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Journal of Arid Land
Journal of Arid Land  2025, Vol. 17 Issue (11): 1623-1648    DOI: 10.1007/s40333-025-0112-9    
Research article     
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
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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 δ=0.00 and observation fraction obs=50.0%, the coefficient of determination (R2) 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 (r) 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.

Key words： data assimilation      surface soil moisture      deep neural networks      Convolutional Long Short-Term Memory (ConvLSTM)      Squeeze-and-Excitation (SE) attention mechanism      Nudging      long-term prediction     
Received: 07 June 2025      Published: 30 November 2025
Corresponding Authors: *FAN Manhong (E-mail: fanmanhong@nwnu.edu.cn)
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FAN Manhong
XIAO Qian
YU Qinghe
ZHAO Junhao
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FAN Manhong, XIAO Qian, YU Qinghe, ZHAO Junhao. A hybrid ConvLSTM-Nudging model for predicting surface soil moisture in the Qilian Mountains, China. Journal of Arid Land, 2025, 17(11): 1623-1648.

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http://jal.xjegi.com/10.1007/s40333-025-0112-9     OR     http://jal.xjegi.com/Y2025/V17/I11/1623

Fig. 1 Schematic diagram of the elevation of the Qilian Mountains
Fig. 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.
Fig. 3 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.
Fig. 4 Model workflow and methodological framework. t represents the current time step, and the number after t (subtracted or added) indicates the number of days to lag or advance; Ct-1 and Ct denote the cell state before and after update; Ht-1 and Ht denote the hidden state before and after update; Conv denotes the convolutional neural network; Ft represents the forget gate; It represents the input gate; Ot represents the output gate; X represents the input feature; C is the number of input channels; K is the number of hidden channels; H and W are the spatial height and width of feature map; Fsq represents the squeeze step; z denotes the channel description vector; Fex represents the excitation step; s denotes the attention weight value; Fscale represents the scale step; Y represents the output feature; and δ 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.
Fig. 5 Loss versus the number of epochs on the training and validation sets. (a), MSE; (b), MAE.
Model Time (h) Convergence epoch Peak GPU (MiB) Model file size (MiB)
CNN 0.1211 19 8481.27 0.11
LSTM 0.1009 25 8024.39 254.84
ConvLSTM 5.7206 6 8820.38 0.17
ConvLSTM-SE 6.3694 12 8791.80 0.40
Table 1 Training cost and resource usage of the four models compared by this study
Fig. 6 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 (R2; d), root mean square error (RMSE; e), Pearson correlation coefficient (r; f), and Bias (g).
Fig. 7 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.
Model MSE ((m3/m3)2) MAE (m3/m3) R2 RMSE (m3/m3) r Bias (m3/m3)
CNN 0.0002 0.0089 0.8790 0.0144 0.9472 -0.0039
LSTM 0.0001 0.0072 0.9458 0.0097 0.9756 -0.0007
ConvLSTM 0.0000 0.0047 0.9728 0.0068 0.9869 -0.0005
ConvLSTM-SE 0.0001 0.0064 0.9522 0.0091 0.9763 0.0006
Table 2 Short-term prediction evaluation metrics
Fig. 8 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), R2 (d), RMSE (e), r, (f), and Bias (g).
Fig. 9 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.
Model MSE ((m3/m3)2) MAE (m3/m3) R2 RMSE (m3/m3) r Bias (m3/m3)
CNN 0.0024 0.0375 -0.4099 0.0492 0.6156 -0.0281
LSTM 0.0059 0.0606 -2.4026 0.0765 0.7804 0.0569
ConvLSTM 0.0008 0.0204 0.5362 0.0282 0.7997 -0.0105
ConvLSTM-SE 0.0011 0.0236 0.3827 0.0326 0.7683 -0.0139
Table 3 Overall evaluation metrics produced for long-term prediction scenario
Model (δ=0.01) 𝜏 obs (%) MSE ((m3/m3)2) MAE (m3/m3) R2 RMSE (m3/m3) r Bias (m3/m3)
CNN-Nudging 0.7 10.0 0.0008 0.0218 0.5064 0.0291 0.7904 -0.0109
20.0 0.0008 0.0209 0.5395 0.0281 0.7738 -0.0023
50.0 0.0006 0.0182 0.6749 0.0236 0.8333 0.0001
LSTM-Nudging 0.6 10.0 0.0094 0.0884 -4.4399 0.0967 0.8246 0.0874
20.0 0.0049 0.0580 -1.8623 0.0702 0.7916 0.0561
50.0 0.0003 0.0142 0.8091 0.0181 0.9350 0.0054
ConvLSTM-Nudging 0.5 10.0 0.0006 0.0176 0.6732 0.0237 0.8442 0.0001
20.0 0.0004 0.0147 0.7531 0.0206 0.8767 0.0001
50.0 0.0002 0.0116 0.8591 0.0156 0.9292 -0.0004
ConvLSTM-SE-Nudging 0.6 10.0 0.0016 0.0312 0.0685 0.0400 0.6918 0.0209
20.0 0.0009 0.0196 0.4972 0.0294 0.7960 0.0013
50.0 0.0004 0.0147 0.7560 0.0205 0.8883 -0.0016
Table 4 Evaluation metrics produced by each model at its optimal Nudging coefficient (τ) with different observation fraction (obs) under observation noise δ=0.01
Fig. 10 Radar chart of evaluation metrics produced for observation fraction (obs) at 10.0% (a), 20.0% (b), and 50.0% (c) under observation noise δ=0.01
Fig. 11 Pixel-averaged SSM time series produced by the four nudging models under observation noise (δ=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.
Fig. 12 Spatial distribution and error maps of SSM obtained for five representative dates when observation noise δ=0.01 and obs=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.
Model 𝜏 obs (%) MSE ((m3/m3)2) MAE (m3/m3) R2 RMSE (m3/m3) r Bias (m3/m3)
CNN-Nudging 1.0 10.0 0.0006 0.0170 0.6746 0.0237 0.8421 -0.0040
20.0 0.0005 0.0148 0.7089 0.0224 0.8482 0.0003
50.0 0.0001 0.0056 0.9168 0.0120 0.9591 -0.0021
LSTM-Nudging 1.0 10.0 0.0054 0.0574 -2.1510 0.0736 0.7452 0.0556
20.0 0.0033 0.0461 -0.8963 0.0571 0.8323 0.0454
50.0 0.0001 0.0045 0.9554 0.0088 0.9804 0.0015
ConvLSTM-Nudging 1.0 10.0 0.0003 0.0110 0.8420 0.0165 0.9188 -0.0005
20.0 0.0002 0.0078 0.9096 0.0125 0.9539 -0.0005
50.0 0.0000 0.0031 0.9762 0.0064 0.9881 -0.0002
ConvLSTM-SE-Nudging 1.0 10.0 0.0010 0.0222 0.4146 0.0317 0.7751 0.0127
20.0 0.0004 0.0117 0.7618 0.0202 0.8888 -0.0008
50.0 0.0001 0.0042 0.9570 0.0086 0.9783 -0.0004
Table 5 Evaluation metrics produced by each model at its optimal Nudging coefficient with different observation fractions under observation noise δ=0.00
Fig. 13 Radar chart of five metrics under observation noise δ=0.00. (a), obs=10.0%; (b), obs=20.0%; (c), obs=50.0%.
Fig. 14 Comparison among the pixel-averaged time series obtained for the four Nudging models at various observation fractions under observation noise δ=0.00 during 1 June-31 December 2021. (a), obs=10.0%; (b), obs=20.0%; (c), obs=50.0%.
Fig. 15 Spatial distribution and error map of SSM obtained for five representative dates when δ=0.00 and obs=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.
Fig. 16 Average metrics produced by different models under different the combination of observation noise (0.00 and 0.01) and observation fraction (10.0%, 20.0%, and 50.0%). (a), MSE; (b), MAE; (c), R2; (d), RMSE; (e), r; (f), Bias.
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