Deep learning for multi-step forecasting of stratospheric wind and temperature profiles over the Tibetan plateau

1 Introduction

Stratospheric wind and temperature structures play an important role in atmospheric vertical coupling, wave propagation, and the exchange of momentum and energy between different atmospheric layers. Reliable prediction of stratospheric wind and temperature profiles is therefore important for characterizing regional atmospheric dynamics and their temporal variability. Over the Tibetan Plateau, complex terrain, modulation by the westerly circulation, and active gravity wave processes jointly produce pronounced regional characteristics and strong spatiotemporal heterogeneity in stratospheric wind and temperature profiles (Chen et al., 2022). Previous studies have shown that gravity wave activity over the Tibetan Plateau is closely related to topography, background wind conditions, and vertical wave propagation processes (Zeng et al., 2017; Khan and Jin, 2018; Chen et al., 2022; Wang et al., 2025). However, high-resolution vertical profile observations in this region remain limited (Xing et al., 2021), constraining systematic understanding and modeling of fine-scale atmospheric structures and their temporal evolution. Therefore, developing intelligent short-term forecasting methods for stratospheric wind and temperature profiles at fixed sites over the Tibetan Plateau using long-term reanalysis data is both scientifically important and practically necessary.

Existing methods for atmospheric wind and temperature forecasting can generally be divided into numerical weather prediction (NWP) models, empirical statistical methods, and artificial intelligence (AI) models. NWP models remain the foundation of operational weather forecasting. By solving discretized atmospheric governing equations and assimilating multi-source observations, they provide quantitative predictions of future atmospheric states (Bauer et al., 2015; Bi et al., 2023; Cantrall et al., 2019; Reichle, 2008). Nevertheless, high-resolution global or regional NWP models require substantial computational resources and are often limited by timeliness, especially in scenarios that demand rapid or flexible forecasting (Bauer et al., 2015; Li Y. et al., 2020; Li X. et al., 2020). Empirical statistical methods infer predictive relationships from historical observations and are computationally efficient, but their ability to represent complex nonlinear physical processes is limited, and their forecast accuracy often fails to meet the requirements of high-resolution spatiotemporal modeling (Solow, 2003; von Storch et al., 2004). This limitation is particularly evident for plateau atmospheric processes, which exhibit strong nonstationarity and multiscale coupling.

In recent years, AI has substantially advanced weather forecasting by enabling data-driven models to learn complex spatiotemporal dependencies directly from extensive historical datasets. For atmospheric profile forecasting, Chen et al. (2024) developed a temperature profile operator model by combining Bidirectional Long Short-Term Memory (BiLSTM) with Deep Operator Network, achieving low cumulative error and good generalization in 48 h iterative forecasts at a low latitude station. Sun et al. (2024) constructed Convolutional Gated Recurrent Unit (ConvGRU) and Convolutional Long Short-Term Memory (ConvLSTM)-based short-term forecasting models for near-surface and multi-isobaric level temperature and wind fields using MERRA-2 data, demonstrating the potential of deep spatiotemporal sequence models for multivariate atmospheric prediction. In addition, neural operator methods have been applied to rapid wind field forecasting, showing higher accuracy than classical ConvLSTM models while also offering flexible grid-independent modeling capability (Chen B. et al., 2023).

At the global medium-range forecasting scale, large deep learning models have also achieved remarkable progress. FourCastNet, proposed by Pathak et al. (2022), uses the Adaptive Fourier Neural Operator to predict global atmospheric variables from ERA5 data and demonstrates the potential of deep learning to accelerate weather forecasting. Pangu-Weather employs a 3D Transformer architecture in Earth-specific coordinates and achieves higher accuracy and efficiency than the ECMWF IFS in many deterministic forecasting tasks (Bi et al., 2023). GraphCast uses graph neural networks to propagate information across multi-level grids and outperforms IFS on most evaluation metrics (Lam et al., 2023). FengWu further improves medium-range forecasting through Transformer-based multimodal fusion (Chen K. et al., 2023), while the FuXi series enhances forecast timeliness and extreme event representation (Chen L. et al., 2023). These studies indicate that recent data-driven weather forecasting models, including Fourier operator models, graph neural networks, and Transformer-based architectures, have achieved forecast skill comparable to that of established NWP systems in several global medium-range forecasting tasks.

Despite these advances, existing AI-based weather forecasting models are still not fully matched to the fixed-site multi-level profile forecasting task considered in this study. Recent data-driven weather models have achieved substantial progress in global or regional gridded forecasting, especially for medium-range prediction of large-scale atmospheric fields. However, their primary objective is usually to improve spatial field prediction over broad domains, rather than to resolve hourly vertical-profile evolution at a specific site. For a fixed site over complex terrain, the forecasting problem is different: the model must extract useful information from a long local history, preserve the vertical coherence of multiple pressure levels, and maintain stable performance over successive forecast lead times. Therefore, methods that perform well in global or regional gridded forecasting are not necessarily optimal for fixed-site stratospheric profile prediction.

A key difficulty in this task is that temporal evolution and vertical structural variability are strongly coupled. Wind and temperature at different pressure levels are not independent, because vertical wind shear, thermal stratification, and wave-related disturbances can link the evolution of adjacent and non-adjacent layers. If pressure levels are treated only as ordinary input channels or separate output dimensions, the ordered vertical structure of the atmosphere may not be sufficiently represented. This may lead to vertically inconsistent forecasts. Therefore, fixed-site profile forecasting requires not only temporal sequence modeling, but also explicit representation of cross-height-level interactions.

Another limitation concerns multi-step forecasting strategy. Direct multi-step prediction can generate the whole forecast horizon in a stable manner and is less exposed to recursive error accumulation. However, it may insufficiently describe the step-to-step adjustment between adjacent future lead times. In contrast, recursive prediction can update the future state sequentially and is more suitable for representing lead-time-dependent evolution, but it is vulnerable to error propagation as the forecast horizon increases. For 24 h profile forecasting, relying only on either direct prediction or recursive prediction may therefore be insufficient. A more suitable framework should combine the stability of direct prediction with the flexibility of recursive correction.

These considerations motivate the proposed Multi-scale Temporal Patch and Vertical-coupling Hybrid Direct-Recursive Network (MTPV-HDRNet). The multi-scale temporal patch encoder is designed to extract historical evolution at different time scales from the 240 h input sequence. The cross-height-level coupling module treats pressure levels as a vertically ordered structure and explicitly models inter-level dependencies. Local patch features provide surrounding spatial-gradient information for the target grid point, which is useful over the complex terrain of the Tibetan Plateau. The hybrid direct-recursive decoder further balances stable multi-step trend prediction with lead-time-dependent correction. This design is intended to improve both forecasting accuracy and vertical profile consistency for fixed-site stratospheric wind and temperature prediction.

2 Data

This study uses the fifth-generation global atmospheric reanalysis product ERA5 (Hersbach et al., 2020; 2017; Molteni et al., 1996), released by the European Centre for Medium-Range Weather Forecasts (ECMWF). Specifically, the ERA5 hourly pressure-level product is used rather than the original model-level product. ERA5 pressure-level data provide upper-air atmospheric variables interpolated onto standard pressure levels from 1000 to 1 hPa, with a horizontal resolution of approximately 0.25° × 0.25° and a temporal resolution of 1 h.

From this dataset, three core variables are selected: zonal wind (U, m s − 1), meridional wind (V, m s − 1), and temperature (T, K). The analysis period covers 9 years from 2016 to 2024. The dataset is divided chronologically rather than randomly to avoid temporal leakage: data from 2016 to 2022 are used for model training, data from 2023 are used for validation, and data from 2024 are reserved for independent testing. The validation year is used for hyperparameter selection, learning-rate scheduling, and early stopping, whereas the final test year is not involved in model optimization. Using a complete year as the test set also allows the evaluation to cover seasonal variability. In the vertical direction, 11 ERA5 pressure levels are selected as forecast levels: 100, 70, 50, 30, 20, 10, 7, 5, 3, 2, and 1 hPa.

A fixed site in the central Tibetan Plateau (90.0°E, 35.0°N) is selected as the target site for vertical profile forecasting. This point lies within the plateau core region and is relatively far from the lateral boundaries of the study domain, which helps reduce the influence of boundary effects. The site is also suitable for evaluating fixed-site profile forecasting because its wind and temperature structures are affected by high terrain, background westerly flow, and vertically propagating disturbances. Using a single fixed site provides a controlled setting for evaluating temporal evolution and cross-level coupling, while minimizing additional uncertainty from horizontal extrapolation.

However, this design is not intended to represent all spatial regimes of the Tibetan Plateau. Atmospheric structures may differ substantially between the western and eastern plateau, as well as between the plateau core and its marginal regions. Therefore, the current conclusions should be interpreted as fixed-site forecasting results, and further multi-site validation is required for regional generalization.

Although ERA5 provides temporally continuous and dynamically consistent atmospheric fields, it should not be regarded as error-free observational truth. ERA5 is a reanalysis product generated through numerical model integration and data assimilation, and its accuracy depends on model physics, the availability and quality of assimilated observations, and the representation of sub-grid-scale processes. This issue is particularly relevant over the Tibetan Plateau, where complex terrain and sparse upper-air observations may introduce additional uncertainty into reanalysis fields. Therefore, the evaluation in this study should be interpreted as an assessment of the model’s ability to reproduce ERA5-consistent wind and temperature profile evolution, rather than as direct verification against independent observations.

3 Methods

3.1 Overall architecture of the proposed model

To achieve short-term joint forecasts of wind and temperature profiles at multiple pressure levels for the fixed site over the Tibetan Plateau, we propose MTPV-HDRNet, a deep learning-based forecasting model whose overall structure is shown in Figure 1. The model takes multivariate historical time series from the past 240 h as input and outputs U, V, and T at 11 pressure levels for the next 24 h. Let the inputs and outputs be denoted as shown in Equation 1:

X ∈ R T i n × L × F , Y ̂ ∈ R T out × L × C , (1)

Here, T i n = 240, T out = 24, L = 11, F is the number of input features, and C = 3 denotes the number of direct prediction variables. The input features represented by F include normalized U, V, and T; temporal metadata represented by sine and cosine functions of hour and day of year; vertical-coordinate metadata including normalized height and logarithmic pressure; and local patch features, including patch mean, patch standard deviation, center-minus-patch-mean difference, and local gradient information. The local patch features are computed from a 5 × 5 ERA5 grid-cell window centered on the target grid cell. For the target atmospheric variables, the patch mean and patch standard deviation are calculated over the 25 grid cells, and the center-minus-patch-mean term is defined as the target-grid-cell value minus the corresponding patch mean. In addition, east-west and north-south local gradient features are estimated from differences between the mean values along opposite patch edges in the longitude and latitude directions, respectively. These features provide temporal, vertical, and local spatial context for fixed-site profile forecasting, while the final evaluation focuses on U, V, and T.

The overall architecture is composed of two components: the Patch Temporal Encoder and the Hybrid Direct-Recursive Decoder. The former is responsible for extracting multi-scale temporal evolution information from long-term historical sequences and generating historical representations that can be used for different forecast horizons in the future; the latter builds on this foundation, combining direct prediction and recursive correction pathways to generate future wind and temperature profiles at multiple heights. Specifically, the encoder first divides the historical sequence into patches along the temporal dimension and obtains temporal features through linear mapping, multiscale temporal mixing, and Transformer encoding. Subsequently, the decoder employs lead-wise query vectors to extract contextual information corresponding to different future forecast horizons from the encoded historical tokens. The decoder then outputs the final forecast results through the direct prediction branch, the autoregressive correction branch, and a gated fusion module.

Compared with conventional single-path methodologies, the model offers three key advantages. Firstly, integrating temporal patching and multi-scale convolutions improves the efficiency with which extended historical sequences are encoded, while increasing the model’s ability to represent change patterns across different temporal scales. Secondly, cross-height interaction modules are incorporated at key stages of the decoder to explicitly model dependencies among pressure levels. This design is intended to preserve coherent vertical structures in stratified atmospheric profiles, rather than treating each pressure level as an isolated output dimension. Thirdly, a hybrid decoding mechanism integrating “direct prediction and recursive correction” has been introduced to improve the model’s ability to depict the dynamic evolution of adjacent future time steps while maintaining overall trend stability. This framework enables the model to balance short-term accuracy and long-term stability while preserving vertical profile structure in complex terrain settings.

3.2 Temporal encoding and hybrid direct-recursive decoding

The main idea of the modeling is to perform structured representation learning simultaneously in the temporal and vertical dimensions. A 240 h input window is used to provide sufficient historical context for multi-step atmospheric profile forecasting. This window covers approximately 10 days of evolution, including multiple diurnal cycles and synoptic-scale variations, while remaining computationally manageable after temporal patching. For temporal encoding, the model divides the 240 h input sequence into several overlapping temporal patches. The length of the patch is denoted by P, and the step size is represented by S. Consequently, the number of patches is given by Equation 2:where N denotes the number of temporal patches.

N = T i n − P S + 1 , (2)

The parameters P and S are set to 12 h and 6 h, respectively. A 12 h patch is used to capture sub-daily atmospheric variations, while the 6 h stride introduces 50% overlap between adjacent patches and preserves temporal continuity. With T i n = 240, P = 12, and S = 6, the input sequence is converted into 39 temporal patch tokens. After flattening, each patch is projected into a unified latent space via a linear layer, and positional encodings are added to maintain temporal order. A multi-scale temporal mixing module composed of multi-branch depthwise separable one-dimensional convolutions then extracts variation patterns across different temporal scales. Using convolution kernels of different sizes enables the module to capture short-term fluctuations, mesoscale evolution, and longer-term trends, thereby improving the model’s ability to represent the multi-scale characteristics of atmospheric time series. Building on this, a Transformer Encoder models long-range dependencies among patches, outputting both patch tokens that encode temporal information and a global historical feature obtained via attention pooling.

During the decoding stage, the 24 forecast lead times are modeled separately rather than treated as homogeneous outputs. For each lead time, the model constructs a dedicated query representation by combining learnable lead embeddings with future temporal metadata. These queries are projected into the latent space and interact with historical patch tokens through cross-attention, allowing the decoder to extract lead-specific historical information. Based on these lead-wise representations, a hybrid direct-recursive decoder is then employed to generate future wind and temperature profiles.

In particular, the direct prediction branch outputs the overall trend across multiple future time steps in a single pass. To enhance robustness, the model introduces a trend-aware baseline branch as a stable background estimate for the direct prediction path. This branch combines persistence information from the latest input state, the recent linear tendency estimated from the input sequence, and nonlinear contextual correction derived from the decoder representation. The persistence component helps maintain short-term stability, the linear-tendency component describes gradual background evolution, and the nonlinear component accounts for deviations from simple extrapolation.

Meanwhile, the autoregressive correction branch uses the hidden state from the previous lead time, the direct prediction for the current lead time, and historical context as inputs. The model performs stepwise state recursion via a GRUCell and introduces a cross-height Transformer at each step to model interactions among hidden states at different pressure levels. This process enables the direct prediction results to be dynamically corrected according to lead-time-dependent evolution. Finally, the model uses a gated fusion mechanism to adaptively integrate the direct prediction and autoregressive correction results, as shown in Equation 3:where G is a fusion gate generated from contextual information.

Y ̂ = G ⊙ Y ar + 1 − G ⊙ Y direct , (3)

Cross-height-level coupling constitutes a key feature of this decoder, as illustrated in Figure 2. To predict atmospheric vertical profiles at fixed sites, the interdependence of different pressure levels must be considered. In a stratified atmosphere, the evolution of one level can be dynamically and thermodynamically linked to that of adjacent and non-adjacent levels. To represent this ordered vertical structure, a cross-height Transformer is introduced into both the direct prediction and recursive correction stages. For each forecast lead time, the hidden representations at the L pressure levels are treated as a vertically ordered token sequence. Multi-head self-attention is applied along the height dimension, followed by residual connections, layer normalization, and a feed-forward network. This structure allows the model to learn cross-level dependencies rather than predicting each level independently. Physically, this design is intended to reduce vertical structural distortion and to preserve the overall morphology of wind and temperature profiles during multi-step forecasting.

3.3 Loss function and structural constraints

In order to enhance multi-variable prediction accuracy, long-lead stability, and vertical structural consistency, a joint loss function is used, as defined in Equation 4. It consists of the main prediction loss, branch auxiliary losses, and structural constraint terms:where L main denotes the main loss for the final fused output, L aux denotes the auxiliary loss applied to the direct prediction branch, the autoregressive correction branch, and the short-lead refinement branch, and L struct denotes the constraint terms related to temporal continuity, vertical structure, and wind-field dynamics.

L = L main + L aux + L struct , (4)

The main prediction loss is formulated as a weighted Smooth L 1 loss, as defined in Equation 5:where N is the total number of elements over which the loss is averaged. The Smooth L 1 transition parameter is set to β = 0.16. Here, w t, w l, and w c denote the lead-time, vertical-level, and variable weights, respectively.

L main = 1 N ∑ t = 1 T out ∑ l = 1 L ∑ c = 1 C w t w l w c SmoothL 1 β y ̂ t , l , c − y t , l , c , (5)

The lead-time weight is designed to emphasize long-lead forecast errors. Letwhere r t is the normalized forecast lead time. The basic lead-time weight is defined in Equation 6:where α = 2.7 and p = 1.90. To further improve long-lead stability, the last k = 8 forecast lead times are additionally emphasized by a tail coefficient τ = 1.45. This setting increases the contribution of long-horizon errors and reduces the tendency of the model to optimize mainly for short-term accuracy.

r t = t − 1 T out − 1 ,

w t 0 = 1 + α r t p , (6)

The vertical-level weight is defined according to the approximate height of each pressure level, as shown in Equation 7:where z l is the approximate height corresponding to the l-th pressure level, and z min and z max are the minimum and maximum heights among the selected pressure levels. Therefore, w l increases from 1.00 at the lowest selected level to 1.42 at the highest selected level. This moderate enhancement encourages the model to pay more attention to upper-level profile errors without excessively suppressing lower-level contributions.

w l = 1 + 0.42 z l − z min z max − z min , (7)

The variable weights are set as shown in Equation 8:

w c = 1.95 , c = U , 2.15 , c = V , 0.88 , c = T . (8)

The larger weights for U and V are used because wind prediction is more sensitive to local dynamical variability and is more difficult than temperature prediction in this task, especially at longer lead times. The V wind weight is slightly larger than the U wind weight to account for the relatively weaker predictability of the meridional wind component.

Auxiliary losses are applied to the direct prediction branch, the autoregressive correction branch, and the short-lead refinement branch, as defined in Equation 9:

L aux = λ dir L dir + λ ar L ar + λ short L short . (9)

The same weighted Smooth L 1 formulation is used for these auxiliary terms. In the experiments, the initial coefficients are set to λ dir = 0.16, λ ar = 0.20, and λ short = 0.16. This auxiliary supervision prevents the final fusion layer from bearing the entire optimization burden and ensures that both the direct and autoregressive paths learn effective forecasting representations.

The structural loss is defined in Equation 10:where L diff constrains lead-to-lead temporal differences, L shear constrains vertical wind-shear consistency, L speed constrains wind-speed magnitude, L vector and L angle constrain wind-vector direction, and L pers penalizes wind predictions that perform worse than the persistence reference. These terms are introduced to reduce physically unrealistic temporal jumps, vertical distortions, and wind-vector inconsistencies during 24-h multi-step forecasting.

L struct = 0.08 L diff + 0.12 L shear + 0.12 L speed + 0.10 L vector + 0.06 L angle + 0.05 L pers , (10)

3.4 Evaluation metrics

The predictive performance of the model for U wind, V wind, and temperature profiles is quantitatively evaluated using mean absolute error (MAE), root mean square error (RMSE), and Pearson correlation coefficient (CORR). These three metrics provide complementary assessments of model performance from different perspectives: MAE measures the average magnitude of prediction errors, RMSE gives greater emphasis to larger errors, and CORR evaluates the consistency between predicted values and ERA5 reference values.

The mean absolute error is defined in Equation 11:where y i denotes the ERA5 reference value, y ̂ i denotes the model prediction, and N denotes the number of evaluated samples. MAE represents the average absolute deviation between the prediction and the reference value. A smaller MAE indicates higher overall prediction accuracy.

M A E = 1 N ∑ i = 1 N y ̂ i − y i , (11)

The root mean square error is defined in Equation 12:

R M S E = 1 N ∑ i = 1 N y ̂ i − y i 2 , (12)

RMSE is more sensitive to large errors because the squared error term assigns greater weight to larger deviations. Therefore, RMSE can more clearly reflect large prediction errors that may occur in regions with strong gradients, localized extrema, or longer forecast lead times. A smaller RMSE indicates stronger overall error control.

The Pearson correlation coefficient is defined in Equation 13:where y ̄ and y ̂ ̄ denote the mean values of the reference and predicted series, respectively. CORR measures the consistency between the predicted and reference variations, with values ranging from − 1 to 1. A CORR value closer to 1 indicates that the model better captures the temporal and vertical evolution characteristics of the target variable.

C O R R = ∑ i = 1 N y ̂ i − y ̂ ̄ y i − y ̄ ∑ i = 1 N y ̂ i − y ̂ ̄ 2 ∑ i = 1 N y i − y ̄ 2 , (13)

In the actual experiments, the aforementioned metrics were statistically analyzed across different vertical levels, forecast lead times, and the entire test set. This was done to systematically evaluate the model’s generalization ability and stability in vertical structure modeling and multi-step forecasting.

4 Results and analysis

4.1 Baseline comparison

As noted in the Data section, ERA5 reanalysis fields are used as the reference in the following evaluation. Therefore, the reported errors and correlations should be interpreted as ERA5-consistent forecasting skill rather than direct validation against independent observations.

To evaluate the effectiveness of the proposed model for 24 h multi-level forecasting at the fixed site, five representative baseline models are selected for comparison: Persistence, Multilayer Perceptron (MLP), Temporal Convolutional Network (TCN), Transformer, and ConvLSTM. The Persistence model assumes that the future atmospheric state remains unchanged from the last observed state. Quantitatively, for each forecast lead time, pressure level, and variable, the Persistence prediction is defined in Equation 14:where x T i n , l , c is the last observed value in the input sequence. This no-change model provides a simple but important reference baseline commonly adopted in data-driven weather forecasting and short-term wind prediction studies (Rasp et al., 2020; Gong et al., 2022; Perr-Sauer et al., 2020).

y ̂ t , l , c = x T i n , l , c , t = 1,2 , … , T o u t , (14)

In addition, MLP, TCN, and Transformer were employed to represent three typical deep learning forecasting paradigms: level-wise static nonlinear mapping, temporal convolutional modeling, and global sequence dependency modeling, respectively. Specifically, the MLP baseline follows the feedforward neural network framework trained by backpropagation and has been widely used in forecasting applications (Rumelhart et al., 1986; Zhang et al., 1998). The TCN baseline adopts causal and dilated convolutions to capture temporal dependencies in sequential data (Bai et al., 2018), while the Transformer baseline relies on the self-attention mechanism to model long-range dependencies (Vaswani et al., 2017; Zhou et al., 2021). ConvLSTM was further included as a strong baseline because it introduces convolutional operations into the recurrent state transition, enabling simultaneous representation of temporal evolution and structural correlations, and has been widely applied to spatiotemporal prediction tasks such as precipitation nowcasting (Shi et al., 2015). All models were trained and evaluated using the same data split, input feature configuration, and evaluation metrics to ensure a fair and reproducible comparison.

As shown in Table 1, MTPV-HDRNet achieves the best overall performance among all compared models, with MAE, RMSE, and correlation coefficients of 2.44 m s − 1, 3.48 m s − 1, and 0.9844 for the U wind; 2.47 m s − 1, 3.54 m s − 1, and 0.8404 for the V wind; and 1.18 K, 1.62 K, and 0.9964 for temperature, respectively. These results demonstrate that the proposed model accurately captures the evolution of wind and temperature profiles while maintaining lower prediction errors and higher temporal consistency.

TABLE 1. Overall comparison of baseline models on the test set.

Bold values indicate the best performance in each metric.

Compared with the Persistence baseline, MTPV-HDRNet reduces the RMSE by 29.3%, 36.1%, and 31.6% for the U wind, V wind, and temperature, respectively, indicating its ability to overcome the limitations of simple persistence extrapolation. Among the deep learning baselines, ConvLSTM performs best, suggesting that recurrent temporal modeling is beneficial for atmospheric profile forecasting. Nevertheless, MTPV-HDRNet further reduces the RMSE by 11.9%, 11.3%, and 7.4% relative to ConvLSTM for the three variables, and improves the V wind correlation coefficient from 0.8029 to 0.8404.

MTPV-HDRNet also consistently outperforms MLP, TCN, and Transformer, showing that static nonlinear mapping, local temporal convolution, and standard self-attention alone are insufficient to fully represent the coupled temporal and vertical dynamics of fixed-site atmospheric profiles. Overall, these comparisons confirm the effectiveness of the proposed model, with consistent gains across both wind and temperature prediction, and particularly for the more dynamically complex wind field forecasting task.

4.2 Ablation study

To further validate the contribution of each key structural module in MTPV-HDRNet to the overall predictive performance, multiple sets of structural ablation experiments were designed. The results of these experiments are shown in Table 2. The full MTPV-HDRNet model achieved the best performance across all three target variables. This result indicates that the proposed structural modules work synergistically to improve the accuracy of fixed-site wind and temperature profile forecasting.

TABLE 2. Ablation study on model components.

Bold values indicate the best performance in each metric.

As shown in Table 2, MTPV-HDRNet achieves the best performance among all ablation variants. The consistent improvements across all variables and metrics indicate that the complete architecture effectively reduces prediction errors while preserving the temporal consistency of atmospheric profiles. Compared with the Direct Only variant, MTPV-HDRNet reduces the RMSE from 3.71 m s − 1 to 3.48 m s − 1 for U, from 3.77 m s − 1 to 3.54 m s − 1 for V, and from 1.74 K to 1.62 K for temperature, suggesting that direct multi-step prediction alone is insufficient to correct lead-time-dependent error accumulation. Although the Recursive Only variant performs relatively well, its higher RMSE values indicate that purely recursive forecasting remains affected by error propagation. The full model therefore benefits from combining the stability of direct prediction with the dynamic refinement capability of recursive modeling.

The removal of hybrid fusion also leads to degraded performance, confirming that adaptive integration of the two prediction pathways is necessary. The direct branch provides a stable multi-step background estimate, while the autoregressive correction branch adjusts the forecast according to lead-time-dependent evolution. Without the gated fusion mechanism, the model is less able to balance these two complementary sources of information. This result supports the design choice of using hybrid decoding rather than relying on a single prediction pathway.

The effects of cross-level coupling and local patch information further demonstrate the importance of structural information in fixed-site profile forecasting. Removing cross-level coupling increases the errors for all three variables, indicating that explicitly modeling dependencies among pressure levels helps preserve vertical profile consistency. From a physical perspective, this is reasonable because wind and temperature at adjacent pressure levels are not independent; instead, they are linked through cross-level dynamical and thermodynamical coupling in a stratified atmosphere. Similarly, removing local patch information also degrades performance, suggesting that even at a fixed site, surrounding spatial-gradient information remains useful. Over the Tibetan Plateau, complex terrain and local heterogeneity can influence wind adjustment and temperature structures around the target site, so local patch statistics provide additional context beyond the single-point time series.

Overall, the ablation results indicate that the performance gains of MTPV-HDRNet are not only numerical but also structurally meaningful. The complete model jointly represents multi-scale temporal evolution, cross-level interactions, local spatial context, and lead-time-dependent correction. These components work together to improve forecasting accuracy while helping maintain physically coherent vertical structures of wind and temperature profiles over complex terrain.

4.3 Analysis of results across different levels

To further clarify the vertical dependence of the model’s predictive accuracy, a systematic analysis of errors and correlations was conducted for U wind, V wind, and temperature at individual pressure levels. The results are displayed in Figure 3. The figure presents the vertical distributions of the MAE, RMSE, and CORR for these three variables at different heights, which are used to characterize the evolution of errors across the entire atmospheric profile and the model’s vertical generalization capability.

The forecast levels are defined using ERA5 standard pressure levels. To facilitate the visualization and interpretation of vertical structures, the pressure level ( P ) is converted to an approximate geometric height ( z ) for plotting, as defined in Equation 15:where H = 7.0 k m is the scale height, P 0 = 1013.25 h P a is the standard sea-level pressure, and P denotes the pressure level. Based on this approximation, the selected 100–1 hPa pressure levels correspond approximately to 16.21–48.45 km. This conversion is used only for visualization and physical interpretation of the vertical coordinate; the model itself is trained and evaluated on pressure-level ERA5 data.

z = H ⁡ ln P 0 P , (15)

As shown in Figure 3, the predictive performance of MTPV-HDRNet exhibits a pronounced height dependence for all target variables. The model achieves higher accuracy at the middle levels, whereas prediction errors increase toward both the lower and upper portions of the vertical profile. This pattern indicates that fixed-site atmospheric profile forecasting is vertically nonuniform and is jointly influenced by temporal predictability and height-dependent dynamical and thermodynamical complexity.

For the wind components, both U and V display a characteristic error profile in which MAE and RMSE decrease from the lower levels to the middle levels and then rise again at higher heights, with the smallest errors near 25 km and a pronounced degradation above 40 km. The U wind maintains high correlations across nearly the entire height range, suggesting that the model reliably captures its dominant vertical variability. In contrast, the V wind shows lower and more fluctuating correlations, reflecting greater difficulty in representing meridional wind variability, particularly localized disturbances and fine-scale vertical structures.

Temperature is predicted more stably and accurately than the wind variables, with lower errors and consistently high correlations at all heights. Although its errors also increase slightly at the lower and upper levels, the deterioration is less pronounced than for U and V, consistent with the smoother evolution and clearer stratification of the thermal field. In summary, Figure 3 demonstrates that the proposed model effectively captures the main vertical structures of wind and temperature profiles, while the lower and upper levels remain more challenging due to stronger wind speed fluctuations and increased dynamic variability.

4.4 Analysis of results across different lead times

To further evaluate the model’s stability and generalization ability under different forecast lead times, Figure 4 shows the prediction performance of U wind, V wind, and temperature over the next 1–24 h as a function of lead time. The figure presents the variation characteristics of MAE, RMSE, and CORR for the three variables, illustrating the accumulation of prediction errors as the forecast horizon extends and the changing consistency between the forecast results and the ERA5 reference values.

As shown in Figure 4, all three variables exhibit clear lead-time dependence. MAE and RMSE increase gradually, whereas CORR decreases as the forecast lead time increases. This pattern reflects the accumulation of prediction errors in multi-step forecasting. Nevertheless, the smooth variation of the curves indicates that MTPV-HDRNet maintains stable performance over the 24 h forecast range.

For the wind components, U and V show similar error growth but different degradation rates. The U wind remains highly correlated with the ERA5 reference values, with CORR decreasing only from 0.9989 at 1 h to 0.9720 at 24 h, suggesting that the model effectively preserves its dominant temporal evolution. In contrast, the V wind degrades more rapidly, with CORR decreasing from 0.9882 to 0.7270 over the same period. This indicates that meridional wind prediction is more sensitive to lead-time-dependent error accumulation than zonal wind prediction.

Within the stratospheric pressure-level range, the zonal wind is often more strongly constrained by the large-scale westerly background circulation. This large-scale constraint can provide a relatively coherent background structure for U wind evolution, which helps explain why the U component maintains high correlation even at longer forecast lead times. By contrast, the V wind component is more sensitive to regional and transient dynamical processes. Over complex terrain, the interaction between background flow and plateau topography can induce cross-mountain flow adjustment, local convergence and divergence, and vertically propagating disturbances. Terrain-induced gravity waves and their upward propagation may further modulate the vertical structure of horizontal winds. Because these processes are often intermittent, vertically localized, and sensitive to the background wind state, they can reduce the temporal persistence of V wind and make its future evolution more difficult to predict.

Temperature shows the highest stability among the three variables. Its RMSE increases from 0.69 K at 1 h to 2.05 K at 24 h, while CORR remains consistently high, decreasing only from 0.9993 to 0.9944. This suggests that the thermal field has stronger temporal continuity and a more regular background structure than the wind field. Figure 4 confirms that the proposed model achieves robust 24 h multi-step forecasting. Among the three variables, temperature is the most predictable, followed by U wind, whereas V wind remains the most challenging.

4.5 Typical case: lead time–height visualization analysis

In addition to statistical evaluation, case analysis provides a direct assessment of the model’s ability to reproduce profile structures, local anomalies, and spatiotemporal evolution. A representative test sample initialized at 22:00 UTC on 19 September 2024 was selected from the independent 2024 test year. The forecasts of the U wind, V wind, and temperature were examined using both time–height distributions and vertical profiles at representative lead times.

Figure 5 compares the ERA5 reference and predicted time–height fields over the 1–24 h forecast range. The model captures the main structures of all three variables. For the U wind, it reproduces the lower-level westerly wind belt and the weaker middle-to upper-level structures, although errors remain in upper-level localized anomalies and regions with rapid structural variation. This indicates that the model can recover the large-scale zonal wind pattern but tends to smooth fine-scale disturbances.

The V wind shows more complex alternation between southerly and northerly winds and stronger local variability, making it more difficult to predict. The model reconstructs its dominant large-scale distribution, but local extrema and fine-scale fluctuations are partly underestimated, leading to larger and broader errors than those of the U wind. In contrast, temperature is reproduced most stably: the predicted field preserves the main vertical stratification and temporal continuity, with relatively small errors mainly appearing in locally variable upper-level regions. These results confirm that the model effectively captures the dominant time–height structures, while fine-scale upper-level wind disturbances, especially for the V wind, remain challenging.

Figure 6 further shows the model’s ability to reproduce vertical profiles at representative lead times. At +1 h, the predicted profiles closely match the reference profiles for all variables, with the best agreement for temperature, followed by the U wind and V wind. As the lead time increases to +6 h and +12 h, the model still preserves the dominant vertical structures, but deviations gradually appear near upper-level extrema and sharp profile transitions. At +24 h, the overall profile shapes remain stable, although errors in local extrema and complex upper-level structures become more evident.

Quantitatively, temperature shows the smallest errors throughout the four lead times, with MAE/RMSE values of 0.430/0.522, 0.741/0.909, 0.729/1.015, and 0.953/1.281 K at +1 h, +6 h, +12 h, and +24 h, respectively. The corresponding MAE/RMSE values are 0.937/1.115, 1.720/2.105, 1.308/1.534, and 2.030/2.371 m s − 1 for the U wind, and 0.997/1.229, 1.573/1.906, 1.967/2.359, and 1.771/2.008 m s − 1 for the V wind. These results confirm that temperature is reproduced most consistently, whereas wind prediction, especially for the V component, is more affected by local extrema and complex upper-level structures.

In general, Figures 5, 6 demonstrate that the model can reliably capture the main time–height patterns and vertical profile structures in this case. The temperature field maintains the strongest agreement with the reference, the U wind is reproduced well in terms of its dominant vertical features, and the V wind remains more challenging due to fine-scale disturbances and local extrema. This behavior is consistent with the statistical analyses, indicating that the model performs best for temperature, followed by U wind, while V wind has the highest prediction difficulty.

5 Discussion and limitations

Although MTPV-HDRNet is a data-driven forecasting model, its performance can be interpreted in relation to the physical characteristics of fixed-site stratospheric profile forecasting over the Tibetan Plateau. The results suggest that the improvement of the proposed model is not only due to increased model complexity, but also to its ability to jointly represent multi-scale temporal variability, cross-level profile coherence, local spatial context, and lead-time-dependent correction. The ablation results support this interpretation: removing cross-level coupling, local patch information, or hybrid fusion leads to degraded performance, indicating that these components contribute to both numerical accuracy and vertical-structure preservation.

The different behaviors of U wind, V wind, and temperature further reflect the variable-dependent predictability of atmospheric profiles. Temperature is predicted most stably, which is consistent with its smoother vertical structure and stronger temporal continuity. U wind also maintains relatively high correlation, likely because the zonal component is more strongly constrained by large-scale background circulation within the selected stratospheric pressure-level range. In contrast, V wind shows lower correlation and faster lead-time degradation, suggesting that meridional wind prediction is more sensitive to regional and transient processes, such as cross-mountain flow adjustment, terrain-related disturbances, and vertically localized anomalies. These factors make deterministic multi-step prediction of V wind more difficult, especially at longer lead times.

Several limitations should also be considered. First, the present study is limited to a single fixed site in the central Tibetan Plateau. This design provides a controlled setting for evaluating temporal evolution and vertical coupling, but it does not fully represent the spatial diversity of the Tibetan Plateau. Atmospheric profiles may differ substantially between the western and eastern plateau, as well as between the plateau core and its marginal regions. Therefore, the current results should be interpreted as fixed-site forecasting performance rather than regional generalization. Future work will extend the framework to additional sites with different topographic and climatic characteristics and further develop regional-scale forecasting models.

Second, the present model provides deterministic forecasts and does not include confidence intervals or probabilistic uncertainty estimates. For practical high-altitude applications, such as platform control and mission planning, uncertainty information is important for risk assessment and decision-making. Therefore, incorporating uncertainty quantification into fixed-site stratospheric profile forecasting will be an important direction for future work.

Finally, the evaluation uses ERA5 reanalysis fields as the reference. ERA5 provides dynamically consistent and temporally continuous atmospheric fields, but it is not an independent observational dataset. Its accuracy may be affected by model physics, assimilation errors, sparse upper-air observations, and representation errors over complex terrain. Therefore, the reported performance should be interpreted as ERA5-consistent forecasting skill. Future work will involve independent validation using radiosonde, lidar, or other vertical profile observations to further assess the observational reliability of the proposed model.

6 Conclusion

This study addresses the short-term forecasting of stratospheric wind and temperature profiles at a fixed site over the Tibetan Plateau. Based on ERA5 pressure-level reanalysis data from 100 to 1 hPa, a 24 h joint forecasting model, MTPV-HDRNet, was developed for U wind, V wind, and temperature. The model integrates multi-scale temporal modeling, cross-height-level coupling, local patch information, and a direct-recursive hybrid decoding strategy to improve the prediction of multi-level atmospheric variables under complex terrain conditions.

The experimental results show that MTPV-HDRNet consistently outperforms the Persistence, MLP, TCN, Transformer, and ConvLSTM baselines in forecasting U wind, V wind, and temperature, indicating its stronger ability to characterize the temporal and vertical evolution of fixed-site wind and temperature profiles. Ablation experiments further demonstrate that cross-height-level coupling, local patch information, recursive refinement, and hybrid decoding each contribute positively to overall forecasting performance. Analyses across vertical levels and forecast lead times show that the model performs best at middle levels, whereas larger errors occur at lower and upper levels. As the forecast lead time increases, prediction errors gradually accumulate and correlations decline. Among the three variables, temperature shows the most stable performance, while V wind remains the most challenging component. Case studies also indicate that the model can reproduce the main time–height structures and vertical profile patterns, although limitations remain in capturing localized upper-level anomalies and fine-scale V wind disturbances.

In conclusion, MTPV-HDRNet provides an effective data-driven approach for short-term deterministic forecasting of fixed-site stratospheric wind and temperature profiles over complex terrain. Future work will focus on multi-site validation, independent observational comparison, and uncertainty quantification to improve the reliability of stratospheric atmospheric profile forecasting.

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Footnotes

Edited by: Huichao Li, Harbin Institute of Technology, China

Reviewed by: Jiao Jing, Chinese Academy of Sciences (CAS), China

Xuanyun Zeng, Harbin Institute of Technology, China