e., probability (of being selected in the sample) learn more proportional to prediction according to Grosenbaugh, 1965). 3P-sampling is a well established and efficient sampling method, resulting in unbiased and thus reliable estimates (e.g., Schreuder et al., 1993). Although mainly used for estimating stand volume by selecting sample trees with a probability proportional to their estimated volume, it has also been used for estimating sparse species (Ringvall and Kruys, 2005) and needle mass (Eckmüllner and Sterba, 2000). Branches with a branch base diameter between 5 and 10 mm were not included in the 3P sample. All 24 selected branches per tree were weighed as a whole for determining

the total fresh mass of the branch (Mtotal). From 12 branches (4 per crown

section) the parts bearing no needles were discarded and the remaining fresh mass (green mass) was weighed again (gMtotal). For 9 trees one branch per crown section was selected randomly, and for each of these branches a random Hydroxychloroquine solubility dmso sample of approx. 200 g from the gMtotal was weighed accurately (gMsample), filled into paper bags, and brought to the laboratory for further measurements to get the dry needle mass. There, these samples were dried for 12 h at 60 °C. After this, the needles were separated from the branches and twigs, and dried again for 12 h at 105 °C. After cooling to room temperature the needles were weighed to get the dry needle mass for the sample (dMNsample). To determine the total dry needle mass of each sample tree (dMNtree) we used the following steps: First Fenbendazole we calculated the ratio of the green mass, gMtotal, to Mtotal, the total mass for 12 branches (4 of each crown section) of each of the 27 sample trees where we had determined gMtotal. equation(1) qgMM=gMtotalMtotalqgMM was then modelled for each tree separately, depending on the branch base diameter (bbd) and the respective crown third. equation(2)

qgMM=a+b⋅bbd+c⋅csl+d⋅csm+e⋅(bbd⋅csl)+f⋅(bbd⋅csm)qgMM=a+b⋅bbd+c⋅csl+d⋅csm+e⋅(bbd⋅csl)+f⋅(bbd⋅csm)where csl and csm are dummy variables for the lower crown section and the middle crown section, respectively. Furthermore, to determine the total dry needle mass of the selected branches (dMNtotal) we needed the ratio of dry needle mass and green mass which we got from the samples in the laboratory with the following equation: equation(3) qdg=dMNsamplegMsampleqdg was not modelled for each tree separately, but as one common model for each stand, i.e., from 27 branches per stand – one branch from each crown third of the 9 sub-sample trees per stand. equation(4) qdg=a+b⋅ln dbh+c⋅bbd+d⋅csl+e⋅csm+f⋅(csl⋅ln dbh)+g⋅(csm⋅ln dbh)+h⋅(csl⋅bbd)+i⋅(csm⋅bbd)where qdg is the ratio according to Eq. (3), dbh, the breast height diameter of the tree, bbd, the branch base diameter, and csm and csl the dummy variables for the respective crown third.