Modeling the location, characteristics, and dynamics of clusters that occur during ecological outbreaks is an important topic in environmental sciences. Motivated by the 1991 to 1996 Jeffrey pine beetle (JPB) forest epidemic attack in the Lake Tahoe Basin, we propose methods that describe the location, shape, and characteristics of spatial clusters formed by infected trees. Our purpose is to introduce a novel functional representation approach to describe the complex shape and characteristics of spatial clusters. For each cluster, we separate the domain into g non-overlapping cones located at the cluster center, and describe the contour as a distance function at the angle theta that defines each cone. Additional information about the cluster (e.g. number of affected trees) can be collected and represented as a function of the cone-specific angle. By expressing the complex JPB-attacked cluster regions as functions of the direction from the cluster center, we develop a method for modeling the association between the shape and size of clusters and various forest attributes. This approach allows to use functional data modeling to quantify the directions of beetle expansion.