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Summary For decades, researchers have thought it was difficult to remove the uncertainty from the estimates of forest carbon storage and its changes on national sales. This is not only because of stochasticity in the data but also the bias to overcome in the computations. Most studies of the estimation, however, ignore quantitative analyses for the latter uncertainty. This bias primarily results from the widely used volume‐biomass method via scaling up forest biomass from limited sample plots to large areas. This paper addresses (i) the mechanism of scaling‐up error occurrence, and (ii) the quantitative effects of the statistical factors on the error. The error compensators were derived, and expressed by ternary functions with three variables: expectation, variance and the power in the volume‐biomass equation. This is based on analysing the effect of power‐law function convexity on scaling‐up error by solving the difference of both sides of the weighted Jensen inequality. The simulated data and the national forest inventory of China were used for algorithm testing and application, respectively. Scaling‐up error occurrence stems primarily from an effect of the distribution heterogeneity of volume density on the total biomass amount, and secondarily from the extent of function nonlinearities. In our experiments, on average 94·2% of scaling‐up error can be reduced for the statistical populations of forest stands in a region. China's forest biomass carbon was estimated as approximately 6·0 PgC or less at the beginning of the 2010s after on average 1·1% error compensation. The results of both the simulated data experiment and national‐scale estimation suggest that the biomass is overestimated for young forests more than others. It implies a necessity to compensate scaling‐up error, especially for the areas going through extensive afforestation and reforestation in past decades. This study highlights the importance of understanding how both the function nonlinearity and the statistics of the variables quantitatively affect the scaling‐up error. Generally, the presented methods will help to translate fine‐scale ecological relationships to estimate coarser scale ecosystem properties by correcting aggregation errors.
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Carbon allocation is an important mechanism through which plants respond to environmental changes. To enhance our understanding of maximizing carbon uptake by controlling planting densities, the carbon allocation module of a process-based model, TRIPLEX-Management, was modified and improved by introducing light, soil water, and soil nitrogen availability factors to quantify the allocation coefficients for different plant organs. The modified TRIPLEX-Management model simulation results were verified against observations from northern Jiangsu Province, China, and then the model was used to simulate dynamic changes in forest carbon under six density scenarios (200, 400, 600, 800, 1000, and 1200 stems ha−1). The mean absolute errors between the predicted and observed variables of the mean diameter at breast height, mean height, and estimated aboveground biomass ranged from 15.0% to 26.6%, and were lower compared with the original model simulated results, which ranged from 24.4% to 60.5%. The normalized root mean square errors ranged from 0.2 to 0.3, and were lower compared with the original model simulated results, which ranged from 0.3 to 0.6. The Willmott index between the predicted and observed variables also varied from 0.5 to 0.8, indicating that the modified TRIPLEX-Management model could accurately simulate the dynamic changes in poplar (Populus spp.) plantations with different densities in northern Jiangsu Province. The density scenario results showed that the leaf and fine root allocation coefficients decreased with the increase in stand density, while the stem allocation increased. Overall, our study showed that the optimum stand density (approximately 400 stems ha−1) could reach the highest aboveground biomass for poplar stands and soil organic carbon storage, leading to higher ecological functions related to carbon sequestration without sacrificing wood production in an economical way in northern Jiangsu Province. Therefore, reasonable density control with different soil and climate conditions should be recommended to maximize carbon sequestration.