Generative Atmospheric Super-Resolution from Heterogeneous In Situ Observations through Composable Interfaces

Yang Xu; Dibyajyoti Chakraborty; Haiwen Guan; Sen Wang; Romit Maulik

cs.LGSep 24, 2026

Generative Atmospheric Super-Resolution from Heterogeneous In Situ Observations through Composable Interfaces

Authors: Yang Xu, Dibyajyoti Chakraborty, Haiwen Guan, Sen Wang, Romit Maulik

Organizations: School of Mechanical Engineering, Purdue University, West Lafayette, Indiana, USA · College of Information Sciences and Technology, The Pennsylvania State University, University Park, Pennsylvania, USA

Abstract

Atmospheric observations are sparse, heterogeneous, and unevenly distributed, whereas many generative atmospheric models learn distributions over regularly gridded multivariate states. Once pretrained, diffusion models can supply atmospheric priors that can be combined with observation-derived likelihood factors in a Bayesian formulation. However, these observation sources differ substantially in geometry and sampling density, complicating the consistent use of their observations within a common inference framework. Here, we formulate this reconstruction problem as generative atmospheric super-resolution and introduce composable observation interfaces for conditioning a single pretrained 13-variable atmospheric diffusion model. The interfaces convert sparse radiosonde (R), clustered aircraft (A), and dense irregular surface-station (S) observations into source-specific likelihood factors that specify where observations constrain the gridded state, how residuals are counted under uneven sampling, and how strongly each source guides posterior sampling. We developed the aircraft and surface observation interfaces using 2019 observations and evaluated the selected interfaces throughout 2020 without further tuning. Compared with reconstructions conditioned only on radiosonde observations, the composed R+A+S interface reduces RMSE evaluated against ERA5 by $9.24\%$ across all 13 state variables over the CONUS domain. The aircraft and surface factors provide complementary improvements in upper-air and surface variables. The R+A+S combination also lowers the Continuous Ranked Probability Score (CRPS), while evaluations at held-out aircraft and surface-station observations show reduced prediction errors. Together, these results demonstrate a modular route for conditioning a pretrained atmospheric generative prior on heterogeneous in situ observations without retraining the underlying model.

Figures & tables

Panel of Figure 1 — Figure 1: Observation sources, evaluated source combinations, and evaluation groups used throughout the study. The surface-targeted group and upper-air temperature and wind group contain the state variables directly constrained by S and A, respectively.

Symbol	Meaning
$\mathcal{M}$ , $\mathcal{K}$	Observation-source and state-variable index sets.
$\mathbf{x}_{0}$ , $\mathbf{x}_{\sigma}$	Clean standardized state and its noise-level- $\sigma$ counterpart.
$\mathbf{x}_{i}$ , $\widehat{\mathbf{x}}_{0,i}$	Current noisy sampler state and denoised clean-state estimate at reverse step $i$ .
$\sigma$ , $\sigma_{i}$	Generic diffusion-noise level and its value at reverse step $i$ .
$\mathbf{y}_{m}$ , $H_{m}$ , $W_{m}$	Final likelihood targets, observation operator, and residual-counting weights for source $m\in\mathcal{M}$ .
$\lambda_{m}$ , $v_{m}(\sigma)$	Likelihood weight and noise-dependent variance term for source $m$ .

Table 1: Core inference and observation-interface notation. Atmospheric states and sampler variables have shape

13\times 128\times 256

; for source

m

\mathbf{y}_{m}\in\mathbb{R}^{N_{m}}

H_{m}:\mathbb{R}^{13\cdot 128\cdot 256}\rightarrow\mathbb{R}^{N_{m}}

, and

W_{m}\in\mathbb{R}^{N_{m}\times N_{m}}

Figure 2: Annual spatial distributions of (a) IGRA radiosonde profiles (R), (b) MADIS ABO aircraft reports (A), and (c) MADIS METAR surface-station reports (S) during 2020 at 00/12 UTC. For visualization, observations are grouped into common latitude–longitude bins of

0.5^{\circ}\times 0.5^{\circ}

, and all panels use the same color scale. For R, each station profile available at an analysis time contributes one count to its bin; for A and S, each report contributes one count. Dashed boxes mark the CONUS domain used for A and S.

Source	Product and sampling geometry	Variables	Spatial domain
Radiosonde (R)	IGRA sparse vertical profiles	$t2m$ , $u10$ , $v10$ , $t500$ , $u500$ , $v500$ , $z500$ , $q500$ , $t850$ , $u850$ , $v850$ , $z850$ , $q850$	Global
Aircraft (A)	MADIS ABO reports clustered along flight routes	$t500$ , $u500$ , $v500$ , $t850$ , $u850$ , $v850$	CONUS domain
Surface station (S)	MADIS METAR surface stations	$t2m$ , $u10$ , $v10$	CONUS domain

Table 2: Observation sources, sampling geometry, target variables, and spatial domains used in this study.

Figure 3: Equal-cell construction illustrated with retained 850-hPa aircraft temperature reports near Chicago. Blue points show individual reports, shaded rectangles show occupied model-grid cells, and orange squares show the associated grid points. The label

n_{a}

gives the number of reports averaged to form the cell-mean target

\bar{y}_{a}

. Stars mark airport locations. Each occupied cell contributes one residual regardless of the number of reports it contains.

Panel of Figure 4 — Figure 4: DPS conditioning with composable observation interfaces. Each source defines its retained targets, state mapping, and residual-counting rule. The resulting likelihood gradients are mapped through the shared denoiser, combined, clipped, and applied as a correction to the reverse-solver update.

Source	Retained observations	Constrained variables	State mapping and residual counting	Likelihood parameters
Radiosonde (R)	IGRA profiles	$t2m$ , $u10$ , $v10$ , $t500$ , $u500$ , $v500$ , $z500$ , $q500$ , $t850$ , $u850$ , $v850$ , $z850$ , $q850$	bilinear interpolation; equal target and channel weights	$\lambda_{\mathrm{R}}=1.0$ $\mathrm{std}_{\mathrm{R}}=5\times 10^{-4}$ $\gamma_{\mathrm{R}}=2\times 10^{-6}$
Aircraft (A)	MADIS ABO reports from ACARS direct, MDCRS/ARINC, and Canadian AMDAR; ${\pm}25$ -hPa windows	$t500$ , $u500$ , $v500$ , $t850$ , $u850$ , $v850$	cell means; equal cell and channel weights	$\lambda_{\mathrm{A}}=0.4$ $\mathrm{std}_{\mathrm{A}}=5\times 10^{-4}$ $\gamma_{\mathrm{A}}=2\times 10^{-5}$
Surface station (S)	MADIS METAR reports	$t2m$ , $u10$ , $v10$	cell means; equal cell and channel weights	$\lambda_{\mathrm{S}}=0.4$ $\mathrm{std}_{\mathrm{S}}=1.25\times 10^{-4}$ $\gamma_{\mathrm{S}}=4\times 10^{-5}$

Table 3: Observation-interface designs and likelihood parameters used in the 2020 evaluation. The R settings are inherited from the previous study, while the A and S settings are selected using the 2019 development cases.

CONUS domain
Conditioning	All 13	Surface-targeted	Upper-air temperature and wind
R+A	$-4.46\%$	$-2.28\%$	$-6.74\%$
R+S	$-5.35\%$	$-13.31\%$	$-2.99\%$
R+A+S	$\mathbf{-9.24\%}$	$\mathbf{-14.17\%}$	$\mathbf{-9.30\%}$
Global
R+A	$+0.006\%$	$-0.018\%$	$-0.002\%$

Table 4: Grouped mean RMSE changes

\overline{\Delta}_{G,\mathcal{K}^{\prime}}^{P}

over 723 matched 2020 analysis times. RMSE is evaluated against ERA5, and changes are relative to R-only conditioning; negative values indicate lower RMSE.

Figure 5: Grouped mean RMSE changes $\overline{\Delta}_{G,\mathcal{K}^{\prime}}^{P}$ over the CONUS domain for R+A, R+S, and R+A+S relative to R-only conditioning across 723 matched analysis times. Negative values indicate lower RMSE.

Figure 6: Per-variable mean RMSE changes

\Delta_{k,G}^{P}

for R+A, R+S, and R+A+S over the CONUS domain. Values are averaged over 723 matched 2020 analysis times. Negative values indicate lower RMSE relative to R-only conditioning.

Figure 7: Selected 2020 analysis time for $t2m$ over the CONUS domain: (a) R-only ensemble mean, (b) R+A+S ensemble mean, (c) ERA5, (d) R-only absolute error, (e) R+A+S absolute error, and (f) their difference, R+A+S minus R-only. Panels (d) and (e) share a color scale capped at their pooled 97.5th percentile; blue and red indicate lower and higher absolute error, respectively. Panel (f) uses a symmetric scale capped at the 97.5th percentile of the absolute changes; blue indicates an error reduction and red an error increase. RMSE decreases from $1.94$ to $1.29$ K.

Figure 8: Selected 2020 analysis time for $v500$ over the CONUS domain for the same case and panel layout as Figure 7 . RMSE decreases from $3.69$ to $2.78\,\mathrm{m\,s^{-1}}$ .

Region	Variable group	$\overline{\Delta}_{G,\mathcal{K}^{\prime}}^{\mathrm{R+A+S}}$ (%)	95% interval (%)
CONUS domain	All 13 variables	$\mathbf{-9.236}$	$\mathbf{[-9.566,-8.918]}$
	Surface-targeted	$\mathbf{-14.173}$	$\mathbf{[-14.759,-13.566]}$
	Upper-air temperature and wind	$\mathbf{-9.301}$	$\mathbf{[-9.825,-8.799]}$
Global	All 13 variables	$-0.0353$	$[-0.0618,-0.0083]$
	Surface-targeted	$-0.1457$	$[-0.1847,-0.1069]$
	Upper-air temperature and wind	$-0.0152$	$[-0.0380,0.0080]$

Table 5: Grouped mean RMSE changes

\overline{\Delta}_{G,\mathcal{K}^{\prime}}^{\mathrm{R+A+S}}

and 95% intervals from the 14-day moving-block bootstrap. Negative values indicate lower RMSE relative to R-only conditioning.

Evaluated source	Conditioning comparison	Mean change	95% interval	Lower-RMSE cases
Surface station (S)	Retained 80% of S added to R+A	$-13.50\%$	$[-14.68,-12.35]\%$	$24/24$
Aircraft (A)	Retained 80% of A added to R+S	$-11.71\%$	$[-14.48,-9.00]\%$	$23/24$

Table 6: RMSE changes at 2020 CONUS observations excluded from conditioning across 24 seasonally distributed analysis times. For each source, 80% of the targets are retained for conditioning and the remaining 20% are used for evaluation. Intervals are 95% paired-analysis-time bootstrap intervals.

Figure 9: RMSE changes at CONUS observations excluded from conditioning across 24 seasonally distributed 2020 analysis times. Panel (a) reports source-level means when the retained 80% of S is added to R+A and the retained 80% of A is added to R+S; panels (b) and (c) report variable-specific changes. Error bars show 95% paired-analysis-time bootstrap intervals, and negative values indicate lower RMSE.

Variable group	RMSE change	CRPS change [95% interval]
All 13 variables	$-9.24\%$	$-9.98\%\;[-10.40,-9.57]$
Surface-targeted variables	$-14.17\%$	$-15.01\%\;[-15.75,-14.27]$
Upper-air temperature and wind variables	$-9.30\%$	$-10.45\%\;[-11.11,-9.83]$

Table 7: Grouped mean percentage changes in ensemble-mean RMSE and empirical CRPS over the CONUS domain for R+A+S relative to R-only conditioning, evaluated with 16-member ensembles at 723 matched 2020 analysis times. Both scores are evaluated against ERA5. Brackets give 95% intervals for the CRPS changes from the 14-day moving-block bootstrap.

Figure 10: Source-specific clean-state likelihood-gradient geometry for one 2020 case before denoiser-Jacobian pullback. Panel (a) shows the fraction of each source’s full-grid squared gradient norm in each variable group. Panel (b) shows pairwise cosine similarity over the CONUS domain for all 13 variables and for the surface-targeted group and upper-air temperature and wind group. N/A indicates that at least one projected gradient has zero norm over the selected variable subset, so the cosine similarity is undefined.

Figure 11: Runtime interaction of the source-specific likelihood gradients along one reverse trajectory. Panel (a) shows their pairwise cosine similarities over the CONUS domain after denoiser-Jacobian pullback. Panel (b) shows each source’s raw-guidance norm as a fraction of the sum of the three norms over all 13 variables on the global model grid. Both diagnostics are computed before the shared summation and clipping operation.

Figure 12: Spatial norms of the source-specific raw runtime guidance along the selected reverse trajectory. Columns show radiosonde (R), aircraft (A), and surface-station (S) contributions, and rows show the first, middle, and final reverse steps. All panels use the same logarithmic color scale, with values at or below $3\times 10^{-3}$ shown in white and the upper limit set by the pooled 99.9th percentile. Dashed rectangles mark the CONUS domain. The norms are computed before the shared summation and clipping operation.

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 13: Monthly mean of the per-analysis-time RMSE between retained MADIS METAR surface-station observations and the corresponding ERA5 values over the CONUS domain: (a) $t2m$ and (b) $u10$ and $v10$ . The observations satisfy the $\pm 60$ -minute temporal-matching, quality-control, and physical-range criteria.

Figure 14: Monthly mean of the per-analysis-time RMSE between retained MADIS ABO aircraft observations and the corresponding ERA5 values over the CONUS domain: (a) $t500$ and $t850$ and (b) $u500$ , $u850$ , $v500$ , and $v850$ . The observations satisfy the final reporting-system selection, quality-control criteria, and $\pm 25$ -hPa pressure-level matching.

Development stage	Candidates compared	Selection criterion	Selected result
A interface design	24 combinations of reporting systems, pressure-matching windows, and residual representations	Mean RMSE changes across all 13 variables and across the upper-air temperature and wind variables	ACARS direct, MDCRS/ARINC, and Canadian AMDAR; ${\pm}25$ -hPa windows; equal-cell mean residuals
S interface design	3 residual representations	Mean RMSE changes across all 13 variables and across the surface-targeted variables	Equal-cell mean residuals
A likelihood parameters	Staged parameter comparisons using R+A	RMSE across the upper-air temperature and wind variables and across all 13 variables	$\lambda_{\mathrm{A}}=0.4$ $\mathrm{std}_{\mathrm{A}}=5\times 10^{-4}$ $\gamma_{\mathrm{A}}=2\times 10^{-5}$
S likelihood parameters	Staged parameter comparisons using R+S	Surface-targeted and all-variable RMSE	$\lambda_{\mathrm{S}}=0.4$ $\mathrm{std}_{\mathrm{S}}=1.25\times 10^{-4}$ $\gamma_{\mathrm{S}}=4\times 10^{-5}$
R+A+S selection	9 combinations of candidate A and S likelihood-parameter settings	Mean RMSE change across all 13 variables as the primary score, with the surface-targeted group and the upper-air temperature and wind group as secondary checks	The selected A and S settings above are combined, producing an $11.961\%$ mean RMSE reduction across all 13 variables in 2019

Appendix

Table 8: Summary of the three stages used to select the A and S interface designs and likelihood parameters from the 24 prespecified 2019 development cases. All reported RMSE changes are computed against ERA5 and relative to R-only conditioning.

Figure 15: Aircraft interface-design comparison using the 24 prespecified 2019 development cases. Rows compare all candidate reporting systems, all systems except TAMDAR, and the selected ACARS direct, MDCRS/ARINC, and Canadian AMDAR systems, each with $\pm 5$ - or $\pm 25$ -hPa pressure-level matching. Columns compare four residual representations. Values are mean all-variable RMSE changes relative to R-only conditioning under the same pre-calibration likelihood parameters. Negative values indicate lower RMSE. The selected design combines the selected reporting systems, $\pm 25$ -hPa matching, and equal-cell mean residuals.

Figure 16: Surface-station residual-representation comparison using the same 24 prespecified 2019 development cases and common pre-calibration likelihood parameters. The paired bars show the mean RMSE changes across all 13 variables and across the surface-targeted variables. Negative values indicate lower RMSE relative to R-only conditioning. Equal-cell mean residuals produce the largest reduction for both variable groups and are retained in the final S interface.

Variable	Unit	R-only RMSE	R+A+S RMSE
$t2m$	$\mathrm{K}$	1.725	1.380
$u10$	$\mathrm{m\,s^{-1}}$	1.605	1.414
$v10$	$\mathrm{m\,s^{-1}}$	1.697	1.507
$z500$	$\mathrm{m^{2}\,s^{-2}}$	112.4	101.8
$z850$	$\mathrm{m^{2}\,s^{-2}}$	84.5	76.1
$u500$	$\mathrm{m\,s^{-1}}$	2.912	2.618

Appendix

Table 9: Physical-unit annual-mean RMSE against ERA5 over the CONUS domain across 723 matched analysis times. Humidity RMSE is shown in

10^{-3}\,\mathrm{kg\,kg^{-1}}

Variable	$\Delta_{k,G}^{\mathrm{R+A+S}}$ (%)	95% interval (%)	Variable	$\Delta_{k,G}^{\mathrm{R+A+S}}$ (%)	95% interval (%)
$t2m$	$-19.686$	$[-20.452,-18.901]$	$u10$	$-11.760$	$[-12.606,-10.929]$
$v10$	$-11.072$	$[-11.913,-10.211]$	$z500$	$-9.017$	$[-10.112,-7.869]$
$z850$	$-9.602$	$[-10.291,-8.876]$	$u500$	$-9.940$	$[-10.734,-9.199]$
$u850$	$-10.124$	$[-10.595,-9.667]$	$v500$	$-11.099$	$[-11.950,-10.256]$
$v850$	$-9.805$	$[-10.319,-9.269]$	$t500$	$-3.930$	$[-5.115,-2.745]$
$t850$	$-10.905$	$[-11.488,-10.311]$	$q500$	$-1.392$	$[-1.602,-1.191]$

Appendix

Table 10: Per-variable mean RMSE changes

\Delta_{k,G}^{\mathrm{R+A+S}}

over the CONUS domain. The 95% intervals are computed using the 14-day moving-block bootstrap. Negative values indicate lower RMSE relative to R-only conditioning.

Figure 17: Per-variable mean RMSE changes

\Delta_{k,G}^{\mathrm{R+A+S}}

over the CONUS domain, with 95% intervals from the 14-day moving-block bootstrap. Negative values indicate lower RMSE relative to R-only conditioning.

Figure 18: Spatial spectra over the CONUS domain at 723 analysis times. Panels (a)–(c) show mean normalized power fractions for a surface-targeted variable, an upper-air wind variable, and a variable not directly constrained by A or S. Panels (d)–(f) show the corresponding ratios to ERA5.

Figure 19: Full-year probabilistic diagnostics over the CONUS domain for R-only and R+A+S conditioning: (a) changes in CRPS and ensemble-mean RMSE relative to R-only conditioning and (b) empirical coverage of the 5th–95th percentile ensemble interval.

Figure 20: Ensemble-dispersion diagnostics over the CONUS domain at 723 matched 2020 analysis times: (a) finite-ensemble-corrected spread–skill ratios and (b) all-variable rank frequencies normalized by the frequency expected under a uniform rank distribution.

Variable	R-only	R+A+S	Variable	R-only	R+A+S
$t2m$	0.721	0.793	$u500$	0.752	0.768
$u10$	0.667	0.664	$u850$	0.701	0.709
$v10$	0.642	0.631	$v500$	0.704	0.724
$z500$	0.577	0.639	$v850$	0.677	0.678
$z850$	0.613	0.680	$t500$	0.856	0.858
$q500$	0.679	0.682	$t850$	0.734	0.777

Appendix

Table 11: Finite-ensemble-corrected spread–skill ratios by state variable over the CONUS domain at 723 matched 2020 analysis times.

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Operational weather prediction at kilometer scales remains computationally prohibitive for traditional numerical weather prediction (NWP) models, limiting forecast access for applications in energy, agriculture, and disaster management that require fine-grained spatiotemporal detail. Here we introduce AirCast-SR, a foundation model for atmospheric super-resolution that downscales global AI weather forecasts from 0.25 degree (~28 km) to 1 km horizontal resolution at hourly temporal resolution, producing 67-hour forecasts of eight coupled surface variables simultaneously. EarthMind-SR employs a three-dimensional U-Net conditioned within a Latent Consistency Model (LCM) diffusion framework, trained on patch-based samples over the contiguous United States (CONUS) using GraphCast forecasts as input and NOAA's Analysis of Record for Calibration (AORC) as the target. The model achieves near-zero bias across all variables and lead times, and its radial power spectral density analysis demonstrates preservation of fine-scale atmospheric structure at wavelengths of 10 km to 100 km where coarser models lose spectral power. We validate EarthMind-SR across three CONUS case studies spanning winter, summer, and spring seasons, and demonstrate zero-shot global transferability over India and Germany using independent surface station observations without any retraining or fine-tuning. As an open-weights foundation model, EarthMind-SR establishes a new paradigm for kilometer-scale AI weather prediction and provides a platform for regional fine-tuning, distillation, and downstream applications in climate services and hazard forecasting.

Abstract

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