The basis for the standing timber estimation in the NFI are the individual tree volumes, which are estimated with the help of allometric equations. Tree stems are very different in their form. Estimations of the bole volume that are based only on the diameter at breast height d_1.3 are, therefore, considerably less precise than estimations that are also based on additional measurements of the tree height (H) and on an upper stem diameter. A higher estimation precision requires an augmented expenditure for the measurements.
Whereas the d_1.3 of all trees was measured in the NFI, an upper diameter (d₇, diameter at 7 meter height) and the tree height were only measured on a subsample, the so-called tariff trees. The volume estimations of the tariff trees that were based on these three measurements (Y_i = f(d_1.3, d₇, H) ) were used to derive tariff functions. The tariff functions estimate individual tree volumes depending only on one measurement variable (the d_1.3), but additionally on various tree, stand, and site attributes. To take three measurements from all trees for volume estimation is not efficient, since the gain in precision is small compared to the expenditure (KAUFMANN 1993; MANDALLAZ 1995; 1997).
In the first NFI, four trees per sample plot were measured on average (i.e. slightly more than one third of all trees) in a sector of 0 to 150 gon of the plots (ZINGG and BACHOFEN 1988). In the second NFI, on average two trees per plot were randomly chosen as tariff trees in this sector. The selection probability was proportional to d_1.3² (KAUFMANN 1993). For the timber assortment, according to the Swiss timber trade customs (Forstwirtschaftliche Zentralstelle 1976), tree stems are broken down into commercial assortments with the help of taper equations, which continuously describe a stem profile from the ground to the top.