EnScale: Generative Climate Downscaling

• EnScale is a multivariate generative downscaling framework that emulates the full conditional distribution p(Y|X) from coarse GCM inputs to fine-scale RCM outputs.
• It employs a two-step method—coarse correction and super-resolution—to jointly model temperature, precipitation, solar radiation, and surface wind with actionable precision.
• The framework integrates energy score-based training and an autoregressive temporal extension (EnScale-t) to efficiently capture conditional variability and improve climate projection consistency.

EnScale is a multivariate, generative downscaling framework that emulates the conditional distribution of high-resolution regional climate model (RCM) outputs from coarse-resolution global circulation model (GCM) inputs. It is designed for the practical problem that future climate projections from GCMs are often too coarse for impact-oriented analysis, while RCMs provide the required refinement at substantial computational cost. EnScale targets the stochastic map $p(Y \mid X)$ from coarse GCM fields $X$ to fine-scale RCM fields $Y$, jointly modeling temperature, precipitation, solar radiation, and surface wind, and extending to temporally consistent daily sequences through the EnScale-t variant (Schillinger et al., 30 Sep 2025).

1. Problem formulation and scientific motivation

EnScale is motivated by the fact that the conditional distribution $p(Y \mid X)$ is broad. For a fixed GCM day $X$, an RCM can produce multiple plausible high-resolution realizations $Y$ because of internal variability. This makes deterministic downscaling insufficient for applications that depend on extremes, multi-day events, or cross-variable consistency. The framework therefore aims to emulate the full conditional distribution rather than a point estimate, and it is trained across multiple GCM–RCM pairs so that pair-specific maps can be learned while shared structure is leveraged across pairs (Schillinger et al., 30 Sep 2025).

The method is defined on a Central Europe domain spanning 0°E to 18.9°E and 42°N to 54.8°N, including land, sea, and the Alps. The target variables are tas, pr, rsds, and sfcWind, while predictors include these fields plus sea level pressure from GCMs. A key design premise is that much of the variability relevant for downscaling arises at coarse scales. In the variance decomposition

$$\mathrm{Var}^\iota(Y \mid X) = \mathbb{E}^\iota[\mathrm{Var}^\iota(Y \mid Z)\mid X] + \mathrm{Var}^\iota(\mathbb{E}^\iota[Y \mid Z]\mid X),$$

the coarse/local ratios averaged over space are reported as tas $\approx 16.76$, sfcWind $\approx 6.05$, rsds $\approx 4.81$, and pr $X$0. The same study reports that, for two RCMs with the same GCM, internal variability dominates structural RCM differences, with variance/model-difference ratios tas $X$1, pr $X$2, sfcWind $X$3, and rsds $X$4 (Schillinger et al., 30 Sep 2025).

These results support the framework’s emphasis on stochastic conditional modeling and joint training across multiple GCM–RCM pairs. A plausible implication is that the dominant uncertainty to be emulated is not only local fine-scale noise but also large-scale conditional variability that persists after conditioning on daily GCM fields.

2. Probabilistic objective and proper scoring-rule training

EnScale is trained with the energy score, a proper scoring rule for multivariate predictive distributions. For a predictive distribution $X$5 and a target $X$6, the multivariate energy score is

$X$7

In the univariate case, the energy score equals the Continuous Ranked Probability Score (CRPS). The unconditional loss is minimized if and only if the model distribution equals the target distribution, and at the minimum the prediction term and variability term are equal (Schillinger et al., 30 Sep 2025).

For conditional modeling, EnScale optimizes

$X$8

The first term is denoted $X$9 and the second $Y$0. A calibrated, sharp model tends to satisfy $Y$1 with small values. In minibatch training, the expectations are approximated by Monte Carlo with two independent samples from $Y$2 for each batch pair $Y$3 (Schillinger et al., 30 Sep 2025).

Because tas, pr, rsds, and sfcWind have different units, EnScale transforms each variable at each location via its empirical CDF $Y$4 to uniform $Y$5 and then to standard normal via $Y$6. Generated outputs are mapped back to native units with $Y$7. GCM predictors are standardized by mean and variance globally per variable. This preprocessing is central to the joint loss, because it makes the norm in the energy score aggregate variables on a common scale while retaining an inverse map to physically interpretable units (Schillinger et al., 30 Sep 2025).

The use of a proper scoring rule distinguishes EnScale from adversarial or diffusion-based training objectives. In the reported comparisons, this objective is associated with stable optimization and calibrated diversity, whereas GAN baselines underestimate variability and default CorrDiff sampling overconstrains temporal ensembles (Schillinger et al., 30 Sep 2025).

3. Two-step generative architecture

EnScale factorizes the downscaling problem into two physically meaningful steps: coarse correction and super-resolution. The first step learns the conditional distribution of average-pooled RCM fields $Y$8 given GCM inputs $Y$9, denoted $p(Y \mid X)$0 for GCM–RCM pair $p(Y \mid X)$1. The second step learns $p(Y \mid X)$2 from the coarsened RCM field $p(Y \mid X)$3 to the full-resolution field $p(Y \mid X)$4. The coarsening is implemented by average pooling $p(Y \mid X)$5 over $p(Y \mid X)$6 patches, producing an $p(Y \mid X)$7 field per variable with resolution comparable to the GCM. The target output is $p(Y \mid X)$8 per variable, and the super-resolution path bridges $p(Y \mid X)$9 (Schillinger et al., 30 Sep 2025).

The coarse-correction model is a dense multilayer perceptron with stochastic inputs, implemented by concatenating Gaussian noise to hidden units, and trained with the energy score. This stage captures large-scale biases and mismatches between GCM and RCM at comparable resolution without attempting fine-scale reconstruction. The super-resolution model is a cascade of four resolution-doubling stages. Each stage contains a deterministic, learnable linear interpolation from nearest neighbors, followed by a stochastic refinement. The interpolation is not fully convolutional: it uses location-specific weights so that topography and land–sea contrast can be represented. In the stochastic refinement, Gaussian noise channels are concatenated, local neighborhoods are aggregated using learnable weights, and a small shared MLP is applied per pixel with weight sharing across space. All variables are processed jointly at this refinement stage, which promotes cross-variable consistency (Schillinger et al., 30 Sep 2025).

Conditioning is implemented by concatenating GCM predictors, day-of-year features given as integer, sine, and cosine, and a one-hot index for the GCM–RCM pair. The pair index is used in the coarse model and the first interpolation in super-resolution. The stochastic refinement MLP is pair-agnostic, and adding pair labels there did not improve performance. The paper reports that the two-step approximation is accurate if $X$0, in which case

$X$1

A heuristic check found at most $X$2 performance loss for temperature and negligible loss for precipitation under this decomposition (Schillinger et al., 30 Sep 2025).

The architectural details are explicit. The coarse and temporal coarse MLPs use 5 hidden layers of sizes 200, 200, 200, 256, 256; Gaussian noise channels of size 10 concatenated at each layer with learnable scaling; ReLU activations; and skip connections. Separate preprocessing layers per input variable are included. In the super-resolution sparse layers, deterministic upsampling uses 9 nearest neighbors; 5 Gaussian noise channels are concatenated; 25 nearest neighbors are aggregated to a latent dimension 12; and the shared per-pixel MLP has two hidden layers of size 12. A small weight decay of $X$3 is used to improve image quality. Optimization uses Adam with learning rate $X$4; the coarse and temporal coarse models are trained for 200 epochs, and the super-resolution stages for 200/200/200/100 epochs, with convergence monitored on validation loss (Schillinger et al., 30 Sep 2025).

4. Temporal extension: EnScale-t

EnScale-t extends the framework from daywise conditional generation to temporally consistent daily sequences. Its central modification is an autoregressive dependency at the coarse scale:

$X$5

This temporal coarse model is another dense MLP with noise, again trained with the conditional energy score. During training it uses average-pooled $X$6 as $X$7; during inference it performs an autoregressive rollout. For $X$8, sampling starts from the marginal coarse model $X$9. For later times, given a sample $Y$0 and $Y$1, the model samples $Y$2 from the temporal coarse model, and then applies the super-resolution model independently to each $Y$3 to obtain $Y$4 (Schillinger et al., 30 Sep 2025).

This design assumes

$Y$5

According to the reported empirical tests, neglecting local-scale temporal dependence causes at most $Y$6 loss for surface wind and no loss for precipitation. The framework therefore localizes temporal dependence to the coarse stage rather than the fine-scale super-resolution stage (Schillinger et al., 30 Sep 2025).

Day-of-year features are retained, but absolute year is omitted so that the method can generalize beyond the training period. No explicit temporal smoothness regularizer is required. The reported temporal-structure results show a marked improvement in lag-1 autocorrelation errors: EnScale-t obtains tas $Y$7, pr $Y$8, sfcWind $Y$9, and rsds $$\mathrm{Var}^\iota(Y \mid X) = \mathbb{E}^\iota[\mathrm{Var}^\iota(Y \mid Z)\mid X] + \mathrm{Var}^\iota(\mathbb{E}^\iota[Y \mid Z]\mid X),$$0, compared with EnScale at tas $$\mathrm{Var}^\iota(Y \mid X) = \mathbb{E}^\iota[\mathrm{Var}^\iota(Y \mid Z)\mid X] + \mathrm{Var}^\iota(\mathbb{E}^\iota[Y \mid Z]\mid X),$$1, pr $$\mathrm{Var}^\iota(Y \mid X) = \mathbb{E}^\iota[\mathrm{Var}^\iota(Y \mid Z)\mid X] + \mathrm{Var}^\iota(\mathbb{E}^\iota[Y \mid Z]\mid X),$$2, sfcWind $$\mathrm{Var}^\iota(Y \mid X) = \mathbb{E}^\iota[\mathrm{Var}^\iota(Y \mid Z)\mid X] + \mathrm{Var}^\iota(\mathbb{E}^\iota[Y \mid Z]\mid X),$$3, and rsds $$\mathrm{Var}^\iota(Y \mid X) = \mathbb{E}^\iota[\mathrm{Var}^\iota(Y \mid Z)\mid X] + \mathrm{Var}^\iota(\mathbb{E}^\iota[Y \mid Z]\mid X),$$4. By contrast, CorrDiff’s default sampling overestimates autocorrelation, while CorrDiff-s improves calibration and diversity but reduces temporal dependence (Schillinger et al., 30 Sep 2025).

The temporal design indicates that EnScale-t is not a generic sequence model imposed on full-resolution weather fields. Rather, it is a coarse-scale autoregressive correction coupled to independent daily super-resolution, with temporal stability maintained in multi-year rollouts because conditioning on $$\mathrm{Var}^\iota(Y \mid X) = \mathbb{E}^\iota[\mathrm{Var}^\iota(Y \mid Z)\mid X] + \mathrm{Var}^\iota(\mathbb{E}^\iota[Y \mid Z]\mid X),$$5 keeps the sequence tied to the GCM daily fields.

5. Data regime, benchmarks, and empirical behavior

The experiments use EURO-CORDEX Central Europe data with eight GCM–RCM pairs: ALADIN63×CNRM-CM5, ALADIN63×MPI-ESM-LR, CCLM4-8-17×CNRM-CM5, CCLM4-8-17×MIROC5, CCLM4-8-17×MPI-ESM-LR, REMO2015×MIROC5, RegCM4-6×CNRM-CM5, and RegCM4-6×MPI-ESM-LR. The temporal coverage is daily data from 1971–2099 under historical + RCP8.5, with leap-day handling to align GCM–RCM calendars. Training uses 1971–2029 and 2040–2089, validation is 10% of train, and testing is split into an “interpolation” regime for 2030–2039 and an “extrapolation” regime for 2090–2099. Inputs are European-domain fields regridded to a regular 2.5° grid covering 40°W–50°E and 25°N–75°N. Additional predictors such as humidity, 500/850 hPa winds, and geopotential were tested but did not improve test loss (Schillinger et al., 30 Sep 2025).

The comparative baselines are deterministic NN (NN-det), EasyUQ, Analogues, WGAN-GP following Harris et al. 2022, CorrDiff, and CorrDiff-s. These baselines emphasize different trade-offs. NN-det is strong for MSE but has no uncertainty and therefore $$\mathrm{Var}^\iota(Y \mid X) = \mathbb{E}^\iota[\mathrm{Var}^\iota(Y \mid Z)\mid X] + \mathrm{Var}^\iota(\mathbb{E}^\iota[Y \mid Z]\mid X),$$6. EasyUQ improves univariate CRPS but breaks spatial and multivariate dependencies. Analogues preserve spatial patterns and variable correlations by construction but are underdispersed in conditional calibration. WGAN-GP performs adequately but underestimates variability and shows blurriness. CorrDiff gives good energy scores and spatial PSDs, while its default sampler yields excessive temporal autocorrelation and limited diversity; CorrDiff-s improves calibration and diversity but reduces temporal dependence (Schillinger et al., 30 Sep 2025).

On the interpolation test averaged across pairs, energy-score results show variable-dependent leadership. For tas, EnScale reports 168.7 versus CorrDiff at 212.5; for pr, EnScale 434.5 versus CorrDiff 414.7; for sfcWind, EnScale 138.4 versus CorrDiff 141.2; and for rsds, EnScale 3478.2 versus CorrDiff 3181.2. CRPS per location places EnScale near-best across variables, with reported values tas 1.20, pr 1.89, sfcWind 0.89, and rsds 24.11, close to CorrDiff. For max-pooled CRPS with patch size $$\mathrm{Var}^\iota(Y \mid X) = \mathbb{E}^\iota[\mathrm{Var}^\iota(Y \mid Z)\mid X] + \mathrm{Var}^\iota(\mathbb{E}^\iota[Y \mid Z]\mid X),$$7, EnScale is among the best and clearly better than EasyUQ, with tas 1.17, pr 4.85, sfcWind 1.09, and rsds 21.56 (Schillinger et al., 30 Sep 2025).

In spatial spectral evaluation, CorrDiff is best by RALSD, with reported examples tas $$\mathrm{Var}^\iota(Y \mid X) = \mathbb{E}^\iota[\mathrm{Var}^\iota(Y \mid Z)\mid X] + \mathrm{Var}^\iota(\mathbb{E}^\iota[Y \mid Z]\mid X),$$8 and sfcWind $$\mathrm{Var}^\iota(Y \mid X) = \mathbb{E}^\iota[\mathrm{Var}^\iota(Y \mid Z)\mid X] + \mathrm{Var}^\iota(\mathbb{E}^\iota[Y \mid Z]\mid X),$$9, while EnScale is second-best or competitive; RALSD-avg confirms the analogues’ spatial fidelity, with EnScale close behind. In calibration, EnScale and EnScale-t are closer to flat rank histograms than CorrDiff or GAN, while analogues are underdispersed. The average miscalibration MCB for locationwise ranks is typically 0.09–0.17 for EnScale, better than CorrDiff. For extremes, locationwise summer 95% quantile errors include pr absolute error $\approx 16.76$0 mm/day for EnScale versus analogues at $\approx 16.76$1, and tas absolute error $\approx 16.76$2C for EnScale versus analogues at $\approx 16.76$3C. Quantile calibration at the 10% and 90% bins is best for EnScale and EnScale-t, and the ECDF+$\approx 16.76$4 transform is specifically reported to allow EnScale to capture zero-precip events that GAN and CorrDiff miss (Schillinger et al., 30 Sep 2025).

Cross-variable structure is another major evaluation category. Reported pairwise correlation errors include pr–sfcWind at 0.044 for EnScale versus 0.166 for EasyUQ, sfcWind–rsds at 0.029, and tas–pr at 0.031. Calibration of differences after marginal standardization to uniform shows EnScale and EnScale-t as best, with MCB $\approx 16.76$5–0.067, while analogues remain underdispersed (Schillinger et al., 30 Sep 2025).

6. Computational profile, limitations, and terminological ambiguity

The reported computational profile is one of EnScale’s defining characteristics. On a single NVIDIA A100 (80 GB), training takes approximately 24 hours for EnScale versus approximately 216 hours for CorrDiff, corresponding to about a tenfold reduction. Inference for generating 100 years with 10 samples per day takes approximately 1.75 hours for EnScale versus approximately 36 hours for CorrDiff, corresponding to about a twentyfold reduction. The model size is approximately 66M parameters for EnScale, compared with CorrDiff’s UNet of approximately 80M used twice, or approximately 160M total. Inference speed is reported to be limited by the inverse data transform; sampling itself can take minutes (Schillinger et al., 30 Sep 2025).

The framework also has explicit limitations. Although the energy score is proper, it is not equally sensitive to all misspecifications, so slight sharpness gains may mask miscalibration. Mild calibration deviations remain, including spatial maxima for some variables. EnScale-t models lag-1 autocorrelation at coarse scales, but local-scale temporal dependence is neglected. The empirical impact is reported as small, yet further improvement could incorporate local autoregression in super-resolution. The training domain and model family are also restricted: Central Europe and eight EURO-CORDEX GCM–RCM pairs. The extrapolation test is described as mild because training extends to 2089, and transfer to unseen GCMs or regions would require retraining and careful validation. Very heavy precipitation remains challenging, and spatial extremes in mountainous regions, especially the Alps, show larger errors. Because EnScale emulates RCMs rather than observations, the reported practical recommendation is to combine it with bias correction methods that preserve multivariate and spatiotemporal structure when “future observations” are required (Schillinger et al., 30 Sep 2025).

The implementation is publicly available at the repository https://github.com/m-schillinger/enscale, with preprocessing scripts and transforms included in the codebase (Schillinger et al., 30 Sep 2025).

A recurrent source of confusion is nomenclature. The name “EnScale” is also used for an unrelated scale-equalization method for multi-level feature fusion in semantic segmentation (Kim et al., 2024), and the term is used in a different sense for a unit-rescaling formalism for numerical simulations (Granot, 2011). A separate telemetry system, “EnclaveScale,” is also abbreviated as “EnScale” in edge-DP data-centre power telemetry (Dang et al., 8 Jun 2026). This suggests that, in technical writing, disambiguation by full title or arXiv identifier is advisable when referring to the climate downscaling framework (Schillinger et al., 30 Sep 2025).