Objective  There are knowledge gaps on stand carbon stock growth model at present. This study developed a stand-level carbon stock growth model system to provide a method for dynamic estimation of regional forest carbon storage with time.

  Method  Taking Larix olgensis plantation in Jilin Province of northeastern China as the research object, the site quality classification algorithm was used to divide all sample plots into three site grades, which were introduced into the model system as dummy variables. The stand carbon stock growth model system was established by simultaneous equations to link stand average height, basal area growth model and stand carbon stock model. The adjusted coefficient of determination ( R_\textadj^2 ), the standard error of the estimated value (SEE) and the average prediction error (MPE) were used to evaluate model performance. The growth process of stand carbon stock under different site grades and stand density index (SDI), and the influence of stand basal area and average height on stand carbon stock were analyzed.

  Result  (1) The R_\textadj^2 of stand average height growth model, basal area growth model and carbon stock model were 0.892, 0.979 and 0.960, respectively, and the MPEs were both less than 2%. (2) Both procedures in the model system (inventory- and model-derived stand average height and basal area) could accurately estimate the stand carbon stock, and the difference was only 0.02 t/ha, so the model system had great generality and stability. (3) Stand carbon stock growth increased with the increasing site grade of sample plots. When the site grade was the same, the growth was slow with SDI less than 1 500 plant/ha; but there were no differences in the growth process among different SDIs larger than 1 500 plant/ha after 40 years, and the optimal SDI for maximum stand carbon stock was about 1 500−2 000 plant/ha. (4) The stand carbon stock increased with the increase of stand basal area and average height, and stand basal area had larger effects on stand carbon than stand average height.

  Conclusion  The growth of stand carbon stock is closely related to the site grade, stand average age, density, basal area and average height. The modeling approach of simultaneous equations is a feasible method for developing the stand carbon stock growth model system. The stand carbon stock growth model system developed by this study could effectively predict stand carbon stock, which providing a tool for understanding the growth of stand carbon stock and forest carbon sink assessment.