Global Sensitivity Analysis of the Historical Carbon Sink across Biomes

The terrestrial biosphere absorbs more CO 2 than it emits, slowing the accumulation of atmospheric CO 2 . However, Earth System Models differ in their Net Biome Productivity (NBP) projections, with inter-model ranges of 2 to 7 PgC yr − 1 by the late 21st century under a fossil-fuel-intensive scenario. We notice that the uncertainty in NBP simulated by the Canadian Land Surface Scheme Including Biogeochemical Cycles (CLASSIC) model is vastly impacted by parameter uncertainty. To address this uncertainty, we conduct a global sensitivity analysis (GSA) for seven grid cells across different biomes. Results of the preliminary screening test show that only 11–15 of 124 input parameters drive the output uncertainty at each location. Among them, the maximum carboxylation rate (vmax) consistently influences multiple output variables. Through the secondary quantitative test, we notice that vmax's impact on NBP declines over time, but other photosynthetic and rooting parameters become more influential. In some locations, higher vmax values reduce NBP, as increased ecosystem respiration and wildfire emissions outweigh gross primary productivity. Despite using approximately eight weeks of computational effort using 120 cores, the sampling uncertainty among the 11–15 parameters is broad. Ranking the parameters based on robustness is difficult. Expanding the analysis to an additional metric, we find that the same parameters that drive the uncertainty of the projected future NBP also drive the uncertainty of the change from the late historical to late future NBP. These results indicate that future optimization efforts related to NBP must consider multiple parameters rather than focussing solely on vmax. By identifying influential parameters and processes, this study enhances our understanding of parametric uncertainty in carbon sink projections and defines a low-dimensional space of influential parameters, aiding future model refinement.

Abstract. Accurate assessments of anthropogenic carbon dioxide (CO2) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere is important to better understand the global carbon cycle, support the climate policy process, and project future climate change. Present-day analysis requires the combination of a range of data, algorithms, statistics and model estimates and their interpretation by a broad scientific community. Here we describe datasets and a methodology developed by the global carbon cycle science community to quantify all major components of the global carbon budget, including their uncertainties. We discuss changes compared to previous estimates, consistency within and among components, and methodology and data limitations. CO2 emissions from fossil fuel combustion and cement production (EFF) are based on energy statistics, while emissions from Land-Use Change (ELUC), including deforestation, are based on combined evidence from land cover change data, fire activity in regions undergoing deforestation, and models. The global atmospheric CO2 concentration is measured directly and its rate of growth (GATM) is computed from the concentration. The mean ocean CO2 sink (SOCEAN) is based on observations from the 1990s, while the annual anomalies and trends are estimated with ocean models. Finally, the global residual terrestrial CO2 sink (SLAND) is estimated by the difference of the other terms. For the last decade available (2002–2011), EFF was 8.3 ± 0.4 PgC yr−1, ELUC 1.0 ± 0.5 PgC yr−1, GATM 4.3 ± 0.1 PgC yr−1, SOCEAN 2.5 ± 0.5 PgC yr−1, and SLAND 2.6 ± 0.8 PgC yr−1. For year 2011 alone, EFF was 9.5 ± 0.5 PgC yr−1, 3.0 percent above 2010, reflecting a continued trend in these emissions; ELUC was 0.9 ± 0.5 PgC yr−1, approximately constant throughout the decade; GATM was 3.6 ± 0.2 PgC yr−1, SOCEAN was 2.7 ± 0.5 PgC yr−1, and SLAND was 4.1 ± 0.9 PgC yr−1. GATM was low in 2011 compared to the 2002–2011 average because of a high uptake by the land probably in response to natural climate variability associated to La Niña conditions in the Pacific Ocean. The global atmospheric CO2 concentration reached 391.31 ± 0.13 ppm at the end of year 2011. We estimate that EFF will have increased by 2.6% (1.9–3.5%) in 2012 based on projections of gross world product and recent changes in the carbon intensity of the economy. All uncertainties are reported as ±1 sigma (68% confidence assuming Gaussian error distributions that the real value lies within the given interval), reflecting the current capacity to characterise the annual estimates of each component of the global carbon budget. This paper is intended to provide a baseline to keep track of annual carbon budgets in the future. All data presented here can be downloaded from the Carbon Dioxide Information Analysis Center (doi:10.3334/CDIAC/GCP_V2013). Global carbon budget 2013

Nitrogen cycle dynamics have the capacity to attenuate the magnitude of global terrestrial carbon sinks and sources driven by CO2 fertilization and changes in climate. In this study, two versions of the terrestrial carbon and nitrogen cycle components of the Integrated Science Assessment Model (ISAM) are used to evaluate how variation in nitrogen availability influences terrestrial carbon sinks and sources in response to changes over the 20th century in global environmental factors including atmospheric CO2 concentration, nitrogen inputs, temperature, precipitation and land use. The two versions of ISAM vary in their treatment of nitrogen availability: ISAM‐NC has a terrestrial carbon cycle model coupled to a fully dynamic nitrogen cycle while ISAM‐C has an identical carbon cycle model but nitrogen availability is always in sufficient supply. Overall, the two versions of the model estimate approximately the same amount of global mean carbon uptake over the 20th century. However, comparisons of results of ISAM‐NC relative to ISAM‐C reveal that nitrogen dynamics: (1) reduced the 1990s carbon sink associated with increasing atmospheric CO2 by 0.53 PgC yr−1 (1 Pg = 1015g), (2) reduced the 1990s carbon source associated with changes in temperature and precipitation of 0.34 PgC yr−1 in the 1990s, (3) an enhanced sink associated with nitrogen inputs by 0.26 PgC yr−1, and (4) enhanced the 1990s carbon source associated with changes in land use by 0.08 PgC yr−1 in the 1990s. These effects of nitrogen limitation influenced the spatial distribution of the estimated exchange of CO2 with greater sink activity in high latitudes associated with climate effects and a smaller sink of CO2 in the southeastern United States caused by N limitation associated with both CO2 fertilization and forest regrowth. These results indicate that the dynamics of nitrogen availability are important to consider in assessing the spatial distribution and temporal dynamics of terrestrial carbon sources and sinks.

Carbon sources and sinks of North America as affected by major drought events during the past 30 years

A novel sensitivity analysis of commercial building hybrid energy-structure performance

Abstract. Global and regional sources and sinks of carbon across the earth's surface have been studied extensively using atmospheric carbon dioxide (CO2) observations and atmospheric chemistry-transport model (ACTM) simulations (top-down/inversion method). However, the uncertainties in the regional flux distributions remain unconstrained due to the lack of high-quality measurements, uncertainties in model simulations, and representation of data and flux errors in the inversion systems. Here, we assess the representation of data and flux errors using a suite of 16 inversion cases derived from a single transport model (MIROC4-ACTM) but different sets of a priori (bottom-up) terrestrial biosphere and oceanic fluxes, as well as prior flux and observational data uncertainties (50 sites) to estimate CO2 fluxes for 84 regions over the period 2000–2020. The inversion ensembles provide a mean flux field that is consistent with the global CO2 growth rate, land and ocean sink partitioning of −2.9 ± 0.3 (± 1σ uncertainty on the ensemble mean) and −1.6 ± 0.2 PgC yr−1, respectively, for the period 2011–2020 (without riverine export correction), offsetting about 22 %–33 % and 16 %–18 % of global fossil fuel CO2 emissions. The rivers carry about 0.6 PgC yr−1 of land sink into the deep ocean, and thus the effective land and ocean partitioning is −2.3 ± 0.3 and −2.2 ± 0.3, respectively. Aggregated fluxes for 15 land regions compare reasonably well with the best estimations for the 2000s (∼ 2000–2009), given by the REgional Carbon Cycle Assessment and Processes (RECCAP), and all regions appeared as a carbon sink over 2011–2020. Interannual variability and seasonal cycle in CO2 fluxes are more consistently derived for two distinct prior fluxes when a greater degree of freedom (increased prior flux uncertainty) is given to the inversion system. We have further evaluated the inversion fluxes using meridional CO2 distributions from independent (not used in the inversions) aircraft and surface measurements, suggesting that the ensemble mean flux (model–observation mean ± 1σ standard deviation = −0.3 ± 3 ppm) is best suited for global and regional CO2 flux budgets than an individual inversion (model–observation 1σ standard deviation = −0.35 ± 3.3 ppm). Using the ensemble mean fluxes and uncertainties for 15 land and 11 ocean regions at 5-year intervals, we show promise in the capability to track flux changes toward supporting the ongoing and future CO2 emission mitigation policies.

In pharmacometrics, understanding a covariate effect on an interested outcome is essential for assessing the importance of the covariate. Variance-based global sensitivity analysis (GSA) can simultaneously quantify contribution of each covariate effect to the variability for the interested outcome considering with random effects. The aim of this study was to apply GSA to pharmacometric models to assess covariate effects. Simulations were conducted with pharmacokinetic models to characterize the GSA for assessment of covariate effects and with an example of quantitative systems pharmacology (QSP) models to apply the GSA to a complex model. In the simulations, covariate and random variables were generated to simulate the outcomes using the models. Ratios of variance explained by each factor (each covariate and random effect) over the overall variance of the outcome were used as sensitivity indices. The sensitivity indices were consistent with the effect size of covariate. The sensitivity indices identified the importance of creatinine clearance on the pharmacokinetic exposure for a renally-excreted drug. These sensitivity indices could be applied to plasma concentrations over time (repeated measurable outcomes over time) as interested outcomes. Using the GSA, each contribution of all of the covariate effects could be efficiently identified even in the complex QSP model. Variance-based GSA can provide insight when considering the importance of covariate effects by simultaneously and quantitatively assessing all covariate and random effects on interested outcomes in pharmacometrics.

Abstract. This REgional Carbon Cycle Assessment and Processes regional study provides a synthesis of the carbon balance of terrestrial ecosystems in East Asia, a region comprised of China, Japan, North and South Korea, and Mongolia. We estimate the current terrestrial carbon balance of East Asia and its driving mechanisms during 1990–2009 using three different approaches: inventories combined with satellite greenness measurements, terrestrial ecosystem carbon cycle models and atmospheric inversion models. The magnitudes of East Asia's terrestrial carbon sink from these three approaches are comparable: −0.293±0.033 PgC yr−1 from inventory–remote sensing model–data fusion approach, −0.413±0.141 PgC yr−1 (not considering biofuel emissions) or −0.224±0.141 PgC yr−1 (considering biofuel emissions) for carbon cycle models, and −0.270±0.507 PgC yr−1 for atmospheric inverse models. Here and in the following, the numbers behind ± signs are standard deviations. The ensemble of ecosystem modeling based analyses further suggests that at the regional scale, climate change and rising atmospheric CO2 together resulted in a carbon sink of −0.289±0.135 PgC yr−1, while land-use change and nitrogen deposition had a contribution of −0.013±0.029 PgC yr−1 and −0.107±0.025 PgC yr−1, respectively. Although the magnitude of climate change effects on the carbon balance varies among different models, all models agree that in response to climate change alone, southern China experienced an increase in carbon storage from 1990 to 2009, while northern East Asia including Mongolia and north China showed a decrease in carbon storage. Overall, our results suggest that about 13–27% of East Asia's CO2 emissions from fossil fuel burning have been offset by carbon accumulation in its terrestrial territory over the period from 1990 to 2009. The underlying mechanisms of carbon sink over East Asia still remain largely uncertain, given the diversity and intensity of land management processes, and the regional conjunction of many drivers such as nutrient deposition, climate, atmospheric pollution and CO2 changes, which cannot be considered as independent for their effects on carbon storage.

This paper mainly reviews some widely used global sensitivity analysis methods for uncertainty structure, in which the uncertainty is described by probability theory. Global sensitivity analysis can be divided into single output global sensitivity analysis and multivariate global sensitivity analysis based on the number of output response of the structure. The single output global sensitivity analysis has been studied by many researchers and obtains widely development. Due to the different ways of representing uncertainty in probability theory (variance, probability density function, cumulative distribution function, etc.), different global sensitivity analysis methods (variance based method, moment-independent method, etc.) have been proposed. For example, the variance based global sensitivity analysis method can reflect the structure of the model itself and has been widely studied and applied in engineering; while the moment independent global sensitivity analysis method has a more comprehensive description of the uncertainty and reflects more uncertainty information. The multivariate output global sensitivity analysis is developed based on the single output global sensitivity analysis and it mainly focuses on the effects of input variables on the uncertainty of the whole multivariate output. For the models with multivariate outputs, the correlation between different outputs exists and it should be considered when performing the global sensitivity analysis. Comparing to the single output global sensitivity analysis, the multivariate output global sensitivity analysis is much more complicated and computational demanding since there are more uncertainty information for the multivariate outputs. The basic theories of different global sensitivity analysis methods are described in detail in order to have better understanding of these methods. Numerical examples are also used to compare these different methods. Through the comparison, the advantages and shortage of different global sensitivity analysis methods are obtained.

Conversion and interconnection of multiple energies have become the main form of energy development in China. This paper analyzes the evolution of energy internet and proposes its basic framework based on summarized typical features. As we all know, the mathematical model in energy internet plays increasingly key role in arranging and optimizing resources as well as predicting work. In real applications, we find many complicated problems of electrical model, such as high-dimensional, multiple peaks, non-linear, inconsistent, and nonconvex. In order to solve them, this paper combines model simulation with Global Uncertainty and Sensitivity Analysis to analyse and predict the scientific problem from a probabilistic viewpoint. Global Sensitivity Analysis aims to find out how changes of multiple parameters affecting working result of electrical model, and to analyze how interactions among parameters influencing model results. While modeling each type of electrical model, Global Sensitivity Analysis are used less, this paper also lists various sensitivity analysis algorithm, and describes kinds of methods of both local and global sensitivity analysis. The research will provide a complete method data base of sensitivity analysis for each model development in electrical system. Furthermore, the combination of uncertainty and sensitivity analysis at home and abroad is beneficial to figure out the difficulties and focuses of connections among researches on sensitivity analysis and its common features and the spatially explicit landscape modeling.

<p>Modern models of environmental and industrial systems have reached a relatively high level of complexity. The latter aspect could hamper an unambiguous understanding of the functioning of a model, i.e., how it drives relationships and dependencies among inputs and outputs of interest. Sensitivity Analysis tools can be employed to examine this issue.</p><p>Global sensitivity analysis (GSA) approaches rest on the evaluation of sensitivity across the entire support within which system model parameters are supposed to vary. In this broad context, it is important to note that the definition of a sensitivity metric must be linked to the nature of the question(s) the GSA is meant to address. These include, for example: (i) which are the most important model parameters with respect to given model output(s)?; (ii) could we set some parameter(s) (thus assisting model calibration) at prescribed value(s) without significantly affecting model results?; (iii) at which space/time locations can one expect the highest sensitivity of model output(s) to model parameters and/or knowledge of which parameter(s) could be most beneficial for model calibration?</p><p>The variance-based Sobol’ Indices (e.g., Sobol, 2001) represent one of the most widespread GSA metrics, quantifying the average reduction in the variance of a model output stemming from knowledge of the input. Amongst other techniques, Dell’Oca et al. [2017] proposed a moment-based GSA approach which enables one to quantify the influence of uncertain model parameters on the (statistical) moments of a target model output.</p><p>Here, we embed in these sensitivity indices the effect of uncertainties both in the system model conceptualization and in the ensuing model(s) parameters. The study is grounded on the observation that physical processes and natural systems within which they take place are complex, rendering target state variables amenable to multiple interpretations and mathematical descriptions. As such, predictions and uncertainty analyses based on a single model formulation can result in statistical bias and possible misrepresentation of the total uncertainty, thus justifying the assessment of multiple model system conceptualizations. We then introduce copula-based sensitivity metrics which allow characterizing the global (with respect to the input) value of the sensitivity and the degree of variability (across the whole range of the input values) of the sensitivity for each value that the prescribed model output can possibly undertake, as driven by a governing model. In this sense, such an approach to sensitivity is global with respect to model input(s) and local with respect to model output, thus enabling one to discriminate the relevance of an input across the entire range of values of the modeling goal of interest. The methodology is demonstrated in the context of flow and reactive transport scenarios.</p><p> </p><p><strong>References</strong></p><p>Sobol, I. M., 2001. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Sim., 55, 271-280.</p><p>Dell’Oca, A., Riva, M., Guadagnini, A., 2017. Moment-based metrics for global sensitivity analysis of hydrological systems. Hydr. Earth Syst. Sci., 21, 6219-6234.</p>

Global parameters sensitivity analysis of modeling water, energy and carbon exchange of an arid agricultural ecosystem

Sensitivity analysis to determine the importance of input variables in groundwater stress

Abstract. Global sensitivity analysis (GSA) is a powerful approach in identifying which inputs or parameters most affect a model's output. This determines which inputs to include when performing model calibration or uncertainty analysis. GSA allows quantification of the sensitivity index (SI) of a particular input – the percentage of the total variability in the output attributed to the changes in that input – by averaging over the other inputs rather than fixing them at specific values. Traditional methods of computing the SIs using the Sobol and extended Fourier Amplitude Sensitivity Test (eFAST) methods involve running a model thousands of times, but this may not be feasible for computationally expensive Earth system models. GSA methods that use a statistical emulator in place of the expensive model are popular, as they require far fewer model runs. We performed an eight-input GSA, using the Sobol and eFAST methods, on two computationally expensive atmospheric chemical transport models using emulators that were trained with 80 runs of the models. We considered two methods to further reduce the computational cost of GSA: (1) a dimension reduction approach and (2) an emulator-free approach. When the output of a model is multi-dimensional, it is common practice to build a separate emulator for each dimension of the output space. Here, we used principal component analysis (PCA) to reduce the output dimension, built an emulator for each of the transformed outputs, and then computed SIs of the reconstructed output using the Sobol method. We considered the global distribution of the annual column mean lifetime of atmospheric methane, which requires ∼ 2000 emulators without PCA but only 5–40 emulators with PCA. We also applied an emulator-free method using a generalised additive model (GAM) to estimate the SIs using only the training runs. Compared to the emulator-only methods, the emulator–PCA and GAM methods accurately estimated the SIs of the ∼ 2000 methane lifetime outputs but were on average 24 and 37 times faster, respectively.

A dimension reduction-based Kriging modeling method for high-dimensional time-variant uncertainty propagation and global sensitivity analysis