考虑参数不确定性的地下水数值模型误差补偿校正方法

doi:10.13745/j.esf.sf.2025.10.25

摘要/Abstract

摘要： 模型结构和参数取值的不确定性是制约地下水模型仿真精度和实现高精度管理应用的关键因素。针对这一问题,本文提出了一种基于观测井观测数据的地下水水头模拟误差补偿校正方法。该方法首先对观测井的模拟水位进行误差校正,再利用反距离插值技术估计误差的空间分布,最后将误差补偿应用于模型中其他网格点,实现整体模拟精度的提升。研究基于自主研发的地下水流数值模拟软件,设计了三种真实非均质介质、定流量和变流量抽注水、不同开采井和观测井数量组合的多种模拟情景,系统评估了均质水文地质模型误差补偿校正方法对水头模拟的效果。结果表明,误差补偿校正后的观测井水头模拟精度显著提高,且精度提升程度与渗透系数的平均值成反比、与其方差成正比。在多井抽水注水及强非均质变流量条件下,均方根误差由1.5 m降至0.25 m。通过对多种校正点数量情景的比较分析发现,所提出的方法在校正点位置的模拟效果显著提升,但对空间范围内地下水水头的整体模拟效果提升较为有限。研究方法可提升已识别地下水数值模型的模拟精度,具有较好的推广应用价值。

关键词: 地下水数值模型, 非均质, 误差校正补偿, 参数不确定性, 模型仿真性

Abstract:

Uncertainty in model structure and parameters remains a critical bottleneck, limiting the accuracy of groundwater simulations and their application in high-precision management. To address this, we proposed an error correction method for simulated hydraulic heads based on observation well data. The method involves three steps: correcting simulated errors at observation wells, interpolating the spatial error distribution using inverse distance weighting, and applying the resulting error field to compensate other grid cells in the model, thereby enhancing overall accuracy. Using an in-house developed numerical groundwater flow model, we designed three heterogeneous scenarios with variable flow rates and different numbers of pumping and observation wells. These scenarios were used to systematically evaluate the method’s performance under homogeneous parameter assumptions. Results indicated a significant improvement in the accuracy of simulated heads at the observation wells. The degree of improvement was inversely proportional to the mean hydraulic conductivity and directly proportional to its variance. Under conditions of multi-well pumping and injection with strong heterogeneity and variable flow rates, the root mean square error decreased from 1.5 m to 0.25 m. Furthermore, analysis of scenarios with different numbers of calibration points showed that while the method significantly improved accuracy at those specific locations, its enhancement of the overall spatial head field was relatively limited. The presented approach offers a practical and effective solution for improving the accuracy of calibrated groundwater models and shows considerable potential for broader application.

Key words: numerical model of groundwater, heterogeneous, error correction, parameter uncertainty, accuracy of model simulation

中图分类号:

X523

胡立堂, 甘霖, 孙建冲, 刘宏博, 田蕾, 沈琦. 考虑参数不确定性的地下水数值模型误差补偿校正方法[J]. 地学前缘, 2026, 33(1): 432-443.

HU Litang, GAN Lin, SUN Jianchong, LIU Hongbo, TIAN Lei, SHEN Qi. Error correction method for groundwater numerical models considering parameter uncertainty[J]. Earth Science Frontiers, 2026, 33(1): 432-443.

图/表 16

图1 模型范围及观测井分布(a)和渗透系数对数分布(b)

Fig.1 Model domain and observation well distribution (a) and logarithmic distribution of hydraulic conductivities (b)

表1 真实与模型概化的渗透系数统计表

Table 1 Statistical parameters of hydraulic conductivities for real sites and model conceptualization

序号	名称	统计值	真实介质条件		概念模型介质条件
1	中等非均质	平均值(m/d)	0.5	模型模拟值作为观测值	0.5	模型模拟值将用于校正前、校正后比较
1	中等非均质	方差(m²/d²)	1.0		0.0
2	强非均质	平均值(m/d)	0.5		0.5
2	强非均质	方差(m²/d²)	2.0		0.0
3	弱非均质	平均值(m/d)	5.0	5.0
3	弱非均质	方差(m²/d²)	0.5	0.0

图2 地下水数值模型网格代码(a)、网格划分(b)、平面(c)和垂向(d)水均衡计算示意图

Fig.2 Schematic figures of grid code (a), grid discretization (b),plan view (c), and vertical water balance calculation (d) in groundwater numerical model

图3 校正前(a)、校正后(b)的地下水水头模拟与观测值散点密度图

Fig.3 Scatter-density distributions between simulated and observed hydraulic heads before (a) and after calibration (b)

图4 校正前后典型观测井O1(a)、O2(b)、O3(c)和O4(d)地下水水头变化曲线

Fig.4 Hydraulic head variation curves of typical observation wells O1 (a), O2 (b), O3 (c), and O4 (d) before and after correction

图5 校正前(a)和校正后(b)第2天地下水水头模拟误差空间分布对比

Fig.5 Comparison of the spatial distribution of hydraulic head simulation errors on the 2nd day before (a) and after (b) calibration

图6 强非均质(a)和弱非均质(b)条件下渗透系数对数值的空间分布

Fig.6 Spatial distribution of the logarithm of hydraulic conductivities under strong (a) and weak (b) heterogeneity conditions

图7 强非均质(a)和弱非均质(b)条件下误差校正后的模拟水头值与观测值散点密度图

Fig.7 Scatter-density distributions between simulated and observed hydraulic head values after error correction under strong (a) and weak (b) heterogeneity conditions

图8 强非均质(a)和弱非均质(b)条件下误差校正后的模拟地下水水头误差分布图

Fig.8 Error distribution maps of simulated hydraulic head after error correction under strong (a) and weak (b) heterogeneity conditions

图9 变流量单井开采时中等非均质(a)、强非均质(b)和弱非均质条件(c)下观测井O1的地下水水头动态变化

Fig.9 Changes of hydraulic head at observation well O1 under moderate (a), strong (b), and weak (c) heterogeneity conditions during variable-rate single-well pumping

图10 不同非均质变流量多井抽注条件下地下水水头和误差值空间分布图:中等非均质条件地下水水头真值(a)、校正前的误差(b)和校正后的误差(c);强非均质条件地下水水头真值(d)、校正前的误差(e)和校正后的误差(f);弱非均质条件地下水水头真值(g)、校正前的误差(h)和校正后的误差(i)

Fig.10 Spatial distribution maps of hydraulic head and error values under variable-rate multi-well pumping and injection conditions with different heterogeneity levels: true hydraulic head (a), error before (b) and after (c) correction under moderate heterogeneity, true hydraulic head (d), error before (e) and after (f) correction under strong heterogeneity, true hydraulic head (g), error before (h) and after (i) correction under weak heterogeneity

图11 不同抽注条件和强非均质条件地下水水头均方根误差变化

Fig.11 Variation of root mean square error of hydraulic head under strong heterogeneity conditions at different extraction scenarios

图12 强非均质变流量单井开采条件下误差校正前(a)和校正后(b)的模拟水头值与观测值的散点密度图

Fig.12 Scatter-density distributions between simulated and observed hydraulic head values before (a) and after (b) error correction under strong heterogeneity during variable-rate single-well pumping conditions

图13 不同校正点数量对观测井地下水水头模拟绝对误差(a)和2天后区域地下水水头绝对误差(b)的对比

Fig.13 Comparison of absolute errors in simulated hydraulic head at observation wells (a) and absolute errors in regional hydraulic head after 2 days (b) under different numbers of calibration points

图14 多井变流量抽注强非均质含水层中观测井O1(a)和O4(b)地下水水头变化曲线

Fig.14 Hydraulic head variation curves for observation wells O1 (a) and O4 (b) simulated by model under multi-well variable flow extraction conditions in strongly heterogeneous media

图15 3d后地下水水头模拟误差分布

Fig.15 Distribution of hydraulic head simulation errors after 3 days

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