Dynamic Characteristics and Trend Prediction of Groundwater Level in Xi’an City, China Based on GM (1, 1) and BP Neural Network Models
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摘要:
地下水是干旱与半干旱地区极其珍贵的自然资源，地下水动态的精准预测与评估关乎着地下水资源的有效保护与合理利用。本研究根据西安市2010～2020年地下水位监测数据，系统分析了西安市地下水位年际、年内动态变化特征，探究了影响地下水位动态的主要因素，通过SPSS对影响地下水位动态的降水量和开采量两个主要因素进行相关性分析，并基于GM（1，1）灰度预测模型和BP神经网络模型对地下水位变动趋势进行了预测。结果表明：①2010～2016年，地下水位整体上呈下降趋势，2016～2020年间，得益于地下水压采和供水设施的不断优化完善，地下水位呈回升趋势。②降水和人为开采均对西安市地下水位变动具有显著影响；地下水位埋深是决定受降水影响程度的关键因素，其中河漫滩地区最为敏感，阶地次之，黄土塬区较弱。地下水开采量与地下水位埋深具有更强的相关性。这凸显了其在调控地下水位动态变化中的主导地位。③地下水位预测结果显示，随着地下水开采量呈现出逐年下降的趋势，研究区地下水整体处于波动上升趋势。本研究对西安市地下水动态的影响因素及预测趋势进行了研究，对地下水资源管理和可持续发展具有重要参考价值。
Abstract:Groundwater is exteremely important in arid and semiarid regions, and the core of its effective protection and rational utilization lies in accurate prediction and evaluation of groundwater dynamics, based on which protection, utilization, and planning strategies are formulated. Based on groundwater level monitoring data from 2010 to 2020 in Xi'an City, this study systematically analyzed the inter-annual and intra-annual dynamic changes in groundwater levels, investigated the main factors influencing groundwater dynamics, and conducted a correlation analysis using SPSS on the two primary factors affecting groundwater dynamics: precipitation and extraction volume. Furthermore, the study utilized the GM (1,1) grey prediction model and the BP neural network model to forecast the trend of groundwater level changes. The results indicate that: ① From 2010 to 2016, the groundwater level showed an overall decreasing trend. However, from 2016 to 2020, due to the yearly reduction in extraction volume and continuous optimization and improvement of water supply facilities, the groundwater level exhibited a rising trend. ② Both precipitation and human extraction significantly impact the groundwater level fluctuations in Xi'an. The depth of the groundwater level is a crucial factor determining the degree of influence from precipitation, with river floodplains being the most sensitive, followed by terraces, and loess plateaus showing the weakest response. The correlation between groundwater extraction volume and groundwater depth is stronger, highlighting its dominant role in regulating groundwater level dynamics. ③ Groundwater level predictions suggest that as groundwater extraction continues to decline annually, the overall groundwater in the study area is on a fluctuating upward trend. This study has conducted research on the influencing factors and prediction trends of groundwater dynamics in Xi'an, which has important reference value for groundwater resource management and sustainable development.
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表 1 2010～2020年西安市降水、开采和地下水位埋深情况表
Table 1. Precipitation, groundwater extraction, and groundwater level depth in Xi'an City from 2010 to 2020
年份 降水量（mm） 降水量变幅（mm） 开采量（亿m3） 地下水位埋深（m） 2010 819 33 6.24 15.15 2011 1002 216 6.01 14.42 2012 659 −127 6.23 15.05 2013 656 −130 6.37 15.48 2014 802 16 9.57 15.11 2015 779 −7 10.01 15.36 2016 656 −130 10.26 15.99 2017 823 37 10.26 15.57 2018 728 −58 10.37 15.56 2019 910 124 10.05 15.44 2020 809 23 9.49 15.23 
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表 2 降雨量变幅、开采量变幅与地下水位埋深相关性分析表
Table 2. Correlation of rainfall, groundwater extraction, and mean groundwater level depth
变量 降雨量 开采量 地下水位埋深 降雨量 1 开采量 −0.176 1 地下水位埋深 −0.673* 0.843** 1
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表 3 地下水开采量灰色预测模型检验
Table 3. Verification of groundwater extraction estimation using grey model
年份 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 光滑检验 0.96 0.51 0.34 0.38 0.29 0.23 0.18 0.15 0.13 0.11 误差检验 0.11 0.24 0.29 0.26 0.18 0.03 0.02 0 0.04 0.05
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表 4 2025～2035年地下水开采量预测结果（亿m3）
Table 4. Prediction results of groundwater extraction from 2025 to 2035 (108 m3)
年份 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 预测结果 5.71 5.62 5.53 5.45 5.36 5.28 5.21 5.12 5.04 4.96 4.89
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表 5 BP网络模型预测精度
Table 5. Accuracy of BP network model prediction
年份 水位实测值（m） BP网络模型 预测值（m） 相对误差（%） 2010 15.15 14.7656 −1.903 2011 14.42 15.2047 −1.807 2012 15.05 15.1268 0.086 2013 15.48 15.1425 −1.443 2014 15.11 15.2049 −4.906 2015 15.36 14.7576 −5.196 2016 15.99 15.2013 −2.273 2017 15.57 14.7323 −4.558 2018 15.56 15.1060 −0.805 2019 15.44 15.0458 −2.553 2020 15.23 14.8329 −2.607
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