the validation, and expand the discussion of assumptions and limitations. We address each major comment point by point below.

read point-by-point responses

  1. Referee: [Large deviation framework and sample enrichment] The procedure of fitting the Landau distribution to historical data and then enriching rare-event samples from this same distribution to estimate large-deviation rate functions (as described in the large deviation framework section) introduces a risk of circularity. The rate functions and subsequent return-time forecasts may be partially determined by the fitted parameters rather than by independent observations, which directly affects the reliability of extrapolations to CMIP6 future climates.

    Authors: We acknowledge the referee's concern about potential circularity. The Landau distribution is fitted to the full historical precipitation record (with parameters determined from the bulk of the data as well as observed extremes), after which enrichment draws additional tail samples solely to improve the finite-sample estimation of the rate function I(x) = lim (-1/n) log P(S_n > x). This follows standard practice in large-deviation applications for rare-event statistics. The rate-function estimates remain anchored to the empirical tail probabilities; the fitted distribution serves only as a sampling tool, not as a replacement for the data. In the revised manuscript we will add an explicit subsection deriving the consistency of the enriched estimator with the original observations, together with a sensitivity analysis that perturbs the Landau parameters within their bootstrap confidence intervals and recomputes the rate functions. revision: partial

  2. Referee: [CMIP6 projections and return time collapse] The claim that return time curves collapse onto a unified relation across emission scenarios (in the CMIP6 mapping results) relies on the accuracy of the enriched rate-function estimates. Without reported cross-validation, error propagation, or out-of-sample testing of the extrapolated return times, the support for this collapse and the derived lifetime-exposure projections is limited.

    Authors: We agree that quantitative validation metrics were insufficiently reported. The observed collapse is an empirical result across multiple CMIP6 models and scenarios, but we will now add (i) a cross-validation exercise that fits the Landau distribution on a random 70 % subset of historical stations and evaluates return-time predictions on the held-out 30 %, (ii) bootstrap-derived uncertainty bands on the rate functions that are propagated through the mapping to future return times, and (iii) a new figure showing the variability of the collapsed curves under these uncertainty estimates. These additions will appear in a dedicated validation subsection. revision: yes

  3. Referee: [Validation and extrapolation discussion] The assumption that the Landau distribution's tail shape and the large-deviation principle remain valid under altered climate statistics in CMIP6 runs (e.g., potential shifts in moisture convergence or convective regimes) is not sufficiently tested. If the tail behavior changes with warming, the enriched estimates become biased, undermining the central forecasting claims.

    Authors: This is a substantive limitation of any extrapolation method. Our central supporting observation is that the return-time curves nevertheless collapse across widely differing emission scenarios in the CMIP6 ensemble, which indirectly suggests robustness of the tail shape under the range of warming realized in those runs. In the revised manuscript we will (a) state the stationarity assumption explicitly in the methods, (b) quantify the degree of collapse with a formal metric (e.g., mean squared deviation from the unified curve), and (c) add a limitations paragraph discussing possible changes in convective regimes or moisture convergence that could alter the tail and outlining how future high-resolution simulations could test this assumption. We cannot, however, perform a direct out-of-sample test against future observations that do not yet exist. revision: partial

Circularity Check

1 steps flagged

Landau-fitted sample enrichment determines large-deviation rate functions by construction

specific steps
  1. fitted input called prediction [Abstract]
    "Enriching rare event samples by the fitted Landau distribution, we obtain more accurate estimates of large deviation rate functions and return times, enabling forecasts beyond historically observed precipitation intensities."

    The rate functions are computed from samples generated by the Landau distribution that was itself fitted to the same historical data; therefore the 'more accurate estimates' and the derived return-time curves are statistically determined by the fit rather than by additional independent rare-event observations.

full rationale

The central derivation fits the Landau distribution to historical precipitation data, then enriches rare-event samples from that same fitted distribution to estimate the large-deviation rate function and return times. Because the enrichment step draws directly from the fitted model, the resulting rate-function values and the subsequent collapse of return-time curves across CMIP6 scenarios are partly fixed by the fit parameters rather than by independent observations of extremes. This matches the 'fitted_input_called_prediction' pattern and undermines the claim that the forecasts are extrapolations beyond the historical record.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The framework rests on fitting Landau parameters at each location and assuming the large-deviation principle applies to the enriched samples; these steps introduce free parameters and domain assumptions not supplied by upstream literature.

free parameters (1)
  • Landau distribution parameters per location
    Fitted to historical precipitation extremes at each grid point to define the tail and enable sample enrichment.
axioms (1)
  • domain assumption Large deviation principle holds for the precipitation time series after Landau enrichment
    Invoked to convert enriched samples into rate functions and return times.

pith-pipeline@v0.9.0 · 5447 in / 1434 out tokens · 66569 ms · 2026-05-10T16:34:22.055859+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

84 extracted references · 84 canonical work pages

  1. [1]

    M. Ghil, V. Lucarini, The physics of climate variability and climate change. Rev. Mod. Phys. 92, 035002 (2020)

    work page 2020

  2. [2]

    M. G. Donat, A. L. Lowry, L. V. Alexander, P. A. O'Gorman, N. Maher, More extreme precipitation in the world's dry and wet regions. Nat. Clim. Chang. 6 (5), 508 -- 513 (2016)

    work page 2016

  3. [3]

    Pfahl, P

    S. Pfahl, P. O'Gorman, E. Fischer, Understanding the regional pattern of projected future changes in extreme precipitation. Nat. Clim. Chang. 7 (6), 423 -- 427 (2017)

    work page 2017

  4. [4]

    Kim, et al., Future changes in extreme heatwaves in terms of intensity and duration over the CORDEX-East Asia Phase Two domain using multi-GCM and multi-RCM chains

    Y.-H. Kim, et al., Future changes in extreme heatwaves in terms of intensity and duration over the CORDEX-East Asia Phase Two domain using multi-GCM and multi-RCM chains. Environ. Res. Lett. 18 (3) (2023)

    work page 2023

  5. [5]

    Wanyama, E

    D. Wanyama, E. L. Bunting, N. Weil, D. Keellings, Delineating and characterizing changes in heat wave events across the United States climate regions. Clim. Change 176 (2) (2023)

    work page 2023

  6. [6]

    L. Wang, G. Huang, W. Chen, T. Wang, Super Drought under Global Warming: Concept, Monitoring Index, and Validation. Bull. Am. Meteorol. Soc. 104 (5), E943 -- E969 (2023)

    work page 2023

  7. [7]

    B. S. Kim, Y. H. Yoon, H. D. Lee, Analysis of changes in extreme weather events using extreme indices. Environ. Eng. Res. 16 (3), 175 -- 183 (2011)

    work page 2011

  8. [8]

    J. E. Bell, et al., Changes in extreme events and the potential impacts on human health. J. Air Waste Manage. Assoc. 68 (4), 265 -- 287 (2018)

    work page 2018

  9. [9]

    J. Bao, B. Stevens, L. Kluft, C. Muller, Intensification of daily tropical precipitation extremes from more organized convection. Sci. Adv. 10 (8), eadj6801 (2024)

    work page 2024

  10. [10]

    Fan, et al., Statistical physics approaches to the complex Earth system

    J. Fan, et al., Statistical physics approaches to the complex Earth system. Phys. Rep. 896, 1--84 (2021)

    work page 2021

  11. [11]

    Zhong, et al., Improved forecasting via physics-guided machine learning as exemplified using ``21.7'' extreme rainfall event in Henan

    Q. Zhong, et al., Improved forecasting via physics-guided machine learning as exemplified using ``21.7'' extreme rainfall event in Henan. Sci. China Earth Sci. 67 (5), 1652 -- 1674 (2024)

    work page 2024

  12. [12]

    R. M. Horton, J. S. Mankin, C. Lesk, E. Coffel, C. Raymond, A Review of Recent Advances in Research on Extreme Heat Events. Curr. Clim. Change Rep. 2 (4), 242 -- 259 (2016)

    work page 2016

  13. [13]

    Marani, M

    M. Marani, M. Ignaccolo, A metastatistical approach to rainfall extremes. Adv. Water Resour. 79, 121 -- 126 (2015)

    work page 2015

  14. [14]

    S. D. Nerantzaki, S. M. Papalexiou, Tails of extremes: Advancing a graphical method and harnessing big data to assess precipitation extremes. Adv. Water Resour. 134 (2019)

    work page 2019

  15. [15]

    Peters, C

    O. Peters, C. Hertlein, K. Christensen, A complexity view of rainfall. Phys. Rev. Lett. 88 (1), 018701 (2001)

    work page 2001

  16. [16]

    S. N. Majumdar, P. von Bomhard, J. Krug, Exactly Solvable Record Model for Rainfall. Phys. Rev. Lett. 122, 158702 (2019)

    work page 2019

  17. [17]

    S. M. Duarte Queir\'os, Statistics of Stochastic Entropy for Recorded Transitions between ENSO States. Phys. Rev. Lett. 133, 094201 (2024)

    work page 2024

  18. [18]

    Lucarini, M

    V. Lucarini, M. D. Chekroun, Detecting and Attributing Change in Climate and Complex Systems: Foundations, Green's Functions, and Nonlinear Fingerprints. Phys. Rev. Lett. 133 (24), 244201 (2024)

    work page 2024

  19. [19]

    Liu, et al., Teleconnections among tipping elements in the Earth system

    T. Liu, et al., Teleconnections among tipping elements in the Earth system. Nat. Clim. Chang. 13 (1), 67--74 (2023)

    work page 2023

  20. [20]

    Peters, J

    O. Peters, J. D. Neelin, S. W. Nesbitt, Mesoscale convective systems and critical clusters. J. Atmos. Sci. 66 (9), 2913 -- 2924 (2009)

    work page 2009

  21. [21]

    Baranowski, et al., Multifractal analysis of meteorological time series to assess climate impacts

    P. Baranowski, et al., Multifractal analysis of meteorological time series to assess climate impacts. Clim. Res. 65, 39 -- 52 (2015)

    work page 2015

  22. [22]

    Krzyszczak, et al., Multifractal characterization and comparison of meteorological time series from two climatic zones

    J. Krzyszczak, et al., Multifractal characterization and comparison of meteorological time series from two climatic zones. Theor. Appl. Climatol. 137 (3-4), 1811 -- 1824 (2019)

    work page 2019

  23. [23]

    Carleo, et al., Machine learning and the physical sciences

    G. Carleo, et al., Machine learning and the physical sciences. Rev. Mod. Phys. 91, 045002 (2019)

    work page 2019

  24. [24]

    Y. Tang, A. Hoffmann, Quantifying information of intracellular signaling: progress with machine learning. Rep. Prog. Phys. 85 (8), 086602 (2022)

    work page 2022

  25. [25]

    J. Choi, H. Kim, K.-H. Kim, J. Lee, Advanced Torrential Loss Function for Precipitation Forecasting. Phys. Rev. Lett. 136 (2), 024201 (2026)

    work page 2026

  26. [26]

    G. D. Madakumbura, C. W. Thackeray, J. Norris, N. Goldenson, A. Hall, Anthropogenic influence on extreme precipitation over global land areas seen in multiple observational datasets. Nat. Commun. 12 (1) (2021)

    work page 2021

  27. [27]

    Yuval, I

    J. Yuval, I. Langmore, D. Kochkov, S. Hoyer, Neural general circulation models optimized to predict satellite-based precipitation observations. arXiv preprint (2024)

    work page 2024

  28. [28]

    Falasca, P

    F. Falasca, P. Perezhogin, L. Zanna, Data-driven dimensionality reduction and causal inference for spatiotemporal climate fields. Phys. Rev. E 109 (4), 044202 (2024)

    work page 2024

  29. [29]

    Ludescher, et al., Network-based forecasting of climate phenomena

    J. Ludescher, et al., Network-based forecasting of climate phenomena. Proc. Natl. Acad. Sci. U.S.A. 118 (47), e1922872118 (2021)

    work page 2021

  30. [30]

    K. Li, M. Wang, K. Liu, J. Fan, Comprehensive study of heavy precipitation events over land using climate network analysis. J. Hydrol. 651, 132582 (2025)

    work page 2025

  31. [31]

    R. E. Benestad, C. Lussana, A. Dobler, Global record-breaking recurrence rates indicate more widespread and intense surface air temperature and precipitation extremes. Sci. Adv. 10 (45), eado3712 (2024)

    work page 2024

  32. [32]

    Touchette, The large deviation approach to statistical mechanics

    H. Touchette, The large deviation approach to statistical mechanics. Phys. Rep. 478 (1-3), 1--69 (2009)

    work page 2009

  33. [33]

    Wilkinson, Large deviation analysis of rapid onset of rain showers

    M. Wilkinson, Large deviation analysis of rapid onset of rain showers. Phys. Rev. Lett. 116 (1), 018501 (2016)

    work page 2016

  34. [34]

    Dematteis, T

    G. Dematteis, T. Grafke, E. Vanden-Eijnden, Rogue waves and large deviations in deep sea. Proc. Natl. Acad. Sci. U.S.A. 115 (5), 855 -- 860 (2018)

    work page 2018

  35. [35]

    V. M. G \'a lfi, V. Lucarini, J. Wouters, A large deviation theory-based analysis of heat waves and cold spells in a simplified model of the general circulation of the atmosphere. J. Stat. Mech. 2019 (3), 033404 (2019)

    work page 2019

  36. [36]

    V. M. Galfi, V. Lucarini, Fingerprinting Heatwaves and Cold Spells and Assessing Their Response to Climate Change Using Large Deviation Theory. Phys. Rev. Lett. 127, 058701 (2021)

    work page 2021

  37. [37]

    Z. Lu, H. Qian, Emergence and Breaking of Duality Symmetry in Generalized Fundamental Thermodynamic Relations. Phys. Rev. Lett. 128, 150603 (2022)

    work page 2022

  38. [38]

    Y. Tang, J. Liu, J. Zhang, P. Zhang, Learning nonequilibrium statistical mechanics and dynamical phase transitions. Nat. Commun. 15 (1), 1117 (2024)

    work page 2024

  39. [39]

    Horvathy, The Non-commutative Landau Problem

    P. Horvathy, The Non-commutative Landau Problem. Ann. Phys. 299, 128--140 (2002)

    work page 2002

  40. [40]

    Jacob, P

    A. Jacob, P. Ohberg, G. Juzeliunas, L. Santos, Landau levels of cold atoms in non-Abelian gauge fields. New J. Phys. 10, 045022 (2008)

    work page 2008

  41. [41]

    Qian, et al., Modelling bivariate extreme precipitation distribution for data-scarce regions using Gumbel-Hougaard copula with maximum entropy estimation

    L. Qian, et al., Modelling bivariate extreme precipitation distribution for data-scarce regions using Gumbel-Hougaard copula with maximum entropy estimation. Hydrol. Process. 32 (2), 212 -- 227 (2018)

    work page 2018

  42. [42]

    Agilan, N

    V. Agilan, N. Umamahesh, What are the best covariates for developing non-stationary rainfall Intensity-Duration-Frequency relationship? Adv. Water Resour. 101, 11 -- 22 (2017)

    work page 2017

  43. [43]

    Sarhadi, E

    A. Sarhadi, E. D. Soulis, Time-varying extreme rainfall intensity-duration-frequency curves in a changing climate. Geophys. Res. Lett. 44 (5), 2454 -- 2463 (2017)

    work page 2017

  44. [44]

    Li, et al., Changes in annual extremes of daily temperature and precipitation in CMIP6 models

    C. Li, et al., Changes in annual extremes of daily temperature and precipitation in CMIP6 models. J. Climate 34 (9), 3441--3460 (2021)

    work page 2021

  45. [45]

    U. Saha, M. Sateesh, Rainfall extremes on the rise: Observations during 1951--2020 and bias-corrected CMIP6 projections for near-and late 21st century over Indian landmass. J. Hydrol. 608, 127682 (2022)

    work page 1951

  46. [46]

    Enayati, O

    M. Enayati, O. Bozorg-Haddad, J. Bazrafshan, S. Hejabi, X. Chu, Bias correction capabilities of quantile mapping methods for rainfall and temperature variables. J. Water Clim. Change 12 (2), 401 -- 419 (2021)

    work page 2021

  47. [47]

    Wu, et al., Beijing Climate Center Earth System Model version 1 (BCC-ESM1): model description and evaluation of aerosol simulations

    T. Wu, et al., Beijing Climate Center Earth System Model version 1 (BCC-ESM1): model description and evaluation of aerosol simulations. Geosci. Model Dev. 13 (3), 977--1005 (2020)

    work page 2020

  48. [48]

    Camuffo, F

    D. Camuffo, F. Becherini, A. della Valle, Relationship between selected percentiles and return periods of extreme events. Acta Geophys. 68 (4), 1201--1211 (2020)

    work page 2020

  49. [49]

    Mondal, A

    S. Mondal, A. K. Mishra, L. R. Leung, Spatiotemporal characteristics and propagation of summer extreme precipitation events over United States: A complex network analysis. Geophys. Res. Lett. 47 (15), e2020GL088185 (2020)

    work page 2020

  50. [50]

    M. A. Osei, et al., Estimation of the return periods of maxima rainfall and floods at the Pra River Catchment, Ghana, West Africa using the Gumbel extreme value theory. Heliyon 7 (5) (2021)

    work page 2021

  51. [51]

    Olivera, C

    S. Olivera, C. Heard, Increases in the extreme rainfall events: Using the Weibull distribution. Environmetrics 30 (4), e2532 (2019)

    work page 2019

  52. [52]

    Papalexiou, D

    S. Papalexiou, D. Koutsoyiannis, C. Makropoulos, How extreme is extreme? An assessment of daily rainfall distribution tails. Hydrol. Earth Syst. Sci. 17 (2), 851--862 (2013)

    work page 2013

  53. [53]

    S. M. Papalexiou, D. Koutsoyiannis, Battle of extreme value distributions: A global survey on extreme daily rainfall. Water Resour. Res. 49 (1), 187--201 (2013)

    work page 2013

  54. [54]

    L \'e vy, Calcul des probabilit \'e s (Gauthier-Villars) (1925)

    P. L \'e vy, Calcul des probabilit \'e s (Gauthier-Villars) (1925)

    work page 1925

  55. [55]

    Bulyak, N

    E. Bulyak, N. Shul'ga, Landau distribution of ionization losses: history, importance, extensions. arXiv preprint (2022)

    work page 2022

  56. [56]

    Gonz \'a lez-Castro, R

    V. Gonz \'a lez-Castro, R. Alaiz-Rodr \' guez, E. Alegre, Class distribution estimation based on the Hellinger distance. Inf. Sci. 218, 146--164 (2013)

    work page 2013

  57. [57]

    De Sherbinin, A

    A. De Sherbinin, A. Schiller, A. Pulsipher, The vulnerability of global cities to climate hazards, in Adapting cities to climate change (Routledge), pp. 129--157 (2012)

    work page 2012

  58. [58]

    Li, et al., Constraining the entire Earth system projections for more reliable climate change adaptation planning

    C. Li, et al., Constraining the entire Earth system projections for more reliable climate change adaptation planning. Sci. Adv. 11 (9), eadr5346 (2025)

    work page 2025

  59. [59]

    Grant, et al., Global emergence of unprecedented lifetime exposure to climate extremes

    L. Grant, et al., Global emergence of unprecedented lifetime exposure to climate extremes. Nature 641 (8062), 374--379 (2025)

    work page 2025

  60. [60]

    A. K. Knapp, et al., Consequences of more extreme precipitation regimes for terrestrial ecosystems. BioScience 58 (9), 811--821 (2008)

    work page 2008

  61. [61]

    D. P. V \'a zquez, E. Gianoli, W. F. Morris, F. Bozinovic, Ecological and evolutionary impacts of changing climatic variability. Biol. Rev. 92 (1), 22--42 (2017)

    work page 2017

  62. [62]

    Zumwald, et al., Understanding and assessing uncertainty of observational climate datasets for model evaluation using ensembles

    M. Zumwald, et al., Understanding and assessing uncertainty of observational climate datasets for model evaluation using ensembles. Wiley Interdiscip. Rev. Clim. Change 11 (5), e654 (2020)

    work page 2020

  63. [63]

    S. D. Nerantzaki, S. M. Papalexiou, Tails of extremes: Advancing a graphical method and harnessing big data to assess precipitation extremes. Adv. Water Resour. 134, 103448 (2019)

    work page 2019

  64. [64]

    Breugem, J

    A. Breugem, J. Wesseling, K. Oostindie, C. Ritsema, Meteorological aspects of heavy precipitation in relation to floods--an overview. Earth-Sci. Rev. 204, 103171 (2020)

    work page 2020

  65. [65]

    Sch \"a r, et al., Percentile indices for assessing changes in heavy precipitation events

    C. Sch \"a r, et al., Percentile indices for assessing changes in heavy precipitation events. Clim. Change 137, 201--216 (2016)

    work page 2016

  66. [66]

    Alrashidi, S

    M. Alrashidi, S. Rahman, M. Pipattanasomporn, Metaheuristic optimization algorithms to estimate statistical distribution parameters for characterizing wind speeds. Renew. Energy 149, 664--681 (2020)

    work page 2020

  67. [67]

    L. Xu, N. Chen, Z. Chen, C. Zhang, H. Yu, Spatiotemporal forecasting in earth system science: Methods, uncertainties, predictability and future directions. Earth-Sci. Rev. 222, 103828 (2021)

    work page 2021

  68. [68]

    Gettelman, et al., The future of Earth system prediction: Advances in model-data fusion

    A. Gettelman, et al., The future of Earth system prediction: Advances in model-data fusion. Sci. Adv. 8 (14), eabn3488 (2022)

    work page 2022

  69. [69]

    E. J. Gumbel, Statistics of Extremes (Columbia University Press) (1958)

    work page 1958

  70. [70]

    Gnedenko, Sur la distribution limite du terme maximum d'une s \'e rie al \'e atoire

    B. Gnedenko, Sur la distribution limite du terme maximum d'une s \'e rie al \'e atoire. Ann. Math. 44 (3), 423--453 (1943)

    work page 1943

  71. [71]

    W. B. Nelson, Applied Life Data Analysis (John Wiley & Sons) (2003)

    work page 2003

  72. [72]

    J. H. Gaddum, Lognormal distributions. Nature 156 (3964), 463--466 (1945)

    work page 1945

  73. [73]

    von Mises , La distribution de la plus grande de n valeurs

    R. von Mises , La distribution de la plus grande de n valeurs. Rev. Math. Union Interbalkanique 1, 141--160 (1936)

    work page 1936

  74. [74]

    A. F. Jenkinson, The frequency distribution of the annual maximum (or minimum) values of meteorological elements. Q. J. R. Meteorol. Soc. 81 (348), 158--171 (1955)

    work page 1955

  75. [75]

    L. D. Landau, On the energy loss of fast particles by ionization. J. Phys. USSR 8, 201--205 (1944)

    work page 1944

  76. [76]

    Chen, Generalization of G \"a rtner-Ellis theorem

    P.-N. Chen, Generalization of G \"a rtner-Ellis theorem. IEEE Trans. Inf. Theory 46 (7), 2752--2760 (2000)

    work page 2000

  77. [77]

    M. D. Donsker, S. R. S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time III . Commun. Pure Appl. Math. 29 (4), 389--461 (1976)

    work page 1976

  78. [78]

    C. M. Rohwer, F. Angeletti, H. Touchette, Convergence of large-deviation estimators. Phys. Rev. E 92 (5), 052104 (2015)

    work page 2015

  79. [79]

    Ragone, F

    F. Ragone, F. Bouchet, Computation of extreme values of time averaged observables in climate models with large deviation techniques. J. Stat. Phys. 179 (5), 1637--1665 (2020)

    work page 2020

  80. [80]

    Luo, et al., Raindrop size distribution and microphysical characteristics of a great rainstorm in 2016 in Beijing, China

    L. Luo, et al., Raindrop size distribution and microphysical characteristics of a great rainstorm in 2016 in Beijing, China. Atmos. Res. 239, 104895 (2020)

    work page 2016

Showing first 80 references.