Filtered density functions for uncertainty assessments of transport in Groundwater

It is estimated that fifty percent of the drinking water is extracted from groundwater sources. But the groundwater quality is threatened by contaminants. Risk assessments are applied to geohydrological systems in order to estimate if they pose a risk through groundwater pollution. These risks not only depend on the impact of the contaminants, but also on the their propagation in the groundwater. Properties of the subsurface have a strong impact on the groundwater flow and therefore also on the transport of solutes. The scarcity of data together with the heterogeneity of the subsurface can cause the uncertainty of the transport predictions to be so large that they cannot be neglected. Consequently, the uncertainty needs to be included in the risk assessments. This is possible by using a geostatistical representation of the subsurface, which results in a probabilistic description of the transport processes. Probability density function (PDF) methods provide an integrated framework to predict the transport of solutes in which uncertainties are incorporated seamlessly. But PDF methods require the assumption of a statistically homogeneous conductivity field. This is problematic. Using spatially averaged quantities instead of stochastic averages, an alternative to PDF methods is found: the filtered density function (FDF) methods. The aim of the research presented here is to develop such an FDF method for predicting the transport in groundwater. Therefore, three steps are necessary. An efficient and accurate numerical solver for FDF equations needs to be developed. In a second step, the parameters contained by the equations have to be filtered. And finally, an appropriate mixing model needs to be found for approximating the unclosed mixing term. The mixing term is of particular interest because it has a direct impact on the uncertainty evolution. In summary, this work contributes towards the development of an FDF framework applied to the transport in groundwater

State Of the Art Report in the fields of numerical analysis and scientific computing. Final version as of 16/02/2020 deliverable D4.1 of the HORIZON 2020 project EURAD.: European Joint Programme on Radioactive Waste Management

Document information Project Acronym EURAD Project Title European Joint Programme on Radioactive Waste Management Project Type European Joint Programme (EJP) EC grant agreement No. 847593 Project starting / end date 1 st June 2019-30 May 2024 Work Package No. 4 Work Package Title Development and Improvement Of NUmerical methods and Tools for modelling coupled processes Work Package Acronym DONUT Deliverable No. 4.

Advective - dispersive contaminant transport towards a pumping well

In this thesis we describe an analytical approximation method for predicting the advective- dispersive transport of a contaminant towards a pumping well. The groundwater flow is assumed to be stationary and essentially horizontal. Due to dispersion contaminant transport is a stochastic process. We derive approximations for the arrival probability (or fraction) of particles at a well, for the mean and variance of the arrival time and for the arrival time distribution at a well. The advective flow yields first order approximations. The effect of longitudinal dispersion is included by expanding the first and second moment of the arrival time in power series of the longitudinal dispersion coefficient. Transversal dispersion only plays a crucial role near the separating streamlines bounding the catchment area of a well. Its effect is analyzed locally with boundary layer techniques. The incorporation of linear equilibrium adsorption and first order decay is rather straightforward. The asymptotic approximations are compared with the results of random walk simulations.A self-contained part of this thesis is devoted to the transport of a kinetically adsorbing contaminant. We show that once the transport of a non-adsorbing contaminant has been computed, the effect of first order kinetics can be incorporated naturally by utilizing a stochastic description of the residence time of particles in the free phase.The results of our research have been implemented in the software package ECOWELL. The input of ECOWELL consists of a head field generated with a numerical flow model. The technical documentation of ECOWELL is part of this thesis. The use of ECOWELL is demonstrated in a case study

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Deriving probabilistic short-range forecasts from a deterministic high-resolution model

In order to take full advantage of short-range forecasts from deterministic high-resolution NWP models, the direct model output must be addressed in a probabilistic framework. A promising approach is mesoscale ensemble prediction. However, its operational use is still hampered by conceptual deficiencies and large computational costs. This study tackles two relevant issues: (1) the representation of model-related forecast uncertainty in mesoscale ensemble prediction systems and (2) the development of post-processing procedures that retrieve additional probabilistic information from a single model simulation. Special emphasis is laid on mesoscale forecast uncertainty of summer precipitation and 2m-temperature in Europe. Source of forecast guidance is the deterministic high-resolution model Lokal-Modell (LM) of the German Weather Service. This study gains more insight into the effect and usefulness of stochastic parametrisation schemes in the representation of short-range forecast uncertainty. A stochastic parametrisation scheme is implemented into the LM in an attempt to simulate the stochastic effect of sub-grid scale processes. Experimental ensembles show that the scheme has a substantial effect on the forecast of precipitation amount. However, objective verification reveals that the ensemble does not attain better forecast goodness than a single LM simulation. Urgent issues for future research are identified. In the context of statistical post-processing, two schemes are designed: the neighbourhood method and wavelet smoothing. Both approaches fall under the framework of estimating a large array of statistical parameters on the basis of a single realisation on each parameter. The neighbourhood method is based on the notion of spatio-temporal ergodicity including explicit corrections for enhanced predictability from topographic forcing. The neighbourhood method derives estimates of quantiles, exceedance probabilities and expected values at each grid point of the LM. If the post-processed precipitation forecast is formulated in terms of probabilities or quantiles, it attains clear superiority in comparison to the raw model output. Wavelet smoothing originates from the field of image denoising and includes concepts of multiresolution analysis and non-parametric regression. In this study, the method is used to produce estimates of the expected value, but it may be easily extended to the additional estimation of exceedance probabilities. Wavelet smoothing is not only computationally more efficient than the neighbourhood method, but automatically adapts the amount of spatial smoothing to local properties of the underlying data. The method apparently detects deterministically predictable temperature patterns on the basis of statistical guidance only