Preamble

J Arid Land (2025) 17(11): 1623–1648 Science Press Springer-Verlag A hybrid ConvLSTM-Nudging model for predicting surface soil moisture in the Qilian Mountains, China FAN Manhong , XIAO Qian, YU Qinghe, ZHAO Junhao College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China

Abstract

Spatiotemporal forecasting of surface soil moisture (SSM) is recognized as a critical scientific issue in precision agricultural irrigation, regional drought monitoring, and early warning systems for extreme precipitation. However, long-term forecasting continues to pose formidable challenges because of the complexity observed across both the spatial and temporal scales. In this study, we used a daily SSM dataset at a 0.05°×0.05° spatial resolution over the Qilian Mountains, China and proposed a hybrid Convolutional Long Short-Term Memory (ConvLSTM)-Nudging model, which combined deep neural networks with data assimilation to increase the accuracy of long-term SSM forecasting. We trained and evaluated the SSM predictive performance of four models (Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), ConvLSTM, and ConvLSTM with Squeeze-and-Excitation (SE) attention mechanism (ConvLSTM-SE)) in both short-term and long-term scenarios. The results showed that all the models perform well under short-term predictions, but the accuracy decrease substantially in long-term predictions. Therefore, we integrated Nudging technique during the long-term prediction phase to assimilate observational information and rectify model biases. Comprehensive evaluations demonstrate that Nudging significantly improves all the models, with ConvLSTM-Nudging achieving the best performance under the 200-d forecasting scenario. Relative to those of the best-performing ConvLSTM model for long-term forecasts, when observation noise =0.00 and observation fraction =50.0%, the coefficient of determination ( ) of ConvLSTM-Nudging increases by approximately 82.1%, while its mean absolute error (MAE) and root mean squared error (RMSE) decrease by approximately 84.8% and 77.3%, respectively; the average Pearson correlation coefficient ( ) improves by approximately 23.6%, and Bias is reduced by 98.1%. These results demonstrated that although pure deep learning models achieve high accuracy in the short-term predictions, they are prone to error accumulation and systematic drift in long-term autoregressive predictions. Integrating data assimilation with deep learning and continuously correcting the state through observation can effectively suppress long-term biases, thereby achieving robust long-term SSM forecasting.

Keywords

data assimilation; surface soil moisture; deep neural networks; Convolutional Long Short-Term Memory (ConvLSTM); Squeeze-and-Excitation (SE) attention mechanism; Nudging; long-term prediction Citation:

FAN Manhong, XIAO Qian, YU Qinghe, ZHAO Junhao. 2025. A hybrid ConvLSTM-Nudging model for predicting surface moisture Qilian Mountains, China.

Journal Land, 17(11):

1 Introduction

Accurately predicting surface soil moisture (SSM) is critical for hydrological modeling, agricultural management, and climate change research (Vereecken et al., 2008). Nevertheless, © Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Science Press and Springer-Verlag GmbH Germany, part of Springer Nature 2025

long-term SSM prediction remains highly challenging because of the complex interplay among atmospheric forcing, surface heterogeneity, and subsurface hydrological processes (Entin et al., 2000; Koster et al., 2004).

Traditional SSM prediction methods are usually based on physical models. For instance, the Richards (1931) equation, a fundamental physical model for soil moisture prediction, is widely used to simulate soil water movement under both saturated and unsaturated conditions. Soil Vegetation Atmosphere Transfer (SVAT) models, such as the Noah land surface model, are applied at regional scales to simulate soil hydrology, atmosphere-vegetation interactions, and climate change (Ek et al., 2003). The Soil Water Atmosphere Plant (SWAP) model comprehensively accounts for soil moisture dynamics, root water uptake by plants, and the evapotranspiration processes driven by climatic conditions (van Dam et al., 2008). The HYDRUS model operates based on the finite-element method to solve coupled problems involving water flow, heat transfer, and solute transport in unsaturated soils, demonstrating strong applicability and versatility (Šimůnek et al., 2008). Although these physical models offer good interpretability, they often perform poorly in practical applications because of parameter uncertainty and inadequate descriptions of complex physical processes (Li et al., 2022a).

In recent years, deep learning models have been widely applied to soil moisture prediction tasks, demonstrating stronger capabilities for learning nonlinear features as well as superior fitting and generalization performance (Ding et al., 2024). Convolutional Neural Networks (CNNs), which were originally proposed by LeCun (1989) for image recognition tasks, are well suited for extracting spatial features from structured data. Since soil moisture and meteorological time series data can be structured as image-like grids, CNNs effectively capture their localized spatial features and apply them to soil moisture modeling. Recurrent Neural Networks (RNNs), on the other hand, excel at processing time series data and are capable of capturing sequential dependencies between variables, enabling the modeling of dynamic soil moisture changes (Connor et al., 1994). However, the standard RNN architecture is prone to gradient vanishing or gradient exploding problems when processing long sequences, which limits its effectiveness in long-distance dependency modeling cases (Mikolov et al., 2011). To overcome this limitation, Hochreiter and Schmidhuber (1997) proposed Long Short-Term Memory (LSTM) neural network, which incorporates a gating mechanism to enhance its ability to model long-term dependencies.

Despite the remarkable success of LSTM in time series modeling tasks, its complex structure still results in high computational costs for both training and prediction (Song et al., 2020). Building upon this foundation, Yu et al. (2021) designed a hybrid model that integrates a CNN and a Gated Recurrent Unit (GRU). The CNN-GRU model consistently outperforms the standalone CNN and GRU models in terms of predicting soil moisture at various depths within the root zone.

Nevertheless, the parallel computations of the convolutional and recurrent units in this structure significantly increase the number of model parameters and the computational cost, and the model is prone to overfitting when the sample size is insufficient. In addition, Li et al. (2022b) integrated an attention mechanism into LSTM model, which further improves its performance across various prediction scenarios and significantly enhances its ability to identify key time steps. Nonetheless, the introduction of the attention mechanism also increases the number of model parameters, making the training process more sensitive to the sample size and noise and introducing training instability and overfitting risks. Convolutional LSTM (ConvLSTM) network, which integrates convolutional structures with recurrent gating mechanisms, is capable of simultaneously capturing spatial and temporal dependencies (Gamboa-Villafruela et al., 2021). It has been successfully applied to spatiotemporal dynamic SSM modeling tasks (Shi et al., 2015; Li et al., 2024a; Lü et al., 2024). ConvLSTM with a Squeeze-and-Excitation (SE) attention mechanism (ConvLSTM-SE) model performs quite well in short-term predictions; however, its performance drops sharply as the prediction timescale increases (Li et al., 2024a). Despite the excellent performance of deep learning in soil moisture prediction scenarios, its purely data-driven nature continues to present certain challenges, especially when addressing sudden environmental events (e.g., rainfall) (Wang et al., 2024). The lack of physical constraints leads to the accumulation of

errors and reduces the generalizability of the model, thereby limiting its stability and reliability in long-term prediction tasks (Cheng et al., 2023).

Data assimilation was originally designed to provide reliable initial conditions for numerical atmospheric forecasting (Charney et al., 1950) and has been increasingly applied in soil hydrology, where it integrates observational data with physical models to improve spatiotemporal soil moisture estimates and characterizes the associated uncertainties. For example, Xu et al. (2020) coupled satellite soil moisture with data assimilation and an integrated drought index at the continental scale, demonstrating that the combined use of these datasets can substantially enhance regional drought detection and monitoring capabilities, thereby underscoring the practical value of assimilation techniques for conducting drought assessments and providing early warnings.

Margulis et al. (2002) proposed the integration of the ensemble Kalman filter (EnKF) with a land surface model to effectively balance the computational efficiency and spatiotemporal resolution achieved when capturing fine-scale soil moisture dynamics. Zhu et al. (2017) employed an EnKF-based differential information assimilation method to successfully extract effective information from noisy data. Gruber et al. (2019) designed an adaptive Kalman filter framework that corrected the deviation between the model outputs and the observational data through triple collocation analysis and Monte Carlo simulation processes. Considering the high cost of acquiring SSM data, Wang et al. (2020) proposed a robust data value analysis framework based on a hybrid data assimilation method. Wang et al. (2023) integrated EnKF with HYDRUS-1D model to improve the accuracy of soil moisture simulations and highlighted the critical influences of ensemble size and observation error on the performance of the assimilation system. Although data assimilation substantially improves the consistency between models and observations and enhances short- to mid-term state estimates, its reliance on accurate physical models, the computational burden imposed on high-dimensional nonlinear systems, and the requirement for high-quality observations limit its applicability for use in certain long-term forecasting and sparse-observation scenarios.

Hybrid strategies that integrate data assimilation with deep learning have recently emerged by combining physical constraints with the representational power of data-driven methods. The Nudging technique was first applied in numerical weather forecasting (Anthes, 1974); it dynamically adjusts the state of utilized model to match observational data through relaxation terms. Pawar et al. (2020) successfully integrated Nudging into data assimilation process for geophysical flows. Utilizing Lorenz-96 system as a testbed, they integrated data assimilation with deep learning and compared the performance of Nudging with that of the extended Kalman filter (EKF), EnKF, and deterministic ensemble Kalman filter (DEnKF). The experiments revealed that Nudging has the potential to assimilate very sparse observational data while avoiding matrix operations such as computing the Kalman gain. Menut et al. (2024) conducted a systematic comparison between the configurations "with or without Nudging and with or without online coupling", finding that adopting Nudging yielded a greater improvement in model skill than online coupling itself did (higher correlations and lower Bias and Root Mean Square Error (RMSE) values). They also reported that Nudging reduced the sensitivity of outputs to different physics configurations by 30.0%–70.0%. Antil et al. (2024) explicitly embedded the Nudging technique into deep network-based data assimilation pipelines, providing empirical demonstrations of stability and convergence and extending the applicability of Nudging under sparse observation settings. Based on the above theoretical and empirical progress, we propose a ConvLSTM-Nudging framework that combines the spatiotemporal modeling capabilities of ConvLSTM with physics-based state correction, with the aim of improving the accuracy of long-term SSM predictions. The main objectives of this study are to: (1) evaluate the performance of CNN, LSTM, ConvLSTM, and ConvLSTM-SE in SSM modeling tasks and in both short- and long-term SSM prediction scenarios; (2) identify the optimal parameters for Nudging technique under varying observation fractions and observation errors; and (3) investigate the effectiveness of Nudging for improving long-term prediction accuracy.

2 Study area and data sources

2.1 Study area

The Qilian Mountains (35°49′–39°58′N, 93°33′–103°54′E) are located between western Gansu Province and northeastern Qinghai Province in China, with an altitude range of 1040–5993 m (Fig. 1 [FIGURE:1]). The overall direction is northwest–southeast, with the terrain being high in the west and low in the east. The area is bordered by the Altun Mountains to the west, the Qinling Mountains and Liupan Mountains to the east, the Qaidam Basin to the south, and the Hexi Corridor to the north. The Qilian Mountains have a semi-arid to arid temperate continental mountain climate, with cool and humid summers and cold and dry winters (Lin et al., 2017; Liu et al., 2024). The average annual sunshine duration is 1744.0000 h, the average annual temperature is approximately 5°C, and the average annual precipitation is approximately 250.00 mm, which is concentrated mainly during summer; in recent years, evaporation has been declining annually, with an average evaporation level being 634.73 mm annually, and the rate of decrease is 4.39 mm/a (Zhou and Li, 2022). The spatial distribution of soil moisture content clearly decreases from east to west (Meng et al., 2021).

Schematic diagram of the elevation of the Qilian Mountains

2.2 Data sources

The daily SSM dataset with a spatial resolution of 0.05°×0.05° over the Qilian Mountains from 2017 to 2021 was obtained from the National Tibetan Plateau/Third Pole Environment Data al. (2020), and Hu et al. (2022) using a random forest-optimized downscaling model (RF-OWCM). It combines a multivariate statistical regression framework with coupled wavelet analysis and performs the generation step by downscaling the Advanced Microwave Scanning Radiometer for Earth Observing System Sensor (AMSR-E) and AMSR2 brightness temperature (TB) based Soil Moisture Active Passive (SMAP) time-expanded daily 0.25°×0.25° land SSM The 30 m resolution digital elevation model (DEM) data in the Qilian Mountains were provided et al. (2020) using Shuttle Radar Topography Mission (SRTM) v.4.1 1s (approximately 30 m) segmented data through format conversion, image stitching, reprojection, and regional clipping.

3.1 ConvLSTM

ConvLSTM extends the inputs and hidden states to three-dimensional tensors (time, height, and

width) and replaces the dense connections in the traditional LSTM model with convolutional operations, thereby enabling the capture of local spatial correlations. The ConvLSTM cell processes the input spatiotemporal tensor C×H×W at each time step while maintaining the hidden state K×H×W and the cell state K×H×W , where , and denote the number of input channels, number of hidden channels, spatial height and width of feature map, respectively. computational operations defined follows (Gamboa-Villafruela et al., 2021; Li et al., 2024a):

Input gate: , (1) Forget gate: , (2) Candidate cell state: , (3) Cell state update: , (4) Hidden state: , (5) Output gate: , (6) where represents the convolution operation; represents the Hadamard product; denotes the sigmoid function; , and denote the input, forget, candidate, and output gates, respectively; was the cell state update; is the hidden state; , and (input-to-gate kernels), , and (hidden-to-gate kernels), , and (cell-to-gate weights) denote the weights of the convolution kernels for the input, forgetting, candidate and output gates, respectively; and , and are the corresponding bias terms for the input gate, forget gate, and output gate, respectively. The ConvLSTM model was built on an encoder–decoder architecture (Fig. 2 [FIGURE:2]). The encoder consisted of two ConvLSTM layers, each with 8 hidden channels and a 3×3 convolution kernel. The input sequence length was set to 14 timesteps, and the same padding was applied to preserve the original spatial resolution. These layers were responsible for extracting the spatiotemporal features of the input sequence. The decoder contained a single ConvLSTM layer with the same number of hidden channels, kernel size, and padding as those of the encoder; this layer was used to generate SSM predictions for the next day. In addition, to prevent model overfitting, we added a dropout layer between the ConvLSTM layers and set the dropout rate to 0.2.

Convolutional Long Short-Term Memory (ConvLSTM) model based on the encoder–decoder framework.

The input data used in this study have a grid width of 207 and a height of 79.

3.2 SE

On the basis of the ConvLSTM model, we introduced SE module (Jin et al, 2022), a channel attention mechanism that enhances the key feature representations of the model by adaptively adjusting the weights of different channels in CNN. Its core goal was to explicitly model the dependencies between channels and improved the performance of the model by filtering the important feature channels and suppressing redundant information. The calculation process of the SE module can be divided into the following three main steps (Hu et al., 2018). (1) Squeeze ( ): global average pooling was performed on the input H×W×C compress the spatial features in each channel into a scalar and obtain the channel description vector . This step could explicitly model the global channel information and alleviated the dependencies between channels. , (7) where is channel description vector in the channel; is feature map in the channel; and are the spatial position indices. (2) Excitation ( ): the channel description vector obtained in the previous stage was input into the two-layer fully connected network to generate an attention weight value each channel. The output dimensionality of the first fully connected layer was is the compression ratio hyperparameter), and the activation function was a Rectified Linear Unit (ReLU). The second layer was restored to 1×1× , and the activation function was the sigmoid function. g z D , (8) where represents a two-layer fully connected gating function; represents the weights matrix; denotes the ReLU activation function; denote the weights matrix learned in two-layer fully connected network. (3) Scale ( scale ): the normalized weight vector obtained above was added to the feature each channel. That is, the values of each channel in were multiplied by the weight of the corresponding channel in to obtain the desired feature , which has the same size as that of feature . The SE module did not change the size of the feature map. scale , (9) where is attention weight value in the channel; and is the feature in the channel.

The architecture of the ConvLSTM-SE model based on the encoder–decoder framework is shown in Figure 3 [FIGURE:3]. The model took 14 consecutive days of spatial raster data as its inputs and used a two-layer ConvLSTM encoder to extract spatiotemporal features. In the decoder, the SE attention mechanism was integrated to extract global information through a fully connected layer and global average pooling, and the feature map was adaptively weighted to enhance the representations of the salient patterns. Afterward, the recalibrated features were passed through the decoder ConvLSTM layer to generate a soil moisture forecast for the next day, thus achieving accurate and efficient SSM prediction.

3.3 Nudging

Nudging, also known as Newtonian relaxation, was originally proposed by Anthes (1974) for initializing meteorological models. As an empirical data assimilation method, Nudging has been widely used in meteorological and hydrological models because it is easy to implement and its computational cost is significantly lower than those of variational and ensemble methods (Stauffer and Seaman, 1990). The core idea was to incorporate a feedback term that is proportional to the ''observation–forecast'' residual into the model equations so that the model state continuously approached the observations while suppressing large-scale errors without degrading the ability of the model to generate realistic mesoscale structures (Conti et al., 2022).

ConvLSTM with Squeeze-and-Excitation attention mechanism (ConvLSTM-SE) based on the encoder–decoder framework. The input data used in this study have a grid width of 207 and a height of 79. , (10) where is the model state (prediction); is the dynamic model operator; is the Nudging gain matrix; and is the observation.

Based on Equation 10, we coupled Nudging with the model prediction process in discrete time using per-pixel correction. Specifically, the model took the most recent days of the given SSM sequence as its input and produced a one-step prediction . If an observation is available on , we applied a pixel-level , with its availability indicated by a binary mask update to the model output: , (11) where represents the assimilated analysis value; and (0,1] is the Nudging coefficient, and no correction is applied when

0. This discretization scheme was equivalent to taking

Equation 10 as a mask-gated diagonal gain (performing a convex combination only at the observed pixels), thereby balancing numerical stability and computational efficiency. Since the SSM observations in this study directly corresponded to the state variable, the observation operator was always an identity matrix.

We adopted output-layer coupling: the analysis field was written back into the input buffer (replacing the newest frame), and together with the preceding –1 frames, formed the input sequence for the next step; "assimilate whenever observations were available" was the default frequency. To reflect sparse observation scenarios, we downsampled the data to 10.0%, 20.0%, and 50.0% availability to construct 0, and we injected Gaussian observation noise , only at pixels with 1, to evaluate the robustness of the model under noise. Guided by the literature-recommended range of 0.1–1.0 (Pawar et al., 2020), we selected the optimal Nudging coefficient via a grid search.

The overall workflow and schematic of the proposed method from data processing and model recursion to Nudging correction are presented in Figure 4 [FIGURE:4]. The research process can be divided into three main steps. (1) Data processing: DEM-assisted clipping was used to obtain the SSM raster sequence for the study area, which is then split into training, validation, and test sets; (2) Model prediction: this section included the prediction processes of two models: ConvLSTM and ConvLSTM-SE. The 14-d observation data acquired from –14 to were used as the initial inputs to generate a prediction for +1. Afterward, the prediction for the previous time step (or the corrected analysis field) was combined with the observation data derived from the previous 13-d to form a new 14-d sequence, which serves as the input for the next step. This process was

Model workflow and methodological framework. represents the current time step, and the number after (subtracted or added) indicates the number of days to lag or advance; and C denote the cell state before and after update; denote the hidden state before and after update; Conv denotes the convolutional neural network; represents the forget gate; represents the input gate; represents the output gate; represents the input feature; is the number of input channels; is the number of hidden channels; are the spatial height and width of feature map; represents the squeeze step; denotes the channel description vector; represents the excitation step; denotes the attention weight value; scale represents the scale step; represents the output feature; and denotes the observation noise. DEM, digital elevation model; SSM, surface soil moisture; SE, Squeeze-and-Excitation; MSE, mean squared error; CNN, convolutional neural network; LSTM, Long Short-Time Memory; ConvLSTM, Convolutional Long Short-Term Memory; ConvLSTM-SE, Convolutional Long Short-Term Memory with Squeeze-and-Excitation attention mechanism. iterated until +200 d. A schematic diagram of the ConvLSTM cell and the SE module structure is shown, with the training and validation loss convergence curves produced for the four models displaying on the right; and (3) Nudging correction: observation masks were constructed at fractions of 10.0%, 20.0%, and 50.0%, and Gaussian noise with 0.01 was added to simulate the

effect of noise on the observations. The prediction field was corrected online, and the corrected

3.4 Evaluation strategy and metrics

In this study, a multi-metric evaluation framework is employed to systematically assess the performance of the developed model. During the model optimization phase, the training and validation sets are optimized with the mean squared error (MSE) as the objective function, while the mean absolute error (MAE) is used to monitor the convergence of the training process. In the model validation phase, the prediction accuracy is quantitatively evaluated on the test set using three error metrics: MSE, MAE, and RMSE. The coefficient of determination ( ) is used to assess the ability of the model to explain the variance in the observed data. Pearson correlation coefficient ( ) is applied to measure the degree of linear correlation between the predicted and observed values, while prediction bias is identified through a bias analysis. This comprehensive evaluation framework not only achieves a quantitative comparison between the predictions and observations but also provides a multidimensional model performance assessment, thereby offering a robust statistical basis for the reliability of the results (Li et al., 2024b; Lü et al., 2024).

The calculation methods for these statistical indicators are presented as follows: , (13) , (15) , (16) , (17) where is the true SSM value; is the mean value of is the predicted or assimilated SSM value; is the mean value of ; and is the number of measured or predicted SSM sample points. Lower values are better for MSE, MAE, RMSE, and the absolute value of Bias, and higher values are better for

4.1 Model training

This study utilized a daily SSM dataset with a spatial resolution of 0.05°×0.05° over the Qilian Mountains from 2017 to 2021 and divided it into strictly chronological and non-overlapping subsets: training (1 January 2017–31 May 2020; 1247 d), validation (1 June 2020–31 May 2021; 365 d), and testing sets (1 June 2021–31 December 2021; 214 d). The subsets were strictly time-ordered with no overlap, and sliding windows were constructed within each subset so that no window crosses a boundary.

We systematically evaluated the training dynamics and generalization of the model. We adopted the Adaptive Moment Estimation (Adam) Optimizer (initial learning rate=0.017), used a 14-dinput sequence and a 1-d prediction horizon, and compared four models: CNN, LSTM, ConvLSTM, and ConvLSTM-SE. The evolution trends exhibited by MSE and MAE over increasing training epochs on the training set (solid lines) and validation set (dashed lines) are shown in Figure 5 [FIGURE:5]. All the model values decrease rapidly during the initial epochs and then stabilize. ConvLSTM and ConvLSTM-SE achieve the lowest overall metrics and the smoothest curves, followed by CNN; LSTM starts with a higher loss and exhibits a brief spike before converging. According to Table 1 [TABLE:1], the numbers of convergence epochs are 19 for CNN, 25 for LSTM, 6 for ConvLSTM, and 12 for ConvLSTM-SE. The total training times required for 100 epochs are 0.1211 h (CNN), 0.1009 h (LSTM), 5.7206 h (ConvLSTM), and 6.3694 h (ConvLSTM-SE). The peak Graphics Processing Unit (GPU) memory usage levels during training are similar across the models, ranging from 8481.27 to 8820.38 MiB (approximately 7.84–8.61 GiB). However, the final file sizes of the models differ significantly: 0.11 MiB for CNN, 0.17 MiB for ConvLSTM, 0.40 MiB for ConvLSTM-SE, and 254.84 MiB for LSTM. The training and validation curves almost overlap, indicating negligible overfitting and strong generalizability. Considering both accuracy and training stability, ConvLSTM-SE and ConvLSTM perform best overall.

Loss versus the number of epochs on the training and validation sets. (a), MSE; (b), MAE.

Training cost and resource usage of the four models compared by this study Model Time (h) Convergence epoch Peak GPU (MiB) Model file size (MiB) ConvLSTM ConvLSTM-SE Note: Time refers to the wall-clock training time required for 100 epochs; convergence epoch denotes the number of epochs before the model satisfies the convergence criterion; peak Graphics Processing Unit (GPU) refers to peak GPU memory observed during training; and model file size denotes the disk size of the saved model file after convergence. CNN, Convolutional Neural Network; LSTM, Long Short-Term Memory; ConvLSTM, Convolutional Long Short-Term Memory; ConvLSTM-SE, ConvLSTM with Squeeze-and-Excitation (SE) attention mechanism.

4.2 Short-term forecasting

During the short-term prediction process, the sliding window-based prediction method was adopted; that is, a fixed-length input window slides gradually in the temporal dimension, and the observed data are used each time for model training and predicting the next moment. In this study, the observed soil moisture data derived from the first 14 d were used as model inputs each time to

predict the soil moisture status on the 15 As shown in Figure 6 [FIGURE:6], all four models capture the seasonal evolution trend of soil moisture, but CNN systematically underestimates the magnitude (persistent negative Bias), and LSTM model also exhibits underestimation, with significant fluctuations in predictions during certain periods and a marked decrease in correlation. In contrast, ConvLSTM and ConvLSTM-SE track the true values closely, maintaining consistently low daily MSE, MAE, and RMSE and high correlations ). To facilitate a more intuitive comparison, we use a uniform color scale in Figure 7 [FIGURE:7] to display the true values and predicted values (soil moisture color bars) of each model, as well as the prediction errors (error color bars). In the northeastern region and the mountain transition zone with significant humidity gradients, ConvLSTM and ConvLSTM-SE more accurately reproduce the observed spatial distribution and fine details, whereas CNN and LSTM exhibit more significant underestimation effects and striped residuals in high-moisture areas.

Time series and daily metrics for short-term prediction of surface soil moisture (SSM) in the Qilian Mountains during 1 June–31 December 2021. (a), ground-truth and predictions from CNN, LSTM, ConvLSTM, and ConvLSTM-SE; (b–g), daily evaluation metrics: MSE (b), MAE (c), coefficient of determination ( ; d), root mean square error (RMSE; e), Pearson correlation coefficient ( ; f), and Bias (g).

Aggregate metrics further confirm the advantage of spatiotemporal modeling: ConvLSTM achieves the best overall performance (MAE=0.0047 m , RMSE=0.0068 m =0.9728, =0.9869), reducing MAE and RMSE by roughly 47.2% and 52.8%, respectively, relative to those of CNN (Table 2 [TABLE:2]). ConvLSTM-SE ranks second in terms of performance, with MAE of 0.0064 m and RMSE of 0.0091 m , representing an approximately 36.8% RMSE reduction relative to that of CNN. In comparison, LSTM performs moderately, with MAE of 0.0072 m and RMSE of 0.0097 m , placing it between ConvLSTM-SE and CNN in terms

of accuracy. The Bias results indicate a notable underestimation effect for CNN (–0.0039 m whereas the other models yield Biases that are close to zero. Overall, ConvLSTM and ConvLSTM-SE, which explicitly capture spatiotemporal coupling and outperform the purely temporal (LSTM) and purely spatial (CNN) baselines in terms of accuracy, stability, and spatial fidelity.

Spatial comparison of soil moisture and errors on representative days. (a1–a4), true values; (b1–b4), CNN prediction results; (c1–c4), CNN absolute error; (d1–d4), LSTM prediction results; (e1–e4), LSTM absolute error; (f1–f4), ConvLSTM prediction results; (g1–g4), ConvLSTM absolute error; (h1–h4), ConvLSTM-SE prediction results; (i1–i4), ConvLSTM-SE absolute error.

Short-term prediction evaluation metrics Note: MSE, mean squared error; MAE, mean absolute error; , coefficient of determination; RMSE, root mean square error; , Pearson correlation coefficient.

4.3 Long-term forecasting

The long-term prediction process is experimented with using a recursive prediction method.

Specifically, a fixed number of observations is selected for each prediction stage, and the results of the previous prediction are used as new inputs to iteratively predict future time periods. This method continuously feeds previous prediction results into the model, thereby having a lasting effect on the subsequent predictions. In the specific experimental design, the observed data acquired from 1 June to 14 June 2021, were used to predict the soil moisture on 15 June 2021.

The observed data from 2 June to 14 June 2021, together with the predicted value for 15 June 2021, were subsequently used as inputs to predict the soil moisture on 16 June 2021. This recursive process continued iteratively until the soil moisture prediction for 31 December 2021 was completed. Starting from 28 June 2021, the model input gradually transitioned to rely on historical predictions, after which the forecasts are generated entirely on the basis of the model's previous outputs. This setup enabled evaluation of error accumulation and drift, and tested model robustness under conditions where no new observations or incomplete observational coverages are available.

Under the recursive setup, the long-range forecasts (Figure 8 [FIGURE:8] for time series and daily metrics, and Figure 9 [FIGURE:9] for spatial fields) exhibit the characteristic accumulation of errors. The detailed performance results are summarized in Table 3 [TABLE:3]. CNN tends to underestimate the results throughout the period, leading to a large negative Bias (Bias= –0.0281 m ), whereas LSTM shows a pronounced positive drift from September onward with a surge in errors, yielding a strongly degraded fit ( = –2.4026 and =0.7804). In contrast, ConvLSTM and ConvLSTM-SE remain more robust during multistep recursion: their daily MSEs, MAEs, and RMSEs remain low and track the ground truth more closely. The overall performance metrics for ConvLSTM are: , RMSE=0.0282 m =0.5362, =0.7997, and Bias= –0.0105 m , and ConvLSTM-SE: MAE=0.0236 m , RMSE=0.0326 m =0.3827, =0.7683, and Bias= –0.0139 m . Relative to CNN (MAE=0.0375 m and RMSE=0.0492 m ), ConvLSTM reduces MAE and RMSE by approximately 45.6% and 42.7%, respectively; and ConvLSTM-SE achieves RMSE reduction of approximately 33.7%. In summary, ConvLSTM model performs best in long-term recursive prediction, but it still has large errors because of the accumulation of multistep recursive errors and thus needs further optimization.

Given that long-term recursive forecasting still results in the accumulation of errors and drift, this study extended the approach from a purely data-driven method to observation-constrained online correction (Nudging). We injected Gaussian random noise with a mean of zero and a variance of =0.01 into the observations to simulate uncertainty, and used noise-free observations =0.00) as a control to systematically evaluate the feasibility and performance of the Nudging correction method under different observation quality conditions.

Under observation noise =0.01, on the basis of the optimal Nudging coefficient of each model ( =0.7 for CNN, =0.6 for LSTM, =0.5 for ConvLSTM, and =0.6 for ConvLSTM-SE), we evaluated different observation fractions ( ) (Table 4 [TABLE:4]; Figs. 10–12). ConvLSTM-Nudging is optimal in terms of most metrics: when =50.0%, MSE and RMSE are 0.0002 (m 0.0156 m , respectively, decreasing by 66.7% and 34.2% relative to those produced when

Time series and daily metrics for long-term prediction of SSM in the Qilian Mountains during 1 June–31 December 2021. (a), ground-truth SSM and predictions from CNN, LSTM, ConvLSTM, and ConvLSTM-SE; (b–g), daily evaluation metrics: MSE (b), MAE (c), (d), RMSE (e), , (f), and Bias (g). =10.0%; increases to 0.8591, and Bias approaches zero (–0.0004 m ), balancing accuracy and stability. LSTM-Nudging is most sensitive to sparse and noisy observations: at =10.0%, it shows a pronounced positive Bias (0.0874 m ) and a negative (–4.4399); =50.0%, MSE and RMSE decrease to 0.0003 (m and 0.0181 m , respectively, (0.8091) increases significantly, indicating that sufficient observations significantly suppress error drift and enhance temporal correlations. The radar charts show that as observation fraction increases from 10.0% to 50.0%, all four models monotonically improve in terms of MSE, MAE, and RMSE metrics, continuously increase, and Bias converges toward zero; among them, ConvLSTM-Nudging demonstrates the best consistency across all six metrics: error convergence, , and improve synchronously, with the smoothest curve fluctuations, reflecting overall balance and robustness (Fig. 10 [FIGURE:10]). Notably, although ConvLSTM-SE-Nudging is superior overall to CNN-Nudging and LSTM-Nudging (except at low observation levels), it does not surpass ConvLSTM without SE, which indicates that channel attention may more easily overweight local noise under noisy observations; this effect weakens when observation fraction increases to 50.0%. The time series (Fig. 11 [FIGURE:11]) and spatial distributions (Fig. 12 [FIGURE:12]) further corroborate this finding: CNN-Nudging tends to exhibit amplitude compression during seasonal transitions, and LSTM-Nudging tends to yield platform Biases at low observation fraction values, whereas ConvLSTM-Nudging better tracks the amplitude and phase and produces smaller and more uniform error patches. Overall, Nudging effectively alleviates systematic underestimation or overestimation issues and reduces the areas with high error concentrations. From the parameter perspective, the optimal Nudging coefficient falls within 0.5–0.7; convolutional spatiotemporal

Spatial distribution of soil moisture and absolute errors produced on representative days. (a1–a4), true values; (b1–b4), CNN prediction results; (c1–c4), CNN absolute error; (d1–d4), LSTM prediction results; (e1–e4), LSTM absolute error; (f1–f4), ConvLSTM prediction results; (g1–g4), ConvLSTM absolute error; (h1–h4), ConvLSTM-SE prediction results; (i1–i4), ConvLSTM-SE absolute error.

Overall evaluation metrics produced for long-term prediction scenario Evaluation metrics produced by each model at its optimal Nudging coefficient (τ) with different observation fraction ( ) under observation noise =0.01 Radar chart of evaluation metrics produced for observation fraction ( ) at 10.0% (a), 20.0% (b), and 50.0% (c) under observation noise =0.01 models tend to adopt a smaller Nudging coefficient value (0.5) to avoid forcing instantaneous noise into the dynamics, whereas sequence memory-based LSTM relies more on observation constraints (with the greatest gains derived from increasing observation fraction). In summary, under observation noise =0.01, ConvLSTM-Nudging achieves the most robust overall performance, with the lowest errors, the highest , and a near-zero Bias, and all four models benefit significantly as observation fraction increases.

Under noise-free observations ( =0.00), the four models were evaluated with their optimal Nudging coefficients all setting to =1.0 (Table 5 [TABLE:5]; Figs. 13–15). Overall, as the observation fraction increases from 10.0% to 50.0%, the error metrics (MSE, MAE, and RMSE) decrease monotonically, the correlation metrics ( ) increase synchronously, and Bias further approaches zero, showing that high-quality and sufficient observations significantly amplify the

Pixel-averaged SSM time series produced by the four nudging models under observation noise ( =0.01) at three observation availabilities during 1 June–31 December 2021. Each curve showed the daily mean over all valid pixels in the test region; the blue line denoted the true vlues. Panels: (a), 10% observation availability; (b), 20% observation availability; (c), 50% observation availability. gains of Nudging. At =50.0%, ConvLSTM-Nudging attains MSE below 0.0001 (m =0.9762, =0.9881, and Bias= –0.0002 m , representing the best overall performance, relative to CNN-Nudging (RMSE=0.0120 m =0.9168), the RMSE is reduced by 46.7%, and increases by 6.5%. In the time series, ConvLSTM-Nudging almost coincides with the ground truth (Fig. 14 [FIGURE:14]), while in space, it presents the smallest and most uniformly distributed error patches (Fig. 15 [FIGURE:15]). LSTM-Nudging remains sensitive to sparse constraints at low observation fractions (at =10.0%, = –2.1510, and Bias=0.0556 m ) but improves most significantly as observation fraction increases: at =50.0%, RMSE decreases to 0.0088 m , and increases to 0.9554, with =0.9804 and Bias=0.0015 m , which indicates that sufficient observations effectively suppress its long-term recursive drift and enhance its temporal consistency. ConvLSTM-SE-Nudging provides the advantage of "channel attention" under noise-free conditions: at =50.0%, RMSE=0.0086 m =0.9570, and =0.9783, which are comparable to those of LSTM-Nudging and significantly better than those of CNN-Nudging; this differs from the noisy case and indicates that the SE mechanism stably enhances the degree of expressiveness under observations with high signal-to-noise ratios. The radar charts provide consistent evidence that the polygons shrink significantly on error axes and expand on axes, and Bias axis converges symmetrically around zero (Fig. 13 [FIGURE:13]). The time series shows that the amplitude compression and phase lag observed during seasonal transitions are essentially eliminated at =50.0% (Fig. 14). The spatial distributions confirm that the areas with high error concentrations decrease significantly, and the residual errors are scattered mainly along transition zones with strong moisture gradients (Fig. 15). Notably, the optimal Nudging coefficient uniformly equals 1.0, which indicates that under noise-free

Spatial distribution and error maps of SSM obtained for five representative dates when observation noise =0.01 and =50.0%. (a1–a4), true values; (b1–b4), CNN-Nudging prediction results; (c1–c4), CNN-Nudging absolute error; (d1–d4), LSTM-Nudging prediction results; (e1–e4), LSTM-Nudging absolute error; (f1–f4), ConvLSTM-Nudging prediction results; (g1–g4), ConvLSTM-Nudging absolute error; (h1–h4), ConvLSTM-SE-Nudging prediction results; (i1–i4), ConvLSTM-SE-Nudging absolute error. conditions, "strong-constraint" correction does not introduce additional noise propagation effects and instead maximizes the model state correction implemented via observations. In summary, observation noise =0.00, all four models benefit significantly from an increased observation fraction, with ConvLSTM-Nudging achieving the best overall performance, ConvLSTM-SE-Nudging and LSTM-Nudging following closely, and CNN-Nudging relatively behind.

Evaluation metrics produced by each model at its optimal Nudging coefficient with different observation fractions under observation noise =0.00 Radar chart of five metrics under observation noise =0.00. (a), =10.0%; (b), =20.0%; (c), =50.0%.

5.1 Model performance

This study systematically evaluates the predictive performance of four models—CNN, LSTM, ConvLSTM, and ConvLSTM-SE—for SSM at different temporal scales and conducts an in-depth analysis of differences in model structures, the effectiveness of Nudging correction mechanism, and the effects of observation data quality and fraction on predictive performance.

In the short-term forecasting process, all four models track seasonal fluctuations, but their performances differ markedly (Figs. 6–7; Table 2). ConvLSTM and ConvLSTM-SE lead in both the temporal and spatial dimensions and better preserve gradients and fine textures in regions with strong humidity gradients, such as the northeastern region and mountainous transition zones.

CNN exhibits systematic underestimation effects, whereas LSTM also exhibits underestimation, with significant fluctuations in predictions during certain periods and a marked decrease in correlation. Explicit spatiotemporal coupling more effectively extracts spatiotemporal information and, overall, outperforms single-dimensional (purely spatial or purely temporal) modeling (Fu et al., 2022; Ge et al., 2023; Zhang et al., 2023).

Over the 200-d long-term autoregressive forecasting horizon, all the models exhibit typical error accumulation effects (Figs. 8–9; Table 3). CNN results in a persistent negative Bias

Comparison among the pixel-averaged time series obtained for the four Nudging models at various observation fractions under observation noise =0.00 during 1 June–31 December 2021 =10.0%; (b), =20.0%; (c), =50.0%. (–0.0281 m ). LSTM results in positive drift starting in September, which leads to a sharp decline in the goodness of fit of this model ( = –2.4026). ConvLSTM and ConvLSTM-SE remain relatively stable; ConvLSTM model achieves MAE and RMSE of 0.0204 and 0.0282 , respectively, reductions of 13.6% and 13.5% relative to those of ConvLSTM-SE, indicating the greater robustness of ConvLSTM architecture in terms of capturing long-term spatiotemporal dependencies (Habiboullah and Louly, 2023; Huang et al., 2023). Although spatiotemporal coupling mitigates the rapid error divergence process to some extent, iterative error propagation in long-horizon autoregression constrains the predictive performance of ConvLSTM (Ding et al., 2025), leaving substantial room for improvement.

We addressed the error accumulation and drift encountered in long-horizon autoregressive forecasting scenarios by introducing the Nudging correction mechanism and systematically evaluating its effects under different observation accuracies ( =0.00 and 0.01) and observation fractions ( =10.0%, 20.0%, and 50.0%) (Tables 4–5; Figs. 10–15) and summarizing the average metrics for an intuitive comparison (Fig. 16 [FIGURE:16]). Overall, CNN-Nudging provides a monotonic improvement as the observation fraction increases under both noise settings, reaching =0.9168 when =0.00 and =50.0%. LSTM-Nudging is most sensitive to sparse and noisy observations: at =10.0% and 20.0%, it yields negative values, and when =0.01 with =10.0%, the corrected of –4.4399 is lower than the uncorrected –2.4026, indicating that observation noise may introduce noise or redundancy (Cohen et al., 2013; Goux et al., 2025); the metric improves markedly when observation fraction increases to 50.0%.

ConvLSTM-SE-Nudging provides stable gains at high signal-to-noise ratios ( =0.00) but tends to overweight local noise under noisy conditions (Liang et al., 2023; Brigato et al., 2025; Feng et al., 2025).

Spatial distribution and error map of SSM obtained for five representative dates when =0.00 and =50.0%. (a1–a4), true values; (b1–b4), CNN-Nudging prediction results; (c1–c4), CNN-Nudging absolute error; (d1–d4), LSTM-Nudging prediction results; (e1–e4), LSTM-Nudging absolute error; (f1–f4), ConvLSTM-Nudging prediction results; (g1–g4), ConvLSTM-Nudging absolute error; (h1–h4), ConvLSTM-SE-Nudging prediction results; (i1–i4), ConvLSTM-SE-Nudging absolute error.

ConvLSTM-Nudging achieves the best overall performance. These results indicate that Nudging significantly suppresses the error accumulation effect in long-horizon autoregression tasks and enhances the stability and spatiotemporal consistency of ConvLSTM (Kozhushko et al., 2022; Antil et al., 2024), but its corrective power remains limited when the initial model errors are large or when the observation fraction is small (Pawar et al., 2020).

The observation fraction has a decisive effect on the effectiveness of Nudging (Fig. 16). As

Average metrics produced by different models under different the combination of observation noise (0.00 0.01) and observation fraction (10.0%, 20.0%, and 50.0%). (a), MSE; (b), MAE; (c), ; (d), RMSE; ; (f), Bias. observation fraction increases from 10.0% to 50.0%, the error metrics of all models decrease monotonically, the correlation metrics continue to increase, and Bias approaches zero. Under observation noise δ=0.01, CNN-Nudging, LSTM-Nudging, ConvLSTM-Nudging, ConvLSTM-SE-Nudging reduce their RMSEs by approximately 18.9%, 81.2%, 34.2%, and 48.8%, respectively, at obs=50.0%, relative to those induced at obs=10.0%; under δ=0.00, RMSE reductions CNN-Nudging, LSTM-Nudging, ConvLSTM-Nudging, ConvLSTM-SE-Nudging are 49.4%, 88.0%, 61.2%, and 72.9%, respectively. These results indicate that introducing more observations leads to better correction effects for the models (Celik and Olson, 2023).

5.2 Limitations and prospects

Although the hybrid ConvLSTM-Nudging model constructed in this study exhibits strong capabilities in the 200-d soil moisture forecasting task, it still has several limitations, which also point out directions for future research. For example, Niu et al. (2025) and Adewole et al. (2024) reported that land surface temperature (LST), root-zone soil moisture (10–40 cm), and the normalized difference vegetation index (NDVI) are key factors that influence soil moisture dynamics, while this study relied only on SSM as the model input. Notably, however, the daily SSM product used here was produced by Qu et al. (2019 and 2021), Chai et al. (2020), and Hu et al. (2022) via multisource integration (e.g., leaf area index (LAI), broadband albedo, fractional vegetation cover, gross primary productivity (GPP), and evapotranspiration (ET)), so exogenous meteorological and remote sensing signals are implicitly encoded in the SSM field even though they are not explicitly ingested as drivers during forecasting. Moreover, although Carlson et al. (2024) and Çıbık et al. (2025) proposed strategies for adaptively selecting the Nudging coefficient, this study adopted an empirically fixed value on the basis of previous literature (Pawar et al., 2020), and the adaptability of the model across different regions and environmental settings remained unverified. In the long-term experiment, we intentionally adopted a fully recursive and driver-free design: the model was initialized with the first 14 d of the test period and then rolled forward daily using only antecedent SSM states (and a static DEM), without any exogenous meteorological forcings. This choice (1) isolates the intrinsic predictability of soil

moisture arising from state persistence and seasonal regularities; (2) avoids the covariate shifts and compounded forecast errors that would arise from externally predicted precipitation and temperature fields; and (3) enhances the operational robustness and reproducibility of the model when high-resolution and latency-free drivers are unavailable; the parsimonious setting also reduces the risk of overfitting under recursive use. Although the current driverless designs help focus on the intrinsic dynamics of the system and improve its robustness, as Xu et al. (2021a) noted, uncertainty in Earth system predictions arises from diverse sources, and the accuracy of spatiotemporal predictions is influenced by a combination of the model structure, initial conditions, and exogenous variables. Therefore, the introduction of reliable exogenous drivers (such as precipitation, temperature, and radiation) in the future is expected to further improve the prediction skill of the model, provided that these data have the required spatiotemporal resolutions and coverage levels. In summary, future research could combine multisource data fusion, network structure optimization, and adaptive parameterization, focusing on data quality control (such as field validations and triple configuration evaluations as described by Xu et al. (2021b) and model uncertainty modeling) to continuously improve the accuracy, robustness, and cross-scenario transferability of soil moisture predictions.

6 Conclusions

In this paper, a hybrid modeling framework that integrates ConvLSTM deep learning model and Nudging data assimilation method was proposed to achieve short- and long-term SSM prediction in the Qilian Mountains. The results show that in short-term forecasting scenarios, ConvLSTM and ConvLSTM-SE models, which explicitly model spatiotemporal coupling relationships, significantly outperform the baseline models that rely solely on spatial or temporal modeling, demonstrating higher prediction accuracy and spatial consistency. In long-term dynamic autoregressive forecasting cases, despite the inevitable accumulation of errors, ConvLSTM series models still exhibit stronger robustness. A further analysis reveals that Nudging correction mechanism effectively suppresses systematic biases and error divergence issues in long-term autoregressive predictions, especially under conditions of no noise or high observation fractions.

The observation fraction is a key factor that influences the Nudging effect, and increasing the observation fraction generally helps improve the performance of the models, with ConvLSTM-Nudging consistently maintaining the best performance across all the experimental conditions.

Conflicts of interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements This research was funded by the National Natural Science Foundation of China (42461053), the Department of Education of Gansu Province: Higher Education Innovation Fund Project (2023B-064), the Youth Doctoral Fund Project (2024QB-014), and the Natural Science Foundation of Gansu Province (25JRRA012).

Author contributions Conceptualization: FAN Manhong, XIAO Qian; Data curation: XIAO Qian, ZHAO Junhao; Methodology: FAN Manhong, XIAO Qian; Investigation: XIAO Qian, YU Qinghe; Formal analysis: FAN Manhong, XIAO Qian; Writing - original draft preparation: XIAO Qian; Writing - review and editing: FAN Manhong, XIAO Qian; Funding acquisition: FAN Manhong; Resources: FAN Manhong, ZHAO Junhao; Supervision: FAN Manhong; Project administration: FAN Manhong; Software: XIAO Qian, YU Qinghe; Validation: XIAO Qian, YU Qinghe; Visualization: XIAO Qian, ZHAO Junhao. All authors approved the manuscript.

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