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Inverse problem in hydrogeology

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Abstract

The state of the groundwater inverse problem is synthesized. Emphasis is placed on aquifer characterization, where modelers have to deal with conceptual model uncertainty (notably spatial and temporal variability), scale dependence, many types of unknown parameters (transmissivity, recharge, boundary conditions, etc.), nonlinearity, and often low sensitivity of state variables (typically heads and concentrations) to aquifer properties. Because of these difficulties, calibration cannot be separated from the modeling process, as it is sometimes done in other fields. Instead, it should be viewed as one step in the process of understanding aquifer behavior. In fact, it is shown that actual parameter estimation methods do not differ from each other in the essence, though they may differ in the computational details. It is argued that there is ample room for improvement in groundwater inversion: development of user-friendly codes, accommodation of variability through geostatistics, incorporation of geological information and different types of data (temperature, occurrence and concentration of isotopes, age, etc.), proper accounting of uncertainty, etc. Despite this, even with existing codes, automatic calibration facilitates enormously the task of modeling. Therefore, it is contended that its use should become standard practice.

Résumé

L’état du problème inverse des eaux souterraines est synthétisé. L’accent est placé sur la caractérisation de l’aquifère, où les modélisateurs doivent jouer avec l’incertitude des modèles conceptuels (notamment la variabilité spatiale et temporelle), les facteurs d’échelle, plusieurs inconnues sur différents paramètres (transmissivité, recharge, conditions aux limites, etc.), la non linéarité, et souvent la sensibilité de plusieurs variables d’état (charges hydrauliques, concentrations) des propriétés de l’aquifère. A cause de ces difficultés, le calibrage ne peut être séparé du processus de modélisation, comme c’est le cas dans d’autres cas de figure. Par ailleurs, il peut être vu comme une des étapes dans le processus de détermination du comportement de l’aquifère. Il est montré que les méthodes d’évaluation des paramètres actuels ne diffèrent pas si ce n’est dans les détails des calculs informatiques. Il est montré qu’il existe une large panoplie de techniques d ‹inversion : codes de calcul utilisables par tout-un-chacun, accommodation de la variabilité via la géostatistique, incorporation d’informations géologiques et de différents types de données (température, occurrence, concentration en isotopes, âge, etc.), détermination de l’incertitude. Vu ces développements, la calibration automatique facilite énormément la modélisation. Par ailleurs, il est souhaitable que son utilisation devienne une pratique standardisée.

Resumen

Se sintetiza el estado del problema inverso en aguas subterráneas. El énfasis se ubica en la caracterización de acuíferos, donde los modeladores tienen que enfrentar la incertidumbre del modelo conceptual (principalmente variabilidad temporal y espacial), dependencia de escala, muchos tipos de parámetros desconocidos (transmisividad, recarga, condiciones limitantes, etc), no linealidad, y frecuentemente baja sensibilidad de variables de estado (típicamente presiones y concentraciones) a las propiedades del acuífero. Debido a estas dificultades, no puede separarse la calibración de los procesos de modelado, como frecuentemente se hace en otros campos. En su lugar, debe de visualizarse como un paso en el proceso de entendimiento del comportamiento del acuífero. En realidad, se muestra que los métodos reales de estimación de parámetros no difieren uno del otro en lo esencial, aunque sí pueden diferir en los detalles computacionales. Se discute que existe amplio espacio para la mejora del problema inverso en aguas subterráneas: desarrollo de códigos amigables al usuario, acomodamiento de variabilidad a través de geoestadística, incorporación de información geológica y diferentes tipos de datos (temperatura, presencia y concentración de isótopos, edad, etc), explicación apropiada de incertidumbre, etc. A pesar de esto, aún con los códigos existentes, la calibración automática facilita enormemente la tarea de modelado. Por lo tanto, se sostiene que su uso debería de convertirse en práctica standard.

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The final manuscript benefitted from comments by Mary Hill, Matt Tonkin and Johan Valstar

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  1. School of Civil Engineering, Technical University of Catalonia, 1-3, Jordi Girona Street, Building D2, 08034, Barcelona, Spain

    Jesús Carrera, Andrés Alcolea, Agustín Medina, Juan Hidalgo & Luit J. Slooten

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  1. Jesús Carrera
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Carrera, J., Alcolea, A., Medina, A. et al. Inverse problem in hydrogeology. Hydrogeol J 13, 206–222 (2005). https://doi.org/10.1007/s10040-004-0404-7

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