This paper proposes non-Gaussian models for parametric spectral estimation with application to event-related desynchronization (ERD) estimation of nonstationary EEG. Existing approaches for time-varying spectral estimation use time-varying autoregressive (TVAR) state-space models with Gaussian state noise. The parameter estimation is solved by a conventional Kalman filtering. This study uses non-Gaussian state noise to model autoregressive (AR) parameter variation with estimation by a Monte Carlo particle filter (PF). Use of non-Gaussian noise such as heavy-tailed distribution is motivated by its ability to track abrupt and smooth AR parameter changes, which are inadequately modeled by Gaussian models. Thus, more accurate spectral estimates and better ERD tracking can be obtained. This study further proposes a non-Gaussian state space formulation of time-varying autoregressive moving average (TVARMA) models to improve the spectral estimation. Simulation on TVAR process with abrupt parameter variation shows superior tracking performance of non-Gaussian models. Evaluation on motor-imagery EEG data shows that the non-Gaussian models provide more accurate detection of abrupt changes in alpha rhythm ERD. Among the proposed non-Gaussian models, TVARMA shows better spectral representations while maintaining reasonable good ERD tracking performance.
Analytical study of the influence of both the pumping well discharge rate and pumping time on contaminant transport and attenuation is significant for hydrological and environmental science applications. This article provides an analytical solution for investigating the influence of both pumping time and travelling time together for one-dimensional contaminant transport in riverbank filtration systems by using the Green's function approach. The basic aim of the model is to understand how the pumping time and pumping rate, which control the travelling time, can affect the contaminant concentration in riverbank filtration systems. Results of analytical solutions are compared with the results obtained using a MODFLOW numerical model. Graphically, it is found that both analytical and numerical solutions have almost the same behaviour. Additionally, the graphs indicate that any increase in the pumping rate or simulation pumping time should increase the contamination in groundwater. The results from the proposed analytical model are well matched with the data collected from a riverbank filtration site in France. After this validation, the model is then applied to the first pilot project of a riverbank filtration system conducted in Malaysia. Sensitivity analysis results highlight the importance of degradation rates of contaminants on groundwater quality, for which higher utilization rates lead to the faster consumption of pollutants.
This article provides an analytical solute transport model to investigate the potential of groundwater contamination by polluted surface water in a two dimensional domain. The clogging of streambed which makes the aquifer partially penetrated by the stream, is considered in the model. The impacts of pumping process, hydraulic conductivity and clogging layer on the quality of water produced from nearby drinking water wells are evaluated. It is found that results are consistent with numerical simulation conducted by MODFLOW software. Moreover, the model is applied using data of contamination occurrence in Malaysia, where high contaminants concentrations are found close to streams. Results show that the pumping activities (rate and time period) are crucial factors when evaluating the risk of groundwater contamination from surface water. Additionally, this study illustrates that the increase in either hydraulic conductivity or leakance coefficient parameters due to the clogging layer will enlarge the area of contamination. The model is able to determine the suitable pumping rate and location of the well so that the contamination plume never reaches the extraction well, which is useful in constructing riverbank filtration sites.
Analytical studies for well design adjacent to river banks are the most significant practical task in cases involving the efficiency of riverbank filtration systems. In times when high pollution of river water is joined with increasing water demand, it is necessary to design pumping wells near the river that provide acceptable amounts of river water with minimum contaminant concentrations. This will guarantee the quality and safety of drinking water supplies. This article develops an analytical solution based on the Green's function approach to solve an inverse problem: based on the required level of contaminant concentration and planned pumping time period, the shortest distance to the riverbank that has the maximum percentage of river water is determined. This model is developed in a confined and homogenous aquifer that is partially penetrated by the stream due to the existence of clogging layers. Initially, the analytical results obtained at different pumping times, rates and with different values of initial concentration are checked numerically using the MODFLOW software. Generally, the distance results obtained from the proposed model are acceptable. Then, the model is validated by data related to two pumping wells located at the first riverbank filtration pilot project conducted in Malaysia.
Modeling three-dimensional contaminant transport released from arbitrary shape source geometries is useful in hydrological and environmental sciences. This article produces several analytical solutions for three-dimensional contaminant transport in a homogeneous and isotropic aquifer by using Green's function with the groundwater flow which is assumed to be in three directions. The solutions are obtained for both finite depth aquifer and semi-infinite depth aquifer. Various types of sources are discussed: point, line, plane, or cuboid sources. The continuous and instantaneous sources are also investigated. A MATLAB coding is developed to calculate the numerical integrals which occur at the solutions. Some solutions are verified with the solutions obtained in the literature. This study confirms the effect of groundwater velocities in all directions on the degree and the directions of contaminant spreading. Additionally, the results highlight the significant effect of the geometrical shape of the contaminant sources on contaminant concentrations for instantaneous and continuous sources. In particular, the cuboid source and the horizontal rectangular source provide the highest concentrations. The analytical solutions developed in this article can be applied for a wide range of contaminant transport.