NDLI: Groundwater parameter estimation using the ensemble Kalman filter with localization

Content Provider	Springer Nature Link
Author	Nan, Tongchao Wu, Jichun
Copyright Year	2010
Abstract	The ensemble Kalman filter (EnKF), an efficient data assimilation method showing advantages in many numerical experiments, is deficient when used in approximating covariance from an ensemble of small size. Implicit localization is used to add distance-related weight to covariance and filter spurious correlations which weaken the EnKF’s capability to estimate uncertainty correctly. The effect of this kind of localization is studied in two-dimensional (2D) and three-dimensional (3D) synthetic cases. It is found that EnKF with localization can capture reliably both the mean and variance of the hydraulic conductivity field with higher efficiency; it can also greatly stabilize the assimilation process as a small-size ensemble is used. Sensitivity experiments are conducted to explore the effect of localization function format and filter lengths. It is suggested that too long or too short filter lengths will prevent implicit localization from modifying the covariance appropriately. Steep localization functions will greatly disturb local dynamics like the 0-1 function even if the function is continuous; four relatively gentle localization functions succeed in avoiding obvious disturbance to the system and improve estimation. As the degree of localization of the L function increases, the parameter sensitivity becomes weak, making parameter selection easier, but more information may be lost in the assimilation process.Le filtre de Kalman d’ensemble (EnKF), une méthode efficace de traitement des données présentant des avantages dans de nombreux cas numériques, est déficiente quand elle est utilisée pour estimer la covariance d’un ensemble de petite taille. La localisation implicite est utilisée pour ajouter le poids pondéré de la distance à la covariance et pour filtrer les corrélations erronées qui affaiblissent la capacité du EnKF à estimer l’incertitude correctement. L’effet de ce type de localisation est étudié dans des cas synthétiques bi et tri-dimensionnels. On trouve que le EnKF avec localisation peut approcher de façon fiable à la fois la moyenne et la variance de la conductivité hydraulique avec une efficacité plus grande; il peut aussi grandement stabiliser le processus de traitement quand un ensemble de petite dimension est considéré. Des expériences de sensibilité ont été conduites pour explorer l’effet du format de la fonction localisation et longueur de filtre. On suggère que des longueurs de filtre trop grandes ou trop petites empêcheront à la localisation implicite de modifier la covariance de façon appropriée. Des fonctions de localisation raides telle la fonction 0-1 perturberont grandement la dynamique locale même si la fonction est continue; quatre fonctions de localisation relativement douces réussissent à éviter les perturbations évidentes du système et améliorent l’estimation. Lorsque le degré de localisation de la fonction L s’accroît, le paramètre sensibilité devient faible, rendant la sélection des paramètres plus aisée, mais d‘avantage d’informations peuvent être perdues dans le processus de traitement.El conjunto del filtro de Kalman (EnKF), un método eficiente de asimilación de datos que muestra ventajas en muchos experimentos numéricos, es deficiente cuando es usado en la aproximación de la covarianza a partir de un conjunto de pequeños tamaños. Se usa la localización implícita para sumar el peso relacionado con la covarianza y a las correlaciones espurias que debilitan la capacidad EnKF’s para estimar correctamente la incerteza. Se estudia este tipo de localización en casos sintéticos bi y tridimensional. Se encuentra que EnKF con localización puede capturar confiablemente tanto el promedio como la varianza del campo de conductividad hidráulica con una mayor, puede también estabilizar grandemente el proceso de asimilación cuando se usa un conjunto de pequeño tamaño. Se llevan a cabo experimentos de sensibilidad para explorar el efecto del formato de la función de la localización y la longitud de los filtros. Se sugiere que las longitudes de filtros demasiado cortas o demasiado largas impiden la localización implícita a partir de la modificación apropiada de la covarianza. Funciones de localización pronunciada perturbarán grandemente la dinámica local como la función 0-1 aún si la función es continua, cuatro funciones de localización relativamente suaves tienen éxito en evitar la perturbación obvia al sistema y mejoran la estimación. A medida que el grado de localización de la función L se incrementa, la sensibilidad de los parámetros se convierten en débiles, haciendo más fácil la selección de los parámetros, pero una mejor información puede ser perdida en el proceso de asimilación.集合卡尔曼滤波 (EnKF) 是一种有效的数据同化方法, 它在数值实验中很有优势, 但在小尺度集合的协方差估计上存在缺陷。隐式定位用于增加协方差中与距离相关的权重, 并过滤掉减弱EnKF准确识别不确定性能力的伪相关。在二维和三维综合情况下对这种定位的效果进行研究, 表明定位EnKF可以可靠高效地获取渗透系数的平均值和方差, 并应用小尺度集合大大地稳固同化过程。应用敏感性实验对定位函数式及滤波长度的有效性进行研究。滤波太长或太短会影响隐式定位对协方差的适当修正。大梯度的定位函数会较明显地干扰局部动力学, 如0-1函数, 即使函数是连续的; 四个相对较和缓的定位函数成功地避免了对系统及参数估计的明显干扰。随着L函数定位度的增加, 参数敏感性变弱, 可使参数选取变的更容易, 但在同化过程中可能会丢失更多的信息。O filtro de Kalman (EnKF), um método de combinação de dados eficiente que apresenta vantagens em muitas aplicações numéricas, é deficiente quando usado na aproximação da covariância a um conjunto pequeno de dados. A localização implícita é usada para aumentar o peso da distância da covariância e filtrar correlações espúrias que debilitam a capacidade do EnKF para estimar a incerteza correctamente. O efeito desse tipo de localização é estudado em casos artificiais a duas e três dimensões. Verifica-se que o EnKF com localização pode capturar de forma confiável a média e a variância do campo da condutividade hidráulica com maior eficiência, mas também pode estabilizar grandemente o processo de combinação quando usado um conjunto pequeno de dados. São realizados exercícios de sensibilidade no sentido de explorar o efeito do formato da função de localização e comprimento do filtro. Sugere-se que comprimentos de filtro muito longos ou muito curtos impedem a localização implícita de modificar a covariância de forma apropriada. Funções de localização exageradas perturbarão grandemente as dinâmicas locais, como a função 0-1, mesmo se a função é contínua; quatro funções de localização relativamente suaves são um êxito em evitar perturbações óbvias para o sistema e melhorar a estimação. Como o grau de localização da função L aumenta, a sensibilidade dos parâmetros torna-se fraca, permitindo fazer uma selecção de parâmetros mais fácil, mas também mais informações podem ser perdidas no processo de combinação.
Starting Page	547
Ending Page	561
Page Count	15
File Format	PDF
ISSN	14312174
Journal	Hydrogeology Journal
Volume Number	19
Issue Number	3
e-ISSN	14350157
Language	Spanish
Publisher	Springer-Verlag
Publisher Date	2010-11-24
Publisher Institution	International Association of Hydrogeologists
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Groundwater flow Inverse modeling Ensemble Kalman filter Localization Distance-dependent function Geology Waste Water Technology Water Pollution Control Water Management Aquatic Pollution Hydrogeology
Content Type	Text
Resource Type	Article
Subject	Earth and Planetary Sciences Water Science and Technology

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