A spatial dynamic approach to ecological modeling: Simulating fire spread.

Abstract

The objective of this dissertation is to develop a new research tool, PROMAP, which will allow the construction of models that satisfy the requirement of spatial distribution and hierarchical interactions within a dynamic framework. An analysis of the form of ecosystems is followed by an examination of current attempts at ecosystem modeling using spatial relationships. An examination of the analytical procedures used in the spatial modeling process, results in a set of criteria that a suitable modeling system should incorporate. These criteria are: the use of real numbers; iterative processing; flexible data retrieval; and neighborhood analytical procedures. The basic configuration of PROMAP is discussed with an emphasis on the mathematical procedures and the capability for designing cellular automata within the system. The representation of biophysical systems into a set of spatial transition functions is described in relation to the development of nested hierarchies called Q-morphisms. Having established the design of PROMAP, a suitable test is devised using the simulation of surface fire spread. A model called FIREMAP is developed and the results are compared to expected fire shapes under Zero State Conditions. These conditions are defined as uniform fuel, zero slope and zero wind with additional factors held constant. Other simulations of fire spread are made by relaxing the conditions to achieve wind driven fires and the response to potential impediments to fire spread. The response of the simulation shows an accurate correspondence between the simulation and the expected fire shape. As a final test of the model, all restrictions are removed and a simulation is made under actual conditions of complex terrain, and non-uniform fuels using data collected on the San Carlos Apache Indian Reservation in southeast Arizona. Deficiencies of PROMAP and FIREMAP are discussed as well as future implications for the FIREMAP model as a management tool.