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Historically, height–diameter models have mainly been developed for mature trees; consequently, few height–diameter models have been calibrated for young forest stands. In order to develop equations predicting the height of trees with small diameters, 46 individual height–diameter models were fitted and tested in young black spruce (Picea mariana) and jack pine (Pinus banksiana) plantations between the ages of 4 to 8 years, measured from 182 plots in New Brunswick, Canada. The models were divided into 2 groups: a diameter group and a second group applying both diameter and additional stand- or tree-level variables (composite models). There was little difference in predicting tree height among the former models (Group I) while the latter models (Group II) generally provided better prediction. Based on goodness of fit (R 2 and MSE), prediction ability (the bias and its associated prediction and tolerance intervals in absolute and relative terms), and ease of application, 2 Group II models were recommended for predicting individual tree heights within young black spruce and jack pine forest stands. Mean stand height was required for application of these models. The resultant tolerance intervals indicated that most errors (95%) associated with height predictions would be within the following limits (a 95% confidence level): [-0.54 m, 0.54 m] or [-14.7%, 15.9%] for black spruce and [-0.77 m, 0.77 m] or [-17.1%, 18.6%] for jack pine. The recommended models are statistically reliable for growth and yield applications, regeneration assessment and management planning. Key words: composite model, linear model, model calibration, model validation, prediction interval, tolerance interval

The Chapman-Richards growth function is used to model jack pine (Pinus banksiana Lamb.) tree height-diameter relationships at provincial, regional, and ecoregional levels. The results suggest that the tree height-diameter relationships of jack pine are significantly different among the geographic regions of Ontario, depending on local climatic, soil, and ecological conditions. In light of this study, the provincial and regional height-diameter models are not appropriate for predicting tree heights at the ecoregional level. Further, applying a specific ecoregional model to other ecoregions will also result in significant biases for predicting local tree heights. The ecoregion-based height-diameter models developed in this study may provide more accurate information on tree growth and development to forest resource managers and planners. Key words: Chapman-Richards growth function, permanent sample plot, non-linear extra sum of square method, forest management

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.

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 Digital leaf physiognomy (DLP) is considered as one of the most promising methods for estimating past climate. However, current models built using the DLP data set still lack precision, especially for mean annual precipitation (MAP). To improve predictive power, we developed five machine learning (ML) models for mean annual temperature (MAT) and MAP respectively, and then tested the precision of these models and some of their averaging compared with that obtained from other models. The precision of all models was assessed using a repeated stratified 10‐fold cross‐validation. For MAT, three combinations of models ( R 2 = .77) presented moderate improvements in precision over the multiple linear regression (MLR) model ( R 2 = .68). For log e (MAP), the averaging of the support vector machine (SVM) and boosting models improved the R 2 from .19 to .63 compared with that of the MLR model. For MAP, the R 2 of this model combination was 0.49, which was much better than that of the artificial neural network (ANN) model ( R 2 = .21). Even the bagging model, which had the lowest R 2 (.37) for log e (MAP), demonstrated better precision ( R 2 = .27) for MAP. Our palaeoclimate estimates for nine fossil floras were also more accurate, because they were in better agreement with independent paleoclimate evidence. Our study confirms that our ML models and their averaging can improve paleoclimatic reconstructions, providing a better understanding of the relationship between climate and leaf physiognomy.

Paleobotanists have long built leaf climate models based on site mean of leaf physiognomic characteristics of woody dicotyledons species (WDS) for estimating past climate. To explore the potential of the order Ericales in estimating paleoclimate, we developed two linear models for each climatic factor. One is based on WDS, and the other is based on both WDS and leaf physiognomic characters of the order Ericales (WDS-E). We found that, compared with WDS models, WDS-E models improved greatly in mean annual precipitation (MAP), growing season precipitation (GSP) and mean annual range in temperature (MART). When the minimum species number of the order Ericales is three per site, the WDS-E models improved the r2 from 0.64 to 0.78 for MART, from 0.23 to 0.61 for ln(MAP), and from 0.37 to 0.64 for ln(GSP) compared with the WDS models. For mean annual temperature (MAT), the WDS-E model (r2 = 0.86) also exhibited a moderate improvement in precision over the WDS model (r2 = 0.82). This study demonstrates that other patterns, such as those of the order Ericales, can contribute additional information towards building more precise paleoclimate models.

Paleobotanists have long built leaf climate models based on site mean of leaf physiognomic characteristics of woody dicotyledons species (WDS) for estimating past climate. To explore the potential of the order Ericales in estimating paleoclimate, we developed two linear models for each climatic factor. One is based on WDS, and the other is based on both WDS and leaf physiognomic characters of the order Ericales (WDS-E). We found that, compared with WDS models, WDS-E models improved greatly in mean annual precipitation (MAP), growing season precipitation (GSP) and mean annual range in temperature (MART). When the minimum species number of the order Ericales is three per site, the WDS-E models improved the r2 from 0.64 to 0.78 for MART, from 0.23 to 0.61 for ln(MAP), and from 0.37 to 0.64 for ln(GSP) compared with the WDS models. For mean annual temperature (MAT), the WDS-E model (r2 = 0.86) also exhibited a moderate improvement in precision over the WDS model (r2 = 0.82). This study demonstrates that other patterns, such as those of the order Ericales, can contribute additional information towards building more precise paleoclimate models.

Abstract Digital leaf physiognomy (DLP) is considered as one of the most promising methods for estimating past climate. However, current models built using the DLP data set still lack precision, especially for mean annual precipitation (MAP). To improve predictive power, we developed five machine learning (ML) models for mean annual temperature (MAT) and MAP respectively, and then tested the precision of these models and some of their averaging compared with that obtained from other models. The precision of all models was assessed using a repeated stratified 10‐fold cross‐validation. For MAT, three combinations of models ( R 2 = .77) presented moderate improvements in precision over the multiple linear regression (MLR) model ( R 2 = .68). For log e (MAP), the averaging of the support vector machine (SVM) and boosting models improved the R 2 from .19 to .63 compared with that of the MLR model. For MAP, the R 2 of this model combination was 0.49, which was much better than that of the artificial neural network (ANN) model ( R 2 = .21). Even the bagging model, which had the lowest R 2 (.37) for log e (MAP), demonstrated better precision ( R 2 = .27) for MAP. Our palaeoclimate estimates for nine fossil floras were also more accurate, because they were in better agreement with independent paleoclimate evidence. Our study confirms that our ML models and their averaging can improve paleoclimatic reconstructions, providing a better understanding of the relationship between climate and leaf physiognomy.

Abstract Biomass has been promoted as a promising energy resource to mitigate global climate change. To evaluate the contribution of biomass utilization to climate change mitigation under the “Grain for Green” program in Northern Shaanxi, China, a soil carbon dynamic model and a life cycle assessment model were integrated to examine the benefits of using Caragana korshinskii Kom. as an energy crop. We found that the annual dry biomass output is maintained at 0.7 Tg during the simulation period (2020–2097). Due to the compensatory effect of biomass regrowth, the global warming potential of biomass‐derived CO 2 emissions is approximately 0.045; therefore, the total annual biogenic CO 2 emission is 57,211 ± 6,168 Mg CO 2 eq. The total annual life cycle CO 2 emissions approach 867,072 Mg CO 2 eq yr −1 . Under the scenario of no biomass removal, final carbon storage ranges from 15.7 to 19.3 TgC, and the highest carbon sequestration rate is 0.47 TgC yr −1 . In comparison with the no biomass removal scenario, the carbon sequestration rate (close to 0 MgC yr −1 ) in the biomass utilization scenario indicates a carbon loss; however, a portion of the carbon loss (31.39–62.09%) can be offset by carbon emission reductions from the substitution of fossil fuels.

Abstract A total of 11,612 black spruce trees were measured from permanent sample plots across the boreal and central regions of Ontario and were used to fit the well-known Chapman-Richards growth model at provincial, regional, and ecoregional scales. The results suggest that the height-diameter relationships of black spruce vary with different geographic regions and scales. There were significant variations in height-diameter relationships for black spruce between boreal and central regions as well as among some of the seven ecoregions. The ecoregion-based height-diameter models presented here will provide more accurate predictions for tree height and, consequently, tree volume than these models developed at both provincial and regional scales. Furthermore, the heterogeneity of tree species should be considered in developing and applying ecoregion-based height-diameter models for predicting local tree height.

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.

Process-based carbon dynamic models are rarely validated against traditional forest growth and yield data and are difficult to use as a practical tool for forest management. To bridge the gap between empirical and process-based models, a simulation using a hybrid model of TRIPLEX1.0 was performed for the forest growth and yield of the boreal forest ecosystem in the Lake Abitibi Model Forest in northeastern Ontario. The model was tested using field measurements, forest inventory data, and the normal yield table. The model simulations of tree height and diameter at breast height (DBH) showed a good agreement with measurements for black spruce (Picea mariana (Mill.) BSP), jack pine (Pinus banksiana Lamb.), and trembling aspen (Populus tremuloides Michx.). The coefficients of determination (R 2 ) between simulated values and permanent sample plot measurements were 0.92 for height and 0.95 for DBH. At the landscape scale, model predictions were compared with forest inventory data and the normal yield table. The R 2 ranged from 0.73 to 0.89 for tree height and from 0.72 to 0.85 for DBH. The simulated basal area is consistent with the normal yield table. The R 2 for basal area ranged from 0.82 to 0.96 for black spruce, jack pine, and trembling aspen for each site class. This study demonstrated the feasibility of testing the performance of the process-based carbon dynamic model using traditional forest growth and yield data and the ability of the TRIPLEX1.0 model for predicting growth and yield variables. The current work also introduces a means to test model accuracy and its prediction of forest stand variables to provide a complement to empirical growth and yield models for forest management practices, as well as for investigating climate change impacts on forest growth and yield in regions without sufficient established permanent sample plots and remote areas without suitable field measurements.