Beyond Pointwise Error: A Multi-Metric Evaluation of Spatial Climate Downscaling

Loys Masquelier; Etienne Le Naour

cs.LGOct 1, 2026

Beyond Pointwise Error: A Multi-Metric Evaluation of Spatial Climate Downscaling

Authors: Loys Masquelier, Etienne Le Naour

Organizations: EDF R&D, Palaiseau, France

Abstract

Climate downscaling aims to reconstruct fine scale spatial fields from coarse resolution inputs. Evaluating the quality of these reconstructions is challenging: low pointwise error can come at the cost of fine scale variability, while realistic spatial variability can be achieved with inaccurate local structures. The evaluation metric can therefore change which method appears to perform best. This work presents a multi metric benchmark comparing five spatial downscaling methods on ERA5 temperature, wind, and precipitation fields. Five criteria assess complementary properties: pointwise error, structural similarity, distribution error, spectral error, and gradient error. The results reveal a systematic trade off between spatial fidelity and fine scale variability. Some methods perform best on pointwise and spatially aligned metrics, but lose high frequency content, while others preserve substantially more spectral variability at the cost of less accurately positioned local structures. Consequently, method rankings change across metrics and variables. These results show that there is no single best downscaling method. Multi metric evaluation is therefore essential for assessing which properties of a climate field are preserved.

Figures & tables

Figure 1: Reconstructions of the same tas field from a common coarse-resolution input. The methods trade off spatial fidelity against fine-scale variability.

Variable	$1-\rho_{1}$	$1-\rho_{1}$ ( $\times$ tas)	MAE U-Net	MAE ( $\times$ tas)
tas	0.011	1.00	0.040	1.00
u10	0.019	1.72	0.068	1.70
v10	0.020	1.79	0.079	1.98
pr	0.045	4.11	0.163	4.08

Table 1: Roughness of the fields (

1-\rho_{1}

) and U-Net MAE, in absolute value and relative to tas .

Panel of Figure 2 — Figure 2: Performance on each metric, normalised score (“best $=1$ ”). The ranking of downscaling methods depends strongly on the property being evaluated. U-Net dominates spatially aligned metrics, whereas SE-OT and CLR dominate spectral fidelity.

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Variable	Metric	U-Net	INR-SR	SE-OT	CLR	Interp
tas	MAE	1.00	0.36	0.49	0.43	0.25
	SSIM	1.00	0.24	0.64	0.66	0.08
	Wass.	1.00	0.17	0.31	0.22	0.25
	Spec.	0.49	0.43	1.00	0.98	0.13
	Grad.	1.00	0.42	0.77	0.75	0.28
u10	MAE	1.00	0.61	0.42	0.40	0.34

Appendix

Table 2: Numerical values of Figure 2 : normalised scores (“best

=1

”)

Type	U-Net	INR-SR	SE-OT	CLR	Interp
tas	0.040 $\pm$ 0.051	0.112 $\pm$ 0.127	0.083 $\pm$ 0.074	0.094 $\pm$ 0.086	0.159 $\pm$ 0.202
u10	0.068 $\pm$ 0.081	0.112 $\pm$ 0.127	0.164 $\pm$ 0.161	0.172 $\pm$ 0.172	0.200 $\pm$ 0.224
v10	0.079 $\pm$ 0.108	0.126 $\pm$ 0.152	0.181 $\pm$ 0.180	0.188 $\pm$ 0.188	0.210 $\pm$ 0.251
u10-v10	0.070 $\pm$ 0.088	0.106 $\pm$ 0.115	0.192 $\pm$ 0.189	0.198 $\pm$ 0.200	0.205 $\pm$ 0.238
pr	0.163 $\pm$ 0.387	0.209 $\pm$ 0.467	0.273 $\pm$ 0.533	0.280 $\pm$ 0.498	0.213 $\pm$ 0.467

Appendix

Table 3: Normalised MAE, mean

\pm

standard deviation - smaller is better.

Type	U-Net	INR-SR	SE-OT	CLR	Interp
tas	0.987	0.945	0.979	0.980	0.832
u10	0.945	0.883	0.821	0.829	0.750
v10	0.939	0.883	0.811	0.819	0.755
u10-v10	0.951	0.904	0.804	0.810	0.761
pr	0.942	0.920	0.871	0.875	0.914

Appendix

Table 4: SSIM - larger is better.

Type	U-Net	INR-SR	SE-OT	CLR	Interp
tas	0.0819	0.478	0.262	0.376	0.324
u10	0.0626	0.170	0.270	0.342	0.219
v10	0.0642	0.165	0.258	0.334	0.210
u10-v10	0.0649	0.137	0.334	0.390	0.214
pr	0.000270	0.000553	0.000642	0.000790	0.000446

Appendix

Table 5: Wasserstein distance - smaller is better.

Type	U-Net	INR-SR	SE-OT	CLR	Interp
tas	32.2	36.0	15.7	16.0	117.8
u10	40.2	39.6	30.8	30.2	119.1
v10	45.5	50.8	31.6	33.0	123.1
u10-v10	43.6	46.5	32.2	32.0	121.1
pr	209.6	211.4	93.6	98.8	335.8

Appendix

Table 6: Spectral error - smaller is better.

Type	U-Net	INR-SR	SE-OT	CLR	Interp
tas	1.090	2.574	1.417	1.445	3.895
u10	0.844	1.210	1.368	1.344	2.192
v10	0.862	1.179	1.302	1.279	1.900
u10-v10	0.818	1.104	1.348	1.328	2.046
pr	0.00326	0.00397	0.00415	0.00394	0.00389

Appendix

Table 7: Gradient error - smaller is better.

Variable	U-Net	INR-SR	SE-OT	CLR	Interp	$1-\rho_{1}$
	MAE ( $\times$ tas)					Roughness ( $\times$ tas)
tas	1.00	1.00	1.00	1.00	1.00	1.00
u10	1.69	1.00	1.98	1.83	1.26	1.72
v10	1.96	1.12	2.18	2.00	1.32	1.79
pr	4.04	1.86	3.30	2.98	1.35	4.11

Appendix

Table 8: MAE (per method) and roughness

1-\rho_{1}

, relative to tas .

Model	Parameters	Training	Inference
		per epoch
U-Net	7 993 408	14.83s	2.00s
INR-SR	2 889 217	15.08s	2.05s
SE-OT	0	—	1.15s
CLR	1 671 680	0.74s	3.00s
Interpolation	0	—	0.15s

Appendix

Table 9: Size and computation time of the models - example with tas

Panel of Figure 3 — Figure 3: Reconstructions for tas and pr

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Dynamical Downscaling Spurious Correlations High-Resolution

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Physics-based climate projections using general circulation models are essential for assessing future risks, but their coarse resolution limits regional decision-making. Statistical downscaling can efficiently add detail, yet many methods treat variables independently, degrading inter-variable relationships that govern compound hazards such as heat stress, drought, and wildfire. Here we show that a diffusion-based multivariate generative framework, combined with bias correction, recovers degraded inter-variable correlations even under a 50

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Abstract

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