Hesham M. Bekhit

Using Markov Chain Monte Carlo to quantify parameter uncertainty and its effect on predictions of a groundwater flow model

A statistical Bayesian framework is used to solve the inverse problem and develop the posterior distributions of parameters for a density-driven groundwater flow model. This Bayesian approach is implemented using a Markov Chain Monte Carlo (MCMC) sampling method. Three sets of data pertaining to the location of the freshwater-seawater transition zone exist for the site, including chemistry data, hydraulic head data and newly collected magnetotelluric (MT) data. A sequential conditioning approach is implemented where the chemistry data and MT-converted salinity are combined as a single data set and are used to first condition the parameter distributions. The head data are subsequently used as a second conditioning data set where the posterior distribution developed by the first conditioning is used as a prior for this second conditioning. Results of this analysis indicate that conditioning on the available data sets yields dramatic reduction of uncertainty compared to unconditioned simulations, especially for the recharge-conductivity ratio. This ratio controls the location of the transition zone, and the conditioning results in a smaller range of variability compared to the distribution used in previous modelling of the site. Using the conditioned distributions to solve the density-driven flow problem in a stochastic framework (i.e., model parameters are randomly sampled from the posterior distributions) results in a range of output flow fields that is much narrower than the previous model. The ensemble mean of these solutions and the uncertainty bounds expressed by the mean+/-one standard deviation lie within the uncertainty bounds of the original model. For the case study shown here, the effect of conditioning data is dominant over the effect of prior information.

Contaminant transport in groundwater in the presence of colloids and bacteria: Model development and verification

Colloids and bacteria (microorganisms) naturally exist in groundwater aquifers and can significantly impact contaminant migration rates. A conceptual model is first developed to account for the different physiochemical and biological processes, reaction kinetics, and different transport mechanisms of the combined system (contaminant-colloids-bacteria). All three constituents are assumed to be reactive with the reactions taking place between each constituent and the porous medium and also among the different constituents. A general linear kinetic reaction model is assumed for all reactive processes considered. The mathematical model is represented by fourteen coupled partial differential equations describing mass balance and reaction processes. Two of these equations describe colloid movement and reactions with the porous medium, four equations describe bacterial movement and reactions with colloids and the porous medium, and the remaining eight equations describe contaminant movement and its reactions with bacteria, colloids, and the porous medium. The mass balance equations are numerically solved for two-dimensional groundwater systems using a third-order, total variance-diminishing scheme (TVD) for the advection terms. Due to the complex coupling of the equations, they are solved iteratively each time step until a convergence criterion is met. The model is tested against experimental data and the results are favorable.

GERD Failure Analysis and the Impacts on Downstream Countries

The Grand Ethiopian Renaissance Dam (GERD) is one of the major dams under construction on the Nile River. Currently, there is a lot of confusion about the impacts of GERD on downstream countries (Sudan and Egypt). One of the major impacts on downstream countries that has attracted a lot of debate is the impact of GERD failure. This paper aims to investigate the impacts of GERD failure in downstream regions using the International River Interface Cooperative (IRIC) two-dimensional analysis model. The study reveals that there could be a catastrophic effect on Sudan especially Roseires, Sennar, and Merowe dams in addition to Al Khartoum City. Also, the study shows that the Aswan High Dam (AHD) will be at risk.

Validation Analysis of the Groundwater Flow and Transport Model of the Central Nevada Test Area

The Central Nevada Test Area (CNTA) is a U.S. Department of Energy (DOE) site undergoing environmental restoration. The CNTA is located about 95 km northeast of Tonopah, Nevada, and 175 km southwest of Ely, Nevada (Figure 1.1). It was the site of the Faultless underground nuclear test conducted by the U.S. Atomic Energy Commission (DOEs predecessor agency) in January 1968. The purposes of this test were to gauge the seismic effects of a relatively large, high-yield detonation completed in Hot Creek Valley (outside the Nevada Test Site [NTS]) and to determine the suitability of the site for future large detonations. The yield of the Faultless underground nuclear test was between 200 kilotons and 1 megaton (DOE, 2000). A three-dimensional flow and transport model was created for the CNTA site (Pohlmann et al., 1999) and determined acceptable by DOE and the Nevada Division of Environmental Protection (NDEP) for predicting contaminant boundaries for the site.

Jonglei Canal Project Under Potential Developments in the Upper Nile States

Nile basin countries are experiencing water scarcity due to rapid growth in population and climate change. This scarcity drew attention to the vast amount of w…

The use of connectivity clusters in stochastic modelling of highly heterogeneous porous media

Stochastic geostatistical techniques are essential tools for groundwater flow and transport modelling in highly heterogeneous media. Typically, these techniques require massive numbers of realizations to accurately simulate the high variability and account for the uncertainty. These massive numbers of realizations imposed several constraints on the stochastic techniques (e.g. increasing the computational effort, limiting the domain size, grid resolution, time step and convergence issues). Understanding the connectivity of the subsurface layers gives an opportunity to overcome these constraints. This research presents a sampling framework to reduce the number of the required Monte Carlo realizations utilizing the connectivity properties of the hydraulic conductivity distributions in a three-dimensional domain. Different geostatistical distributions were tested in this study including exponential distribution with the Turning Bands (TBM) algorithm and spherical distribution using Sequential Gaussian Simulation (SGSIM). It is found that the total connected fraction of the largest clusters and its tortuosity are highly correlated with the percentage of mass arrival and the first arrival quantiles at different control planes. Applying different sampling techniques together with several indicators suggested that a compact sample representing only 10% of the total number of realizations can be used to produce results that are close to the results of the full set of realizations. Also, the proposed sampling techniques specially utilizing the low conductivity clustering show very promising results in terms of matching the full range of realizations. Finally, the size of selected clusters relative to domain size significantly affects transport characteristics and the connectivity indicators.

Impacts of the Upper Nile Mega Projects on the Water Resources of Egypt

This chapter explores the potential impacts of the River Nile mega projects on water resources of Egypt. The addressed mega projects are located on the White Nile, the Blue Nile, and the Main Nile up to Lake Nasser. The mega projects are mainly categorized as Irrigation; Canalization (streaming); and Power generation projects (Dams). The impacts on the water resources of Egypt were thoroughly investigated in different but interrelated dimensions. The main impact is the shortage of water reaching the most arid zone on the Nile in Egypt. Such shortage of water will create a chain reaction influencing at large all the environmental activities in Egypt (total environmental impact). The impacts include crop and fish production and farmers income, present and future reclaimed land (other developments), salt water intrusion, soil salinity, supply intakes and intakes for water treatment plants, main canals and rayahs, ecological imbalance, tourism industry, health risks, generation of hydropower, Dam failure impacts, and socio-economic impacts.

Uncertainty Reduction for Parameters of a Seawater Intrusion Model using Markov Chain Monte Carlo

The Milrow underground nuclear test was one of three tests that were conducted on Amchitka Island, Alaska. A stochastic groundwater flow and contaminant transport model was created for the site which propagated uncertainty in input parameters through flow and transport simulations to yield an output with a wide range of uncertainty. The Consortium for Risk Evaluation with Stakeholder Participation (CRESP) sponsored field efforts in the summer of 2004, which yielded data pertaining to the location of the freshwater lens, derived from geophysical surveys on the island. These data are compared to the groundwater model input distributions for verification, and then the distributions are tightened around the new data for uncertainty reduction using a Markov Chain Monte Carlo approach. The geophysical data resulted in a transition zone location much deeper than that identified from the salinity profile at a borehole drilled on the island near Milrow ground zero. A number of scenarios are investigated in which reduction of parameter uncertainty through the use of Markov Chain Monte Carlo is evaluated using the salinity data alone, the geophysical data alone, and all data together. Due to the inconsistency between the salinity data and the geophysical logs, the use of these data sets combined does not yield a reduction of uncertainty similar to that obtained by using the geophysical logs alone. A hypothetical scenario is used where the geophysical interpretation is assumed to be consistent with the salinity data and the resulting reduction of uncertainty is found to be significant.