A solution to the inverse problem in groundwater hydrology based on Kalman filtering

Ferraresi, M.; Todini, E.; Vignoli, R.

doi:10.1016/s0022-1694(96)80025-4

Cited by 26 publications

(9 citation statements)

References 9 publications

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“…Key algorithmic considerations in the implementation of a particle filter include how many particles to use and what type of sampling/resampling procedures to invoke in each iteration, design choices which are application-dependent to the extent that they are entwined with properties of the model's functions f and h as well as the distributions characterizing the system disturbances d k , measurement noises v k and initial state x 0 . The reader interested in more details is encouraged to consult available tutorial papers and texts (Arulampalam et al 2002;Doucet and Johansen 2011). The following sections present a particle filter that solves the parameter estimation problems for both non-leaky and leaky unsteady aquifer cases.…”

Section: General Solution Methodologymentioning

confidence: 99%

“…Recent work along these lines in the geoscience literature includes Noh et al (2011), studying surface water hydrologic problems, and Pasetto et al (2012), comparing the performance of the ensemble Kalman filter and a particle filter for a synthetic hydrogeologic case. Particle filtering is especially popular for object tracking and robotic navigation problems in electrical engineering and computer science, where numerous survey papers are now available (Arulampalam et al 2002;Doucet and Johansen 2011).…”

Section: Technical Rationalementioning

confidence: 99%

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Particle Filters to Estimate Properties of Confined Aquifers

Field

Tavrisov

Brown

et al. 2016

Water Resour Manage

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Involving a limited resource, the assessment of groundwater aquifers is of utmost importance. A key component of any such assessment is the determination of key properties that permit water resource managers to estimate aquifer drawdown and safe yield. This paper presents a particle filtering approach to estimate aquifer properties from transient data sets, leveraging recently published analytically-derived models for confined aquifers and using sample-based approximations of underlying probability distributions. The approach is examined experimentally through validation against three common aquifer testing problems: determination of (i) transmissivity and storage coefficient from non-leaky confined aquifer performance tests, (ii) transmissivity, storage coefficient, and vertical hydraulic conductivity from leaky confined aquifer performance tests, and (iii) transmissivity and storage coefficient from non-leaky confined aquifer performance tests with noisy data and boundary effects. On the first two well-addressed problems, the results using the particle filter approach compare favorably to those obtained by other published methods. The results to the third problem, which the particle filter approach can tackle more naturally than the previously-published methods, underscore the flexibility of particle filtering and, in turn, the promise such methods offer for a myriad of other geoscience problems.

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Section: General Solution Methodologymentioning

confidence: 99%

Section: Technical Rationalementioning

confidence: 99%

Particle Filters to Estimate Properties of Confined Aquifers

Field

Tavrisov

Brown

et al. 2016

Water Resour Manage

View full text Add to dashboard Cite

show abstract

“…In groundwater hydrology, sequential data assimilation and Kalman filter methods have long been used (e.g., Ferraresi et al, 1996;Eppstein and Dougherty, 1996;Hantush and Mariño, 1997). Particularly, and increasingly, popular is the ensemble Kalman filter (EnKF) (Evensen, 1994) or versions thereof.…”

Section: Erdal and O A Cirpka: Joint Inference Of Recharge And Cmentioning

confidence: 99%

Joint inference of groundwater–recharge and hydraulic–conductivity fields from head data using the ensemble Kalman filter

Erdal¹,

Cirpka²

2016

Hydrol. Earth Syst. Sci.

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Abstract.Regional groundwater flow strongly depends on groundwater recharge and hydraulic conductivity. Both are spatially variable fields, and their estimation is an ongoing topic in groundwater research and practice. In this study, we use the ensemble Kalman filter as an inversion method to jointly estimate spatially variable recharge and conductivity fields from head observations. The success of the approach strongly depends on the assumed prior knowledge. If the structural assumptions underlying the initial ensemble of the parameter fields are correct, both estimated fields resemble the true ones. However, erroneous prior knowledge may not be corrected by the head data. In the worst case, the estimated recharge field resembles the true conductivity field, resulting in a model that meets the observations but has very poor predictive power. The study exemplifies the importance of prior knowledge in the joint estimation of parameters from ambiguous measurements.

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“…A few examples are reviewed in the following. Ferraresi et al [11] estimated hydraulic conductivities and pressure heads at a case study site applying the KF to a linearized Darcy flow model. Katul et al [21] and Cahill et al [4] modeled the field-scale drainage by Richard's equation, assimilating the measured time serial potential data into the model by EKF, while searching for optimal parameters in the hydraulic conductivity function using a merit function derived from the EKF.…”

Section: Data Assimilationmentioning

confidence: 99%

“…Following the idea of calculating R kjkÀ1 and R kjk ( [11]), since Eðz k Þ ¼ 0, Covðz k Þ and Covðx k Àx kjkÀ1 ;z k Þ can be calculated by incorporating perturbation of observations:…”

Section: Data Assimilation Frameworkmentioning

confidence: 99%