Reverse flow routing in open channels: A Bayesian Geostatistical Approach

D’Oria, Marco; Tanda, Maria Giovanna

doi:10.1016/j.jhydrol.2012.06.055

Cited by 28 publications

(17 citation statements)

References 15 publications

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“…Among many inversion approaches, the Bayesian quasi‐linear geostatistical approach [ Kitanidis , ] is a versatile method to estimate unknown subsurface parameters and quantify the corresponding uncertainty rigorously. The geostatistical approach has been applied to many engineering applications such as contaminant source identification [ Snodgrass and Kitanidis , ], historical groundwater contaminant distribution estimation [ Michalak and Kitanidis , ], tracer data inversion [ Nowak and Cirpka , ; Fienen et al ., ], hydraulic tomography [ Li et al ., ; Cardiff et al ., ; Cardiff and Barrash , ], upstream flow estimation in rivers [ D'Oria and Tanda , ], atmospheric modeling [ Yadav et al ., ; Miller et al ., ], and others.…”

Section: Introductionmentioning

confidence: 99%

Large‐scale hydraulic tomography and joint inversion of head and tracer data using the Principal Component Geostatistical Approach (PCGA)

Lee

Kitanidis

2014

Water Resources Research

112

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The stochastic geostatistical inversion approach is widely used in subsurface inverse problems to estimate unknown parameter fields and corresponding uncertainty from noisy observations. However, the approach requires a large number of forward model runs to determine the Jacobian or sensitivity matrix, thus the computational and storage costs become prohibitive when the number of unknowns, m, and the number of observations, n increase. To overcome this challenge in large-scale geostatistical inversion, the Principal Component Geostatistical Approach (PCGA) has recently been developed as a ''matrixfree'' geostatistical inversion strategy that avoids the direct evaluation of the Jacobian matrix through the principal components (low-rank approximation) of the prior covariance and the drift matrix with a finite difference approximation. As a result, the proposed method requires about K runs of the forward problem in each iteration independently of m and n, where K is the number of principal components and can be much less than m and n for large-scale inverse problems. Furthermore, the PCGA is easily adaptable to different forward simulation models and various data types for which the adjoint-state method may not be implemented suitably. In this paper, we apply the PCGA to representative subsurface inverse problems to illustrate its efficiency and scalability. The low-rank approximation of the large-dimensional dense prior covariance matrix is computed through a randomized eigen decomposition. A hydraulic tomography problem in which the number of observations is typically large is investigated first to validate the accuracy of the PCGA compared with the conventional geostatistical approach. Then the method is applied to a largescale hydraulic tomography with 3 million unknowns and it is shown that underlying subsurface structures are characterized successfully through an inversion that involves an affordable number of forward simulation runs. Lastly, we present a joint inversion of head and tracer test data using MODFLOW and MT3DMS as coupled black-box forward simulation solvers. These applications demonstrate the advantages of the PCGA, i.e., the scalability to high-dimensional inverse problems and the ability to utilize multiple forward models as black boxes.

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Section: Introductionmentioning

confidence: 99%

Large‐scale hydraulic tomography and joint inversion of head and tracer data using the Principal Component Geostatistical Approach (PCGA)

Lee

Kitanidis

2014

Water Resources Research

112

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“…Koussis et al (2012) reoriented the Muskingum routing scheme to step back sequentially; they found also in this case grid design to be important, although that routing scheme is more robust than reverse solvers of the St. Venant equations. D' Oria andTanda (2012) andD'Oria et al (2014) determined the upstream hydrograph via a geostatistical Bayesian optimisation approach applied to the equations of St. Venant that does not entail a back-stepping procedure. Szöllósi-Nagy (1987) treated the related case of optimal flood control for minimising downstream flood damage and Leonhardt et al (2014) reversecalculated the rainfall causing an observed flow event.…”

Section: Reverse Routing Of Flood Wavesmentioning

confidence: 99%

Reverse flood and pollution routing with the lag-and-route model

Koussis

Mazi

2016

Hydrological Sciences Journal

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“…These references are by no means exhaustive and serve only to highlight the importance of the overall problem of parameter estimation. The Bayesian Geostatistical Approach (BGA) [13] has become popular for estimating aquifer hydraulic parameters [14][15][16], inflow time series to river sections [17,18] or flow hydrograph in different contexts [19,20] and has been implemented in a freeware software named bgaPEST [21].…”

Section: Introductionmentioning

confidence: 99%

Characterization of Hydraulic Heterogeneity of Alluvial Aquifer Using Natural Stimuli: A Field Experience of Northern Italy

D’Oria

Zanini

2019

Water

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This study investigates the hydraulic heterogeneity of the alluvial aquifer underneath the dam and the stilling basin of a flood protection structure in Northern Italy. The knowledge of the interactions between the water in the reservoir upstream of the dam and the groundwater levels is relevant for the stability of the structure. A Bayesian Geostatistical Approach (BGA) combined with a groundwater flow model developed in MODFLOW 2005 has been used to estimate the hydraulic conductivity (HK) field in a context of a highly parameterized inversion. The transient hydraulic heads collected in 14 monitoring points represent the calibration dataset; these observations are the results of the hydraulic stresses induced by the variations of the lake stage upstream of the dam (natural stimuli). The geostatistical inversion was performed by means of a computer code, bgaPEST, developed according to the free PEST software concept. The results of the inversion show a moderate degree of heterogeneity of the estimated HK field, consistent with the alluvial nature of the aquifer and the other information available. The calibrated groundwater model is useful for simulating the interactions between the reservoir and the studied aquifer under different flood scenarios and for forecasting the hydraulic head levels due to strong flood events. The use of natural stimuli is useful for obtaining information for aquifer heterogeneity characterization.

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Reverse flow routing in open channels: A Bayesian Geostatistical Approach

Cited by 28 publications

References 15 publications

Large‐scale hydraulic tomography and joint inversion of head and tracer data using the Principal Component Geostatistical Approach (PCGA)

Large‐scale hydraulic tomography and joint inversion of head and tracer data using the Principal Component Geostatistical Approach (PCGA)

Reverse flood and pollution routing with the lag-and-route model

Characterization of Hydraulic Heterogeneity of Alluvial Aquifer Using Natural Stimuli: A Field Experience of Northern Italy

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