Graduate Students Seminar

Speaker 1: Luan Nguyen

Title

Compartment-based modeling of reaction-diffusion systems and the choice of mesh size

Abstract

Reaction-diffusion systems have been found in many interesting phenomena ranging from pattern formation to spatial ecology.  Compartment-based method is introduced to study the stochastic modeling of these systems and its relationship to PDE models can be shown. Example of the method will be given. It has been known that the compartment size in simulation algorithm needs choosing carefully in order to describe the problem correctly. It is still open problem on how this size is picked. We will go over some previously proposed bounds in the literature that offers some appropriate choices for the compartment size.

Speaker 2: Reetam Majumder

Title

Hidden Markov Models for multi-site daily precipitation generation

Abstract

Weather ensembles are an integral part of weather forecasting, and can also be used to test the sensitivity and performance of climate models. Among meteorological variables, simultaneous simulation of precipitation at multiple sites presents unique challenges since precipitation has a semi continuous distribution with a point mass at zero and a continuous distribution on the positive real line. We explore the use of Hidden Markov Models as proposed by *Hughes and Guttorp (1994)* and *Robertson et al. (2006)*. The model's strengths and shortcomings when dealing with spatially gridded satellite data are discussed, and research directions for improvements are proposed. The ensemble generation is illustrated for the Potomac River Basin in the east coast of the USA over a spatial grid of 387 points, using daily precipitation data for 2001-2018 from the Integrated Multi-satellitE Retrievals for GPM (IMERG) dataset.