interpolation of precipitation under topographic influence at different time scales 1 in this paper new methodologies for interpolating rainfall data in individual time intervals ranging from a day to a year using gaussian copulas and unsymmetrical v copulas with a variety of treatments of altitude as an exogenous variable are described for shorter time aggregations zeros were treated as censored variables for each selected time step the marginal distributions of precipitation amounts were modeled using nonparametric density estimators while the spatial dependence structures were estimated using a maximum likelihood methodology the methodology was compared to other common geostatistical interpolators such as ordinary kriging and external drift kriging several measures of bias and error structure have been used to assess the efficacy of the methods in a range of comparative split sampling studies the data set chosen for the study comprises daily precipitation time series over 41 years in three regions in germany measured at more than 1200 locations over a large area 126 144 km2 among the many findings in the paper the ones that stand out are i correlation between precipitation and topography increases with the length of time interval and is significantly improved by directional smoothing of topography ii the copula methods are superior to kriging methods in terms of quality of interpolation bias and uncertainty estimation iii the treatment of zeros as censored variables improves interpolation quality for daily and pentad values monthly and annual data in this region present no dry periods iv the copula methods yield full conditional distributions of estimates at a target point in an interval improving substantially on the simple uncertainty estimates derived from kriging and v the gauss copula in particular performs best overall in terms of computational efficiency combined with useful error profiles in the interpolations and of all methods is the most realistic in its error estimates

stochastic reconstruction and interpolation of precipitation fields using combined information of commercial microwave links and rain gauges for the reconstruction and interpolation of precipitation fields we present the application of a stochastic approach called random mixing generated fields are based on a data set consisting of rain gauge observations and path averaged rain rates estimated using commercial microwave link cml derived information precipitation fields are received as linear combination of unconditional spatial random fields where the spatial dependence structure is described by copulas the weights of the linear combination are optimized such that the observations and the spatial structure of the precipitation observations are reproduced the innovation of the approach is that this strategy enables the simulation of ensembles of precipitation fields of any size each ensemble member is in concordance with the observed path averaged cml derived rain rates and additionally reflects the observed rainfall variability along the cml paths the ensemble spread allows additionally an estimation of the uncertainty of the reconstructed precipitation fields the method is demonstrated both for a synthetic data set and a real world data set in south germany while the synthetic example allows an evaluation against a known reference the second example demonstrates the applicability for real world observations generated precipitation fields of both examples reproduce the spatial precipitation pattern in good quality a performance evaluation of random mixing compared to ordinary kriging demonstrates an improvement of the reconstruction of the observed spatial variability random mixing is concluded to be a beneficial new approach for the provision of precipitation fields and ensembles of them in particular when different measurement types are combined

a bayesian mixture modeling approach for flow conditioned multiple point statistical facies simulation from uncertain training images 1 multiple point statistics mps provides a systematic approach for pattern based simulation of complex discrete geologic objects from a conceptual training image ti as prior model the ti contains the general shape geometry and connectivity structures of complex patterns and encodes the related higher order spatial statistics of the expected features conditioning mps simulated facies on flow data poses a challenging nonlinear inverse problem for estimating discrete parameter fields additionally the pattern imitating nature of mps simulation implies that the simulated facies inherit the spatial structure of the features in the ti since tis are constructed from uncertain geologic information and imperfect assumptions the resulting simulated facies may fail to predict the correct flow and transport behavior in the subsurface environment it is therefore prudent to account for the full range of structural variability in describing the geologic facies distribution by considering multiple tis here we present a bayesian mixture model for adaptive and efficient sampling of conditional facies from multiple uncertain tis we partition the posterior distribution of facies into individual conditional densities of the tis and estimate the corresponding mixture weights from the likelihood function for each ti to implement the conditional sampling we apply a recently developed ensemble kalman filter enkf based probability conditioning method whereby enkf is used to invert the flow data and obtain a facies probability map soft data to guide conditional facies simulation from each ti we demonstrate the suitability of the proposed bayesian mixture modeling approach using several numerical experiments in fluvial formations with uncertain orientation and structural connectivity

the kakutani property and the fixed point property of topological spaces with abstract convexity abstract the paper deals with the usual fixed point property and the following kakutani property of a space x for every upper semicontinuous function from x to non empty closed convex subsets of x there exists x0 such that x0 x0 we derive this property of x from various separation properties of convex subsets of x and a kind of local convexity of x convexity in our setup is given in an abstract axiomatic way special emphasis is given to the case where x has the form of a product the obtained results cover several known fixed point theorems ky fan glicksberg wallace and special cases of eilenberg montgomery we also discuss an open problem concerning the fixed point property of finite posets and its role in proving more advanced theorems

copula based geostatistical models for groundwater quality parameters 1 groundwater quality parameters exhibit considerable spatial variability geostatistical methods including the assessment of variograms are usually used to characterize this variability copulas offer an interesting opportunity to describe dependence structures for multivariate distributions bivariate empirical copulas can be used as an alternative to variograms and covariance functions for the description of the spatial variability rank correlations of these copulas express the strength of the dependence independently of the marginal distributions and thus offer an alternative to the variograms empirical copulas for four quality parameters chloride sulfate ph and nitrate obtained from a large scale groundwater quality measurement network in baden wurttemberg germany are calculated they indicate that the spatial dependence structure of the investigated parameters is not gaussian two theoretical copula based models are presented in this paper a gaussian and a non gaussian bootstrap based statistical tests using stochastic simulation of the multivariate distributions are used to investigate the appropriateness of the models according to the test results the gaussian copula is rejected for most of the parameters while the non gaussian alternative is not rejected in most cases

recursive bayesian estimation of conceptual rainfall runoff model errors in real time prediction of streamflow conceptual rainfall runoff models account for the spatial dynamics of hydrological processes in a basin using simple spatially lumped storage flow relations such rough approximations introduce model errors that are often difficult to characterize here we develop and apply a methodology that recursively estimates and accounts for model errors in real time streamflow prediction settings by adding time dependent random noise to the internal states storages of the hydrological model magnitude of the added noise depends on a precision inverse variance parameter that is estimated from rainfall runoff data a recursive bayesian technique is used for estimation posteriors of hydrological parameters and states are updated through time with an ensemble kalman filter whereas the posterior of the precision parameter is updated recursively using a novel gamma density approximation technique applying this algorithm to different model error scenarios allows identification of the main source of model errors the methodology is applied to short term streamflow prediction with the hymod rainfall runoff model in a semi cold semi humid basin in iran results show that i streamflow prediction in this snow dominated basin is more affected by model errors in the slow flow than the quick flow component of the model ii accounting for model errors in the slow flow component improves both low and high flow predictions and iii predictive performance further improves by accounting for hymod parameter uncertainty in addition to model errors overall accounting for model errors increased nash sutcliffe efficiency by 1 5 reduced mean absolute error by 2 43 and improved probabilistic predictive performance by 50 80

bayesian computation via the gibbs sampler and related markov chain monte carlo methods the use of the gibbs sampler for bayesian computation is reviewed and illustrated in the context of some canonical examples other markov chain monte carlo simulation methods are also briefly described and comments are made on the advantages of sample based approaches for bayesian inference summaries

influence of soil structure and root water uptake strategy on unsaturated flow in heterogeneous media 1 we analyze the combined effects of the spatial variability of soil hydraulic properties and the water uptake by plant roots on unsaturated water flow for this analysis we use a simplified macroscopic root water uptake model which is usually applied only for homogeneous or layered soil and therefore we also determine whether it is applicable for multidimensional heterogeneous media analytical solutions for mean and variance of pressure head first order second moment approximations in layered media and numerical solutions of two dimensional 2 d autocorrelated multi gaussian and non multi gaussian parameter fields are analyzed for steady state and transient flow conditions for non gaussian topological features that have little influence on the mean and the variance of the pressure field if root water uptake is ignored we test whether the influence is significant if root water uptake is accounted for the results reveal that in field structures with large patches of coarse material local regions with pressure head values at the wilting point develop these are surrounded by wet material without a compensation mechanism for local stress the global transpiration demand is not met if local wilting occurs various compensation mechanisms are tested that depend respectively on the saturation the relative conductivity or a strategy where the deficit in the global uptake rate is equally distributed to unstressed locations the strategies lead to a global actual transpiration rate at the potential value and attenuate the formation of locally wilted areas wilted regions can however still occur and may be an artifact of the simplified model concept as root soil interactions are neglected therefore simplified macroscopic models for root water uptake should be used with caution in heterogeneous media

contact structures equivariant spin bordism and periodic fundamental groups using contact surgery and equivariant bordism theory we prove the existence of contact structures on all 5 dimensional spin manifolds with certain finite fundamental groups

multivariate copula analysis toolbox mvcat describing dependence and underlying uncertainty using a bayesian framework we present a newly developed multivariate copula analysis toolbox mvcat which includes a wide range of copula families with different levels of complexity mvcat employs a bayesian framework with a residual based gaussian likelihood function for inferring copula parameters and estimating the underlying uncertainties the contribution of this paper is threefold a providing a bayesian framework to approximate the predictive uncertainties of fitted copulas b introducing a hybrid evolution markov chain monte carlo mcmc approach designed for numerical estimation of the posterior distribution of copula parameters and c enabling the community to explore a wide range of copulas and evaluate them relative to the fitting uncertainties we show that the commonly used local optimization methods for copula parameter estimation often get trapped in local minima the proposed method however addresses this limitation and improves describing the dependence structure mvcat also enables evaluation of uncertainties relative to the length of record which is fundamental to a wide range of applications such as multivariate frequency analysis

improved spatial prediction a combinatorial approach 1 this paper presents a combinatorial approach for improving spatial predictions first copulas are used to interpolate a spatially distributed point rainfall field to a uniform spatial grid it is observed that results vary substantially depending on the parameters chosen for interpolation leading to the hypothesis that it may be advantageous to estimate copula parameters locally or to combine local and global copula predictions it is found that by modifying the method of forecast combinations prediction errors in the spatial interpolation of rainfall can be reduced although this method of combining predictions is applied in the context of rainfall interpolation using local and global copula predictions it can be used on other spatial variables and interpolation methods

enhancing multiple point geostatistical modeling 1 graph theory and pattern adjustment in recent years higher order geostatistical methods have been used for modeling of a wide variety of large scale porous media such as groundwater aquifers and oil reservoirs their popularity stems from their ability to account for qualitative data and the great flexibility that they offer for conditioning the models to hard quantitative data which endow them with the capability for generating realistic realizations of porous formations with very complex channels as well as features that are mainly a barrier to fluid flow one group of such models consists of pattern based methods that use a set of data points for generating stochastic realizations by which the large scale structure and highly connected features are reproduced accurately the cross correlation based simulation ccsim algorithm proposed previously by the authors is a member of this group that has been shown to be capable of simulating multimillion cell models in a matter of a few cpu seconds the method is however sensitive to pattern s specifications such as boundaries and the number of replicates in this paper the original ccsim algorithm is reconsidered and two significant improvements are proposed for accurately reproducing large scale patterns of heterogeneities in porous media first an effective boundary correction method based on the graph theory is presented by which one identifies the optimal cutting path surface for removing the patchiness and discontinuities in the realization of a porous medium next a new pattern adjustment method is proposed that automatically transfers the features in a pattern to one that seamlessly matches the surrounding patterns the original ccsim algorithm is then combined with the two methods and is tested using various complex two and three dimensional examples it should however be emphasized that the methods that we propose in this paper are applicable to other pattern based geostatistical simulation methods

sequential ensemble based optimal design for parameter estimation the ensemble kalman filter enkf has been widely used in parameter estimation for hydrological models the focus of most previous studies was to develop more efficient analysis estimation algorithms on the other hand it is intuitively understandable that a well designed sampling data collection strategy should provide more informative measurements and subsequently improve the parameter estimation in this work a sequential ensemble based optimal design seod method coupled with enkf information theory and sequential optimal design is proposed to improve the performance of parameter estimation based on the first and second order statistics different information metrics including the shannon entropy difference sd degrees of freedom for signal dfs and relative entropy re are used to design the optimal sampling strategy respectively the effectiveness of the proposed method is illustrated by synthetic one and two dimensional unsaturated flow case studies it is shown that the designed sampling strategies can provide more accurate parameter estimation and state prediction compared with conventional sampling strategies optimal sampling designs based on various information metrics perform similarly in our cases the effect of ensemble size on the optimal design is also investigated overall larger ensemble size improves the parameter estimation and convergence of optimal sampling strategy although the proposed method is applied to unsaturated flow problems in this study it can be equally applied in any other hydrological problems this article is protected by copyright all rights reserved

almost contact 5 manifolds are contact the existence of a contact structure is proved in any homotopy class of almost contact structures on a closed 5 dimensional manifold

multivariate type g matern stochastic partial differential equation random fields for many applications with multivariate data random field models capturing departures from gaussianity within realizations are appropriate for this reason we formulate a new class of multivariate non gaussian models based on systems of stochastic partial differential equations with additive type g noise whose marginal covariance functions are of matern type we consider four increasingly flexible constructions of the noise where the first two are similar to existing copula based models in contrast with these the last two constructions can model non gaussian spatial data without replicates computationally efficient methods for likelihood based parameter estimation and probabilistic prediction are proposed and the flexibility of the models suggested is illustrated by numerical examples and two statistical applications less

a robust geostatistical approach to contaminant source identification 1 estimation under model uncertainty remains a practical concern in many scientific and engineering fields a commonly encountered example in groundwater remediation is the contaminant source identification problem like many other inverse problems contaminant source identification is inherently ill posed and is sensitive to both data and model uncertainties model uncertainties which may be introduced at virtually any stage of a model building process can adversely affect estimator performance if they are not accounted for properly in this paper a robust geostatistical approach rgs which is extended from the geostatistical inversion approach gs is used to solve linear estimation problems the uncertainties in both model and covariance matrices are taken into account in the rgs formulation the nominal correlation structural parameters are estimated using a structural analysis procedure the resulting minimax optimization problem is solved using semidefinite programming techniques the rgs is generic and can be applied to any problem for which the gs is suitable and the upper bound of uncertainty can be quantified the rgs is illustrated for source release history identification in a two dimensional aquifer where the model uncertainty is caused by variability in hydraulic conductivity it is shown that when the model is perfectly known the rgs solution coincides with that of the gs when the model has uncertainty the rgs is robust against unknown variations from a nominal model and its overall performance is better than that of the gs using the same nominal model

streamflow prediction in ungauged catchments using copula based dissimilarity measures 1 there are many procedures in the available literature to perform prediction in ungauged basins commonly the euclidean metric is used as a proxy of the hydrologic dissimilarity here we propose a procedure to find a metric on the basis of dissimilarity measures that are estimated from pairwise empirical copula densities of runoff a metric is then defined in an transformed space of basin descriptors whose parameterization is obtained with a variance reducing technique a hydrologic model was run in an ungauged basin with sets of global parameters obtained from the k nearest neighboring donor basins using various metrics to take into account the uncertainty of its parameterization hydrologic model parameters were regionalized with a multiscale parameter regionalization technique whose transfer function parameters were found via calibration the streamflow in an ungauged basin was found as an ensemble streamflow prediction to account for the uncertainties of the transfer function parameters as well as those to define the metric this technique was applied in 38 german basins ranging in size from 70 to 4000 km2 for each basin a number of catchment descriptors and several climatic indices were quantified e g mean slope aspect shape factor mean elevation and mean monthly temperature in january among others daily streamflow time series correspond to the period from 1961 to 2000 simulated daily discharge was validated with a jackknife cross validation technique nash sutcliffe efficiencies obtained in this way ranged between 0 76 and 0 86 these results suggested that the proposed technique would produce reasonable results in ungauged basins

a hybrid regularized inversion methodology for highly parameterized environmental models 1 a hybrid approach to the regularized inversion of highly parameterized environmental models is described the method is based on constructing a highly parameterized base model calculating base parameter sensitivities and decomposing the base parameter normal matrix into eigenvectors representing principal orthogonal directions in parameter space the decomposition is used to construct super parameters super parameters are factors by which principal eigenvectors of the base parameter normal matrix are multiplied in order to minimize a composite least squares objective function these eigenvectors define orthogonal axes of a parameter subspace for which information is available from the calibration data the coordinates of the solution are sought within this subspace super parameters are estimated using a regularized nonlinear gauss marquardt levenberg scheme though super parameters are estimated tikhonov regularization constraints are imposed on base parameters tikhonov regularization mitigates over fitting and promotes the estimation of reasonable base parameters use of a large number of base parameters enables the inversion process to be receptive to the information content of the calibration data including aspects pertaining to small scale parameter variations because the number of super parameters sustainable by the calibration data may be far less than the number of base parameters used to define the original problem the computational burden for solution of the inverse problem is reduced the hybrid methodology is described and applied to a simple synthetic groundwater flow model it is then applied to a real world groundwater flow and contaminant transport model the approach and programs described are applicable to a range of modeling disciplines copyright 2005 by the american geophysical union

estimating effective model parameters for heterogeneous unsaturated flow using error models for bias correction 1 estimates of effective parameters for unsaturated flow models are typically based on observations taken on length scales smaller than the modeling scale this complicates parameter estimation for heterogeneous soil structures in this paper we attempt to account for soil structure not present in the flow model by using so called external error models which correct for bias in the likelihood function of a parameter estimation algorithm the performance of external error models are investigated using data from three virtual reality experiments and one real world experiment all experiments are multistep outflow and inflow experiments in columns packed with two sand types with different structures first effective parameters for equivalent homogeneous models for the different columns were estimated using soil moisture measurements taken at a few locations this resulted in parameters that had a low predictive power for the averaged states of the soil moisture if the measurements did not adequately capture a representative elementary volume of the heterogeneous soil column second parameter estimation was performed using error models that attempted to correct for bias introduced by soil structure not taken into account in the first estimation three different error models that required different amounts of prior knowledge about the heterogeneous structure were considered the results showed that the introduction of an error model can help to obtain effective parameters with more predictive power with respect to the average soil water content in the system this was especially true when the dynamic behavior of the flow process was analyzed

two dimensional characterization of hydraulic heterogeneity by multiple pumping tests 1 the conventional analysis of pumping tests by type curve methods is based on the assumption of a homogeneous aquifer applying these techniques to pumping test data from real heterogeneous aquifers leads to estimates of the hydraulic parameters that depend on the choice of the pumping and observation well positions in this paper we test whether these values may be viewed as pseudo local values of transmissivity and storativity which can be interpolated by kriging we compare such estimates to those obtained by geostatistical inverse modeling where heterogeneity is assumed in all stages of estimation we use drawdown data from multiple pumping tests conducted at the test site in krauthausen germany the geometric mean values of transmissivity and storativity determined by type curve analysis are very close to those obtained by geostatistical inversion but the conventional approach failed to resolve the spatial variability of transmissivity in contrast the estimate from geostatistical inversion reveals more structure this indicates that the estimates of the type curve approaches can not be treated as pseudo local values concerning storativity both analysis methods show strong fluctuations because the variability of all terms making up the storativity is small we believe that the estimated variability of storativity is biased we examine the influence of measurement error on estimating structural parameters of covariance functions in the inversion we obtain larger correlation lengths and smaller prior variances if we trust the measured data less

geostatistical interpolation using copulas 1 in many applications of geostatistical methods the dependence structure of the investigated parameter is described solely with the variogram or covariance functions which are susceptible to measurement anomalies and implies the assumption of gaussian dependence moreover the kriging variance respects only observation density data geometry and the variogram model to address these problems we borrow the idea from copulas to depict the dependence structure without the influence of the marginal distribution the methodology and basic hypotheses for application of copulas as geostatistical methods are discussed and the gaussian copula as well as a non gaussian copula are used in this paper copula parameters are estimated using a division of the observations into multipoint subsets and a subsequent maximization of the corresponding likelihood function the interpolation is carried out with two different copulas where the expected and median values are calculated from the copulas conditioned with the nearby observations the full conditional copulas provide the estimation distributions for the unobserved locations and can be used to define confidence intervals which depend on both the observation geometry and values observations of a large scale groundwater quality measurement network in baden wurttemberg are used to demonstrate the methodology five groundwater quality parameters chloride nitrate ph sulfate and dissolved oxygen are investigated all five parameters show non gaussian dependence the copula based interpolation results of the five parameters are compared to the results of conventional ordinary and indicator kriging different statistical measures including mean squared error relative differences and probability scores are used to compare cross validation and split sampling results of the interpolation methods the non gaussian copulas give better results than the geostatistical interpolations validation of the confidence intervals shows that they are more realistic than the estimation variances obtained by ordinary kriging

a spatial markov model for the evolution of the joint distribution of groundwater age arrival time and velocity in heterogeneous media the evolution of the joint distribution of groundwater age velocity and arrival times based on a markov model for the velocities of fluid particles in heterogeneous porous media has been quantified an explicit evolution equation for the joint distribution of age arrival time and particle velocity is derived which is equivalent to a continuous time random walk for age velocity and arrival time the approach is fully parameterized by the correlation model and the distribution of groundwater flow velocities the transition probability for subsequent particle velocities along streamlines is implemented by a copula which is an efficient method to generate a correlated velocity series with prescribed marginal distribution we discuss different solution methods based on finite differences and random walk particle tracking the latter is based on continuous time random walks whose transition times are obtained kinematically from the flow velocities specifically we discuss a renormalization scheme to accelerate the particle tracking simulations based on the definition of aggregate particle transitions while at the same time renormalizing velocity correlation the impact of velocity correlation and velocity distribution on the evolution of age at different distances from the inlet plane is also studied at distances of the order of the correlation length persistent particle velocities give the same behavior as stochastic streamtube models for velocity distributions which give rise to transition times with finite variance the age distributions evolve toward an inverse gaussian for heavy tailed weighting times they evolve toward stable distribution as the distance from the inlet increases

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

modeling complex geological structures with elementary training images and transform invariant distances 1 we present a new framework for multiple point simulation involving small and simple training images the use of transform invariant distances by applying random transformations expands the range of structures available in the simple patterns of the training image the training image is no longer regarded as a global conceptual geological model but rather a basic structural element of the subsurface complex geological structures are obtained whose spatial structure can be parameterized by adjusting the statistics of the random transformations on the basis of field data or geological context in most cases such parameterization is possible by adjusting two numbers only this method allows us to build models that 1 reproduce shapes corresponding to a desired prior geological concept and 2 are in phase with different types of field observations such as orientation hydrofacies or geophysical measurements the main advantage is that the training images are so simple that they can be easily built even in 3 d we apply the method on a synthetic example involving seismic data where the transformation parameters are data driven we also show examples where realistic 2 and 3 d structures are built from simplistic training images with transformation parameters inferred using a small number of orientation data

best unbiased ensemble linearization and the quasi linear kalman ensemble generator 1 linearized representations of the stochastic groundwater flow and transport equations have been heavily used in hydrogeology e g for geostatistical inversion or generating conditional realizations the respective linearizations are commonly defined via jacobians numerical sensitivity matrices this study will show that jacobian based linearizations are biased with nonminimal error variance in the ensemble sense an alternative linearization approach will be derived from the principles of unbiasedness and minimum error variance the resulting paradigm prefers empirical cross covariances from monte carlo analyses over those from linearized error propagation and points toward methods like ensemble kalman filters enkfs unlike conditional simulation in geostatistical applications enkfs condition transient state variables rather than geostatistical parameter fields recently modifications toward geostatistical applications have been tested and used this study completes the transformation of enkfs to geostatistical conditioning tools on the basis of best unbiased ensemble linearization to distinguish it from the original enkf the new method is called the kalman ensemble generator keg the new context of best unbiased ensemble linearization provides an additional theoretical foundation to enkf like methods such as the keg like enkfs and derivates the keg is optimal for gaussian variables toward increased robustness and accuracy in non gaussian and nonlinear cases sequential updating acceptance rejection sampling successive linearization and a levenberg marquardt formalism are added state variables are updated through simulation with updated parameters always guaranteeing the physicalness of all state variables the keg combines the computational efficiency of linearized methods with the robustness of enkfs and accuracy of expensive realization based methods while drawing on the advantages of conditional simulation over conditional estimation such as adequate representation of solute dispersion as proof of concept a large scale numerical test case with 200 synthetic sets of flow and tracer data is conducted and analyzed

kakutani property of the polytopes implies kakutani property of the whole space abstract this paper deals with the following property of a space x for every upper semicontinuous function from x to nonempty closed convex subsets of x there exists x 0 which is in x 0 we derive this property of x from the same property assumed to hold for the polytopes in x convexity in our setup is given in an abstract axiomatic way the results are also reformulated in the order theoretical language of continuous lattices our results directly generalize a an extension of the kakutani fixed point theorem to compact convex sets in locally convex spaces due to ky fan and i l glicksberg and b the fixed point theorem of wallace concerning set valued functions on trees

inverse sequential simulation a new approach for the characterization of hydraulic conductivities demonstrated on a non gaussian field inverse sequential simulation iss is a new inverse modeling approach for the characterization of hydraulic conductivity fields based on sequential simulation it is described and demonstrated in a synthetic aquifer with non gaussian spatial features and compared against the normal score ensemble kalman filter ns enkf the new approach uses the sequential simulation paradigm to generate realizations borrowing from the ensemble kalman filter the idea of using the experimental nonstationary cross covariance between conductivities and piezometric heads computed on an ensemble of realizations the resulting approach is fully capable of retrieving the non gaussian patterns of the reference field after conditioning on the piezometric heads with results comparable of those obtained by the ns enkf

a shuffled complex evolution metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters author s vrugt ja gupta hv bouten w sorooshian s abstract markov chain monte carlo mcmc methods have become increasingly popular for estimating the posterior probability distribution of parameters in hydrologic models however mcmc methods require the a priori definition of a proposal or sampling distribution which determines the explorative capabilities and efficiency of the sampler and therefore the statistical properties of the markov chain and its rate of convergence in this paper we present an mcmc sampler entitled the shuffled complex evolution metropolis algorithm scem ua which is well suited to infer the posterior distribution of hydrologic model parameters the scem ua algorithm is a modified version of the original sce ua global optimization algorithm developed by duan et al 1992 the scem ua algorithm operates by merging the strengths of the metropolis algorithm controlled random search competitive evolution and complex shuffling in order to continuously update the proposal distribution and evolve the sampler to the posterior target distribution three case studies demonstrate that the adaptive capability of the scem ua algorithm significantly reduces the number of model simulations needed to infer the posterior distribution of the parameters when compared with the traditional metropolis hastings samplers

a markov chain monte carlo scheme for parameter estimation and inference in conceptual rainfall runoff modeling a fully bayesian approach to parameter estimation and inference in conceptual rainfall runoff models crrms is presented computations are performed using a markov chain monte carlo mcmc method based on the metropolis hastings algorithm single site and block updating schemes are used for model parameters subject to nonnegativity restrictions as well as interval equality and order constraints diagnostics for the convergence of the markov chain and crrm assessment are also considered the mcmc approach produces samples from the joint posterior distribution of the model parameters this provides more information than single point estimates and avoids the need to use a normal approximation to the posterior as the basis for inference the methodology is demonstrated using an eight parameter conceptual rainfall runoff model and two case studies from southeastern australia the first case study considers a watershed with high runoff yield over a 12 year period the second case study considers a watershed with low yield over a 17 year period the results indicate that 1 bayesian methods provide an objective framework for model criticism and choice 2 the proposed strategies for handling constraints on model parameters are effective 3 the model parameters are sensitive to likelihood function selection 4 the conventional approach of using a power transformation and an autoregressive process to stabilize error variance and model dependence in the residuals may have limited success and 5 some care is required in the implementation of the mcmc approach and reliable results will be difficult to obtain when crrm complexity exceeds the limitations of the rainfall runoff data at hand a key finding is that the mcmc scheme presented herein provides a powerful means of identifying specific inadequacies in the structure of crrms

simulation of earth textures by conditional image quilting training image based approaches for stochastic simulations have recently gained attention in surface and subsurface hydrology this family of methods allows the creation of multiple realizations of a study domain with a spatial continuity based on a training image ti that contains the variability connectivity and structural properties deemed realistic a major drawback of these methods is their computational and or memory cost making certain applications challenging it was found that similar methods also based on training images or exemplars have been proposed in computer graphics one such method image quilting iq is introduced in this paper and adapted for hydrogeological applications the main difficulty is that image quilting was originally not designed to produce conditional simulations and was restricted to 2 d images in this paper the original method developed in computer graphics has been modified to accommodate conditioning data and 3 d problems this new conditional image quilting method ciq is patch based does not require constructing a pattern databases and can be used with both categorical and continuous training images the main concept is to optimally cut the patches such that they overlap with minimum discontinuity the optimal cut is determined using a dynamic programming algorithm conditioning is accomplished by prior selection of patches that are compatible with the conditioning data the performance of ciq is tested for a variety of hydrogeological test cases the results when compared with previous multiple point statistics mps methods indicate an improvement in cpu time by a factor of at least 50

bayesian inverse problem and optimization with iterative spatial resampling 1 measurements are often unable to uniquely characterize the subsurface at a desired modeling resolution in particular inverse problems involving the characterization of hydraulic properties are typically ill posed since they generally present more unknowns than data in a bayesian context solutions to such problems consist of a posterior ensemble of models that fit the data up to a certain precision specified by a likelihood function and that are a subset of a prior distribution two possible approaches for this problem are markov chain monte carlo mcmc techniques and optimization calibration methods both frameworks rely on a perturbation mechanism to steer the search for solutions when the model parameters are spatially dependent variable fields obtained using geostatistical realizations such as hydraulic conductivity or porosity it is not trivial to incur perturbations that respect the prior spatial model to overcome this problem we propose a general transition kernel iterative spatial resampling isr that preserves any spatial model produced by conditional simulation we also present a stochastic stopping criterion for the optimizations inspired from importance sampling in the studied cases this yields posterior distributions reasonably close to the ones obtained by a rejection sampler but with a greatly reduced number of forward model runs the technique is general in the sense that it can be used with any conditional geostatistical simulation method whether it generates continuous or discrete variables therefore it allows sampling of different priors and conditioning to a variety of data types several examples are provided based on either multi gaussian or multiple point statistics

compressibility a property of topological spaces related to abstract convexity abstract an abstract operation of hull in a set y associates with every finite set f y a set hull f y a topological space x is said to be compressible into a topological space y equipped with an operation of hull if for every sequence a1 an of open sets covering x and every y1 yn yn there exists a continuous function x y such that for every x x x hull y i x a i the concept of compressibility is extremely useful when dealing with problems of the existence of fixed points continuous selections or with kkm property the obtained results generalize several known theorems they also provide a broad range of new original results

entropy copula method for single site monthly streamflow simulation 1 an entropy copula method is proposed for single site monthly streamflow simulation in this method the joint distribution of adjacent monthly streamflows is constructed using the copula method whereas the marginal distribution of streamflow for each month is derived using the entropy method then the conditional distribution is derived from which monthly streamflow is generated moment statistics of monthly streamflow such as mean standard deviation and skewness can be modeled by the entropy based marginal distribution while the dependence structure between streamflows of adjacent months can be modeled by the copula based joint distribution the proposed entropy copula method can be extended by incorporating an aggregate variable for modeling the interannual dependence application to the simulation of monthly streamflow from the colorado river illustrates the effectiveness of the proposed method

a fast and exact method for multidimensional gaussian stochastic simulations extension to realizations conditioned on direct and indirect measurements recently dietnch and newsam 1993 derived a fast and exact method for generating unconditional realizations of a stationary multidimensional gaussian random field on a rectangular sampling grid the method is based on embedding the random field covariance matrix in a larger positive definite matrix with circulant block circulant structure the circulant structure of the embedding matrix means that a square root of this matrix can be efficiently computed by the fast fourier transform realizations are then generated by multiplying vectors of white noise by this square root this paper extends the method to generating realizations conditioned on direct and or indirect measurements of the field collected at an arbitrary set of scattered data points

a gibbs sampler for inequality constrained geostatistical interpolation and inverse modeling 1 interpolation and inverse modeling problems are ubiquitous in environmental sciences in many applications the parameters being estimated or mapped have physical constraints such as nonnegativity e g concentration hydraulic conductivity solubility limits censored data e g due to dry wells or detection limits and other physical boundaries or missing data geostatistical interpolation and inverse modeling techniques have often been applied for estimating such parameters but these methods typically cannot enforce physical constraints this paper describes a statistically rigorous and computationally efficient gibbs sampler a markov chain monte carlo technique based on an a priori truncated gaussian distribution model which allows for multiple and variable physical constraints to be enforced within a geostatistical framework sample interpolation and inverse modeling applications confirm that estimates uncertainty bounds and conditional simulations reflect the specified constraints leading to conclusions that are more consistent with the underlying conceptual model and provide a more accurate measure of the posterior uncertainty of the parameters being estimated in addition especially in inverse modeling applications a posteriori confidence bounds are narrower even in areas where constraints are not imposed the method is applicable in multiple dimensions for data with or without measurement error and with any variogram model

parameter estimation by ensemble kalman filters with transformed data approach and application to hydraulic tomography 1 ensemble kalman filters enkfs are a successful tool for estimating state variables in atmospheric and oceanic sciences recent research has prepared the enkf for parameter estimation in groundwater applications enkfs are optimal in the sense of bayesian updating only if all involved variables are multivariate gaussian subsurface flow and transport state variables however generally do not show gaussian dependence on hydraulic log conductivity and among each other even if log conductivity is multi gaussian to improve enkfs in this context we apply nonlinear monotonic transformations to the observed states rendering them gaussian gaussian anamorphosis ga similar ideas have recently been presented by beal et al 2010 in the context of state estimation our work transfers and adapts this methodology to parameter estimation additionally we address the treatment of measurement errors in the transformation and provide several multivariate analysis tools to evaluate the expected usefulness of ga beforehand for illustration we present a first time application of an enkf to parameter estimation from 3 d hydraulic tomography in multi gaussian log conductivity fields results show that 1 ga achieves an implicit pseudolinearization of drawdown data as a function of log conductivity and 2 this makes both parameter identification and prediction of flow and transport more accurate combining enkfs with ga yields a computationally efficient tool for nonlinear inversion of data with improved accuracy this is an attractive benefit given that linearization free methods such as particle filters are computationally extremely demanding

on a mapping approach to investigating the bootstrap accuracy a simple mapping approach is proposed to study the bootstrap accuracy in a rather general setting it is demonstrated that the bootstrap accuracy can be obtained through this method for a broad class of statistics to which the commonly used edgeworth expansion approach may not be successfully applied we then consider some examples to illustrate how this approach may be used to find the bootstrap accuracy and show the advantage of the bootstrap approximation over the gaussian approximation for the multivariate kolmogorov smirnov statistic we show the error of bootstrap approximation is as small as that of the gaussian approximation for the multivariate kernel type density estimate we obtain an order of the bootstrap error which is smaller than the order of the error of the gaussian approximation given in rio 1994 we also consider an application of the bootstrap accuracy for empirical process to that for the copula process

a constrained robust least squares approach for contaminant release history identification 1 contaminant source identification is an important type of inverse problem in groundwater modeling and is subject to both data and model uncertainty model uncertainty was rarely considered in the previous studies in this work a robust framework for solving contaminant source recovery problems is introduced the contaminant source identification problem is first cast into one of solving uncertain linear equations where the response matrix is constructed using a superposition technique the formulation presented here is general and is applicable to any porous media flow and transport solvers the robust least squares rls estimator which originated in the field of robust identification directly accounts for errors arising from model uncertainty and has been shown to significantly reduce the sensitivity of the optimal solution to perturbations in model and data in this work a new variant of rls the constrained robust least squares crls is formulated for solving uncertain linear equations crls allows for additional constraints such as nonnegativity to be imposed the performance of crls is demonstrated through one and two dimensional test problems when the system is ill conditioned and uncertain it is found that crls gave much better performance than its classical counterpart the nonnegative least squares the source identification framework developed in this work thus constitutes a reliable tool for recovering source release histories in real applications

real time groundwater flow modeling with the ensemble kalman filter joint estimation of states and parameters and the filter inbreeding problem 1 real time groundwater flow modeling with filter methods is interesting for dynamical groundwater flow systems for which measurement data in real time are available the ensemble kalman filter enkf approach is used here to update states together with parameters by adopting an augmented state vector approach the performance of enkf is investigated in a synthetic study with a two dimensional transient groundwater flow model where 1 only the recharge rate is spatiotemporally variable 2 only transmissivity is spatially variable with lnt2 1 0 or 3 with lnt2 2 7 and 4 both recharge rate and transmissivity are uncertain a combination of 1 and 3 the performance of enkf for simultaneous state and parameter estimation in saturated groundwater flow problems is investigated in dependence of the number of stochastic realizations the updating frequency and updating intensity of log transmissivity the amount of measurements in space and time and the method iterative versus noniterative enkf among others satisfactory results were also obtained if both transmissivity and recharge rate were uncertain however it was found that filter inbreeding is much more severe if hydraulic heads and transmissivities are jointly updated than if only hydraulic heads are updated the filter inbreeding problem was investigated in more detail and could be strongly reduced with help of a damping parameter which limits the intensity of the perturbation of the log transmissivity field an additional reduction of filter inbreeding could be achieved by combining two measures 1 inflating the elements of the predicted state covariance matrix on the basis of a comparison between the model uncertainty and the observed errors at the measurement points and 2 starting the flow simulations with a very large number of realizations and then sampling the desired number of realizations after one simulation time step by minimizing the differences between the local cpdfs and bivariate cpdfs of hydraulic head for the large ensemble and the corresponding cpdfs for the reduced ensemble the two measures which cause very limited cpu costs allowed making 100 stochastic realizations for the reproduction of the states as efficient as 200 500 untreated stochastic realizations

analytical relationship between gaussian and transformed gaussian spatially distributed fields 1 a transformation of a gaussian random field results in a change of the spatial dependence in simple terms the range and the shape of a variogram are different between an underlying gaussian and a transformed gaussian field there is a relationship between the underlying and the transformed spatial dependence this paper shows how this relationship can be expressed analytically rather than generating multidimensional random fields and conducting spatial statistical analysis we develop an accurate and efficient approach based on a unique mapping of the correlation coefficients of the original multi gaussian fields to the transformed correlation coefficients to evaluate the spatial correlation of transformed non gaussian random fields for any type of geostatistical parameterization such a mapping can also yield accurate estimation of the spatial correlation of the underlying gaussian field given the spatial correlation of the transformed field results indicate that 1 a nonlinear transformation of spatially distributed fields usually changes the spatial dependence structure and 2 the relationship between the dependence structures of the underlying and the transformed field can be expressed analytically and it is sufficient to do this in one dimension we use the developed approach to investigate the change of correlations of connected random fields generated by the absolute value transformation results show 1 the correlation lengths of the underlying gaussian fields are 1 67 and 2 64 times of those of transformed non gaussian fields for gaussian and exponential covariance models respectively 2 the anisotropic ratio does not change and 3 the anticorrelation in hole effect correlation models disappear

gaussian and non gaussian inverse modeling of groundwater flow using copulas and random mixing 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

review of parameter identification procedures in groundwater hydrology the inverse problem the purpose of this survey is to review parameter identification procedures in groundwater hydrology and to examine computational techniques which have been developed to solve the inverse problem parameter identification methods are classified under the error criterion used in the formulation of the inverse problem the problem of ill posedness in connection with the inverse problem is addressed typical inverse solution techniques are highlighted the review also includes the evaluation of methods used for computing the sensitivity matrix statistics which can be used to estimate the parameter uncertainty are outlined attempts have been made to compare and contrast representative inverse procedures and direction for future research is suggested

existence and classification of overtwisted contact structures in all dimensions we establish a parametric extension h principle for overtwisted contact structures on manifolds of all dimensions which is the direct generalization of the 3 dimensional result from 12 it implies in particular that any closed manifold admits a contact structure in any given homotopy class of almost contact structures

efficient pairwise composite likelihood estimation for spatial clustered data spatial clustered data refer to high dimensional correlated measurements collected from units or subjects that are spatially clustered such data arise frequently from studies in social and health sciences we propose a unified modeling framework termed as geocopula to characterize both large scale variation and small scale variation for various data types including continuous data binary data and count data as special cases to overcome challenges in the estimation and inference for the model parameters we propose an efficient composite likelihood approach in that the estimation efficiency is resulted from a construction of over identified joint composite estimating equations consequently the statistical theory for the proposed estimation is developed by extending the classical theory of the generalized method of moments a clear advantage of the proposed estimation method is the computation feasibility we conduct several simulation studies to assess the performance of the proposed models and estimation methods for both gaussian and binary spatial clustered data results show a clear improvement on estimation efficiency over the conventional composite likelihood method an illustrative data example is included to motivate and demonstrate the proposed method

a reassessment of the groundwater inverse problem this paper presents a functional formulation of the groundwaterflow inverse problem that is sufficiently general to accommodate most commonly used inverse algorithms unknown hydrogeological properties are assumed to be spatial functions that can be represented in terms of a possibly infinite basis function expansion with random coefficients the unknown parameter function is related to the measurements used for estimation by a forward operator which describes the measurement process in the particular case considered here the parameter of interest is the large scale log hydraulic conductivity the measurements are point values of log conductivity and piezometric head and the forward operator is derived from an upscaled groundwaterflow equation the inverse algorithm seeks the most probable or maximum a posteriori estimate of the unknown parameter function when the measurement errors and parameter function are gaussian and independent the maximum a posteriori estimate may be obtained by minimizing a least squares performance index which can be partitioned into goodness of fit and prior terms when the parameter is a stationary random function the prior portion of the performance index is equivalent to a regularization term which imposes a smoothness constraint on the estimate this constraint tends to make the problem well posed by limiting the range of admissible solutions the gaussian maximum a posteriori problem may be solved with variational methods using functional generalizations of gauss newton or gradient based search techniques several popular groundwater inverse algorithms are either special cases of or variants on the functional maximum a posteriori algorithm these algorithms differ primarily with respect to the way they describe spatial variability and the type of search technique they use linear versus nonlinear the accuracy of estimates produced by both linear and nonlinear inverse algorithms may be measured in terms of a bayesian extension of the cramer rao lower bound on the estimation error covariance this bound suggests how parameter identifiability can be improved by modifying the problem structure and adding new measurements

factor copula models for replicated spatial data abstractwe propose a new copula model that can be used with replicated spatial data unlike the multivariate normal copula the proposed copula is based on the assumption that a common factor exists and affects the joint dependence of all measurements of the process moreover the proposed copula can model tail dependence and tail asymmetry the model is parameterized in terms of a covariance function that may be chosen from the many models proposed in the literature such as the matern model for some choice of common factors the joint copula density is given in closed form and therefore likelihood estimation is very fast in the general case one dimensional numerical integration is needed to calculate the likelihood but estimation is still reasonably fast even with large datasets we use simulation studies to show the wide range of dependence structures that can be generated by the proposed model with different choices of common factors we apply the proposed model to spatial temperature data and com

bayesian assessment of the expected data impact on prediction confidence in optimal sampling design 1 incorporating hydro geo logical data such as head and tracer data into stochastic models of subsurface flow and transport helps to reduce prediction uncertainty because of financial limitations for investigation campaigns information needs toward modeling or prediction goals should be satisfied efficiently and rationally optimal design techniques find the best one among a set of investigation strategies they optimize the expected impact of data on prediction confidence or related objectives prior to data collection we introduce a new optimal design method called predia gnosis preposterior data impact assessor predia derives the relevant probability distributions and measures of data utility within a fully bayesian generalized flexible and accurate framework it extends the bootstrap filter bf and related frameworks to optimal design by marginalizing utility measures over the yet unknown data values predia is a strictly formal information processing scheme free of linearizations it works with arbitrary simulation tools provides full flexibility concerning measurement types linear nonlinear direct indirect allows for any desired task driven formulations and can account for various sources of uncertainty e g heterogeneity geostatistical assumptions boundary conditions measurement values model structure uncertainty a large class of model errors via bayesian geostatistics and model averaging existing methods fail to simultaneously provide these crucial advantages which our method buys at relatively higher computational costs we demonstrate the applicability and advantages of predia over conventional linearized methods in a synthetic example of subsurface transport in the example we show that informative data is often invisible for linearized methods that confuse zero correlation with statistical independence hence predia will often lead to substantially better sampling designs finally we extend our example to specifically highlight the consideration of conceptual model uncertainty

effective and efficient algorithm for multiobjective optimization of hydrologic models 1 practical experience with the calibration of hydrologic models suggests that any single objective function no matter how carefully chosen is often inadequate to properly measure all of the characteristics of the observed data deemed to be important one strategy to circumvent this problem is to define several optimization criteria objective functions that measure different complementary aspects of the system behavior and to use multicriteria optimization to identify the set of nondominated efficient or pareto optimal solutions in this paper we present an efficient and effective markov chain monte carlo sampler entitled the multiobjective shuffled complex evolution metropolis moscem algorithm which is capable of solving the multiobjective optimization problem for hydrologic models moscem is an improvement over the shuffled complex evolution metropolis scem ua global optimization algorithm using the concept of pareto dominance rather than direct single objective function evaluation to evolve the initial population of points toward a set of solutions stemming from a stable distribution pareto set the efficacy of the moscem ua algorithm is compared with the original mocom ua algorithm for three hydrologic modeling case studies of increasing complexity

multivariate hydrological frequency analysis using copulas 1 this article presents the modeling of multivariate extreme values using copulas our approach allows us to model the dependence structure independently of the marginal distributions which is not possible with standard classical methods the methodology has been applied on two different problems in hydrology the first application is concerned with the combined risk in the framework of frequency analysis four copulas have been tested on peak flows from the watershed of peribonka in quebec canada the second application relates to the joint modeling of peak flows and volumes three copulas have been applied to the watershed of the rimouski river in quebec canada this approach using copulas is promising since it allows us to take into account a wide range of correlation which can happen in hydrology

coping with model error in variational data assimilation using optimal mass transport classical variational data assimilation methods address the problem of optimally combining model predictions with observations in the presence of zero mean gaussian random errors however in many natural systems uncertainty in model structure and or model parameters often results in systematic errors or biases prior knowledge about such systematic model error for parametric removal is not always feasible in practice limiting the efficient use of observations for improved prediction the main contribution of this work is to advocate the relevance of transportation metrics for quantifying nonrandom model error in variational data assimilation for nonnegative natural states and fluxes transportation metrics also known as wasserstein metrics originate in the theory of optimal mass transport omt and provide a nonparametric way to compare distributions which is natural in the sense that it penalizes mismatch in the values and relative position of masses in the two distributions we demonstrate the promise of the proposed methodology using 1 d and 2 d advection diffusion dynamics with systematic error in the velocity and diffusivity parameters moreover we combine this methodology with additional regularization functionals such as the l1 norm of the state in a properly chosen domain to incorporate both model error and potential prior information in the presence of sparsity or sharp fronts in the underlying state of interest

posterior population expansion for solving inverse problems solving inverse problems in a complex geologically realistic and discrete model space and from a sparse set of observations is a very challenging task extensive exploration by markov chain monte carlo mcmc methods often results in considerable computational efforts most optimization methods on the other hand are limited to linear continuous model spaces and the minimization of an objective function what often proves to be insufficient to overcome these problems we propose a new ensemble based exploration scheme for geostatistical prior models generated by a multiple point statistics mps tool the principle of our method is to expand an existing set of models by using posterior facies information for conditioning new mps realizations the algorithm is independent of the physical parametrization it is tested on a simple synthetic inverse problem when compared to two existing mcmc methods iterative spatial resampling isr and interrupted markov chain monte carlo imcmc the required number of forward model runs was divided by a factor of 8 12

blocking moving window algorithm conditioning multiple point simulations to hydrogeological data 1 connectivity constraints and measurements of state variables contain valuable information on aquifer architecture multiple point mp geostatistics allow one to simulate aquifer architectures presenting a predefined degree of global connectivity in this context connectivity data are often disregarded the conditioning to state variables is usually carried out by minimizing a suitable objective function i e solving an inverse problem however the discontinuous nature of lithofacies distributions and of the corresponding objective function discourages the use of traditional sensitivity based inversion techniques this work presents the blocking moving window algorithm bmw aimed at overcoming these limitations by conditioning mp simulations to hydrogeological data such as connectivity and heads the bmw evolves iteratively until convergence 1 mp simulation of lithofacies from geological geophysical data and connectivity constraints where only a random portion of the domain is simulated at every iteration i e the blocking moving window whose size is user defined 2 population of hydraulic properties at the intrafacies 3 simulation of state variables and 4 acceptance or rejection of the mp simulation depending on the quality of the fit of measured state variables the outcome is a stack of mp simulations that 1 resemble a prior geological model depicted by a training image 2 honor lithological data and connectivity constraints 3 correlate with geophysical data and 4 fit available measurements of state variables well we analyze the performance of the algorithm on a 2 d synthetic example results show that 1 the size of the blocking moving window controls the behavior of the bmw 2 conditioning to state variable data enhances dramatically the initial simulation which accounts for geological geophysical data only and 3 connectivity constraints speed up the convergence but do not enhance the stack if the number of iterations is large

real connective k theory and the quaternion group let ko be the real connective k theory spectrum we compute ko bg and ko bg for groups g whose sylow 2 subgroup is quaternion of order 8 using this we compute the coefficients t ko g of the g fixed points of the tate spectrum t ko for g s12 3 and g q8 the results provide a counterexample to the optimistic conjecture of greenlees and may 9 conj 13 4 by showing in particular that t ko g is not a wedge of eilenberg mac lane spectra as occurs for groups of prime order

a selection theorem for topological convex structures a continuous selection theorem has been obtained for multivalued functions the values of which are convex sets of certain synthetic convex structures applications are given related with superextensions semi lattices spaces of order arcs trees whitney levels in hyperspaces and geometric topology applications to traditional convexity in vector spaces involve beer s approximation theorem and a fixed point theorem of dugundji granas some other applications a o an invariant arc theorem appear elsewhere

inverse modeling of groundwater flow using model reduction numerical groundwater flow models often have a very high number of model cells greater than a million such models are computationally very demanding which is disadvantageous for inverse modeling this paper describes a low dimensional formulation for groundwater flow that reduces the computational burden necessary for inverse modeling the formulation is a projection of the original groundwater flow equation on a set of orthogonal patterns i e a galerkin projection the patterns empirical orthogonal functions are computed by a decomposition of the covariance matrix over an ensemble of model solutions those solutions represent the behavior of the model as a result of model impulses and the influence of a chosen set of parameter values for an interchangeable set of parameter values the patterns yield a low dimensional model as the number of patterns is often small an advantage of this model is that the adjoint is easily available and most accurate for inverse modeling for several synthetical cases the low dimensional model was able to find the global minimum efficiently and the result was comparable to that of the original model for several cases our model even converged where the original model failed our results demonstrate that the proposed procedure results in a 60 time reduction to solve the groundwater flow inverse problem greater efficiencies can be expected in practice for large scale models with a large number of grid cells that are used to compute transient simulations