- Broad-scale estimates of above ground forest biomass (AGB) are typically produced by applying individual-tree equations to inventory data consisting of measurements from probabilistically or purposively selected trees. The associated uncertainty for these estimates depends primarily on three sources of error that interact and propagate: (1) measurement error, the quality of the tree-level measurement data used as inputs for the individual-tree equations; (2) model error, the uncertainty about the equations predictions themselves; and (3) sampling error, the uncertainty due to having obtained a probabilistic or purposive sample, rather than a census, of the trees on a given area of forest land. Often only sampling error is accounted for, resulting in an underestimation of the actual uncertainty for estimates of AGB. With an increased importance placed on accurate estimation of AGB for broader scales comes an increased need to credible portray the true magnitude of their associated uncertainties.
One additional benefit of accounting for all three sources of uncertainty is that it provides an opportunity to observe possible gains in precision to be had by addressing measurement error. Terrestrial LiDAR is a high-precision instrument that has proven useful in forest inventory applications. Several studies have assessed the performance of this technology in extracting tree-level metrics. However, no research efforts exist that have taken this information and subsequently assessed the impact of this measurement performance on the total uncertainty of broad-scale estimates of forest-related parameters, such as AGB.
This study aims to compare the total propagated error for two sets of regional-level component equations for lodgepole pine AGB, and for two sets of high-precision instruments by accounting for all three of these sources of error. The two sets of models compared included a set of newly-developed component ratio method (CRM) equations, and a set of component AGB equations currently used by the Forest Inventory and Analysis (FIA) unit of the United States Department of Agriculture (USDA) Forest Service. Instrument comparisons made were between a phase-based terrestrial laser scanner (TLS) and traditional forest inventory instruments, which in this study were a Spencer combination tape and a Trupulse Laser Rangefinder 360R. Monte Carlo simulations were used to propagate measurement, model and sampling error, and to compare total uncertainty between models, and between instruments. Input variables for the equations were diameter at breast height, total tree height and height to crown base; these were extracted from the terrestrial LiDAR data through the creation of automated algorithms.
Relative contributions for measurement, model and sampling error using the current regional equations were 5%, 2% and 93%, respectively, and 13%, 55% and 32%, respectively using the CRM equations. Relative standard error (RSE) values for the current regional and CRM equations with all three error types accounted for were 20.7% and 36.8%, respectively. Relative contributions for measurement, model and sampling error for the TLS were 5%, 70% and 25%, respectively, and 11%, 66% and 23%, respectively using the traditional instruments. RSE values for the TLS and traditional instruments, with all three error types accounted for, were 52.1% and 54.4%, respectively. Results for the model comparisons indicate that per acre estimates of AGB using the CRM equations are far less precise than those produced with the current set of regional equations. Results for the instrument comparisons indicate the TLS can in fact reduce uncertainty in broad-scale estimates of AGB attributed to measurement error.