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DySCo: Dynamically consistent data-driven downscaling of extremes in climate projections

S. Stamatelopoulos, M. Wang, I. Lopez-Gomez, L. Zepeda-Nunez, Z. Y. Wan, R. Carver, F. Sha, T. P. Sapsis

arXiv:2608.21998v1cs.LGmath.NAphysics.ao-ph

TL;DR

Regional climate risk assessment needs high-resolution projections, but GCMs are computationally prohibitive at regional scales and observationally trained corrections may not preserve GCM dynamics. DySCo creates paired training trajectories by nudging an emulator toward coarsened reanalysis, then produces dynamically coherent downscaling with performance analogous to the larger GenFocal baseline.

  • Problem

    Regional risk assessment needs fine-scale projections, but GCM computational costs limit regional resolution and preserving GCM dynamics is challenging for observationally trained corrections.

    Source: §1 · p. 2, §4 · p. 13

  • Method

    DySCo creates paired training trajectories by nudging an emulator toward coarsened reanalysis, then trains a supervised downscaling operator.

    Source: §1 · p. 3, §2.0.2 · p. 4

  • Results

    DySCo stays dynamically coherent with LENS2 while achieving analogous performance to the larger-scale GenFocal baseline, with better marginal performance for some climatological variables.

    Source: §4 · p. 14

  • Takeaways & Limitations

    In the demonstrated case study, DySCo enables attribution of extreme events in coarse GCM output to fine-scale processes.

    Source: §4 · p. 15

    The demonstrated regional operator is smaller-scale; matching GenFocal’s scale and complexity remains future work.

    Source: §4 · p. 14

Abstract

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Regional climate risk assessment is critical for applications such as infrastructure design, disaster forecasting, and insurance resource allocation. However, estimating regional (i.e., high-spatial-resolution) risk with global climate models (GCMs) remains computationally prohibitive, which has driven the development of downscaling methods for coarse GCM outputs. Downscaling is vital for rare events, since quantifying their extreme properties requires high spatial resolution and very long GCM simulations. These methods non-intrusively increase GCM resolution while correcting statistical biases from unresolved fine-scale processes, thereby improving the accuracy of extreme event statistics with long return periods. A key challenge is preserving dynamical consistency, as freely evolving GCM trajectories are not expected to track the observational dataset used for training the correction operator. This is critical for causal extreme event analyses, where storyline-based risk assessment, i.e., extreme event catalogs, is necessary for effective planning. We address this challenge by introducing Dynamically and Statistically Consistent downscaling (DySCo), a non-intrusive framework yielding high-resolution climate projections consistent with coarse GCM dynamics. DySCo relies on a data-driven reformulation of nudging to create dynamically paired training trajectories without intrusive GCM modifications. Using these paired trajectories, we train a dynamically and statistically consistent, two-stage operator. We evaluate the method by downscaling the Community Earth System Model v2 Large Ensemble (LENS2) in time and space towards historical reanalysis. Results show DySCo achieves superior dynamical consistency with the coarse GCM trajectories, essentially applying a minimal, causal correction to the GCM, preserving top statistical performance comparable to state-of-the-art unsupervised models.

Significance Statement

DySCo uses data-driven trajectory pairing to produce high-resolution climate projections that preserve the dynamical storylines of coarse GCM outputs. This non-intrusive approach addresses a key limitation of statistical downscaling for causal analysis of extreme events.

Significance Statement

  • DySCo uses data-driven trajectory pairing to preserve coarse GCM dynamical storylines in high-resolution projections.This addresses the physical inconsistency that can limit statistical downscaling for causal analysis of extreme events.Source: Significance Statement · p. 2
  • DySCo’s non-intrusive approach reduces computational barriers to localized risk estimates that are prohibitive with global climate models.Source: Significance Statement · p. 2
  • DySCo’s dynamically consistent localized insights support infrastructure design, disaster forecasting, and regional planning.Source: Significance Statement · p. 2

1 Introduction

DySCo addresses the need for regional climate risk projections by creating paired training trajectories from unpaired GCM outputs and reanalysis, enabling downscaled extremes to remain dynamically coherent with their GCM drivers. The paper evaluates the framework on CESM2 LENS2 over CONUS against ERA5.

Introduction

  • Regional risk decisions need fine-scale projections, but GCMs are computationally prohibitive at regional scales and cannot resolve the spatiotemporal correlations of compound extremes.The stated applications include infrastructure, energy planning, flood forecasting, and insurance allocation.Source: §1 · p. 2
  • RCMs resolve regional processes but are costly for large ensembles and O(100)-year extremes, while quantile mapping and interpolation often miss correlations needed for extreme-risk assessment.Machine-learning downscaling can learn nonlinear scale mappings at lower cost [17], but often requires temporally aligned high-resolution data from RCMs [17] or newly nudged GCM simulations.Source: §1 · p. 2
  • GenFocal [20] generates physically coherent downscaled trajectories conditioned on coarse GCM output, but does not enforce strict causal coherence with the GCM driver, limiting storyline attribution.Its debiasing and super-resolution stages can produce trajectories that aggregate to target statistics, but do not explicitly tie localized weather to the large-scale forcing.Source: §1 · pp. 2–3
  • DySCo uses a GCM emulator nudged toward coarsened reanalysis to create paired training data from unpaired GCM outputs and observational targets, without costly RCM or nudged GCM simulations.The resulting model-agnostic, scalable supervised framework is designed to keep fine-scale extremes dynamically coherent with their large-scale atmospheric drivers.Source: §1 · p. 3
  • DySCo downsamples CESM2 LENS2 over CONUS to ERA5 resolution, comparing full 100-member ensemble statistics with ERA5 outside the training record and assessing dynamical coherence with the coarse GCM driver.The evaluation examines both statistical fidelity and coherence with the GCM trajectory.Source: §1 · p. 3

2 Methods

DySCo uses LENS2 as a coarse driver and ERA5 as a high-resolution reference to downscale four surface climate variables over CONUS summers, from daily 1.5° inputs to 2-hourly 0.25° outputs.

2.0.1 Problem decomposition: debiasing and super-resolution

  • DySCo separates low-resolution debiasing from probabilistic super-resolution, using data-driven nudging for tractable correction and reserving the latter stage for unresolved fine-scale variability.The 6-fold spatial and 12-fold temporal increase makes deterministic super-resolution ill-posed, while the large climate datasets make computational efficiency essential.Source: §2.0.1 · p. 4

2.0.2 The nudging-based supervised learning problem

  • Nudging creates supervised pairs by keeping a trajectory’s fast dynamics governed by the original system while steering its slow dynamics toward the reference; the relaxation timescale τ balances tracking against dynamical fidelity.If τ is too large, trajectories diverge from the reference; if too small, they depart too far from the original dynamics and may not generalize to new inputs.Source: §2.0.2 · pp. 4–5

2.0.3 Non-intrusive nudging via data-driven emulation

  • A data-driven surrogate enables nudging without modifying the GCM: a Gaussian emulator represents climate fields with PCA modes whose coefficients are modeled as autoregressive processes driven by yearly global-mean temperature.The surrogate is nudged in coefficient space toward ERA5 fluctuations; its trajectories are reconstructed as physical fields for training the debiasing map.Source: §2.0.3 · pp. 5–6

2.0.4 The debiasing operator: a balance between statistical and dynamical learning

  • The debiasing operator adapts rectified flow to nudged supervised pairs by combining its distributional objective with direct integration error, balancing the two learning signals with λ.A spatiotemporal U-ViT parameterizes the operator, with λ set to 10.0.Source: §2.0.4 · pp. 6–7

2.0.5 The super-resolution operator

  • The super-resolution operator uses a conditional diffusion model to sample the residual between ERA5 high-resolution fields and their linear interpolation from coarse ERA5 inputs.The sampled residual is added back to the interpolated field to reconstruct the high-resolution output.Source: §2.0.5 · p. 7

2.0.6 The end-to-end operator

  • During training, DySCo downsamples ERA5 to the LENS2 resolution, nudges an emulator toward that reference, and trains the debiasing and conditional diffusion operators; inference applies debiasing before super-resolution.The two operators are trained independently: the diffusion model samples high-resolution ERA5 fields conditioned on the coarse input.Source: §2.0.6 · p. 8

3 Results

Across the unseen 100-member LENS2 ensemble for 2010–2019, DySCo is evaluated for dynamical coherence, marginal statistical reliability, and multivariate cyclone trajectories against ERA5 and baseline methods.

3.0.1 Dynamical coherence of corrected trajectories

  • DySCo’s ACC is about 0.73 versus GenFocal’s 0.15 for pressure and humidity, while coherence is preserved through super-resolution for temperature and wind speed.Temporal coherence is also higher for DySCo than GenFocal; DySCo exceeds BCSD for mean-sea-level pressure, while the methods are comparable across variables and both are far above GenFocal.Source: §3.0.1 · p. 10, Figure 3 · p. 11, Figure 4 · p. 12

3.0.3 Generated cyclone spatiotemporal trajectories

  • DySCo and GenFocal better capture ERA5 cyclone track probabilities than BCSD, and DySCo and GenFocal reproduce Gulf landfalls where BCSD fails.The landfall histogram uses 250 years of downscaled data; Gulf performance matters because the region is climatologically relevant and challenging to model.Source: §3.0.3 · pp. 12–13

3.0.2 Statistical reliability of downscaled data

  • DySCo improves mean-sea-level-pressure marginal metrics over GenFocal and matches or outperforms it on wind speed, while temperature and humidity are comparable or worse.GenFocal performs best on diagnosed Heat Index, with DySCo between GenFocal and BCSD. Across local neighborhoods, downscaled distributions match ERA5 and recover high-resolution spatial correlations, including coastline features unresolved by LENS2.Source: §3.0.2 · pp. 11–12, Table 1 · p. 13

4 Conclusion

DySCo is a non-intrusive, model-agnostic supervised framework for downscaling that aims to preserve both GCM dynamical coherence and statistical consistency. The conclusion reports comparable climatological performance to unsupervised GenFocal with a smaller operator, while identifying future directions for improving fidelity and extending the approach.

4 Conclusion

  • DySCo uses nudging and a low-cost climate emulator [27] to create paired training trajectories, and was evaluated from LENS2 to ERA5 at 6-fold spatial and 12-fold temporal resolution increases.The evaluation used a supervised adaptation of GenFocal [20], combining distribution matching with supervised learning.Source: §4 · pp. 13–14
  • A smaller regional DySCo operator stayed dynamically coherent with LENS2 and achieved performance analogous to GenFocal, improved some climatological-variable marginals, and populated Gulf coastal cyclone landfalls missed by BCSD.The authors present these results as demonstrating the central thesis of the work: computationally efficient training data generation can support a smaller model without sacrificing the cited performance properties.Source: §4 · p. 14
  • Future work could scale the approach to industry-level resources, use a global debiasing model with more climatological variables, and develop an emulator better adapted to the GCM’s fast dynamics.The authors expect the fuller climatological input to improve performance and the adapted emulator to yield higher-fidelity training data.Source: §4 · pp. 14–15
  • The authors state that DySCo can be translated beyond climate downscaling to computational fluid dynamics and other multiscale, multifidelity dynamical-system domains.Source: §4 · p. 15
  • Without paired historical data, DySCo defines a computationally tractable, fully data-driven supervised problem that supports attributing coarse-GCM extreme events to fine-scale processes and balancing resources against model complexity and dynamical dissimilarity.The conclusion describes the resulting framework as a route to scalable and generalizable dynamically coherent downscaling.Source: §4 · p. 15

A Debiasing operator dependence on the supervised signal parameter

The supervised-signal parameter λ balances supervised and unsupervised debiasing, with λ = 10 indicated as an optimal value for improving temperature, wind speed, and humidity without reducing pressure performance.

A Debiasing operator dependence on the supervised signal parameter

  • Larger λ weights a direct integration term that penalizes deviation from the exact reference output, shifting the operator from unsupervised learning at λ → 0 toward supervised learning at λ →∞.Thus, λ controls departure from the original unsupervised GenFocal debiasing formulation.Source: A Debiasing operator dependence on the… · p. 23
  • λ = 10 is indicated as optimal: temperature, wind speed, and humidity performance improves with λ, while pressure stays constant except for a decrease at λ = 50.The assessment reports MAB, MWD, and MPE during training against coarse-scale ERA5 data.Source: A Debiasing operator dependence on the… · p. 23

B Hyperparameters

The hyperparameters for the debiasing operator Gdeb and super-resolution operator Gsr are summarized in Tables 2 and 3, respectively.

B Hyperparameters

C Bias Correction and Spatial Disaggregation

The multi-variable spatiotemporal BCSD formulation [20] uses ERA5 climatology to bias-correct LENS2 inputs, then spatially and temporally disaggregates them. Its steps use location- and day-of-year climatologies and historical data aligned by day of year.

C Bias Correction and Spatial Disaggregation

  • BCSD [20] uses ERA5 target data from training years 1980–1999; its target y is z downsampled to the LENS2 input x resolution, and climatological means and standard deviations are computed by location and day-of-year.Source: C Bias Correction and Spatial… · pp. 23–24
  • The bias-corrected data are cubically interpolated to the target resolution, then shifted to match the climatological mean of daily-averaged ERA5.The daily-averaged dataset retains ERA5’s spatial resolution.Source: C Bias Correction and Spatial… · pp. 24–25
  • Temporal disaggregation samples historical ERA5 data aligned by day of year, removes each sample’s daily mean, and substitutes the bias-corrected trajectory’s daily mean.This produces a daily dataset consistent with the daily-averaged bias-corrected trajectory.Source: C Bias Correction and Spatial… · pp. 24–25

D Cyclone Tracking Algorithm

The cyclone-tracking algorithm identifies trajectories using pressure and wind criteria, then calibrates pressure depressions against ERA5 cyclone statistics for the 1995–1999 reference period.

D Cyclone Tracking Algorithm

  • Tracks require a 200 Pa pressure minimum below 10 m within 5.0 GCD, winds above 10 m/s for 2 days, nodes no farther than 8.0 GCD apart, 54-hour duration, and maximum speed of 40 knots [20].Source: D Cyclone Tracking Algorithm · p. 25
  • The open-source Tempest Extremes package identifies the features, with the instantaneous-speed filter applied to its output.Source: D Cyclone Tracking Algorithm · p. 25
  • To address underestimated pressure depressions, the method calibrates each model’s pressure using 1995–1999 training data and a conditional affine transformation [20] [48].Ambient pressure is 1010 hPa; K is selected by comparing cyclone count, track length, and duration with ERA5.Source: D Cyclone Tracking Algorithm · p. 25
  • The optimal 1/K values were 0.9 for DySCo, 0.9 for BCSD, and 1.0 for GenFocal.The ablation selected K by minimizing summed relative errors in cyclone count, track length, and duration against ERA5; 1/K = 1 means no calibration.Source: D Cyclone Tracking Algorithm · p. 25

E Marginal Metrics

The section defines three marginal metrics for comparing downscaled variables with target reanalysis: mean absolute bias, mean Wasserstein distance, and percentile error. It also specifies the spatial averaging used for Table 1.

E Marginal Metrics

  • Mean absolute bias (MAB) aggregates spatially the absolute, time-averaged differences between ensemble-averaged inputs and targets for each variable.Bias is computed at each location before spatial aggregation.Source: E Marginal Metrics · pp. 25–26
  • Mean Wasserstein distance (MWD) averages location-specific Wasserstein-1 distances between input and target distributions, integrated by quadrature over their union of sorted quadrature points.MWD complements MAB by measuring distributional misalignment in the bulk probability mass.Source: E Marginal Metrics · p. 26
  • Percentile error complements MAB and MWD by evaluating distribution tails, particularly for large percentile values.Percentiles are computed for each variable and location.Source: E Marginal Metrics · p. 26
  • For Table 1, spatial averages are computed over land and weighted spherically by area.Source: E Marginal Metrics · p. 26

F Temporal Coherence

The section defines temporal coherence between LENS2 and debiased outputs, then summarizes it across ensemble members and locations to assess coherence by variable and frequency.

F Temporal Coherence

  • Coherence compares each LENS2 signal with a method’s debiased low-resolution output at each ensemble member, variable, frequency, and location.The section defines this metric for x as the LENS2 ensemble and xdeb as the debiased output.Source: F Temporal Coherence · p. 26
  • The spectra use discrete Fourier transforms with standard Welch estimators, and coherence ranges from 0 to 1; values approaching 0 indicate no consistent phase or amplitude relationship.Source: F Temporal Coherence · p. 26
  • The coherence metric is calculated for each variable and frequency, aggregating ensemble members uniformly and locations with spherical weights; Figure 12 instead reports a version aggregated across variables.Figure 12 shows temporal coherence between the input LENS2 driver and debiased fields, with the 5th and 95th percentile range shaded.Source: F Temporal Coherence · p. 27, Figure 12 · p. 29

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