An efficient simulation-optimization coupling for management of coastal aquifers

Couplage efficace simulation et optimisation pour la gestion des aquifères côtiers

Un acoplamiento eficiente de simulación y de optimización para la gestión de los acuíferos costeros

沿海含水层管理一个有效率的模拟-最优化耦合

Um acoplamento simulação-otimização eficiente para gerenciamento de aquíferos costeiros

Abstract

Seawater intrusion in coastal aquifers is a major environmental problem and efficient tools are needed to assist decision making. Decision tools are often simulation models (which evaluate probable actions) combined with optimization algorithms (which search for optimum management decisions). A coupling between simulation models and optimization algorithms for management of coastal aquifers is presented. The simulation models are based on the sharp-interface approximation where the decision variables do not affect the discretized system matrix. For such problems, a transformation of the system matrix prior to optimization is proposed which supports rapid solution of the linear system of equations during the optimization stage, for different values of decision variables. The method is applied to a hypothetical simulation of a coastal aquifer on the Greek island of Santorini, where the proposed simulation-optimization coupling method is employed to maximize pumping rates subject to environmental constraints that protect the aquifer from seawater intrusion. Various packages were tested in order to investigate their efficiency in solving the linear system pertinent to the case study. The proposed method, based on coupling of equations, is found to be very efficient in terms of computational cost. In particular, for the problem examined, it is at least 50 times faster than standard methods, depending on the grid size.

Résumé

L’intrusion d’eau salée dans les aquifères côtiers est un problème environnemental majeur et des outils efficaces sont nécessaires pour aider à la prise de décision. Les outils d’aide à la décision sont souvent des modèles de simulation (qui évaluent les actions probables) associés à des algorithmes d’optimisation (qui recherchent des décisions de gestion optimales). Un couplage de modèles de simulation à des algorithmes d’optimisation pour la gestion des aquifères côtiers est présenté. Les modèles de simulation sont basés sur l’approximation de l’interface abrupte entre eaux douces et eaux salées pour lequel les variables utiles pour la décision n’affectent par la matrice du système discrétisé. Pour de tels problèmes, une transformation de la matrice du système avant optimisation est proposée, qui permet une solution rapide du système linéaire des équations lors de la phase d’optimisation, pour différentes valeurs de variables utiles pour la décision. La méthode est appliquée à la simulation hypothétique d’un aquifère côtier de l’île grecque de Santorin, pour lequel la méthode proposée de couplage simulation-optimisation est employée pour maximiser les débits de pompage sujets aux contraintes environnementales qui protègent l’aquifère d’une intrusion d’eau de mer. Différentes combinaisons ont été testées afin d’étudier leur efficacité dans la résolution du système linéaire pertinent pour le cas d’étude. La méthode proposée, basée sur le couplage des équations, est très efficace en termes de temps de calcul. En particulier, pour le problème examine, il est au moins 50 fois plus rapide que les méthodes classiques, fonction de la taille de la grille considérée.

Resumen

La intrusión marina en los acuíferos costeros es un problema ambiental importante y se necesitan herramientas eficientes para ayudar a la toma de decisiones. Las herramientas de decisión son a menudo modelos de simulación (que evalúan las probables acciones) combinados con algoritmos de optimización (que buscan las decisiones de óptimas de gestión). Se presenta un acoplamiento entre los modelos de simulación y algoritmos de optimización para la gestión de los acuíferos costeros. Los modelos de simulación se basan en la aproximación de una interfaz marcada donde las variables de decisión no afectan a la matriz del sistema discretizado. Para este tipo de problemas, se propone una transformación de la matriz del sistema antes de la optimización, que apoya una solución rápida del sistema lineal de ecuaciones durante la etapa de optimización, para diferentes valores de variables de decisión. El método se aplica a una simulación hipotética de un acuífero costero en la isla griega de Santorini, donde se emplea el método de acoplamiento de simulación y de optimización propuesto para maximizar las tasas de bombeo con limitaciones medioambientales que protegen el acuífero de la intrusión de agua de mar. Se ensayaron varios paquetes para investigar su eficiencia en la resolución del sistema lineal pertinente para el caso de estudio. Se encuentra que el método propuesto, sobre la base del acoplamiento de ecuaciones, es muy eficiente en términos de costo computacional. En particular, el problema examinado, es al menos 50 veces más rápido que los métodos estándar, dependiendo del tamaño de cuadrícula.

摘要

沿海含水层的海水入侵是一个主要的环境问题,需要有效率的工具来支持决策。决策工具通常是模拟模型(评价可能的行为)结合最优化算法(寻找最优化管理决策)。本文展示了沿海含水层管理模拟模型和最优化算法之间的耦合。模拟模型基于截面近似值,在截面上,决策变量不影响离散系统基质。针对这样的问题,提出了最优化前系统基质的转化,转化对不同的决策变量值在最优化阶段支撑公式线性系统的快速解决。方法应用于希腊圣托里尼岛一个沿海含水层的假定模拟中,在这个地方,采用所述的模拟-最优化耦合方法提出了确保含水层免受海水入侵情况下的最大抽水量。实验了各种方案以调查每个方案在解决与实例研究有关的线性系统中的效率。所述的方法基于公式的耦合,发现在计算费用上非常有效率。尤其是对于检查的问题,至少比标准方法快50倍,这取决于网格的大小。

Resumo

Intrusão de água marinha em aquíferos costeiros é um importante problema ambiental e ferramentas eficientes para assessorar a tomada de decisão são necessários. Ferramentas de decisão são geralmente modelos de simulação (que avaliam ações prováveis) combinados com algoritmos de otimização (que procuram por decisões de gerenciamento ótimas). Um acoplamento entre modelos de simulação e algoritmos de otimização para o gerenciamento de aquíferos costeiros é apresentado. Os modelos de simulação são baseados na aproximação da interface abrupta onde as variáveis de decisão não afetam o sistema matricial discretizado. Para tais problemas, uma transformação no sistema matricial antes da otimização é proposta, a qual suporta soluções rápidas do sistema de equações lineares durante o estágio de otimização, para diferentes valores das variáveis de decisão. O método é aplicado a uma simulação hipotética de um aquífero costeiro na ilha Grega de Santorini, onde o método de acoplamento simulação-otimização é empregado para maximizar a taxas de bombeamento sujeitas a restrições ambientais que protegem o aquífero da intrusão de água do mar. Vários pacotes foram testados com o propósito de investigar suas eficiências em solucionar o sistema linear pertinente à cada estudo de caso. O método proposto, baseado no acoplamento de equações, é considerado muito eficiente em termos de custos computacionais. Em particular, para o problema examinado, isso é ao menos 50 vezes mais rápido do que métodos padrões, dependendo do tamanho da malha.

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Acknowledgements

This work was partially supported by the California Department of Food and Agriculture under agreement No. FREP 11-0301.

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Correspondence to George Kourakos.

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Published in the theme issue “Optimization for Groundwater Characterization and Management”

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Kourakos, G., Mantoglou, A. An efficient simulation-optimization coupling for management of coastal aquifers. Hydrogeol J 23, 1167–1179 (2015). https://doi.org/10.1007/s10040-015-1293-7

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Keywords

  • Coastal aquifers
  • Seawater intrusion
  • Groundwater management
  • Optimization
  • Greece