A historical meta‐analysis of global terrestrial net primary productivity: are estimates converging?

Net primary productivity (NPP) is one of the most important ecosystem parameters, representing vegetation activity, biogeochemical cycling, and ecosystem services. To assess how well the scientific community understands the biospheric function, a historical meta‐analysis was conducted. By surveying the literature from 1862 to 2011, I extracted 251 estimates of total terrestrial NPP at the present time (NPP_T) and calculated their statistical metrics. For all the data, the mean±standard deviation and median were 56.2±14.3 and 56.4 Pg C yr^–1, respectively. Even for estimates published after 2000, a substantial level of uncertainty (coefficient of variation by ±15%) was inevitable. The estimates were categorized on the basis of methodology (i.e., inventory analysis, empirical model, biogeochemical model, dynamic global vegetation model, and remote sensing) to examine the consistency among the statistical metrics of each category. Chronological analysis revealed that the present NPP_T estimates were directed by extensive field surveys in the 1960s and 1970s (e.g., the International Biological Programme). A wide range of uncertainty remains in modern estimates based on advanced biogeochemical and dynamic vegetation models and remote‐sensing techniques. Several critical factors accounting for the estimation uncertainty are discussed. Ancillary analyses were performed to derive additional ecological and human‐related parameters related to NPP. For example, interannual variability, carbon‐use efficiency (a ratio of NPP to gross photosynthesis), human appropriation, and preindustrial NPP_T were assessed. Finally, I discuss the importance of improving NPP_T estimates in the context of current global change studies and integrated carbon cycle research.     

Quantifying uncertainty in predictions of invasiveness, with emphasis on weed risk assessment

Using the Australian Weed Risk Assessment (WRA) model as an example, we applied a combination of bootstrapping and Bayesian techniques as a means of explicitly estimating the posterior probability of weediness as a function of an import risk assessment model screening score. Our approach provides estimates of uncertainty around model predictions, after correcting for verification bias arising from the original training dataset having a higher proportion of weed species than would be the norm, and incorporates uncertainty in current knowledge of the prior (base-rate) probability of weediness. The results confirm the high sensitivity of the posterior probability of weediness to the base-rate probability of weediness of plants proposed for importation, and demonstrate how uncertainty in this base-rate probability manifests itself in uncertainty surrounding predicted probabilities of weediness. This quantitative estimate of the weediness probability posed by taxa classified using the WRA model, including estimates of uncertainty around this probability for a given WRA score, would enable bio-economic modelling to contribute to the decision process, should this avenue be pursued. Regardless of whether or not this avenue is explored, the explicit estimates of uncertainty around weed classifications will enable managers to make better informed decisions regarding risk. When viewed in terms of likelihood of weed introduction, the current WRA model outcomes of ‘accept’, ‘further evaluate’ or ‘reject’, whilst not always accurate in terms of weed classification, appear consistent with a high-expected cost of mistakenly introducing a weed. The methods presented have wider application to the quantitative prediction of invasive species for situations where the base-rate probability of invasiveness is subject to uncertainty, and the accuracy of the screening test imperfect.     

Quantifying Uncertainty in Predictions of Invasiveness

Using the Australian weed risk assessment (WRA) model as an example, we applied a combination of bootstrapping and Bayesian techniques as a means for explicitly estimating the posterior probability of weediness as a function of an import risk assessment model screening score. Our approach provides estimates of uncertainty around model predictions, after correcting for verification bias arising from the original training dataset having a higher proportion of weed species than would be the norm, and incorporates uncertainty in current knowledge of the prior (base-rate) probability of weediness. The results confirm the high sensitivity of the posterior probability of weediness to the base-rate probability of weediness of plants proposed for importation, and demonstrate how uncertainty in this base-rate probability manifests itself in uncertainty surrounding predicted probabilities of weediness. This quantitative estimate of the weediness probability posed by taxa classified using the WRA model, including estimates of uncertainty around this probability for a given WRA score, would enable bio-economic modelling to contribute to the decision process, should this avenue be pursued. Regardless of whether or not this avenue is explored, the explicit estimates of uncertainty around weed classifications will enable managers to make better informed decisions regarding risk. When viewed in terms of likelihood of weed introduction, the current WRA model outcomes of ‘accept’, ‘further evaluate’, or ‘reject’, whilst not always accurate in terms of weed classification, appear consistent with a high expected cost of mistakenly introducing a weed. The methods presented have wider application to the quantitative prediction of invasive species for situations where the base-rate probability of invasiveness is subject to uncertainty, and the accuracy of the screening test imperfect     

Estimating Uncertainty in Ecosystem Budget Calculations

Ecosystem nutrient budgets often report values for pools and fluxes without any indication of uncertainty, which makes it difficult to evaluate the significance of findings or make comparisons across systems. We present an example, implemented in Excel, of a Monte Carlo approach to estimating error in calculating the N content of vegetation at the Hubbard Brook Experimental Forest in New Hampshire. The total N content of trees was estimated at 847 kg ha⁻¹ with an uncertainty of 8%, expressed as the standard deviation divided by the mean (the coefficient of variation). The individual sources of uncertainty were as follows: uncertainty in allometric equations (5%), uncertainty in tissue N concentrations (3%), uncertainty due to plot variability (6%, based on a sample of 15 plots of 0.05 ha), and uncertainty due to tree diameter measurement error (0.02%). In addition to allowing estimation of uncertainty in budget estimates, this approach can be used to assess which measurements should be improved to reduce uncertainty in the calculated values. This exercise was possible because the uncertainty in the parameters and equations that we used was made available by previous researchers. It is important to provide the error statistics with regression results if they are to be used in later calculations; archiving the data makes resampling analyses possible for future researchers. When conducted using a Monte Carlo framework, the analysis of uncertainty in complex calculations does not have to be difficult and should be standard practice when constructing ecosystem budgets.     

Probabilistic methods for addressing uncertainty and variability in biological models: application to a toxicokinetic model

Population variability and uncertainty are important features of biological systems that must be considered when developing mathematical models for these systems. In this paper we present probability-based parameter estimation methods that account for such variability and uncertainty. Theoretical results that establish well-posedness and stability for these methods are discussed. A probabilistic parameter estimation technique is then applied to a toxicokinetic model for trichloroethylene using several types of simulated data. Comparison with results obtained using a standard, deterministic parameter estimation method suggests that the probabilistic methods are better able to capture population variability and uncertainty in model parameters.     

中国陆地植被净初级生产力遥感估算

该文在综合分析已有光能利用率模型的基础上,构建了一个净初级生产力(NPP)遥感估算模型,该模型体现了3方面的特色:1)将植被覆盖分类引入模型,并考虑植被覆盖分类精度对NPP估算的影响,由它们共同决定不同植被覆盖类型的归一化植被指数(NDVI)最大值;2)根据误差最小的原则,利用中国的NPP实测数据,模拟出各植被类型的最大光能利用率,使之更符合中国的实际情况;3)根据区域蒸散模型来模拟水分胁迫因子,与土壤水分子模型相比,这在一定程度上对有关参数实行了简化,使其实际的可操作性得到加强。模拟结果表明,1989~1993年中国陆地植被NPP平均值为3.12 Pg C (1 Pg=10¹⁵ g),NPP模拟值与观测值比较接近,690个实测点的平均相对误差为4.5%;进一步与其它模型模拟结果以及前人研究结果的比较表明,该文所构建的NPP遥感估算模型具有一定的可靠性,说明在区域及全球尺度上,利用地理信息系统技术将遥感数据和各种观测数据集成在一起,并对NPP模型进行参数校正,基本上可以实现全球范围不同生态系统NPP的动态监测。     

Estimating net primary productivity of grasslands from field biomass measurements in temperate northern China

Data on field biomass measurements in temperate grasslands of northern China (141 samples from 74 sites) were obtained from 23 Chinese journals, reports and books. Net primary productivity (NPP) of grasslands was estimated using three algorithms (peak live biomass, peak standing crop and maximum minus minimum live biomass), respectively, based on availability of biomass data in sites. 135 samples which have aboveground biomass (AGB) measurements, have peak AGB ranges from 20 to 2021 g m^–2 (mean = 325.3) and the aboveground NPP (ANPP) ranges from 15 to 1647.1 g m^–2 per year (mean = 295.7). 72 samples which have belowground biomass (BGB) measurements, have peak BGB ranges from 226.5 to 12827.5 g m^–2 (mean = 3116) and the belowground NPP (BNPP) ranges from 15.8 to 12827.5 g m^–2 per year (mean = 2425.6). In total 66 samples have the total NPP (TNPP), ranging from 55.3 to 13347.8 g m^–2 per year (mean = 2980.3). Mean peak biomass and NPP varied from different geographical sampling locations, but they had a general rough regularity in ten grasslands. Meadow, mountain and alpine grasslands had high biomass and NPP (sometimes including saline grassland). Forested steppe, saline grassland and desert had median values. Meadowed and typical steppes had low biomass and NPP (sometimes including desert). The lowest biomass and NPP occurred in deserted steppe and stepped desert. Grassland ANPP has significant positive relationships with annual and summer precipitation as well as summer temperature (all p<0.01). However, grassland BNPP and TNPP have more significant negative relationships with summer temperature (p<0.01) than with annual temperature (p<0.05). The analysis of climate – productivity correlations implied that aboveground productivity is more controlled by rainfall, whereas belowground and total productivity is more influenced by temperature in the temperate grasslands of northern China. The present study might underestimate grassland NPP in northern China due to limitation of biomass measurements. Data on relative long-term aboveground and belowground biomass dynamics, as well as data of standing dead matter, litterfall, decomposition and turnover, are required if grassland NPP is to be more accurately estimated and the role of temperate grasslands in the regional to global carbon cycles is to be fully appreciated. This revised version was published online in June 2006 with corrections to the Cover Date.     

单木生物量模型估计区域尺度生物量的不确定性

采用系统抽样体系江西省固定样地杉木连续观测数据和生物量数据,通过Monte Carlo法反复模拟由单木生物量模型推算区域尺度地上生物量的过程,估计了江西省杉木地上总生物量。基于不同水平建模样本量n及不同决定系数R~2的设计,分别研究了单木生物量模型参数变异性及模型残差变异性对区域尺度生物量估计不确定性的影响。研究结果表明:2009年江西省杉木地上生物量估计值为(19.84±1.27)t/hm~2,不确定性占生物量估计值约6.41%。生物量估计值和不确定性值达到平稳状态所需的运算时间随建模样本量及决定系数R~2的增大而减小;相对于模型参数变异性,残差变异性对不确定性的影响更小。     

Framework for modelling data uncertainty in life cycle inventories

Modelling data uncertainty is not common practice in life cycle inventories (LCI), although different techniques are available for estimating and expressing uncertainties, and for propagating the uncertainties to the final model results. To clarify and stimulate the use of data uncertainty assessments in common LCI practice, the SETAC working group ‘Data Availability and Quality’ presents a framework for data uncertainty assessment in LCI. Data uncertainty is divided in two categories: (1) lack of data, further specified as complete lack of data (data gaps) and a lack of representative data, and (2) data inaccuracy. Filling data gaps can be done by input-output modelling, using information for similar products or the main ingredients of a product, and applying the law of mass conservation. Lack of temporal, geographical and further technological correlation between the data used and needed may be accounted for by applying uncertainty factors to the non-representative data. Stochastic modelling, which can be performed by Monte Carlo simulation, is a promising technique to deal with data inaccuracy in LCIs.     

森林生物量估算中模型不确定性分析

单木生物量估算是区域森林生物量估算的基础。量化单木生物量模型中各种不确定性来源,分析各不确定性来源对森林生物量估算的影响,可为提高森林生物量估算精度提供理论依据。基于52株杉木地上部分生物量实测数据,建立杉木单木地上部分生物量一元与二元模型。在两种模型形式下,根据临安市2009年森林资源连续清查数据中杉木实测数据,分析单木生物量模型中所包含的2种不确定性,即模型参数不确定性和模型残差变异引起的不确定性。最后利用误差传播定律计算单木生物量模型总不确定性。结果表明,基于一元生物量模型的临安市杉木生物量估计均值为6.94 Mg/hm~2,由一元模型残差变异引起的生物量不确定性约为11.1%,模型参数误差引起的生物量不确定性约为14.4%,一元生物量模型估算合成不确定性为18.18%。基于二元生物量模型的临安市杉木生物量估计均值为7.71 Mg/hm~2,模型残差变异引起的不确定性约为7.0%,模型参数误差引起的不确定性约为8.53%,二元生物量模型估算合成不确定性为11.03%。研究表明模型参数不确定性随建模样本的增加逐渐降低,当建模样本由30增加到40再增加到52时,一元生物量模型模型参数不确定性分别为20.26%、16.19%、14.4%,二元生物量模型分别为13.09%、9.4%、8.53%。此外,建模样本的增加对残差变异不确定性也有一定影响,当建模样本由30增加到42再增加到48时,一元模型残差变异不确定性分别为15.2%,12.3%和11.7%;二元模型残差变异不确定性分别为13.3%,9.4%和8.3%。在2种不确定性来源中模型参数不确定性对估计结果影响最大,其次为模型残差变异。由于模型残差变异、参数不确定性与建模样本有关,因此可以通过增加建模样本来减小模型参数不确定性。二元生物量模型总的不确定性要低于一元生物量模型。     

Estimating carbon carrying capacity in natural forest ecosystems across heterogeneous landscapes: addressing sources of error

Evaluating contributions of forest ecosystems to climate change mitigation requires well‐calibrated carbon cycle models with quantified baseline carbon stocks. An appropriate baseline for carbon accounting of natural forests at landscape scales is carbon carrying capacity (CCC); defined as the mass of carbon stored in an ecosystem under prevailing environmental conditions and natural disturbance regimes but excluding anthropogenic disturbance. Carbon models require empirical measurements for input and calibration, such as net primary production (NPP) and total ecosystem carbon stock (equivalent to CCC at equilibrium). We sought to improve model calibration by addressing three sources of errors that cause uncertainty in carbon accounting across heterogeneous landscapes: (1) data‐model representation, (2) data‐object representation, (3) up‐scaling. We derived spatially explicit empirical models based on environmental variables across landscape scales to estimate NPP (based on a synthesis of global site data of NPP and gross primary productivity, n=27), and CCC (based on site data of carbon stocks in natural eucalypt forests of southeast Australia, n=284). The models significantly improved predictions, each accounting for 51% of the variance. Our methods to reduce uncertainty in baseline carbon stocks, such as using appropriate calibration data from sites with minimal human disturbance, measurements of large trees and incorporating environmental variability across the landscape, have generic application to other regions and ecosystem types. These analyses resulted in forest CCC in southeast Australia (mean total biomass of 360 t C ha^?1, with cool moist temperate forests up to 1000 t C ha^?1) that are larger than estimates from other national and international (average biome 202 t C ha^?1) carbon accounting systems. Reducing uncertainty in estimates of carbon stocks in natural forests is important to allow accurate accounting for losses of carbon due to human activities and sequestration of carbon by forest growth.     

Effects of the torso boundary and internal conductivity interfaces in electrocardiography: An evaluation of the ‘Infinite medium’ approximation

The analytic, eccentric spheres model of the torso was used to examine the validity of approximating the ‘infinite medium’ potential by integrating ‘finite medium potentials’ over the torso surface. Although idealized, the analytic model is sophisticated enough for all important torso conductivity and geometry parameters to be preserved in the formulation. The model generates both ‘finite medium’ potentials (for which the torso is surrounded by air) and also ‘infinite medium’ potentials (for which the outermost layer of the torso extends outward to infinity). The finite medium torso potentials were integrated over the torso surface in accordance with the approximation used by many investigators in an effort to make the surface distribution more representative of the primary cardiac sources. The resulting potential distribution was compared with the true infinite medium potential, in which the effects of internal inhomogeneities (secondary sources) were taken into account. The difference between the two representations was found to be significant, and caution should be used when interpreting such data.     

Dynamical estimation of neuron and network properties II: path integral Monte Carlo methods

Hodgkin–Huxley (HH) models of neuronal membrane dynamics consist of a set of nonlinear differential equations that describe the time-varying conductance of various ion channels. Using observations of voltage alone we show how to estimate the unknown parameters and unobserved state variables of an HH model in the expected circumstance that the measurements are noisy, the model has errors, and the state of the neuron is not known when observations commence. The joint probability distribution of the observed membrane voltage and the unobserved state variables and parameters of these models is a path integral through the model state space. The solution to this integral allows estimation of the parameters and thus a characterization of many biological properties of interest, including channel complement and density, that give rise to a neuron’s electrophysiological behavior. This paper describes a method for directly evaluating the path integral using a Monte Carlo numerical approach. This provides estimates not only of the expected values of model parameters but also of their posterior uncertainty. Using test data simulated from neuronal models comprising several common channels, we show that short (<50 ms) intracellular recordings from neurons stimulated with a complex time-varying current yield accurate and precise estimates of the model parameters as well as accurate predictions of the future behavior of the neuron. We also show that this method is robust to errors in model specification, supporting model development for biological preparations in which the channel expression and other biophysical properties of the neurons are not fully known.     

广西黄冕林场次生常绿阔叶林生物量及净第一性生产力

应用相对生长法和样方收获法,测定了广西黄冕林场天然次生常绿阔叶林的地上、地下生物量及林分净第一性生产力．阔叶林总生物量为99．96t·hm^-2,其中地上部分占69．41％,地下部分(根系)占30．59％．林分叶面积指数为6．50．全林净第一性生产力为24．65t·hm^-2·年^-1,其中地上部分占44．54％。根系占55．46％．     

Sources of Variability in Net Primary Production Predictions at a Regional Scale: A Comparison Using PnET-II and TEM 4.0 in Northeastern US Forests

Because model predictions at continental and global scales are necessarily based on broad characterizations of vegetation, soils, and climate, estimates of carbon stocks and fluxes made by global terrestrial biosphere models may not be accurate for every region. At the regional scale, we suggest that attention can be focused more clearly on understanding the relative strengths of predicted net primary productivity (NPP) limitation by energy, water, and nutrients. We evaluate the sources of variability among model predictions of NPP with a regional-scale comparison between estimates made by PnET-II (a forest ecosystem process model previously applied to the northeastern region) and TEM 4.0 (a terrestrial biosphere model typically applied to the globe) for the northeastern US. When the same climate, vegetation, and soil data sets were used to drive both models, regional average NPP predictions made by PnET-II and TEM were remarkably similar, and at the biome level, model predictions agreed fairly well with NPP estimates developed from field measurements. However, TEM 4.0 predictions were more sensitive to regional variations in temperature as a result of feedbacks between temperature and belowground N availability. In PnET-II, the direct link between transpiration and photosynthesis caused substantial water stress in hardwood and pine forest types with increases in solar radiation; predicted water stress was relieved substantially when soil water holding capacity (WHC) was increased. Increasing soil WHC had little effect on TEM 4.0 predictions because soil water storage was already sufficient to meet plant demand with baseline WHC values, and because predicted N availability under baseline conditions in this region was not limited by water. Because NPP predictions were closely keyed to forest cover type, the relative coverage of low- versus high-productivity forests at both fine and coarse resolutions was an important determinant of regional NPP predictions. Therefore, changes in grid cell size and differences in the methods used to aggregate from fine to coarse resolution were important to NPP predictions insofar as they changed the relative proportions of forest cover. We suggest that because the small patches of high-elevation spruce-fir forest in this region are substantially less productive than forests in the remainder of the region, more accurate NPP predictions will result if models applied to this region use land cover input data sets that retain as much fine-resolution forest type variability as possible. The differences among model responses to variations in climate and soil WHC data sets suggest that the models will respond quite differently to scenarios of future climate. A better understanding of the dynamic interactions between water stress, N availability, and forest productivity in this region will enable models to make more accurate predictions of future carbon stocks and fluxes. Received 19 June 1998; accepted 25 June 1999.     

Importance of dose‐response model form in probabilistic risk assessment: A case study of health effects from methylmercury in fish

We compared the effect of uncertainty in dose‐response model form on health risk estimates to the effect of uncertainty and variability in exposure. We used three different dose‐response models to characterize neurological effects in children exposed in utero to methylmercury, and applied these models to calculate risks to a native population exposed to potentially contaminated fish from a reservoir in British Columbia. Uncertainty in model form was explicitly incorporated into the risk estimates. The selection of dose‐response model strongly influenced both mean risk estimates and distributions of risk, and had a much greater impact than altering exposure distributions. We conclude that incorporating uncertainty in dose‐response model form is at least as important as accounting for variability and uncertainty in exposure parameters in probabilistic risk assessment.     

Net Primary Production and Canopy Nitrogen in a Temperate Forest Landscape: An Analysis Using Imaging Spectroscopy, Modeling and Field Data

Understanding spatial patterns of net primary production (NPP) is central to the study of terrestrial ecosystems, but efforts are frequently hampered by a lack of spatial information regarding factors such as nitrogen availability and site history. Here, we examined the degree to which canopy nitrogen can serve as an indicator of patterns of NPP at the Bartlett Experimental Forest in New Hampshire by linking canopy nitrogen estimates from two high spectral resolution remote sensing instruments with field measurements and an ecosystem model. Predicted NPP across the study area ranged from less than 700 g m⁻² year⁻¹ to greater than 1300 g m⁻² year⁻¹ with a mean of 951 g m⁻² year⁻¹. Spatial patterns corresponded with elevation, species composition and historical forest management, all of which were reflected in patterns of canopy nitrogen. The relationship between production and elevation was nonlinear, with an increase from low- to mid-elevation deciduous stands, followed by a decline in upper-elevation areas dominated by evergreens. This pattern was also evident in field measurements and mirrored an elevational trend in foliar N concentrations. The increase in production from low-to mid-elevation deciduous stands runs counter to the generally accepted pattern for the northeastern U.S. region, and suggests an importance of moisture limitations in lower-elevation forests. Field measurements of foliar N, wood production and leaf litterfall were also used to evaluate sources of error in model estimates and to determine how predictions are affected by different methods of acquiring foliar N input data. The accuracy of predictions generated from remotely sensed foliar N approached that of predictions driven by field-measured foliar N. Predictions based on the more common approach of using aggregated foliar N for individual cover types showed reasonable agreement in terms of the overall mean, but were in poor agreement on a plot-by-plot basis. Collectively, these results suggest that variation in foliar N exerts an important control on landscape-level spatial patterns and can serve as an integrator of other underlying factors that influence forest growth rates.     

庙岛群岛南五岛生态系统净初级生产力空间分布及其影响因子

净初级生产力(NPP)估算对于海岛碳源/汇研究具有重要意义。以庙岛群岛南五岛为例,结合CASA模型和区域特征构建NPP估算模型,借助RS和GIS技术进行NPP估算,进而分析南五岛NPP空间分布特征及其影响因子。结果表明:南五岛NPP总量为11043.52 t C/a,平均密度为340.19 g C m~(-2)a~(-1),处于全国平均水平,高于同纬度的西部地区,低于东部沿海大陆地区;夏季NPP总量占全年的80%左右,春季和秋季分别占11%和7%,冬季仅占1.3%;不同海岛的NPP平均密度由大到小依次为大黑山岛、北长山岛、庙岛、南长山岛和小黑山岛,各岛NPP平均密度与建设用地比例呈明显负相关;不同地表覆盖类型的NPP平均密度由大到小依次为阔叶林、针叶林、农田、草地、建设用地和裸地,林地具有较高的NPP值,说明南五岛的人工林建设具有重要生态作用;NDVI和地表覆盖类型是NPP最主要的影响参数,地形参数通过影响NDVI和地表覆盖类型间接作用于NPP结果;NPP与土壤p H、有效磷、全磷、全钾呈显著负相关,与全氮、总碳、总有机碳呈显著正相关,与含水量、速效钾和含盐量之间相关关系不明显。     

Estimating net primary productivity from grassland biomass dynamics measurements

To address the need for a high quality data set based upon field observations suitable for parameterization, calibration, and validation of terrestrial biosphere models, we have developed a comprehensive global database on net primary productivity (NPP). We have compiled field measurements of biomass and associated environmental data for multiple study sites in major grassland types worldwide. Where sufficient data were available, we compared aboveground and total NPP estimated by six computational methods (algorithms) for 31 grassland sites. As has been found previously, NPP estimates were 2–5 times higher using methods which accounted for the dynamics of dead matter, compared with what is still the most commonly applied estimate of NPP (maximum peak live biomass). It is suggested that assumptions such as the use of peak biomass as an indicator of NPP in grasslands may apply only within certain subbiomes, e.g. temperate steppe grasslands. Additional data on belowground dynamics, or other reliable estimates of belowground productivity, are required if grasslands are to be fully appreciated for their role in the global carbon cycle.