Spatiotemporal cross-attention hybrid network for weather forecasting in complex terrain

Abstract

Weather forecasting in complex terrain, such as the karst landscapes of Guizhou, faces the dual challenge of capturing microscale topographic effects and macroscale atmospheric dynamics. Existing models often struggle to balance local spatiotemporal patterns with long-range dependencies. To address this, we present a novel hybrid architecture that integrates ConvLSTM and Transformer via a Spatiotemporal Cross-Attention (STCA) mechanism. Our approach utilizes an STL-VMD preprocessing pipeline to decompose non-stationary meteorological signals into stationary subsequences, effectively separating trend and seasonal components. The architecture synergizes ConvLSTM’s local feature extraction with Transformer’s global correlation modeling, while the STCA module dynamically bridges spatial and temporal information through multi-scale convolution and adaptive gating. Validated across 33 meteorological stations in Guizhou over a 51-year period (1961–2011), our model demonstrates superior performance. Compared to baseline LSTM models, temperature forecasting achieves an 18.99% reduction in RMSE (), and notably, precipitation forecasting achieves a 27.74% reduction in RMSE with a substantial 54.08% improvement in . The results confirm the model’s robustness and generalization capability for operational forecasting in topographically complex regions.

Introduction

Accurate precipitation and temperature forecasting is fundamental to water resource management, agricultural planning, and disaster prevention, with profound implications for ecological sustainability and socioeconomic development. This challenge intensifies in regions characterized by complex topography, where microscale terrain-induced variations interact with macroscale atmospheric circulation patterns. Guizhou Province in southwestern China exemplifies such complexity: with mountainous and hilly terrain comprising over 90% of its total area, dramatic elevation gradients, and predominant karst geomorphology, the region presents substantial difficulties for conventional meteorological prediction approaches.

Traditional forecasting methodologies predominantly rely on statistical models calibrated using historical observations. Time series analysis techniques, particularly the ARIMA model proposed by Albeladi et al.¹, have demonstrated effectiveness in capturing temporal autocorrelation for short-term precipitation forecasting. Regression-based approaches further seek to quantify relationships between precipitation and auxiliary meteorological variables, including temperature, humidity, and atmospheric pressure. Sa’idah et al. reported that Holt–Winters exponential smoothing can provide satisfactory performance for reservoir rainfall forecasting under specific conditions². Despite their computational efficiency and interpretability, these statistical methods exhibit inherent limitations in representing nonlinear dynamics and complex spatiotemporal dependencies, which constrain their applicability in accurate precipitation forecasting. However, these studies only provide general descriptions of limitations and lack in-depth analysis of critical technical flaws, such as the insufficient integration of spatial terrain features and global long-range dependencies, which motivated the proposed spatiotemporal cross-attention hybrid network.

The advent of deep learning has catalyzed significant advances in meteorological forecasting. Li et al. demonstrated that basin-specific model architectures are essential for capturing regional hydrological characteristics³. Johny and Pai proposed a VMD-LSTM hybrid framework integrating signal decomposition with recurrent neural networks to enhance monthly rainfall prediction accuracy⁴. Chen et al. developed a two-stream convolutional Long Short-Term Memory (LSTM) architecture that substantially improves nowcasting performance by jointly modeling temporal and spatial features⁵. However, Jin et al. noted that despite promising results in seasonal precipitation forecasting across China, prediction accuracy in complex terrain regions such as Guizhou remains insufficient for operational applications⁶. Pareek et al. emphasized the necessity of region-specific model customization through their optimized MVC-LSTM framework⁷. Akbar et al. compared seasonal ARIMA and LSTM models, confirming the superiority of deep learning approaches under complex meteorological conditions⁷. However, these deep learning approaches still fail to effectively couple local terrain-sensitive spatial features and global long-range temporal dependencies, which is the core issue addressed in this study.

LSTM networks have become a prevailing approach for rainfall prediction owing to their strong capability in modeling long-range temporal dependencies. Zheng et al. proposed the TISE-LSTM model by integrating spatiotemporal interaction modules, which significantly enhanced the spatial resolution of short-term rainfall forecasts⁸. Similarly, Oddo et al. demonstrated the effectiveness of convolutional LSTM architectures in precipitation prediction, highlighting their potential for capturing complex precipitation dynamics⁹.

Attention mechanisms have substantially enhanced model performance by enabling selective focus on salient features. Tao et al. demonstrated that multi-scale LSTM with attention mechanisms significantly improves monthly precipitation forecasting¹⁰. Kiran et al. developed an attention-augmented LSTM model integrated with convolutional modules, exhibiting superior performance in rainfall prediction tasks¹¹. Jyostna et al. combined Ensemble Empirical Mode Decomposition (EEMD) with LSTM to construct a hybrid framework with enhanced spatiotemporal coverage¹². Zhu et al. further demonstrated that hybrid deep learning architectures can effectively address the forecasting difficulties brought by topographic complexity in regional hydrometeorological prediction¹³. While attention mechanisms and multi-scale modeling advance prediction accuracy, challenges persist in computational efficiency and adaptability.

Transformer architectures represent a paradigm shift in sequence modeling for meteorological applications. Guo and Mao validated LSTM-Transformer hybrid models specifically for long-term precipitation forecasting, demonstrating their effectiveness in capturing the nonlinear and non-stationary characteristics of hydrometeorological time series¹⁴. Jiang et al. proposed Transformer-enhanced spatiotemporal neural networks, substantially improving post-processing of numerical weather predictions¹⁵. Ling et al. introduced the RNDiff model combining conditional diffusion with Transformers, demonstrating advantages in nowcasting applications¹⁶. Kabir et al. presented novel LSTM-Transformer architectures for time series prediction¹⁷. However, these approaches suffer from high computational complexity and extensive training data requirements. Recent studies have confirmed that the integration of signal decomposition and deep learning greatly improves the accuracy of hydrological forecasting¹⁸. Addressing data scarcity and extreme hydrological events is essential to enhance the generalization ability of forecasting models¹⁹.

Data preprocessing innovations have proven critical for model performance enhancement. Zhao et al. proposed STL-OMS for traffic flow prediction, achieving significant accuracy improvements through seasonal-trend decomposition and optimization²⁰. Tebong et al. developed an STL (Seasonal-Trend Decomposition using Loess) integration framework with deep learning²¹. Zhao et al. introduced a Variational Mode Decomposition-Convolutional Neural Network-Gated Recurrent Unit (VMD-CNN-GRU) hybrid model incorporating spatiotemporal characteristics for short-term wind power forecasting. Ahmadi et al. designed a VMD (Variational Mode Decomposition) and machine learning hybrid methodology for river runoff prediction²². Tamilselvi et al. demonstrated that wavelet-LSTM effectively handles non-stationary sequences²³. Mohammed et al. reduced prediction errors through a sliding window discrete wavelet transformer²². Hu et al. proposed stream LSTM models with improved adaptability to dynamic environments²⁴. Ma et al. enhanced seasonal forecasting by integrating spatiotemporal evolution characteristics²⁵. Despite these advances, challenges remain in balancing computational efficiency with model stability.

To address the aforementioned limitations, this paper presents a novel hybrid deep learning framework for precipitation and temperature forecasting in complex terrain. The principal contributions are as follows:

• Advanced preprocessing pipeline: We propose an STL-VMD decomposition framework that separates trend and seasonal components from meteorological time series while transforming non-stationary signals into stationary subsequences, providing a robust foundation for downstream modeling.

• Hybrid spatiotemporal architecture: We develop a ConvLSTM-Transformer integration enhanced with a novel spatiotemporal cross-attention mechanism.

• Comprehensive validation in complex terrain: We conduct extensive experiments across 33 meteorological stations in Guizhou’s karst region, demonstrating substantial performance improvements over baseline methods. The model achieves robust generalization across 32 validation sites, confirming its effectiveness for operational forecasting in topographically complex regions.

The remainder of this paper is organized as follows: Section "Study area and data" describes the study area and data source. Section "Methodology" presents Methodology. Section "Experimental results and analysis" discusses experiment results. Section "Conclusion" concludes the paper and outlines future research directions.

Study area and data

Transformer architecture

The Transformer architecture has demonstrated powerful feature representation capacity for complex spatiotemporal data through its self-attention mechanism. This study employs a Transformer encoder composed of multi-head attention mechanisms^26–28 and feedforward neural networks to process multimodal meteorological features^29,30.

The fused features undergo processing through multi-head attention, which enables the model to attend to information from different representation subspaces jointly. Let the fused input features be denoted as X. For each attention head, three transformations are applied to generate query (Q), key (K), and value (V) matrices:

1

where are learnable projection matrices that transformer the input features into appropriate subspaces for attention computation.

The self-attention mechanism computes attention weights by measuring the compatibility between queries and keys, scaled by the square root of the key dimension to stabilize gradients during training. These weights determine how much each position should attend to every other position in the sequence:

2

Rather than relying on a single attention function, the multi-head attention mechanism projects input features in parallel onto h different subspaces, allowing the model to capture diverse types of relationships within the data. The outputs from all attention heads are concatenated and linearly transformed to obtain the final fused attention representation:

3

where is the output projection matrix and h denotes the number of attention heads.

The fused attention features are subsequently processed through a position-wise feedforward neural network consisting of two linear transformations with a ReLU activation function in between. This component introduces additional nonlinearity and enhances the model’s capacity to capture complex feature interactions:

4

where X represents the output of the multi-head self-attention layer; and denote the weight matrix and bias vector of the first layer; and represent the weight matrix and bias vector of the second layer. The hidden layer dimension of the feedforward network is set to 32 to balance model complexity and expressive power. The feature interaction patterns learned by the Transformer are not constrained to specific network structures and can adapt to precipitation and temperature patterns across diverse complex terrains, thereby enhancing applicability and robustness in practical applications.

Seasonal-trend decomposition using LOESS

Seasonal-Trend decomposition using LOESS (STL) provides a robust framework for decomposing time series into interpretable components. Based on locally weighted polynomial regression, STL exhibits high computational efficiency and strong robustness in estimating trend and seasonal components, making it particularly suitable for preprocessing meteorological time series data. The method supports both additive and multiplicative decomposition modes, which can be selected based on the characteristics of the time series:The non-stationary meteorological time series are decomposed using the STL-VMD framework to obtain stable subsequences. Specifically, the original sequence is first decomposed by STL into three components: trend, seasonal, and residual. The residual component, which contains the high-frequency variations, is then further decomposed by VMD. The number of modes K in VMD is set to 4, which is determined through sensitivity analysis.The processed components are then used as inputs for the subsequent prediction model.The decomposed subsequences after STL‑VMD are constructed into a spatiotemporal matrix with the shape of (time × station × feature) and fed into the ConvLSTM module. No spatial interpolation onto a regular grid is conducted. The elevation of each meteorological station is incorporated as an auxiliary auxiliary feature and concatenated with meteorological variables to form the final model input.

5

where represents the original time series, denotes the seasonal component capturing periodic variations, represents the trend component reflecting long-term changes, and denotes the residual component containing irregular fluctuations and noise.

Variational mode decomposition

Variational Mode Decomposition (VMD), proposed by Dragomiretskiy et al., represents an advanced signal processing technique that decomposes the original signal into discrete intrinsic mode functions. Unlike empirical decomposition methods, VMD formulates the decomposition as a constrained variational problem, providing high adaptability and strong robustness while effectively enabling signal denoising. This characteristic makes VMD particularly valuable for preprocessing non-stationary meteorological signals.

The VMD algorithm proceeds through three fundamental steps. First, the Hilbert Transformer is applied to compute each mode’s analytic signal , obtaining its one-sided spectrum. This transformation enables the algorithm to work independently with the frequency content of each mode. Second, each mode and its corresponding center frequency are shifted to the baseband, demodulating the signal. Third, the bandwidth of each mode is estimated through the Gaussian smoothness of the demodulated signal.

The core of VMD lies in formulating a constrained variational problem that minimizes the sum of estimated bandwidths for all modes while ensuring that the modes sum to the original signal:

6

where f(t) represents the original signal, denotes the k-th mode of f(t), represents the center frequency of , δ (t) denotes the Dirac distribution, K represents the number of modes, t denotes time, represents the vector norm, represents the time derivative, and j is the imaginary unit.

By introducing a quadratic penalty factor α and Lagrange multiplier λ, Equation (10) is transformed into an unconstrained optimization problem, which is solved iteratively using the alternating direction method of multipliers (ADMM). The iterative solutions for and in the frequency domain are

7

8

where n denotes the iteration number; , , , and represent the Fourier transforms of f(t), , λ (t), and , respectively. The center frequency is updated as the center of gravity of the power spectrum of each mode, ensuring physically meaningful frequency estimates. The center frequency is updated as the center of gravity of the power spectrum of each mode, ensuring physically meaningful frequency estimates. This study adopts the additive decomposition mode for both precipitation and temperature time series to separate seasonal components, trend components and residual noise.

Study area overview

Guizhou Province is in southwestern China, bordered by Hunan Province to the east, Guangxi and Yunnan provinces to the south, Sichuan Province to the west, and Chongqing Municipality to the north. The meteorological data utilized in this study were obtained from 33 stations across Guizhou Province, provided by the Guizhou Meteorological Bureau. Figure 1 presents the geographical location of Guizhou Province and the spatial distribution of these meteorological stations. The color scheme in the map serves to distinguish different administrative regions³¹. The purchased dataset does not include detailed geographic location information for individual stations, so unique station IDs cannot be labeled on the map.

Fig. 1.

Geographical location of Guizhou province and distribution of meteorological stations.

Data description

This study employs monthly precipitation (mm) and temperature (C) data from 33 meteorological stations in Guizhou Province, spanning the period from 1961 to 2011. The dataset was obtained from the National Meteorological Information Center of the China Meteorological Administration. Guizhou’s complex topography, characterized predominantly by mountainous terrain with significant karst formations, results in a climate system exhibiting pronounced spatial heterogeneity and strong nonlinear characteristics. The 33 monitoring stations are distributed across an elevation gradient ranging from 137 to 2930 meters, effectively capturing the spatiotemporal heterogeneity of regional precipitation patterns. Furthermore, the complex terrain induces multi-scale atmospheric interactions that lead to frequent and abrupt extreme weather events. This distinctive climatic context is ideal for validating model adaptability to complex meteorological conditions. The geographical coordinates (latitude, longitude) and altitude of each meteorological station are included as key auxiliary input features. These topographic variables are explicitly incorporated into the model input to account for the significant influences of complex terrain in Guizhou Province.The latitude, longitude, and altitude of each meteorological station are explicitly included as key auxiliary input features. These topographic variables are essential for characterizing terrain effects and improving prediction accuracy in complex mountainous and karst regions.The analysis period is restricted to 1961–2011 to ensure the use of a homogeneous, complete, and consistent long-term observational dataset with uniform station records and quality control. This 51-year period is sufficient to characterize long-term climatic trends and spatiotemporal variability in Guizhou’s complex terrain. Extension to more recent years will be included in future work to assess model performance under ongoing climate warming.Monthly average precipitation was adopted to avoid bias caused by the different number of days in each month.

Methodology

LSTM prediction model

LSTM networks have emerged as the preferred architecture for precipitation and temperature forecasting due to their capacity to model nonlinear relationships in time series data. LSTM exhibits strong robustness to noisy and incomplete observations while maintaining high prediction accuracy in complex environments. The LSTM architecture overcomes key limitations of traditional Recurrent Neural Networks (RNNs) through the introduction of three gating mechanisms, namely the forget gate, input gate, and output gate. These gates regulate the flow of information within the network, allowing relevant historical information to be retained while redundant information is discarded, thereby alleviating the gradient vanishing and explosion problems commonly observed in conventional RNNs^32,33. Owing to the incorporation of memory cells that preserve information over long time horizons, LSTM is particularly suitable for time series modelling tasks involving long-term dependencies, such as precipitation and temperature prediction. In comparison with traditional RNN models, LSTM demonstrates a superior capability to capture temporal dynamics by effectively learning seasonal variations and periodic fluctuation patterns. The core components of the LSTM prediction model^34–36 operate through a series of gating mechanisms that control information flow. The forget gate determines which information from the previous hidden state should be discarded. It computes a weighted sum of the previous hidden state (containing historical precipitation and temperature information) and the current input feature (e.g. current precipitation), applying the sigmoid activation function. The network discards outdated information when current precipitation and temperature deviate significantly from historical patterns. The forget gate is expressed as:

9

where denotes the weight matrix and represents the bias term of the forget gate. The input gate works with the forget gate to determine which new information should be incorporated into the cell state . It employs the sigmoid activation function to process the weighted sum of and . When precipitation and temperature suddenly increase, this mechanism preserves and records the new information. Simultaneously, a candidate cell state is computed using the hyperbolic tangent activation function, representing the potential influence of new input features on . These components are expressed as

10

where and denote the weight matrix and bias term for the input gate, while and represent the candidate cell state’s weight matrix and bias term. The cell state constitutes the core of the LSTM architecture, governing information flow and retention across time steps. It integrates conditions affecting precipitation and temperature at the current time step by combining information from the previous cell state (modulated by the forget gate) with the candidate cell state (modulated by the input gate). This selective integration mechanism enables the network to maintain relevant long-term dependencies while adapting to new meteorological patterns. The cell state update is expressed as

11

where ⊙ represents element-wise multiplication. Finally, the output gate determines which information from the cell state should be exposed to subsequent layers and time steps. After processing through the \tanh activation function^37,38, the output gate combines with this result to determine the current hidden state . When the current time step falls within the same seasonal or cyclic period, allows more information to flow into the hidden state, enabling more accurate predictions. The hidden state encapsulates the most crucial information for forecasting precipitation and temperature, serving as the output for the current time step and input for the subsequent time step. The output gate and hidden state are formulated as:

12

where and denote the output gate’s weight matrix and bias term.

Proposed hybrid architecture

The proposed hybrid deep learning framework integrates multiple complementary techniques to address the challenges of precipitation and temperature forecasting in complex terrain. Figure 2 illustrates the overall architecture of the proposed system. The Methodology begins with STL-VMD preprocessing for feature extraction, which serves a dual purpose: separating trend and seasonal characteristics inherent in meteorological time series, and decomposing non-stationary signals into stationary subsequences more amenable to neural network modeling.

Fig. 2.

Proposed hybrid deep learning framework for precipitation and temperature forecasting. The architecture integrates STL-VMD preprocessing, ConvLSTM for local feature extraction, Transformer for global correlation modeling, and spatiotemporal cross-attention for information fusion.

Building upon this preprocessing foundation, the architecture integrates ConvLSTM and Transformer modules through a novel spatiotemporal cross-attention mechanism. This integration exploits the complementary strengths of both architectures: ConvLSTM leverages convolutional operations to capture terrain-sensitive local spatial features and short-term temporal dependencies, while the Transformer’s self-attention mechanism models global meteorological correlations across all monitoring stations and long-range temporal dependencies. The spatiotemporal cross-attention mechanism serves as a bridge, effectively connecting spatial information with temporal dynamics through multi-scale convolution and adaptive gating. This design enables comprehensive integration of temporal trends and spatial attributes, facilitating accurate capture of complex precipitation and temperature evolution patterns in karst terrain.

Spatiotemporal cross-attention mechanism

The spatiotemporal cross-attention mechanism constitutes a central innovation of the proposed architecture, as it enables effective fusion of spatial and temporal information. As shown in Fig. 3, this mechanism is particularly well suited to precipitation forecasting tasks that demand an integrated representation of spatiotemporal dependencies. In contrast to conventional attention mechanisms that operate exclusively within either the spatial or temporal domain, the proposed cross-attention design supports bidirectional information interaction between these two dimensions, thereby enhancing the model’s capacity to capture complex spatiotemporal patterns.

Fig. 3.

Architecture of the spatiotemporal cross-attention mechanism. The mechanism comprises spatial and temporal attention modules that bidirectionally exchange information, enabling comprehensive integration of spatiotemporal features.

The proposed mechanism achieves this integration through two complementary and interactively coupled modules:

Physically-informed spatial attention: The spatial attention module explicitly incorporates temporal context to capture spatial correlations among meteorological stations. In precipitation forecasting, rainfall distribution within a given region is inherently interdependent rather than isolated, as it is shaped by historical temporal dynamics and interactions with surrounding areas. By embedding temporal information, this module effectively characterizes the evolution of spatial patterns, thereby enabling the representation of processes such as the propagation of weather systems and the modulation of precipitation by topographic influences.

Spatially-aware temporal attention: Conversely, the temporal attention module integrates spatial features to more effectively characterize temporal dynamics. For example, temporal precipitation variability within a watershed is strongly conditioned by spatial attributes, including terrain configuration, elevation gradients, and land-cover heterogeneity across subregions. By jointly modeling these spatial characteristics with temporal sequences, the module can discern latent patterns such as seasonality modulated by topography and the seasonal and interannual evolution of precipitation driven by local geographic factors. This interactive spatiotemporal coupling facilitates a more comprehensive representation of precipitation processes, thereby enhancing the model’s capacity to capture complex precipitation evolution and improving predictive performance under diverse meteorological conditions.

Experimental setup and evaluation metrics

Implementation details

All experiments were conducted on a workstation equipped with an Intel Core i7-12700H processor (2.30 GHz) and an NVIDIA GTX 1060 GPU with 3 GB of memory. Model training hyperparameters were carefully configured to balance convergence efficiency and generalization performance. Specifically, the models were trained for 30 epochs using a learning rate of 0.001 and a batch size of 32. The dataset was temporally partitioned into a training set (1961–2001, year < 2002) and a test set (2002–2011, year \ge 2002). This chronological division ensures that model evaluation reflects realistic forecasting scenarios, wherein future observations are predicted solely based on historical data. Furthermore, this approach effectively prevents data leakage and provides a robust assessment of the model’s generalization capability.

To ensure a fair comparison among all comparative models, the same set of hyperparameters was applied to all six configurations. These hyperparameters, including learning rate, batch size, training epochs, and optimizer settings, were determined in advance and kept fixed across all experiments. Keeping hyperparameters consistent avoids performance differences caused by different tuning processes and guarantees the comparability of experimental results.

Evaluation metrics

Model performance was assessed using three complementary metrics that capture different aspects of prediction accuracy. Root Mean Square Error (RMSE) quantifies the deviation between predicted and true values, providing a measure that penalizes large errors more heavily than small ones due to the squaring operation. The computation proceeds through three steps: first, calculating the squared error for each prediction , then averaging these squared errors across all samples, and finally taking the square root of the mean to maintain dimensional consistency with the original data. Lower RMSE values indicate superior model performance, making this metric particularly useful for identifying models that minimize large prediction errors:

13

Mean Absolute Error (MAE) provides a complementary perspective by directly computing the average absolute error between predicted and true values. Unlike RMSE, MAE treats all errors equally without amplifying larger deviations, offering a more intuitive interpretation of average prediction error magnitude. This metric is particularly valuable when the impact of outliers should not dominate the performance assessment:

14

The coefficient of determination () reflects the model’s explanatory power for variance in the target variable, quantifying the proportion of variance captured by the model relative to a naive baseline that predicts the mean value. An value approaching 1 indicates that the model successfully explains most of the variance in the data, while values near 0 suggest performance comparable to mean prediction. This metric is formulated as:

15

where denotes the true value, represents the predicted value, is the mean of true values, and n is the number of samples.

Loss function design

The training objective comprises multiple loss components specifically designed to address the unique challenges of meteorological forecasting in complex terrain. This composite loss function balances general prediction accuracy with specific requirements such as accurate capture of extreme events and temporal trend consistency.

The base loss employs Huber loss, which combines the advantages of mean squared error for small errors and mean absolute error for large errors. This formulation provides robustness to outliers while maintaining sensitivity to typical prediction errors. The Huber loss transitions smoothly between quadratic and linear regimes based on a threshold parameter δ:

16

where y represents the true value, denotes the predicted value, and δ is the threshold parameter typically set to 1.0.

To enhance model performance on these high-impact events, an extreme loss component is incorporated that specifically penalizes prediction errors for precipitation values exceeding the 90th percentile:

17

where represents the 90% quantile of precipitation data. This component ensures the model allocates additional capacity to accurately capture extreme events without sacrificing performance on typical conditions.

Temporal consistency is enforced through a trend loss component that constrains the predicted rate of change to match the observed rate of change. This constraint helps maintain physical plausibility of predictions by ensuring that predicted trends align with actual meteorological dynamics:

18

where the trend differences are defined as the first-order temporal differences:

19

For temperature prediction, the loss weight is dynamically adjusted during training to adapt to the specific characteristics of the temperature time series. The dynamic weighting mechanism employs a sigmoid transformation to constrain the weight within a predefined range:

20

where the initial weight , resulting in a dynamic range of [0.4, 0.8] that balances stability with adaptability.

The precipitation loss function integrates the three aforementioned components with carefully tuned weights to balance their relative contributions. The composite loss is formulated as:

21

where the weight vector assigns the highest importance to extreme event prediction while maintaining substantial contributions from base accuracy and trend consistency. This composite loss function enhances the model’s capability to handle the full spectrum of precipitation patterns, from routine daily variations to extreme events, while maintaining temporal coherence in predictions.

Experimental design and regional coverage

To comprehensively evaluate the proposed hybrid architecture, we conducted extensive experiments across 33 meteorological stations distributed throughout Guizhou Province. These stations were selected to represent the region’s diverse topographic and climatic characteristics, ensuring robust assessment of model performance under varying environmental conditions. The experimental framework employs six different algorithms for comparative analysis, enabling systematic evaluation of the contributions from different architectural components.

The input data comprises monthly average temperature and precipitation records from each region, while the prediction task involves forecasting the monthly average temperature and precipitation for the subsequent month based on the preceding seven months of observations. The selection of the seven-month input window is determined by the seasonal monsoon characteristics of the study area and comparative sensitivity analysis, which can adequately capture the cumulative hydrothermal and atmospheric circulation signals for stable monthly prediction. This sliding window approach simulates operational forecasting scenarios where models must generate predictions using only the historical data available during the forecast. Table 1 presents the detailed performance metrics for temperature and precipitation prediction across all 33 regions, demonstrating the spatial variability of prediction accuracy and highlighting regions where the complex terrain poses particular challenges for meteorological forecasting.Significant spatial differences in prediction metrics can be clearly observed. Stations located in high-relief karst areas with large elevation variations and fragmented landforms show larger forecasting errors, because intricate topographic conditions disrupt local meteorological consistency and aggravate the nonlinearity of precipitation variation. In comparison, areas with gentle and continuous terrain maintain more stable climatic patterns and achieve better model performance. This contrast intuitively reflects the direct influence of topographic complexity on regional prediction accuracy.

Table 1.

Temperature and precipitation prediction performance across 33 regions in Guizhou province.

Station name	Temp RMSE	Temp MAE	Temp	Precip RMSE	Precip MAE	Precip
Sandu	1.2749	1.0001	0.9630	58.8513	41.4990	0.7203
Danzhai	1.3830	1.0334	0.9592	43.9712	31.7065	0.8156
Renhuai	1.3703	1.1012	0.9627	31.6244	22.8576	0.6916
Liuzhi	1.3631	0.9961	0.9480	48.3678	34.2198	0.7972
Ceheng	1.3063	0.9915	0.9460	44.4898	32.9153	0.7677
Jianhe	1.3608	1.0441	0.9638	39.8167	29.5516	0.7403
Wuchuan	1.3243	1.0547	0.9673	42.0167	29.6489	0.7632
Dafang	1.3289	0.9972	0.9585	34.4065	24.6043	0.7046
Tianzhu	1.3337	1.0292	0.9688	43.3851	31.2313	0.7474
Anlong	1.2100	0.8845	0.9525	39.7724	28.4828	0.8020
Pingtang	1.2453	0.9348	0.9635	38.8127	29.0784	0.8189
Kaiyang	1.4063	1.0735	0.9593	36.1860	26.6755	0.7438
Xifeng	1.4122	1.0683	0.9588	32.3536	24.4771	0.8096
Shibing	1.2202	0.9496	0.9708	35.3864	27.8460	0.7220
Pu’an	1.3089	0.9310	0.9477	42.6981	31.4495	0.8117
Zheng’an	1.3746	1.0801	0.9638	45.0929	33.4281	0.6083
Jiangkou	1.2683	0.9980	0.9715	37.1285	27.9056	0.8140
Yanhe	1.3669	1.1171	0.9659	37.8082	27.9065	0.9140
Yuping	1.3565	1.0607	0.9686	38.3609	29.3382	0.7389
Qianxi	1.4085	1.0183	0.9597	41.3396	29.9209	0.6025
Shiqian	1.3612	1.0808	0.9662	36.1435	27.8183	0.7064
Fuquan	1.3704	1.0489	0.9616	38.5466	29.0779	0.7749
Ziyun	1.2342	0.8685	0.9575	42.9630	29.3754	0.8313
Nayong	1.2820	0.9452	0.9588	36.1835	26.2071	0.7716
Zhijin	1.3470	1.0032	0.9545	42.1955	31.1720	0.8373
Suiyang	1.2988	1.0234	0.9667	39.3983	28.4955	0.7255
Zhenfeng	1.2216	0.8597	0.9556	39.2886	27.7374	0.8470
Chishui	1.1661	0.9548	0.9707	35.4413	26.3106	0.7590
Daozhen	1.1762	0.9441	0.9731	36.2825	27.9885	0.7419
Jinping	1.3358	1.0215	0.9676	47.2317	36.1404	0.6214
Zhenyuan	1.2786	1.0010	0.9692	41.5274	29.8984	0.6532
Leishan	1.4938	1.0742	0.9528	45.8120	34.4033	0.7832
Majiang	1.4385	1.0412	0.9577	46.7741	33.8205	0.6986

Metrics include RMSE, MAE, and for temperature (C) and precipitation (mm) forecasting.

Comparative analysis of prediction models

Analysis of the test data from 33 meteorological stations reveals substantial performance differences among the six weather prediction algorithms examined in this study. Table 2 compares model performance for both temperature and precipitation forecasting tasks. The results demonstrate clear advantages of the proposed hybrid architecture while providing insights into the contributions of individual components.

Table 2.

Comparative performance of different prediction algorithms for temperature and precipitation forecasting.

Model	Temperature			Precipitation			Params	Inference time (s)
	RMSE	MAE		RMSE	MAE
LSTM	1.6348	1.2410	0.9401	56.6567	40.3587	0.4965	62302	0.0245
Transformer	1.6190	1.1584	0.9473	57.8522	40.5890	0.5043	159454	0.0501
LSTM_STL_VMD	1.6488	1.2429	0.9393	57.3466	41.3680	0.4868	65142	0.0296
Transformer_STL_VMD	1.7031	1.2445	0.9417	58.5320	41.1178	0.4926	160374	0.0581
Transformer_LSTM_STL_VMD	1.6745	1.2647	0.9435	55.9764	39.3856	0.5430	215094	0.0635
Transformer_ConvLSTM_STL_VMD	1.3242	1.0070	0.9642	40.9406	29.8143	0.7650	1000430	0.1775

The proposed Transformer_ConvLSTM_STL_VMD model demonstrates superior performance across all metrics. Significant values are in bold.

For temperature prediction, the proposed Transformer_ConvLSTM_STL_VMD hybrid architecture achieves optimal performance with an RMSE of 1.3242, representing an 18.99% improvement over the baseline LSTM model. This substantial improvement demonstrates the effectiveness of integrating multiple complementary components. Interestingly, the standalone Transformer model (RMSE 1.6190) exhibits slightly superior performance to LSTM (RMSE 1.6348), suggesting that the self-attention mechanism is better suited for modeling global patterns in temperature time series. However, models incorporating STL_VMD decomposition without the full hybrid architecture show decreased performance, indicating that naive signal decomposition may disrupt inherent characteristics of temperature series when not properly integrated with spatial feature extraction mechanisms.This limitation is also applicable to precipitation datasets, which present stronger nonlinearity and spatiotemporal heterogeneity in practical modeling.

This experiment reports the average single-step inference time for predicting one-month data at a single station for temperature and precipitation of each model, based on 10 years of meteorological data from 33 regions. The precipitation prediction results reveal more pronounced performance differences among the models. The Transformer_ConvLSTM_STL_VMD architecture achieves a commanding lead with an of 0.7650, representing a 54.08% improvement over the baseline LSTM model. This breakthrough can be attributed to the synergistic effect of ConvLSTM’s spatial feature extraction capability and Transformer’s long-range dependency modeling. The performance of Transformer_LSTM_STL_VMD ( = 0.5430) demonstrates that simple architectural combinations yield moderate improvements, while pure decomposition models without spatial convolution components perform poorly. These results underscore the importance of the spatiotemporal cross-attention mechanism in effectively integrating information from multiple scales and modalities.

Experimental results and analysis

Temperature prediction performance analysis

Figure 4 compares the performance of various deep learning models in temperature time series prediction, presenting both the observed temperature trajectory and predictions from all six models. The visualization employs data from the Anlong region as a representative case study, selected for its moderate topographic complexity and typical seasonal temperature patterns.

Fig. 4.

Comparison of observed and predicted temperature time series for the Anlong region. The proposed Transformer_ConvLSTM_STL_VMD model (orange) demonstrates superior tracking of seasonal trends and short-term fluctuations compared to baseline models.

The baseline LSTM model can capture fundamental temperature trends but exhibits limited accuracy in predicting detailed fluctuations and extreme values. The temporal smoothing inherent in the recurrent architecture results in predictions that lag behind rapid temperature transitions, particularly during seasonal transitions and synoptic-scale weather events. The Transformer model improves performance in long-term dependency modeling because of its self-attention mechanism, which enables it to directly access information from distant time steps. However, the Transformer still exhibits response lag to abrupt temperature changes, suggesting limitations in capturing high-frequency variations despite its strength in modeling long-range patterns.

Models incorporating STL_VMD decomposition (LSTM_STL_VMD and Transformer_STL_VMD) show mixed results. While decomposition successfully separates trend and seasonal components, the isolated processing of these components without spatial context integration fails to improve overall prediction accuracy. In some cases, decomposition degrades performance by disrupting the natural coupling between different temporal scales in the temperature signal.

The proposed Transformer_ConvLSTM_STL_VMD model achieves the closest alignment with observed temperatures across all time periods. The prediction curve exhibits high fidelity in capturing gradual seasonal variations and rapid synoptic-scale fluctuations. This superior performance stems from the model’s ability to simultaneously decompose multiple scales while maintaining spatial coherence through ConvLSTM and integrating global patterns through the Transformer attention mechanism. The spatiotemporal cross-attention module proves particularly effective in this context, enabling the model to dynamically weight the contributions of spatial and temporal features based on the current meteorological context.

Figure 5 presents scatter plots comparing predicted versus observed temperatures across the full range of temperature values encountered in the dataset. This visualization provides complementary insights into model performance characteristics across different temperature regimes. The baseline Transformer and LSTM models perform reasonably well at temperature extremes (both low and high temperatures). However, exhibits decreased accuracy in the mid-range temperatures that constitute the majority of observations. This pattern suggests that these models may be overfitting to extreme values in the training data while failing to capture the subtle variations in typical conditions adequately.

Fig. 5.

Scatter plots of predicted versus observed temperatures across all 33 regions. The proposed model (bottom right) shows superior alignment with the ideal 1:1 line (dashed) across the full temperature range, particularly in mid-range values where baseline models exhibit larger deviations.

Models augmented with STL and VMD decomposition show improved overall consistency, but mid-range temperature prediction accuracy remains suboptimal. The scattered distribution of prediction points around the ideal 1:1 line indicates persistent systematic biases that decomposition alone cannot address. In contrast, the Transformer_ConvLSTM_STL_VMD model exhibits substantially improved performance across the entire temperature spectrum. The tight clustering of prediction points around the diagonal, particularly in the mid-range temperatures, demonstrates the effectiveness of the spatiotemporal cross-attention mechanism in achieving balanced performance across diverse meteorological conditions. This comprehensive improvement validates the proposed architectural innovations and confirms that integrating spatial convolution, temporal attention, and multi-scale decomposition successfully addresses the limitations of simpler approaches.

Precipitation prediction performance analysis

Precipitation forecasting presents substantially greater challenges than temperature prediction due to precipitation events’ highly intermittent and spatially heterogeneous nature. Figure 6 illustrates the predicted versus observed precipitation time series, again using the Anlong region as a representative case. As a classic recurrent neural network architecture, LSTM’s prediction curve roughly follows the overall trend of observed precipitation but exhibits substantial deviations in capturing detailed variations. The model produces overly smooth predictions that fail to capture the interannual and seasonal fluctuation characteristics of monthly precipitation, resulting in systematic underestimation of precipitation intensity and variability.

Fig. 6.

Comparison of observed and predicted precipitation time series for the Anlong region. The proposed Transformer_ConvLSTM_STL_VMD model demonstrates exceptional capability in capturing inter-annual and seasonal precipitation variability.

The Transformer model demonstrates a notable ability to capture long-term dependencies in the precipitation sequence. Its prediction curve somewhat agrees with observed values in most years, reflecting the model’s capacity to learn seasonal patterns and inter-annual variability.

The proposed Transformer_ConvLSTM_STL_VMD model achieves remarkable alignment between predicted and observed precipitation across the entire time series. The prediction curve exhibits high fidelity in capturing annual precipitation fluctuation patterns, successfully reproducing regular precipitation cycles. Whether during years with moderate seasonal variability or years with anomalous precipitation totals, the predicted curve maintains consistent phase and amplitude agreement with observations.

The scatter plot analysis presented in Fig. 7 quantitatively assesses prediction accuracy across the full range of precipitation values. Substantial differences emerge among the models regarding prediction accuracy for annual precipitation. The fusion framework model demonstrates significantly superior performance to single-architecture models across all precipitation regimes. The Transformer_ConvLSTM_STL_VMD model achieves prediction points closest to the measured values, with an value of 0.82, substantially exceeding those of other models (ranging from 0.65 to 0.67). Correspondingly, the model achieves the lowest RMSE (37.91 mm) and MAE (27.98 mm) among all evaluated approaches.

Fig. 7.

Scatter plots of predicted versus observed precipitation across all 33 regions. The proposed Transformer_ConvLSTM_STL_VMD model (bottom right) demonstrates superior performance across the full precipitation range, with particularly notable improvements in capturing high precipitation values (>300 mm) where baseline models exhibit systematic underestimation.

In the low precipitation regime (less than 100 mm per month), LSTM and Transformer models exhibit scattered prediction points with high variance, indicating poor reliability for light precipitation events. Models incorporating STL-VMD decomposition, particularly Transformer_LSTM_STL_VMD, show improved stability in this regime, suggesting that multi-scale decomposition helps resolve low-intensity precipitation signals that might otherwise be obscured by noise. However, systematic biases remain evident in these intermediate models.

The high precipitation regime (exceeding 300 mm per month) reveals critical limitations of traditional models. LSTM and Transformer consistently underestimate large precipitation values systematically, with prediction points falling substantially below the ideal 1:1 line. This bias reflects these models’ difficulty in extrapolating beyond the typical range of precipitation values encountered during training. In contrast, the Transformer_ConvLSTM_STL_VMD model, incorporating convolutional modules, demonstrates superior capability in capturing large precipitation values. Prediction points cluster tightly around the ideal line with the narrowest confidence interval among all models. This performance advantage can be attributed to the model’s multi-scale processing architecture: ConvLSTM captures local spatial patterns, STL-VMD decomposition separates the effective precipitation signal from background variability, and the Transformer attention mechanism integrates large-scale atmospheric circulation information. The spatiotemporal cross-attention mechanism integrates these heterogeneous information sources, thereby facilitating accurate precipitation predictions.

These results comprehensively validate the advantages of the multi-module collaborative architecture for complex meteorological prediction tasks. The consistent performance improvements across diverse precipitation regimes and geographic regions demonstrate the robustness and generalization capability of the proposed approach, confirming its suitability for operational weather forecasting applications in topographically complex regions. To further support this claim, current operational monthly precipitation forecasting systems in Guizhou typically yield an value below 0.60. In comparison, our model achieves an of 0.765, showing a clear improvement and strong potential for practical operational use.

Conclusion

Accurate precipitation and temperature forecasting is critical for water resource management and disaster mitigation in topographically complex regions such as Guizhou’s karst landscapes, where terrain-induced variations create highly nonlinear meteorological dynamics that challenge traditional forecasting methods. Our study proposes a novel hybrid deep learning framework integrating STL-VMD preprocessing, ConvLSTM spatial feature extraction, and Transformer-based global attention mechanisms. The architecture employs three key innovations: STL-VMD decomposition transforms non-stationary meteorological signals into stationary subsequences; ConvLSTM-Transformer integration captures both local spatial features and long-range temporal dependencies; and spatiotemporal cross-attention enables dynamic fusion of spatial and temporal information through adaptive gating.

Comprehensive validation using 51 years of observations (1961–2011) from 33 stations demonstrates substantial improvements over baseline LSTM. For temperature prediction, the model achieves 18.99% and 26.13% reductions in RMSE and MAE with of 0.9642. Precipitation forecasting shows even greater gains: 27.74% RMSE reduction and 54.08% improvement to 0.7650, with superior capability in capturing extreme events exceeding 300 mm per month. Consistent performance across 32 of 33 regions confirms robust generalization. These results demonstrate successful integration of multi-scale decomposition, spatial feature extraction, and global attention mechanisms for complex terrain meteorological forecasting. The framework provides actionable support for disaster prevention and water resource management in southwestern China, with potential for technology transfer to other topographically complex regions. Future work will focus on several concrete and practical directions. First, we plan to extend the model to sub-daily (e.g. hourly or 6-hourly) forecasting to capture short-lived extreme weather events. Second, we will develop probabilistic forecasting capabilities to provide uncertainty estimates, which are critical for risk assessment and decision-making. Third, we will incorporate physical constraints from numerical weather prediction models into the deep learning framework to improve interpretability and physical consistency. Finally, we aim to deploy the model in an operational setting for real-time weather forecasting in Guizhou Province, including further optimization for computational efficiency.

Author contributions

Zongyun Yang and Haiwei Sang: Writing–original draft. Haiwei Sang: Writing–review and editing. Yongtao Wang: Methodology, Data curation. Qiao Wang: Conceptualization, Methodology. Jian Liu and Yuling Chen: Formal analysis, Investigation. Kaiyin Du and Lianyan Mou: Writing–review and editing.

Funding

This work was supported by the Guizhou Provincial Science and Technology Achievement Transformation and Industrialization Plan Project (DS(2025) General 001, HaiWei Sang) and the Guizhou Provincial Science and Technology Department Project (QianKeHe Service Enterprise016, HaiWei Sang).

Data availability

All research data were obtained from the Guizhou Water Resources Bulletin and the Guizhou Statistical Yearbook, which are publicly available.

Declarations

Competing interests

The authors declare no competing interests.

Ethical approval

All authors adhered to the ethical responsibilities of authors.

Consent to publish

The authors declare that they consent to publish this manuscript.