基于注意力机制LSTM神经网络的北方岩溶大泉水位预测研究

doi:10.13745/j.esf.sf.2025.10.1

地学前缘 ›› 2026, Vol. 33 ›› Issue (1): 419-431.DOI: 10.13745/j.esf.sf.2025.10.1

基于注意力机制LSTM神经网络的北方岩溶大泉水位预测研究

黄林显¹(), 徐征和¹, 支传顺¹, 李双², 刘治政², 邢立亭¹, 朱恒华³, 王晓玮³, 毕雯雯⁴, 胡晓农¹^,^*()

1.济南大学水利与环境学院, 山东济南 250022
2.山东省地质调查院, 山东济南 250013
3.山东省国土空间生态修复中心, 山东济南 250014
4.山东省地矿工程勘察院(山东省地质矿产勘查开发局八○一水文地质工程地质大队), 山东济南 250014

收稿日期:2025-06-20 修回日期:2025-10-10 出版日期:2026-01-25 发布日期:2025-11-10
通信作者: *胡晓农(1962—),男,教授,博士生导师,主要从事海岸带水文地质及岩溶地质方面的研究工作。E-mail: stu_huxn@ujn.edu.cn
作者简介:黄林显(1982—),男,副教授,硕士生导师,主要从事岩溶水文地质研究工作。E-mail: stu_huanglx@ujn.edu.cn
基金资助:
国家自然科学基金项目(42577088);国家自然科学基金重点项目(42430712);山东省自然科学基金项目(ZR2024MD009)

Research on groundwater level prediction of northern karst spring of China based on LSTM-Attention neural network

HUANG Linxian¹(), XU Zhenghe¹, ZHI Chuanshun¹, LI Shuang², LIU Zhizheng², XING Liting¹, ZHU Henghua³, WANG Xiaowei³, BI Wenwen⁴, HU Xiaonong¹^,^*()

1. School of Water Conservancy and Environment, University of Jinan, Jinan 250022, China
2. Shandong Institute of Geological Survey, Jinan 250013, China
3. Shandong Provincial Territorial Spatial Ecological Restoration Center, Jinan 250014, China
4. Shandong Provincial Geo-mineral Engineering Exploration Institute (No.801 Hydrogeological and Engineering Exploration Brigade of Shandong Provincial Bureau of Geology and Mineral Exploration and Development), Jinan 250014, China

Received:2025-06-20 Revised:2025-10-10 Online:2026-01-25 Published:2025-11-10

摘要/Abstract

摘要：

岩溶地下水是北方岩溶区重要供水水源,准确预测其水位动态对地下水资源科学管理和保护具有重要意义。但岩溶含水系统具有强烈的非均质性和各向异性,导致其水位动态往往体现出非平稳及非线性波动状态,造成进行地下水位预测时易产生较大误差。论文提出一种耦合注意力机制(Attention)和长短时记忆(LSTM,Long Short-Term Memory)神经网络的多变量趵突泉地下水位预测模型,利用泉域2013—2024年日降水(代表补给项)及水汽压、日气温和开采量(代表排泄项)进行模型训练和预测,结果表明:①采用BEAST(Bayesian Estimator of Abrupt Change, Seasonality, and Trend) 算法对1958—2024年趵突泉水位时间序列进行分解,共识别出四个突变点并以此为依据将水位动态划分为四个阶段;②互相关分析揭示降雨和趵突泉水位动态变化之间存在2~3个月的时间滞后,表明两者之间动态变化较为一致;③所提出的预测模型以多种变量(降水量、水汽压、气温及开采量)作为模型输入,不同变量间的交互作用可相互验证,能有效提升预测精度;④采用正弦函数拟合日气温数据,可消除测量误差影响,能在一定程度上提高预测精度;⑤相较于单一LSTM神经网络和门控循环单元(GRU)神经网络,LSTM_Attention神经网络由于引入注意力机制,能聚焦更重要特征的影响,从而显著提高预测精度,其水位预测RMSE和R²值分别为0.13 m和0.94。总体来说,本文所提出的LSTM_Attention神经网络岩溶地下水位预测模型具有较强的准确性和稳定性,可为岩溶地下水位精确预测提供借鉴。

关键词: 北方岩溶, 水位预测, 多变量模拟, LSTM_Attention神经网络

Abstract:

Karst groundwater serves as a critical water source in northern karst regions of China, and accurately forecasting its water level dynamics is essential for the scientific management and conservation of groundwater resources. However, the inherent strong heterogeneity and anisotropy of karst aquifer systems often result in non-stationary and nonlinear groundwater fluctuations, posing significant challenges for reliable prediction and frequently leading to considerable errors. This study proposes a multivariate groundwater level forecasting model for the Baotu Spring, based on the integration of an attention mechanism and a long short-term memory (LSTM) neural network. The model is trained and validated using daily data from 2013 to 2024, including precipitation (as a proxy for recharge), vapor pressure, air temperature, and groundwater extraction volume (as indicators of discharge). The main findings are as follows: (a) The BEAST (Bayesian Estimator of Abrupt Change, Seasonality, and Trend) algorithm was applied to the 1958-2024 Baotu Spring groundwater level time series, identifying four abrupt change points. Based on these, the time series was segmented into four distinct stages. (b) Cross-correlation analysis revealed a time lag of approximately 2-3 months between precipitation and groundwater level variations, suggesting a strong dynamic coupling between the two variables. (c) The proposed model incorporates multiple input variables (precipitation, vapor pressure, temperature, and extraction volume). The interplay among these variables enhances model interpretability and contributes to improved forecasting accuracy. (d) Daily temperature data were smoothed using a sinusoidal fitting function, which effectively reduces measurement noise and improves prediction performance. (e) Compared to standard LSTM and gated recurrent unit (GRU) models, the LSTM-Attention model demonstrates superior predictive capability. By leveraging the attention mechanism to prioritize influential features, it achieved a root mean square error (RMSE) of 0.13 m and a coefficient of determination (R²) of 0.94. In summary, the LSTM-Attention-based forecasting model exhibits robust accuracy and stability, offering valuable insights into the precise prediction of groundwater dynamics in karst environments.

Key words: northern karst, prediction of groundwater dynamics, multivariate modeling, LSTM-Attention neural network

中图分类号:

P641.2
TP183

黄林显, 徐征和, 支传顺, 李双, 刘治政, 邢立亭, 朱恒华, 王晓玮, 毕雯雯, 胡晓农. 基于注意力机制LSTM神经网络的北方岩溶大泉水位预测研究[J]. 地学前缘, 2026, 33(1): 419-431.

HUANG Linxian, XU Zhenghe, ZHI Chuanshun, LI Shuang, LIU Zhizheng, XING Liting, ZHU Henghua, WANG Xiaowei, BI Wenwen, HU Xiaonong. Research on groundwater level prediction of northern karst spring of China based on LSTM-Attention neural network[J]. Earth Science Frontiers, 2026, 33(1): 419-431.

图/表 15

图1 济南泉域水文地质图(据文献[19]修改) 1 —间接补给区;2—直接补给区;3—汇集排泄区;4—河流水库;5—地层分界线;6—断裂带;7—剖面线;8—太古宙变质岩;9—裸露-半裸露奥陶系碳酸盐岩;10—寒武纪碳酸盐岩;11—泉群;12—气象站。

Fig.1 Hydrogeological map of Jinan Spring area. Modified after [19].

图2 II' 地质剖面图(据文献[19]) 1 —太古宙侵入岩;2—寒武系馒头组灰岩;3—寒武系张夏组灰岩;4—寒武系崮山组+长山组灰岩;5—寒武系凤山组灰岩;6—奥陶系碳酸盐岩;7—岩浆岩;8—第四系沉积物;9—泉。

Fig.2 Geological profile of II'. Adapted from [19].

图3 趵突泉水位时间序列分解及突变点检测

Fig.3 Time series decomposition and abrupt change detection in Baotu Spring groundwater levels

图4 2013—2024年趵突泉日水位及日降雨对比图

Fig.4 Comparison of daily groundwater level and rainfall in Baotu Spring from 2013 to 2024

图5 降雨和趵突泉水位动态互相关分析

Fig.5 Cross-correlation analysis between rainfall and groundwater level in Baotu Spring

图6 2013—2024年日均气温原始数据与正弦拟合曲线

Fig.6 Raw data and sinusoidal fitting curve of daily average temperature from 2013 to 2024

图7 LSTM神经网络整体结构

Fig.7 Structure of LSTM neural network

图8 自注意力机制结构图

Fig.8 Self-attention mechanism structure diagram

图9 LSTM_Attention预测模型框架图

Fig.9 Framework of LSTM_Attention prediction model

图10 LSTM_Attention模型预测结果(拟合温度)

Fig.10 Prediction results of LSTM_Attention model (with fitted temperature)

图11 原始气温和拟合气温泉水位预测结果对比

Fig.11 Spring groundwater level prediction results of raw and fitted temperature

图12 输入原始温度和拟合温度的预测误差(RMSE和R2)

Fig.12 Prediction error of raw and fitted temperature(RMSE和R2)

图13 不同方法趵突泉水位预测结果

Fig.13 Prediction results of Baotu Spring groundwater level using different methods

图14 不同方法预测误差(RMSE和R2)

Fig.14 Prediction errors of different methods(RMSE和R2)

图15 预测误差小提琴图

Fig.15 Violin plot of forecast error

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基于注意力机制LSTM神经网络的北方岩溶大泉水位预测研究

Research on groundwater level prediction of northern karst spring of China based on LSTM-Attention neural network

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