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Abstract Background In recent decades the future of global forests has been a matter of increasing concern, particularly in relation to the threat of forest ecosystem responses under potential climate change. To the future predictions of these responses, the current forest biomass carbon storage (FCS) should first be clarified as much as possible, especially at national scales. However, few studies have introduced how to verify an FCS estimate by delimiting the reasonable ranges. This paper addresses an estimation of national FCS and its verification using two-step process to narrow the uncertainty. Our study focuses on a methodology for reducing the uncertainty resulted by converting from growing stock volume to above- and below-ground biomass (AB biomass), so as to eliminate the significant bias in national scale estimations. Methods We recommend splitting the estimation into two parts, one part for stem and the other part for AB biomass to preclude possible significant bias. Our method estimates the stem biomass from volume and wood density (WD), and converts the AB biomass from stem biomass by using allometric relationships. Results Based on the presented two-step process, the estimation of China’s FCS is performed as an example to explicate how to infer the ranges of national FCS. The experimental results demonstrate a national FCS estimation within the reasonable ranges (relative errors: + 4.46% and − 4.44%), e.g., 5.6–6.1 PgC for China’s forest ecosystem at the beginning of the 2010s. These ranges are less than 0.52 PgC for confirming each FCS estimate of different periods during the last 40 years. In addition, our results suggest the upper-limits by specifying a highly impractical value of WD (0.7 t∙m − 3 ) on the national scale. As a control reference, this value decides what estimate is impossible to achieve for the FCS estimates. Conclusions Presented methodological analysis highlights the possibility to determine a range that the true value could be located in. The two-step process will help to verify national FCS and also to reduce uncertainty in related studies. While the true value of national FCS is immeasurable, our work should motivate future studies that explore new estimations to approach the true value by narrowing the uncertainty in FCS estimations on national and global scales.

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.

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.

The method of forest biomass estimation based on a relationship between the volume and biomass has been applied conventionally for estimating stand above- and below-ground biomass (SABB, t ha−1) from mean growing stock volume (m3 ha−1). However, few studies have reported on the diagnosis of the volume-SABB equations fitted using field data. This paper addresses how to (i) check parameters of the volume-SABB equations, and (ii) reduce the bias while building these equations. In our analysis, all equations were applied based on the measurements of plots (biomass or volume per hectare) rather than individual trees. The volume-SABB equation is re-expressed by two Parametric Equations (PEs) for separating regressions. Stem biomass is an intermediate variable (parametric variable) in the PEs, of which one is established by regressing the relationship between stem biomass and volume, and the other is created by regressing the allometric relationship of stem biomass and SABB. A graphical analysis of the PEs proposes a concept of “restricted zone,” which helps to diagnose parameters of the volume-SABB equations in regression analyses of field data. The sampling simulations were performed using pseudo data (artificially generated in order to test a model) for the model test. Both analyses of the regression and simulation demonstrate that the wood density impacts the parameters more than the allometric relationship does. This paper presents an applicable method for testing the field data using reasonable wood densities, restricting the error in field data processing based on limited field plots, and achieving a better understanding of the uncertainty in building those equations.

Abstract Forest above‐ground biomass (AGB) is often estimated by converting the observed tree size using allometric scaling between the dry weight and size of an organism. However, the variations in biomass allocation and scaling between tree crowns and stems due to survival competition during a tree's lifecycle remain unclear. This knowledge gap can improve the understanding of modelling tree biomass allometry because traditional allometries ignore the dynamics of allocation. Herein, we characterised allometric scaling using the dynamic ratio ( r ) of the stem biomass (SB) to AGB and a dynamic exponent. The allometric models were biologically parameterised by the r values for initial, intermediate and final ages rather than only a regression result. The scaling was tested using field measurements of 421 species and 2213 different‐sized trees in pantropical regions worldwide. We found that the scaling fluctuated with tree size, and this fluctuation was driven by the trade‐off relationship of biomass allocation between the tree crown and stem depending on the dynamic crown trait. The allometric scaling between SB and AGB varied from 0.8 to 1.0 for a tree during its entire lifecycle. The fluctuations presented a general law for the allometric scaling of the pantropical tree biomass and size. Our model quantified the trade‐off and explained 94.1% of the allometric relationship between the SB and AGB (93.8% of which between D 2 H and AGB) for pantropical forests, which resulted in a better fit than that of the traditional model. Considering the effects of the trade‐off on modelling, the actual biomass of large trees could be substantially greater than conventional estimates. These results highlight the importance of coupling growth mechanisms in modelling allometry and provide a theoretical foundation for better describing and predicting forest carbon accumulation.