基于PatchTST的地下水位预测模型

A multi-variable groundwater level prediction model based on PatchTST

摘要

【目的】准确、快速的预测地下水水位动态变化特征，对地下水科学管控尤为重要，但针对多因素影响下的地下水位中长期预测研究较少。【方法】为提高地下水位中长期预测能力，构建了一种基于PatchTST的多变量地下水位中长期预测模型(PatchTST-GWL),利用互相关函数分析了地下水开采量、地表补水量、降雨量、侧向补给等影响因素间的多元相关性及地下水水位变化的滞后性，对北京市西郊地区4眼典型浅层监测井地下水水位进行了中长期预测，采用纳什系数(NSE)、均方根误差(RMSE)、平均绝对误差(MAE)评估了模型性能及准确性，并基于控制变量法分析了模型可解释性。【结果】结果显示：随着预测期增加，PatchTST-GWL模型预测精度逐渐提升，各监测井90 d、180 d预测期地下水水位模拟结果NSE系数均提升至0.9以上，MAE、MSE、RMSE较Attention-Bi-LSTM、SVM常用深度学习模型降低10%~80%。【结论】PatchTST-GWL模型对中长期地下水水位预测性能优势明显，模型通过引入互相关函数计算地下水开采、降雨、地表补水、侧向补给变化过程对地下水水位变化过程影响的滞后期，有效提升了模型预测精度，同时模型预测结果与各影响因子变化的响应规律符合客观物理规律，呈现出较好的可解释性。该模型可准确、快速的进行地下水水位预测，为科学评估与合理利用地下水提供有效支撑。

Abstract

[Objective] Accurate and rapid prediction of dynamic groundwater level changes is crucial for scientific groundwater management, yet long-term predictions influenced by multiple factors remain insufficiently researched. [Methods] To enhance the capability of long-term groundwater level forecasting, a multivariate long-term prediction model based on PatchTST(PatchTST-GWL) was developed. This model utilized cross-correlation functions to analyze the multivariate correlations and lag effects among factors like groundwater extraction, surface water recharge, rainfall, and lateral recharge. Long-term forecasts were conducted on groundwater levels in four typical shallow monitoring wells in the western suburbs of Beijing. The model performance and accuracy were assessed using the Nash-Sutcliffe Efficiency(NSE), Root Mean Square Error(RMSE), and Mean Absolute Error(MAE). The model's interpretability was also analyzed using the controlled variable method. [Results] The result showed that the prediction accuracy of the PatchTST-GWL model improves with the extension of the forecasting period. For 90 and 180 days forecasting periods, the NSE coefficients of groundwater level simulations exceeded 0.9 across all monitoring wells, with MAE, MSE, and RMSE reductions of 10% to 80% compared to commonly used deep learning models like Attention-Bi-LSTM and SVM. [Conclusion] The PatchTST-GWL model exhibits a significant advantage in the performance of long-term groundwater level predictions. By incorporating cross-correlation functions to calculate the lag effects of groundwater extraction, rainfall, surface water recharge, and lateral recharge changes on groundwater levels, the model significantly enhances prediction accuracy. Furthermore, the predictions align with the response patterns of various influencing factors, consistent with objective physical laws, demonstrating good interpretability. This model can accurately and swiftly predict groundwater levels, effectively supporting scientific assessments and rational utilization of groundwater resources.

关键词

地下水水位预测 / Transformer / 多头注意力机制 / 降雨 / 人类活动 / PatchTST-GWL / 人工智能 / 中长期预测

Key words

groundwater level prediction / Transformer / multi-head attention / rainfall / human activity / PatchTST-GWL / artificial intelligence / medium and long term forecast

基金资助

北京市自然科学基金项目(8232032)

国家自然科学基金项目(52209005)

水利部重大科技项目(SKS-2022044)

北京学者培养经费资助项目(GZ-2024-002-SZY)