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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.

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.

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 spruce budworm (SBW) defoliates and kills conifer trees, consequently affecting carbon (C) exchanges between the land and atmosphere. Here, we developed a new TRIPLEX-Insect sub-model to quantify the impacts of insect outbreaks on forest C fluxes. We modeled annual defoliation (AD), cumulative defoliation (CD), and tree mortality. The model was validated against observed and published data at the stand level in the North Shore region of Québec and Cape Breton Island in Nova Scotia, Canada. The results suggest that TRIPLEX-Insect performs very well in capturing tree mortality following SBW outbreaks and slightly underestimates current annual volume increment (CAI). In both mature and immature forests, the simulation model suggests a larger reduction in gross primary productivity (GPP) than in autotrophic respiration (Ra) at the same defoliation level when tree mortality was low. After an SBW outbreak, the growth release of surviving trees contributes to the recovery of annual net ecosystem productivity (NEP) based on forest age if mortality is not excessive. Overall, the TRIPLEX-Insect model is capable of simulating C dynamics of balsam fir following SBW disturbances and can be used as an efficient tool in forest insect management.

Abstract Microbial physiology plays a critical role in the biogeochemical cycles of the Earth system. However, most traditional soil carbon models are lacking in terms of the representation of key microbial processes that control the soil carbon response to global climate change. In this study, the improved process‐based model TRIPLEX‐GHG was developed by coupling it with the new MEND (Microbial‐ENzyme‐mediated Decomposition) model to estimate total global soil organic carbon (SOC) and global soil microbial carbon. The new model (TRIPLEX‐MICROBE) shows considerable improvement over the previous version (TRIPLEX‐GHG) in simulating SOC. We estimated the global soil carbon stock to be approximately 1195 Pg C, with 348 Pg C located in the high northern latitudes, which is in good agreement with the well‐regarded Harmonized World Soil Database (HWSD) and the Northern Circumpolar Soil Carbon Database (NCSCD). We also estimated the global soil microbial carbon to be 21 Pg C, similar to the 23 Pg C estimated by Xu et al. (2014). We found that the microbial carbon quantity in the latitudinal direction showed reversions at approximately 30°N, near the equator and at 25°S. A sensitivity analysis suggested that the tundra ecosystem exhibited the highest sensitivity to a 1°C increase or decrease in temperature in terms of dissolved organic carbon (DOC), microbial biomass carbon (MBC), and mineral‐associated organic carbon (MOC). However, our work represents the first step toward a new generation of ecosystem process models capable of integrating key microbial processes into soil carbon cycles. , Key Points Traditional soil carbon models are lacking in their representation of key microbial processes that control the soil carbon response to global climate change A Ecosystem model (TRIPLEX‐MICROBE) offers considerable improvement over a previous version (TRIPLEX‐GHG) in simulating soil organic carbon Our work is the first step toward a new generation of ecosystem process models that integrate key microbial processes into soil carbon cycles

Abstract Climate change has a profound impact on the global carbon cycle, including effects on riverine carbon pools, which connect terrestrial, oceanic, and atmospheric carbon pools. Until now, terrestrial ecosystem models have rarely incorporated riverine carbon components into global carbon budgets. Here we developed a new process‐based model, TRIPLEX‐HYDRA (TRIPLEX‐hydrological routing algorithm), that considers the production, consumption, and transport processes of nonanthropogenic dissolved organic carbon (DOC) from soil to river ecosystems. After the parameter calibration, model results explained more than 50% of temporal variations in all but three rivers. Validation results suggested that DOC yield simulated by TRIPLEX‐HYDRA has a good fit ( R 2  = 0.61, n  = 71, p  < 0.001) with global river observations. And then, we applied this model for global rivers. We found that mean DOC yield of global river approximately 1.08 g C/m 2  year, where most high DOC yield appeared in the rivers from high northern or tropic regions. Furthermore, our results suggested that global riverine DOC flux appeared a significant decrease trend (average rate: 0.38 Pg C/year) from 1951 to 2015, although the variation patterns of DOC fluxes in global rivers are diverse. A decreasing trend in riverine DOC flux appeared in the middle and high northern latitude regions (30–90°N), which could be attributable to an increased flow path and DOC degradation during the transport process. Furthermore, increasing trend of DOC fluxes is found in rivers from tropical regions (30°S–30°N), which might be related to an increase in terrestrial organic carbon input. Many other rivers (e.g., Mississippi, Yangtze, and Lena rivers) experienced no significant changes under a changing environment. , Key Points Terrestrial ecosystem models rarely incorporate riverine DOC components into the global carbon cycle The TRIPLEX‐HYDRA model simulates the spatiotemporal variation in the DOC fluxes in global rivers The global riverine DOC flux simulated by the TRIPLEX‐HYDRA model has significantly decreased from 1951 to 2015

It is increasingly being recognized that global ecological research requires novel methods and strategies in which to combine process‐based ecological models and data in cohesive, systematic ways. In process‐based model applications, inherent spatial and temporal heterogeneities found within terrestrial ecosystems may lead to the uncertainties of model predictions. To reduce simulation uncertainties due to inaccurate model parameters, the Markov Chain Monte Carlo (MCMC) method was applied in this study to improve the estimations of four key parameters used in the process‐based ecosystem model of TRIPLEX‐FLUX. These four key parameters include a maximum photosynthetic carboxylation rate of 25°C (Vmax), an electron transport (Jmax) light‐saturated rate within the photosynthetic carbon reduction cycle of leaves, a coefficient of stomatal conductance (m), and a reference respiration rate of 10°C (R10). Seven forest flux tower sites located across North America were used to investigate and facilitate understanding of the daily variation in model parameters for three deciduous forests, three evergreen temperate forests, and one evergreen boreal forest. Eddy covariance CO 2 exchange measurements were assimilated to optimize the parameters in the year 2006. After parameter optimization and adjustment took place, net ecosystem production prediction significantly improved (by approximately 25%) compared to the CO 2 flux measurements taken at the seven forest ecosystem sites. Results suggest that greater seasonal variability occurs in broadleaf forests in respect to the selected parameters than in needleleaf forests. This study also demonstrated that the model‐data fusion approach by incorporating MCMC method is able to better estimate parameters and improve simulation accuracy for different ecosystems located across North America.

The boreal forests, identified as a critical “tipping element” of the Earth's climate system, play a critical role in the global carbon budget. Recent findings have suggested that terrestrial carbon sinks in northern high-latitude regions are weakening, but there has been little observational evidence to support the idea of a reduction of carbon sinks in northern terrestrial ecosystems. Here, we estimated changes in the biomass carbon sink of natural stands throughout Canada's boreal forests using data from long-term forest permanent sampling plots. We found that in recent decades, the rate of biomass change decreased significantly in western Canada (Alberta, Saskatchewan, and Manitoba), but there was no significant trend for eastern Canada (Ontario and Quebec). Our results revealed that recent climate change, and especially drought-induced water stress, is the dominant cause of the observed reduction in the biomass carbon sink, suggesting that western Canada's boreal forests may become net carbon sources if the climate change–induced droughts continue to intensify.

Methane accounts for 20% of the global warming caused by greenhouse gases, and wastewater is a major anthropogenic source of methane. Based on the Intergovernmental Panel on Climate Change greenhouse gas inventory guidelines and current research findings, we calculated the amount of methane emissions from 2000 to 2014 that originated from wastewater from different provinces in China. Methane emissions from wastewater increased from 1349.01 to 3430.03 Gg from 2000 to 2014, and the mean annual increase was 167.69 Gg. The methane emissions from industrial wastewater treated by wastewater treatment plants ( E It ) accounted for the highest proportion of emissions. We also estimated the future trend of industrial wastewater methane emissions using the artificial neural network model. A comparison of the emissions for the years 2020, 2010, and 2000 showed an increasing trend in methane emissions in China and a spatial transition of industrial wastewater emissions from eastern and southern regions to central and southwestern regions and from coastal regions to inland regions. These changes were caused by changes in economics, demographics, and relevant policies. , Key Points Methane emission from wastewater from 2000 to 2014 was calculated to increase from 1349.01 Gg to 3430.03 Gg. Methane emission from wastewater from 2015 to 2020 was estimated to increase from 3875.30 Gg to 5212.75 Gg. A spatial transition of methane emission from wastewater was found and discussed in the present study.

Plants interact to the seasonality of their environments, and changes in plant phenology have long been regarded as sensitive indicators of climatic change. Plant phenology modeling has been shown to be the simplest and most useful tool to assess phenol–climate shifts. Temperature, solar radiation, and water availability are assumed to be the key factors that control plant phenology. Statistical, mechanistic, and theoretical approaches have often been used for the parameterization of plant phenology models. The statistical approaches correlate the timing of phenological events to environmental factors or heat unit accumulations. The approaches have the simplified calculation procedures, correct phenological mechanism assumptions, but limited applications and predictive abilities. The mechanistic approaches describe plant phenology with the known or assumed “cause–effect relationships” between biological processes and key driving variables. The mechanistic approaches have the improved parameter processes, realistic assumptions, broad applications, and effective predictions. The theoretical approaches assume cost–benefit tradeoff strategies in trees. These methods are capable of capturing and quantifying the potential impacts and consequences of global climate change and human activity. However, certain limitations still exist related to our understanding of phenological mechanisms in relation to (1) interactions between plants and their specific climates, (2) the integration of both field observational and remote sensing data with plant phenology models across taxa and ecosystem type, (3) amplitude clarification of scale-related sensitivity to global climate change, and (4) improvements in parameterization processes and the overall reduction of modeling uncertainties to forecast impacts of future climate change on plant phenological dynamics. To improve our capacity in the prediction of the amplitude of plant phenological responses with regard to both structural and functional sensitivity to future global climate change, it is important to refine modeling methodologies by applying long-term and large-scale observational data. It is equally important to consider other less used but critical factors (such as heredity, pests, and anthropogenic drivers), apply advanced model parameterization and data assimilation techniques, incorporate process-based plant phenology models as a dynamic component into global vegetation dynamic models, and test plant phenology models against long-term ground observations and high-resolution satellite data across different spatial and temporal scales.