Spatiotemporal Interpolation of Meteorological Fields in Complex Terrain Using Deep Graph Neural Networks

Abstract

To address sparse meteorological data and the “smoothing effect” over complex terrain, this study proposes a spatiotemporal model based on a Diffusion Graph Convolutional Network (DG model). Focusing on Quanzhou, China, and using 2020–2024 data from 198 stations, the model integrates diffusion graph convolution and residual learning to capture nonlinear meteorological patterns. Ensemble experiments (100 iterations) demonstrate that the DG model significantly outperforms Ordinary Kriging and the KCN baseline in stability and accuracy. Specifically, it improves mountainous temperature prediction by 23.4% (40.0% vs. KCN) through terrain-adaptive weighting, effectively reproducing physical distribution characteristics. Furthermore, the model reduces inherent ERA5 reanalysis bias by integrating historical station data while maintaining background consistency. Validated against spatial-only (OSI) and temporal-only (OTI) variants, the DG model offers a robust approach for high-resolution meteorological reconstruction in complex terrain.

1. Introduction

Spatiotemporal interpolation refers to a technique that infers values at unsampled locations and times from limited and discretely distributed observations through mathematical modeling, thereby extending sparse measurements into a continuous spatiotemporal field. In meteorology, the availability of high–spatiotemporal-resolution gridded data is essential for understanding land–atmosphere processes. However, due to complex geographical conditions and the high costs associated with the construction and maintenance of ground-based stations, in situ meteorological observations are often sparse and unevenly distributed [1]. As a result, spatiotemporal interpolation plays a central role in meteorological applications. It serves not only as a fundamental tool for generating high-resolution meteorological fields, but also as the basis for data downscaling and intelligent grid correction in numerical weather prediction, thereby supporting a wide range of downstream tasks [2]. For example, in watershed hydrological modeling, precision agriculture, and the assessment of extreme events such as typhoons and heavy rainfall, continuous and accurate precipitation and temperature fields can substantially reduce model uncertainty and provide a robust scientific foundation for climate monitoring and disaster risk reduction.

For a long time, classical geostatistical methods, represented by Kriging, have been the mainstream choice for spatial interpolation. The objective analysis method proposed by Cressman [3] laid the foundation for interpolation, while ordinary Kriging (Ordinary Kriging, OK), based on variogram theory, achieves an unbiased optimal estimation by quantifying spatial autocorrelation. To account for the controlling effect of topography on meteorological variables, Hudson and Wackernagel [4] introduced external drift Kriging, which incorporates elevation as a covariate to correct the altitude-dependent variation in air temperature. These methods exhibit robust performance in regions with flat terrain and uniformly distributed stations, effectively exploiting the spatial statistical dependence of the observations.

However, in complex terrain settings, traditional geostatistical methods exhibit critical limitations, as they rely heavily on a relatively uniform distribution of observation stations. In mountainous and hilly regions such as Quanzhou, stations are often clustered in valleys, while monitoring gaps at higher elevations lead to pronounced “smoothing effects” in the interpolated fields, making it difficult to capture local-scale microclimatic features [5]. Moreover, Kriging methods are based on Gaussian processes, and their computational cost increases cubically with sample size. More importantly, the strict assumptions of stationarity and Gaussianity make it challenging to represent the strong nonlinearity and nonstationarity of meteorological variables—such as precipitation—under complex terrain conditions [6]. Traditional interpolation models also follow a transductive learning paradigm, with model parameters fixed to a specific configuration of stations. Once the observation network changes dynamically (e.g., through the addition or removal of stations), the model must be recomputed or retrained, resulting in limited flexibility and an inability to meet the requirements of dynamic interpolation in modern meteorological operations.

To overcome the limitations of traditional methods, graph neural networks (Graph Neural Networks, GNNs) have been introduced into meteorological applications. Unlike convolutional neural networks (CNNs), which require regularly gridded inputs, GNNs treat meteorological stations as nodes in a graph and are therefore well suited to discretely and irregularly distributed observation networks [7]. Through message-passing mechanisms, GNNs can capture complex nonlinear dependencies that extend beyond simple geographical distance in meteorological interpolation. Appleby [8] proposed the Kriging Convolutional Network (KCN), which combines graph structures with Kriging concepts and demonstrated the effectiveness of graph-based models in extracting spatial features. In addition, GNNs possess inductive capabilities, effectively addressing the “transductive limitation” of traditional approaches. The IGNNK model proposed by Wu [9] learns a random-walk matrix to endow the model with inductive inference ability, enabling it to generalize to unseen stations without retraining. More recent studies, such as the MIGN model [10] and DeepKriging [11], further demonstrate the superiority of GNNs in dynamic grid mapping and probabilistic prediction. Furthermore, in the context of complex terrain, a study over the Swiss Alps by Miralles [12] showed that observation-guided GNNs significantly outperform traditional numerical models. Comparative studies by Jeong and Koo [13] and Huang [14] also confirm that integrating deep learning with geostatistics is an effective approach for enhancing the representation of complex spatiotemporal variability.

Building upon these pioneering works, yet aiming to address the specific challenges posed by complex topography where standard GNNs often struggle to capture elevation-dependent variations, this study develops an improved spatiotemporal inference framework based on the diffusion graph neural network architecture (referred to as the DG model). Distinct from generic graph-based interpolation methods, the proposed model is specifically optimized for meteorological tasks in complex terrain. It integrates a diffusion graph convolution module with a terrain-adaptive mechanism, allowing the model to dynamically adjust propagation weights according to elevation gradients rather than relying solely on horizontal distances. Historical observations from meteorological stations or grids are used as inputs. Spatial dependency features are first extracted through the diffusion graph convolution module, after which temporal evolution is modeled by the introduced adaptive diffusion module to finally produce meteorological variables at multiple target time steps for each station. Using Quanzhou in Fujian Province as the study area, this study employs daily precipitation and mean air temperature data from 198 stations during 2020–2024 to construct this terrain-aware deep learning model and to evaluate its performance in high-resolution interpolation analysis of meteorological data over complex regions.

2. Dataset and Methods

2.1. Dataset

This study selects Quanzhou, located on the southeastern coast of China (24.4–26.0° N, 117.5–119.1° E), as the study area. Quanzhou, situated in the southeastern coastal region of Fujian Province, exhibits a subtropical maritime monsoon climate with complex and highly variable meteorological conditions. The region features diverse topography, encompassing coastal plains and inland hills, which poses significant challenges for the spatial interpolation accuracy of meteorological variables. After removing anomalous stations, a total of 198 valid stations were retained, with all data derived from daily precipitation and mean temperature records in Quanzhou during 2020–2024.The distribution of the sampling sites is shown in Figure 1.

The gridded data were obtained from the ERA5 reanalysis dataset of temperature and precipitation provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) for the corresponding period [15], with a spatial resolution of 0.25° × 0.25°. The dataset can be accessed at the following link: https://cds.climate.copernicus.eu/datasets/reanalysis-era5-single-levels-timeseries?tab=download (accessed before 1 February 2026).

2.2. Model Design

The core architecture of the proposed DG model integrates diffusion graph convolutional modules [16] with a deep residual learning mechanism, specifically designed for the spatiotemporal inference and interpolation of meteorological variables. The model takes historical observation sequences from meteorological stations and their spatial relationships as inputs. By stacking multiple layers of diffusion graph convolutional modules, it captures high-order spatial dependency features, while the residual connections enhance the training stability of the deep network. The model ultimately outputs predicted values of meteorological variables for all stations during the target time periods.

The DG model is built upon a graph neural network architecture, with its core comprising a learnable bidirectional diffusion convolution module (D_GCN) and a residual correction structure, as illustrated in Figure 2. To comprehensively capture the spatial propagation patterns of meteorological variables, the model first constructs two adjacent matrices, A_q and A_h representing the inherent geographical connections among stations and the implicit meteorological correlations, respectively. To effectively extract meteorological features in non-Euclidean space, the D_GCN module is designed as the backbone for feature extraction. This module incorporates a diffusion graph convolution mechanism, aiming to emulate the physical diffusion and propagation processes of meteorological variables (e.g., temperature, humidity) within a non-uniform observation network. Considering the continuity and complexity of atmospheric dynamics, D_GCN employs a K-order Chebyshev polynomial approximation to efficiently capture multi-level spatial features, ranging from local microclimatic environments to large-scale background fields. Specifically, for an input feature X and a given support matrix A∈{A_q, A_h}, the diffusion process is defined in a recursive manner to capture spatial dependencies from order 0 to K, effectively modeling the propagation and attenuation patterns of meteorological signals over space.

$${\mathrm{X}}_0=\mathrm{X}$$

(1)

$${\mathrm{X}}_1=\mathrm{A}\mathrm{X}$$

(2)

$${\mathrm{X}}_{\mathrm{k}}=2\mathrm{A}{\mathrm{X}}_{\mathrm{k}-1}-{\mathrm{X}}_{\mathrm{k}-2},\mathrm{for} \mathrm{k}\ge 2$$

(3)

Here, X_k denotes the diffusion feature at order k, which encompasses information from neighbors within k diffusion steps. This recursive design effectively simulates the physical diffusion process of meteorological variables, which attenuate with distance. Finally, the output H of the D_GCN layer is a linearly weighted combination of multi-order diffusion features from both graphs:

$$\mathrm{H}=\mathsf{\sigma }\left(\sum _{\mathrm{s}\in \{{\mathrm{A}}_{\mathrm{q}},{\mathrm{A}}_{\mathrm{h}}\}}{\displaystyle \sum _{\mathrm{k}=0}^{\mathrm{K}}}\left({\mathrm{X}}_{\mathrm{k}}^{\left(\mathrm{s}\right)}{\mathsf{\Theta }}_{\mathrm{k}}\right)+\mathrm{b}\right)$$

(4)

Here, Θ_k is the learnable parameter matrix corresponding to the k-th order, b is the bias term, and σ(⋅) denotes the activation function (ReLU). This mechanism ensures that the model can simultaneously capture local microclimatic features and large-scale atmospheric circulation effects.

To accurately characterize the nonlinear temporal evolution of meteorological variables and to address the signal attenuation problem in deep networks when extracting complex spatiotemporal patterns, a hierarchical residual connection mechanism is introduced in the DG architecture. The main body of the model consists of a four-level cascaded diffusion graph convolution structure. The first three layers (GNN1 to GNN3) are designed to project surface observation time series into a high-dimensional feature space, thereby disentangling the complex nonlinear interactions among atmospheric variables. To prevent the loss of critical initial physical signals during deep feature extraction, residual paths are introduced between layers. The output feature at the l-th layer, H^(l) is computed as follows:

$${\mathrm{H}}^{\left(\mathrm{l}\right)}={\mathrm{D}\text{\_}\mathrm{GCN}}_{\mathrm{l}}\left({\mathrm{H}}^{\left(\mathrm{l}-1\right)},{\mathrm{A}}_{\mathrm{q}},{\mathrm{A}}_{\mathrm{h}}\right)+{\mathrm{H}}^{\left(\mathrm{l}-1\right)}$$

(5)

This design enables the model to perform more efficient error backpropagation, significantly enhancing its ability to capture long-term meteorological dependencies. GNN4 employs a linear activation function to reconstruct the extracted high-order spatiotemporal features back into the physical space, producing predictions of meteorological variables at the target stations.

During model training and parameter optimization, a mixed-precision training strategy was adopted to balance computational cost and numerical accuracy, and the Adam optimizer was employed to minimize the error between simulated and observed values. Overall, this architecture combines the spatial modeling capability of the diffusion process with the information-preserving properties of residual connections, enabling the synergistic perception and fine-grained inference of the spatiotemporal evolution of meteorological fields.

2.3. Evaluation Method

To evaluate the forecasting performance of the model, the regional root mean square error (RMSE) is defined as:

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{{\mathrm{N}}_{\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{s}}}}\sum _{\mathrm{j}}^{{\mathrm{N}}_{\mathrm{l}\mathrm{a}\mathrm{t}}}\sum _{\mathrm{k}}^{{\mathrm{N}}_{\mathrm{l}\mathrm{o}\mathrm{n}}}{\left({\mathrm{f}}_{\mathrm{i},\mathrm{j},\mathrm{k}}-{\mathrm{t}}_{\mathrm{i},\mathrm{j},\mathrm{k}}\right)}^2}$$

(6)

Here, i denotes the corresponding time; N_lat and N_lon represent the number of stations along latitude and longitude, respectively; N_forecasts is the total number of interpolated stations; f_(i,j,k) denotes the model’s interpolated value at time i for the station at latitude j and longitude k; and t_(i,j,k) represents the observed value at the corresponding station and time.

3. Results

3.1. Analysis of Station-to-Station Interpolation Results

For model performance evaluation, 30 stations are randomly selected as hidden validation points, with their distribution shown in Figure 1. The interpolation performance of the DG model is compared with that of the KCN model and the OK method. To eliminate the randomness of single experiments, an ensemble test involving 100 random selections of hidden stations was conducted, with the shaded areas in the figures representing the standard deviation range of the multiple experiments. Specifically, data from the first 90% of the time points serve as the training set X to test the performance of the KCN and OK methods on the remaining 10% of time points. The DG model, with an input sequence length of h = 6 (i.e., the previous six days, t-6~t-1), simultaneously outputs the interpolated values for the current day (t0). The newly predicted data are then iteratively fed back as inputs for subsequent forecasts. By leveraging graph neural networks to deeply integrate the temporal dynamics and spatial distribution characteristics of meteorological variables, the model achieves accurate reconstruction and correction of data in unobserved regions.

To visually compare the temporal stability of the model predictions over different time spans and to assess performance under extreme or transitional weather conditions, Figure 3 presents the time stability of temperature and precipitation forecasts. During May 2024 to January 2025, DG consistently achieves significantly lower root mean square error (RMSE) in temperature predictions than both the OK and KCN models. Its average RMSE is 0.40 °C, far superior to 1.21 °C for OK and 1.84 °C for KCN (Figure 3a). Examining the trend curves, although all three models experience slight error fluctuations in October due to seasonal climate transitions, DG exhibits noticeably narrower error fluctuations and confidence intervals. This indicates that DG maintains superior interpolation performance compared to KCN and OK, both during the high temperatures of summer and the gradually decreasing temperatures of autumn and winter.

The time series of precipitation RMSE further reveals the performance differences in the models under varying precipitation intensities (Figure 3b). DG achieves an average RMSE of 1.98 mm/day across the entire period, significantly lower than 3.45 mm/day for OK and 3.22 mm/day for KCN. Notably, during the rainy season from May to September, the errors of OK and KCN increase substantially as precipitation intensifies and then decrease markedly after October. As shown in Figure S1 (Supplementary Materials), the error varies across different seasons.

To compare the interpolation performance of the DG model, KCN model, and OK method across different terrains,

Table 1. Performance comparison of the DG model, KCN model, and OK method across different topographic zones.

Terrain Zone	Number of Stations	Temperature					Precipitation
		OK	DG	KCN	Error Reduction (Compared to OK)	Error Reduction (Compared to KCN)	OK	DG	KCN	Error Reduction (Compared to OK)	Error Reduction (Compared to KCN)
Low Elevation	9	0.40	0.39	1.32	2.6%	70.5%	5.46	4.71	5.66	13.7%	16.8%
Medium Elevation	11	0.67	0.59	1.16	12.0%	49.1%	6.10	5.29	5.87	13.3%	9.9%
High Elevation	10	1.11	0.85	1.37	23.4%	40.0%	7.04	5.99	6.10	14.9%	1.8%

presents model evaluation results based on terrain subdivisions. It is evident that terrain complexity has a significant differential impact on the simulation accuracy of temperature and precipitation. For temperature, the low-elevation areas exhibit generally small errors for the DG and OK methods due to relatively flat topography, with DG achieving an average RMSE of 0.39 °C, slightly better than 0.40 °C for OK. However, the KCN model performs poorly in this region, with an RMSE as high as 1.32 °C. As elevation increases, temperature fluctuates with altitude, leading to a marked increase in error for OK (rising to 1.11 °C) and consistently high error for the KCN model (1.37 °C). DG, however, substantially reduces estimation bias in high-elevation regions, achieving an RMSE of 0.85 °C, representing a 23.4% improvement over OK and a remarkable 40.0% improvement over the KCN model.

In contrast, for the more spatially heterogeneous precipitation data, DG consistently outperforms both the OK method and the KCN model across different regions. Even in low-elevation areas, DG achieves an average RMSE of 4.71 mm/day, representing a 13.7% reduction compared to 5.46 mm/day for OK and a 16.8% reduction compared to 5.66 mm/day for the KCN model. Particularly in high-elevation regions with dramatic terrain variations, DG effectively overcomes the smoothing effect of traditional geostatistical methods under sparse station distribution, reducing the average RMSE from 7.04 mm/day (for OK) to 5.99 mm/day, a 14.9% decrease. Although the KCN model (6.10 mm/day) performs better than OK in high-elevation precipitation interpolation, it remains less accurate than the DG model. Overall, DG demonstrates stable performance in flat regions and exhibits stronger adaptability and superior predictive accuracy than traditional methods and other deep learning models in complex mountainous terrains.

3.2. Gridded-to-Station Interpolation

Since numerical forecasts and reanalysis datasets are primarily provided as gridded outputs, while operational applications often require station-based variable predictions, this study further evaluates the performance of the DG model, KCN model, and OK method for gridded-to-station interpolation in the Quanzhou area. Specifically, the DG model integrates ERA5 reanalysis data with continuous prior observations at stations (t-6~t-1) to perform spatiotemporal interpolation and modeling of station temperature and precipitation at the prediction time (t0). The experimental window remains from May 2024 to January 2025, and all meteorological stations within the study area are used to evaluate model performance.

Figure 4 illustrates the monthly evolution of RMSE for station interpolation based on gridded data using the DG, KCN, and OK models. For temperature interpolation, the monthly mean RMSE is 0.43 °C for DG, 1.26 °C for OK, and 1.80 °C for KCN, with DG reducing the error by approximately 66% compared to OK and significantly outperforming the KCN model. For precipitation, despite the spatial heterogeneity caused by strong convective precipitation events in summer, DG achieves a monthly mean RMSE of 2.07 mm/day, significantly lower than 3.60 mm/day for OK and 3.34 mm/day for the KCN model. Notably, all three models exhibit peak errors in September, the month with the strongest rainfall during the rainy season, but DG maintains a mean RMSE of 3.78 mm/day, demonstrating the most significant robustness and accuracy improvement compared to the OK and KCN models.

These results indicate that DG clearly outperforms both OK and the KCN model in gridded-to-station interpolation. A possible explanation is that ERA5 gridded data, as reanalysis fields, contain systematic model biases and insufficiently assimilated station observations, which can cause direct OK interpolation to produce errors at local stations. In contrast, DG deeply integrates prior station observations along with ERA5 data, which partially mitigates local biases in the reanalysis and demonstrates the reliability of DG for high-precision gridded-to-station interpolation.

To further compare the performance of the DG model, KCN model, and OK method, temperature and precipitation case studies are selected for detailed analysis: the temperature analysis on 7 July 2024, and the precipitation analysis on 15 June 2024. The predicted results are compared with station observations (OBS) and the corresponding ERA5 gridded background field data for the same periods.

As shown in Figure 5, for the temperature case on 7 July 2024, DG accurately reproduces the inland-cool and coastal-warm gradient pattern across the Quanzhou area (Figure 5b), achieving an RMSE of only 0.41 °C. In contrast, although OK captures the main spatial distribution, its RMSE reaches 1.58 °C, and the KCN model also performs unsatisfactorily in this case, with an RMSE of 1.94 °C, failing to effectively correct the biases in the background field. Comparing the differences between the methods and the observations (Figure 6) reveals that DG exhibits a more uniform error distribution relative to ERA5, indicating that it corrects local station biases while maintaining high physical consistency with the large-scale background field. The largest biases occur mainly in the northeastern part of Quanzhou and some coastal stations, with local deviations reaching up to 11.2 °C.

For the precipitation case on 15 June 2024, DG achieves an RMSE of 11.79 mm/day, whereas OK yields an RMSE of 31.29 mm/day and the KCN model yields an RMSE of 18.90 mm/day. Observations indicate a pronounced heavy rainfall zone along the southeastern coast of Quanzhou, exhibiting significant spatial heterogeneity. However, the OK analysis (Figure 5g) is overly smoothed and underestimates the overall values, mainly because the ERA5 reanalysis data fail to capture the intense rainfall event in the southeast. Although the KCN model (Figure 5h) outperforms the OK method to some extent by capturing partial precipitation signals, it fails to accurately reconstruct the rainfall intensity in the high-value zone. In contrast, DG (Figure 5f) successfully predicts this high-precipitation area, with a spatial distribution closely matching the observations, thereby more accurately reflecting both the intensity and spatial pattern of the localized heavy rainfall event. Differences between the predictions of the methods and the observations (Figure 6) further highlight the DG model’s advantage in capturing this extreme precipitation, while both the OK method and the KCN model exhibit varying degrees of pronounced error clustering in the southeastern part of Quanzhou, particularly in the heavy rainfall region. Together, the interpolation results from these two cases demonstrate that DG, by leveraging its inherent strengths and incorporating prior station observations, achieves substantially better predictive performance than the OK method and conventional deep learning models for both temperature fields and precipitation fields with localized heavy rainfall.

To quantitatively assess the contribution of spatiotemporal coordination in model to meteorological interpolation accuracy and spatial pattern reconstruction, the interpolation performance of the full DG model is compared with two ablation variants: a model retaining only spatial information (OSI) and a model retaining only temporal information (OTI). OSI focuses on learning the interactions among grid points at each time step by modeling the dependencies between the target location and surrounding stations, while neglecting prior temporal evolution along the time axis. In contrast, OTI removes spatial connections among stations and relies solely on learning the temporal evolution of historical observations at individual stations to predict meteorological variables at the current time step.

Figure 7a–d visually illustrate the super-resolution reconstruction capability of different models for the spatial distribution of temperature on 2 July 2024. Observations indicate a pronounced northwest–cool and southeast–warm temperature pattern across Quanzhou, with temperatures generally below 30 °C in the high-elevation mountainous regions of the northwest. Among all compared models, the DG model (Figure 7b) shows the highest similarity to the observed temperature field, accurately capturing the southeast–northwest-oriented warm tongue structure and achieving the lowest mean RMSE. In contrast, OSI exhibits a clear systematic cold bias with weak horizontal spatial contrasts, resulting in a high RMSE of 6.46 °C. OTI, while able to reproduce the general southeast–northwest temperature gradient, displays pronounced over-smoothing, leading to a substantially smaller extent of the cold center compared to the observations.

Figure 7e–h compare the spatial patterns of the precipitation fields. The daily accumulated precipitation on 15 June 2024 further highlights the differences among the models in capturing localized heavy rainfall events. By effectively integrating prior temporal evolution signals with the spatial distribution information from reanalysis data at the current time step through the graph neural network, DG successfully reproduces both the exact location and intensity of the heavy precipitation center. OSI exhibits pronounced over-smoothing, leading to the loss of key features of the heavy rainfall center. This behavior is likely related to the limited capability of the ERA5 reanalysis data to represent this event; nevertheless, its RMSE (26.41 mm/day) remains lower than that of OK (31.29 mm/day). OTI captures the general spatial distribution and high-value bands of precipitation reasonably well, but its overall RMSE (12.48 mm/day) is still higher than that of DG. In addition, the predicted precipitation center shows a positional shift relative to the observations and underestimates the peak intensity.

The experimental results from the two case studies demonstrate that DG, which simultaneously integrates multidimensional spatiotemporal information, effectively corrects the prediction biases arising from reliance solely on the temporal evolution of prior station observations or on the spatial distribution of reanalysis data at the current time step. By repeatedly learning the evolutionary trends of historical observations and incorporating the spatial patterns of surrounding reanalysis grid data, DG more accurately reconstructs both the location and intensity of localized heavy precipitation centers.

To comprehensively evaluate the predictive performance of different methods, Figure 8a–d present the long-term spatial distribution characteristics of temperature interpolation errors for each approach. Among them, DG performs best, achieving an average RMSE of 0.35 °C, indicating that it consistently maintains high prediction accuracy in both topographically complex inland mountainous areas and coastal regions influenced by land–sea interactions. In contrast, although OK shows generally good performance (with an average RMSE of 0.87 °C), regions with relatively large errors appear along the northeastern coastal margins of Quanzhou and in parts of the central mountainous areas, where the maximum RMSE exceeds 7 °C. This is likely associated with sparse station coverage or boundary effects, which tend to amplify interpolation errors. OSI exhibits larger biases than the other methods, with widespread high-error regions, indicating that relying solely on spatial distance weighting is insufficient to capture regional temperature variability. Although OTI incorporates temporal information from prior station observations, its error distribution is highly uneven. By neglecting the geographical relationships among stations, the model forms isolated high-error zones around multiple stations, suggesting a limited ability to represent the spatial continuity of temperature fields.

Figure 8e–h depict the long-term spatial distribution of precipitation errors. The long-term error patterns further confirm the capability of DG in analyzing precipitation fields with strong spatiotemporal heterogeneity. Specifically, DG achieves the lowest precipitation prediction error, with an average RMSE of 3.10 mm/day. OK yields an average RMSE of 6.50 mm/day, which is approximately 210% of that of DG, indicating substantially poorer interpolation performance, particularly in the central and northern mountainous regions of Quanzhou. OSI exhibits a high average RMSE of 8.44 mm/day. This is mainly because precipitation is highly discontinuous in space, and OSI, which relies solely on spatial distance weighting, tends to average strong rainfall areas with surrounding rain-free regions, leading to pronounced over-smoothing and an underestimation of precipitation peaks. In contrast, OTI performs better than OSI (RMSE of 3.59 mm/day), likely because it captures the temporal persistence of precipitation from prior station observations. However, due to the absence of explicit geographical information, the error distribution of OTI appears as isolated patchy patterns, indicating persistent biases in predicting the spatial displacement of precipitation systems.

4. Conclusions

To address the challenges posed by sparse and unevenly distributed meteorological stations under complex terrain conditions in the Quanzhou region, this study develops a spatiotemporal inference framework for meteorological variables based on an inductive graph neural network (the DG model). Using high-resolution meteorological observation data from 2020 to 2024, the performance of the proposed model in temperature and precipitation interpolation is systematically evaluated. Through comparative analyses with the OK method, the KCN model, and models with different feature combinations, the following main conclusions are drawn:

In station-to-station interpolation applications, DG demonstrates substantially higher overall prediction accuracy and stability than OK and the KCN model. Specifically, DG achieves average RMSE values of 0.40 °C for temperature and 1.98 mm/day for precipitation over the Quanzhou region, all of which are clearly lower than those obtained by OK (1.21 °C and 3.45 mm/day) and KCN (1.84 °C and 3.22 mm/day). This improvement mainly stems from DG’s strong capability in spatial feature representation and, more importantly, its ability to effectively extract the temporal evolution characteristics of meteorological variables from prior station observations. By learning from historical observation sequences, the model accurately captures the persistent evolution of meteorological fields. Moreover, DG exhibits pronounced advantages over OK and KCN in mountainous areas and transition zones between mountainous and low-elevation regions, improving temperature prediction accuracy by 23.4% compared to OK and up to 40.0% compared to KCN in complex terrain. By incorporating terrain features, DG adaptively adjusts interpolation weights according to elevation variations, thereby accurately reproducing the physical patterns of temperature lapse rates and terrain-induced precipitation enhancement, while avoiding excessive smoothing of local extremes.

In the gridded-to-station interpolation application, DG preserves the large-scale spatial patterns of ERA5 while significantly enhancing its sensitivity and accuracy in capturing rapid short-term weather variations by incorporating temporal information from prior station observations. For temperature interpolation, the monthly mean RMSE values of DG, OK, and KCN are 0.43 °C, 1.26 °C, and 1.80 °C, respectively, corresponding to an error reduction of approximately 66% for DG compared to OK. For precipitation interpolation, despite the spatial heterogeneity induced by strong convective activity in summer, DG still achieves a substantially lower monthly mean RMSE (2.07 mm/day) than OK (3.60 mm/day) and KCN (3.34 mm/day). In particular, during September, when rainfall intensity peaks in the rainy season, DG attains an average RMSE of 3.78 mm/day, yielding the most pronounced improvement over OK and KCN.

Ablation experiments comparing the OSI (spatial-only) and OTI (temporal-only) models further confirm the irreplaceable role of spatiotemporal coupling in addressing nonlinear meteorological processes. Because OSI neglects the temporal evolution of meteorological variables, it exhibits pronounced systematic biases in temperature simulations and weakens precipitation extremes due to excessive smoothing. In contrast, although OTI is able to capture temporal variability, the lack of geographical spatial constraints leads to positional errors in precipitation patterns, resulting in localized regions with large errors. By comparison, DG deeply integrates neighborhood spatial features and dynamic temporal evolution through a graph neural network, effectively correcting the systematic biases and spatial misalignments inherent in single-dimension models. As a result, DG achieves more accurate high-resolution predictions of meteorological variables.

Finally, the proposed DG architecture possesses “inductive” reasoning capabilities, offering a potential intelligent grid-correction solution for modern meteorological operations. Unlike traditional interpolation methods, which are constrained by fixed parameters and lack flexibility, this model can generalize to stations that were not included in the training set. Consequently, DG is not only applicable to historical data reconstruction but also remains effective when the observation network undergoes dynamic adjustments, such as the addition or removal of stations, without requiring retraining. This provides a robust technical foundation for constructing high-resolution regional meteorological monitoring grids with spatiotemporal dynamic awareness.