Oral Comprehensive Exam Study Plan: Simulating Processes with Spatial Variability

Ecological processes play a critical role in shaping the world in which we live and guiding our interactions with it. As humans we are consistently attempting to predict, understand and sometimes control the behaviour of the natural world. Whether we are trying to forecast the upcoming seasonal rains, recreating a forest fire to understand why it burned in a particular manner, or making land management decisions towards a particular future objective, computer models and simulations can be of crucial assistance. The discipline of computer simulation, whether the simulated processes be computer related, business oriented, ecological, etc., is a discipline as old as computing and is well understood. Accurately and efficiently simulating time (as discrete events) is also well understood. However, many processes, particularly ecological processes which are ongoing over a large spatial range have a spatial component which substantially increases the time and complexity of the computations involved. To date most of the existing work in spatial modeling is raster-based; also known as grid-based. Raster-based models contain a spatial array of fixed-size entities for which every computation must be run at each time step interval. This presents a paradox where the accuracy of the simulation may require a fine grained spatial scale, but the application may require a fast input/output turn around to have usable results. These goals are in tension and we believe that there exist more efficient methods of modeling space to achieve both accurate simulations and efficient computation. To research more efficient methods of spatial modeling one must have a firm understanding of several different areas. In this paper we define our research area: variable resolution spatial modeling. We describe the how the problem of accurately and efficiently simulating time has been solved and draw a parallel for how we anticipate solving the problem of simulating space. We then outline the requirements for understanding the key problems and open research questions. We then propose a reading list and study plan for the Oral Comprehensive Exam, a requirement set forth by the Graduate Education Committee.