Optimizing efficiency of height modeling for extensive forest inventories

Although critical to monitoring forest ecosystems, inventories are expensive. This paper presents a generalizable method for using an integer programming model to examine tradeoffs between cost and estimation error for alternative measurement strategies in forest inventories. The method is applied to an example problem of choosing alternative height-modeling strategies for 1389 plots inventoried by field crews traveling within an 82.5 × 10⁶ ha region of the west coast of North America during one field season. In the first part of the application, nonlinear regional height models were constructed for 38 common species using a development data set of 137 374 measured tree heights, with root mean square error varying from 6.7 to 2.1 m. In the second part of the application, alternative measurement strategies were examined using a minimal cost objective subject to constraints on travel time and estimation error. Reduced travel time for field crews can be a significant portion of the cost savings from modeling tree heights. The optimization model was used to identify a height-modeling strategy that, given assumptions made, resulted in <10% of maximum average plot volume error, >33% of potential measurement cost savings, and small bias for estimates of regional volume and associated sampling error (0.1% and 0.4%, respectively).