投审稿入口
Impact of groundwater levels at different temporal scales on calculation accuracy of annual shallow groundwater storage variation
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摘要:
为了探究不同时间尺度水位（时刻及日、月、年平均）对区域浅层地下水储变量计算精度的影响，以2019年邯郸平原浅层地下水为研究对象，采用网格法和泰森多边形法分别计算各时间尺度下的地下水储变量，并进行对比分析。结果表明：相同时间尺度水位下，2种方法计算结果较为接近，最大差异为0.114亿m3。对于不同时间尺度水位，月平均水位与时刻水位（理论上计算精度更高）计算结果偏离程度最大，网格法与泰森多边形法分别相差0.727亿m3和0.611亿m3，偏离程度呈随机性；年平均水位与时刻水位计算结果差距较小（0.015亿m3），但接近程度也呈随机性。对于网格法，年平均水位计算结果受网格尺度影响不大（最大相差0.011亿m3）；非年尺度下，计算精度随网格细化而提升。当网格分辨率优于1 km时，网格法计算精度高于泰森多边形法；但当规则剖分网格尺度接近于泰森多边形平均分区面积时，泰森多边形法计算精度更高。研究结果可为合理选用不同时间尺度水位数据，提高地下水储变量计算精度，科学评估地下水超采治理效果提供方法支撑。
Abstract:ObjectiveThis study aims to examine the influence of groundwater level at different temporal scales (specifically hourly, daily, monthly, and annual average water levels) on the accuracy of annual shallow groundwater storage variation calculations.
MethodsThe shallow groundwater system of the Handan Plain in 2019 was selected as the study object. The grid method and the Thiessen polygon method were applied to calculate groundwater storage variations using water level data at different temporal scales, and the results were compared to evaluate differences in calculation accuracy.
ResultsThe results indicated that, for the same temporal scale, groundwater storage variation estimates obtained using the grid method and the Thiessen polygon method were generally consistent, with a maximum difference of
0.0114 billion m3. At different temporal scales, both methods showed that the results calculated using monthly average water levels deviated the most from those calculated using hourly water levels, which were considered more accurate in theory. The deviations were0.0727 billion m3 for the grid method and0.0611 billion m3 for the Thiessen polygon method, with no consistent directional bias. In contrast, estimates using annual average water levels exhibited relatively small discrepancies compared to those calculated using hourly water levels, with a difference of0.0015 billion m3. However, the degree of agreement also exhibited randomness. For the grid method, the estimated results based on annual average water levels did not change significantly with grid size, with a maximum difference of0.0011 billion m3. At non-annual temporal scales, calculation accuracy improved as the grid resolution became finer. The grid method yielded more accurate results than the Thiessen polygon method when the grid resolution was finer than 1 km. However, the Thiessen polygon method demonstrated superior accuracy when the grid cell size of regular partition approached the average area of Thiessen polygons.ConclusionThese findings provide theoretical and methodological support for the rational selection of water level data at different temporal scales, thereby improving the accuracy of groundwater storage variation calculations, which is essential for evaluating the effectiveness of groundwater overexploitation control strategies.
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图 1 研究区位置及浅层地下水监测井分布图
注：审图号：GS（2019）1835号（自然资源部监制）；底图未做改动
Figure 1. Location of study area and distribution of shallow groundwater monitoring wells
图 3 研究区监测井水位数据异常检测图
Figure 3. Anomaly detection of water level data of monitoring well
图 4 2019年邯郸平原区年初年末时刻水位等值线图
Figure 4. Contour maps of hourly water levels at beginning and end of 2019 in Handan Plain
图 5 2019年邯郸平原区年初年末水位变幅等值线图
Figure 5. Contour maps of water level variation at beginning and end of 2019 in Handan Plain
图 6 年初和年末时刻水位变异函数图
Figure 6. Variogram plots of hourly water levels at beginning and end of year
图 7 2种方法不同时间尺度水位计算储变量对比
Figure 7. Comparison of groundwater storage variations calculated by two methods with water levels at different temporal scales
图 8 研究区不同时间尺度水位数据利用泰森多边形法计算水位变幅图示
Figure 8. Diagrams of water level variation calculated using Thiessen polygon method with water level data at different temporal scales in the study area
图 9 研究区月、年平均水位与时刻水位计算储变量对比
注：a，b图分别为月、年平均水位与时刻水位计算储变量对比图。蓝线交点表示2类数据计算的年初和年末平均水位在水位过程线上的位置；红线交点表示年初和年末时刻水位在过程线上的位置；红色箭头表示2种水位在年初和年末的差距
Figure 9. Comparison of groundwater storage variation calculated using monthly and annual average water levels and hourly water levels in the study area
图 10 研究区不同空间尺度网格和不同时间尺度水位下2种方法计算储变量差异对比
Figure 10. Comparison of differences in groundwater storage variation calculated by two methods under different grid sizes and water levels at different temporal scales in the study area
图 11 研究区同一时间尺度水位不同尺度网格计算储变量差异对比
Figure 11. Comparison of differences in groundwater storage variation calculated using different grid sizes at same temporal scale in the study area
图 12 网格法与泰森多边形法剖分单元对比示意图
Figure 12. Schematic diagram of partition units in grid method and Thiessen polygon method
表 1 变异函数模型评价参数
Table 1. Evaluation parameters of variogram model
水位 变程/km 块金/m2 基台/m2 块金系数 平均误差/m 年初时刻 37.73 23.29 260.54 8.94% −0.063 年末时刻 38.12 28.77 248.21 11.59% −0.134 年初日平均 34.53 24.92 247.36 10.07% −0.063 年末日平均 38.62 26.43 247.69 10.67% −0.143 年初月平均 34.85 24.89 242.58 10.26% −0.088 年末月平均 32.18 25.52 261.84 9.75% −0.106 年初年平均 36.53 31.83 271.73 11.71% −0.138 年末年平均 33.17 33.58 282.32 11.89% −0.121 
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表 2 研究区2019年不同时间尺度水位数据采用泰森多边形法计算的储变量对比
Table 2. Comparison of groundwater storage variation calculated using Thiessen polygon method with water level data at different temporal scales of 2019 in the study area
不同水位数据 加权平均水位/m 储变量/亿m3 年初 年末 水位变幅 时刻水位 23.270 22.652 −0.618 −2.189 日平均水位 23.280 22.657 −0.623 −2.216 月平均水位 23.018 22.227 −0.791 −2.800 年平均水位 22.858 22.272 −0.586 −2.076
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表 3 2种方法其他尺度水位与时刻水位计算的储变量差异对比
Table 3. Comparison of differences in groundwater storage variation calculated by two methods with water levels at other temporal scales and hourly water levels
A−A/亿m3 B−A/亿m3 C−A/亿m3 D−A/亿m3 网格法
泰森多边形法0 −0.145 −0.727 −0.015 0 −0.027 −0.611 0.113 注：时刻水位计算的储变量记作A，日平均记作B，月平均记作C，年平均记作D；B−A表示日平均水位计算的储变量减去时刻水位计算的储变量
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表 4 研究区单位面积储变量差异对比
Table 4. Comparison of differences in groundwater storage variation per unit area in the study area
方法 单位面积储变量/(万m3·km−2) 与时刻水位差距/(万m3·km−2) 网格法 泰森多边形法 差距 网格法 泰森多边形法 时刻水位 −2.762 −2.931 −0.169 0.000 0.000 日平均水位 −2.954 −2.949 0.005 −0.193 −0.018 月平均水位 −3.729 −3.726 0.003 −0.968 −0.795 年平均水位 −2.781 −2.763 0.018 −0.020 0.168
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表 5 多种情况下2种方法计算的储变量结果
Table 5. Groundwater storage variation calculated by two methods under multiple conditions
方法 网格尺寸 储变量/亿m3 时刻水位 日平均水位 月平均水位 年平均水位 网格法 泰森多边形分区 −2.215 −2.245 −2.779 −2.068 10 km×10 km −1.959 −1.984 −2.662 −2.083 5 km×5 km −2.034 −2.159 −2.773 −2.079 1 km×1 km −2.066 −2.213 −2.801 −2.087 300 m×300 m −2.075 −2.220 −2.802 −2.090 泰森
多边形法泰森多边形分区 −2.189 −2.216 −2.800 −2.076
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