Station2Radar: Query‑Conditioned Gaussian Splatting for Precipitation Field
Authors: Doyi Kim
Minseok Seo
Changick Kim
Venue: ICLR 2026 Poster (2026)
Keywords: climate change
precipitation
Primary area: other topics in machine learning (i.e., none of the above)
TL;DR: We introduce Query-Conditioned Gaussian Splatting (QCGS) for generating gridded rainfall fields. Unlike standard 2D Gaussian splatting that renders the entire image, QCGS focuses only on queried regions, reducing wasted computation.

Abstract: Precipitation forecasting relies on heterogeneous data sets. Weather radar is accurate, but coverage is geographically limited and costly to maintain.  Weather stations provide accurate but sparse point measurements, while satellites offer dense, high-resolution coverage without direct rainfall retrieval. To overcome these limitations, we propose Query-Conditioned Gaussian Splatting (QCGS), the first framework to fuse automatic weather station (AWS) observations with satellite imagery for generating radar-like rainfall fields. Unlike conventional 2D Gaussian splatting, which renders the entire image plane, QCGS selectively renders only queried rainfall regions, avoiding unnecessary computation in non-precipitating areas while preserving sharp precipitation structures. The framework combines a radar point proposal network that identifies rainfall-support locations with an implicit neural representation (INR) network that predicts Gaussian parameters for each point. QCGS enables efficient, resolution-flexible rainfall field generation in real time. Through extensive evaluation with benchmark precipitation products, QCGS demonstrates over 50\% improvement in RMSE compared to conventional gridded rainfall products, and consistently maintains high performance across multiple spatiotemporal scales.

Published as a conference paper at ICLR 2026
STARION2RADAR: QUERY-CONDITIONED GAUSSIAN SPLATTING FOR PRECIPITATION FIELD
Doyi Kim, Minseok Seo, Changick Kim
Korea Advanced Institute Science and Technology (KAIST) (doy kim, mi nseok. sec, changi ckkkkkt st ac kr
ABSTRACT
Precipitation forecasting relies on heterogeneous data. Weather radar is accurate, but coverage is geographically limited and costly to maintain. Weather stations provide accurate but sparse point measurements, while satellites offer dense, high- resolution coverage without direct rainfall retrieval. To overcome these limitations, we propose Query- Seeyy-Conditioned Gaussian Splatting (QCGS), the first framework to fuse automatic weather station (AWS) observations with satellite imagery for generating precipitation fields. Unlike conventional 2D Gaussian splatting, which renders the entire image plane, QCGS selectively renders only queried precipita- tion regions, avoiding unnecessary computation non-precipitating areas while preserving sharp precipitation structures. The framework combines a radar point proposal network that identifies rainfall-support locations with implicit neural representation (INR) network that predicts Gaussian parameters for each point. QCGS enables efficient, -ollution-flexible precipitation field generation real time. Through extensive evaluation with benchmark precipitation products, QCGS demonstrates over 50% improvement RMSE compared to conventional gridded precipitation products, and consistently maintains high performance across multiple spatiotemporal scales.
INTRODUCTION
Recent data-driven models, including transformer-basee (Pathak et al. (2022): Bi et al. et al. [2023;; Nguyen et al. (2023); CCen et al.] (2023a b) and diffusiio-basee (Price et al. (2025)
22233 : Lam
forecasters trained on ERA5, now rival or surpass traditional numerical weather prediction (NWP) models at medium ranges (up 15 days).
Yet precipitation remains particularly challenging (Bonavita 2024
Liu et al. 2024 An et al. 2025).
Both operational NWP systems and current global data-driven models operate at coarse resolutions of tens of kilometers (c.g., ERA5), whereas the precipitation features most relevant for local impacts emerge at sub-grid scales, intermittenlly and locally This scale mismatch complicates observation and limits the usefulness of forecasts for downstream decisions. Historically, short-range precipitation prediction relied radar echo extrapolation at its native resolution, since NWP could not resolve small-scale convection. Operational systems therefore propagate reflectivity fields using optical-floo methods such Lucas-Kanade (Pulkkinen al. 2019), with forecast skill fundamentally constrained by radar fidelity. Deep learning reinforced this paradigm. Centric benchmarks (Veillette et al. 2020) enabled progression of models from ConvLSTM (Shi
2015) diffusion- based nowcasting approaches (Gao et al. 2023: Yu et al. 2024a Gong et al. 2024a b) to achieve strong short-lead performance. However, precipitation forecasting is far from sol solved. Most pipelines assume radar as the primary input, but radar networks are costly and geographically limited, making these approaches feasible mainly in regions like Europe and the United States. Moreover, radar resolution is effectively fixed, limiting the representation of processes occurring below that scale.
These limitations motivate approaches that move beyond radar-only inputs. Conventional attempts to construct precipitation fields without radar have relied on statistical interpolation from gauges.
Corresponding author.
'Rainfall often forms in localized, rapidly evolving structures smaller than the pixels of global models, leaving these subgrid-scale processes unresolved in numerical weather prediction models.

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Published as a conference paper at ICLR 2026
Emptrical weighting
Learnable weighting
(a) Weather Station
Multiquadric
(c) QCGS (Ours)
(d) Radar (GT)
Interpolation
Figure I: Construction of precipitation fields from (a) sparse AWS observations. (b) Empirical kernel- based interpolation oversmooths and blurs rainfall boundaries. (c) QCGS leverages satellite context and gauge anchors to selectively place Gaussians, producing resolution-flexibl and structurally consistent fields. (d) Ground-truth radar at km resolution for reference.
Methods such as Barnes interpolation, kriging, or optimal interpolation (Barnes) 1964
Alaka &
Elvander 1972. Biau et al. 1999) represent observations by assigning Gaussian weights across grid. While effective in principle, these methods tend to blur sharp precipitation boundaries and are highly sensitive to station density and empirically chosen kernel parameters.
Recently, satellite-only approaches such as Sat2Radar (Veillette et al., 2020 Park et al. 2025) have been proposed to approximate precipitation fields directly from spaceborne imagery. How- ever, satellite estimates carry substantial bias and uncertainty, often produce outputs only at fixed resolutions, and cannot directly leverage the physical accuracy of gauges. In parallel, several fusion- based approaches have been explored, correcting satellite products or radar imagery with gauge observations (Benoit 2021 Ruan et al.,, [025 Curcio al. (222).. These methods improve grid- ded precipitation estimates by bringing them closer to ground values, but they operate strietly on fixed-resolution grids and do not cover continuous, resolution-free field reconstructions. Moreover, approaches such as [Benoit (202T) require radar reflectivity as input, whereas our goal is explicitly radar-free precipitation generation.
In summary, radar-based methods have inherently limited spatial coverage and fixed resolution, making them unable resolve fine-scale rainfall features operational importance.
In this work, we propose combining satellite imagery with automatic weather station (AWS) measure- ments to generate precipitation fields without requiring radar. Our key insight that Gaussian weight- ing, long used in objective analysis. is representationally equivalent to Gaussian Splatting (Kerbl al. 2023). Traditional interpolation computes a weighted sum of point observations using Gaussian kernels. GS generalizes this idea by modeling each observation as a "Gaussian blob" with learnable parameters, enabling cooluution-annosti rendering and selective allocation of computation.
Formally, weegsted interpolation query location is
Σ Kx - ms) M/i Σ/ Ko 11))
Saw(x)
where ys is the observation at station and K₂ is a Gaussian kernel. Gaussian Splatting (GS) instead defines
N
fas (x) = Σ Kxx (x -1))
(2)
i=1
with learnable amplitude a; and covariance E, Classical Gaussian weighting is recovered special case of GS with fixed isotropic kernels, while GS further allows anisotropy, adaptive amplitudes, and resolution-frec rendering, which are key advantages for representing sharp and localized precipitation fields.
We introduce Query-Conditioned Gaussian Splatting (QCGS) for precipitation field generation. QCGS takes satellite imagery and automatic weather station (AWS) observations as inputs and outputs a continuous precipitation field arbitrary resolution, without requiring radar. Unlike
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Published as a conference paper at ICLR 2026
standard GS, which directly fits Gaussian primitives to ground-trute truth fields, QCGS conditions its Gaussian parameters on satelliteAWSS context, enabling generalization across regions and seasons.
QCGS consists of three components: (1) Selective rendering, which evaluates only precipitation- supporting regions, suppressing non-rain areas and improving efficiency. (2) satelttelliee fusion, where dense satellite features provide spatial coverage and sparse AWS gauges act as accurate anchors, jointly proposing candidate Gaussian locations. (3) INR-based parameterization, in which an implicit neural network maps local satellite features and query locations Gaussian parameters (amplitude and covariance), enabling adaptive, anisotropic blob shapes and resolution-free rendering.
Through this design, QCGS moves beyond traditional empirical weighting (Fig. D and produces high-resolution precipitation fields that preserve sharp structures, are computationally efficient, and generalize effectively.
2
RELATED WORK
We discuss three related areas: Gaussian Splatting for efficient field generation, Implicit Neural Representations (INR) for conrdinate-conditioeedd modeling, and data-driven methods in meteorology.
2.1
GAUSSIAN SPLATTINGG
accelerates NeRF (Mildenhall et al. 2021] by representing scenes with Gaussian primitives and avoiding redundant rendering, enabling real real-time time performance (Wu al. 2024 Huang et al. 2024 Yu al. 2024b; Guédon & Lepetit 2024 Yang et al. 2024). Recent work has extended this idea to 2D images for compression and super-resolution such GaussianImage (Zhang al. 2024). Image-GS (Zhang et al. 2025), and LIG (Zhu et al.
3D Gaussian Splatting (3DGS) Kerbl et al. 2023
2025), which allocate Gaussians adaptively based on gradients or frequency content. Follow-ups like GaussianSR (Hu et al., 2025). ContinuousSR (Peng et al. 2025), and GSASR (Chen al. 2025) introduced kernel banks and feed-forward prediction for scalability and generalization. While effective, these methods remain ipage-specific, motivating our extension precipitation fields.
2.2 IMPLICIT NEURAL REPRESENTATIONS
2020) encodes signals as continuous coordinate-to-value mappings, widely applied 3D scene reconstruction (Mildenhall et 2021 Barron et al., 2021 Martin-Bruse Brualla et al. 2021 Barron et al. 2022 Müller et al.) 2022). image compression, and arbitrary super- resolution (Chen et al.) 2021 Yang et al. 2021 Lee Jin 2022 Cao al., 2023). Its strength lies in resolution-free modeling, but INRs must query all coordinates and lack explicit spatial structure, limiting efficiency. Nonetheless, their representational flexibility motivates our query-conditioned adaptation for precipitation fields.
INR (Sitzmann et al.
2.3 APPLICATIONS OF DEEP LEARNING IN METEOROLOGY
Deep learning has transformed meteorology. especially in precipitation nowcasting and weather prediction. ConvLSTM (Shi et al. 2015) pioneered spatiotemporal forecasting, followed by GAN-
based (Ravuri et al. 2021) and transformer based (Bi et al. 2023) approaches that rival or surpass
NWP models. More recent methods span precipitation forecasting (Veillette et al. 2020 Gao et al.)
2022b; Yoon et al. 2023 Gao et al. 2023 Gong et al. 2024a Yu et al. (202a)) and global atmospheric
variable prediction Bii al. 2023 Lam et al. 2023; Xiao et al., 2023 Chen al. 2023b Xu et al. 2024 Kochkov et al. 2024). Despite progress, most rely on radar or reanalysis data (e.g.. ERA5).
Recent data assimilation methods (Xiao al. | (2023) attempt reduce this dependency, but to our knowledge, our work is the first to directly generate precipitation initial conditions from satellite and station data.
3 PRELIMINARIES
We summarize the key notions from the perspective of 2D image rendering.
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AWS Enander
SAMPLING
GAUSSIAN FARAMETER ESTIMATOR
Roinfall Eatmmrr Cy)
GAT Blocks
AWS Cross steeton
Jome snj Eoei
GAT
CAT
Randerk
Mixed Damplin
Conv Encoder
Com Encoder
Cone Dacoani
Decotte
Corw Carw becoote
CTX
OY
Com
Pepueci
Prlicer
Fiud Rader
Condition
Figure 2: Overview of the proposed QCGS pipeline. AWS observations and satellite BT imagery points. A rainfall-aw -aware
are fused to produce coarse surrogate field and candidate sampling strategy and an INR-based Gaussian estimator then predict splatting parameters, yielding resolution-flexible precipitation fields through selective Gaussian rendering.
Implicit Neural Representations (INR). An INR models an image continuous function
=
that maps spatial coordinates R² to pixel values. Rendering an H X image requires evaluating fo at all pixel centers X E Ω which scales as O(HW). INRs are resolution- freee and differentiable coordinates, but dense querying makes high-resolution synthesis slow.
Gaussian Splatting. 3D Gaussian Splatting (3DGS) represents a scene as set of anisotropic 3D Gaussian primitives. Each primitive has center μ* 12 covariance Σg E S opacity og. and color Rendering proceeds by projecting the Gaussians to the image plane, linearizing the covariance with the Jacobian of the projection, and compositing front-to-back with depth ordering:
K
((u) = Σ (u) ou (T( Cs.
where (u) is the accumulated transmittance and Gu(u) the screen-space Gaussian footprint.
In contrast, 2D Gaussian Splatting (2DGS) removes geometry- elements and operates directly on the image plane. No 3D positions, projections, depth ordering required. Each primitive is simply a 2D Gaussian with center
P4 E ER,
E
02 E R.
The rendered value at a pixel location x E is
K
((x)
a2 exp - (x
T 1x mi))
Thus, 2DGS retains the resolution- free rendering benefits of 3DGS while being simpler and computa- tionally cheaper, making it well suited represent sharp, localized precipitation fields.
METHOD
As illustrated in Fig. 2 QCGS follows three-stage pipeline that fuses AWS gauge observations with satellite imagery to generate precipitation fields. Importantly, the radar point proposal network and the Gaussian rendering module trained separately.
We first train the radar point proposal network to produce reliable rainfall-support locations, and then train the Gaussian rendering stage top of these fixed proposals. Thus, QCGS operates as a two-stage model in terms of training, even though the full pipeline consists three conceptual components.
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4.1 TASK DEFINITION
We aim to estimate a high-resolution precipitation field Rx(x) using two inputs at time t: a satellite
image Y FRR and sparse AWS measurements X { E Z} observed at irregular spatial coordinates (14)-
Formally, the goal is to learn a mapping
Fe: (Y) (x(x,
x X
where denotes a continuous 2D spatial domain. Unlike standard Sat Sat-RRadar image-to-image translation (Park al., 2025), our input consists of both dense image and irregular point set, and the output must be defined at arbitrary query locations rather than on a fixed grid.
Because the satellite image coarse km resolution) and the output precipitation field may be queried at much finer scales (e.g., 0.5 km or continuous coordinates), the task also exhibits a super- resolution nature:
R Rcoarse
7
Snae.
inneel
[2coarse
The model parameters are estimated by minimizing reconstruction loss against radar observations during training:
θe
= arg min Fo(Y, x*)
In summary, the task a hybrid problem combining image + point fusion, continuous field recon- struction, and resolution-free rendering.
4.2 RADAR POINT PROPOSAL NETWORK
Automatic weather station (AWS) observations provide direct gauge measurements of rainfall. Although they offer ground truth rainfall values, the data are sparse and often contain missing values outliers. In contrast, satellite-basel based brightness temperature (BT) imagery Y E R Hx provides dense spatial coverage and is generally reliable, but only correlates indirectly with precipitation. We combine these two complementary sources to compensate for their respective limitations.
At each time step t E T, the set AWS observations is defined as
X
{af i I}. I [I........
where æ denotes the rainfall measured at station i and [Z] is the number of stations. Since X may include missing values and anomalies, we employ a graph attention network (Velickovic et al. 2017) fa Oz) to extract robust representation:
(x²).
The satellite BT image Yt is processed by an encoder-decoder network f5(5; to produce dense rainfall prediction:
Rt = fy
where the AWS representation 2t is fused into the decoder via cross-attention.
During training, the model parameters are optimized by minimizing the mean squared error (MSE) between the predicted rainfall ît' and the radar-derived ground truth R²:
LMSE
1
Σ ST
R R21
T
4.3 RAINFALL-AWARE POINT SAMPLING
In precipitation forecasting, light rain rarely leads to disasters, while heavy precipitation events much more likely to trigger hazards and high-impact events. Therefore, the most critical objective is to accurately predict regions of heavy precipitation. Uniformly sampling points across the entire prediction field fe' is inefficient, treats all regions equally regardless of their importance. To

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Ground wuth (Radrr
(9) Unifsm surpling
Rdge sunglng
(6) Henvy nin smpling
Mised sompling
Figure 3: Visualization different point sampling strategies for precipitation fields. (a) Ground truth radar field, (b) uniform sampling. (c) edge-based sampling, (d) heavy-rain sampling, and (e) our mixed strategy. Uniform sampling provides overall coverage but lacks details heavy rainfall regions. Edge-based sampling emphasizes boundaries but overlooks fine-scale structure. Heavy-rain sampling concentrates points on intense precipitation, leaving light-rain areas underrepresented. In contrast, our mixed strategy balances intensity-ave aware sampling with spatial coverage across the field.
overcome this limitation, we design sampling strategy that incorporates three factors: (1) gradients of it' to emphasize edges, (2) uniform coverage within ft' and (3) rainfall intensity to prioritize heavy-rain regions.
We denote image-domain coordinates as x E Ω2 and write (x) for its rainfall value.
Let R' E l! be a coarse precipitation field at time t, and define the rain- mask as
S (x R (x) T}:
with threshold т. We then construct convex mixture of three normalized terms:
Pinit (x) Gs, (x) + BUs + Hxxx,
ar 1,B,7200 20, 3
where
((xxS.)) Us, (x) En. F(
Gs, (x)
(xCC&: ([ E ((S..) (VR(h)))
H(x)
exp( (sp(R"(xs)/2) (x)) En.e expi (t.ae)(
Here, V (x) denotes the spatial gradient of the coarse precipitation field, T 0 is temperature parameter controlling the sharpness toward heavy-rain pixels, and æ > 0 a small constant (set to
10 in our experiments) introduced to ensure numerical stability when the denominator approaches zero.
4.4 INR-BASED GAUSSIAN PARAMETER ESTIMATOR
Our objective to generate dense, high-quality precipitation fields from satellite imagery and sparse AWS observations, even without radar ground truth. Conventional Gaussian splatting methods are typically optimized per image and may not generalize across scenes. We instead design an INR-based estimator that predicts Gaussian parameters only at rainfall-suppon queries, avoiding unnecessary computation in dry regions.
Given proposal points (m)) (u uy (()))) 1 from the Radar Point Proposal Network,
(x)
the estimator is conditioned intermediate satellite features (Y!, 2²) HR' "'''"">DD Through cross-attention, we predict Gaussian parameters
(x)) {o(")) ((m)) (m), (n))..
where
(n) (()) define the covariance Σ(n) E 82 and (n) controls the Gaussian amplitude. At AWS stations with nonzero rainfall, we directly set (n) = ((m), anchoring the field to ground-truth observations.
(a!") .0 3
Training minimizes reconstruction error against radar fields with regularization:
Σ [2 R²)x))
A Σ (a) + + Ao Σ (n)
XEN

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The final precipitation map is rendered by differentiable 2D Gaussian splatting:
(x)x
Σ
(n) exp (- -x (-
( (x (x-111)))
with p(m)= (ub"), Ut ) This operator is fully differentiable, enabling end-to-end training,
EXPERIMENTS
We evaluate QCGS on satellite and AWS gauge data from 2023 and compare it against classical gridded precipitation products (IMERG from NASA, MSWEP from the University of Maryland, GSMaP from JAXA) as well as deep learning baselines based on image-to-image translation.
5.1 EXPERIMENTAL SETTING
Dataset. We use three data sources: (i) automatic weather station (AWS) gauges providing sparse point-wise rainfall measurements over land, (ii) GK2A geostationary satellite imagery (IR 10.5 μm channel, km resolution), and (iii) KMA HSP weather radar fields (0.5 km resolution). We crop the study domain to 480xx80 grid (35.5 157--37.8M high. Models are trained on hourly data from 2019-2022 and evaluated on 2023 data, Although training is performed 2 km resolution, we also evaluate at 0.5 km to demonstrate the ability of QCGS to render rainfall fields at arbitrary scales.
-119.11
where gauge density is relatively
Evaluation Metrics. We evaluate QCGS using RMSE for overall error and LPIPS (Zang et al. 2018) for perceptual similarity. For grid-point verification, we report Critical Success Index (CSI), Categorical CSI, Fraction Skill Score (FSS: Roberts & Lean (2008) with a 5 window, and bias. We also compute Pearson and Spearman correlations assess spatial patterns and extremes.
Comparison Methods. We benchmark QCGS against three categories of baselines. For classical interpolation, we use Barnes (Barnes) 1973), Multi-quadric(MQ Nuss & Titley (1994), and Kriging (Lucas et al. 2022) methods. For operational products, we include IMERG (Huffman et al. 2015) (NASA), a global 0.1º multi-satellite retrieval widely used in hydrology; MSWEP (Beck) et al. 2019) (University of Maryland), long-tero 0.1 dataset that blends gauges, satellite, and reanalysis ysis; and GSMaP (Mega et al., 2018) (JAXA), a near-real-time 0.1º product combining passive microwave radiometers with geostationary infrared sensors. We also include the GK2A 2-km rain rate product as a regional quantitative precipitation estimate. For data-driven baselines, we compare against NPM (Park et al. 2025), the first model demonstrate precipitation forecasting from satellite imagery alone, where we use the satellite-to-rade stage for fairness; BBDM (Li al. 2023), diffusion- based image-to-ine to-image framework adapted for precipitation downscaling; and Pix2PixHD (Wang et al. 2018). a conditional GAN commonly applied to satellite-to toliiite-t--riffalll mapping, though it may struggle to preserve sharp convective structures.
By comparing against both operational references and learning- bbaed models, we aim to evaluate QCGS against broad spectrum of established standards and state-of-the deep methods.
Implementation Details. We fix the number of query points to K=6000, which provides an optimal balance between fidelity and efficiency. The surrogate radar field A is produced by a ConvNeXt No-baaedt U-Net with four encoder/decoder stages and skip connections, using Group Normalization and GELU activations. AWS observations are embedded via a three-layer Graph Attention Network (8 heads, hidden size 128) and fused with satellite features in the decoder through cross-attention.
For point selection, we adopt a rainfall-aware strategy combining edge, intensity, and uniform terms (0.3/0.4/0.3), with non-maximum suppression avoid redundancy. Each query is passed to five- layer MLP INR (hidden size 128 with sinusoidal positional encoding), which predicts Gaussian parameters {az: Ty P, a.). At AWS sites with nonzero rainfall, is set directly the observed value, anchoring the generated fields.
Training uses Adam (1 x 10 initial Ir, 1x 10-5 weight decay, cosine schedule, gradient clipping at 1.0), with batch size 16 for 100 epochs. Regularization terms X, = 10-3 3 and X, = 10 -4 prevent over-smoothing. All experiments are conducted on 8XNVIDIA H200 GPUs.
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Table Quantitative results across multiple spatiotemporal scales. Each block shows the number of evaluated cases in parentheses. QCGS is trained at 2 km and downsampled to 0.1 1 for comparison with global products. Best scores per block are in bold.
Temporal scale (cuses)
Calegory
Method
Res.
RMSE,
LPIPS,
CSI1
FSS1
CC1
Biases
Data driven
Pis2PidHD
0.5 km
2.45
0.62
0.59
0.71
0.55
0.82
Data-driven
0.5
1.95
0.58
0.78
0.88
Data driven
BBDM
0.5 km
1.68
0.54
0.64
0.84
0.75
0.93
Snapshot (1154)
Satellite Product
GK2A
2.0 km
2.89
0.40
0.37
Classcal Interp-
Bares
2.0 km
2.56
0.39
0.47
0.68
0.42
0.98
Classical Interp.
Kriging
2.0 km
2.43
0.40
0.69
1.03
Classical Interp.
3DMQ
2.0 km
2.47
0.41
0.49
0.68
0.44
1.00
Ours
QCGS QCGS
0.5 km
1.23
0.49
0.74
0.91
0.90
1.02
Ours
2.0 km
1.00
0.19
0.76
0.96
0.93
1.03
Satellite Product
IMERG
0.1"
1.66
0.34
0.50
0.72
0.42
0.85
Hourly (1 154)
Satellite Product
GSMaP
0.1"
1.95
0.38
0.43
0.64
0.78
Ours
QCGS
0.1"
1.33
0.21
0.66
0.93
0.74
0.97
Satellite Product
IMERG
14.08
0.33
0.92
Daily (70)
Satellite Product
GSMaP
0.11
15.89
0.35
0.92
0.82
0.70
0.88
Satellite Product
MSWEP
0.32
0.91
Ours
QOGS
0.1"
6.68
0.21
0.93
0.99
0.95
1.02
5.2 QUANTITATIVE RESULTS
Comparison with data-driven approaches. All data-driven baselines (Pix2PixHD, NPM. BBDM) were trained and evaluated directly at 0.5 km resolution for fairness. In contrast, QCGS was trained only at km resolution and later rendered to 0.5 km during evaluation. Despite this apparent disadvantage, QCGS consistently achieved the best performance across the evaluated metrics (Table This robustness can be explained by two key design choices.
First, QCGS explicitly fuses AWS observations. Although gauges are sparse, their ground- accuracy provides strong local anchors that substantially enhance field reconstruction and help correct biases that purely satellite-driven models may struggle to address. Our ablation study (Sec. (5.4) confirms this, since removing AWS information causes sharp decline in both pixel-wise accuracy and spatial correlation.
Second, QCGS leverages Gaussian Splatting (GS) to achieve resolution-free rendering. While existing models are tied to the resolution of their training grid (for example, 0.5 km), GS allows QCGS to generate rainfall fields arbitrary resolutions while focusing computation on rainfall-support regions. This capability preserves fine-scale convective boundaries without requiring retraining, in contrast to conventional super-resolution methods that often blur or oversmooth extremes.
Taken together. AWS fusion and GS-based resolution free rendering explain why QCGS outperforms models trained at higher resolution. Table Table/Thigh highhights this advantage clearly, showing that even with 2 km training QCGS surpasses state-of-the-arr 0.5 km baselines in both accuracy and structural fidelity.
Comparison with classical interpolation. Classical interpolation methods such as Barnes, Kriging, and 3DMQ rely on fixed kernel functions to spread each gauge observation across the grid. As shown in Table D. these approaches produce smooth rainfall patterns with limited structural fidelity. Their RMSE values remain above 2.4 at km resolution, and their CSI and FSS scores remain around 0.57-0.50 and 0.68-0.69, respectively. This reflects the limitation of using static, often isotropic kernels that do not explicitly adapt to precipitation geometry, leading to blurred boundaries and underestimation.
In contrast, QCGS learns anisotropic and spatially adaptive Gaussian primitives conditioned on satellite features, enabling sharper and more metcorologically consistent rainfall structures. QCGS reduces RMSE to 1.00 at 2 km, and improves CSI from 0.50 (Kriging) to 0.76 and FSS from 0.69 to 0.96, representing substantial improvements across the evaluated metrics. These results suggest that QCGS can be viewed as a learnable generalization of classical kernel-weit kergel-weighted interpo- lation, with substantially improved representational flexibility for rishuuenonuttin precipitation field reconstruction.
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(a) IMERG
(b) GSMaP
(c) MSWEP
(d) OCGS(Ourg
(c) Radanory
Case 2023-082 10223-0--11
Total 701.2
Total diff.
1091.1
2461-2
Total 423.3
Total 3973.0
Case 2023-12-15
Total diff. -5130.2
Total diff. 2566.3
Total diff. 996.5
Total dift. 271.8
Total 6860.1
Case 2023-12-2 12-15
(9 PSD plot
2023-08-11
Spotial wavonumtr 1100groc)
WONDRUmect (1Mlgroc)
Figure 4: Panels (e) show the comparison of daily accumulated rainfall (mm, day) between radar
and four rainfall products: IMERG, GSMaP, MSWEP, and QCGS. The "Total diff." values (mm, day) denote the spatially integrated difference from radar for each product. Panel (f) presents the PSD) across spatial scales (since 1 111 km, wavenumber of ((1/degree) corresponds approximately to spatial scale of 110 km.)
Comparison with operational products. We benchmarked QCGS against operational datasets including IMERG, GSMaP, and MSWEP. These products provide global coverage, are purely satellite-driven, and apply sophisticated bias correction using rain gauges and reanalysis, which often reduces systematic errors. Nevertheless, as shown in Table ! QCGS achieves consistently lower RMSE and higher correlation, despite being trained only with regional satellite imagery and sparse AWS measurements.
For fairness, 10-minute radar was aggregated into hourly means and daily accumulations, and all datasets were reprojected to radar coordinates using GDAL. QCGS outputs were trained at 2 km and later downsampled to 0.1% grids for comparison.
A key advantage of QCGS is that AWS fusion anchors local rainfall intensities, enabling sharper and more accurate regional fields than purely satellite products. At the same time, this also repre- sents limitation: whereas IMERG, GSMaP, and MSWEP remain purely satellite-based and thus globally deployable, QCGS currently depends on sparse but precise ground observations. other words, QCGS delivers higher fidelity at regional scales, while operational products retain broader applicability.
5.3
QUALITATIVE RESULTS
Case study and spectral analysis. Figure compares daily accumulated precipitation from radar, three operational products (IMERG, GSMaP, MSWEP), and QCGS. QCGS produces fields that are visually closer to radar, with reduced absolute differences and better preservation of localized convective cells. By contrast, GSMaP systematically underestimates intensity, while IMERG and MSWEP exhibit case-dependent over- and underestimation.
The power spectral density (PSD) analysis further shows that QCGS closely follows the radar spectrum across most scales, retaining both large-scale organization and mesoscale structure. Operational products lose variance at high wavenumbers, with MSWEP appearing oversmoothed. QCGS slightly overestimates the smallest scales, reflecting both preserved subgrid variation and minor artifacts. Overall, QCGS shows improved preservation of the spectral balance of precipitation fields relative to existing products.

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Table 2: Comprchensive ablation study on CSI. (a) Effect of architecture choices: AWS fusion and Gaussian Splatting (GS) progressively improve performance. (b) Effect of sampling strategy: combining gradient, regular, and heavy-rain sampling yields the best CSI. (c) Effect of the number of query points: performance saturates around 6-0000. Best results are in bold.
Reg.
Grad.
Heavy
CSI
Architecture
CSIT
0.68
K points
CSI1
0.71
AWS (only)
0.53
1000
0.69
0.70
U-Net (ConvNeXt)
0.62
3000
0.72
0.73
AWS fusion
0.73
6000
0.76
0.74
AWS fusion + GS (ours)
0.76
9000
0.77
0.72
(a) Architecture.
0.76
(c) Number query points.
(b) Sampling strategy.
5.4 ABLATION STUDY
Architecture (Table2((a) Starting from U-Net (ConvNeXt) trained for satellite-to-ratee -trrdar transla- tion, adding AWS fusion provides a clear improvement by anchoring rainfall intensities at gauge lo- cations. Incorporating Gaussian Splatting (GS) further improves performance by enabling resolution- free rendering of localized rainfall, achieving the highest CSI.
Sampling strategy (Table (b))).. Regular interval sampling alone performs the worst, while gradient- or heavy-rain-based strategies provide moderate gains. Combining all three (gradient, regular, heavy-rain) yields the best CSI (0.76), highlighting the importance of jointly covering boundaries, background regions, and rainfall extremes.
Number of query points (Table (c). Increasing the number of sampled points K steadily improves CSI up to K =60000, where the score reaches 0.76. Using more points (K =9000) yields only a marginal gain (0.77) while increasing computation, so we adopt K=6000 as the default trade-off between accuracy and efficiency.
6 CONCLUSION
We introduced Query- -onddiiCnde Gaussian Splatting (QCGS), a framework for generating high- quality precipitation fields from sparse and heterogeneous observations. By treating each observation as a Gaussian kernel and conditioning splatting on satellite imagery, QCGS selectively renders rainfall regions, reducing computation while preserving sharp boundaries. The integration of Implicit Neural Representations further enables resolution-fiee parameterization and improved generalization across regions and seasons. Extensive experiments indicate that QCGS reduces representativeness errors, reconstructs rainfall even in gauge-sparse settings, and produces resolution-fiexe -iexxible fields that align closely with radar observations. These outputs are valuable not only for data assimilation but also as high-quality training data for data-driven forecasting, bridging the gap between point-based and gridded products. Overall, QCGS provides a scalable and physically consistent approach to multi-source precipitation integration, offering promising pathway for enhancing both traditional NWP systems and emerging Al-based weather prediction models.
Limitations and Future Work Despite its strengths, QCGS has two main limitations. First, the method relies on automatic weather station (AWS) data anchor rainfall intensities. In regions with insufficient gauge networks, its applicability is therefore limited. Second, our experiments were confined to the regional scale; scaling up the approach the global domain remains an open challenge.
Looking forward, we see two promising directions. An intriguing observation that fields already align more closely with AWS measurements than raw radar reffectivity, even without any reflectivity- seteecivvity-t--riniiii to-rainfall correction (Fig. 6). This suggests that QCGS may reduce certain biases present in conventional redar-derive products. Future work will further investigate this property, with the long-term goal of extending QCGS toward a scalable, global system that can complement or substitute radar-based precipitation monitoring.
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ACKNOWLEDGMENTS
This work was supported by the Institute of Information and Communications Technology Planning and Evaluation (IITP) grant funded by the Korean government (MSIT) (No. RS-2025-02263055
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Figure 5: Examples of consecutive one-hour QCGS-generated frames. The last three frames exhibit rainfall patterns that were absent in the first three, indicating temporal inconsistencies. Such frame- to-frame mismatch can hinder the performance of video prediction models that rely on coherent temporal dynamics.
A APPENDIX
A.1 INFERENCE DATA FOR PRECIPITATION FORECASTING
We further evaluated the utility of
radar fields as inference inputs for data-driven precipitation forecasting models. Specifically, we tested three representative baselines: MetNet- v2 (Sonderby al. 2020 SimVP (Gao al. 2022a). and PreDiff (Gao al. 2023). We followed standard nowcasting protocol in which seven past frames at ten-minute intervals are used as input and six future frames (up to +60 minutes) are predicted. MetNet-v2 directly predicts precipitation at the target lead time, while PreDiff and Sim VP follow many-to-many forecasting scheme.
All baselines were originally trained only in the radar radar setting, and we performed no retraining or adaptation when using QCGS inputs. Despite this clear train to test mismatch, QCGS-driven forecasting still preserved meaningful predictive skill. As summarized Table 3 the CSI at the I mm threshold decreased from 0.664 to 0.381 for PreDiff and from 0.591 to 0.252 for SimVP. MetNet-v2 showed only a small decrease, from 0.390 to 0.374.
We attribute this degradation to two main factors. First, QCGS does not currently enforce temporal coherence across frames, and this results in inconsistencies in the time dimension (see Fig. 5 Second, QCGS produces fields that closer to AWS gauge values, while radar reflectivity is empirically calibrated to rain rate through the standard Z-R relationship. This creates a mismatch for forecasting models that were trained only with radar inputs.
The smaller degradation observed in MetNet-v2 consistent with its single-step prediction design, which is less sensitive inter-frame consistency than many-to-many models.
Future work includes extending QCGS with temporal conditioning to provide coherent dynam- ies across consecutive frames, and retraining downstream forecasting models directly on QCGS- generated inputs. This may reduce the performance gap between QCGS-based and radar-based forecasting.
Table 3: Forecasting performance at +60 minutes using Baselines were trained only on radar-to-radar data and used without retraining.
radar fields inputs.
Model
CSI@ 1mm (R (R+R)
CSI@ 1mm (QCGS-P) -R)
MetNet-v2 Sønderby et al. (2020)
0.390
0.374
Sim Gao et al. (2022a)
0.591
0,252
PreDiff Gao et al. 2023)
0.664
0.381
A.2 QCGS VS. RADAR
Radar rainfall products are derived by converting reflectivity (Z) into rain rate (R) through empirical Z-R relations. As such, they not direct rainfall measurements and often suffer from systematic biases, especially in convective storms or orographically complex regions. In contrast, QCGS is trained radar targets but incorporates AWS anchors inference. Interestingly, the resulting fields
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QCGS rain rate (mm/h)
Radee rain rate (xmm hb)
Bardd.1 R3458-0.15
Bardd RMS004A1
CCH0-53
CC-0
AWS rain rate (mm/h)
AWS rain rute (mmn/h)
Figure 6: Bias, RMSE, and correlation coefficient (CC) of AWS rain rate compared with QCGS and radar. QCGS consistently achieves lower bias and RMSE and higher CC relative to radar, demonstrating closer agreement with gauge observations.
often align more closely with gauge observations than radar-derived rainfall. This suggests that QCGS not only reproduces radar-like like spatial patterns but also implicitly corrects radar biases by leveraging point-level AWS data.
Figure 6 provides quantitative evidence: compared to radar, QCGS achieves lower bias and RMSE and higher correlation coefficients when evaluated against AWS observations. These improvements indicate that the inclusion AWS anchors yields rainfall fields that are more consistent with ground observations.
Figure S presents case studies where gridded fields are directly matched with AWS locations. Here, QCGS preserves rainfall intensity more faithfully relative gauge measurements, particularly in high-rainfall events. Importantly, AWS evaluations were performed using standard point-to-grid matching with spatial averaging, ensuring that the observed improvements are not an artifact of directly injecting AWS values but reflect genuine gains in field representation.
Taken together, these findings highlight potential paradigm shift: QCGS offers rainfall maps that are simultaneously radar- consistent and gauge-calibrated, bridging the gap between remote sensing products and in-situ truth. In the long term, this property suggest that QCGS could serve as complementary approach to radar-derived rainfall estimates, particularly in settings where gauge information available.
2023/06/14 13 UTC
2023/08/18 08 UTC
aNSE 222 ton des
BMSE 200 lan dar)
RASE 145 ia
RMAS 05 iun.lee
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2023/09/15 14 UTC
BoSSE desh
KMASE dayl
RMSE onn day
RMSE 0 day?
Weather
Radar
QCUS
Weather
OCGS
Figure 7: Case studies comparing QCGS and radar against AWS stations. Gridded fields are spatially matched to AWS locations, showing that QCGS preserves local rainfall intensities more faithfully than radar.
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Table CSI scores different rainfall thresholds (mm/hour) using hourly data. QCGS is evaluated at multiple spatial resolutions (0.5, 2, and 10 km).
Threshold
QCGS (0.5 km)
QCGS (2 km)
QCGS (10 km)
IMERG
GSMaP
0.657
0.703
0.506
0.366
0.308
0,415
0,483
0.306
0.140
0.129
10
0.311
0.401
0.232
0.046
0.065
Table 5: Categorical POD, FAR, and CSI scores at different rainfall thresholds (mm, day) for daily accumulation data.
POD
FAR
CSI
Threshold
10
50
100
10
50
100
10
50
100
QCGS
0.703
0.579
0.646
0.125
0.329
0.423
0.657
0.455
0.434
IMERG
0.679
0.369
0.117
0.267
0.616
0.614
0.541
0.173
0.039
GSMaP
0.591
0.358
0.277
0.262
0.710
0.754
0.493
0.165
0.119
MSWEP
0.714
0.315
0.096
0.286
0.554
0.584
0.553
0.191
0.067
A.3 ADDITIONAL QUANTITATIVE ANALYSIS
Beyond continuous metrics such as RMSE and correlation, is important to evaluate precipitation skill a categorical manner across different rainfall intensities. provide more complete assessment, present two complementary threshold-bont based analyses.
Table reports CSI scores at 5, and 10 mm using hourly data. These thresholds reflect light, moderate, and heavy rainfall. QCGS consistently outperforms satellite products across all intensity levels, and the improvement most pronounced for heavy rainfall, where accurate detection is erucial.
To complement the hourly evaluation, Table presents daily POD, FAR, and CSI metrics at 10, 50, and 100 mm per day. This daily-scale analysis captures the model's ability to detect accumulated precipitation extremes, which are critical for hydrological and disaster-related applications. QCGS achieves the best POD and CSI across all daily thresholds, while maintaining reasonable FAR values. In contrast, satellite products either miss many high-rainfall days or exhibit high false-alarm rates.
Together, the hourly and daily analyses provide comprehensive characterization of model perfor- mance. QCGS consistently surpasses satellite products across all intensity levels and temporal scales, confirming its ability reconstruct precipitation structure more faithfully than existing methods.
A.4 CROSS-DOMAIN EXPERIMENTAL RESULTS
As shown in Fig. we use Regions I and (top) for training, while Regions 3 and 4 (bottom) are excluded from training. p the experimental results. QCGS shows only small performance drop in unseen regions. We believe this is due to two reasons: (1) although the regions differ, they are geographically close and share similar meteorological patterns, and (2) the number of activated AWS stations varies significantly depending on the rainfall intensity. For example, heavy-rain days may activate more than 700 AWS stations, while light-rain days may activate fewer than 100. This naturally exposes the model to diverse spatial AWS configurations during training.
A.5 VISUAL QUALITY ABLATION STUDY
Figure 9 presents a qualitative comparison among Radar, QCGS, AWS-only, and Satellite-only baselines. The AWS-only reconstruction exhibits isolated Gaussian blobs, which occur because point-based gauge measurements cannot fully represent the entire spatial domain. The Satellite-only baseline appears noticeably blurred, largely due to relying solely pixel-wise MSE loss without ground-level anchors. In contrast, QCGS produces sharper, more coherent precipitation structures that closely resemble radar observations, benefiting from its Gaussian splatting- based rendering and
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Metric
Cross-domain
In-domain
RMSEL
1.01
1.00
CSIT
0.76
0.76
Bias=I
1.03
1.03
FSS=1 (ne=5)
0.96
0,96
LPIPS
0.25
0.19
pCCt
0.93
0.93
rCC,
0.91
0.92
Figure 8: Training and evaluation regions. Regions and are used for model training, while Regions 3 and 4 are excluded.
Table 6: Cross-domain evaluation results.
2023-05-26 01:00
AWStpoint) only
only
Chalp
CSI-0.33
Oull
2023-08-24 00:00
OCGS
N/Stpointt
Sacellite only
CM-5223
2023-09-15 03:00
OCGS
AWSipoint) only
Sacollto only
PODE 71
JABE-OO
Figure 9: Visual comparison of Radar, QCGS, AWS-only, and Satellite-only across different cases.
AWS-satellite fusion. These visual results further confirm that QCGS delivers superior perceptual fidelity compared to other ablated variants.
A.6 ADDITIONAL QUALITATIVE ANALYSIS
This section reports qualitative examples, which are randomly sampled rather than cherry-picked, to ensure fair illustration of model behavior.
Figure TO highlights a representative case. Radar reports area of intense rainfall, whereas QCGS produces similar spatial pattern but with lower intensity. At first glance, this could be interpreted as an underestimation by QCGS. However, inspection of AWS gauge measurements (case: 0023-03-12 04:00) reveals that strong rainfall was not observed at ground level. This indicates that this instance, radar likely overestimated rainfall intensity, while QCGS produced fields consistent with in-situ truth. Such cases highlight the value of incorporating gauge anchors, which allow QCGS to mitigate biases inherent in radar-only products.
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Published as a conference paper at ICLR 2026
Case 2023-03-12 04:00
MERO
Case 2023-06-14 13:00
NEWM AF UE Heckisnn
MERGUEE modican
0L0S MT wer.
OCSS #133 MAOL
(a) Observations
(b) Global ruin products
(c) QCGS(Ours)
Figure 10: Qualitative comparison of observations, global rainfall products, and QCGS. QCGS preserves scale precipitation structures and reduces large-scale biases relative to conventional products.
Figure 12 13 show selected challenging cases in which QCGS underperforms relative conventional products. While QCGS achieves competitive performance in most cases, these examples reveal limitations in capturing the spatial extent and intensity of rapidly evolving convective systems, likely due to limited constraint from sparse AWS anchors. These cases emphasize that QCGS is not universally superior under all conditions and point to potential directions for improvement, such as incorporating temporal coherence or additional observation sources.
A.7 VISUAL QUALITY COMPARISON WITH CLASSICAL INTERPOLATION
Figure 11 presents a qualitative comparison between classical interpolation methods (Barnes, Krig- ing, and 3D Multiquadric) and the AWS-only variant of QCGS. All methods evaluated under identical input, target, and output conditions to ensure fair comparison. As shown in the figure, QCGS produces noticeably sharper and more coherent precipitation structures compared classical approaches, demonstrating superior visual quality.
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Published as a conference paper at ICLR 2026
2023-05-05 16:00
Radar
AWS only
Barnss
Kriging
3D MQ
ESI-0
CS100.05
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Rader
AWS only
Barnes
Kriging
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IMSL-1122
CSI+0.30
CSie0.52
CSie0.52
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Radar
AWS only
Barnes
Kriging
3D MO
65-0015
CS
CS 6067
C5
2023-11-03 09:00
Radar
AWS only
Barnes
Kriging
3D MQ
1,42 ES1-DA5
(20-0.66
CS--0.6
Figure 11: Qualitative comparison between classical interpolation methods and QCGS (AWS-only).
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Published as a conference paper at ICLR 2026
Racar et <m resolution
OCGS at km resolution
OCGS at 0.1" resolution
IMERG at 0.1" resolution
GSMaP at 0.1 resolution
IIM5C=5.77 051-0.15
ES 3
CSI-0.00
Racar km resolution
resolution
GSMaP at 0.1 resolution
RuddE
RA 25
RM
RAGE
km
D.47
RMS5-1.07
RASE 1,31
Racar at km resclution
QCGS at km resolution
QCGS 0.1 resolution
IMERG at 0.1" resolution
GSMaP at 0.1 resolution
AMSE- CSteo PL
BesE-111
RM OS 75
RMSE-11 CS
S1-0
Racar at km on
QCGS at km resolution
QOGS at 0.1 resolution
IMERG at 0.1 resolution
GSMaP at 0.1 resolution
SMSF DuR CStay 85
RMSSE CSlee 70
RM 15 (Steb.33
Racar at km resclution
QCGS at km resolution
QCGS 0.1" resolution
IMERG at 0.1" resolution
GSMaP at C.1' resolution
CS 188
CS-0090
CS-
CS
(a) Radar
(b) QCGS(Ours)
(c) Benchmark
Figure 12: Qualitative comparison precipitation fields from radar, QCGS, IMERG, and GSMaP. Radar provides the reference, while QCGS preserves fine-scale structures more faithfully than global products. IMERG and GSMaP show smoother fields with biases convective regions.
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Published as a conference paper at ICLR 2026
Radar at <m resolution
OCGS at 2 km resolution
OCGS at 0.1" resolution
IMERG at 0. resolution
GSMaP at 0.1 resolution
T00EE00.34 ES 60
CSS 0.3L
OCGS resolution
resolution
IMERG resolution
GSMaP 0.1 resolution
HoSsE11. 48
Iesp L37
IMMUERI,CC 45
I0SB2 1:45
Racar km resolution
GCGS
IMERG 0.1" resolution
GSMaP at 0.1 resolution
RMSE 33
RMSE-7 23 (S/
Racar at km resolution
OCGS at km resolution
OCGS at 0.1" resolution
IMERG at 0.1" resolution
GSMaP at 0.1 resolution
SS dab
CR 75
ESA E2
Racar resolution
QCGS resolution
QCGS 0.1" resolution
IMERG 0.1" resolution
GSMaP 0.1" resolution
cRie0.5
CSimb.41
Radar at km resolution
OCGS at 2 km resolution
OCGS at 0.1" resolution
IMERG at 0.1 resolution
GSMaP at 0.1 resolution
CSA
CS D4
(a) Radar
(b) QCGS(Ours)
(c) Benchmark
Figure 13: Qualitative comparison precipitation fields from radar, QCGS, IMERG, and GSMaP. Radar provides the reference, while QCGS preserves fine-scale structures more faithfully than global products. IMERG and GSMaP show smoother fields with biases convective regions.
23


Reviews:
[{"review_id": "3Y0xQavDpI", "reviewer": "Reviewer_SZyX", "summary": "This paper introduces Query-Conditioned Gaussian Splatting (QCGS), a novel framework that generates high-resolution precipitation fields by fusing satellite imagery with sparse automatic weather station (AWS) data, eliminating the need for radar. Unlike traditional methods, QCGS selectively renders only rainfall-prone areas using learnable Gaussian kernels, which preserves sharp precipitation structures and improves computational efficiency. It combines a radar proposal network for locating rainfall areas with an implicit neural network that predicts Gaussian parameters. Evaluations show QCGS significantly outperforms existing gridded products and deep learning baselines, reducing RMSE by over 50% and maintaining high accuracy across various spatiotemporal scales.", "questions": "Are the Radar Point Proposal Network and the Gaussian Reconstruction component trained separately? The description of this in the paper is quite confusing.\n\nWhere is the precipitation prediction that the paper consistently emphasizes? The proposed method does not demonstrate predictive functionality and appears more like a precipitation downscaling approach. The authors are requested to provide a detailed explanation.\n\nHow many 2D Gaussian disks are there per sampling point?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 1, "contribution": 3, "strengths": "This paper presents a highly novel approach for directly generating high-quality precipitation maps from satellite and station image data by combining 2D Gaussian Splatting with predictions from a feed-forward network. Although similar methods have been widely used in the SVG domain, this application is relatively innovative in the field of meteorology, and the presented results appear to be effective.", "weaknesses": "1. Figure 2 lacks clear identification of variables and models, which prevents a clear correlation with the methods section in the main text. The authors are strongly advised to revise Figure 2.\n\n2. The notation system in the Methods section is quite confusing. For example, the meanings of symbols such as *u* and *p* are not clearly defined. A more detailed explanation of the symbol system is required.\n\n3. Although the paper introduces a relatively novel hybrid representation (combining feed-forward network predictions with 2D Gaussian splatting for detail refinement), the overall description of the task is very unclear. Since ICLR is a broad interdisciplinary community where not all readers are meteorology experts, the presentation of the paper may cause significant confusion among readers.", "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": "R58dX5sW01", "reviewer": "Reviewer_UPz5", "summary": "This paper proposes Query-Conditioned Gaussian Splatting (QCGS), an innovative framework for reconstructing high-resolution precipitation fields from heterogeneous data sources—sparse automatic weather station (AWS) observations and dense satellite imagery. QCGS employs a radar-point proposal network to identify rain-supporting regions and combines a rain-aware point sampling strategy to selectively sample query locations. Subsequently, an Implicit Neural Representation (INR) network, conditioned on local satellite features, predicts Gaussian parameters (amplitude and covariance) for each query point. Experimental results show that QCGS outperforms existing data-driven baselines and operational products across multiple metrics, particularly in preserving rainfall structure and enabling resolution-agnostic rendering.", "questions": "1. Comparison with Baselines and Assimilation Methods: As noted in Weakness 1, could the authors explain why QCGS was not compared with deep learning data assimilation methods specifically designed for sparse observations, such as DiffDA or variants of 4DVarFormer? What are the fundamental differences between these approaches and QCGS in handling heterogeneous meteorological data?\n\n2. Evaluation on Heavy Rainfall Events: As noted in Weakness 2, can the authors provide detailed results for Probability of Detection (POD) and False Alarm Ratio (FAR) at different rainfall intensity thresholds (e.g., ≥ 50.0 mm/day or ≥ 200.0 mm/day), along with a breakdown of CSI by intensity level? Since RMSE can be overly sensitive to extreme values, these metrics are crucial for assessing the model’s ability to capture heavy rainfall events.\n\n3. Physical Interpretability of INR Parameters: The INR predicts Gaussian parameters {σₓ, σᵧ, ρ, α}. Does the covariance matrix Σ (determined by σₓ, σᵧ, ρ) of the Gaussian primitives have a clear physical interpretation in the context of precipitation fields—e.g., is it related to the spatial scale or shape of meteorological features? Were any physical constraints or regularizations applied to these parameters during training?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "1 Sound and Effective Fusion Mechanism: The method successfully uses sparse but accurate AWS point observations as anchors for rainfall intensity, integrating them with satellite imagery that provides dense contextual information. This design for fusing heterogeneous data sources mitigates the limitations of individual data types and improves the accuracy of the reconstructed field.\n\n2 Resolution Agnosticism: By leveraging INR-based parameterization and Gaussian Splatting (GS) rendering, the model enables resolution-agnostic field generation—models trained at lower resolutions can render high-resolution outputs (e.g., 0.5 km), significantly enhancing the method's practicality and scalability.\n\n3 Clarity and Thoroughness: The paper is well-structured, with detailed descriptions of methodological components (e.g., rain-aware sampling strategy, INR parameterization), making the approach clear and reproducible.", "weaknesses": "1. Incomplete Baselines and Missing Assimilation Comparison: The current baselines mainly focus on direct image-to-image translation (e.g., Pix2PixHD, BBDM) and purely satellite-based forecasting (e.g., NPM). Given that the core task of this work—reconstructing precipitation fields from observations—falls more closely within the scope of data assimilation (DA) or objective analysis in meteorology, the paper should consider comparisons with deep learning-based DA methods designed for sparse or heterogeneous observations, such as DiffDA or 4DVarFormer. At minimum, the authors should clearly discuss the theoretical and experimental distinctions between QCGS and traditional objective analysis methods (e.g., Barnes Interpolation, Optimal Interpolation, or Kriging), and possibly include comparisons with more sophisticated classical interpolation techniques.\n\n2. Missing Key Meteorological Metrics: While RMSE and correlation coefficients measure overall field agreement, categorical (threshold-based) metrics are critical for evaluating the accurate detection of heavy precipitation events. Although the paper reports CSI, FSS, and Bias, it lacks essential categorical metrics for precipitation, such as Probability of Detection (POD) and False Alarm Ratio (FAR) at specific rainfall thresholds. We suggest explicitly including a breakdown of the CSI by rainfall intensity levels (graded CSI).", "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": "alvhFGygeR", "reviewer": "Reviewer_4rLn", "summary": "This paper proposes STATION2RADAR (QCGS) — Query-Conditioned Gaussian Splatting — a novel framework that fuses satellite imagery and automatic weather station (AWS) observations to generate high-resolution precipitation fields without radar data. Unlike conventional interpolation or satellite-only methods, QCGS treats each observation as a learnable Gaussian kernel whose parameters are predicted via an implicit neural representation (INR) conditioned on local satellite context. The model selectively renders only rainfall-support regions, enabling efficient and resolution-free precipitation field generation. Experiments show that QCGS reduces RMSE by over 50% compared to existing global precipitation products (IMERG, GSMaP, MSWEP) and outperforms deep learning baselines even when trained at lower resolution.", "questions": "In Stage 1, how does the inclusion or exclusion of station data affect the visual quality of the reconstruction? Similarly, how does adding or removing the Gaussian representation influence the visualization results? I encourage the authors to analyze and present these effects in future versions of the paper.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "* Novel cross-domain idea: Introduces Gaussian Splatting and INR concepts from computer vision into meteorology for efficient precipitation field synthesis.\n* Superior accuracy: Achieves substantially lower RMSE and higher spatial correlation than both operational satellite products and deep learning baselines.\n* This paper is well-written.", "weaknesses": "* The comparison in Table 1 appears unfair. As stated in Lines 409–410, the baselines used for comparison are global coverage products, whereas QCGS is trained only within a regional domain (as mentioned in Lines 320–321). This makes the comparison not entirely appropriate. Including both (a) comparisons between QCGS-generated global precipitation fields and other global-scale products, and (b) comparisons between QCGS’s regional outputs and regional precipitation datasets, would make the claimed advantages of QCGS more convincing.\n\n* The generalization ability across different regions has not been demonstrated. Although QCGS takes only AWS and satellite imagery as inputs, its training ground truth (GT) is derived from regional radar precipitation fields. The paper only presents results within the radar-covered regions. Without evidence of cross-regional generalization, QCGS may lack real-world applicability — since regions with radar data can already rely on radar, and regions without radar would not benefit from QCGS if it cannot generalize beyond the training region. I suggest splitting the original dataset into four subregions, training on two of them, and testing on the other two to assess cross-regional transferability.\n\n* Minor comment: The claim in Lines 096–097 that the model “outputs a continuous precipitation field on an arbitrary scale” is not rigorous. Experimentally, the authors do not show that QCGS can reproduce weather phenomena at scales beyond those present in the GT data. Theoretically, since the GT is derived from 0.5 km resolution radar fields, there is no source of information for finer-scale phenomena.", "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": "132MTXBWan", "reviewer": "Reviewer_M5eP", "summary": "The paper proposes a method for fusing sparse accurate measurements to complement the dense satellite imagery. The method belongs to radar-free precipitation forecasting, motivated by the cost of radars and their limited geographic coverage. For the reasons of computational efficiency, the authors use selective rendering, where they choose to render only areas with precipitation. They fuse dense satellite data with sparse raingauge data using a customised architecture of Graph Attention for sparse raingauge observations and convolutional architecture for the dense satellite imagery, and then they perform rendering using implicit neural representation (INR) based parameterisation, mapping satellite features and locations into Gaussian parameters (amplitude and covariance), which is used in a Gaussian splatting rendering. The advantage of such rendering is that it ensures that the results are scale-invariant.", "questions": "1. It would be interesting to know, given that the method also uses the dense satellite imagery, whether it is possible to use it in a radar imagery in a same way as for the satellite imagery.\n\nThe current rating reflects that there're outstanding questions related to the significance and comparison with the existing work. I would expect author to clarify upon these.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "The paper tackles an important topic of fusion between the sparse raingauge data and the dense satellite imagery. \n\nQuality: the paper is well written, and to the best of my knowledge, the methodology does not contain errors\n\nClarity: the paper is clearly written and seems to be reproducible\n\nSignificance: the proposed methodology is complementary to the existing ones using radar imagery", "weaknesses": "Originality: while the method looks to me original, there are a number of publications on similar topic, Fusion of satellite and gauge precipitation observations [1,3], as well as different but linked radar and rain gauge data fusion [2] (which is different from the topic yet it may be comparable methodologically). I would suggest the authors contrast the methodology, and importantly, problem statement to the proposed one.\n\nSignificance: while the method is sound, it is based on the successfully combined existing methods (graph attention network, convolutional model, implicit neural representations, Gaussian splatting), so it would be good it seems like the motivation hinges on the novelty of application. It is important therefore to outline explicitly, perhaps in the introduction, how the authors see the contributions\n\nQuality: while the authors are performing the ablation study removing rain gauges, it would be also quite beneficial to see if one can execute an ablation study removing the satellite imagery (i.e. removing the convolutional features from the Radar point proposal network). I would expect the quality to drop significantly, but it would be interesting to see for the completeness of analysis. \n\n[1] Ruan et al (2025) Fusion of satellite and gauge precipitation observations through coupling spatio-temporal properties with tree-based machine learning, Journal of Hydrology\n\n[2] Benoit (2020) Radar and Rain Gauge Data Fusion Based on Disaggregation of Radar Imagery\n\n[3] Curcio et al (2025) Towards a Spatiotemporal Fusion Approach to Precipitation Nowcasting, arXiv", "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)