This study aims to construct a stand-level model for estimating the carbon stock of Cunninghamia lanceolata forests applicable to Jiangxi Province based on the national standard “Tree Biomass Models and Related Parameters to Carbon Accounting for Major Tree Species” (GB/T 43648-2024), to improve the accuracy and reliability of the estimation.

Three theoretical growth equations—Logistic, Modified Weibull, and Gompertz—were used as the base models for this study. Two types of power function form, referred to as ND_g^φ and N^δD_g^φ, were introduced to reflect the density of the stand, resulting in six models for estimating carbon stock in variable-density stands. Additionally, the commonly used power-law allometric equation was included in the model comparison framework. The nonlinear weighted least squares method was employed for parameter fitting, and the optimal model was established through model evaluation and testing. To further validate the effectiveness of the constructed model, a systematic comparison was conducted between the estimates from the optimal model and those obtained using traditional methods.

1) The modified Weibull equation, incorporating the power function form ND_g^φ, achieves the highest coefficient of determination (R²=0.973) and the lowest standard error of estimate (SEE=3.004 t·hm^-2). Additionally, it demonstrates minimal values for total relative error (TRE=0.06%), mean systematic error (MSE=-0.07%), mean prediction error (MPE=1.77%), mean percent standard error (MPSE=8.99%), and Akaike Information Criterion (AIC=920.6). TRE and MSE are maintained within ±3%, while MPE and MPSE meet the general accuracy requirements of less than 3% and 15%, respectively. Furthermore, the model's residuals show significant improvements in heteroscedasticity and normality; 2) Compared with the traditional methods, the modified Weibull equation demonstrates the best performance with an R² of 0.978 and a parameter m of 0.950. The parameter n is not significantly different from 0 (P>0.1), and the absolute value of TRE is the lowest at 2.89%. Additionally, the systematic bias between the predicted values and the observed values is not significant (P>0.1). Among traditional methods, the BEF method shows an R² of 0.974 and a parameter m of 0.934. Like the modified Weibull equation, its parameter n is not significantly different from 0 (P>0.1). However, the TRE is 10.57%, indicating a significant systematic underestimation of the predicted values (P<0.001), with an average of 1.427 t·hm^-2 lower than the observed values. In contrast, the CBEF1 and CBEF2 methods yield R² of 0.792 and 0.872, respectively. Their parameter m values are 0.575 and 0.681, with parameter n values of 10.921 and 8.715. The TRE for CBEF1 and CBEF2 methods are -13.17% and -12.36%, respectively, indicating a significant systematic overestimation of the predicted values (P<0.05). On average, the predicted values exceed the observed values by 4.227 t·hm^-2 and 3.673 t·hm^-2, respectively.

The modified Weibull equation, developed according to the national standard, is optimal for estimating carbon stock in Cunninghamia lanceolata forests within the study area. Its estimation results are more accurate and reliable than those of traditional methods, offering greater practical value in application.