地下水是保障我国水资源供给、粮食生产以及生态安全的重要资源。在过去数十年高速的社会经济发展过程中，粗放的地下水资源开发利用导致了一系列环境地质问题。华北平原作为全球典型的地下水超采区之一，一直备受关注。国内出台了大量针对性的地下水超采治理顶层设计与规划，例如“华北地区地下水超采综合治理”和“河湖复苏计划”等。在这种情势下，河流生态补水成为兼具恢复河流生态环境和含水层水源涵养的重要手段，并将成为常态。其中，永定河生态补水是北京市地下水系统恢复的重要措施之一。生态补水、地下水开采和降水等新水情影响下地下水位的高时间分辨率准确预测，是当前地下水精准管理和水资源综合决策的重要议题，该问题的解决有助于准确判定地下水位变化的形势，并及时优化调整生态补水和地下水开采等管理方案。

本论文围绕上述实际需求，以永定河生态补水实践为例，系统研究了高时间分辨率上针对新水情下的地下水位准确预测问题。在阐述国内外相关问题研究进展基础上，综合利用水均衡、Mann-Kendall趋势分析等方法研究了地下水位动态特征和影响要素，以期为机器学习和物理机制模型（PBM）提供准确的输入变量和判定地下水运动的关键过程；进而针对地下水位和地表径流快速短期预测问题，提出了马斯京根洪水演进算法预测径流和随机森林方法预测地下水位相耦合的方法。通过增加地表径流过程和具有物理意义的输入变量，实现了地下水位预测领域机器学习模型的改进；再针对地下水物理运动过程和长期预测问题，提出了马斯京根洪水演进算法预测径流和数值模型预测地下水位相耦合的方法；针对机器学习和PBM如何有效联合使地下水位预测更加准确的问题，采用将PBM输出引入长短期记忆网络（LSTM）模型并增加降雨滞后补给过程的方式，探讨了LSTM模型效率的提升程度。主要工作内容和结论如下：

（1）利用水均衡、Mann-Kendall趋势分析、相关性分析等多种方法解析了地下水位的变动特征。2000年之前，地下水位基本处于动态平衡状态；2000~2014年为地下水位快速下降阶段，下降趋势为-0.75 m/年；2015年后，地下水位开始回升。月和天尺度上，地下水位的变动呈现复杂的非线性。研究区河道渗漏量大、距离河道1 km范围内的区域，地下水位可在18天内升高5 m，后又在20天内回落0.8 m。随着离河距离的增加，地下水位最大抬升幅度逐渐减小，开始出现抬升的时间逐渐延后，可达到20天甚至更长。且地下水位变动特征由“先升高后减小”，逐渐转变为“缓慢升高”，直至不再受河流生态补水的影响。

（2）利用随机森林耦合马斯京根洪水演进算法的方式实现了生态补水过程中地下水位和地表径流的快速短期预测和对机器学习模型的改进。12眼地下水位观测井和3个径流站点的验证结果显示，地下水位模拟的均方根误差（RMSE）在0.1~1.4 m之间，径流模拟的RMSE在11.8~15.9 m³/s之间。在官厅水库总放水量为1.7×10⁸ m³情景下，当其径流量大于75 m³/s时，固安站的径流量将达到5 m³/s以上。考虑不同补水情景，地下水位最大抬升幅度可达到20 m。且随着离河距离的增加，地下水位抬升幅度逐渐减小，自河流上游至下游，地下水位抬升幅度亦有减小趋势，与地下水位真实响应过程相似。

（3）利用数值模型耦合马斯京根洪水演进算法的方式实现了生态补水过程中地下水位和地表径流的长期预测。径流模拟的RMSE在3.8~4.7 m³/s之间。地下水位模拟值与真实值之间绝对误差小于0.5 m、1.0 m和2.0 m的数据占比分别为36%、63%和88%。京良路以上河段周围，生态补水对地下水位抬升的作用显著，贡献率可超过70%。在不同降水量、地下水开采和生态补水情景下，9年后研究区地下水位的抬升幅度在4.08~8.57 m之间，生态补水的贡献率在7.88%~36.59%之间。地下水位的上升会带来潜在的污染风险，且生态补水会加重此种风险。

（4）采用在LSTM模型中引入PBM的输出数据和考虑降雨补给滞后过程的方式改进了LSTM模型。直接预测地下水位的LSTM模型（LSTM-H-ORI）和先预测PBM模拟误差再利用预测值矫正PBM模拟水位的LSTM模型（LSTM-dH-ORI）用于分析所提方法的有效性。相较于PBM，LSTM模型在地下水位短期预测方面具有优势，而PBM则在长期预测方面更具优势。PBM输出的地下水位作为额外的输出特征和均衡数据作为额外的输入特征可分别更好地提高LSTM-H-ORI和LSTM-dH-ORI的模拟精度。当LSTM-H-ORI的模拟精度较差（纳什效率系数，NSE＜0）或PBM的模拟精度较好（NSE＞0）时，与PBM输出数据的结合最有可能提高预测精度。当LSTM-dH-ORI的模拟精度中等（00.6）时，与PBM的输出数据结合反而有可能导致模拟精度降低。通过添加降雨补给滞后的物理过程，所有观测井地下水位的模拟精度都得到了提升，验证阶段NSE平均提高0.16。

本研究将为生态补水过程中地下水位的短期和长期预测以及机器学习方法在地下水位预测领域的改进提供方法和理论参考。

Groundwater is an important resource for ensuring the supply of water resources, food production, and ecological security in China. The extensive utilization of groundwater resources has led to a series of environmental geologic problems in the past few decades. As one of the typical over-exploitation zones in the world, North China Plain has attracted much attention. A large number of top-level designs and plans have been introduced, such as "Comprehensive Control of Groundwater over-exploitation in North China" and "Recovery Plans of Rivers and Lakes". Ecological water replenishment (EWR) has become an important tool for restoring river ecology and groundwater resource conservation. The accurate prediction of groundwater level with high temporal resolution under the influence of new water regime such as EWR, groundwater exploitation, and precipitation is an important issue in current groundwater management and decision-making of water resources. The solution to this problem helps to accurately determine the trend of groundwater level and optimize management plans such as EWR and groundwater exploitation in a timely manner.

This paper focuses on the actual demand mentioned above and takes the practice of EWR in Yongding River as an example to study the problem of accurate prediction of groundwater level under new water regime conditions at high temporal resolution systematically. Based on the survey of the research literature, the dynamic characteristics of groundwater level were studied using methods such as water balance and Mann-Kendall trend analysis. These will provide accurate input variables and determine key process of groundwater movement for machine learning model and physics-based model (PBM). Then, aiming at the problem of rapid short-term prediction of groundwater level and runoff, this paper proposed a coupled model that using Maskingum method to predict runoff and using the random forest regression (RFR) method to predict groundwater level. In addition, machine learning model was improved by adding the surface process and the input variable with physical significance. To address the physical movement process and long-term prediction of groundwater level, a coupled model was established for predicting runoff using the Maskingum method and predicting groundwater level using numerical model. In order to solve the problem about combining machine learning and PBM to make the prediction of groundwater level more accurate, this paper introduced the output data from PBM and lag process of precipitation recharge into long-term and short-term memory network (LSTM) model and explored the improvement degree of LSTM model efficiency. The main results are summarized as follows:

(1) The characteristics of groundwater level changes were analyzed using the methods of water balance, Mann-Kendall trend analysis and correlation analysis. Before 2000, groundwater level were in dynamic equilibrium, while in a rapid decline stage during 2000-2014 with the decreasing trend of -0.75 m/year. After 2015, groundwater level began to rise. The variation of groundwater level on the monthly and daily time scales is more complex and nonlinear. In areas with large river leakage and a distance of 0-1 km from the river, the groundwater level can rise by 5 m within 18 days, and then fall back by 0.8 m within 20 days. As the distance from the river increases, the maximum lifting amplitude of groundwater level gradually decreases and the time when the groundwater level begins to rise gradually delays, possibly reaching 20 days. Besides, the characteristics of groundwater level change from "rising and then decreasing" to "slowly rising" until no longer affected by EWR.

(2) Rapid short-term prediction for groundwater level and runoff during EWR and improvement of machine learning model were achieved using the method of RER coupled with Muskingum formula. The root mean square error (RMSE) of simulated groundwater level is between 0.1-1.4 m for selected 12 observation wells and RMSE of simulated runoff is between 11.8-15.9 m³/s for 3 gauging stations in the stage of verification. Under the scenarios that the total discharge of Guanting Reservoir is 170 million m³, when the runoff of Guanting Reservoir is greater than 75 m³/s, the runoff of Gu'an station will reach more than 5 m³/s. The maximum increase of the groundwater level will reach more than 20 m. In addition, as the distance from the river increases and reaches to the downstream, the biggest rise of the groundwater level gradually decreases, which is similar to the real response process of groundwater level.

(3) The long-term prediction for groundwater level and runoff in the process of EWR was achieved using a numerical model coupled with the Muskingum formula. The RMSE of simulated runoff is between 3.8-4.7 m³/s in gauging stations used for validation. The data of absolute error between simulated and observed groundwater level that less than 0.5, 1.0, and 2.0 m accounts for 36%, 63%, and 88%, respectively. Around the reach above Jingliang Road, EWR contributes to the rise of groundwater level significantly with a contribution rate of over 70%. Under different scenarios of precipitation, groundwater exploitation, and EWR, the groundwater level rise between 4.08-8.57 m and the contribution rate of EWR is between 7.88%-36.59% in next 9 years. The rise of groundwater level may pose a potential pollution risk, and EWR will exacerbate this risk.

(4) The LSTM model in groundwater level prediction was improved by introducing the output data from PBM and adding lag processes of precipitation recharge. Two original LSTM models were established: (1) the model for predicting groundwater level directly (LSTM-H-ORI); (2) the model for predicting simulated errors from PBM and then following by correction of simulated groundwater level from PBM using predicted values (LSTM-dH-ORI).Compared with PBM, LSTM have advantages in short-term prediction, while PBM have advantages in long-term prediction. The accuracy of the original LSTM-H-ORI and LSTM-dH-ORI models can be better improved by using the groundwater level from PBM as additional output feature and balance data from PBM as additional input feature, respectively. When the simulation accuracy of LSTM-H-ORI is poor (Nash-Sutcliffe efficiency coefficient, NSE<0) or the accuracy of from PBM is well (NSE>0), the combination of LSTM-H-ORI and the output data from PBM is most likely to improve the prediction accuracy. When the simulation accuracy of LSTM-dH-ORI is moderate (00.6), combining with the output data from PBM may lead to a decrease in accuracy. By adding lag process of precipitation recharge, the accuracy of all observation wells has been improved, with an average improved accuracy of 0.16 for NSE.

This study will provide methods and theoretical references for the short-term and long-term prediction of groundwater level in the process of EWR, as well as the improvement of machine learning models.