Precision and accuracy in determining tree heights are important considerations for field-based measurements. This is especially true when heights are used to predict derived values (e.g., volume models to estimate carbon sequestration) or to ground-truth remotely sensed information (e.g., evaluating LIDAR). Portable laser hypsometers promising centimeter-level accuracy in tree height measurements have recently been introduced. However, by default, these devices use a trigonometric approach to height calculation that is prone to significant error. This approach, commonly called the tangent method, only approximates tree height under most conditions.
Fortunately, these laser hypsometers can use a different trigonometric procedure known as the sine method that eliminates virtually all of the tangent assumptions. Measurements taken on an open-grown, 75.4-cm DBH loblolly pine (Pinus taeda) on the University of Arkansas-Monticello campus show the differences between these techniques. A series of transects were extended from the base of this loblolly pine, each one 45 degrees from the next. Up to 3 observations along each transect were made at varying distance (18 to 100 m) from the pine. At each viewpoint, a tangent height of the highest apparent living foliage was measured with a laser hypsometer, followed then by the sine height of that exact same foliage. Finally, using the sine method and the “continuous” measurement mode of the hypsometer, the highest visible point of the crown from that observation spot was made. By definition, “true” height was determined to be the maximum sine height observed from all of the different observation points.
Results/Conclusions
The tangent method heights averaged 1.5 m taller than the true height (24.2 m), and several estimates exceeded 3.5 m for this generally straight, open-grown individual. Overall, tangent measurements were positively skewed and biased towards overestimates of tree height. Sine height measures made of the same “high” point of the crown had the opposite pattern—their heights were negatively skewed, and always underestimated tree height. Sine heights taken when scanning the whole crown produced a slightly negatively skewed trend, with more consistency in the height values returned. Proximity to the tree considerably affected the departure for each measurement approach, with the closer observations (those <30 m from the tree) more likely to produced flawed heights, especially with the tangent method. Though not as easy as the tangent method to apply, the sine method is more accurate and robust under many conditions, and yields a more reliable height estimate.
