Organizations: Department of Computer Science, The University of Alabama, Tuscaloosa, Alabama, USA · Department of Geography, The University of Alabama, Tuscaloosa, Alabama, USA
High-resolution surface solar radiation (SSR) is important for solar forecasting and grid operation. However, physically consistent reanalysis products are too coarse to resolve localized cloud-driven variability. In this paper, we study a multisource downscaling task that reconstructs high-resolution SolarCube SSR fields from coarse ERA5 radiative variables and co-registered satellite channels. The task is challenging because a single ERA5 grid cell may contain both sunlit and cloud-shadowed regions. As a result, the missing high-resolution correction can be spatially sharp and inherently ambiguous. One-stage predictors often oversmooth these structures. Post-hoc refinement also introduces a stage-wise mismatch: the generator is optimized independently, even though its output determines the refiner's initial state. We introduce SolarFlowRefiner, a refinement-aware flow-matching framework for SSR downscaling. A conditional FlowMatch generator first predicts a normalized correction to an upsampled ERA5 baseline. The refiner is then trained on prediction-conditioned states between the current FlowMatch output and the target residual. This exposes the refiner to the structured errors produced by the generator. The refinement objective is also backpropagated through the FlowMatch sampler, allowing generation and correction to be jointly optimized for the final reconstruction. Experiments on a day-blocked ERA5--SolarCube benchmark show consistent improvements over standalone generation and post-hoc refinement. More broadly, SolarFlowRefiner provides a general strategy for coupling generative predictors with iterative correctors.
Figures & tables
Figure 1: Overview of SolarFlowRefiner. ERA5 radiative variables and SolarCube auxiliary channels condition a FlowMatch residual generator, which predicts an initial normalized residual relative to the upsampled ERA5 SSR baseline. A PDE-style refiner then performs iterative correction updates over K=8 refinement levels before reconstructing the high-resolution SSR field. In SolarFlowRefiner, the refinement loss is backpropagated through both the refiner and the FlowMatch sampler, making generation refinement-aware.
Method
MAE ↓
RMSE ↓
SSIM ↑
LPIPS ↓
FID ↓
Bicubic
137.22
169.61
0.339
0.664
290.15
EDSR
29.53
42.71
0.675
0.187
46.03
RCAN
14.81
24.11
0.724
0.177
44.92
SwinIR
16.71
26.91
0.712
0.183
39.21
HAT
15.25
24.07
0.726
0.171
37.73
ResShift
13.94
20.68
0.725
0.159
36.47
Table 1: Test-set SSR downscaling performance. Lower is better for MAE, RMSE, LPIPS, and FID; higher is better for SSIM. All metrics are computed after reconstructing the physical SSR field from the predicted normalized residual.
Conditioning
MAE ↓
RMSE ↓
SSIM ↑
LPIPS ↓
FID ↓
ERA5 only
21.82
36.21
0.651
0.172
41.90
SolarCube only
17.31
24.70
0.710
0.155
37.10
ERA5 + SolarCube
11.13
17.11
0.827
0.137
36.23
Table 2: SolarFlowRefiner input-channel ablation. The ERA5 SSR baseline is used for residual reconstruction in all settings; the ablation changes only the conditioning channels provided to the learned generator and refiner.
Figure 2: Qualitative SSR reconstruction and error maps for a held-out test sample. The top row shows reconstructed SSR fields for Bicubic/ERA5, deterministic baselines, generative baselines, refinement variants, and the SolarCube ground truth. The bottom row shows the corresponding error maps computed as prediction minus ground truth, with per-sample MAE and RMSE reported below each panel.
Figure 3: Performance gain versus scene complexity. Scene complexity is computed as the mean Sobel gradient magnitude over z-scored SolarCube auxiliary channels vis047 , vis086 , ir133 , and cm . Each gray point is a held-out test sample. Red curves show binned mean MAE gain with standard-error bars, where gain is baseline MAE minus SolarFlowRefiner MAE. Positive values indicate that SolarFlowRefiner has lower error than the baseline.
Appendix figures & tables6 assets
Supplementary material from the paper’s appendix.
Appendix
Split
Samples
Fraction
Train
32,159
70%
Validation
4,519
10%
Test
8,994
20%
Appendix
Table 3: Dataset split used for model selection and final evaluation.
Figure 4: Global distribution of the 12 test tiles/sites. Marker color shows the fraction of test samples at each site for which SolarFlowRefiner has the lowest MAE among the learned comparison models. The right panel expands the North American cluster.
Tile
Code
Station
Region
Latitude
Longitude
Test samples
1
BON
Bondville
Illinois, USA
40.052
-88.373
745
2
FPK
Fort Peck
Montana, USA
48.308
-105.102
746
3
GWN
Goodwin Creek
Mississippi, USA
34.255
-89.873
744
4
DRA
Desert Rock
Nevada, USA
36.624
-116.019
756
5
PSU
Penn State University
Pennsylvania, USA
40.720
-77.931
743
6
SXF
Sioux Falls
South Dakota, USA
43.734
-96.623
736
Appendix
Table 4: Test sites used in the spatial analysis.
Tile
Site
ResShift
FlowMatch
FlowRefiner-ODE
FlowRefiner-PDE
SolarFlowRefiner
1
BON
11.87
12.03
11.62
11.31
10.03
2
FPK
17.31
18.72
19.07
16.45
13.55
3
GWN
10.78
10.22
10.16
10.28
9.19
4
DRA
12.44
12.24
12.56
12.69
10.95
5
PSU
12.53
11.78
11.59
12.43
9.66
6
SXF
17.36
17.56
17.39
16.66
14.35
Appendix
Table 5: Per-site mean MAE in Wm−2 for the learned models. Lower is better.
Figure 5: Qualitative comparison across test sites. Each row shows one sample from a different tile/site, and columns compare ResShift, FlowMatch, FlowRefiner-ODE, FlowRefiner-PDE, SolarFlowRefiner, and the SolarCube ground truth. MAE and RMSE are reported below each reconstruction in physical SSR units; the ground-truth column has zero error by definition.
Baseline
Mean MAE gain
Lower-error samples (%)
p -value
ResShift
2.97
73.5
<10−300
FlowMatch
4.24
66.4
<10−300
FlowRefiner-ODE
4.11
63.6
3.23×10−304
FlowRefiner-PDE
2.63
69.0
<10−300
Appendix
Table 6: Paired Wilcoxon signed-rank tests comparing per-sample MAE between each learned baseline and SolarFlowRefiner on the 8,994 held-out test samples.
Decisions about heat, frost and flooding are made locally, yet reanalyses and climate models resolve tens of kilometres. Generative downscalers add kilometre-scale detail with uncertainty, but are tied to a grid, costly to sample and lack a tractable likelihood. Here we introduce CD-FFM, a functional flow-matching model that treats the high-resolution field as a continuous random field that one model can query at any location and resolution. Its velocity acts pointwise, so spatial variability comes from a noise prior fitted to the observed spectrum and every observation has an exact likelihood. Downscaling ERA5 to 1 km daily temperature over Fennoscandia, CD-FFM lowers the continuous ranked probability score by 27-31% against regression and 12-18% against a forty-times larger neural operator in each of three test years, and outperforms a CorrDiff-style diffusion model while sampling about fifty times faster. The same model transfers to precipitation and makes large kilometre-scale ensembles affordable.
Zhi-Song Liu, Helmi Toropainen, Ammar Kheder +1
Department of Computational Engineering, LUT University, Lappeenranta, Finland. · Institute for Atmospheric and Earth System Research (INAR), University of Helsinki, Helsinki, Finland. · Atmospheric Modelling Center, Lahti (AMC-Lahti), Lahti, Finland.
Fine-resolution precipitation estimates support flood risk assessment and water management, but coarse satellite products cannot resolve rainfall within each grid cell. Generative models address this ambiguity by producing ensembles of plausible high-resolution rainfall fields. Among these models, rectified flows generate samples by iteratively transforming random noise into rainfall fields. Reducing the number of sampling steps accelerates generation but can make ensemble members too similar, understating uncertainty. We propose a scale-recursive rectified flow that generates broad patterns before local details and guides sampling-step allocation by comparing ensemble variability with prediction error across spatial scales. Validation scores and rainfall power spectra constrain the allocation to avoid excessive amplification. In satellite-to-radar downscaling over the contiguous United States, our analysis identified broad rainfall patterns as the main source of insufficient ensemble variability under reduced sampling budgets. Allocating more steps to the coarse flow improved probabilistic accuracy and rain detection across training seeds at fixed architecture and computational cost. The proposed model also achieved better probabilistic accuracy with shorter sampling time than a nonrecursive flow using more steps.
Generative machine learning is an increasingly important complement to dynamical downscaling for producing high-resolution precipitation projections, with diffusion models currently the leading approach. Flow matching is a related generative framework that has recently achieved strong results across image, video and other domains, and shown early promise for downscaling. We train a flow matching model to map daily precipitation from 8 km to 2 km over a convective-scale domain centred on Singapore, and benchmark it against CPMGEM, a score-based diffusion model. Flow matching achieves consistently better spatial skill: higher fractions skill score at every precipitation threshold and neighbourhood scale tested, and tighter structure and amplitude components of the SAL score with comparable location skill. However, flow matching underestimates the upper tail of the precipitation distribution, resulting in a dry bias in the climatological mean. These results suggest that flow matching is a competitive generative framework for convective-scale precipitation downscaling, particularly well suited to capturing spatial structure.