An-Najah Staff

This paper presents a methodology for groundwater quality monitoring network design. This design takes into account uncertainties in aquifer properties, pollution transport processes, and climate. The methodology utilizes a statistical learning algorithm called relevance vector machines (RVM), which is a sparse Bayesian framework that can be used for obtaining solutions to regression and classification tasks. Application of the methodology is illustrated using the Eocene Aquifer in the northern part of the West Bank, Palestine. The procedure presented in this paper utilizes a Monte Carlo (MC) simulation process to capture the uncertainties in recharge, hydraulic conductivity, and nitrate reaction processes through the application of a groundwater flow model and a nitrate fate and transport model. This MC modeling approach provides several thousand realizations of nitrate distribution in the aquifer. Subsets of these realizations are then used to design the monitoring network. This is done by building a best-fit model of nitrate concentration distribution everywhere in the aquifer for each Monte Carlo subset using RVM. The outputs from the RVM model are the distribution of nitrate concentration everywhere in the aquifer, the uncertainty in the characterization of those concentrations, and the number and locations of “relevance vectors” (RVs). The RVs form the basis of the optimal characterization of nitrate throughout the aquifer and represent the optimal locations of monitoring wells. In this paper, the number of monitoring wells and their locations where chosen based on the performance of the RVM model runs. The results from 100 model runs show the consistency of the model in selecting the number and locations of RV‘s. After implementing the design, the data collected from the monitoring sites can be used to estimate nitrate concentration distribution throughout the entire aquifer and to quantify the uncertainty in those estimates.

The Monte Carlo method was shown to be a very powerful technique in solving the Boltzmann equation by particle simulation. Its simple concept, straightforward algorithm, and its adaptability to include new features (such as, gravity, electric field, geomagnetic field, and different collision models) make it useful tool in space plasma physics, and a powerful test of results obtained with other mathematical methods. We have used Monte Carlo method to solve Boltzmann equation, which describes the motion of a minor ion in a background of ions under the effect of external forces and Coulomb collisions with background ions. We have computed the minor ion velocity distribution function, drift velocity, density, temperatures and heat fluxes. As an application, Monte Carlo simulation method has been adapted to determine the O ⁺ velocity distribution function, O ⁺ density, O ⁺ drift velocity, O ⁺ temperatures, and O ⁺ heat fluxes for Coulomb Milne problem.

Altitude profiles for O+ ion velocity distribution functions, O+ parallel and perpendicular temperatures, O+ temperature anisotropy, O+–O+ and O+–O collision frequencies and O+ temperature partition coefficients β|| and β⊥ are obtained in the auroral ionosphere (150 km–500 km). A Monte Carlo simulation was used to investigate the behavior of O+ ions that are E×B drifting through a background of neutrals O, with the effects of O+–O resonant charge exchange and polarization interactions as well as O+–O+ Coulomb collisions. We have found, for low altitudes, the effect of O+–O+ Coulomb collisions is negligible and, as electric field increases, O+–O collision rate increases, therefore non-Maxwellian features of fO+ appeared and becomes pronounced at large electric fields, O+ temperature increases, νO+–O increases, νO+–O+ decreases, O+ temperature partition coefficients β|| decreases and β⊥ increases. As altitude increases, the effect of O+–O+ Coulomb collision becomes significant, and for constant electric field, the non-Maxwellian features of O+ distributions are reduced, T⊥O+ decreases, T|| O+ increases, O+ temperature anisotropy decreases, νO+–O decreases, νO+–O+ increases with altitude and reaches its maximum at 300 km and then decreases, β|| increases and β⊥ decreases. However, as E increases, the O+–O collision frequency increases, while O+–O+ collision frequency decreases, β|| decreases, β⊥ increases, νO+–O increases, νO+–O+ decreases. Monte Carlo simulation of the effect of O+–O+ Coulomb collision on the O+ temperature partition coefficients β|| and β⊥, which has not been taken into account so far, is to increase β|| and decreases β⊥. We believe that the Monte Carlo calculations presented here provided the best description to date of auroral F-region O+ velocity distributions, O+ temperature and O+ temperature partition coefficients β|| and β⊥ in the presence of the electric field, primarily because of the self consistent handling of O+–O+ and O+–O collisions.

The polar wind is an ambipolar plasma outflow from the terrestrial ionosphere at high latitudes. As the ions drift upward along geomagnetic flux tubes, they move from collision-dominated to collisionless regions. A Monte Carlo simulation was used to calculate the temperature and Coulomb collision frequency in the polar wind. The simulation properly accounted for the divergence of geomagnetic field lines, the gravitational force, the polarization electric field, and Coulomb collisions. The temperature was found to increase with altitude and then decreases due to the interplay between frictional heating due to Coulomb collisions and adiabatic cooling (due to diverging geomagnetic field). The Coulomb collision frequency was found to decrease with altitude. As altitude increases, the ions are accelerated by the upward directed ambipolar electric field and become less coupled with the background ions. One of the objectives is to study the consequences of a velocity distribution function with an enhanced high energy tail for the injected ions. As the number of high energy ions increases in the tail of the velocity distribution at the injection point (i.e. kappa parameter decreases), the temperature increases and decreases.