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Karst groundwater is a critical freshwater resource for numerous regions worldwide. Monitoring and predicting karst spring discharge is essential for effective groundwater management and the preservation of karst ecosystems. However, the high heterogeneity and karstification pose significant challenges to physics-based models in providing robust predictions of karst spring discharge. In this study, an interpretable multi-step hybrid deep learning model called selective EEMD-TFT is proposed, which adaptively integrates temporal fusion transformers (TFT) with ensemble empirical mode decomposition (EEMD) for predicting karst spring discharge. The selective EEMD-TFT hybrid model leverages the strengths of both EEMD and TFT techniques to learn inherent patterns and temporal dynamics from nonlinear and nonstationary signals, eliminate redundant components, and emphasize useful characteristics of input variables, leading to the improvement of prediction performance and efficiency. It consists of two stages: in the first stage, the daily precipitation data is decomposed into multiple intrinsic mode functions using EEMD to extract valuable information from nonlinear and nonstationary signals. All decomposed components, temperature and categorical date features are then fed into the TFT model, which is an attention- based deep learning model that combines high-performance multi-horizon prediction and interpretable insights into temporal dynamics. The importance of input variables will be quantified and ranked. In the second stage, the decomposed precipitation components with high importance are selected to serve as the TFT model’s input features along with temperature and categorical date variables for the final prediction. Results indicate that the selective EEMD-TFT model outperforms other sequence-to-sequence deep learning models, such as LSTM and single TFT models, delivering reliable and robust prediction performance. Notably, it maintains more consistent prediction performance at longer forecast horizons compared to other sequence-to-sequence models, highlighting its capacity to learn complex patterns from the input data and efficiently extract valuable information for karst spring prediction. An interpretable analysis of the selective EEMD-TFT model is conducted to gain insights into relationships among various hydrological processes and analyze temporal patterns.
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This content will become publicly available on April 1, 2026
Simulation of Spring Discharge Using Deep Learning, Considering the Spatiotemporal Variability of Precipitation
Abstract Sparse precipitation data in karst catchments challenge hydrologic models to accurately capture the spatial and temporal relationships between precipitation and karst spring discharge, hindering robust predictions. This study addresses this issue by employing a coupled deep learning model that integrates a variation autoencoder (VAE) for augmenting precipitation and a long short‐term memory (LSTM) network for karst spring discharge prediction. The VAE contributes by generating synthetic precipitation data through an encoding‐decoding process. This process generalizes the observed precipitation data by deriving joint latent distributions with improved preservation of temporal and spatial correlations of the data. The combined VAE‐generated precipitation and observation data are used to train and test the LSTM to predict spring discharge. Applied to the Niangziguan spring catchment in northern China, the average performance of NSE, root mean square error, mean absolute error, mean absolute percentage error, and log NSE of our coupled VAE/LSTM model reached 0.93, 0.26, 0.15, 1.8, and 0.92, respectively, yielding 145%, 52%, 63%, 70% and 149% higher than an LSTM model using only observations. We also explored temporal and spatial correlations in the observed data and the impact of different ratios of VAE‐generated precipitation data to actual data on model performances. This study also evaluated the effectiveness of VAE‐augmented data on various deep‐learning models and compared VAE with other data augmentation techniques. We demonstrate that the VAE offers a novel approach to address data scarcity and uncertainty, improving learning generalization and predictive capability of various hydrological models. However, we recognize that innovations to address hydrologic problems at different scales remain to be explored.
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- Award ID(s):
- 1933779
- PAR ID:
- 10581013
- Publisher / Repository:
- American Geophysical Union
- Date Published:
- Journal Name:
- Water Resources Research
- Volume:
- 61
- Issue:
- 4
- ISSN:
- 0043-1397
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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