Rabih Ghostine

Bio: Rabih Ghostine is an academic researcher from École Normale Supérieure. The author has contributed to research in topics: Shallow water equations & Discontinuous Galerkin method. The author has an hindex of 11, co-authored 19 publications receiving 259 citations. Previous affiliations of Rabih Ghostine include Institut national des sciences appliquées & Centre national de la recherche scientifique.

An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter

Abstract: In this paper, an extended SEIR model with a vaccination compartment is proposed to simulate the novel coronavirus disease (COVID-19) spread in Saudi Arabia. The model considers seven stages of infection: susceptible (S), exposed (E), infectious (I), quarantined (Q), recovered (R), deaths (D), and vaccinated (V). Initially, a mathematical analysis is carried out to illustrate the non-negativity, boundedness, epidemic equilibrium, existence, and uniqueness of the endemic equilibrium, and the basic reproduction number of the proposed model. Such numerical models can be, however, subject to various sources of uncertainties, due to an imperfect description of the biological processes governing the disease spread, which may strongly limit their forecasting skills. A data assimilation method, mainly, the ensemble Kalman filter (EnKF), is then used to constrain the model outputs and its parameters with available data. We conduct joint state-parameters estimation experiments assimilating daily data into the proposed model using the EnKF in order to enhance the model’s forecasting skills. Starting from the estimated set of model parameters, we then conduct short-term predictions in order to assess the predicability range of the model. We apply the proposed assimilation system on real data sets from Saudi Arabia. The numerical results demonstrate the capability of the proposed model in achieving accurate prediction of the epidemic development up to two-week time scales. Finally, we investigate the effect of vaccination on the spread of the pandemic.

Application of a second‐order Runge–Kutta discontinuous Galerkin scheme for the shallow water equations with source terms

Abstract: The present work addresses the numerical prediction of discontinuous shallow water flows by the application of a second-order Runge-Kutta discontinuous Galerkin scheme (RKDG2). The unsteady flow of water in a one-dimensional approach is described by the Saint Venant's model which incorporates source terms in practical applications. Therefore, the RKDG2 scheme is reformulated with a simple way to integrate source terms. Further, an adequate boundary conditions handling, by the theory of characteristics, was overviewed to be adapted to the external points of the mesh, as well as to some points of local invalidity of the Saint Venant's model. To validate the proposed technique, steady and transient test problems (all having a reference solution) were considered and computed by means of the overall method. The results were illustrated jointly with the reference solution and the results carried out by a traditional second-order finite volume (FV2) scheme implemented with the same techniques as the RKDG2. The proposed method has proven its practical consideration when solving discontinuous shallow water flow involving: non-prismatic channels, various cross-sections, smoothly varying bed topography and internal boundary conditions. Copyright © 2007 John Wiley & Sons, Ltd.

Comparative study of 1D and 2D flow simulations at open-channel junctions

Abstract: In this paper, a comparison between the 1D and 2D approaches for simulating combining flows at open-channel junctions is presented. The two approaches are described allowing for a full comprehension of flow modelling. For flows in an open-channel network, mutual effects exist among the channel branches at a junction. Therefore, the 1D Saint-Venant equations for the branch flows are supplemented by various junction models. The existing models are of empirical nature and depend on the flow regime and thus are not practical in all cases. The numerical approximation of the two approaches is performed by the Runge–Kutta discontinuous Galerkin scheme and tested using defined flow problems to illustrate the results of the two approaches. Comparisons are conducted for supercritical, transitional and subcritical flows, indicating the validity range of the 1D approach and the advantages of the 2D approach.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

Abstract: The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

Closure of "Model for Flood Propagation on Initially Dry Land"

Abstract: A model is presented for the simulation of shallow water flow and, specifically, flood waves propagating on a dry bed. The governing equations are transformed to an equivalent system valid on a deforming coordinate system and are solved by a dissipative finite-element technique. A second-order difference scheme is employed for the integration in time. The implicit nonlinear equations resulting from the weak formulations are solved by the Newton-Raphson method, and the set of linear algebraic equations generated is solved by a frontal algorithm. A deforming grid generation scheme is introduced in the dissipative finite-element formulation to account for the effects of the propagating or receding wave fronts on dry land. The accuracy and stability of the model is examined by comparing the model results with observed data from an experimental field test. Results of trial runs for the simulation of overland flow are also presented.

An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter

Abstract: In this paper, an extended SEIR model with a vaccination compartment is proposed to simulate the novel coronavirus disease (COVID-19) spread in Saudi Arabia. The model considers seven stages of infection: susceptible (S), exposed (E), infectious (I), quarantined (Q), recovered (R), deaths (D), and vaccinated (V). Initially, a mathematical analysis is carried out to illustrate the non-negativity, boundedness, epidemic equilibrium, existence, and uniqueness of the endemic equilibrium, and the basic reproduction number of the proposed model. Such numerical models can be, however, subject to various sources of uncertainties, due to an imperfect description of the biological processes governing the disease spread, which may strongly limit their forecasting skills. A data assimilation method, mainly, the ensemble Kalman filter (EnKF), is then used to constrain the model outputs and its parameters with available data. We conduct joint state-parameters estimation experiments assimilating daily data into the proposed model using the EnKF in order to enhance the model’s forecasting skills. Starting from the estimated set of model parameters, we then conduct short-term predictions in order to assess the predicability range of the model. We apply the proposed assimilation system on real data sets from Saudi Arabia. The numerical results demonstrate the capability of the proposed model in achieving accurate prediction of the epidemic development up to two-week time scales. Finally, we investigate the effect of vaccination on the spread of the pandemic.

Ensemble flood forecasting: Current status and future opportunities

Abstract: Ensemble flood forecasting has gained significant momentum over the past decade due to the growth of ensemble numerical weather and climate prediction, expansion in high performance computing, growing interest in shifting from deterministic to risk-based decision-making that accounts for forecast uncertainty, and the efforts of communities such as the international Hydrologic Ensemble Prediction Experiment (HEPEX), which focuses on advancing relevant ensemble forecasting capabilities and fostering its adoption. With this shift, comes the need to understand the current state of ensemble flood forecasting, in order to provide insights into current capabilities and areas for improvement, thus identifying future research opportunities to allow for better allocation of research resources. In this paper, we provide an overview of current research activities in ensemble flood forecasting and discuss knowledge gaps and future research opportunities, based on a review of 70 papers focussing on various aspects of ensemble flood forecasting around the globe. Future research directions include opportunities to improve technical aspects of ensemble flood forecasting, such as data assimilation techniques and methods to account for more sources of uncertainty, and developing ensemble forecasts for more variables, for example flood inundation, by applying techniques such as machine learning. Further to this, we conclude that there is a need to not only improve technical aspects of flood forecasting, but also to bridge the gap between scientific research and hydro-meteorological model development, and real-world flood management using probabilistic ensemble forecasts, especially through effective communication.