PUMA publications for /group/simtech/randomThu May 18 11:32:12 CEST 2017{3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA}{SIAM JOURNAL ON SCIENTIFIC COMPUTING}{4}{A2209-A2231}{UNCERTAINTY QUANTIFICATION FOR HYPERBOLIC CONSERVATION LAWS WITH FLUX COEFFICIENTS GIVEN BY SPATIOTEMPORAL RANDOM FIELDS}{Article}{38}{2016}hyperbolic field; field} finite Carlo quantification; Monte method; differential uncertainty random Ornstein-Uhlenbeck {stochastic volume flux equation; spatiotemporal Gaussian partial process; function; {In this paper hyperbolic partial differential equations (PDEs) with random coefficients are discussed. We consider the challenging problem of flux functions with coefficients modeled by spatiotemporal random fields. Those fields are given by correlated Gaussian random fields in space and Ornstein-Uhlenbeck processes in time. The resulting system of equations consists of a stochastic differential equation for each random parameter coupled to the hyperbolic conservation law. We de fine an appropriate solution concept in this setting and analyze errors and convergence of discretization methods. A novel discretization framework, based on Monte Carlo finite volume methods, is presented for the robust computation of moments of solutions to those random hyperbolic PDEs. We showcase the approach on two examples which appear in applications-the magnetic induction equation and linear acoustics both with a spatiotemporal random background velocity field.}Thu May 18 11:32:12 CEST 2017{2000 FLORIDA AVE NW, WASHINGTON, DC 20009 USA}{WATER RESOURCES RESEARCH}{JUN}{6}{4504-4526}{Gaussian and non-Gaussian inverse modeling of groundwater flow using copulas and random mixing}{Article}{52}{2016}random modeling; non-Gaussianity} mixing; {inverse copula; {This paper presents a new copula-based methodology for Gaussian and non-Gaussian inverse modeling of groundwater flow. The presented approach is embedded in a Monte Carlo framework and it is based on the concept of mixing spatial random fields where a spatial copula serves as spatial dependence function. The target conditional spatial distribution of hydraulic transmissivities is obtained as a linear combination of unconditional spatial fields. The corresponding weights of this linear combination are chosen such that the combined field has the prescribed spatial variability, and honors all the observations of hydraulic transmissivities. The constraints related to hydraulic head observations are nonlinear. In order to fulfill these constraints, a connected domain in the weight space, inside which all linear constraints are fulfilled, is identified. This domain is defined analytically and includes an infinite number of conditional fields (i.e., conditioned on the observed hydraulic transmissivities), and the nonlinear constraints can be fulfilled via minimization of the deviation of the modeled and the observed hydraulic heads. This procedure enables the simulation of a great number of solutions for the inverse problem, allowing a reasonable quantification of the associated uncertainties. The methodology can be used for fields with Gaussian copula dependence, and fields with specific non-Gaussian copula dependence. Further, arbitrary marginal distributions can be considered.}