GeoFAR: Geography-Informed Frequency-Aware Super-Resolution for Climate Data
Authors: Chang Xu
Gencer Sumbul
Li Mi
Robin Zbinden
Devis Tuia
Venue: ICLR 2026 Poster (2026)
Keywords: climate downscaling
image super-resolution
implicit neural representation
earth observation
environmental science
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)

Abstract: Super-resolving climate data is crucial for fine-grained decision-making in various domains, ranging from agriculture to environmental conservation. However, existing super-resolution approaches struggle to generate the high-frequency spatial information present in climate data, especially over regions showing complex terrain variability. A key obstacle lies in a frequency bias existing in both deep neural networks (DNNs) and climate data: DNNs exhibit such bias by overfitting to low-frequency information, which is further exacerbated by the prevalence of low-frequency components in climate data (e.g., plains, oceans). As a consequence, geography-dependent high-frequency details are hard to reconstruct from coarse climate inputs with DNNs. To improve the fidelity of climate super-resolution (SR), we introduce GeoFAR: by explicitly encoding climatic patterns at different frequencies, while learning implicit geographical neural representations (i.e., related to location and elevation), our approach provides frequency-aware and geography-informed representations for climate SR, thereby reconstructing fine-grained climate information at high resolution. Experiments show that GeoFAR is a model-agnostic approach that can mitigate high-frequency prediction errors in both deterministic and generative SR models, demonstrating state-of-the-art performance across various spatial resolutions, atmospheric variables, and downscaling ratios. Datasets and code are available at https://eceo-epfl.github.io/GeoFAR/.

Published as a conference paper at ICLR 2026
GEOFAR:
AWARE GEOGRAPHY-INFORMER FREQUENCY- FOR CLIMATE DATA
Chang Xu'; Gencer Sumbul', Li Mi Robin Zbinden', Devis Tuia
'EPFL, Switzerland "ETH Zurich, Switzerland
ABSTRACT
Super-resolving climate data is crucial for fine-grained decision-making in vari- ous domains, ranging from agriculture to environmental conservation. However, existing super-resolution approaches struggle generate the high-frequency spa- tial information present in climate data, especially over regions showing complex terrain variability. A key obstacle lies in frequency bias existing both deep neural networks (DNNs) and climate data: DNNs exhibit such bias by overfit- ting low-frequency information, which is further exacerbated by the preva- Ience of low-frequency components in climate data (e.g., plains, oceans). As a consequence, geography-dependent high-frequency details are hard to recon- struct from coarse climate inputs with DNNs. To improve the fidelity of cli- mate super-resolution (SR), we introduce GcoFAR: by explicitly encoding cli- matic patterns different firqquencies, while learning implicit geographical neu- ral representations (i.e., related to location and elevation), our approach pro- vides frequency-aweer aware and Soography-informee representations for climate SR, thereby reconstructing fine-grained climate information at high resolution. Ex- periments show that GeoFAR is model-agnostic approach that can mitigate high-frequency prediction errors in both deterministic and generative SR mod- els, demonstrating state-of offthee-rt performance across various spatial resolutions. atmospheric variables, and downscaling ratios. Datasets and code are available at: fetsss://ece-eple www.tgg.tt.b............ 1o/GeoFAR/
INTRODUCTION
The inherent complexity of the climate system leads to complex regional climate variations at local scales. As example, NOAA's HeatWatch campaigns show intra-urban air-temperature differ- ences of up to 99C in records only a few kilometers apart, mostly due to terrain and ventilation variability (NOAA Climate Program Office, 2025). Fine-grained, accurate climate observations or estimations are thus crucial for site-specific decision-making in areas as diverse as agriculture, envi- ronmental conservation, and hydrological management.
Climate downscaling provides a way to obtain such fine-scale climate details from coarse inputs by either physics-based dynamical methods or data-driven statistical methods (Sun et al. 2024). With respect to the latter, climate downscaling has come to be formulated as super-resolution (SR) task with deep learning methods (Vandal et al. 2017 Stengel et al. 2020: Baño- et al. 2022).
Compared to physics- based dynamical models, deep neural networks (DNNs) achieve competitive performance with much lower computational cost (Lopez-Gomez et al. 2025), making image SR approaches effective solution for climate downscaling.
However, the loss of high-frequency details remains a challenge in image SR (Jiang et al. 2021 Wang al. 2020), and this is exacerbated in climate SR. Compared natural images (Martin et al. 2001). climate data is severely biased towards low-frequency components, as shown in the comparison of frequency distributions in Figure [a] The frequency distribution in climate data is also location- and alevation-dependen plains are dominated by low-frequency variations, whereas mountainous regions contain richer high-frequency content. The inherent frequency bias of deep neural networks (Rahaman et al. 2019) is further exacerbated by this geographical bias in climate
"Correspondence: chang.xu@epfl.ch

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Published as a conference paper at ICLR 2026
ERAS (12m)
CERRA (T2m)
BSD100
BRAS (12m)
1.0
Cumulative Magnituk
6
1.0
55
4
0.6
0.8
Globe
0.6
CERRA (T2m)
0.4
0.2
0.0
0.0
Normalized Froquency
Furope
Mountains
(a) Frequency Distribution
(b) Prediction Bias (Laplace filtered)
Figure I: Frequeney bias in climate super-resolution. (a) Climate data (ERAS, CERRA) contains much higher low-frequency information compared to natural images (BSD100) (x-axis: the radial spatial frequency scaled [0.1]; y-axis: the sum of Fourier frequency magnitudes in each bin). (b) An example of SR results shows -egrapph-ddeeedeettt high-frequee frequency errors: the Laplace filtered prediction bias highlights errors over polar regions (Globe), coastlines (Furope), and mountains.
SR: DNNs are prone to fit the large amount of smoothly changing regions (e.g, ocean and plains), and fail to reproduce the high-frrquency climate details, usually associated with complex terrain variabil- ity. Such bias toward low frequencies leads to over-smoothed or hallucinated regional estimations (see Appendix A.8 This behavior of geography-dependee
high-frequency loss is illustrated in Figure [b] the Laplace filtered prediction bias (where darker blue denotes a larger high-frequency deficit) reveals a concentrated high-frequency error over polar regions, coastlines, and mountains.
To address the above-mentioned challenges in climate SR, we introduce a Geography-Infooe Informed and Frequency-Aware Super-Resolution (GeoFFRR approach for high-fidelity climate downscaling. Ge- oFAR mitigates the low-freqq freeuueeeenyy aggregation in climate data by learning fine tieeggranedd Frequency- Aware Representations (FAR) with frequency-aware convolution kernels that explicitly encode both low-frequency components and high-frequency details. In addition, GeoFAR learns implicit neural representations for geography (Geo-INR) specific to climate SR. Geo-INR goes beyond location- only encoding in prior studies (RuBwurm al.) 2024 Mai et al. 2020 by jointly encoding location and elevation (terrain)-specific implicit representations to inform climate SR, thereby capturing the dependency of climate states on fine- fine-grained geographical characteristics.
Experiments on three heterogeneous climate downscaling datasets (ERA5, PRISM, and the pro- posed CERRA high-resolun resolutin datasets) show that GeoFAR learns frequency-await and geography- informed representations to accurately reconstruct local-scale climate information. Our proposed boography-informee learning (Geo-INR) outperforms baselines that stack elevation channel to the atmospheric variables for SR. Across both deterministic and generative SR base- lines, GeoFAR significantly reduces high-frequency prediction errors and achieves state-of-the-an performance: 1) across global (ERA5), global-to-local
additional
and local downscaling (CERRA) settings (Table 2) on both surface (e.g., 2m-temperature) and pressure-level variables (e.g., coapotential-500hPP temperature-85001 with errors below half unit (Table 3b). In summary, our contributions are:
(Table Ba); and 3) of 44-+5.5km +5.5kmm resolution gains
We propose eengrapph-Inffrmaa and Frequency-Aware (GeoFAR) approach for high-fidelity climate SR: GeoFAR learns fine fine-grained frequency-aware representations for climate data and modulates these representations with geographical implicit neural representations.
GeoFAR effectively tackles the goography-dependeen frequency bias in climate SR: by mitigating low-frequency aggregation and reconstructing geography-related high-frequency climatic details, GeoFAR yields significant improvements in regions with complex terrain.
Experiments reanalysis (ERA5, CERRA) and observational (PRISM) climate data demonstrate GeoFAR's 's adaptability to both deterministic and generative baselines, achieving state-of of-te--f-thhann the-art performance across diverse spatial resolutions, atmospheric variables, and downscaling ratios.
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2
RELATED WORK
2.1 CLIMATE DOWNSCALING
Traditional climate downscaling methods simulate regional climate from global climate models. This is referred as dynamical downscaling (Tapiador et al. 2020; Sun et al. (024). While grounded in physical principles, dynamical downscaling is computationally expensive and inherits the biases of the global models. Data-driven statistical downscaling (Sun et al. 2024) has achieved competi- tive accuracy at much lower computational cost with growing adoption of DNNs inspired by image super-resolution (SR) (Dong et al., 2016 Lim et al. 2017 Liang et al. (02I). We categorize these SR-based approaches into deterministic and generative models. Deterministic models learn a sin- gle mapping from coarse-scale to higher-resolution climate data by minimizing the loss at the pixel level. Early works, such as DeepSD (Vandal et al., 2017), utilize cascade convolutional neural net- work (CNN) blocks with concatenated climate and topographic inputs. More recent methods further extend DeepSD to downscale multi-modal ensembles (Baño-Medina et al. (022) or integrate atmo- spheric processes as constraints de Roda Husman al. 2024| Chen al., 20022) However, deter- ministic models tend to smooth the high-frequency details and do not model prediction uncertainty. Generative modely address these challenges by sampling from distribution conditioned on the low-resolution image, therefore learning to represent fine-scale details and capture local variations and extremes. Previous efforts have applied Generative Adversarial Networks (GANs, (Goodfellow et al. 2020)) for physics-informer climate downscaling (Stengel et al. 2020 lotti et al. 2005| Li & models (Liu & TTag 2025
|
Cao| 2025] Lopez-Gomez et al. 2025). More recently, diffusion-
Ho et al. 2020) have been adapted to iteratively denoise coarse inputs, surpassing deterministic models in fine-scale variance and offering probabilistic outputs for climate downscaling (Watt &
Mansfield 2024 Srivastava et al.) 2024). Despite this progress, existing studies do not explicitly frequency characteristics of climate downscaling, leading to limited utilization of the (geographic) domain knowledge to modulate fighfrreuency content in complex terrains, and therefore often resulting in oversmoothed SR outputs.
investigate the geography-dependee
2.2 FAERUE MODELING
Every signal (from audio, images, videos) exhibits combination of high and low frequency components, while DNNs are known to be biased towards low frequency components: they con- verge well on low-frequency components but struggle with the high-frequency ones (Schwarz al.) 2021 Tancik et al. [020]] Xu et al., 2020). This has motivated line of work on improving high- frequency modeling for both generic architectures and task-specific settings. Generic methods, in- cluding periodic activation functions (Sitzmann et al. 2020), Fourier Neural Operators (Li et al.) Vision Transformers (Bai et 2022 Lee et al.) 2025), aim to enhance the representation of high-frequency information regardless of the downstream task. Task-specific frequency-aware methods (e.g., using Wavelet Transform (Kingsbury (001)) are proposed to en- hance high-frequee figgffrry components (Jiang et al.) 20211; Wu et al.) 2023) in image reconstruction, eliminate small artifacts in SR (Korkmaz et al.] [2024] Fuoli et al. [222 Kim et al., 2025), or com- press the model with frequency-awas models (Xie et al. (021). Another line of frequency-awar modeling introduces attention mechanisms to enhance specific frequency components. Frequency attention first decouples channels into different frequency bands, and then learns frequency-awar reweighting (Qin et al. [022]] Ulieny et al. 2022, Chen et al. (2024). However, classic wavelct- approaches with four frequency bands tend to provide limited separation of nigh-frrequecy content in climate data, whose distribution is concentrated at low frequencies. On the contrary, learnable frequency attention is mainly designed for recognition tasks (e.g.. classification) and can further exacerbate the loss of high-frequee figh-frequency information due to its frequency truncation and the neural network's 's inherent bias towards low frequencies. A fine-grained and unbiased decoupling method tailored for climate data is still missing.
202T], and frequency-
2.3 GEOGRAPITY- INFORMEDD LEARNING
Climatic processes are strongly shaped by geography, since sharp changes in location and terrain can produce pronounced local climatic responses (Pepin & Lundquist] 2008). Consequently, it is impor- tant for climate models to incorporate geography (i.e. location and elevation information) to improve their physical realism, internal consistency, and predictive performance. In the context of climate
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Convs
FAR
Backbone
Z
Condition
JR
Geolocation
Termin
Geo-INR
G(x)
(a)
The Proposed GeoFAR Approach
limes
FCK,
Goolocation (A.
PCKg
lili Lulle
SIREN
G(X)
FCK
Elevation
FCK
Latt
Terain k(4
Diff
Proj
Aspect
(b) FAR: Frequency- Representation
(c) Geo-INR: Implicit Neural Representation for Geogruphy
Figure 2: An overview of GeoFAR. (a) Model pipeline, which can be directly plugged into de- terministic models or used the generator in generative models. (b) The frequency-awer repre- sentation decomposes the image into frequency subbands with frequency-awe convolution kernels (FCK). (c) Geo- encodes both location and terrain information for infformm SR.
downscaling, classic methods usually incorporate location as geographically weighted regression enhance performance (Zhao al. 2017), and topography is sometimes used additional predictor (Fiddes & Gruber] (014) For example, recent deep learning-band maaing climate downscaling approaches have included elevation as an additional channel input CNNs (Vandal et al. 2017). However, simply stacking elevation alongside climate variables is suboptimal: the model has to process together fundamentally different data types. A growing line of research exploring how to better encode geographic priors into deep learning models for a wide range of geospatial tasks (e.g., species distribution modeling (Cole al. 2023), satellite image classification (Ayush et al.) 2021). weather forecasting (Verma et al. 2024 ). These works project geographic locations into implicit neural representations to more faithfully capture spatial relationships and better inform the downstream task (Mai et al. 2020 RuBwurm et al. 2024). However, geographic implicit represen- tations remain underexplored in chimate downscaling: climatic states vary significantly with both location and elevation, making essential to go beyond current single-facee factor methods (conditioning on location or elevation) and rather jointly condition the super-resolution process on both.
GEOGRAPHY-INFORREE
FREQUENCY-AWARE SUPER-RESOLUTEE
Let an atmospheric variable defined on grid I E HxW for representation learning with neural networks (Nguyen et al. 2023), where H x W is the spatial extent, either defined for the whole globe or for a specific region at given resolution. Climate downscaling seeks to provide a high-resolution output JHn E TR. H' xW conditioned on the input T.
To enhance the fidelity of climate downscaling, GeoFAR aims to learn geography inffommdd and frequency-aware climate representations E x specific to SR, where each spatial location associated with d-dimensional feature vector. The resulting model-agnostic representations can be fed to either deterministic or generative SR pipelines (see Appendix(A.3 for the details of the Ge- oFAR adaptation to different SR models). As shown in Figure 2h. GeoFAR first applies a frequency- aware projector Ps to obtain frequeney-aware representations L = (1) E xx Then, GeoFAR encodes geography implicit neural representations G E IB HxW Finally, we perform pixel-wise frequency-ave conditioning between I and G (i.e., feature seat modulation) (Perez
et al. 2018), getting:
M I ④ G,
where @ denotes per-pic per-pixel multiplication. This is followed by three 3 x 3 refinement convolutions, yielding Z. These representations are then fed into the SR backbone to predict the target image I whose learning process is supervised by the Mean Squared Error (MSE) loss by default. In what
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follows, we separately explain frequency-aware (Figure 2p) and geography informed (Figure 2 representation learning of GeoFAR.
3.1 FREQUENCY-AWARE REPRESENTATION LEARNING
Encoding different frequency components separately is beneficial for neural networks capture pat- terns at different frequencies (Fuoli et al. 2021 Pan et al. 2022 Patro & Agneeswaran 2023). For climate SR, we introduce Frequency-ANy encodes both freuefryyenccy variability (local-scale climate fluctuations) and low-frequency com- ponents (macro climate state) into separate channels, as shown Figure Unlike Discrete Wavelet Transforms (DWT), where the decomposed data (LL/LH/HL/HH) is mostly concentrated in the low- frequency subband (LL), we design Frequency-award Convolution Kernel (FCK) that achieves multi-granular FAR to avoid low-frequency aggregation in climate data (See Appendix A.8).
Representation (FAR) learning method that explicitly
The FCK weights are parameterized directly by the bases of the Discrete Cosine Transform (DCT), such that each kernel corresponds to specific frequency component. By fixing kernel weights with DCT bases of varying frequencies, the convolution acts as a localized filter bank that decouples the input into multiple variants, each one emphasizing specific frequency band. Such filter bank tains many high-frequency sensitive kernels. By repeatedly sampling high-frequency components in the data, the network is exposed to more high-frequency inputs, which strengthens its reliance on these components for target reconstruction. Formally, for a patch / E gaxw in the 2D grids
I E R HxW the 2D DCT is defined as:
N-IN-1 C(u,v) c() EE P(z,y) cos
π 72x + 1)u
T T2y + 1)
CO8
2N
2NV
where N is the block size, (z, y) are the spatial coordinates, (u, v) denote frequency indices rang- ing from 0 to N 1, with larger values corresponding to higher frequencies. c(u) and c(v) are normalizing constants. The corresponding DCT basis function given by:
T (2x + 1)u
T(yy +11
Bu, v) c(u)c(v) cos
COS
2NV
2N
We leverage these bases to define the weights of the convolution kernels: each kernel in the FCK is aligned with one basis function with frequency pair fn = (u, v). For each patch, the frequency- specific response is obtained via:
N-IN-1 Σ P(z, y) (x,
(1,) = Σ
(4)
== ==
We use FCK to convolve across all patches and apply different frequencies to different channels, yielding frequency-aware representations I x where d N2.
3.2 IMPLICIT NEURAL REPRESENTATION FOR GEOGRAPHY
Implicit neural representation (INR) allows to learn a continuous mapping between the input coor- dinates and the output signal with neural networks. When trained on sufficient data, INRs can either memorize signals with near-lossless fidelity or learn coordinate-feature functions that generalize across coordinates, powering view synthesis, data compression, and geo-embeddings (Mildenhall
et al. 2021 Huang & Hoefler 2023 Mai et al. 2020; Rußwurm et al. 2024).
Here, we introduce an INR for geography (Geo-INR) that jointly encodes the location- and terrain- driven characteristics of climate processes. To this end, we define climate downscaling on the 3D geographic manifold M
S2 x R. Each point on M is x (A, o, h) with latitude À [- 2: and longitude & e [-T, л) defined on the unit sphere S?, while surface elevation à E R. Our goal is to learn mapping of each point to geographical representation of dimension d:
G: G:M+R
G(x) NN(PE(x)),
(5)
where PE is the positional encoding function and NN a neural network that projects positional encodings into geographical implicit representations. The full map the 3D geographic manifold
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is thus projected the grid coordinate space G R Concretely. Geo-INR employs fine-scale spherical location encoding and lirain-difffrentiall encoding at the target resolution for PE, and their joint use within an NN for geography-informed inffrmedd representations, which are explained separately in the following.
Spherical location encoding. We first encode (A, Φ) with band-limited apherical-harmonee (SH) expansion. Let (YZ") Je20, jmlsee be the real SH basis (E: degree, m: order) orthonormal on S²:
[ (w)(w) Y (w) dw 6mm
(6)
882
We truncate at degree L, yielding a multiscale and rotation- aware encoding:
m=-e... () Y?" (X, m= RR(++1)²
where smaller captures large-scale patterns on the sphere and larger & represents fine details; Y cigenfunctions of the Laplace-Beer Beltremm operator with eigenvalue (((+1) (Atkinson & Han 2012 RuBwurm et al. 2024 In practice, we use = 7, giving rise to [L + 1)2 64 SH channels.
-itreinniifferentiall encoding. Beyond location, climate states also depend both absolute eleva- tion and local slope information. In addition to absolute elevation h, which is an implicit function of locations h h2,, Ø), add first-order surface derivatives with respect the latitude and longitude directions to better reflect the slope information:
Vish(A, の) = (axh, 0ah1).
(00))((a)))
Elevation and slope information then jointly define the terrain vector:
T(h(,, ()) = [M(A. Φ), 0xh(A, o), 0ah(A,, Φ)] E R
A learnable (3x3 conv) layer V R p( is used to align the clevation with aspect informa- tion, producing terrain-differential encoding T = (T)
Geography-informed representation. We first define the final positional encoding of Geo-INR as the linear fusion of spherical location and terrain-differential encodings:
PE(x) (A, + T(h(),)) o)) E Rdo
(10)
where do is unified as the number of SH channels. The positional encodings are then passed through a SIREN (Sitzmann et al. 2020)- MIPP
G(x) fx o fK- ....o (PE(x)), fa(z) =in(w) Waz by),
(11)
where We controls the angular period of sinusoidal waves, Wa and bę are learnable weights and bias of the tthh layer. Leveraging SIREN's ability model fine details, we project the positional en- codings to the composite geographical representation G(x) E Rd of each point on the 3D manifold that helps the SR backbone reconstruct region-specifi structures.
4 EXPERIMENTS
4.1 EXPERIMENTAL SETUP
Datasets and experimental settings. We conduct experiments on three heterogeneous climate databases: ERA5 Reanalysis (Hersbach et al.] 2020). PRISM (PRISM Climate Group 2025), CERRA RRidll et al., 2024). which are explained in detail Appendix A.2 We also assess the model's 's generalization to satellite observations with MODIS (Appendix A.7). To assess the effec-
tiveness of GeoFAR on different spatial resolutions, atmospheric variables, and downscaling ratios, we consider the following settings:
Spatial resolutions. We assess the model on global (ERA5: 5.625 to ERA5: 2.8125"), global-to- local (ERA5: 2.8125 to PRISM: 0.75"), and local (CERRA: 22km to CERRA: 11km) SR scales. For the global and global-to-local settings, we follow the ClimateLearn benchmark (Nguyen et al.) 2023):: we downscale 2m-temperature (T2m) in ERA5 from 5.625 to 2.8125 with hourly inter- vals in the global setting: in the global-to-local setting, we downscale daily max T2m from a reanalysis dataset to observational dataset (from 2.8125 ERAS data to 0.75% PRISM) over the same region at daily intervals. For the local setting, we construct a new high-resolution SR dataset by processing the CERRA database, and use T2m with 3-hour updates.

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Table 1: Results on global (ERA5: 5.625 to 2.8125%), global-to-local (ERA5: 2.8125 PRISM: 0.75%), and local settings (CERRA: 22km to 11km) on T2m (K). We omit Pearson's correlation coefficient (r) in global and local downscaling settings since all models achieve r z 1.0. Values in bold and underlined indicate the best and second-best results among learning-based methods. For RMSE and LFD, lower values indicate better performance; for mean bias, values closer to 0.0 are better; and for Pearson's 's higher values are better.
Global Downscaling
Global-to- Local Downscaling
Local Downscaling
RMSE
MB
LFD
RMSE
MB
Pearson
LFD
RMSE
MB
LFD
Nearest
3.116
-0.022
11,028
2.911
-0.051
0.893
9.257
0.663
0.000
11.664
Bilinear
2,457
-0.02
10.665
2.637
0.125
0.910
8,997
0.517
0.000
11.165
ResNet
1.138
0.004
9.173
1.636
-0.152
0.964
8.093
0.345
0.110
10.205
U-Net
1.103
0.004
9.114
1.501
-0.094
0.970
7.953
0.272
0.068
9.769
ViT
1.121
0.009
9.154
2.163
-0.147
0.937
8.652
0.380
0.033
10.496
EDSR
1,164
-0.007
9.221
2.860
0.315
0.914
9.073
0.243
0.058
9.647
FFL
L.140
-0.003
9.187
2.175
-0.196
0,937
8.705
0.710
0.011
11.824
SwinIR
L.177
0.002
9.141
1.879
-0.087
0,952
8.392
0.212
-0.001
9,450
SRFormer
L.138
0.000
9.176
1.877
-0.094
0,952
8.390
0.219
0.001
9.499
SRGAN
1.149
0.007
9.196
1,718
-0.143
0,961
8.206
0.245
0.000
9.739
DeepSD
1.396
0.002
9.590
1,955
-0.198
0,949
8.451
0.344
-0.004
10.401
FACL
1.373
0.156
9.490
7.240
0.133
0,928
10.182
0.700
-0.053
11.761
SmCL
2.184
-0.002
10.508
2.637
0.125
0,910
8.997
0.465
0.000
11.014
STVD
I,310
-0.029
9,462
1,781
-0.185
0,960
8.288
0.255
-0.065
9.747
ClimateDiffuse
1,451
0.005
9.679
2.279
-0.097
0,955
8,582
0.265
-0.011
9.858
DSFNO
1.265
0.019
9.397
1.546
-0.032
0.968
8.015
0.343
0.004
10.397
GeoPAR[SRGAN]
1.137
0.002
9.175
1,561
-0.089
0,967
7.971
0.192
0.001
9,240
[DSNNO]
1.126
-0.003
9.160
1,474
-0.121
0.971
7.904
0.190
0.000
9,234
GeoFAR[[Vi]
1.099
0.001
9.117
1.745
-0.097
0.959
8.226
0.191
-0.001
9,245
GeoFAR[U-Net]
1.076
0.001
9.068
1.468
-0.137
0.972
7.836
0.180
0.003
9.127
Atmosphercc variables. In addition to single-variable experiments, we also perform a joint down- scaling of multi-variables with CERRA (22km 11km), including: 2m-temperature (T2m). 10m- (Rh2m), surface- presssure (Sp). In complement to the surface-level results, we also perform global-scale downscaling of several pressure-level variables: we downscale geopotential-500hP. (Z500) and temperature-850hP (T850) in the global setting using ERA5.
l-ccomponent-o-vvwe of- (10u). ofin-v-component-o-wwinii (10v), fim-relative-ummiie
Downscaling ratios. In this setting, we explore different downscaling ratios from the first (local) setting on the CERRA dataset. We propose two more challenging downscaling ratios: 4x (from 22km to 5.5km) and 8 (from 44km to 5.5km). This is to evaluate the model's ability to recover high-frequency and high-resolution details from very coarse input.
Comparison methods. We compare GeoFAR with both generic methods and climate-oriented methods for climate SR, leading to one of the most comprehensive comparisons to date in the ma- chine learning community. Generic methods include ResNet (He et al. 2016). U-Net (Ronneberger
et al., 2013). ViT (Dosovitskiy et al., (021), EDSR (Lim et al.] (207]). FFL (Jiang et al. 2021), SwinIR (Liang et al.) 2021). SRFormer (Zhou et al. 2023), and SRGAN (Ledig et al. 2017). Climate-oriented methods include DeepSD) (Vandal et al.) (017), FACL (Yan et al., [2024), and SmCL (Harder et al. 2023). Detailed descriptions of baselines and their implementations can be
found in the Appendix A.4
Metries. We use two types of evaluation metrics: spatial domain and frequency-aware metrics. By following previous works (Nguyen al. 2023), Rooted Mean Square Error (RMSE), Mean Bias (MB), and Pearson Coefficient are used to evaluate the SR performance in the spatial domain. Log Frequency Distance (LFD, (Jiang et al. 202T and proposed Wavelet-based Metric are used for the frequency-aware evaluation in Section 4.4
4.2 COMPARATIVE PERFORMANCE
Results across spatial resolutions. Table shows the SR results on global (ERA5), global-to-local (ERAS-PRISM), and local (CERRA) scales. GeoFAR is adaptable to both deterministic baselines
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Table 2: Results on joint downscaling of multiple variables with CERRA (22km 11km).
12mm (K)
10u (ms 1
10v (ms 1)
Rh2m (%)
Sp (Pa)
RMSE
L.FD
RRSFE
MB
LED
RMSE
MB
LED
RMSB
MB
L.FD
RMSE
MB
L.FD
VIT
0.457
0.033 10.966
0.341 0.002 10.395 0.355 -0.011
10.472
1.799 -0.012
13.708
277.719
-11.007
23.808
GeoFAR 0.262
0.001 9.859
0.184
0.000 9.163 0.186 0.000 9.187 1.215
-0.003
12.921
47.922
0.375
20.291
Table 3: Results on ERA5 pressure-level variables (Z500, T850: 5.625 to 2.8125") and larger downscaling ratios on the CERRA dataset (T2m, K). [S] and [U] denote GeoFAR using SRGAN and U-Net as baselines, respectively.
(a) Results on Z500 and T850 of ERA5
(b) x4, x8 upsampling results on CERRA
7550 (m's-2)
T850 (K)
22--5.km (x4)
445m5.5km (x8)
RMSF
MB
L.FD
RMSE
MB
LFD
RMSE
MB
LFD
RMSE
MB
LFD
Bilincar
134.063
0.028
18.564
1,504
0.001
9.699
Bilinear
0.610
0.000
12.878
0.861
0.000
13.578
U-Net
49.060
-0,980
16.661
0.973
0.001
8.883
U-Net
0.326
0.068
11.517
0.482
0.034
12.389
VIT
51.023
0.799
16.748
0.999
0.002 8.941
ViT
0.458
0.077
12.072
0,564
-0.011
12.706
EDSR
52,602
-1.758
16.794
1.040
-0.015 9.010
EDSR
0.299
0.031
11.495
0.449
0.039
12.307
SRGAN
50.374
0.905
16.715
1.039
-0.059
9.005
SRGAN
0.375
0.030
11,943
0.594
0.047
12.859
DeepSD
60.469
0.069
17.073
1.152
-0.004
9.216
DccpSD
0.388
0.024
12.024
0.579
0.034
12.815
GeoFAR[S]
50.170
-0.780
16.713
1.024
0.006
8,983
GeoFAR[[)
0,253
-0.002
11.172
0.434
-0.001
12.244
GeoFAR[U]
48.683
-0.195
16.651
0.971
-0.001 8.881
GcoFAR[U]
0.235
0.000
11.023
0.393
0.005
12.047
(e.g., U-Net, ViT, DSFNO) and generative methods (e.g., SRGAN). When applied to simple deter- ministic baselines such as U-Net, GeoFAR outperforms not only advanced generic SR methods (e.g., SRFormer) but also climate-speddt specific SR methods that incorporate domain priors (e.g.. DeepSD with elevation input, SmCL with physics constraints), achieving the ofte-offthhearr performance across all three settings. These gains are significant, especially in the local-scale fine-grained downscal- ing (CERRA) setting: the RMSE decreases by 0.092, and the by 0.642 compared to U-Net. Results also indicate that the gains of geography-infornee learning affected by spatial resolution: as the resolution increases (from ERA5 CERRA), fine-grained geography informmed representations enable more precise modulation of local-scale SR, yielding larger performance gains.
domainn LFD is reduced
Results across atmospheric variables. In Table 2 we also report results for a joint SR of mul- tiple variables. For fair comparison, we stack all variables as channels for both the VIT and the ViT-based GeoFAR. Due to fundamentally different physical meanings of variables, jointly super- resolving them with a shared model does not necessarily improve the performance (e.g.. the RMSE increases from 0.380 to 0.457 on T2m, ViT). Nevertheless, GeoFAR still provides consistent im- provement across variables, especially for variables strongly tied to terrain variability such as surface pressure. In addition to surface-level atmospheric variables, Table 3a provides SR results on differ- ent pressure levels (i.e., cropotential-500hhP Z500, temperature- Hamperature-85OhPat T850). The SR of these pressure-level variables is even more challenging than surface-level variables since their variability is dominated by atmospheric dynamics with comparatively weak high-frequency energy (Nastrom) & Gage 1985; SSkamrock et al. 20014), and high sensitivity to location errors since small displace- ments of ridges or frontal zones can cause large losses (Ebert) 20088. Despite these challenges, our approach (for both UNet and SRGAN adaptation) yields consistent gains over other methods on both Z500 and T850, achieving the state-of-the performance.
Results across downscaling ratios. We also investigate how models perform on more challenging downscaling ratios. Table (3b] shows the SR results on the CERRA high-resolution dataset with x4, x8 downscaling ratios. At these ratios, local-scale fine-grained information is heavily smoothed and blurred in the input, and thus pixel-wise errors are nearly doubled as we move from x2 (T to x8. Nevertheless, GeoFAR degrades slowly, and the RMSE is always kept under 0.5, while the Mean Bias is near 0, consistently outperforming the other methods at various scales. This suggests that, even when the input is eight times coarser than the target, GeoFAR still yields locally consistent results relative to real-world atmospheric conditions (with RMSE < 0.5 Kelvin at x8). Overall, GeoFAR is robust to large downscaling factors, maintaining low error and near-zero bias while consistently outperforming the other methods, which is crucial for real-world applications.
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4.3 ABLATION STUDY
We quantify the contribution of each GeoFAR component compared to alternative design choices.
Comparison with alternative designs. The grey rows in Table show the results for design choices different from ours. As an alternative to our FCK, the Discrete Wavelet Transform (DWT) is com- monly used to perform frequency decomposition. However, this strategy (Table w/ w/DWT) does not improve results on both datasets, probably due to the unbalanced low and high-frequency compo- nents in different wavelength channels (LL/LH/HL/HH), aggravating the already skewed frequency distribution. In addition, as an alternative to Geo-INR, we concatenate the input data with the ele- vation map when super-resolving the target field. Results in Table f (w/ Elevation) show that this simple fusion only yields minor gain, mainly due to the domain gap with the target variable and limited interaction with input variables.
Individual effectiveness. The black rows in Table 4 show the changes in metrics by adding each component of GeoFAR one by one. We begin with a strong residual baseline (+Residual): instead of regressing the high- resolution image directly, the model pre- diets the residual between the input and the target, directing capacity to high-frequency corrections. Based on this, incorporating
Table 4: Ablation study on both local-scale and global-scale T2m (K) downscaling (x2).
CERRA
ERA5
RMSE
MB
LFD
RMSE
MB
LFD
VIT
0.380
0.033
10.496
1,125
0.001
9.184
w/ DWT
0.434
0.013
10.787
1.139
0.007
9.186
w/ Elevation
0.381
0.018
10.451
1.117
-0.005
9.146
frequency-aware (+ FCK) and geography-
Residual
0.233
0.003
9.664
1.110
0.003
9.141
+ FCK
0,216
0.000
9.493
1,100
0.001
9.118
informed (+ Geo-INR) representations fur-
+ 2D--INR
0.198
-0.001
9.310
1.099
0.008 9.118
ther reduces the RMSE on both global and
Geo-INR
0.191
-0.001
9.245
1.099
0.001 9.113
local datasets. Jointly modeling location and elevation in INR performs better than the location-only method (+ 2D-INR). Fine-grained local-scale SR benefits more from our approach by learning accurate mapping between the geographical data and target variables.
4.4
BEYOND GENERIC METRICS: IN-DEPTH ANALYSES OF GEOFAR EFFECTIVENESS
VIT
GeoFAR[VIT]
GeoFARIVITT
0.35
Represencationn
0.30
GcoRAR Frediction
0.25
0.20
BMSE
RMSE
0.20
0.15
0.15
3
1.0
0.10
0.05
0.2
0.00
0.00.0
Normalized Frequency
Normalized Prequency
Wavelet bands
0
0.5
Elevation
25
3.5
(a) Input Frequency
(b) Prediction Frequency
(c) FA RMSE
(d) EA RMSE
Figure 3: Frequency and elevation encoding analyses. On CERRA, we compare the frequency distribution of (a) input data with GeoFAR representations; and (b) the output predictions of Geo- FAR[ViT] and VIT. We also perform: (c) frequency- -aaar (FA) evaluation on Wavelet decomposed subbands; and (d) elevation aware (EA) evaluation across increasing elevations by comparing Geo- FAR[ViT] with VIT.
To further investigate the effectiveness of GeoFAR, we conduct in-depth frequency-aware and geography-awart analyses, beyond generic SR metrics. We first perform a frequency analysis on CERRA to assess how GeoFAR affects lcarning in the frequency domain. In climate data, low- frequency components are usually related to large-scale structures (e.g., meridional temperature gradients), whereas the high-frequency components capture localized events such sharp frontal zones and topographically induced anomalies. Figure Ba| shows the frequency distributions of the raw input data and the frequency-aware climate representations: the high-frequency information of the input data has been enhanced by learning frequency- aware variants of the input data, miti- gating the low-frequency bias in DNNs. This mitigation is also reflected in the output predictions as shown in Figure 33;; GeoFAR generates more figh-freuunccy components than VIT. We also perform frequency-awan evaluation to analyze how accurate the enhanced high-frequency infor-

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Prodictions
GeoFAR [V]]]
VIT
GcoFAR [ViT]
(a) Results CERRA
(b) Results on ERAS
Figure 4: An example of super-resolved climate data. Compared to ViT, GeoFAR addresses the oversmoothing by recovering high-frequency details in complex terrains on (a) CERRA and (b) ERA5. Meanwhile, GeoFAR significantly mitigates the prediction bias in both datasets.
mation is: we first decouple different frequency components predictions with DWT into four bands (LL/LH/HL/HH)) then calculate RMSE for each band. Results in Figure3c|shor a consistent reduction of RMSE across frequency bands, with high-frequency subband (HH) showing the largest relative improvement. This indicates that GeoFAR improves the reconstruction of both large-scale and fine-scale local climate structures.
Second, we perform analyses to investigate how GeoFAR performs in different regions. In Figure 3d we first group regions according to elevation ranges, then evaluate the RMSE within each group: the RMSE has been consis- tently reduced from lowlands to high plateaus, while the most significant gains observed at high elevations: in regions over 3km eleva- tion, RMSE significantly drops from 1.755 to 0.210, showing the particular benefit of terrain- guided Geo-INR in complex mountainous ar- eas. In Europe, such high-elevation areas are concentrated in the Alps and Pyrenees, where rugged topography induces rapidly varying atmospheric fields, making SR particularly challenging. The super-resolved climate data in Figure 4a| shows that even in the challenging Alps, GeoFAR repro- duces fine-grained temperature patterns between adjacent valleys and ridges and recovers local de- tails under geographic conditioning. To further probe the learned geography-informel representa- tions, we measure the dot- dot-product similarities of a predefined location with respect to the full map. FigureB]shor high similarity between a city in the Alps (Zermatt) and other mountainous regions (e.g., Pyrenees); in comparison, the representation of Napoli (a relatively flat coastal city) aligns more with other flat areas and regions close the Mediterranean Sea.
Zermatt
Stnttery
Napuli
Figure 5: GeoFAR representation similarities. Red (black) indicates higher (lower) similarity, for Zermatt (left) and Napoli (right).
CONCLUSION AND OUTLOOK
Super-resolving climate data is crucial for fine-grained mapping of local climate states. In this pa- per, we introduce GeoFAR, a model-agnostic approach that learns frequency-aware and geography- informed representations for high-fidelity climate super-resolution. Across three datasets spanning multiple spatial resolutions, atmospheric variables, and downscaling factors, GeoFAR consistently improves both deterministic and generative baselines by recovering high high-frequency structure and modulating outputs specific to real-world location and terrain variations. With its broad adaptabil- ity, GeoFAR lays the groundwork for precise, geography-awan and physically consistent climate downscaling. We hope our findings can provide valuable insights for preserving the inherent re- lationships between geographic factors and climate states during downscaling, and inform broader applications such as weather forecasting and climate projections.
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6 ACKNOWLEDGEMENT
We thank Hugo Porta for the discussion and the code for downloading the MODIS dataset. We thank all the anonymous reviewers for their constructive comments. We acknowledge the support from CSC and the funding under the Horizon Europe grant 101213369 DVPS.
REPRODUCIBILITY STATEMENT
We provide all necessary details to ensure reproducibility. Model descriptions and experimental setups are described the main text and the appendix. The CERRA dataset and code are available at /tttps://eceo-ppt ....ggitth........ i ro/GeoFAR/
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Robbie A Watt and Laura A Mansfield. Generative diffusion- based downscaling for climate. arXiv preprint arXiv:2404. 17752, 2024.
Zhijie Wu, Yuhe Jin, and Kwang Moo Yi. Neural fourier filter bank. In IEEE Conference on Computer Vision and Pattern Recognition, pp. 14153-14163, 2023.
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Kai Xu, Minghai Qin, Fei Sun, Yuhao Wang, Yen-Kuang Chen, and Fengbo Ren. Learning in the frequency domain. In IEEE Conference on Computer Vision and Pattern Recognition, June 2020.
Chiu-Wai Yan, Shi Quan Foo, Van Hoan Trinh, Din Yeung, Ka-Hing Wong, and Wai-Kin Wong- Fourier amplitude and correlation loss: Beyond using 12 loss for skillful precipitation nowcasting. Advances in Neural Information Processing Systems, 37: 37:100007-10004. 2024.
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A APPENDIX
The appendix contains the following information:
summary of notations and variables (Section A.1
Data (Section
A.2
Evaluation metrics (Section A.3
Comparison methods (Section A.4
Detailed method description (Section A.5)
Implementation details (Section A.6
Additional experiments: robustness and generalization, hyper-parameter analysis, more ablations for Geo-INR, computational cost, physical fidelity (Section A.7
super-resolution results from both deterministic and generative models, trequency-wwar representations, terrain information (Section A.8
Additional visualization:
Limitations and future works (Section A.9
LLM usage (Section A.10
A.1 A SUMMARY OF NOTATIONS AND VARIABLES
We summarize the main notations in the paper in Table S and summarize the metcorological vari-
ables studied in this work Table
Table Summary main notations.
Symbol
Description
Dimension
Low-resolution input field
R #
JRR
High-resolution target field
R xw'
I5
Frequency-aware representation
RdxHxw
Pe
Frequency- projection
P I I Rx
G
Geographical implicit neural representation
M
Frequency-aware geography-informe representation
RdxHxw
P
Data patch
Rhx
C
Discrete cosine transformed data patch
NNNN
N
DCT block size
scalar
(x,v)
Spatial coordinates
R2
(u,v)
Frequency indices
R2
Bu
DCT basis
NNN
Pu
Frequency-specific response
RNNN
(,)
Latitude, longitude, and elevation coordinate
R3
M
3D geographic manifold
S2 R
G
Implicit neural mapping
M - Rd
PE
Positional encoding
PE IR3 - Rd
NN
Neural network
NN de - Rd
Ym
Spherical harmonic basis
82
YL
Truncated spherical harmonics encoding
R(++1)2
T
Terrain vector
E3
Terrain-differential encoding
R3
V
Learnable layer for terrain-differential encoding
V R + ((L+1)²
fR
Sinusoidal activation function
fx : IR + Rd
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Table 6: Summary of meteorological variables.
Abbreviation Full Name
Source
Unit
T2m
2m temperature
ERA5, CERRA
Z500
geopotential 500hPa
ERA5
m²s
T850
temperature 850hPa
ERA5
10u
10m component of wind
CERRA
ms
10v
10m component of wind
CERRA
ms
Rh2m
2m relative humidity
CERRA
Sp
surface pressure
CERRA
Pa
LST
land surface temperature
MODIS
SKT
skin temperature
ERA5-Land
K
A.2 DATA
A.2.1 DATASET DETAILS
ERA5 Reanalysis. ERA5 Reanalysis (Hersbach ct al. (2200) is maintained by the European Center for Medium-Range Weather Forecasting (ECMWF).. ERA5 is a reanalysis that combines diverse ob- servational data with forecasts from the state-of-the-a art Integrated Forecasting System (IFS). It pro- vides the estimation of the state of the atmosphere and land-surface variables at any given time. In its raw format, ERA5 provides hourly data from 1979 to the present on 0.25 global grid, covering a range of atmospheric variables at 37 pressure levels addition to surface conditions. We prepro- cess the 2m-temperature (T2m), geopotential at 500hPa (Z500), and temperature at 850hPa (T850) in ERA5 according to the ClimateLearn benchmark into 5.625 (32x64) and 2.8125 (64x 128) global grids with hourly updates for climate downscaling, we use the years 1981-2015 for training. the year 2016 for validation, and 2017-2016 for testing.
PRISM. PRISM (PRISM Climate Group, 2025) is dataset of observed atmospheric variables, including precipitation and temperature, covering the conterminous United States at varying spatial and temporal resolutions from 1895 to the present. At its highest publicly available resolution,
PRISM provides daily data on 4 x 4 km grid, corresponding to matrix of 621 x 1405 cells. Following the ClimateLearn benchmark, we process daily max T2m in PRISM to 0.75%. We crop the corresponding regions in ERA5 to align with PRISM when downscaling. The training period is from 1981 to 2015, validation is in 2016, and the testing period from 2017 to 2018
CERRA. Copernicus European Regional Reanalysis for Europe (CERRA) is pan-European re- gional reanalysis produced by C3S/ECMWF at 5.5 km horizontal resolution, with the core produc- tion spanning September 1984 to June 2021. For single-variable experiments (Table] Table Bb), we specifically employ the 2-m air lemperature (t2m) field available as single-level variable via the C3S Climate Data Store. For our experiments, we use bilinear interpolation to process the native 5.5 km data (1069 x 1069) to grids of 5.5 (1068 x 1068). 11 (534 x 534), 22 (267 x 267), and 44 (133 133) km with 3-hour updates define multiple evaluation settings, for training, 2018-2021 for validation and testing. For multi-variable experiments (Table 2). we employ the 2m-temperature (T2m), catt---commonet-o--viiiiie (10v), 2m-relative-humidity (Rh2m), and surface-presssuree (Sp). The native 5.5 km data are further preprocessed with bilinear interpolation grids of 11 (534 534), 22 (267 267) km with 3-hour updates for the 2x super-resolution. The training set is from 2010 to 2017, and the val/test sets are from 2018 to 2021, leading large-scale
2010-2017
(10u), 10m-v-component-
downscaling dataset of roughly 200GB.
MODIS. Moderate Resolution Imaging Spectroradiometer (MODIS) is a satellite from NASA, whose data are used to create a number of operational products. To assess the model's 's general- ization ability on this data source, we construct a new dataset aiming at downscaling the daily skin temperature (SKT) from ERAS-Land to the MODIS land surface temperature (LST), Specifically, we download both datasets over Switzerland, which is a very challenging region with complex at- mospheric processes, due to its complex alpine topography. We preprocess ERA5-Land to 11 km resolution (21 x 46), and MODIS to roughly 1.1 km resolution (210 x 460) via bilinear interpolation, leading to a challenging setting of x 10 downscaling. The training set from 2018 to 2022, and the testing set is from 2023.
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A.2.2 DATA PRE-PROCESSING
We normalize both the input and target image I RRx stabilize model training:
(1x,))~ T(x,y)=
(x. E (I,.... HJ x f1...., W).
(12)
σ +E
where j and the mean and standard deviation (computed ensures numerical stability. In addition, we add constant offset (1.0) to the frequency-aware repre- sentation f. to prevent near-zero entries in L from nullifying the contribution of the geographical embedding during the per-pixel product.
the training set), and
A.3 EVALUATION METHODS
In the introduction, we use the Laplace operator to filter the prediction bias in Figure 1 In the experiment section, we use two types of evaluation metrics: spatial domain and frequency-aware metrics.
A.3.1 LAPLACE OPERATOR
In Figure 1 we use the Laplace operator as a high-hihh sish-passsss filter to visualize the prediction bias. The Laplace operator is written
02
0²1
V
+
(13)
Ox.2
0y²
f indexes the prediction bias in 2D;
8 dx is the second derivative of with respect to z-direction measuring curvature or varia- tion along x.
82 is the second derivative along the y-direction. 0zz
The Laplacian highlights details, high fregefrryyenc features, and regions where prediction bias changes sharply, while smoothing out low-frequency components.
A.3.2 SPATIAL DOMAIN METRICS
RMSE (Rooted Mean Square Error):
N
H
W
ΣΣ L(D) (XAas Xk.r)?
RMSE
(14)
N
H W
k = 1, N indexes samples;
i= 1,.... H and I,...,
.., W index grid rows and columns; Xv. is the ground-truth value at pixel (i,ji of sample k;
a is the corresponding prediction:
L(t) is an optional latitude (row) weight. We use the normal RMSE without reweight-
ing, so L(i) set to
MB (Mean Bias): measures the difference between the spatial mean of the prediction and the spatial of the ground truth. A positive mean bias shows overestimation, while a negative mean bias shows an underestimation of the mean value.
MB N W
X
1
ΣΣΣ
Xkai
(15)
W
where N is the number samples, H x W the grid size, XR.i. the ground truth, and X the prediction.
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Pearson Coefficient: measures the correlation between the prediction and the ground truth. We first flatten the prediction X and ground truth X, and compute the metric follows:
cov X)
Px.x
(16)
σ x
where cov(:.) is the covariance and 0x xx are standard deviations. The coefficient mea- sures linear association, with range [-1, 1] perfect positive, 0 no linear correlation,
1 = =perfcct negative).
A.3.3
FREQUENCY-AWARE METRICS
Log Frequency Distance (LFD) Jiang et al. 2021
H-IW-1
LFD log
1
ΣΣ ==0 v=0
(, - Fg(u, v) v)) +
(17)
H x W
where Fp(u, (u, v), (u, v) denote the Fourier transformed predictions and ground truth, spectively, the logarithm is only used to scale the value into a reasonable range. A lower LFD is better.
Wavelet-based Metric: In order to evaluate the performance on different frequency bands in Figure Be) we use the Discrete Wavelet Transform (DWT) to decouple the predicted image and the ground truth target into four bands (LL/LH/HL/HH), then evaluate the RMSE for each band.
Kinetic Energy Spectral RMSE (RMSEKE): assess the scale-dependent consistency of the predicted wind fields, we compare their isotropic kinetic energy (KE) spectra (Bol- giani et al. 2022) to the one the ground truth. Given horizontal winds w(x, y) and u(z y). remove the spatial mean, apply 2D Hann window, and compute the 2D Fourier transform to obtain the KE power spectral density PSD(k kyy) 1 (lū(k. kyy)
(6kkz k.),:,))))) 1)) Using the radial wavenumber k, / VA2. + -.g. perform ring averaging in Fourier space to obtain isotropic KE spectrum Es (k) ) for batch index b and wavenum- ber bin i. We then define the kinetic energy spectral RMSE between predicted E (k:) and target spectra (k;) as
B
N EE(K.)
RMSEKF
E(()))
(18)
B
N
This error directly measures how well the model reproduces the distribution of kinetic energy across spatial scales.
A.4 COMPARISON METHODS
We re-implemented both generic methods and climate-oriented methods for climate SR, making one of the most comprehensive comparisons to date in the machine learning community.
A.4.1 GENERIC METHODS
Generic methods include ResNet (He et al.
2016 U-Net (Ronneberger et al. 2015). ViT (Dosovit-
skiy et al. 2021), EDSR (Lim et al. 2017)
FFL (Tiagg et al.] (021). SwinIR (Liang et al. 2021). SRFormer [Zhou et al.) 2023), and SRGAN (Leiig et al. 2017). The implementations of ResNet, U-Net. and ViT follow the ClimateLeam paper (Nguyen et al. (023) to ensure a fair comparison.
EDSR EDSR (Lim al. 2017) is refined version of the ResNet architecture for SR. EDSR removes batch normalization layers and simplifies residual blocks, making it better suited for single- image super-resolution. The simplified architecture enables the construction of deeper networks stabilized via residual scaling, which significantly boosts SR results. We implement EDSR with 28 residual blocks which aligns with the implementation of ResNet in Climatel.eam.
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FFL Focal Frequency Loss (FFL (Jiagg et al. 2021)) frequency components that are difficult to synthesize. By down-weighting the low-frequency com- ponents and emphasizing the textures and details in reconstructed images. Though primarily applied to generative models (e.g., VAE, pix2pix, StyleGAN2). We build the FFL. based the ViT model in Climateleeam.
encourages models to adaptively focus
components, FFL helps preserve and recover fine
SwinIR SwinlR (Liang et al. 2021) is based on the Swin Transformer (Liu et al. 2021 The architecture comprises three stages: shallow feature extraction, deep feature extraction using resid- ual Swin Transformer blocks (RSTBs), and high-qualijg image reconstruction. SwinIR leverages the Swin Transformer's 's hicrarchical haftedd-indow attention within a residual learning framework. We set the depths to [3, 3, 3, 3] and num heads to 4 for better alignment with the parameters of ViT in ClimateLearn.
SRFormer SRFormer (Zhou al. 2023 introduces a permuted self-attention (PSA), which strikes an appropriate balance between the channel and spatial information for self-attention. PSA enables efficient computation of long-range pairwise correlations within significantly larger atten- tion windows, achieving better coverage of spatial context. We set the depths to [3, 3, 3, 3] and num_heads for better alignment with the parameters of ViT in Climateleearn
SRGAN SRGAN (Ldiig et al. 2017) is the first generative adversarial network (GAN) frame- work designed to produce photo-realistic high-resolution images at 4x upscaling factors. SRGAN employs perceptual loss that combines a content loss based high-level feature maps from pretrained VGG network and an adversarial loss from a discriminator, encouraging reconstructions that lie on the manifold of natural images. To balance the model parameters, build the SRGAN with 16 residual blocks in the generator and convolutional blocks in the discriminator.
A.4.2 CLIMATH-ORIENTED METHODS
Climate-oriented methods include DeepSD Vandal et al. 2017), FACL (Yan et al. 2024), and SmCL. (Harder al. 2023)
DeepSD DeepSD (aandal et al. 2017) adapts stacked Super- Coper-Resolution Convolutional Neural Networks (SRCNNs) for climate data downscaling. Each SRCNN performs a small upscaling step, and stacking them enables large-scale resolution enhancement, similar to multi-stage image super- resolution pipelines. The method also integrates high-resolution static features such as elevation as auxiliary inputs, analogous conditioning strategies in SR models. We train the DeepSD with the original architecture proposed in (Vandal et al. (017).
FACL Fourier Amplitude and Correlation Loss (FACL (Yan et al. 2024 comprises com- plementary components: Fourier Amplitude Loss (FAL) and Fourier Correlation Loss (FCL). FAL constrains the Fourier amplitude of model outputs to better capture spectral content, while FCL ad- dresses missing or misaligned phase information by enforcing correlation structures in the frequency domain. We build the FACL based the ViT model ClimateLearn.
SmCL SmCL Harder et al. 2023) introduces climate downscaling method that incorporates
hard physical constraints (e.g., conservation of mass or energy) directly into the model architecture, ensuring physically consistent high-resolution outputs. We build the SmCL based the ViT model in Climatel.ean
ClimateDiffuse ClimateDiffuse (Watt & Mansfield 2024) performs climate downscaling gen- erative task with diffusion model, providing both target prediction and probability estimation, which can be used for risk assessment. ClimateDiffuse serves as simple yet effective baseline to assess the capability of diffusion-based models for climate variables.
STVD STVD (Srivastava et al., 2024) extends recent video diffusion methods to super-resolving precipitation data by combining deterministic model with temporally-condiiionn diffusion model to generate dent climate downscaling that aligns with the setting of this paper.
patterns. We adapt this model to perform temporally indepen-
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DSFNO DSFNO YYng et al. 2024) formulates statistical downscaling as learning resolution- agnostic operator in Fourier space. It is trained on low-/high-resolution pairs with a small, fixed upsampling factor and is then applied in zero-shot fashion to downscale inputs to unseen higher resolutions. In this paper, we train DSFNO on our datasets and use as the backbone on which we build our proposed method GeoFAR.
A.5 DETAILED METHOD DESCRIPTION
In this section, we explain how to plug our approach into deterministic and generative baselines given the geography-informed representation Z:
Deterministic downscaling learns single mapping by empirical risk minimization:
i arg min E JuR) (Jo(Z)) ]n
(19)
where L is typically an e, based loss, and fe upsamples the input to the HR grid. Geo-INR steers fo toward geography-consisten high frequency details while maintaining fidelity.
Generative downscaling like SRGAN (Ledig et al. 2017) can also be plugged with our method for geo-conditioned learning to better generate plausible gigh-frequeny details. Let go be the Geo Reo-conditioned generator that maps Z to an HR image, and D a discriminator. The generator update minimizes fidelity loss via the Mean Squared Error (MSE):
min La = (o) THR [2]
(20)
while the discriminator update minimizes the binary cross-entropy (BCE) loss corresponding to the classic minimax game:
min CD -E log D& - E log (1 (I-Do(go(2) (goo)))))
This updates the adversarial training signal on D3 (as in SRGAN) while directing 9o strictly toward high-fidelity reconstruction via MSE. The Geo-INR modulation anchors the generation of high- resolution data geography information (location and terrain), helping recover region-specific high- frequency details and mitigating GAN artifacts.
A.6 IMPLEMENTATION DETAILS
All experiments are run on a working station with one NVIDIA RTX A5500 GPU and Intel Xeon Silver 4410Y CPU (1 socket, 12 physical cores, threads/core).
We implement our method and re-implement baselines using the ClimateLearm training pipeline (Nguyen et al., [203). For ERA5 and PRISM, we train for 50 epochs with batch size 16, learning rate 2 x 10 and weight decay 10-4 For CERRA (x2), we train for 20 epochs with batch size 4, learning rate 2 x 10-1, and weight decay 2 10-1 For CERRA (x4, x8), we keep the learning rate and weight decay at 2 x and reduce the batch size to 1 due to memory constraints. For ERA5 to MODIS,
train for 50 epochs with batch size 8, learning rate 2 x 10" 4 and weight decay 1 x 10-1 Early stopping applied in all settings if the validation loss does not decrease for 5 consecutive epochs.
In GeoFAR, we set the embedding dimension d to 64, and use two layers of SIREN to embed the geographical information. For FCK, set the kernel size (N) to the stride to and the zero- padding to length 4, so that we generate 64 (N2) channels aligned with the dimension d of Geo-INR.
A.7 ADDITIONAL EXPERIMENTS
Robustness and generalization. We investigate GeoFAR's robustness random initialization, its sensitivity to smoothed low-resolution inputs, and its ability to generalize to remote sensing observations:
Table 7 reports the performance of GeoFAR downscaling CERRA T2m from 22 km to 11 km under different initialization seeds. The performance is stable across the different seeds: RMSE remains unchanged, the mean bias and LFD only fluctuate within =00002.
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Table Robustness and generalization analysis that investigates GeoFAR's robustness (a) initial- ization seeds and (b) smoothed inputs (Methods with denote results with original inputs), as well as (c) models' generalization on downscaling ERA5 (SKT, 11km) to MODIS land surface tempera- ture (LST, 1. 1.1k)).
(a) Initialization seeds
(b) Smoothed inputs (CERRA x2)
(c) ERA5 to MODIS
Seed
RMSE
MB
L.FD
Method
RMSE
MB
L.D
Method
RMSE Pearson
MB
0
0.191
-0.001
9.245
VIT
0.380
0.033
10,496
VIT
3,474
0.771
1.822
23
0.191
0.000
9.243
VIT
0.436
0.071
10.824
U-Net
3,715
0.720
1.696
149
0.191
0.001
9.242
Geo
0.191
-0.000
9.245
GeoFAR[ViT]
3.266
0.766
0.309
71
0.191
-0.002
9.244
GeoTAR[[iT]
0.213
0.003
9.466
GeoFAR[U-Net]
2.718
0.844
0.717
Table 8: Additional experiments on CERRA (x2) that investigate (a) the effects of the number of embeddings on accuracy and inference speed (FPS), (b) the effects of different positional encodings, and (c) the utility of information from terrain vectors in GeoFAR. 'Elevation' means only using location and elevation as the input of INR, 'Vectors' mean using the location and terrain-differential vector input.
(a) Embedding dimension
(b) Positional encoding
(c) Terrain vector
Dim.
RMSE
MB
LFD
FPS
PF
RMSE
MB
LFD
Vector
RMSE
MB
L.FD
36
0.192
-0.001
9.254
11.3
Direct
0.195 -0.001
9,256
w/o
0.198 -0.001 9.310
64
0.191
-0.001
9.245
11.1
Space2Vec
0.192
0.001 9.253
Elevation
0.193
-0.001
9.260
100
0.190
0.000
9.235
10.7
SH
0.191
-0.001 9.245
Vectors
0.191
-0.001 9.245
Table 7b compares performances when using smoothed inputs versus the original inputs (CERRA 22 km) for downscaling CERRA 11 km. In the main paper, we constructed the CERRA dataset by downsampling the raw data from 5.5km to resolution variants for SR using bilinear interpo- lation. Here, we assess robustness to smoothed input simulations by first downsampling the raw data to 11 km and then to 22 km, applying Gaussian smoothing with a = 1 at each stage to obtain the smoothed inputs. Compared to the results without Gaussian smoothing, both methods suffer from a slight decrease of performance (RMSE, VIT: 0.380 + 0.436, GeoFAR: 0.191 - 0.213). However, GeoFAR still substantially improves the baseline (RMSE: 0.436 - 0.213) and shows better robustness to input degradation (RMSE: ViT 0.380 vs. 0.436, GeoFAR: 0.191 vs. 0.213).
To analyze the generalization ability on diverse data products, Table 7c presents the results on downscaling from ERA5-Land (SKT, 1 1kmm to MODIS (LST. 1.1km), i.e. when training the model to downscale from reanalysis products (ERA5) to remote sensing observations (MODIS). This task more challenging than other settings due to large domain and resolution gaps between the input and output, leading to higher errors than observed on the ERA5 and CERRA datasets [T. Nonetheless, this challenging dataset still benefits from GeoFAR, with RMSE and Mean Bias markedly reduced with respect to both the ViT (RMSE: 3.474 + 3. 3,266) and U-Net (RMSE: 3.715 + 2.718) baselines.
Hlyper-paraeee analysis. Table 8a presents the effects of the embedding dimension in Equa- (SH) channels (i.e.. d). Increasing SH channels from 36 100 reduces RMSE by 0.002 and LFD by 0.019, while slightly decreasing the inference speed by 0.6 frames per second (FPS). To balance accuracy and cost, we use d 64 in all experiments.
tion 5 We set L E (5, 6, 6. yielding (L+1)² = {36, 64, 100} spherical-harmontt
More ablations for Geo-INR. Table 8b compares three location encoders (latitude/ongitudee based): Direct stacks (lat, lon) into d channels as INR input; Space2 Véc uses sine and cosine func- tions of different frequencies to encode positions in space (Mai et al.) 2020); SH uses spherical harmonics (Rußwurm et al. 2024). Among them, SH achieves the best overall performance, so we adopt it as our default location encoder. Table 8c evaluates terrain-aware embeddings of the SH location encoder. Removing dirainndifferentiall cues degrades RMSE by ~ 4% (from 0.191 to 0. 0.198) and worsens the frequency metric LFD (from 9.245 to 9.310). Using only elevation partially recovers accuracy (RMSE 0. 193). The composite terrain- differrnniill embedding yields the best results (RMSE 0.191, LFD 9.245).
top
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comparison of model size (millions of parameters) and inference speed (frames per second, FPS). All models are tested on working station with RTX A5500 GPU, on the CERRA dataset with input image size 534 534.
Table 9:
Model
ResNet
U-Net
VIT SRGAN EDSR SwinIR GeoFAR[U-Nei] GeoFAR[ViT] GeoFAR[SRGAN]
#Params (M)
8.3
11.6
9.0
2.3
12.5
3.5
7.0
Speed (FPS)
3.8
14.1
15.0
16.6
5.2
12.8
11.0
11.1
11.7
Predictioms
Bioo
(0) Vir-based
GcoFAR [V]]]
[T
Predictions
Biss
VIT
GeoFAR [ViT]
GeoFAR [VI]]
Predictions
(b) SRGAN-NN-aEE based
Dias
SRGAN
GeoFAR [SRGAN]
SRGAN
GeoFAR [SRGAN]
Figure 6: More examples of the super-resolution results on CERRA. (a) Results from ViT-based methods; (b) Results from ERGAN-based methods.
Computational cost. Table compares the model size of baseline methods and proposed method. Compared to baseline models like U-Net, our proposed approach only introduces 0.9M additional parameters and slightly slows down the performance by about 3 FPS. Even image of 11 le resolution (534 x 534) covering the whole Europe, GeoFAR is able to run at over 11 FPS on RTX A5500 GPU, offering favorable trade-off between extra computation and accuracy gains.
target
Physical fidelity. We evaluate the physi- cal fidelity of predicted wind fields (10u, 10v)) on CERRA x2. IO the RMSE for the 10m zonal and meridional winds, as well as the kinetic energy spec- tral RMSE (RMSE&E. equation 18). for the VIT baseline and GeoFAR. GeoFAR substantially reduces the pointwise errors of both 10u and 10v, and, more impor-
Table 10: Comparison of physical fidelity for 10m winds using RMSE and kinetic energy spectral RMSE (RMSExE) CERRA.
Method
RMSE
RMSE
RMSFRE
VIT GeoFAR[ViT]
0.341
0.355
60.998
0.184
0.186
18.857
tantly, lowers RMSE&E from 60.998 to 18.857, indicating much closer match to the target ki- netic energy distribution and a higher physical fidelity of the reconstructed wind fields across the frequency components.
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Prediction
Bias
VIT
GeoFAR [VT]]
GeoFAR [VI]
Prodictions
Blas
VIT
GooFAR [Vi]]
VIT
GooFAR [VIT]
Figure 7: More examples of the super-resolution results ERA5.
A.8 VISUAL RESULTS
this section, we provide more visualizations of the super-resolution results (covering both deter- ministic models and generative models), well visualizations of the terrain information.
More results on CERRA and ERA5. Figure and Figure 7 provides more examples on the CERRA and ERA5 dataset, covering both deterministic methods (i.e., ViT, GeoFAR[ViT) and gen- erative methods (i.e., SRGAN, GeeFAR[SRGAN]] In these two figures, we provide more examples of different regions
the globe: from Iceland, the Scandinavian Peninsula, the Alps, Ana- tolia, our proposed method consistently improves the fidelity and reduces the prediction bias in the super-resolved results of baseline models. Compared deterministic models, generative baselines provide a better modeling of high-frequency information, as shown in Figure 6 (b). Nevertheless, the method proposed this paper further alleviates artifacts and reduces the prediction bias caused by terrain on the basis of GAN. Moreover, we also note that the gains are generally more visible on CERRA (5.5 km) than on the much coarser ERA5 grid (2.81259), where each grid aggregates information over larger areas. Nevertheless, even on ERAS we still observe reduced bias in difficult regions with strong high- frequecyyy variability, such as Alaska and the Balkan Peninsula (Figure) 7).
Frequency-ave aware representations. Figure provides some examples of the frequency-aware rep- resentations in different channels: the first/third row shows images convolved by FCK, and the sec- ond/fourth shows the corresponding Fourier spectrum. As the frequency indices increase, the image shows increasing frequency, and the Fourier spectrum shows higher energy towards boundary regions. Compared to the DWT-decomposed subbands (Figure 99, which mostly concentrated in the I.I. band, FAR shows a more fine-grained representation frequency components and balanced energy distribution in different channels, which is crucial for the rrequencybbiased climate data.
Terrain information. To the elevation map the globe and Europe, which is used to get the terrain vectors in our Geo-informed representations.
A.9 LIMITATIONS AND FUTURE WORKS
In this paper, we focused on learning frequency- patterns and geo-informed representations to for climate downscaling. A limitation is that our geographic factors mainly characterize the land sur- face, whereas atmospheric dynamics at multiple pressure levels also shape near-surface variability. Extending the framework to multi-dimennional implicit neural representations that are conditioned on pressure level, height, and key atmospheric variables (e.g., winds, humidity) is a natural next step. A second limitation is our viriaevvriable setting: varialva relationships between vari- ables (e.g., among temperature, humidity, pressure, precipitation, and wind) are not explicitly mod-
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Published as a conference paper at ICLR 2026
Image
Spectrum
Imago
Speetrrm
Figure 8: Examples of the first eight subbands from FAR of 64 subbands (ERA5)..
Image
Spectrum
LH
HL
Figure 9: Examples of the decomposed subbands from DWT (ERA5).
eled. Future directions include multi-variable, physically consistent downscaling via shared latent fields and cross-variable operators, and the incorporation of soft or hard physical constraints (e.g., hydrostatic balance, thermodynamic identities) through solvers. More broadly, how to jointly capture cross- variable dependencies while enforcing physical consistency and providing calibrated uncertainty estimates remains an important open question.
losses differentiable
Elevation (Bm)
Elevation
0.0
ERAS Elevation Map
CERRA Elevation Map
Figure 10: The elevation maps of ERAS and CERRA.
A.10 LLM USAGE
We used LLMs as assistive tools during the writing this paper. Specifically, LLMs were employed for polishing grammar and improving clarity. LLMs were not involved in research ideation and experimental design.
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Reviews:
[{"review_id": "bsiiWTRQEX", "reviewer": "Reviewer_s9rN", "summary": "The paper proposes GeoFAR, a new method for climate downscaling. GeoFAR resolves the oversmoothness issue of existing deep learning models by explicitly encoding input data at different frequencies and injecting the model with geographical neural representations for location and elevation. Experiments show that GeoFAR performs better than existing baselines and helps mitigate high-frequency prediction errors in both deterministic and generative models.", "questions": "- The Frequency-aware Convolution Kernels are fixed convolution kernels. Can they be learned so that the model is more data-driven?\n- Can the proposed method be applied to multi-variable data? The experiments trained separate models for each variable, but I believe it's beneficial to use multiple variables in the input, so the model can exploit interactions between them and make better predictions.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "- The paper aims to address an important problem in climate downscaling: oversmoothness and bias towards low-frequency information.\n- The paper is well-written and the proposed method is relatively simple (which is good).", "weaknesses": "I have two main concerns: the soundness of the proposed method and the significance of the empirical results.\n- The two proposed components, explicit frequency-aware encoding and geographical representation learning, aim to exploit high frequencies in the input, but what I think is more important is the output or ground-truth. When we train a deep learning model with an MSE loss, for example, regardless of how the model processes the input data, it can still learn to over-optimize for the low-frequency information in the ground-truth, and thus will still predict oversmooth fields.\n- In practice, since the lower-resolution input is often smoother, exploiting high-frequency information in the input itself seems like a minimal gain.\n- Empirically, there are only minor improvements when using GeoFAR, especially when compared with the UNet baseline. In the ablation study, I believe that if the Unet architecture is used, the difference would be minimal.\n- Qualitative results in Figures 4 and 7 also show almost identical predictions of the ViT model with or without GeoFAR.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "tqMJXq0WUb", "reviewer": "Reviewer_AjLx", "summary": "The paper proposed GeoFAR to address the issue of overfitting to low-frequency components in climate data downscaling. GeoFAR explicitly encodes climatic patterns at different frequencies and use the location and elevation information. The model was evaluted in both deterministic and generative super-resolution models over different datasets with various spatial resolutions, atmospheric variables, and downscaling ratios.", "questions": "Please better explain the novelty of paper in terms of the model structure design. What is the key contribution of the frequency-aware convolution kernel?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1.\tThe paper addresses an important issue in climate downscaling that existing models are often biased toward low-frequency components.\n2.\tThe paper conducts comprehensive experiments over different datasets, different downscaling ratios over different variables and the ablation experiments show the improvements brought by each component of the proposed approach.", "weaknesses": "1.\tThe proposed model appears to use a combination of geolocation aware encoding and frequency-aware convolution kernel, which are similar to existing ideas. As example, the novelty of the frequency-aware convolution kernel using 2D DCT with N×N grid instead of 4 zones is not clear. It seems 2D DCT as the kernel weight has also been used in computer vision models such as Harmonic Convolutional Networks. Fcanet also uses similar idea to take DCT as the weight.\nHarmonic convolutional networks based on discrete cosine transform. Pattern Recognition.\nFcanet: Frequency channel attention networks. In Proceedings of the IEEE/CVF international conference on computer vision.\n\n2.\tThough the model has compared many baseline models such as generative and deterministic models, the baseline models are a little bit out of date. For generative models, including more newer super resolution models will be helpful, like: Precipitation downscaling with spatiotemporal video diffusion. Advances in Neural Information Processing Systems. 2024.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "5omP8j9iOi", "reviewer": "Reviewer_oWKs", "summary": "GeoFAR: Geography-Informed Frequency-Aware Super-Resolution for Climate Data\nIn this paper, the authors introduce GeoFAR, a novel approach to climate data super-resolution that explicitly addresses the frequency bias of neural networks and the geography-dependent variability that is inherent to climate data. The paper integrates a Frequency-Aware Representation (FAR), which is a convolutional module leveraging Discrete Cosine Transform (DCT) bases that separate and encode high- and low-frequency information. This approach also uses a Geography-Informed Implicit Neural Representation (Geo-INR), which uses a coordinate-based representaiton that jointly encodes spatial and elevation information using spherical harmonics and SIREN networks. GeoFAR can be used with any deterministic or generative SR model, and the authors impressively demonstrate SOTA results across different spatial resolutions, atmospheric variables, and downscaling ratios.", "questions": "* are the reported quantitative results averaged over multiple training seeds, or based on a single run?\n* can you elaborate on how the frequency-aware and geography-informed components interact during training? for instance, does the Geo-INR modulate the FAR in a spatially adaptive way tied to physical processes, or mainly improve general representation quality?\n* this is more of an aside, but the paper shows results for temperature and geopotential. how well does GeoFAR generalize to other variables (e.g., precipitation, humidity) with different spatial-frequency characteristics?\n* how sensitive is the model’s performance to the truncation degree (L) in the spherical harmonics encoding? have you explored trade-offs between model accuracy and computational cost?\n* could you clarify whether Geo-INR can be pretrained or shared across datasets/variables, or must it be trained jointly with each SR model?\n* is there a timeline or specific repository planned? are there any preprocessing scripts or model-specific configurations that will be included for reproducibility?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "* well-framed motivation (Figure 1 is strong), supported by innovative design using frequency- and geography-aware representations\n* having a model-agnostic design makes this approach easily adaptable\n* the authors include extensive experiments across datasets, resolutions, and atmospheric variables to demonstrate the improvements from their approach. there seems to be consistent improvement over baselines, and the work clearly demonstrates that GeoFAR helps with high-frequency fidelity and reduces bias.\n* analysis is well-structured, with comprehensive ablation studies and frequency+elevation sensitivity studies (Figure 5 was particularly interesting)", "weaknesses": "* not a necessity, but it would make the dense notation and equations in  more intuitive with a diagram (it could even go in the supplementary materials)\n* although the comparisons in the authors’ experiments are broad, there are few diffusion baselines included (SR3 from Saharia et al. 2023; Watt & Mansfield 2024) in quantitative analysis and other methods could be helpful to look into (PhIREGAN from Stengel et al. 2020), despite being mentioning that they are strong recent approaches\n* while the quantitative analysis is very informative on the whole, it would be food to include statistical analysis with variance across seeds if this is possible\n* to more robustly evaluate the physical fidelity of the predictions, consider using additional evaluation frameworks such as generating kinetic energy spectra from the wind fields\n* section 4.4 has the beginnings of this, but the paper would benefit by a deeper discussion of how to physically interpret the frequency and geography components and how they related to known phenomena\n* in the appendix, it would be good to include a brief discussion of computational cost/runtime scaling…efficiency is another dimension that’s important to consider in the practical deployability of these methods\n* it would be helpful to cite the relevant frequency-aware transformer works and coordinate-based climate model papers; the authors may also need to reference some work in the neural operators space (see Li et al. 2021) because they also tackle spectral bias in physical modeling", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "8FeIO8uyHv", "reviewer": "Reviewer_vEup", "summary": "The authors argue that during image super-resolution using DNNs, DNNs tend to preserve low-frequency structures while neglecting the retention of high-frequency components. This leads to performance degradation when applying DNNs to meteorological data super-resolution tasks, which are predominantly low-frequency. To address this issue, the authors propose GeoFAR, a plug-and-play module. GeoFAR encodes input data into frequency-domain representations and additionally introduces implicitly encoded spatial information as input to the DNN, thereby improving performance on climate data super-resolution tasks dominated by low-frequency content. The authors validate the effectiveness of their method across multiple datasets and various network architectures.", "questions": "1. Can the authors validate the accuracy of their downscaling model using observational data—for example, by comparing against ground meteorological station measurements (evaluating accuracy at station-corresponding grid locations), MODIS LST (compared with ERA5 SKT), and GPM IMERG precipitation data (compared with ERA5 precipitation)?\n\n2. Can the authors provide additional details regarding dataset construction and validate the reasonableness of their approach? For instance, do the downsampled data exhibit similar high-frequency content and entropy to real-world low-resolution observations? To my knowledge, directly interpolating HR remote sensing data to LR resolution often retains excessive high-frequency details—a phenomenon easily verifiable by downsampling Sentinel-2 data to 500m and comparing it with MODIS data. The remote sensing community typically simulates LR data using multi-stage downsampling combined with smoothing. Could different dataset construction strategies lead to different conclusions?\n\n3. The authors repeatedly emphasize in the related work that existing DNNs fail to preserve high-frequency information and produce overly smooth outputs. However, as shown in Table 1, most tested DNNs already yield reasonably good results, and GeoFAR does not demonstrate a fundamental improvement. Does this suggest the authors overstate the limitations of current methods?\n\n4. GeoFAR essentially performs input-level data augmentation without modifying the internal architecture of the DNN. Will the injected high-frequency information still be forgotten by the network? Does GeoFAR truly address the core issue, or does it merely provide a superficial fix?\n\n5. How does GeoFAR compare against methods that explicitly incorporate frequency-domain considerations at the operator level? What about the latest methods from CVPR or ICCV 2025? Could GeoFAR be combined with them for even greater gains? (This would help substantiate the claim that GeoFAR is truly plug-and-play.)\n\n6. As an open-ended question: how well does GeoFAR perform on super-resolution of various remote sensing indices—for example, NDVI (from MODIS 500m to Landsat 30m)? Super-resolution of remote sensing indices is more amenable to cross-validation using independent high-resolution observational data.\n\n7. Can the authors add a clear statement of contributions? Currently, the paper’s contributions remain vague.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. GeoFAR is a plug-and-play method, and the authors demonstrate that it is better suited for meteorological data super-resolution tasks compared to commonly used encoding methods such as DWT.\n\n2. GeoFAR shows performance improvements across multiple neural network architectures, suggesting that performing super-resolution in the frequency domain is a more suitable approach for meteorological data super-resolution, offering new insights to the community.\n\n3. Implicitly encoding spatial information into features usable by neural networks is an important research direction in recent years, and the authors present a compelling practical application in the context of super-resolution.", "weaknesses": "Overall, I find this an interesting paper, but the experimental validation raises concerns:\n\n1. Directly downsampling high-resolution data to low resolution to form LR-HR pairs is an unreasonable practice. Such interpolation retains excessive high-frequency information. Given that the authors do not provide a detailed description of dataset construction, I question the validity of their datasets. Retaining excessive high-frequency details in the LR data constitutes information leakage—could this be the actual reason why GeoFAR, which optimizes in the frequency domain, appears effective? As shown in Table 1, comparing Global-to-Local Downscaling and Local Downscaling, the UNet results indicate that when the task involves real low-resolution to high-resolution data (e.g., ERA5-PRISM), the improvement from GeoFAR is significantly smaller than in simulated LR-HR scenarios.\n\n2. The current experimental results lack comprehensive validation. In quantitative remote sensing, it is common practice to use multiple independent data sources for cross-validation—for example, jointly using reanalysis data and actual remote sensing observations—rather than relying solely on reanalysis data.\n\n3. The paper suffers from significant writing issues, including imbalanced content depth, insufficient discussion of key issues, and poor organization. For instance, the related work section merely lists numerous existing methods without establishing a clear causal chain between “existing approaches” and the “problems summarized at the end of the section,” nor does it validate certain claims. Specifically, in Section 2.2, the authors hastily assert that “current methods remain based on natural images while poorly mimicking the biased frequency distribution of climate data,” yet they fail to provide a mathematical explanation for why existing methods underperform on meteorological data, nor do they compare against recent frequency-domain-based super-resolution methods presented at major conferences (e.g., BF-STVSR, DiffFNO).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)