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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
TL;DR
Regional climate risk assessment needs fine-scale extreme-event projections, but GCMs are too coarse and computationally expensive, while standard downscaling may not preserve GCM dynamics. DySCo creates dynamically paired training trajectories with a data-driven nudging reformulation and produces high-resolution projections that remain dynamically coherent with the coarse driver while achieving comparable statistical performance to state-of-the-art unsupervised models.
Problem
GCMs cannot efficiently provide the fine regional resolution and extreme-event detail needed for actionable climate risk assessment.
Method
DySCo uses a data-driven GCM emulator and nudging toward coarsened reanalysis to create paired trajectories for a dynamically and statistically consistent supervised downscaling operator.
Results
DySCo remains dynamically coherent with the LENS2 driver while achieving analogous performance to the larger-scale GenFocal baseline and improving some climatological marginals.
Takeaways & Limitations
DySCo enables computationally tractable supervised downscaling that supports fine-scale attribution of coarse-GCM extreme events to regional processes.
Takeaways & Limitations
The demonstrated operator is smaller than GenFocal and uses a generic emulator, leaving scale and broader climatological-variable coverage for future work.
Abstract
from arXiv · showhide
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 addresses the need for localized climate-risk estimates by targeting the physical-consistency problems that limit statistical downscaling for causal analysis of extreme events.
- Motivation: Localized risk estimates are often needed for climate-sensitive applications, but producing them with global climate models is computationally prohibitive.The passage identifies this computational barrier as a motivation for downscaling.
- Limitation: Current statistical downscaling methods efficiently increase resolution but frequently disrupt the physical consistency of trajectories.This tradeoff undermines the physical fidelity of downscaled trajectories.
- Contribution: DySCo is introduced as a downscaling framework designed to overcome this limitation and improve reliability for causal analysis of extreme events.The supplied passage begins describing a data-driven approach, but the mechanism is truncated.
1 Introduction
DySCo addresses the need for high-resolution, dynamically coherent climate risk projections by turning downscaling into supervised learning without costly regional climate models or nudged GCM simulations. It creates paired training data with a learned GCM emulator and evaluates CESM2 LENS2 downscaling against ERA5 and dynamical coherence.
- Motivation: GCM computational costs prevent the fine regional resolutions needed for infrastructure, energy, flood, and financial climate-risk decisions.GCMs provide robust large-scale trends but are too costly for finer regional scales.
- Challenge: Downscaling must represent fine-scale processes, model biases, and probabilistic super-resolution despite chaotic dynamics and unavailable temporally aligned training data.These constraints make supervised learning difficult and motivate alternative formulations.
- Related work: GenFocal generates physically coherent trajectories conditioned on coarse GCM output but sacrifices direct dynamical coherence with the GCM, limiting storyline-based attribution.Dynamical coherence matters when regional impacts must be attributed to the specific GCM driver.
- Contribution: DySCo formulates supervised downscaling without costly RCM or nudged-GCM simulations by learning a GCM emulator and nudging it toward coarsened reanalysis data.The emulator-based procedure creates paired training data for the supervised learning problem.
- Evaluation: DySCo downscales the 100-member CESM2 LENS2 ensemble over CONUS to ERA5 resolution and evaluates out-of-training-record ensemble statistics and dynamical coherence.The evaluation compares the full downscaled ensemble against ERA5 data and assesses preservation of dynamical coherence.
2 Methods
DySCo learns a non-intrusive correction from coarse LENS2 projections toward ERA5 while increasing resolution, using paired trajectories generated without modifying the GCM. The method separates low-resolution debiasing from probabilistic super-resolution to address chaotic divergence, ill-posed mappings, and computational scale.
- Data and setup: DySCo maps daily 1.5° LENS2 inputs over CONUS to bias-corrected 0.25° and 2-hourly outputs toward ERA5.The correction is localized to an approximately 60° × 30° CONUS domain.
- Data and setup: Training uses 1980–1999 data from ERA5 and 4 LENS2 members, with 2000–2009 validation and 2010–2019 testing across all 100 members.The model trains on 20 simulation years and is evaluated on 250 simulation years during summer months.
- Two-stage downscaling: The method decomposes downscaling into low-resolution debiasing followed by an independent super-resolution map, addressing distinct correction and resolution challenges.The present resolution increase is 6-fold spatially and 12-fold temporally, making deterministic super-resolution ill-posed because one input can have many high-resolution realities.
- Dynamical pairing: Nudging generates training pairs (x_nudged, y) whose trajectories track the reference while retaining the original model’s fast dynamics, enabling supervised learning of x_nudged → y.The relaxation timescale τ balances fidelity to the original dynamics against suppression of chaotic divergence; unsuitable τ values harm coherence or generalization.
- Surrogate dynamics: Because directly re-implementing a GCM with nudging is difficult, DySCo uses a surrogate G_surr that only needs to capture fast LENS2 dynamics sufficiently for the learned map to generalize.The method identifies a multivariate Gaussian emulator from GEN2 as a candidate surrogate and notes a trade-off between surrogate quality and map quality.
- Super-resolution: The super-resolution stage conditions a diffusion model on low-resolution reanalysis y to generate probabilistic full-resolution fields z.This reflects that the y → z mapping is inherently probabilistic.
3 Results
DySCo preserves the coarse GCM’s physical and temporal dynamics while producing high-resolution fields with strong distributional fidelity. Across marginal statistics and tropical-cyclone features, it generally matches or improves upon GenFocal and outperforms BCSD in key dynamical and landfall assessments.
- Dynamical coherence: DySCo preserves the nonlinear temperature–pressure relationship and fine-scale topographic modulation while remaining strictly aligned with the LENS2 driver.The case study concerns a Pacific Northwest heatwave with a surface thermal low near 1008 hPa.
- Dynamical coherence: Across the LENS2 ensemble, DySCo’s ACC results confirm the case-study dynamical coherence, especially for pressure and humidity, whereas GenFocal’s evolution diverges from the GCM driver.ACC is evaluated for both intermediate debiased fields and final downscaled outputs.
- Distributional fidelity: DySCo improves mean-sea-level pressure across MAB, MWD, and MPE relative to GenFocal, while temperature and humidity are analogous or worse and wind speed is analogous or better.BCSD performs worse for pressure, remains competitive for humidity and temperature, and is consistently better for wind speed.
- Extreme-event features: DySCo and GenFocal better capture ERA5 tropical-cyclone track distributions than BCSD, which fails to represent Gulf landfall probabilities and locations.The evaluation tracks cyclone trajectories using wind speed and mean-sea-level pressure and assesses first landfall impacts.
4 Conclusion
DySCo is a non-intrusive, model-agnostic supervised downscaling framework designed to preserve both dynamical and statistical consistency with coarse GCM drivers. Its LENS2-to-ERA5 evaluation combines computationally efficient paired-trajectory generation with strong statistical performance and enables causal attribution of coarse-scale extreme events to fine-scale processes.
- Contribution: DySCo ensures dynamical and statistical consistency with the GCM driver, supporting causal extreme-event analysis and storyline-based risk assessment.The framework is non-intrusive, model-agnostic, and supervised.
- Method: DySCo uses nudging and a low-cost climate emulator to generate fully data-driven paired trajectories for supervised downscaling.The approach does not require paired historical data.
- Evaluation: The LENS2-to-ERA5 evaluation increased resolution 6-fold spatially and 12-fold temporally, using a supervised adaptation of the unsupervised GenFocal model.This adaptation merges distribution matching with supervised learning.
- Results: A smaller regional debiasing operator remained dynamically coherent with LENS2 while achieving analogous performance to the larger-scale unsupervised GenFocal baseline.It also performed better in some marginals of the spatiotemporal climatological distribution.
- Future work: Future work includes larger global debiasing models, faster-dynamics emulators, and applications to computational fluid dynamics and other multiscale dynamical systems.Larger models could match GenFocal’s scale and complexity while retaining the supervised problem’s dynamically coherent signal.
- Implications: The supervised DySCo operator enables attribution of coarse-GCM extreme events to fine-scale processes while allowing computational resources to be balanced against input complexity.This capability is demonstrated in the case study in Figure 2.
7 Author contributions
The authors collectively contributed to the study’s conceptualization and methodology, with Stamatelopoulos additionally leading implementation, analysis, data curation, writing, and visualization.
- Author contributions: Stamatios Stamatelopoulos contributed across conceptualization, methodology, software, validation, formal analysis, data curation, writing, and visualization.His writing contributions covered both original-draft preparation and review and editing.
- Author contributions: Mengze Wang contributed to conceptualization, methodology, and software.
- Author contributions: Ignacio Lopez-Gomez and Leonardo Zepeda-N´u˜nez contributed to conceptualization, methodology, formal analysis, and writing review and editing.
- Author contributions: Zhong Yi Wan contributed to conceptualization and methodology.
A Debiasing operator dependence on the supervised signal parameter
The debiasing operator’s λ parameter tunes the learned signal from unsupervised toward supervised correction. Performance generally improves with λ up to an apparent optimum of λ = 10, although pressure worsens at λ = 50.
- λ controls the operator’s departure from unsupervised GenFocal, ranging from supervised learning as λ →∞ to unsupervised learning as λ →0.Larger λ weights direct integration that penalizes deviations between input and exact reference output.
- Performance for temperature, wind speed, and humidity increases with λ, whereas pressure remains constant and humidity decreases at the largest value of λ = 50.The reported measures are MAB, MWD, and MPE against coarse-scale ERA5 y during training.
- λ = 10 is indicated as an optimal value because it exploits the supervised signal to improve the performance of the first three variables.The comparison uses MAB (18), MWD (20), and MPE (22) for Gdeb(x; λ) against coarse-scale ERA5 y.
B Hyperparameters
This section summarizes the hyperparameters used for the debiasing and super-resolution operators.
- B Hyperparameters: Tables (2) and (3) summarize the hyperparameters for the debiasing operator Gdeb and super-resolution operator Gsr, respectively.
C Bias Correction and Spatial Disaggregation
The BCSD procedure uses climatological training data to correct biases in LENS2 inputs before spatial interpolation and temporal disaggregation toward the ERA5 target. It combines climatological statistics, cubic interpolation, and day-of-year-aligned sampling from historical data.
- Bias Correction: BCSD is trained on the 1980–1999 ERA5 climatology, using downsampled ERA5 y and daily-averaged ERA5 zdaily alongside the LENS2 input x.The target ERA5 dataset z is downsampled to the LENS2 input resolution and separately averaged daily for intermediate processing.
- Bias Correction: Bias correction computes debiased anomalies from climatological means and standard deviations evaluated at each location and day of year.The climatological mean and standard deviation are computed separately for each location and day-of-year.
- Spatial Disaggregation: The bias-corrected field xBC is cubically interpolated to the target spatial resolution, then its mean is shifted using the climatological mean of zdaily.This step performs the spatial-resolution increase while aligning the corrected field with the daily climatology.
- Temporal Disaggregation: Temporal disaggregation randomly samples historical ERA5 data z aligned with the day-of-year entries of the bias-corrected ensemble trajectory.The sampled daily dataset is normalized by removing its daily mean before substitution into the corrected trajectory.
D Cyclone Tracking Algorithm
The cyclone tracker identifies trajectories using pressure minima, wind-speed persistence, spatial and temporal continuity, and speed limits. Because LENS2 underestimates pressure depressions, cyclone-tracking pressure is calibrated against ERA5 statistics by optimizing K over a discrete set of values.
- Tracking criteria: Accompanying wind speeds must exceed 10ms−1 for at least 2 days.This persistence condition helps define spatiotemporal cyclone trajectories.
- Tracking criteria: Trajectory nodes may be separated by at most 8.0 GCD, trajectories must last at least 54 hours, and instantaneous track speed cannot exceed 40 knots.These constraints enforce spatial continuity, minimum duration, and physically plausible motion.
- Implementation: The criteria are identified with the open-source Tempest Extremes package, with the instantaneous speed filter applied to its output.Tempest Extremes provides the tracking implementation.
- Pressure calibration: To correct LENS2 pressure-depression underestimation, pressure is calibrated over [1995, 1999] by minimizing summed relative errors in cyclone count, track length, and duration against ERA5.The procedure evaluates 1/K ∈{0.1, 0.2, ..., 1}, where 1/K = 1 denotes no calibration, and selects the optimal value per model.
E Marginal Metrics
The section defines three marginal metrics comparing downscaled variables with target reanalysis: mean absolute bias, mean Wasserstein distance, and percentile error. These metrics separately assess climatological bias, bulk-distribution alignment, and distributional tails, with spatial averages area-weighted over land.
- Metric definitions: Mean absolute bias (MAB) quantifies systematic deviations of climatological variables from the target reanalysis climate.Bias is defined per variable and location as the time-averaged difference between ensemble-averaged input and target, then spatially aggregated for each variable.
- Metric definitions: Mean Wasserstein distance (MWD) compares corresponding input and target distributions at each variable and location.The Wasserstein-1 metric is computed between the corresponding distributions, with the mean distance then formed across locations.
- Metric definitions: Percentile error evaluates distributional tails for large p, complementing MAB and MWD.MAB targets systematic deviations, whereas MWD identifies misalignment in the bulk of probability mass.
- Aggregation: Table 1 uses spatial averages over land with spherical area weighting.
F Temporal Coherence
This section defines temporal coherence between LENS2 ensemble signals and debiased low-resolution outputs using spectral relationships, then aggregates it across ensemble members and spatial locations to evaluate each variable and frequency. Figure 12 reports a variable-aggregated version comparing input LENS2 drivers with debiased fields.
- Definition: Temporal coherence Cohe,v,f,i,j measures the relationship between LENS2 ensemble signals and debiased low-resolution outputs by member, variable, frequency, and location.The coherence is defined between x, the LENS2 ensemble, and xdeb, the debiased low-resolution output of a downscaling method.
- Spectral estimation: The underlying spectra are computed from discrete Fourier transforms using standard Welch estimators.The spectral-density formulation supports coherence evaluation in the frequency domain.
- Interpretation: Coherence values lie in [0, 1], with γ →0 indicating no phase- or amplitude-consistent relationship between the two signals.The passage specifies the interpretation of the lower-end coherence limit.
- Aggregation: Coherence performance is aggregated across ensemble members and spatial locations to produce a metric for each variable and frequency.Spatial aggregation uses appropriate spherical weights, while ensemble members are uniformly weighted.
- Results: Figure 12 reports temporal coherence between the input LENS2 driver and debiased fields after aggregation across variables.The figure includes a shaded region representing the 5th and 95th percentile range.