LiDAR based prediction of forest biomass using hierarchical models with spatially varying coefficients

Chad Babcock, Andrew O. Finley, John B. Bradford, Randall Kolka, Richard Birdsey, Michael G. Ryan

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


Many studies and production inventory systems have shown the utility of coupling covariates derived from Light Detection and Ranging (LiDAR) data with forest variables measured on georeferenced inventory plots through regression models. The objective of this study was to propose and assess the use of a Bayesian hierarchical modeling framework that accommodates both residual spatial dependence and non-stationarity of model covariates through the introduction of spatial random effects. We explored this objective using four forest inventory datasets that are part of the North American Carbon Program, each comprising point-referenced measures of above-ground forest biomass and discrete LiDAR. For each dataset, we considered at least five regression model specifications of varying complexity. Models were assessed based on goodness of fit criteria and predictive performance using a 10-fold cross-validation procedure. Results showed that the addition of spatial random effects to the regression model intercept improved fit and predictive performance in the presence of substantial residual spatial dependence. Additionally, in some cases, allowing either some or all regression slope parameters to vary spatially, via the addition of spatial random effects, further improved model fit and predictive performance. In other instances, models showed improved fit but decreased predictive performance-indicating over-fitting and underscoring the need for cross-validation to assess predictive ability. The proposed Bayesian modeling framework provided access to pixel-level posterior predictive distributions that were useful for uncertainty mapping, diagnosing spatial extrapolation issues, revealing missing model covariates, and discovering locally significant parameters.

Original languageEnglish (US)
Pages (from-to)113-127
Number of pages15
JournalRemote Sensing of Environment
StatePublished - Nov 1 2015

Bibliographical note

Funding Information:
This work was partially supported by grants from the National Science Foundation DMS-1106609 , EF-1137309 , EF-1241874 , and EF-1253225 , National Aeronautical and Space Administration Carbon Monitoring System and NNH08AH971 , and the USDA Forest Service . Special thanks to the anonymous reviewers.

Publisher Copyright:
© 2015.


  • Bayesian hierarchical models
  • Forest biomass
  • Gaussian process
  • Geospatial
  • LiDAR
  • Markov chain Monte Carlo


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