Objective  Picea schrenkiana var. tianschanica is the most widely distributed species forming the ecological and public welfare forests in the mountainous regions of Xinjiang. Exploring the changes in carbon storage in artificial Picea schrenkiana var. tianschanica forests based on age classes and its impact on allometric growth relationships between tree height and diameter at breast height can provide important theoretical references for accurately estimating their growth status, biomass, and carbon storage distribution. This can also serve as a theoretical basis for scientifically evaluating the ecological benefits of artificial Picea schrenkiana var. tianschanica forests within a regional scope and formulating compensation decisions.

Methods Taking artificial Picea schrenkiana var. tianschanica forests of different ages as the research objects, field surveys were conducted to obtain data on tree height(H) and diameter at breast height(D). Typical empirical models were used to estimate the average biomass and average carbon storage of forests of different ages. The original data on tree height and diameter at breast height were transformed using logarithmic, power function and first-order differential transformations. Five different modeling approaches, namely exponential, power, logarithmic, linear, and quadratic functions, were employed to establish height-diameter at breast height models. The optimal fitting model was selected based on the goodness of fit(R²).

Results As the forest age increases, the carbon storage of artificial Picea schrenkiana var. tianschanica forests at different ages exhibits an "N"-shaped trend. The highest R² and best performance were achieved when the data were transformed using the logarithmic method and fitted using a quadratic function.

Conclusion The constructed allometric growth model can be used as a reference for estimating the tree height and diameter at breast height of artificial Picea schrenkiana var. tianschanica forests aged between 30 to 60 years, providing a theoretical basis for predicting forest growth.