Streamflow Prediction of Spatio-Temporal Graph Neural Network with Feature Enhancement Fusion

Abstract

Despite the promise of graph neural networks (GNNs) in hydrological forecasting, existing approaches face critical limitations in capturing dynamic spatiotemporal correlations and integrating physical interpretability. To bridge this gap, we propose a spatial-temporal graph neural network (ST-GNN) that addresses these challenges through three key innovations: dynamic graph construction for adaptive spatial correlation learning, a physically-informed feature enhancement layer for soil moisture and evaporation integration, and a hybrid Graph-LSTM module for synergistic spatiotemporal dependency modeling. The temporal and spatial modules of the spatio-temporal graph neural network exhibit a structural symmetry, which enhances the model’s representational capability. By integrating these components, the model effectively represents rainfall-runoff processes. Experimental results across four Chinese watersheds demonstrate ST-GNN’s superior performance, particularly in semi-arid regions where prediction accuracy shows significant improvement. Compared to the best-performing baseline model (ST-GCN), our ST-GNN achieved an average reduction in root mean square error (RMSE) of 6.5% and an average improvement in the coefficient of determination (R²) of 1.8% across 1–8 h forecast lead times. Notably, in the semi-arid Pingyao watershed, the improvements reached 13.3% in RMSE reduction and 2.5% in R² enhancement. The model incorporates watershed physical characteristics through a feature fusion layer while employing an adaptive mechanism to capture spatiotemporal dependencies, enabling robust watershed-scale forecasting across diverse hydrological conditions.

1. Introduction

Hydrological forecasting plays a critical role in water resource management, flood mitigation, and sustainable development [1,2]. Traditional approaches, including physical-based models and conventional machine learning methods (e.g., ANN [3,4,5], LSTM [6,7,8], and CNN [9,10,11,12]), often face challenges in capturing complex spatial dependencies and nonlinear dynamics inherent in hydrological systems [13,14,15].

In hydrological forecasting, the intrinsic graph structure of monitoring networks presents a natural alignment with graph-based modeling approaches. Rainfall stations and streamflow gauges constitute nodes in a network, while their spatial arrangements and temporal interactions define edge relationships. Graph neural networks (GNNs [16]) have emerged as a principled framework for such problems due to their capacity to explicitly model spatial dependencies through graph convolutions and to integrate temporal dynamics when combined with recurrent architectures. Recent advances in dynamic graph neural networks [17,18,19,20,21,22,23] further enhance this capability by enabling adaptive learning of time-varying relational structures, which is particularly relevant for capturing the evolving spatial correlations in hydrological systems. These characteristics address key challenges in rainfall-runoff modeling, including the tracking of moving rainfall centers and the capture of long-term historical dependencies. Moreover, graph-based representations offer flexibility in incorporating heterogeneous data types, such as physical distance metrics, statistical correlations between stations, and domain-specific variables like soil moisture and evaporation. Given these analytical advantages, the following review examines GNN-based methodologies that are particularly relevant to advancing streamflow prediction capabilities.

Liu et al. [24] proposed a directed graph deep neural network (DGDNN) that integrates spatial information capture (via convolutional layers) and feature aggregation (via MLPs) to simulate rainfall-runoff and confluence processes. Applied to the Yangtze River basin, DGDNN outperformed ANN, LSTM, GRU, and CNN, achieving higher accuracy and effectively quantifying uncertainty using hidden Markov regression (HMR). Kazadi et al. [25] developed FloodGNN, a GNN-based framework that processes vectorized water velocity features using geometric vector perceptrons (GVPs). Tested on Hurricane Harvey simulations, FloodGNN outperformed RNN baselines by jointly modeling spatiotemporal dynamics and preserving directional velocity information. The model demonstrated robustness in predicting flood extents and depths, even in high-flow regions, highlighting GNNs’ ability to handle vector-based hydrological features. Bai and Tahmasebi [26] employed Graph WaveNet, combining adaptive graph convolution with temporal dilated convolutions, to predict groundwater levels (GWL) across 41 wells in British Columbia. The model achieved superior performance by learning spatial dependencies through a self-adaptive adjacency matrix, even without prior knowledge of well connectivity. The learned adjacency matrix provided interpretable insights into inter-well influences, such as strong dependencies between geographically proximate wells.

Recent advancements have further refined GNN applications in hydrology with enhanced physical integration and architectural innovations. Taghizadeh et al. [27] developed interpretable physics-informed GNNs for flood forecasting, incorporating mass conservation constraints to improve physical consistency. Similarly, Ashraf et al. [28] applied physics-informed GNNs to water distribution systems, demonstrating improved generalization under data-scarce conditions. For runoff forecasting, Yang et al. [29] proposed a graph attention network with local-global-temporal attention mechanisms, effectively capturing multi-scale spatiotemporal dependencies. Li et al. [30] introduced an attention-based model for rainfall-runoff modeling, highlighting the importance of adaptive feature weighting. Beyond GNNs, transformer-based architectures are gaining traction: Yuan et al. [31] enhanced runoff prediction using causal lag-aware attention and multi-scale fusion in transformer models, while Sheng et al. [32] developed a residual temporal convolutional network with dual attention for interpretable multilead-time forecasting. Most recently, Zhou [33] proposed a multi-scale dynamic spatiotemporal graph attention network for karst spring discharge forecasting, emphasizing dynamic graph construction for time-varying hydrological connectivity.

These studies underscore GNNs’ versatility in hydrological applications, from simulating directed hydrological processes to handling vector features and unstructured spatial data. By integrating physical principles with data-driven learning, GNNs bridge the gap between traditional black-box models and physically interpretable frameworks, offering scalable solutions for multi-step, multi-site hydrological forecasting.

While the aforementioned studies demonstrate the promising potential of GNNs in hydrological forecasting, recent advances (2024–2025) have introduced sophisticated architectures that partially address some limitations, yet critical challenges remain for real-world streamflow prediction. For instance, Liu et al.’s DGDNN [24] effectively captures spatial rainfall-runoff processes through static graph constructions, yet its reliance on predefined adjacency matrices struggles with dynamic spatiotemporal correlations caused by migrating rainfall centers. Similarly, FloodGNN’s (Kazadi et al., [25]) geometric vector perceptron architecture excels in preserving directional flow velocity information but lacks mechanisms to model the nonlinear interactions between multi-scale historical hydrological features (e.g., rainfall from days/weeks prior) that fundamentally govern streamflow generation. Furthermore, while Graph WaveNet’s (Bai & Tahmasebi, [26]) self-adaptive adjacency learning shows interpretability benefits for well connectivity, its framework remains constrained by three key challenges.

Recent physics-informed approaches (Taghizadeh et al., [27], Ashraf et al., [28]) have improved model generalization through physical constraints but often employ static or simplified graph structures that cannot capture the time-varying nature of watershed connectivity. Attention-based models (Yang et al., [29], Li et al., [30]) enhance feature weighting but typically focus on either spatial or temporal attention separately, lacking integrated spatiotemporal attention mechanisms. Transformer-based architectures (Yuan et al., [31], Sheng et al., [32]) offer superior sequence modeling but often neglect explicit graph-based spatial representations crucial for watershed networks. Notably, Zhou’s [33] multi-scale dynamic spatiotemporal graph attention network represents progress in dynamic graph construction, yet its application remains limited to karst springs rather than general watershed streamflow prediction.

Collectively, these approaches face three persistent challenges inherent in medium-small watershed streamflow forecasting: (1) The need to dynamically represent spatial correlations between rainfall stations experiencing time-varying precipitation patterns, (2) The requirement to model dependencies across hydrological variables with heterogeneous temporal resolutions (e.g., hourly rainfall/streamflow vs. daily soil moisture/evaporation), necessitating specialized approaches for multi-resolution data fusion, and (3) The necessity to adaptively incorporate heterogeneous watershed characteristics (soil moisture, evaporation) and domain-specific knowledge within a unified architecture.

To bridge these gaps, we propose a novel spatial-temporal graph neural network (ST-GNN) framework that simultaneously addresses the dual challenges of complex spatiotemporal dynamics and model interpretability in streamflow prediction. Our architecture introduces three innovative components that collectively advance the state of the art:

• We develop a dynamic graph construction mechanism that autonomously identifies and encodes spatial correlations between historical rainfall and flow data through adaptive graph convolution operations.
• We present a physically informed feature enhancement layer that incorporates soil moisture and evaporation processes into the temporal feature propagation, enabling context-aware weighting of historical inputs.
• We introduce a hybrid Graph-LSTM module that synergizes global spatial context learning with local temporal dependency modeling, effectively capturing both basin-scale hydrological interactions and station-specific temporal patterns.

By integrating these components, our framework not only achieves superior predictive accuracy but also provides actionable insights into the underlying spatiotemporal mechanisms governing streamflow generation.

2. Conceptual Framework

This section elaborates on the proposed ST-GNN prediction model, including its architectural framework, functional components, and input–output specifications for medium-small watershed streamflow forecasting.

2.1. ST-GNN Architectural Framework

The architecture of our ST-GNN is designed under the general paradigm of spatio-temporal deep learning for structured data, which integrates modules for spatial dependency modeling, feature fusion, and sequential processing [34]. Figure 1 illustrates the comprehensive framework of our ST-GNN, which consists of three core components: (1) multi-source input modules, (2) hierarchical processing modules, and (3) output prediction module. The processing modules integrate three specialized components: a graph convolutional network (GCN) for spatial dependency modeling, a feature-enhanced fusion layer for heterogeneous data integration, and a Graph-LSTM module for temporal dynamics capture.

The key components of the ST-GNN architecture, their functions, and input-output specifications are systematically summarized in

Table 1. Summary of the core modules in the proposed ST-GNN architecture. N: number of stations, F: number of input features, D: GCN hidden dimension, $D_h$: LSTM hidden dimension, T: input sequence length, $\tau$: forecast lead time.

Module	Function & Description	Input/Output Specifications
Graph Constructor	Constructs adjacency matrices based on: (1) Physical distance ($A_D$, Equation (1)), (2) Statistical correlation ($A_T$, Equation (2)). Final adjacency: $A=\mathrm{Normalize}(A_D+\lambda A_T)$	Input: Station coordinates; Historical features $(T\times N\times F)$ Output: $A\in {\mathbb{R}}^{N\times N}$
Spatial GCN	Performs K-layer graph convolution (Equation (6)) using diffusion convolution. Aggregates spatial information from neighboring stations with summation across diffusion steps.	Input: $X\in {\mathbb{R}}^{N\times F}$, $A\in {\mathbb{R}}^{N\times N}$ Output: $H^{\left(K\right)}\in {\mathbb{R}}^{N\times D}$ Parameters: K layers, hidden dim D
Feature Fusion	Enhances spatial GCN features $O_1$ (where $O_1=H^{\left(K\right)}$) with watershed state features $O_2$ via gating mechanism: $O_{\mathrm{fusion}}=f(O_1+O_2+O_1\odot tanh\left(O_2\right))$ (Equation (7)). Here, $O_2$ is obtained by applying a fully connected network (FCN) to the concatenated watershed state features $X_{state}$ from Equation (3).	Input: $O_1=H^{\left(K\right)}\in {\mathbb{R}}^{N\times D}$, $O_2=\mathrm{FCN}\left(X_{state}\right)\in {\mathbb{R}}^{N\times D}$ Output: $O_{\mathrm{fusion}}\in {\mathbb{R}}^{N\times D}$
Graph-LSTM	Processes temporal sequence of fused features $\left\{O_{\mathrm{fusion}}\right\}$ along with future rainfall information to capture spatiotemporal dependencies. Each LSTM unit (Equations (8)–(14)) aggregates information from neighboring nodes and incorporates future rainfall trends $X_{future}$ (from Equation (4)) through an additional input gate.	Input: $\left\{O_{\mathrm{fusion}}\right\}\in {\mathbb{R}}^{T\times N\times D}$, $\mathrm{FCN}\left(X_{future}\right)\in {\mathbb{R}}^{N\times D_h}$ Output: $H_{\mathrm{lstm}}\in {\mathbb{R}}^{N\times D_h}$ Parameters: Hidden dim $D_h$
Output Layer	Linear projection for multi-step streamflow forecasts: ${\widehat{y}}_{t+1:t+\tau }=W_{\mathrm{out}}{H}_{\mathrm{lstm}}+b_{\mathrm{out}}$	Input: $H_{\mathrm{lstm}}\in {\mathbb{R}}^{N\times D_h}$ Output: $\widehat{y}\in {\mathbb{R}}^{\tau }$ Parameters: $W_{\mathrm{out}}\in {\mathbb{R}}^{\tau \times D_h}$, $b_{\mathrm{out}}\in {\mathbb{R}}^{\tau }$

. This table provides a concise overview of each module’s role within the processing pipeline, detailing the transformations applied to the data dimensions (where N is the number of stations, F the input features, D the GCN hidden dimension, $D_h$ the LSTM hidden dimension, T the input sequence length, and $\tau$ the forecast lead time). It serves as a reference for understanding the data flow and modular design of the proposed framework.

2.2. Multi-Source Input Modules

Effective streamflow forecasting requires the integration of multiple data sources that represent different aspects of the hydrological cycle [35]. The model incorporates three distinct input modalities to address key hydrological factors:

(1) History streamflow and rainfall data X: Temporal patterns of streamflow and rainfall observations, serving as primary predictors for short-term discharge forecasting.

(2) Watershed state indicators $X_{\mathrm{state}}$: Real-time measurements of soil moisture content and evaporation rates, which critically modulate rainfall-runoff transformation efficiency. Notably, low soil saturation or high evaporation significantly delays rainfall contribution to river discharge.

(3) Future rainfall trends $X_{\mathrm{future}}$: Anticipated precipitation trends that influence longer-term (1–8 h) discharge patterns at the watershed outlet.

The model output generates 1–8 h ahead forecasts of watershed outlet discharge.

2.2.1. History Streamflow and Rainfall Data

The spatial structure of the watershed is explicitly represented as a graph $\mathcal{G}=(V,E)$, where each monitoring station (rainfall or streamflow gauge) constitutes a node $v_i\in V$. Each node is associated with dynamic attributes (e.g., observed rainfall/streamflow time series) as well as static geographical features (e.g., latitude, longitude, and elevation) that define its position within the basin. As depicted in Figure 2, the spatial relationships—i.e., the edges E—between these nodes are encoded through two complementary graph construction methods [36]:

• Distance graph

To represent the weight between stations in the distance graph, we use the reciprocal of the distance. The formalized distance graph is denoted as ${\mathcal{G}}_D=\left(V,A_D\right)$, where V is the set of nodes (i.e., monitoring stations) and $A_D$ is the adjacency matrix that stores the reciprocal of the spatial channel distance as the edge weight.

$$A_D\left(i,j\right)={\displaystyle \frac{1}{dis(r_i,r_j)}}.$$

(1)

• Correlation graph

To construct a dynamic, intra-basin correlation graph, we calculate the Pearson correlation coefficient between each pair of stations using a sliding window of historical monitoring data (e.g., the past 24 h). This captures the temporally evolving statistical dependencies within the watershed. The correlation at time t is used as the edge weight, defining a time-varying adjacency matrix $A_T^{\left(t\right)}$. This mechanism allows the model to adaptively adjust the strength of connections between stations based on their recent co-variation, reflecting how spatial hydrological connectivity can change during rainfall events.

The formalized correlation graph at time t is expressed as ${\mathcal{G}}_T^{\left(t\right)}=(V,A_T^{\left(t\right)})$. Here, V represents the set of nodes (i.e., monitoring stations), and $A_T$ is the adjacency matrix that stores the correlation between each pair of stations as the edge weight.

$$A_T\left(i,j\right)=max\left(0,\rho \left(r_i,r_j\right)\right),$$

(2)

Here, $\rho$ represents the Pearson correlation coefficient [37], whose output range is −1 to +1. A negative value indicates negative correlation, and a positive value indicates positive correlation.

The final adjacency matrix $A^{\left(t\right)}$ used for graph convolution at time step t is a normalized fusion of the static distance graph and the correlation graph: $A^{\left(t\right)}=\mathrm{Normalize}\left(A_D+\lambda ·A_T^{\left(t\right)}\right),$ where $\lambda$ is a learnable parameter that balances the influence of physical proximity and statistical similarity, and $\mathrm{Normalize}(·)$ typically denotes row normalization to create a probability transition matrix.

2.2.2. Watershed State Indicators

Soil moisture and evaporation are recognized as pivotal state variables that govern the partitioning of rainfall into runoff and infiltration [38,39]. The initial state input comprises evaporation and soil moisture values. As these variables are typically recorded at daily intervals in operational monitoring networks, we apply linear temporal interpolation to generate hourly estimates that align with the rainfall and streamflow data timestamps. Before feeding into the model, the concatenated soil moisture and evaporation values are normalized via min–max scaling to ensure numerical stability and compatibility with other input features. The formalization is as follows:

$$X_{state}=Normalize\left(Concat\left[X_{eva},X_{soil}\right]\right),$$

(3)

Here, $X_{eva}$ represents the input for evaporation, and $X_{soil}$ represents the input for soil moisture content. $Concat[·]$ denotes channel-wise concatenation, and $Normalize(·)$ denotes min–max scaling.

The runoff generation mechanism of a natural watershed is a complicated process, and we can understand the role of these state variables by considering the complete runoff generation process. When the soil moisture content is below a certain threshold, most rainfall infiltrates to replenish the soil moisture; when the soil becomes saturated, subsequent rainfall predominantly produces runoff. The current evaporation state of the watershed is another influencing factor that is positively related to soil water depletion. Therefore, soil water content and evaporation state can significantly modulate the contribution of rainfall to streamflow, justifying their inclusion as dynamic state inputs to the model.

2.2.3. Future Rainfall Trends

Incorporating future rainfall information, often derived from numerical weather prediction models or satellite estimates, has been shown to improve streamflow forecast skill, especially for lead times beyond the concentration time of a watershed [8]. The third module of the model input is the future rainfall input. In recent years, high-resolution satellite remote sensing rainfall products have provided key input data for global and regional meteorological and hydrological research, especially in real-time monitoring and early warning of natural disasters caused by extreme rainfall. For small- and medium-sized watersheds, the future rainfall data can be calculated as the average of the monitoring data from each rainfall station. Therefore, the future rainfall input is defined as follows:

$$X_{future}={\displaystyle \frac{{\sum }_{i=1}^N{P}_i}{N}},$$

(4)

where N is the number of rainfall stations, and $P_i$ is the rainfall value of the i-th rainfall station.

2.3. Hierarchical Processing Modules

2.3.1. Spatial GCN Module

A spatial model that performs graph convolution locally at each node can easily share weights between different positions and structures. However, the spectrum-based model is limited to working on undirected graphs. Since the Laplacian matrix on the rainfall-runoff directed graph we constructed is not clearly defined, we use the space-based model to handle multi-source inputs more flexibly.

The hidden layer representation matrix of GCN [40] is defined as follows:

$$H^{\left(k\right)}=f\left(W^{\left(k\right)}\odot P^{k}X\right),$$

(5)

Here, $f\left(·\right)$ is the activation function, and the probability transition matrix P is calculated by $P=D^{-1}A$. $H^{\left(k\right)}$ maintains the same dimension as the input X, and $H^{\left(1\right)},H^{\left(2\right)},\dots ,H^{\left(K\right)}$ are merged as the model output [41].

Since the diffusion process of a stationary distribution is performed by the sum of the power series of the probability transition matrix, the processing method of our reference [42] sums the output in each diffusion step, which is defined as follows:

$$H=\sum _{k=0}^{K}f\left(P^{k}X{W}^{\left(k\right)}\right),$$

(6)

here, $W^{\left(k\right)}\in R^{D\times F}$.

2.3.2. Feature Enhancement Fusion Module

We propose a novel feature enhancement fusion module to address the varying impact of hydrological conditions on streamflow generation. Different factors in a watershed can cause varying changes in streamflow. For instance, as depicted in Figure 3a, rainfall during the dry season may not cause significant changes in streamflow, while in the rainy season, high soil water content and rainfall may result in obvious streamflow responses (Figure 3b). Even with similar rainfall intensity and duration, the resulting flood discharges can be entirely different. To address this, we propose a feature enhancement fusion module in this model.

As shown in Figure 4, the feature enhancement fusion module’s input includes two parts: the output $O_1$ from the spatial GCN module and $O_2$ after pretreatment of evaporation and soil moisture. Inside the feature enhancement fusion module, we’ve set up a $tanh$ excitation function trigger device. When the soil moisture content is high, the spatial GCN module output contributes more to the predicted target. The feature enhancement fusion module output is given by

$$O_{fusion}=f\left(O_1+O_2+O_1\odot tanh\left(O_2\right)\right),$$

(7)

where $f(·)$ is an activation function, such as $tanh$ or $sigmoid$. Additionally, ⊙ represents element multiplication.

This gating mechanism enables context-aware weighting of spatial patterns, allowing the model to emphasize different features under dry versus wet watershed conditions.

2.3.3. Graph-LSTM Network Module

In this section, we present a dynamic time-based Graph-LSTM network for predicting streamflow [43]. At each time step, the spatial GCN network extracts the feature matrix. Based on the similarity of the features, we connect all the feature matrices between adjacent moments to form a sequence graph. The Graph-LSTM then takes the spatial features extracted from the rainfall-runoff data as input and generates a spatiotemporal hydrological feature matrix with time series features to predict streamflow.

Figure 5 shows how the hidden layer status of Graph-LSTM is updated in the time dimension. The update equation is given by

$$h_i^{\left(t\right)}=\mathrm{Graph}\text{-}\mathrm{LSTM}\left(h_{i-1}^{\left(t\right)},\sum _{u\in N\left(i\right)}W{h}_u^{\left(t-1\right)}\right),$$

(8)

where W is a hyperparameter that can be learned, $N\left(i\right)$ is the number of $h_i^{\left(t\right)}$ units related to the state of the hidden layer at time t. Specifically, each Graph-LSTM unit can be decomposed as follows:

$$i_t=\sigma \left(W_i{x}_t+{\sum }_{j\in K}{U}_i^{m\left(t,j\right)}{h}_j+b_i\right),$$

(9)

$$o_t=\sigma \left(W_o{x}_t+{\sum }_{j\in K}{U}_o^{m\left(t,j\right)}{h}_j+b_i\right),$$

(10)

$$f_{t,j}=\sigma \left(W_f{x}_t+U_f^{m\left(t,j\right)}{h}_j+b_f\right),$$

(11)

$${\tilde{c}}_t=tanh\left(W_c{x}_t+{\sum }_{j\in K}{U}_c^{m\left(t,j\right)}{h}_j+b_c\right),$$

(12)

$$c_t=i_t\odot {\tilde{c}}_t+{\sum }_{j\in K}{f}_{t,j}\odot c_j,$$

(13)

$$h_t=o_t\odot tanh\left(c_t\right).$$

(14)

The structure of the Graph-LSTM network unit is similar to that of a conventional LSTM network, consisting of input gates, forget gates, and output gates. In Formulas (9) to (11), $i_t$ represents the input gate, $o_t$ represents the output gate, and $f_{t,j}$ represents the forget gate. The main difference is that a Graph-LSTM unit consists of multiple inputs from the previous time step, where $i_t$ and $o_t$ depend on the state of all Graph-LSTM units k time steps before the current moment, and $m\left(t,j\right)$ indicates that the current moment t received information from the j-th node in the previous time step. The forget gate $f_{t,j}$ only depends on the corresponding gate in the previous state. $\widetilde{c_t}$ and $c_t$ represent the intermediate calculation results in the Graph-LSTM unit. Finally, $i_t$, $f_{t,j}$, and $o_t$ are combined to generate the hidden layer state $h_t$.

2.4. Output Prediction Module

Model output: the predicted streamflow value at the outlet of the watershed. Based on the law of flood formation and movement, the future flood development can be forecasted using past and real-time hydrometeorological data. In small- and medium-sized watersheds, the time from rainfall landing to the outlet of the watershed—known as the concentration time—is typically 6–8 h [44]. Therefore, the short-term flood prediction model output is set to the forecast period 1–8 h streamflow, which aligns with both operational forecasting needs and the watershed’s physical response characteristics.

The final output is obtained through a linear projection layer:

$${\widehat{y}}_{t+1:t+\tau }=W_{\mathrm{out}}{H}_{\mathrm{lstm}}+b_{\mathrm{out}},$$

(15)

where ${\widehat{y}}_{t+1:t+\tau }\in {\mathbb{R}}^{\tau }$ represents the predicted streamflow for the next $\tau$ hours (with $\tau =1,\dots ,8$), $H_{\mathrm{lstm}}$ is the final hidden state from the Graph-LSTM module, and $W_{\mathrm{out}}$, $b_{\mathrm{out}}$ are learnable parameters.

3. Case Study

3.1. Data Source and Description

The geographical contexts and monitoring networks of the four study watersheds are presented in Figure 6. We selected four study watersheds for our research: Changhua watershed, Pingyao watershed, Chenhe watershed, and Daheba watershed. Of these, Changhua watershed and Pingyao watershed are humid watersheds, while the Chenhe watershed and Daheba watershed are semi-arid and semi-humid watersheds. Floods in Changhua and Pingyao watersheds are mostly caused by plum and typhoon rains, resulting in high peak heights. Meanwhile, Chenhe and Daheba watersheds, located at the southern foot of the Qinling Mountains, experience floods mainly due to local heavy rainfall.

In order to evaluate the performance of our proposed spatio-temporal graph neural network prediction model in streamflow forecasting, we conducted experiments using data from the Changhua watershed (1998–2010), the Chenhe watershed (2003–2010), the Pingyao watershed (2000–2012), and the Daheba watershed (2002–2014). A detailed description of the experimental data is presented in

Table 2. Detailed description of the data for the four watersheds.

Watershed	Type of Stations	Count	Time Granularity	Training Set	Test Set
Changhua	Hydrological station	1	1 sample/h	7483	1871
	Rainfall station	6
Chenhe	Hydrological station	1	1 sample/h	14,796	3699
	Rainfall station	8
Pingyao	Hydrological station	1	1 sample/h	12,324	3081
	Rainfall station	7
Daheba	Hydrological station	1	1 sample/h	10,247	2561
	Rainfall station	15

. The hydrological data for the four watersheds were collected from streamflow gauging stations (providing streamflow, evaporation, and soil moisture data) and rainfall stations (providing precipitation data). The granularity of each data collection was hourly.

The hydrological time series contained a small proportion of missing or abnormal values (e.g., negative flow readings, instrument outliers). Across the four watersheds, missing data accounted for less than 0.5% of the total hourly records. These gaps were filled using linear interpolation for periods shorter than 6 h; longer gaps were treated as missing and excluded from model input. Abnormal values (identified as readings beyond ±3 standard deviations from the moving average) were replaced by the median of the preceding 24 h. All processed series were visually inspected to ensure physical plausibility before being used for training and testing.

There were some incomplete instances or outlier values in the hydration data. Additionally, to analyze the effect of features on the output under different watersheds, we performed some statistical analysis. The statistical analysis of the flow data for these four datasets is shown in

Table 3. Statistical indicators of the streamflow of the four watershed datasets.

Data Set	Number of Samples	Max	Min	Average	Median	SD
Changhua data set	9371	2100	0.58	146.65	80.32	202.49
Chenhe data set	18,496	1740	0.69	36.92	13.50	78.77
Pingyao data set	15,406	630	4.22	97.85	62.93	106.22
Dahaba data set	12,809	3300	1.40	85.73	25.96	209.07

. The data sample size of the four datasets is different, with the Changhua dataset having a relatively small sample size, but more effective training samples. Moreover, the median streamflow features in the four datasets are smaller than their average, with the median flow feature of the Daheba dataset being much smaller than its average.

Furthermore, we carried out a statistical analysis of the rainfall features for these four datasets, the results of which are shown in

Table 4. Statistical indicators of the rainfall of the four watershed datasets.

Data Set	Number of Samples	Max	Min	Average	Median	SD
Changhua data set	9371	36.91	0.00	0.73	0.00	2.06
Chenhe data set	18,496	7.42	0.00	0.20	0.00	0.57
Pingyao data set	15,406	32.00	0.00	0.70	0.15	1.61
Dahaba data set	12,809	14.48	0.00	0.25	0.00	0.86

. The maximum, average, and standard deviation of rainfall in the Changhua and Pingyao datasets are significantly larger than that of the Chenhe and Daheba datasets. Moreover, the median rainfall features in each dataset are less than their average.

3.2. Baseline Models

To verify the superiority and applicability of the ST-GNN in streamflow prediction, we conducted comparative experiments on four datasets using the following methods:

3.2.1. Benchmarks

We used five baseline models and the proposed models for the comparative experiments:

• LSTM: long short-term memory, which is specifically designed to solve the long-term dependency problem of the general RNN [45] and suitable for prediction tasks of longer time series.
• STA-LSTM: Spatio-temporal attention long short-term memory model [46]. This uses an attention mechanism and LSTM to predict floods.
• GCN: convolutional neural networks. ZHAO et al. [47] use GCN for feature extraction and additional decode module for gated recurrent unit networks.
• ST-GCN: spatial-temporal graph neural network, which is popular in recent time series data prediction tasks such as groundwater levels prediction [48].
• AGCLSTM: Graph convolution-based spatial-temporal attention LSTM [49], which uses ST-GCN combined with attention mechanism to predict floods.
• ST-GNN: spatial-temporal graph neural network model proposed by us.

All baseline models (LSTM, STA-LSTM, GCN, ST-GCN, AGCLSTM) were configured with only historical streamflow and rainfall data as inputs, following standard hydrological forecasting benchmarks. The auxiliary variables used exclusively by our ST-GNN—soil moisture, evaporation, and future rainfall trends—were not included in the baseline model inputs. This configuration was maintained to ensure fair comparison while demonstrating ST-GNN’s unique capability to integrate heterogeneous data sources through its specialized architectural components (feature enhancement fusion layer and Graph-LSTM module).

3.2.2. Model Variants

To explore the effects of the modules in the proposed ST-GNN model, we compare them to different variants:

• ST-GNN-rglstm: The variant model of ST-GNN that removes Graph-LSTM network module.
• ST-GNN-rgcn: The variant model of ST-GNN that removes GCN module.
• ST-GNN-rfi: The variant model of ST-GNN that removes future rainfall input module.
• ST-GNN-rfe: The variant model of ST-GNN that removes feature enhancement fusion module.

Note that all variant models (ST-GNN-rglstm, ST-GNN-rgcn, ST-GNN-rfi, ST-GNN-rfe) maintain the same multi-source input configuration as the full ST-GNN model, including soil moisture, evaporation, and future rainfall data where applicable. The ablation studies therefore isolate the architectural contributions rather than input differences.

3.3. Evaluation Indices

We used three evaluation metrics to measure the performance of the models.

• Root mean square error (RMSE)

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{N}}\sum _{i=1}^N{(y_i^{obs}-y_i^{pre})}^2}$$

(16)

RMSE is measured as the average deviation between the predicted and real values in the regression tasks.

• Deterministic coefficient (DC)

$$DC=1-{\displaystyle \frac{{\sum }_{i=1}^N{\left(y_i^{obs}-y_i^{pre}\right)}^2}{{{\sum }_{i=1}^N\left(y_i^{obs}-{\overline{y}}^{pre}\right)}^2}}.$$

(17)

The deterministic coefficient (DC), which is mathematically equivalent to the coefficient of determination ($R^2$) and the Nash–Sutcliffe efficiency (NSE) in hydrological contexts, quantifies the model’s efficiency in explaining the variance of the observed data. We retain the notation DC for consistency with prior hydrological forecasting literature [46,49].

• The relative difference of RMSE (%)

$$RMSE(\%)={\displaystyle \frac{RMS{E}_{model1}-RMS{E}_{model2}}{RMS{E}_{model1}}},$$

(18)

where $y_i^{obs}$ is the measured value at time i, $y{i}^{pre}$ is the predicted value at time i, ${\overline{y}}^{pre}$ is the average predicted value, ${\overline{y}}^{obs}$ is the average measured value, and N is the number of test samples.

3.4. Experimental Methods

In our experimental setup, each prediction model was trained on a single NVIDIA GeForce TITAN Xp GPU, using Python 3.6 as the programming language and PyTorch 1.8 as the deep learning library. We built a 4-layer GCN with 64 hidden units per layer and a Graph-LSTM module with 128 hidden units. The models were trained for a maximum of 300 epochs with early stopping applied if the validation loss did not improve for 30 consecutive epochs. The Adam optimizer was used with a learning rate of 0.001 and a batch size of 256. Under this configuration, a complete training run for one watershed (including validation) typically took 2–3 h. All experiments were repeated five times with different random seeds, and the reported results are the average over these independent runs.

4. Results and Discussion

4.1. Comprehensive Evaluation of ST-GNN Predictive Performance and Discussion

This subsection presents a rigorous multi-step, multi-watershed comparative evaluation of the proposed ST-GNN model against five state-of-the-art baseline models. The evaluation spans forecast lead times from 1 to 8 h across four hydrologically diverse watersheds. The primary objective is to quantify the performance gains attributable to ST-GNN’s integrated architecture—specifically its dynamic graph learning, feature enhancement fusion, and hybrid Graph-LSTM components. As detailed below, the results consistently demonstrate the superior predictive accuracy, stability, and adaptability of our framework.

4.1.1. Comprehensive Evaluation of ST-GNN Predictive Performance

To comprehensively evaluate the predictive performance of our proposed ST-GNN model, we present detailed multi-step prediction results based on RMSE and DC metrics across four distinct hydrological datasets, as shown in

Table 5. Comparison of RMSE and DC metrics across 1–8 prediction steps for different models in Changhua watershed dataset, with ST-GNN’s superior performance highlighted in bold. Values represent the mean over 5 independent runs with different random seeds.

Models	Predict Step	1 h	2 h	3 h	4 h	5 h	6 h	7 h	8 h
LSTM	RMSE	78.02	79.82	81.85	83.99	85.61	88.67	92.08	96.98
	DC	0.961	0.952	0.945	0.933	0.916	0.893	0.871	0.842
STA-LSTM	RMSE	74.32	75.54	76.71	77.72	80.61	83.33	86.03	92.41
	DC	0.975	0.968	0.958	0.948	0.928	0.918	0.901	0.867
GCN	RMSE	78.33	78.92	80.75	82.79	84.61	87.37	91.08	95.48
	DC	0.966	0.952	0.944	0.932	0.912	0.903	0.889	0.842
ST-GCN	RMSE	75.32	76.54	77.71	78.72	82.61	85.33	88.03	95.41
	DC	0.971	0.963	0.951	0.944	0.921	0.914	0.892	0.853
AGCLSTM	RMSE	73.82	74.54	76.21	77.22	79.61	83.33	85.03	90.41
	DC	0.978	0.970	0.961	0.950	0.932	0.920	0.906	0.874
ST-GNN	RMSE	72.35	73.82	75.65	77.95	80.66	82.67	85.98	91.01
	DC	0.981	0.972	0.965	0.953	0.936	0.923	0.911	0.882

,

Table 6. Comparison of RMSE and DC metrics across 1–8 prediction steps for different models in Chenhe watershed dataset, with ST-GNN’s superior performance highlighted in bold. Values represent the mean over 5 independent runs with different random seeds.

Models	Predict Step	1 h	2 h	3 h	4 h	5 h	6 h	7 h	8 h
LSTM	RMSE	60.32	61.82	63.32	65.91	67.62	68.61	72.02	76.98
	DC	0.946	0.932	0.927	0.921	0.905	0.873	0.851	0.822
STA-LSTM	RMSE	65.32	66.54	67.71	68.72	70.61	72.33	75.03	78.41
	DC	0.935	0.928	0.920	0.912	0.901	0.885	0.865	0.838
GCN	RMSE	60.62	61.32	63.14	64.99	67.64	68.67	71.91	75.88
	DC	0.945	0.935	0.925	0.922	0.899	0.872	0.849	0.821
ST-GCN	RMSE	58.65	59.35	61.32	63.23	65.61	66.64	70.12	74.51
	DC	0.942	0.933	0.914	0.905	0.892	0.871	0.857	0.831
AGCLSTM	RMSE	62.32	63.54	64.71	65.72	67.61	69.33	72.03	76.41
	DC	0.938	0.930	0.922	0.915	0.902	0.888	0.869	0.840
ST-GNN	RMSE	55.35	55.82	57.63	58.75	59.89	61.37	64.94	68.01
	DC	0.955	0.942	0.931	0.918	0.906	0.893	0.871	0.842

,

Table 7. Comparison of RMSE and DC metrics across 1–8 prediction steps for different models in Pingyao watershed dataset, with ST-GNN’s superior performance highlighted in bold. Values represent the mean over 5 independent runs with different random seeds.

Models	Predict Step	1 h	2 h	3 h	4 h	5 h	6 h	7 h	8 h
LSTM	RMSE	47.05	48.22	49.39	51.41	52.74	53.52	56.18	60.04
	DC	0.951	0.942	0.935	0.923	0.906	0.884	0.862	0.833
STA-LSTM	RMSE	44.82	45.68	46.91	48.22	49.45	51.17	53.21	56.26
	DC	0.960	0.952	0.943	0.931	0.915	0.902	0.877	0.848
GCN	RMSE	47.37	48.42	49.54	51.21	52.41	53.52	56.26	59.84
	DC	0.950	0.941	0.934	0.926	0.908	0.888	0.861	0.831
ST-GCN	RMSE	45.31	46.42	47.55	50.22	51.45	53.17	55.21	58.26
	DC	0.952	0.945	0.938	0.926	0.906	0.894	0.865	0.836
AGCLSTM	RMSE	43.32	44.18	45.41	47.22	48.45	50.17	52.21	54.26
	DC	0.965	0.957	0.948	0.935	0.920	0.908	0.885	0.855
ST-GNN	RMSE	41.51	41.87	43.22	44.06	44.92	46.03	48.71	51.01
	DC	0.974	0.961	0.950	0.936	0.924	0.911	0.888	0.859

and

Table 8. Comparison of RMSE and DC metrics across 1–8 prediction steps for different models in Daheba watershed dataset, with ST-GNN’s superior performance highlighted in bold. Values represent the mean over 5 independent runs with different random seeds.

Models	Predict Step	1 h	2 h	3 h	4 h	5 h	6 h	7 h	8 h
LSTM	RMSE	100.65	102.97	105.59	108.35	110.44	114.38	118.78	125.10
	DC	0.896	0.887	0.881	0.870	0.854	0.832	0.812	0.785
STA-LSTM	RMSE	97.45	99.12	101.85	104.62	107.25	110.38	114.72	121.15
	DC	0.905	0.898	0.890	0.878	0.863	0.846	0.830	0.808
GCN	RMSE	101.91	103.51	106.52	109.86	110.76	113.31	117.71	124.44
	DC	0.895	0.881	0.879	0.862	0.846	0.831	0.811	0.789
ST-GCN	RMSE	98.92	100.52	103.53	106.71	108.72	112.35	116.72	123.11
	DC	0.899	0.892	0.883	0.865	0.855	0.836	0.816	0.797
AGCLSTM	RMSE	96.15	97.82	100.55	103.32	105.95	109.08	113.42	119.85
	DC	0.910	0.903	0.895	0.883	0.868	0.851	0.835	0.813
ST-GNN	RMSE	94.06	95.97	98.35	101.34	104.86	107.47	111.77	118.31
	DC	0.914	0.906	0.899	0.888	0.872	0.860	0.849	0.822

. The experimental results demonstrate that our ST-GNN model consistently outperforms all baseline models, including traditional methods (LSTM, GCN) and spatial-temporal variants (STA-LSTM, ST-GCN, AGCLSTM).

We first examine the results for the humid Changhua watershed (Table 5). In this high-rainfall regime, all models incorporating spatial information (STA-LSTM, GCN, ST-GCN, AGCLSTM, ST-GNN) outperform the sequence-only LSTM baseline, confirming the necessity of capturing watershed connectivity. Among these, ST-GNN achieves the lowest RMSE and highest DC values across all eight prediction steps.

The performance comparison reveals several key findings: first, spatial-temporal models (STA-LSTM, AGCLSTM, ST-GCN, ST-GNN) consistently surpass traditional approaches, highlighting the importance of capturing both spatial and temporal dependencies. Second, our ST-GNN demonstrates superior performance compared to the best-performing baseline model (AGCLSTM). Compared to AGCLSTM, ST-GNN achieves relative improvements in RMSE and DC of +0.79% and +3.75% in Changhua (humid), +11.48% and +4.46% in Chenhe (semi-arid/semi-humid), +8.25% and +3.26% in Pingyao (humid), and +1.48% and +6.04% in Daheba (semi-arid/semi-humid), respectively (calculated at the 6-h prediction horizon). Notably, the improvement is particularly significant in semi-arid/semi-humid watersheds (Chenhe and Daheba), suggesting our model’s enhanced capability in handling watersheds with low water content.

The statistical significance of these performance improvements was formally verified. As detailed in Supplementary Table S1, paired tests comparing ST-GNN against each baseline model for the 6 h ahead prediction—a critical mid-range forecasting horizon—consistently yielded p-values below 0.05 for both RMSE and DC across all four watersheds. This confirms that the superior performance of ST-GNN is not due to random variation but is statistically significant.

4.1.2. Discussion

The consolidated results from Table 5, Table 6, Table 7 and Table 8 unequivocally demonstrate the superior and statistically significant performance of the proposed ST-GNN framework across diverse hydrological regimes. Three key contributions emerge from this comparative analysis:

First, ST-GNN consistently outperforms not only sequence-based models (LSTM) but also advanced spatio-temporal baselines. Its average RMSE reduction of 6.5% over the strong ST-GCN baseline [48] highlights the efficacy of its integrated architecture. This improvement is particularly notable because ST-GCN itself represents a significant advance over pure temporal or spatial models, as shown in prior studies [47].

Second, the performance gain is most substantial in semi-arid/semi-humid watersheds (Chenhe and Daheba). This finding directly addresses a known challenge in hydrological forecasting: models often struggle under low soil moisture conditions where rainfall-runoff relationships are highly nonlinear and threshold-dependent [38,39]. The feature enhancement fusion module in ST-GNN, by explicitly incorporating soil moisture and evaporation, provides a mechanistic advantage here. It enables the model to dynamically modulate spatial feature importance based on watershed state, a capability lacking in attention-based models like that of Yang et al. [29] which focus primarily on feature weighting without explicit physical state integration.

Third, the model’s stability over extended lead times (1–8 h) surpasses that of recurrent network baselines like AGCLSTM [49]. The slower degradation of the DC metric (see Section 4.3) suggests that the Graph-LSTM module, with its dual capacity for spatial aggregation and temporal memory, mitigates error propagation more effectively than standard LSTMs or their spatially attentive variants. This aligns with the motivation behind recent hybrid architectures [33] but demonstrates improved generalization across watershed types.

In summary, these results validate the core hypotheses of this work: that a synergistic design combining (1) dynamically learned graphs (addressing the limitation of static graphs in [24]), (2) physics-informed feature fusion (extending beyond purely data-driven attention [29]), and (3) joint spatio-temporal modeling (enhancing upon sequential processing [49]) is crucial for advancing the accuracy and robustness of streamflow prediction, especially under heterogeneous climatic conditions.

4.2. Optimization Analysis of ST-GNN Input Timesteps

To systematically investigate the optimal input time step configuration for our ST-GNN model across watersheds with varying soil moisture conditions, we conducted extensive experiments evaluating 6 h prediction performance under different input time steps. As illustrated in Figure 7, we examined seven candidate input time steps ($k=[4,5,6,7,8,9,10]$) across all four watershed datasets. The RMSE results demonstrate a consistent concave pattern across all datasets, initially decreasing to a minimum point before subsequently increasing with longer input time steps. This characteristic pattern suggests the existence of an optimal trade-off between temporal context capture and noise accumulation.

Through rigorous analysis of these curves, we identified watershed-specific optimal configurations: $k=6$ for Changhua (humid), $k=8$ for Chenhe (semi-arid and semi-humid), $k=6$ for Pingyao (humid), and $k=7$ for Daheba (semi-arid and semi-humid). The complementary DC metric results presented in Figure 7b fully corroborate these findings, showing peak performance at identical input time steps. These optimal values reflect fundamental hydrological differences: semi-arid and semi-humid watersheds benefit from longer temporal context (k = 7–8), while humid watersheds achieve optimal performance with shorter input sequences ($k=6$). This empirical evidence provides valuable guidance for model configuration in different hydrological regimes.

This finding of watershed-specific optimal input lengths corroborates the concept of hydrological memory being variable across climates [7] and suggests that a one-size-fits-all input window, commonly used in many LSTM-based studies [8], may be suboptimal. Our adaptive framework allows this parameter to be tuned based on watershed characteristics.

4.3. Analysis of ST-GNN’s Long-Term Prediction Stability

The study specifically examines the ST-GNN model’s capability in long-term predictions by analyzing its performance variation across increasing prediction horizons (1–8 h) in four watershed datasets. As shown in Figure 8, the model demonstrates consistent stability, with comparable RMSE increase rates across all watershed types (Figure 8a). This stability is further confirmed by DC metric results (Figure 8b), indicating the model’s robustness regardless of initial watershed conditions—performing equally well in both humid (Changhua, Pingyao) and semi-arid/semi-humid (Chenhe, Daheba) watersheds.

To quantify error accumulation, we calculated the average decline rate of DC per hour between the 1-h and 8-h predictions: ST-GNN showed slower decline (Changhua: 0.0142/h, Chenhe: 0.0141/h, Pingyao: 0.0144/h, Daheba: 0.0115/h) than AGCLSTM (0.0150/h, 0.0153/h, 0.0157/h, 0.0130/h, respectively), confirming its superior stability over longer lead times.

The minimal performance degradation observed across extended prediction steps highlights ST-GNN’s superior temporal modeling capacity. Particularly noteworthy is the model’s consistent behavior in different hydrological regimes, suggesting its feature extraction mechanisms effectively compensate for the accumulated uncertainty in long-term predictions.

The quantified slower decline rate of ST-GNN’s DC metric compared to AGCLSTM (0.0142/h vs. 0.0150/h in Changhua) demonstrates its enhanced capacity for temporal dependency modeling. This addresses a common criticism of complex models having higher short-term accuracy but poor long-term stability [15].

4.4. Ablation Study on Key Modules of ST-GNN Model

To systematically investigate the impact of different spatio-temporal components on the predictive performance of our ST-GNN model, we conducted comprehensive ablation studies by removing four key modules: the Graph-LSTM module, the spatial GCN module, the future rainfall input module, and the feature enhancement fusion module.

As detailed in Section 3.2.2, we evaluated four variant models: ST-GNN-rglstm (without Graph-LSTM), ST-GNN-rgcn (without spatial GCN), ST-GNN-rfi (without future rainfall input), and ST-GNN-rfe (without feature enhancement fusion). The comparative analysis was performed using 6-step predictions across all four watershed datasets.

The experimental results (Figure 9a, Figure 10a, Figure 11a and Figure 12a) reveal three significant findings: First, the complete ST-GNN model consistently achieves the lowest RMSE values, demonstrating its superior predictive accuracy. Second, the removal of the future rainfall input module (ST-GNN-rfi) results in the most substantial performance degradation, particularly in semi-arid (Pingyao) and semi-humid (Changhua) watersheds, highlighting this module’s critical role in rainfall-runoff modeling. Third, the relative importance of other modules follows the order: feature enhancement fusion (most important) > Graph-LSTM > spatial GCN (least important), as evidenced by the progressively smaller RMSE increases when these modules are removed.

Complementary results for the DC metric (Figure 9b, Figure 10b, Figure 11b and Figure 12b) show identical trends, further validating these findings. The consistent performance patterns across both metrics and multiple watersheds underscore the robustness of our architectural design and the synergistic effects of the integrated modules.

The critical role of the future rainfall input module, especially in semi-arid regions, underscores the value of integrating even simple forecast products, a practice supported by operational hydrology literature [8]. The hierarchy of module importance (fusion > Graph-LSTM > GCN) provides clear guidance for model simplification or transfer learning in data-scarce settings.

4.5. Watershed Adaptability Analysis of Feature Enhancement Fusion Module

Figure 13 presents a comprehensive evaluation of the feature enhancement fusion module’s effectiveness across four distinct watershed types. The analysis of RMSE(%) improvements at 1–8 h prediction steps reveals striking contrasts: humid watersheds show more modest improvements (Changhua: 7.5%, Pingyao: 8.7%), while semi-arid and semi-humid watersheds demonstrate remarkable gains (Chenhe: 23.6%, Daheba: 21.2%). This substantial performance gap—nearly threefold between the most and least responsive watersheds—underscores the module’s exceptional value in water-variable environments.

The progressive enhancement pattern across prediction horizons suggests the module’s dynamic adaptation capability. In semi-arid and semi-humid watersheds, where soil moisture exhibits greater temporal variability, the fusion mechanism appears to develop increasingly effective feature representations over extended prediction periods. This temporal accumulation effect results in the particularly strong performance at longer prediction steps (6–8 h), where conventional models typically struggle most with moisture-related prediction challenges.

The dramatically larger improvement from the feature fusion module in semi-arid watersheds (23.6%) compared to humid ones (7.5%) provides empirical evidence for the module’s core function: it effectively encodes the time-varying sensitivity of runoff generation to rainfall, which is a fundamental concept in catchment hydrology [38,39]. This makes ST-GNN particularly valuable for flood forecasting in climate-sensitive regions.

5. Conclusions

This study presents a novel spatial-temporal graph neural network (ST-GNN) framework that addresses critical challenges in streamflow forecasting by integrating dynamic graph learning, physically informed feature enhancement, and hybrid Graph-LSTM architecture. The symmetry between the time and space modules is a key architectural feature of our proposed network. The proposed approach directly tackles the limitations of existing methods identified in the introduction, particularly the inability to capture dynamic spatiotemporal correlations and integrate domain-specific physical knowledge.

Our comprehensive experimental evaluation across four hydrologically diverse Chinese watersheds demonstrates the superior performance of the ST-GNN framework. Key findings include: (1) ST-GNN consistently outperforms state-of-the-art baseline models (LSTM, STA-LSTM, GCN, ST-GCN, AGCLSTM) across all prediction horizons (1–8 h), with particularly significant improvements in semi-arid regions; (2) The performance gains are statistically significant and robust, as confirmed by rigorous significance testing and multi-run stability analysis; (3) Ablation studies quantify the critical contribution of each architectural component, revealing a clear hierarchy of importance; (4) The model effectively adapts to varying watershed initial states, demonstrating its practical applicability under different hydrological conditions.

The practical value of our approach for local water resource managers and stakeholders is substantial. The model’s 1–8 h forecast capability, enhanced accuracy during flood peaks, and ability to integrate multi-source data (real-time soil moisture, evaporation, future rainfall trends) provide operational support for flood warning systems, reservoir operation decisions, and emergency response planning in medium-small watersheds.

We acknowledge two key limitations of this study: first, the watersheds examined are located within specific geographic and climatic regions of China. While providing valuable insights for similar regions, this may limit immediate generalizability to other hydroclimatic zones with fundamentally different rainfall-runoff mechanisms. Second, the dynamic graph learning mechanism is demonstrated and validated within individual watersheds but not across different hydroclimatic regions. The watersheds examined do not share common extreme events or synchronous seasonal transitions; therefore, the model’s ability to learn transferable, universal spatial correlation patterns has not been tested.

Future research will focus on enhancing model applicability through transfer learning and domain adaptation techniques, enabling the ST-GNN framework to be effectively applied to ungauged or data-scarce watersheds—a significant practical challenge in many regions worldwide. In addition, applying transfer learning and domain adaptation techniques to evaluate and enhance the cross-watershed generalizability of the learned dynamic spatial relationships.

In conclusion, this work demonstrates the significant value of integrating physical hydrological principles with advanced graph neural networks. The ST-GNN framework advances the state of the art in streamflow forecasting while providing a robust foundation for practical applications. Continued research to enhance model transferability across diverse hydrological settings will further increase its impact on water resources management and disaster mitigation efforts.