physics.ao-phSep 15, 2026

Efficient Analog-Initialized Latent Transport for Spatially Coherent Probabilistic Downscaling from Global to Kilometer Scales

Authors: Ophélia Miralles

Organizations: Norwegian Meteorological Institute, Oslo, Norway

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Abstract

Probabilistic downscaling must represent kilometer-scale structure left unresolved by a deterministic regional prediction. We introduce an analog-initialized latent transport method that uses historical regional residuals as a meteorologically informed empirical source. A frozen graph neural network predicts the deterministic state from the Integrated Forecasting System (IFS). For each input, residuals from 20 training dates with similar IFS conditions initialize the ensemble. A conditional flow-matching model transports these fields in a carefully designed 65-factor, 100,000-node latent space, and a grid decoder reconstructs 81 atmospheric channels including precipitation at 2.5km spacing. On a season- and cycle-balanced 2025 test, ensemble CRPS improves over deterministic mean absolute error for all 81 variables. Matched analogs improve point and spatial errors over Gaussian initialization and reduce spectral error compared with covariance matching. Comparisons with released CorrDiff, a local CorrDiff-mini model and full grid EDM provide context on the 2023 validation sample. Total training of the downscaling model takes approximately 12h on one NVIDIA H200, and inference takes about 12s per 81-field member. The frozen networks also generate fields over France when supplied with local static data and a high-resolution IFS-derived analog bank. The method combines empirical initialization with whole-domain latent transport for computationally practical regional ensembles.

Figures & tables

Figure 1: The complete analog-initialized latent transport system. At inference (solid arrows), the current N320 IFS state and regional static data first produce a deterministic downscaled field. A 32-component description of the same IFS state is used to find similar training dates and draw 20 distinct analog residuals. Each residual is evolved in the 65-factor, 100,000-node latent space using 20 Heun updates, then the latent-to-grid decoder reconstructs and adds the stochastic correction. Dashed arrows show regional targets used to form training residuals and fit the transport and decoder. Precipitation follows the same logic through a separate transformed path. The diagram uses μ(x,s)\mu(x,s) for Dθ(x,s)D_{\theta}(x,s) and cc for the conditioning features c(x)c(x) .
Figure 2: Triangular meshes with a progressively increasing number of nodes from left to right, covering the Nordic regional domain. Nested refinement inserts centroids of the largest interior Delaunay triangles.
Figure 3: Schematic illustration of analog selection. The current N320 IFS state (star) is compared with 1,000 archived training states (grey) using Euclidean distance in the 32-dimensional whitened similarity space. The 64 closest dates form the candidate pool (green), and 20 different dates are drawn uniformly for the ensemble; four draws are outlined in orange. Each draw supplies the complete regional residual from one past date, including all 65 factors. Only two axes are used here to visualize the 32-dimensional search.
Figure 4: Source distribution ablation results on 32 test cases with 20 members. Bars are control error minus matched-analog-transport error; positive values favour matched analog transport.
Figure 5: Six-hour precipitation at 1800 UTC 1 March 2025, in millimetres (left) and surface temperature in Kelvin on 3 October 2025 (right).
Figure 6: Six-hour precipitation verification on the 96-case 2025 test. Left: occurrence reliability at 0.1 mm, comparing forecast probability with observed frequency. Right: quantile–quantile diagnostics for all amounts and conditional positive amounts. Diagonals denote agreement. Occurrence reliability and marginal amount distributions assess different aspects of the ensemble.
Figure 7: Six-hour precipitation spectra (left) and variograms (right).
Figure 8: 10-m zonal wind at 1200 UTC 7 November 2023, in m s -1 . The upper row shows the N320 IFS input and MEPS target; the lower row compares member 1 from the analog transport model, CorrDiff ( NVIDIA, 2026 ) and the full grid EDM. CorrDiff is plotted within its available coverage, with the same approximately 6-km native output used in the quantitative comparison.
FieldRMSE reduction (%) [95% CI]Spectrum-error reduction (%)
2-m temperature16.1 [11.1, 20.8]34.7
10-m zonal wind12.3 [9.1, 15.3]42.2
10-m meridional wind14.7 [11.7, 17.6]44.3
10-m wind speed−1.3-1.3 [ −4.0-4.0 , 1.4]36.7
Table 1: Paired relative errors of the analog transport model against the released NVIDIA COSMO-REA6 CorrDiff checkpoint ( NVIDIA, 2026 ) ; positive values favour the analog transport model. Member 1 is scored on 50 October–December 2023 validation dates.
Figure 9: Spatial dependence and scale content over the Nordic domain over 50 validation dates, using member 1 from each method. Left: aggregate variograms; right: anomaly power spectra. Black curves denote MEPS; blue, green and orange denote the analog transport model, CorrDiff ( NVIDIA, 2026 ) and full grid EDM. Shading shows 95% case-bootstrap intervals.
Figure 10: Contextual intercomparison on 50 validation cases. Positive values favour analog transport. Bars show relative error reductions; whiskers show paired 95% case-bootstrap intervals. Field labels are 2-m temperature (2t), dew point (2d), 10-m wind components (10u, 10v), total column water (tcw) and six-hour precipitation (tp).
Selected training stagesH200 wall time
Deterministic downscaler2 h 02 min
Atmospheric transport3 h 31 min
Grid decoder4 h 26 min
Precipitation transport2 h 15 min
Selected-stage total12 h 14 min
Table 2: Training wall times for the selected model chain on one H200.
ModelTrainingH200 inferenceNative outputs
Analog transport12 h 14 min (H200)12.3 s per member80 atmospheric fields + precipitation
Released CorrDiffUnreportedabout 5.8 s per sample45 fields
CorrDiff Taiwan≈21,500\approx 21{,}500 H100 GPU-hUnreported4 fields
Full grid EDM≈60,000\approx 60{,}000 GPU-h30–60 s per timestamp16 surface fields
Table 3: Training and inference budgets with each system’s native output scope. Analog transport and released CorrDiff inference were measured on H200; full grid EDM figures were communicated to the author.
Figure 11: France-centred 2-m temperature for the frozen-weight execution example, in kelvin. Panels show N320 IFS input, the deterministic downscaler and a generated field. The system uses Nordic-trained weights, France-specific static fields and an O1280-derived historical source bank. The common colour scale shows the deterministic contribution and the additional generated structure.
Selected networkUpdatesPeak learning rateWarm-up updates
Deterministic downscaler10,0006.25×10−56.25\times 10^{-5}1,000
Atmospheric transport3,0001.5×10−51.5\times 10^{-5}100
Precipitation transport10,0005×10−55\times 10^{-5}500
Table 4: Optimization schedules for the selected system. Learning rates follow cosine decay to 3×10−73\times 10^{-7} after warm-up. The source distribution controls use the separate 10,000-update protocol described in Section 3.3 .
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