Turning that realization into a predictive mathematical model is not a simple matter. Working with co-author Gregory P. Asner at the Carnegie Institution for Science in Stanford, Calif., Kellner created the model, which provides a probabilistic accounting of whether the height change in a pixel is likely to be the normal growth of the incumbent tree, a takeover by a neighboring tree, or another branch of the incumbent tree.
The model doesn't just work for this forest but potentially for different kinds of forests, Kellner said, because its interpretation of the data is guided by the data itself. The model uses what seems to be the forest's normal rate of growth to determine when evidence of vertical growth is more than plausible and therefore a possible signal of lateral overtopping.
"While we can all agree that a 20-meter increase over two years is definitely not vertical growth, where you put the boundary, is a necessarily subjective decision," Kellner said. "The neat thing about the analytical framework is you have the data choosing for you. The data arbitrate when a given height change is judged to be vertical rather than lateral, and that is based on the unique neighborhood around that position and what we've observed in the rest of the data."
So even in an area where growth is quite uniform, the model can still predict whether a height change is due to growth or a takeover. Accounting for several neighborhoods, including some with more variance, can delineate trends such as how close trees have to be before one could overtop another.
Using the model, Kellner and Asner gained a number of insights beyond the huge incumbency advantage. They found that a tree's height was
|Contact: David Orenstein|