Differential equation models of wildfire suppression allocation - Masarie, Alex Taylor, author; Wei, Yu, advisor; Oprea, Iuliana, committee member; Thompson, Matt, committee member; Belval, Erin, committee member (Colorado State University. Libraries, 2018)
(CHAPTER 1) Current policy calls for efficient and effective wildfire response, which requires an understanding of the system's complexity. Data visualization often provides key insight to initiate any normative modeling effort to reveal best practices when implementing the policy. This chapter outlines a procedure to make MATLAB structures from a resource tracking database. We prepared a wildfire suppression allocation database, built an animation and graphical user interface, and initiated our investigation of differential equations using GIS maps and phase plane as descriptive aides. (CHAPTER 2) Efficient and effective wildland fire response requires interregional coordination of suppression resources. We developed a mathematical model to examine how scarce resources are shared. This chapter outlines how we collected and processed the data, set up the model, and applied both to identify best-fit parameters. We interpret model outputs on interregional test cases that reflect the difficult tradeoffs in this resource allocation problem. By regressing a linear system of ordinary differential equations with GIS-data for demand predictors like suppression resource use, ongoing fire activity, fire weather metrics, accessibility, and population density onto pre-smoothed Resource Ordering Status System (ROSS) wildfire personnel and equipment requests, we fit a national scale regression. We interpret these parameters, report additional statistical properties, and indicate how these findings might be interpreted for personnel and equipment sharing by examining test cases for national, central/southern Rockies, and California interregional sharing. Abrupt switching behavior across medium and high alert levels was found in test cases for national, central/southern Rockies, and California interregional sharing. Workloads are expected to increase over time as well. (CHAPTER 3) Accumulation of burnable forest fuels is changing natural wildfire regimes. Recent megafires are an unintended consequence. Our capability to suppress unwanted fires stems from a complex national sharing process in which specialized firefighting resources mobilize around the United States. This work elaborated a coupled system of PDE equations and tested them on an archive of risk and allocation data from 2011-2016. This chapter poses a consistent math model for wildfire suppression management that explains how spatiotemporal variation in fire risk impacts allocation. Analogies between the seasonal flow of fire suppression demand potential and dynamics of physical flows are outlined for advection, diffusion, reaction, rotation, and feedback. To orient these mathematical methods in the context of resource allocation, we present multi-fire management examples varying in scope from local demand interactions on the Holloway/Barry Point/Rush Fires in 2012 to large perturbations in national allocation. We prototype objective functions.