Harnessing data assimilation and spatial autocorrelation for forest inventory

Qing Xu, Bo Li, Ronald E. McRoberts, Zengyuan Li, Zhengyang Hou

Research output: Contribution to journalArticlepeer-review


Spatially explicit uncertainties in forest above-ground biomass predictions for population units are underestimated if spatial structure in the form of residual spatial autocorrelation and heteroscedasticity is ignored. Methods that consider the spatial structure of biomass model residuals are needed to comprehensively estimate, as well as to effectively reduce, the uncertainty in biomass predictions, for pursuing higher levels of precision for measurement, reporting and verification of forest carbon stocks. The objectives of the study were threefold: (1) to demonstrate a spatial data assimilation (DA) procedure that harnesses small-footprint airborne LiDAR, the best linear unbiased predictor (BLUP) and the spatial structure of biomass model residuals to reduce prediction variances of individual tree biomass and plot-level biomass density; (2) to derive a variance estimator that decomposes the variance into components associated with corresponding error sources; and (3) to compare prediction variances for three methods used to calibrate a height-based allometric model for tree biomass: ordinary least squares (OLS), generalized least squares (GLS), and spatial DA using the BLUP. Five major conclusions are drawn. First, for individual tree biomass predictions, spatial DA decreased prediction variance by 40% and 20% relative to OLS and GLS. Because the decrease in residual variability accounted for 98% of the decrease in prediction variance in total, the assimilation effect was the largest for reducing residual variability. Second, for biomass density predictions, DA decreased prediction variance by 3% and 49% relative to OLS and GLS, with the largest decrease in residual covariance. Accumulated gain in precision for individual tree predictions in the DA procedure was offset by precision loss caused by residual covariance and the variance associated with omission and commission errors while predicting individual tree biomass from the LiDAR data. Third, OLS, which assumed no spatial structure, underestimated prediction variance for LiDAR-predicted biomass density by 48%. Fourth, from the perspective of prediction accuracy, DA reduced the RMSE for individual tree biomass predictions by 11% and 14% and reduced the RMSE for biomass density predictions by 28% and 33% relative to OLS and GLS. Fifth, the omission/commission difference model was effective for correcting the systematic prediction error in the LiDAR-predicted biomass density. Overall, the proposed spatial DA procedure demonstrated great potential for reducing the uncertainty in forest biomass predictions, thereby facilitating more efficient biomass inventories. The procedure can be generalized to other dependent variables of interest given their correlations with new information from LiDAR.

Original languageEnglish (US)
Article number113488
JournalRemote Sensing of Environment
StatePublished - Apr 1 2023


  • Data assimilation
  • Heterogeneous variance
  • Prediction variance
  • Spatial autocorrelation
  • Spatially structured
  • Variance decomposition

ASJC Scopus subject areas

  • Soil Science
  • Geology
  • Computers in Earth Sciences


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