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Measuring and modeling continuous quality distributions of soil organic matter
S. Bruun, G. I. gren, B. T. Christensen,L. S. Jensen
Biogeosciences (BG) & Discussions (BGD) , 2010,
Abstract: An understanding of the dynamics of soil organic matter (SOM) is important for our ability to develop management practices that preserve soil quality and sequester carbon. Most SOM decomposition models represent the heterogeneity of organic matter by a few discrete compartments with different turnover rates, while other models employ a continuous quality distribution. To make the multi-compartment models more mechanistic in nature, it has been argued that the compartments should be related to soil fractions actually occurring and having a functional role in the soil. In this paper, we make the case that fractionation methods that can measure continuous quality distributions should be developed, and that the temporal development of these distributions should be incorporated into SOM models. The measured continuous SOM quality distributions should hold valuable information not only for model development, but also for direct interpretation. Measuring continuous distributions requires that the measurements along the quality variable are so frequent that the distribution approaches the underlying continuum. Continuous distributions lead to possible simplifications of the model formulations, which considerably reduce the number of parameters needed to describe SOM turnover. A general framework for SOM models representing SOM across measurable quality distributions is presented and simplifications for specific situations are discussed. Finally, methods that have been used or have the potential to be used to measure continuous quality SOM distributions are reviewed. Generally, existing fractionation methods will have to be modified to allow measurement of distributions or new fractionation techniques will have to be developed. Developing the distributional models in concert with the fractionation methods to measure the distributions will be a major task. We hope the current paper will help generate the interest needed to accommodate this.
Measuring the Complexity of Continuous Distributions  [PDF]
Guillermo Santamaría-Bonfil,Nelson Fernández,Carlos Gershenson
Physics , 2015,
Abstract: We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We find that a broad range of common parameters found in Gaussian and scale-free distributions present high complexity values. We also explore the relationship between our measure of complexity and information adaptation.
Evaluation of modelling approaches for predicting the spatial distribution of soil organic carbon stocks at the national scale  [PDF]
M. P. Martin,T. G. Orton,E. Lacarce,J. Meersmans,N. P. A. Saby,J. B. Paroissien,C. Jolivet,L. Boulonne,D. Arrouays
Statistics , 2015, DOI: 10.1016/j.geoderma.2014.01.005
Abstract: Soil organic carbon (SOC) plays a major role in the global carbon budget. It can act as a source or a sink of atmospheric carbon, thereby possibly influencing the course of climate change. Improving the tools that model the spatial distributions of SOC stocks at national scales is a priority, both for monitoring changes in SOC and as an input for global carbon cycles studies. In this paper, we compare and evaluate two recent and promising modelling approaches. First, we considered several increasingly complex boosted regression trees (BRT), a convenient and efficient multiple regression model from the statistical learning field. Further, we considered a robust geostatistical approach coupled to the BRT models. Testing the different approaches was performed on the dataset from the French Soil Monitoring Network, with a consistent cross-validation procedure. We showed that when a limited number of predictors were included in the BRT model, the standalone BRT predictions were significantly improved by robust geostatistical modelling of the residuals. However, when data for several SOC drivers were included, the standalone BRT model predictions were not significantly improved by geostatistical modelling. Therefore, in this latter situation, the BRT predictions might be considered adequate without the need for geostatistical modelling, provided that i) care is exercised in model fitting and validating, and ii) the dataset does not allow for modelling of local spatial autocorrelations, as is the case for many national systematic sampling schemes.
Spatial distribution of soil organic carbon stocks in France  [PDF]
M. P. Martin,M. Wattenbach,P. Smith,J. Meersmans
Biogeosciences Discussions , 2010, DOI: 10.5194/bgd-7-8409-2010
Abstract: Soil organic carbon plays a major role in the global carbon budget, and can act as a source or a sink of atmospheric carbon, whereby it can influence the course of climate change. Changes in soil organic soil stocks (SOCS) are now taken into account in international negotiations regarding climate change. Consequently, developing sampling schemes and models for estimating the spatial distribution of SOCS is a priority. The French soil monitoring network has been established on a 16 km × 16 km grid and the first sampling campaign has recently been completed, providing circa 2200 measurements of stocks of soil organic carbon, obtained through an in situ composite sampling, uniformly distributed over the French territory. We calibrated a boosted regression tree model on the observed stocks, modelling SOCS as a function of other variables such as climatic parameters, vegetation net primary productivity, soil properties and land use. The calibrated model was evaluated through cross-validation and eventually used for estimating SOCS for the whole of metropolitan France. Two other models were calibrated on forest and agricultural soils separately, in order to assess more precisely the influence of pedo-climatic variables on soil organic carbon for such soils. The boosted regression tree model showed good predictive ability, and enabled quantification of relationships between SOCS and pedo-climatic variables (plus their interactions) over the French territory. These relationship strongly depended on the land use, and more specifically differed between forest soils and cultivated soil. The total estimate of SOCS in France was 3.260 ± 0.872 PgC for the first 30 cm. It was compared to another estimate, based on the previously published European soil organic carbon and bulk density maps, of 5.303 PgC. We demonstrate that the present estimate might better represent the actual SOCS distributions of France, and consequently that the previously published approach at the European level greatly overestimates SOCS.
Spatial distribution of soil organic carbon stocks in France
M. P. Martin, M. Wattenbach, P. Smith, J. Meersmans, C. Jolivet, L. Boulonne,D. Arrouays
Biogeosciences (BG) & Discussions (BGD) , 2011,
Abstract: Soil organic carbon plays a major role in the global carbon budget, and can act as a source or a sink of atmospheric carbon, thereby possibly influencing the course of climate change. Changes in soil organic carbon (SOC) stocks are now taken into account in international negotiations regarding climate change. Consequently, developing sampling schemes and models for estimating the spatial distribution of SOC stocks is a priority. The French soil monitoring network has been established on a 16 km × 16 km grid and the first sampling campaign has recently been completed, providing around 2200 measurements of stocks of soil organic carbon, obtained through an in situ composite sampling, uniformly distributed over the French territory. We calibrated a boosted regression tree model on the observed stocks, modelling SOC stocks as a function of other variables such as climatic parameters, vegetation net primary productivity, soil properties and land use. The calibrated model was evaluated through cross-validation and eventually used for estimating SOC stocks for mainland France. Two other models were calibrated on forest and agricultural soils separately, in order to assess more precisely the influence of pedo-climatic variables on SOC for such soils. The boosted regression tree model showed good predictive ability, and enabled quantification of relationships between SOC stocks and pedo-climatic variables (plus their interactions) over the French territory. These relationships strongly depended on the land use, and more specifically, differed between forest soils and cultivated soil. The total estimate of SOC stocks in France was 3.260 ± 0.872 PgC for the first 30 cm. It was compared to another estimate, based on the previously published European soil organic carbon and bulk density maps, of 5.303 PgC. We demonstrate that the present estimate might better represent the actual SOC stock distributions of France, and consequently that the previously published approach at the European level greatly overestimates SOC stocks.
Measuring and modelling concurrency
Larry Sawers
Journal of the International AIDS Society , 2013, DOI: 10.7448/ias.16.1.17431
Abstract: This article explores three critical topics discussed in the recent debate over concurrency (overlapping sexual partnerships): measurement of the prevalence of concurrency, mathematical modelling of concurrency and HIV epidemic dynamics, and measuring the correlation between HIV and concurrency. The focus of the article is the concurrency hypothesis – the proposition that presumed high prevalence of concurrency explains sub-Saharan Africa's exceptionally high HIV prevalence. Recent surveys using improved questionnaire design show reported concurrency ranging from 0.8% to 7.6% in the region. Even after adjusting for plausible levels of reporting errors, appropriately parameterized sexual network models of HIV epidemics do not generate sustainable epidemic trajectories (avoid epidemic extinction) at levels of concurrency found in recent surveys in sub-Saharan Africa. Efforts to support the concurrency hypothesis with a statistical correlation between HIV incidence and concurrency prevalence are not yet successful. Two decades of efforts to find evidence in support of the concurrency hypothesis have failed to build a convincing case.
Modelling of directional data using Kent distributions  [PDF]
Parthan Kasarapu
Computer Science , 2015,
Abstract: The modelling of data on a spherical surface requires the consideration of directional probability distributions. To model asymmetrically distributed data on a three-dimensional sphere, Kent distributions are often used. The moment estimates of the parameters are typically used in modelling tasks involving Kent distributions. However, these lack a rigorous statistical treatment. The focus of the paper is to introduce a Bayesian estimation of the parameters of the Kent distribution which has not been carried out in the literature, partly because of its complex mathematical form. We employ the Bayesian information-theoretic paradigm of Minimum Message Length (MML) to bridge this gap and derive reliable estimators. The inferred parameters are subsequently used in mixture modelling of Kent distributions. The problem of inferring the suitable number of mixture components is also addressed using the MML criterion. We demonstrate the superior performance of the derived MML-based parameter estimates against the traditional estimators. We apply the MML principle to infer mixtures of Kent distributions to model empirical data corresponding to protein conformations. We demonstrate the effectiveness of Kent models to act as improved descriptors of protein structural data as compared to commonly used von Mises-Fisher distributions.
Organic aerosol and global climate modelling: a review
M. Kanakidou, J. H. Seinfeld, S. N. Pandis, I. Barnes, F. J. Dentener, M. C. Facchini, R. Van Dingenen, B. Ervens, A. Nenes, C. J. Nielsen, E. Swietlicki, J. P. Putaud, Y. Balkanski, S. Fuzzi, J. Horth, G. K. Moortgat, R. Winterhalter, C. E. L. Myhre, K. Tsigaridis, E. Vignati, E. G. Stephanou,J. Wilson
Atmospheric Chemistry and Physics (ACP) & Discussions (ACPD) , 2005,
Abstract: The present paper reviews existing knowledge with regard to Organic Aerosol (OA) of importance for global climate modelling and defines critical gaps needed to reduce the involved uncertainties. All pieces required for the representation of OA in a global climate model are sketched out with special attention to Secondary Organic Aerosol (SOA): The emission estimates of primary carbonaceous particles and SOA precursor gases are summarized. The up-to-date understanding of the chemical formation and transformation of condensable organic material is outlined. Knowledge on the hygroscopicity of OA and measurements of optical properties of the organic aerosol constituents are summarized. The mechanisms of interactions of OA with clouds and dry and wet removal processes parameterisations in global models are outlined. This information is synthesized to provide a continuous analysis of the flow from the emitted material to the atmosphere up to the point of the climate impact of the produced organic aerosol. The sources of uncertainties at each step of this process are highlighted as areas that require further studies.
Organic aerosol and global climate modelling: a review  [PDF]
M. Kanakidou,J. H. Seinfeld,S. N. Pandis,I. Barnes
Atmospheric Chemistry and Physics Discussions , 2004,
Abstract: The present paper reviews existing knowledge with regard to Organic Aerosol (OA) of importance for global climate modelling and defines critical gaps needed to reduce the involved uncertainties. All pieces required for the representation of OA in a global climate model are sketched out with special attention to Secondary Organic Aerosol (SOA): The emission estimates of primary carbonaceous particles and SOA precursor gases are summarized. The up-to-date understanding of the chemical formation and transformation of condensable organic material is outlined. Knowledge on the hygroscopicity of OA and measurements of optical properties of the organic aerosol constituents are summarized. The mechanisms of interactions of OA with clouds and dry and wet removal processes parameterisations in global models are outlined. This information is synthesized to provide a continuous analysis of the flow from the emitted material to the atmosphere up to the point of the climate impact of the produced organic aerosol. The sources of uncertainties at each step of this process are highlighted as areas that require further studies.
MODELLING OF A STOCHASTIC CONTINUOUS SYSTEM  [cached]
Martin Albertyn,Paul S. Kruger
South African Journal of Industrial Engineering , 2012,
Abstract: The key objective is to develop a method which can be utilized to model a stochastic continuous system. A system from the "real world" is used as the basis for the simulation modelling technique that is presented. The conceptualization phase indicates that the model has to incorporate stochastic and deterministic elements. A method is developed that utilizes the discrete simulation ability of a stochastic package (ARENA), in conjunction with a deterministic package (FORTRAN), to model the continuous system. (Software packages tend to specialize in either stochastic, or deterministic modelling.) The length of the iteration time interval and adequate sample size are investigated. The method is authenticated by the verification and validation ofthe defined model. Two scenarios are modelled and the results are discussed . Conclusions are presented and strengths and weaknesses of this method are considered and discussed .
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