Abstract
In the numerical simulation of groundwater flow, uncertainties often affect the precision of the simulation results. Stochastic and statistical approaches such as the Monte Carlo method, the Neumann expansion method and the Taylor series expansion, are commonly employed to estimate uncertainty in the final output. Based on the first-order interval perturbation method, a combination of the interval and perturbation methods is proposed as a viable alternative and compared to the well-known equal interval continuous sampling method (EICSM). The approach was realized using the GFModel (an unsaturated-saturated groundwater flow simulation model) program. This study exemplifies scenarios of three distinct interval parameters, namely, the hydraulic conductivities of six equal parts of the aquifer, their boundary head conditions, and several hydrogeological parameters (e.g. specific storativity and extraction rate of wells). The results show that the relative errors of deviation of the groundwater head extremums (RDGE) in the late stage of simulation are controlled within approximately ±5% when the changing rate of the hydrogeological parameter is no more than 0.2. From the viewpoint of the groundwater head extremums, the relative errors can be controlled within ±1.5%. The relative errors of the groundwater head variation are within approximately ±5% when the changing rate is no more than 0.2. The proposed method of this study is applicable to unsteady-state confined water flow systems.
Résumé
Dans la simulation numérique de l’écoulement des eaux souterraines, les incertitudes affectent souvent la précision des résultats de la simulation. Des approches stochastiques et statistiques, telles que la méthode de Monte Carlo, la méthode d’expansion de Neumann et l’expansion des séries de Taylor, sont couramment utilisées pour estimer l’incertitude dans le résultat final. Sur la base de la méthode de perturbation d’intervalle du premier ordre, une combinaison des méthodes d’intervalle et de perturbation est proposée comme une alternative viable et comparée à la méthode bien connue d’échantillonnage continu à intervalle égal (EICSM). L’approche a été réalisée à l’aide du programme GFModel (un modèle de simulation de l’écoulement des eaux souterraines non saturé-saturé). Cette étude illustre des scénarios de trois paramètres d’intervalle distincts, à savoir les conductivités hydrauliques de six parties égales de l’aquifère, leurs conditions de charge aux limites, et plusieurs paramètres hydrogéologiques (par ex. l’emmagasinement spécifique et le débit de pompage aux puits). Les résultats montrent que les erreurs relatives de déviation des extrêmes de charge des eaux souterraines (RDGE) dans la dernière phase de la simulation sont contrôlées à environ ±5% lorsque le taux de variation du paramètre hydrogéologique n’est pas supérieur à 0,2. Les erreurs relatives de la variation des charges de l’eau souterraine se situent dans une gamme d’environ ±5% lorsque le taux de variation ne dépasse pas 0.2. Du point de vue des extrêmes des charges hydrauliques des eaux souterraines, les erreurs relatives peuvent être contrôlées à ±1.5%. La méthode proposée dans cette étude est applicable aux systèmes d’écoulement d’eau confinés en régime transitoire.
Resumen
Las incertidumbres en la simulación numérica del flujo de aguas subterráneas suelen afectar a la precisión de los resultados. Los enfoques estocásticos y estadísticos, como el método de Montecarlo, el método de expansión de Neumann y la expansión en series de Taylor, se emplean habitualmente para estimar la incertidumbre en el resultado final. Basándose en el método de perturbación de intervalo de primer orden, se propone una combinación de los métodos de intervalo y perturbación como alternativa viable y se compara con el conocido método de muestreo continuo de intervalo equivalente (EICSM). El enfoque se realizó utilizando el programa GFModel (un modelo de simulación de flujo subterráneo no saturado). Este estudio ejemplifica escenarios de tres parámetros de intervalo distintos, a saber, las conductividades hidráulicas de seis partes iguales del acuífero, sus condiciones de carga límite y varios parámetros hidrogeológicos (por ejemplo, la estratificación específica y la tasa de extracción de los pozos). Los resultados muestran que los errores relativos de desviación de los valores extremos de las cargas de las aguas subterráneas (RDGE) en la última etapa de la simulación se controlan dentro de un margen aproximado de ±5% cuando la tasa de variación del parámetro hidrogeológico no es superior a 0.2. Desde el punto de vista de los límites de las aguas subterráneas, los errores relativos pueden controlarse dentro del ±1.5%. Los errores relativos de la variación de la carga de agua subterránea están dentro de aproximadamente ±5% cuando la tasa de cambio no es superior a 0.2. El método propuesto en este estudio es aplicable a los sistemas de flujo de agua confinada en estado estacionario.
摘要
地下水流的数值模拟中不确定性经常会影响模拟结果的精度。通常采用随机和统计方法(例如蒙特卡洛方法, Neumann展开法和泰勒级数展开法)来估计最终输出的不确定性。基于一阶区间摄动方法, 提出了区间和摄动方法相结合的方法, 并将其与众所周知的等间隔连续采样方法(EICSM)进行了比较。该方法是使用GFModel(饱和非饱和地下水流模拟模型)程序实现的。这项研究以三个不同的区间参数情景为例, 即含水层六个相同部分的渗透系数, 其边界水头状况以及几种水文地质参数(例如单位储水系数和井开采率)。结果表明, 当水文地质参数变化率不超过0.2时, 模拟后期的地下水位极值(RDGE)的相对误差控制在±5%以内。地下水头极值的相对误差可以控制在±1.5%以内。当变化率不超过0.2时, 地下水位变化的相对误差在±5%以内。本研究提出的方法适用于非稳态承压水流系统。
Resumo
Na simulação numérica do fluxo de água subterrânea, as incertezas geralmente afetam a precisão dos resultados da simulação. Abordagens estocásticas e estatísticas, como o método de Monte Carlo, o método de expansão de Neumann e a expansão em série de Taylor, são comumente empregadas para estimar a incerteza no produto final. Com base no método de perturbação de intervalo de primeira ordem, uma combinação dos métodos de intervalo e perturbação é proposta como uma alternativa viável e comparada ao conhecido método de amostragem contínua em intervalos iguais (MACINI). A abordagem foi realizada usando o programa GFModel (um modelo de simulação de fluxo subterrâneo não saturado). Este estudo exemplifica cenários de três parâmetros de intervalo distintos, a saber, as condutividades hidráulicas de seis partes iguais do aquífero, suas condições de queda de limite e vários parâmetros hidrogeológicos (por exemplo, armazenamento específico e taxa de extração de poços). Os resultados mostram que os erros relativos de desvio dos extremos da carga do lençol freático (RDGE) no estágio final da simulação são controlados em aproximadamente ± 5% quando a taxa de alteração do parâmetro hidrogeológico não é mais que 0.2. Do ponto de vista dos extremos da carga do lençol freático, os erros relativos podem ser controlados dentro de ± 1.5%. Os erros relativos da variação da altura do lençol freático estão dentro de aproximadamente ± 5% quando a taxa de mudança não é mais do que 0.2. O método proposto neste estudo é aplicável a sistemas de fluxo de água confinado em estado transiente.
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Data availability statement
The Groundwater Flow Model (GFModel) that supports the findings of this study is available from the corresponding author upon reasonable request, and interested parties should contact the corresponding author for further information.
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Funding
This work was supported by the National Key Research and Development Program of China (No. 2019YFC1805400) and the Fundamental Research Funds for the Central Universities (No.2020ZDPY0201), and the National Natural Science Foundation of China (No.41202179; No.51209109), and the Essential Science Indicators (ESI) Fund of Geosciences from the China University of Mining and Technology, and the project was funded by the Priority Academic Program Development of Jiangsu higher education institutions (PAPD).
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Dong, G., Wang, Y., Tian, J. et al. Groundwater head uncertainty analysis in unsteady-state water flow models using the interval and perturbation methods. Hydrogeol J 29, 1871–1883 (2021). https://doi.org/10.1007/s10040-021-02341-z
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DOI: https://doi.org/10.1007/s10040-021-02341-z