@article{fdi:010071366,
  title = {{D}imensionality reduction for efficient {B}ayesian estimation of groundwater flow in strongly heterogeneous aquifers},
  author = {{M}ara, {T}. {A}. and {F}ajraoui, {N}. and {G}uadagnini, {A}. and {Y}ounes, {A}nis},
  editor = {},
  language = {{ENG}},
  abstract = {{W}e focus on the {B}ayesian estimation of strongly heterogeneous transmissivity fields conditional on data sampled at a set of locations in an aquifer. {L}og-transmissivity, {Y}, is modeled as a stochastic {G}aussian process, parameterized through a truncated {K}arhunen-{L}o{S}ve ({KL}) expansion. {W}e consider {Y} fields characterized by a short correlation scale as compared to the size of the observed domain. {T}hese systems are associated with a {KL} decomposition which still requires a high number of parameters, thus hampering the efficiency of the {B}ayesian estimation of the underlying stochastic field. {T}he distinctive aim of this work is to present an efficient approach for the stochastic inverse modeling of fully saturated groundwater flow in these types of strongly heterogeneous domains. {T}he methodology is grounded on the construction of an optimal sparse {KL} decomposition which is achieved by retaining only a limited set of modes in the expansion. {M}ode selection is driven by model selection criteria and is conditional on available data of hydraulic heads and (optionally) {Y}. {B}ayesian inversion of the optimal sparse {KLE} is then inferred using {M}arkov {C}hain {M}onte {C}arlo ({MCMC}) samplers. {A}s a test bed, we illustrate our approach by way of a suite of computational examples where noisy head and {Y} values are sampled from a given randomly generated system. {O}ur findings suggest that the proposed methodology yields a globally satisfactory inversion of the stochastic head and {Y} fields. {C}omparison of reference values against the corresponding {MCMC} predictive distributions suggests that observed values are well reproduced in a probabilistic sense. {I}n a few cases, reference values at some unsampled locations (typically far from measurements) are not captured by the posterior probability distributions. {I}n these cases, the quality of the estimation could be improved, e.g., by increasing the number of measurements and/or the threshold for the selection of {KL} modes.},
  keywords = {{H}eterogeneous porous media ; {S}tochastic inverse modeling ; {K}arhunen-{L}oeve ; expansion ; {M}arkov {C}hain {M}onte {C}arlo},
  booktitle = {},
  journal = {{S}tochastic {E}nvironmental {R}esearch and {R}isk {A}ssessment},
  volume = {31},
  numero = {9},
  pages = {2313--2326},
  ISSN = {1436-3240},
  year = {2017},
  DOI = {10.1007/s00477-016-1344-1},
  URL = {https://www.documentation.ird.fr/hor/fdi:010071366},
}