ABSTRACT
This chapter briefly introduces geostatistical estimation techniques, with emphasis on the context of forest inventory. The mathematical and numerical tools required for a good understanding of this subject are more sophisticated than those presented so far and formal proofs will not be given here. The theory was first described by Matheron (1965) and was developed primarily at the Ecole des Mines de Paris, to address practical problems in the mining and oil industries. Mathematically speaking, it dealt originally with stochastic processes defined in the euclidian plane 2 or space 3, but has since been partially extended to spatiotemporal processes. Its current range of applications is nowadays very large: mining, petrology, soil physics, meteorology, oceanography, etc, and forestry. Excellent general references are books by Christensen (1990), Cressie (1991), Wackernagel (2003), and Schabenberger and Gotway (2005). In addition, Mandallaz (1993, 2000) addresses some specific problems associated with forest inventories from an advanced mathematical perspective, further illustrating the theory with an extensive case study, particularly with respect to small area estimations. As mentioned above, geostatistical methods are purely model-dependent. A key issue is the modeling of the underlying spatial covariance function. Once that function or, rather, its variogram is available, the optimal linear estimation is determined via Kriging. This term was coined by Matheron in honor of Krige, a geologist in South Africa. The first section in this chapter will present the concept of variogram, which generalizes, in some sense, the covariance function.
