Spatial simulation of forest using Bayesian state-space models and remotely sensed data

Jörgen Wallerman 1, Coomaren P. Vencatasawmy 2 and Lennart Bondesson 3
1 Department of Forest Resource Management and Geomatics,
Swedish University of Agricultural Sciences,
SE-901 83 Umeå, Sweden
Tel.: + 46 (0)90 786 8570; Fax: + 46 (0)90 778 116
2 Aviva,  Aviva plc, St Helen's, 1 Undershaft,
London EC3P  3DQ
Tel: +44 (0)20 7662 7157; Fax: +44 (0)20 7662 4122
3 Department of Mathematics and Mathematical Statistics, 
Umeå University, 
SE-901 87 Umeå, Sweden
Tel.: + 46 (90) 786 6529; Fax: + 46 (0)90 786 7658 

Utilizing spatial properties of forest attributes may provide increased accuracy in forestry remote sensing applications, compared to  common non-spatial methods. Spatial models are often complex and their inference are usually difficult, though. Such problems may be addressed using Bayesian models, estimated using the computer-intensive Markov-Chain Monte Carlo (MCMC) stochastic simulation methods. This article presents a Bayesian state- space model of forest attributes using field measurements and remote sensing data. The model is defined on a spatial lattice where each lattice cell corresponds to the spatial extent of one raster cell measurement in the remote sensing data. As prior distribution function, the Conditional Autoregressive model (CAR) is utilized since it is well defined for simulation using the Gibbs sampler. The parameters of the CAR were estimated using a variogram model. Inference is provided by the MCMC method Gibbs sampler, a method which allows inference of very complex models. That is, estimation is made by simulating from the posterior distribution (conditional to the available field measurements and remote sensing data). A case- study is presented where the model is applied to produce a 5917 ha large raster map of forest stem volume using field measurements and Landsat 5 TM data in northern Sweden. This corresponds to estimation of a parameter vector of size exceeding 360 000. The mapping accuracy was assessed using sampled field plots and field measured forest stands, not utilized in the model. Simulations made using Gibbs Sampler did converge to reasonable realizations of the forest, in spite of the very large size of the estimated parameter vector. The general mapping accuracy was low, though, 76.1% root mean square error (RMSE), in per cent of the mean, for raster cell (25 by 25m) predictions, and 60.5% RMSE for stand (0.5 – 22.1 ha) predictions. The methodology shows substantial potential although further development of the model would clearly be beneficial.

Keywords: Markov-Chain Monte Carlo, Gibbs Sampler, Bayesian models, forestry, Remote Sensing

In: Caetano, M. and Painho, M. (eds). Proceedings of the 7th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, 5 – 7 July 2006, Lisboa, Instituto Geográfico Português

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