Random location of fuel treatments in wildland community interfaces: a percolation approach

We explore the use of spatially correlated random treatments to reduce fuels in landscape patterns that appear somewhat natural while forming fully connected fuelbreaks between wildland forests and developed protection zones. From treatment zone maps partitioned into grids of hexagonal forest cells representing potential treatment sites, we selected cells to be treated at random using an algorithm that provides a varying degree of treatment clustering. One thousand or more such maps were used as sample replicates for parameter settings that included landscape size, fraction of area treated, and degree of clustering to test whether continuous fuelbreaks were formed in an acceptable proportion of cases. A shortest path network optimization model was solved for each sample landscape to determine the presence or absence of a continuous fuelbreak and to measure the length of the most direct fuelbreak when one or more were present. By varying the fraction of area treated in a bisection search, we were able to estimate the minimum amount of treatment needed. Results indicated that between 54% and 88% of a forest would need to be treated to form fuelbreaks in 60% or more of the landscapes we modeled.