Allometric model of the height–diameter curve for even-aged pure stands of Japanese cedar (Cryptomeria japonica)

Abstract

We derived an allometric model of the height–diameter curve for even-aged pure stands, which was a modification of the earlier model proposed by Inoue (2000a). An individual-dependent allometric equation was used as the height–diameter curve. Using the discriminant analysis method, all trees composed of a stand were stratified into upper and lower trees. It was assumed that both relationships between mean tree height H _m and upper tree height H _u and between mean DBH D _m and mean DBH of upper trees D _u could be described by the time-dependent allometric power equations. The height–diameter curve showed an average relationship between tree height and DBH of a given stand at a given time, and hence it could be assumed that the height–diameter curve contained two points (D _m , H _m ) and (D _u , H _u ). With these assumptions, we derived an allometirc model of height–diameter curve, which allowed the coefficients of the curve to be estimated from mean tree height and mean DBH. The proposed model was fitted to Japanese cedar (Cryptomeria japonica D. Don) data. The error ratio of the allometric model ranged from 2.254% to 13.412% (mean = 6.785%), which was significantly smaller than that of the earlier model. When the error of mean tree height was ±1.0 m or less, the effect of the error of mean tree height on the error ratio was comparatively small. This suggested that the error of ±1.0 m in mean tree height could be accepted in the estimation of height–diameter curve using the allometric model. These features enable us to combine the allometric model with Hirata’s vertical angle-count sampling or growth models. In conclusion, the allometric model would be one of the most practical and convenient approaches for estimating the height–diameter relationship of even-aged pure stands.