Error correction method for groundwater numerical models considering parameter uncertainty

doi:10.13745/j.esf.sf.2025.10.25

Abstract

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

CLC Number:

X523

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.

Figures/Tables 16

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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