Compatible Models of Carbon Content of Individual Trees on a Cunninghamia lanceolata Plantation in Fujian Province,China

We tried to establish compatible carbon content models of individual trees for a Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.) plantation from Fujian province in southeast China. In general, compatibility requires that the sum of components equal the whole tree, meaning that the sum of percentages calculated from component equations should equal 100%. Thus, we used multiple approaches to simulate carbon content in boles, branches, foliage leaves, roots and the whole individual trees. The approaches included (i) single optimal fitting (SOF), (ii) nonlinear adjustment in proportion (NAP) and (iii) nonlinear seemingly unrelated regression (NSUR). These approaches were used in combination with variables relating diameter at breast height (D) and tree height (H), such as D, D²H, DH and D&H (where D&H means two separate variables in bivariate model). Power, exponential and polynomial functions were tested as well as a new general function model was proposed by this study. Weighted least squares regression models were employed to eliminate heteroscedasticity. Model performances were evaluated by using mean residuals, residual variance, mean square error and the determination coefficient. The results indicated that models with two dimensional variables (DH, D²H and D&H) were always superior to those with a single variable (D). The D&H variable combination was found to be the most useful predictor. Of all the approaches, SOF could establish a single optimal model separately, but there were deviations in estimating results due to existing incompatibilities, while NAP and NSUR could ensure predictions compatibility. Simultaneously, we found that the new general model had better accuracy than others. In conclusion, we recommend that the new general model be used to estimate carbon content for Chinese fir and considered for other vegetation types as well.