22 January 2013 Science Briefs

SNAMP PUB #14: Allometric equation choice impacts lidar-based forest biomass estimates: A case study from the Sierra National Forest, CA

Article Title: Allometric equation choice impacts lidar-based forest biomass estimates: A case study from the Sierra National Forest, CA.

Authors: Feng Zhao, Qinghua Guo, Maggi Kelly.

Research Highlights:

  1. Lidar data can be used to map biomass in forests.

  2. However, the availability of, and uncertainly in, equations used to estimate tree volume allometric equations influences the accuracy with which LiDAR data can predict biomass volume.

  3. Many lidar metrics, including those derived from individual tree mapping are useful in estimating biomass volume.

Measurement of above ground vegetation or biomass at local, regional and global scales is critical for estimating global carbon storage and assessing ecosystem response to climate change and anthropogenic disturbances. Lidar (light detection and ranging) remote sensing is generally regarded as an accurate method to map biomass because lidar sensors provide more detailed information on canopy structure with the added dimension of vertical height. Most research describing the use of lidar data to estimate biomass volume uses statistical analysis to infer a relationship between ground-based biomass volume, developed from field data and allometric equations (those equations that describe the relative growth of a tree, or part of a tree and its volume), and lidar data. However, there are many such allometric equations to choose from. In the Sierra Nevada, there are two main choices: equations developed from forest inventory data gathered throughout the entire United States (from a Forest Service publication authored by Jenkins and others (see note below for reference)), and equations for the western US region using data from the Forest Inventory and Analysis Program (FIA) collected in in the pacific northwest region of the United States (see note below for reference)). There are no equations currently available developed specifically from data collected in the Sierra Nevada. In this paper we examined how the choice of allometric equation influences results of predicted biomass. While this is only a case study for a single region, findings based on this sample study could also be relevant to forests in other regions where allometric equations using region-specific data are lacking.


  1. quantify the difference in the regional biomass volume estimates calculated from these two sets of allometric equations; and

  2. investigate how the selection of allometric equations influence lidar regression modeling of biomass volume in a sample site in the Sierra National Forest, CA.

We used a total of 121 SNAMP forest inventory 0.05-acre plots (each plot had a 12.62 m radius area around an accurately located plot center). Within each plot forest structural attributes, including tree species, diameter at breast height (DBH), height and height to live crown base, were recorded. We then estimated plot level biomass volume (including leaves, branches, and stems) using two sets of allometric equations: the national level Jenkins allometric equations and the regional level allometric equations used by the FIA program. For each plot, biomass volume was calculated for each individual tree and then was aggregated at the plot scale. We then used a multiple linear regression method to study the relationship between estimated biomass volume and predictive variables from lidar data. We evaluated the performance of these two sets of equations by comparing R2 (correlation coefficient) and RMSE (root mean squared error) for plot-level biomass volume and density.

There were large differences in biomass density statistics between the two allometric equations. The range of biomass density in our plots is large: 38.6–1132.9 Mg/ha for the Jenkins allometric equations compared to 28.8–1442.0 Mg/ha for the regional allometric equations. (17.2-505.3 tons/acre versus 12.8-643.1tons/acre in English units) R2 and RMSE values show that the regional FIA equations performed better the national ones, suggesting that in most conditions regional allometric equations are preferred. Models that included lidar metrics describing individual trees, and an empirically derived relationships between tree height and DBH, as additional variables, were stronger.


  1. Published biomass volume allometric equations from regional and national sources can give substantial variation in plot-level biomass estimates, especially in denser plots. Thus, care should be taken when substituting national scale allometric equations in regional biomass studies and vice versa.
  2. The mean height of individual trees explained a large proportion of variation in the regression modeling of biomass. This is expected, as most estimates of tree volume rely on height.
  3. This study illustrates the value of including an empirical relationship between tree DBH and height for more accurate biomass estimates.
  4. This analysis further supports the concerns that national allometric equations for regional biomass volume estimates might favor more commonly measured species, and do a poorer job estimating species that are less commonly measured.

Reports mentioned:
Jenkins, J.C., Chojnacky, D.C., Heath, L.S., Birdsey, R.A., 2004. Comprehensive database of biomass equations for North American tree species. General Technical Report NE-319. USDA Forest Service, Newtown Square, Pennsylvania, USA.

Waddell, K.L., and B. Hiserote. 2005. The PNW-FIA Integrated Database User Guide: A Database of Forest Inventory Information for California, Oregon, and Washington (V2.0). Pacific Northwest Research Station, Portland, Oregon, USA.

Full Reference:
Zhao, F., Q. Guo and M. Kelly. Allometric equation choice impacts lidar-based forest biomass estimates: A case study from the Sierra National Forest, CA. Agricultural and Forest Meteorology 165: 64–72

The full paper is available here.

For more information about the SNAMP project and the Spatial team, please see the: Spatial Team Website.

To learn more about lidar data, check out our lidar FAQs sheet. For more information on lidar data in SNAMP, see the spatial team website: http://snamp.cnr.berkeley.edu/teams/spatial, and our spatial team newsletters that focus on lidar: Vol. 2, No. 3, and Vol. 5, No. 1.

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