SolarFlowRefiner: Refinement-Aware Flow Matching for Surface Solar Radiation Downscaling

Udbhav Srivastava; Antonita Racheal; Yiheng Chen; Runlong Yu; Xinyue Ye

cs.LGAug 21, 2026

SolarFlowRefiner: Refinement-Aware Flow Matching for Surface Solar Radiation Downscaling

Authors: Udbhav Srivastava, Antonita Racheal, Yiheng Chen, Runlong Yu, Xinyue Ye

Organizations: Department of Computer Science, The University of Alabama, Tuscaloosa, Alabama, USA · Department of Geography, The University of Alabama, Tuscaloosa, Alabama, USA

Abstract

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 $\downarrow$	RMSE $\downarrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$
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 $\downarrow$	RMSE $\downarrow$	SSIM $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$
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

\mathrm{W\,m^{-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	$3.23\times 10^{-304}$
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.

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