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Nitrogen (N) loss through ammonia $$({\mathrm{NH}}_{3})$$ volatilization in agricultural soils is a significant source of atmospheric $${\mathrm{NH}}_{3}$$ , contributing to low N use efficiency in crops, risk to human health, environmental pollution, and is an indirect source of nitrous oxide $$({\mathrm{N}}_{2}\mathrm{O})$$ emissions. Our objective was to develop an ammonia volatilization method within the DayCent ecosystem model that incorporates key 4R N management practices (right type, right rate, right placement, and right timing) that influence $${\mathrm{NH}}_{3}$$ volatilization associated with application of urea-based nitrogen fertilizers to agricultural soils. The $${\mathrm{NH}}_{3}$$ volatilization method was developed with Bayesian calibration using sampling importance resampling methods and Bayes factors to select the level of complexity in the model that best represents $${\mathrm{NH}}_{3}$$ volatilization given the observed data. The final model included urea hydrolysis and the influence of urease inhibitors; short-term soil pH changes following fertilization; fertilizer incorporation into the soil (mechanically and through irrigation/precipitation); and specification of the fertilizer placement method (i.e. broadcast vs. banding and surface vs incorporated). DayCent predicts $${\mathrm{NH}}_{3}$$ volatilization with a root-mean-squared error of 158 (95% interval ranging from 133 to 192), bias of 7 (95% interval ranging from − 106 to 102) g NH3-N ha−1 day−1, and with a Bayesian R2 value of 0.39 (95% interval ranging from 0.17 to 0.62). Furthermore, the model incorporates key management options influencing $${\mathrm{NH}}_{3}$$ volatilization related to placement method and fertilizer type with and without urease inhibitors that can be used to evaluate management and policy options for reducing losses of NH3 from urea fertilization.

Experiments that longitudinally collect RNA sequencing (RNA-seq) data can provide transformative insights in biology research by revealing the dynamic patterns of genes. Such experiments create a great demand for new analytic approaches to identify differentially expressed (DE) genes based on large-scale time-course count data. Existing methods, however, are suboptimal with respect to power and may lack theoretical justification. Furthermore, most existing tests are designed to distinguish among conditions based on overall differential patterns across time, though in practice, a variety of composite hypotheses are of more scientific interest. Finally, some current methods may fail to control the false discovery rate. In this paper, we propose a new model and testing procedure to address the above issues simultaneously. Specifically, conditional on a latent Gaussian mixture with evolving means, we model the data by negative binomial distributions. Motivated by Storey (2007) and Hwang and Liu (2010), we introduce a general testing framework based on the proposed model and show that the proposed test enjoys the optimality property of maximum average power. The test allows not only identification of traditional DE genes but also testing of a variety of composite hypotheses of biological interest. We establish the identifiability of the proposed model, implement the proposed method via efficient algorithms, and demonstrate its good performance via simulation studies. The procedure reveals interesting biological insights, when applied to data from an experiment that examines the effect of varying light environments on the fundamental physiology of the marine diatom Phaeodactylum tricornutum.

A one-year angler intercept survey was conducted on the lower 17 miles of the Passaic River, an urban industrialized river that flows through Newark, New Jersey. The purpose of the survey was to co...

Adoption of no-till management on croplands has become a controversial approach for storing carbon in soil due to conflicting findings. Yet, no-till is still promoted as a management practice to stabilize the global climate system from additional change due to anthropogenic greenhouse gas emissions, including the 4 per mille initiative promoted through the UN Framework Convention on Climate Change. We evaluated the body of literature surrounding this practice, and found that SOC storage can be higher under no-till management in some soil types and climatic conditions even with redistribution of SOC, and contribute to reducing net greenhouse gas emissions. However, uncertainties tend to be large, which may make this approach less attractive as a contributor to stabilize the climate system compared to other options. Consequently, no-till may be better viewed as a method for reducing soil erosion, adapting to climate change, and ensuring food security, while any increase in SOC storage is a co-benefit for society in terms of reducing greenhouse gas emissions., Facultad de Ciencias Agrarias y Forestales

Agriculture soils are responsible for a large proportion of global nitrous oxide (N2O) emissions—a potent greenhouse gas and ozone depleting substance. Enhanced-efficiency nitrogen (N) fertilizers (EENFs) can reduce N2O emission from N-fertilized soils, but their effect varies considerably due to a combination of factors, including climatic conditions, edaphic characteristics and management practices. In this study, we further developed the DayCent ecosystem model to simulate two EENFs: controlled-release N fertilizers (CRNFs) and nitrification inhibitors (NIs) and evaluated their N2O mitigation potentials. We implemented a Bayesian calibration method using the sampling importance resampling (SIR) algorithm to derive a joint posterior distribution of model parameters that was informed by N2O flux measurements from corn production systems a network of experimental sites within the GRACEnet program. The joint posterior distribution can be applied to estimate predictions of N2O reduction factors when EENFs are adopted in place of conventional urea-based N fertilizer. The resulting median reduction factors were − 11.9% for CRNFs (ranging from −51.7% and 0.58%) and − 26.7% for NIs (ranging from −61.8% to 3.1%), which is comparable to the measured reduction factors in the dataset. By incorporating EENFs, the DayCent ecosystem model is able to simulate a broader suite of options to identify best management practices for reducing N2O emissions.

Marine recreational fishing from shore and from private boats in Hawaiʻi is monitored via the Hawaiʻi Marine Recreational Fishing Survey (HMRFS), using an access point intercept survey to collect catch rate information, and the Coastal Household Telephone Survey (CHTS) to collect fishing effort data. In response to a recent HMRFS review, roving surveys of shoreline fishing effort and catch rate, an aerial fishing effort survey, and a mail survey of fishing effort were tested simultaneously on one of the main Hawaiian Islands (Oʻahu) and compared with the current HMRFS approach for producing shoreline fishing estimates. The pilot roving surveys were stratified by region (rural vs urban), shift (three 4-h periods during the day), and day type (weekday vs weekend). A pilot access point survey of private boat fishing was also conducted on Oʻahu, using an alternate sampling design created by NOAA Fisheries’ Marine Recreational Information Program (MRIP). Three overlapping 6-h time blocks and site clusters with unequal inclusion probabilities were used to cover daytime fishing. Group catch was recorded for an entire vessel rather than individual catch, which is the current standard for MRIP intercept surveys. Although catch estimates from the pilot private boat survey were comparable to the current HMRFS catch estimates, the catch estimates from the pilot roving survey were lower than the HMRFS estimates. HMRFS uses effort data from the CHTS, which includes both day and night fishing in all areas, to estimate total catch, whereas effort data from the roving shoreline survey covered only daytime fishing from publicly accessible areas. We therefore suggest that a roving survey conducted during the day should have complementary surveys to include night fishing and fishing in remote and private/restricted areas. Results from these pilot studies will be used to improve the current surveys of marine recreational fishing activities in Hawaiʻi.

Small-angle X-ray scattering (SAXS) is a technique that yields low-resolution structural information of biological macromolecules by exposing a large ensemble of molecules in solution to a powerful...

In the U.S. Forest Service’s Forest Inventory and Analysis (FIA) program, as in other natural resource surveys, many auxiliary variables are available for use in model-assisted inference about finite population parameters. Some of this auxiliary information may be extraneous, and therefore model selection is appropriate to improve the efficiency of the survey regression estimators of finite population totals. A model-assisted survey regression estimator using the lasso is presented and extended to the adaptive lasso. For a sequence of finite populations and probability sampling designs, asymptotic properties of the lasso survey regression estimator are derived, including design consistency and central limit theory for the estimator and design consistency of a variance estimator. To estimate multiple finite population quantities with the method, lasso survey regression weights are developed, using both a model calibration approach and a ridge regression approximation. The gains in efficiency of the lasso estimator over the full regression estimator are demonstrated through a simulation study estimating tree canopy cover for a region in Utah.

Nonlinear dynamical systems are encountered in many areas of social science, natural science, and engineering, and are of particular interest for complex biological processes like the spiking activity of neural ensembles in the brain. To describe such spiking activity, we adapt the Volterra series expansion of an analytic function to account for the point-process nature of multiple inputs and a single output (MISO) in a neural ensemble. Our model describes the transformed spiking probability for the output as the sum of kernel-weighted integrals of the inputs. The kernel functions need to be identified and estimated, and both local sparsity (kernel functions may be zero on part of their support) and global sparsity (some kernel functions may be identically zero) are of interest. The kernel functions are approximated by B-splines and a penalized likelihood-based approach is proposed for estimation. Even for moderately complex brain functionality, the identification and estimation of this sparse fun...

We consider small area estimation for the departure times of recreational anglers along the Atlantic and Gulf coasts of the United States. A Bayesian area-level Fay–Herriot model is considered to obtain estimates of the departure time distribution functions. The departure distribution functions are modelled as circular distributions plus area-specific errors. The circular distributions are modelled as projected normal, and a regression model is specified to borrow information across domains. Estimation is conducted through the use of a Hamiltonian Monte Carlo sampler and a projective approach onto the probability simplex. The Canadian Journal of Statistics 44: 416–430; 2016 © 2016 Statistical Society of Canada

Fine stratification is commonly used to control the distribution of a sample from a finite population and to improve the precision of resulting estimators. One-per-stratum designs represent the finest possible stratification and occur in practice, but designs with very low numbers of elements per stratum (say, two or three) are also common. The classical variance estimator in this context is the collapsed stratum estimator, which relies on creating larger “pseudo-strata” and computing the sum of the squared differences between estimated stratum totals across the pseudo-strata. We propose here a nonparametric alternative that replaces the pseudo-strata by kernel-weighted stratum neighborhoods and uses deviations from a fitted mean function to estimate the variance. We establish the asymptotic behavior of the kernel-based estimator and show its superior practical performance relative to the collapsed stratum variance estimator in a simulation study. An application to data from the U.S. Consumer Expe...

Discrete event simulations (DES) provide a powerful means for modeling complex systems and analyzing their behavior. DES capture all possible interactions between the entities they manage, which makes them highly expressive but also compute-intensive. These computational requirements often impose limitations on the breadth and/or depth of research that can be conducted with a discrete event simulation.This work describes our approach for leveraging the vast quantity of computing and storage resources available in both private organizations and public clouds to enable real-time exploration of discrete event simulations. Rather than directly targeting simulation execution speeds, we autonomously generate and execute novel scenario variants to explore a representative subset of the simulation parameter space. The corresponding outputs from this process are analyzed and used by our framework to produce models that accurately forecast simulation outcomes in real time, providing interactive feedback and facilitating exploratory research.Our framework distributes the workloads associated with generating and executing scenario variants across a range of commodity hardware, including public and private cloud resources. Once the models have been created, we evaluate their performance and improve prediction accuracy by employing dimensionality reduction techniques and ensemble methods. To make these models highly accessible, we provide a user-friendly interface that allows modelers and epidemiologists to modify simulation parameters and see projected outcomes in real time. Our approach enables fast, accurate forecasts of discrete event simulations.The framework copes with high dimensionality and voluminous datasets.We facilitate simulation execution with cycle scavenging and cloud resources.We create and evaluate several predictive models, including ensemble methods.Our framework is made accessible to end users through an interactive web interface.

Benefits of carbon sequestration in agricultural soils are well recognized, and process-based models have been developed to better understand sequestration potential. However, most studies ignore the uncertainty arising during model prediction—a critical requirement for scientific understanding, policy implementation and carbon emission trading. Furthermore, the dependencies created in process-based models due to many parameters and a relatively small set of empirical data hinder parameterization. We have implemented a Bayesian approach using the sampling importance resampling (SIR) method to calibrate the DayCent ecosystem model for estimating soil organic carbon (SOC) stocks, and to quantify uncertainty in model predictions. A SOC dataset compiled from 19 long-term field experiments, representing 117 combinations of management treatments, with 491 measurements of SOC, was split into independent datasets for model calibration and evaluation. The most important DayCent model parameters were identified through a global sensitivity analysis (GSA) for parameterization and SIR was used to calibrate the model and produce posterior distributions for the most sensitive parameters. On average, the Bayesian calibration reduced the model uncertainty by a factor of 6.6 relative to the uncertainty associated with the prior. The Bayesian model analysis framework will allow for ongoing updates to the model as new datasets and model structural improvements are made in future research, and overall provide a stronger basis for models to support policy and management decisions associated with GHG mitigation through C sequestration in agricultural soils.

The efficient use of auxiliary information to improve the precision of estimation of population quantities of interest is a central problem in survey sampling. We consider nonparametric regression estimation using much weaker assumptions on the superpopulation model in more general survey situations. Complex designs such as multistage and multiphase sampling are often employed in many large-scale surveys. Nonparametric model-assisted estimators, based on local polynomial regression, for two-stage and two-phase sampling designs are proposed. The local polynomial regression estimator is a nonparametric version of the generalized regression (GREG) estimator and shares most of the desirable properties of the generalized regression estimator. The estimator of the finite population total for two-stage element sampling with complete cluster auxiliary information is a linear combination of cluster total estimators, with sample-dependent weights that are calibrated to known control totals. The nonparametric estimator for two-phase sampling with a regression model for between-phase inference is also expressed as a weighted linear sum of the study variable of interest over a second-phase sample, in which the weights are not calibrated directly to known control totals, but are calibrated to the Horvitz-Thompson estimators of known control totals over a first-phase sample. Asymptotic design unbiasedness and design consistency of the estimators are established, and consistent variance estimators are proposed. Simulation experiments indicate that the local polynomial regression estimators are more efficient than parametric regression estimators under model misspecification, while being nearly as good when the parametric mean function is correctly specified.

International audience; Inference for the parametric distribution of a response given covariates is considered under informative selection of a sample from a finite population. Under this selection, the conditional distribution of a response in the sample, given the covariates and given that it was selected for observation, is not the same as the conditional distribution of the response in the finite population, given only the covariates. It is instead a weighted version of the conditional distribution of interest. Inference must be modified to account for this informative selection. An established approach in this context is maximum “sample likelihood”, developing a weight function that reflects the informative sampling design, then treating the observations as if they were independently distributed according to the weighted distribution. While the sample likelihood methodology has been widely applied, its theoretical foundation has been less developed. A precise asymptotic description of a wide range of informative selection mechanisms is proposed. Under this framework, consistency and asymptotic normality of the maximum sample likelihood estimators are established. The theory allows for the possibility of nuisance parameters that describe the selection mechanism. The proposed regularity conditions are verifiable for various sample schemes, motivated by real problems in surveys. Simulation results for these examples illustrate the quality of the asymptotic approximations, and demonstrate a practical approach to variance estimation that combines aspects of model-based information theory and design-based variance estimation.

Variational approximations provide fast, deterministic alternatives to Markov Chain Monte Carlo for Bayesian inference on the parameters of complex, hierarchical models. Variational approximations are often limited in practicality in the absence of conjugate posterior distributions. Recent work has focused on the application of variational methods to models with only partial conjugacy, such as in semiparametric regression with heteroskedastic errors. Here, both the mean and log variance functions are modeled as smooth functions of covariates. For this problem, we derive a mean field variational approximation with an embedded Laplace approximation to account for the non-conjugate structure. Empirical results with simulated and real data show that our approximate method has significant computational advantages over traditional Markov Chain Monte Carlo; in this case, a delayed rejection adaptive Metropolis algorithm. The variational approximation is much faster and eliminates the need for tuning parameter selection, achieves good fits for both the mean and log variance functions, and reasonably reflects the posterior uncertainty. We apply the methods to log-intensity data from a small angle X-ray scattering experiment, in which properly accounting for the smooth heteroskedasticity leads to significant improvements in posterior inference for key physical characteristics of an organic molecule.

Model-assisted survey regression estimators combine auxiliary information available at a population level with complex survey data to estimate finite population parameters. Many prediction methods, including linear and mixed models, nonparametric regression, and machine learning techniques, can be incorporated into such model-assisted estimators. These methods assume that observations obtained for the sample can be matched without error to the auxiliary data. We investigate properties of estimators that rely on matching algorithms that do not in general yield perfect matches. We focus on difference estimators, which are exactly unbiased under perfect matching but not under imperfect matching. The methods are investigated analytically and via simulation, using a study of recreational angling in South Carolina to build a simulation population. In this study, the survey data come from a stratified, two-stage sample and the auxiliary data from logbooks filed by boat captains. Extensions to regression estimators under imperfect matching are discussed.

This paper reviews the design-based, model-assisted approach to using data from a complex survey together with auxiliary information to estimate finite population parameters. A general recipe for deriving model-assisted estimators is presented and design-based asymptotic analysis for such estimators is reviewed. The recipe allows for a very broad class of prediction methods, with examples from the literature including linear models, linear mixed models, nonparametric regression and machine learning techniques.

The general projected normal distribution is a simple and intuitive model for directional data in any dimension: a multivariate normal random vector divided by its length is the projection of that vector onto the surface of the unit hypersphere. Observed data consist of the projections, but not the lengths. Inference for this model has been restricted to the two-dimensional (circular) case, using Bayesian methods with data augmentation to generate the latent lengths and a Metropolis-within-Gibbs algorithm to sample from the posterior. We describe a new parameterization of the general projected normal distribution that makes inference in any dimension tractable, including the important three-dimensional (spherical) case, which has not previously been considered. Under this new parameterization, the full conditionals of the unknown parameters have closed forms, and we propose a new slice sampler to draw the latent lengths without the need for rejection. Gibbs sampling with this new scheme is fast and easy, leading to improved Bayesian inference; for example, it is now feasible to conduct model selection among complex mixture and regression models for large data sets. Our parameterization also allows straightforward incorporation of covariates into the covariance matrix of the multivariate normal, increasing the ability of the model to explain directional data as a function of independent regressors. Circular and spherical cases are considered in detail and illustrated with scientific applications. For the circular case, seasonal variation in time-of-day departures of anglers from recreational fishing sites is modeled using covariates in both the mean vector and covariance matrix. For the spherical case, we consider paired angles that describe the relative positions of carbon atoms along the backbone chain of a protein. We fit mixtures of general projected normals to these data, with the best-fitting mixture accurately describing biologically meaningful structures including helices, $\beta$ -sheets, and coils and turns. Finally, we show via simulation that our methodology has satisfactory performance in some 10-dimensional and 50-dimensional problems.

Kernel density estimation of the probability density function (pdf) of a response variable is considered under informative selection from a finite population. The informative selection implies that the conditional pdf of a response, given that it was selected for observation, is not the same as the inferential target, which is the unconditional pdf of the response in the superpopulation. Instead, the pdf of the observations (sample pdf) is a weighted version of the superpopulation pdf of interest. Properties of the standard kernel density estimator are described under an asymptotic framework that covers a wide range of informative selection mechanisms. The theory allows for the possibility that the selection mechanism has a parametric structure. A variety of adjustments (parametric or nonparametric) to account for the informative selection are proposed, and investigated via simulation.

Terrestrial CO2 flux estimates are obtained from two fundamentally different methods generally termed bottom-up and top-down approaches. Inventory methods are one type of bottom-up approach which uses various sources of information such as crop production surveys and forest monitoring data to estimate the annual CO2 flux at locations covering a study region. Top-down approaches are various types of atmospheric inversion methods which use CO2 concentration measurements from monitoring towers and atmospheric transport models to estimate CO2 flux over a study region. Both methods can also quantify the uncertainty associated with their estimates. Historically, these two approaches have produced estimates that differ considerably. The goal of this work is to construct a statistical model which sensibly combines estimates from the two approaches to produce a new estimate of CO2 flux for our study region. The two approaches have complementary strengths and weaknesses, and our results show that certain aspects of the uncertainty associated with each of the approaches are greatly reduced by combining the methods. Our model is purposefully simple and designed to take the two approaches’ estimates and measures of uncertainty at ‘face value’. Specifically, we use a constrained least-squares approach to appropriately weigh the estimates by the inverse of their variance, and the constraint imposes agreement between the two sources. Our application involves nearly 18,000 flux estimates for the upper midwest United States. The constrained dependencies result in a non-sparse covariance matrix, but computation requires only minutes due to the structure of the model.

Small-angle X-ray scattering (SAXS) is a technique for obtaining low-resolution structural information about biological macromolecules, by exposing a dilute solution to a high-intensity X-ray beam and capturing the resulting scattering pattern on a two-dimensional detector. The two-dimensional pattern is reduced to a one-dimensional curve through radial averaging; that is, by averaging across annuli on the detector plane. Subsequent analysis of structure relies on these one-dimensional data. This paper reviews the technique of SAXS and investigates autocorrelation structure in the detector plane and in the radial averages. Across a range of experimental conditions and molecular types, spatial autocorrelation in the detector plane is present and is well-described by a stationary kernel convolution model. The corresponding autocorrelation structure for the radial averages is non-stationary. Implications of the autocorrelation structure for inference about macromolecular structure are discussed.

Soils contain the largest terrestrial pool of carbon, and have large annual transfers of carbon with biomass pools and the atmosphere. Agricultural land use and management, and changes in climate have significant impacts on soil carbon, and if managed with conservation practices agricultural soils could be enhanced while sequestering carbon and mitigating greenhouse gas emissions. To better inform national climate change policy decisions for agricultural lands, robust and accurate estimates of soil organic carbon (SOC) stock changes are needed at regional to national scales. The design of a national soil monitoring network for carbon on agricultural lands is discussed including determination of sample size, allocation, and site-scale plot design. A quantitative case study is presented using modeled estimates of SOC stock change variability and a set of soil sample measurements to evaluate a potential network design for U.S. agricultural lands. Stratification by climate, soil, and land use with sites alloc...

Many environmental data sets have a continuous domain, in time and/or space, and complex features that may be poorly modelled with a stationary (in space and time) Gaussian process (GP). We adapt stochastic volatility modelling to this context, resulting in a stochastic heteroscedastic process (SHP), which is unconditionally stationary and non-Gaussian. Conditional on a latent GP, the SHP is a heteroscedastic GP with non-stationary (in space and time) covariance structure. The realizations from SHP are versatile and can represent spatial inhomogeneities. The unconditional correlation functions of SHP form a rich isotropic class that can allow for a smoothed nugget effect. We apply an importance sampling strategy to implement pseudo maximum likelihood parameter estimation for the SHP. To predict the process at unobserved locations, we develop a plug-in best predictor. We extend the single-realization SHP model to handle replicates across time of SHP realizations in space. Empirical results with simulated data show that SHP is nearly as efficient as a stationary GP in out-of-sample prediction when the true process is a stationary GP, and outperforms a stationary GP substantially when the true process is SHP. The SHP methodology is applied to enhanced vegetation index data and US NO3 deposition data for illustration.

The cube method proposed by Deville and Tille (2004) enables the selection of balanced samples: that is, samples such that the Horvitz–Thompson estimators of auxiliary variables match the known totals of those variables. As an exact balanced sampling design often does not exist, the cube method generally proceeds in two steps: a “flight phase” in which exact balance is maintained, and a “landing phase” in which the final sample is selected while respecting the balance conditions as closely as possible. Deville and Tille (2005) derive a variance approximation for balanced sampling that takes account of the flight phase only, whereas the landing phase can prove to add non-negligible variance. This paper uses a martingale difference representation of the cube method to construct an efficient simulation-based method for calculating approximate second-order inclusion probabilities. The approximation enables nearly unbiased variance estimation, where the bias is primarily due to the limited number of simulations. In a Monte Carlo study, the proposed method has significantly less bias than the standard variance estimator, leading to improved confidence interval coverage.

Understanding sensitive behaviors-those that are socially unacceptable or non-compliant with rules or regulations-is essential for creating effective interventions. Sensitive behaviors are challenging to study, because participants are unlikely to disclose sensitive behaviors for fear of retribution or due to social undesirability. Methods for studying sensitive behavior include randomized response techniques, which provide anonymity to interviewees who answer sensitive questions. A variation on this approach, the quantitative randomized response technique (QRRT), allows researchers to estimate the frequency or quantity of sensitive behaviors. However, to date no studies have used QRRT to identify potential drivers of non-compliant behavior because regression methodology has not been developed for the nonnegative count data produced by QRRT. We develop a Poisson regression methodology for QRRT data, based on maximum likelihood estimation computed via the expectation-maximization (EM) algorithm. The methodology can be implemented with relatively minor modification of existing software for generalized linear models. We derive the Fisher information matrix in this setting and use it to obtain the asymptotic variance-covariance matrix of the regression parameter estimates. Simulation results demonstrate the quality of the asymptotic approximations. The method is illustrated with a case study examining potential drivers of non-compliance with hunting regulations in Sierra Leone. The new methodology allows assessment of the importance of potential drivers of different quantities of non-compliant behavior, using a likelihood-based, information-theoretic approach. Free, open-source software is provided to support QRRT regression.

Process-based model analyses are often used to estimate changes in soil organic carbon (SOC), particularly at regional to continental scales. However, uncertainties are rarely evaluated, and so it is difficult to determine how much confidence can be placed in the results. Our objective was to quantify uncertainties across multiple scales in a process-based model analysis, and provide 95% confidence intervals for the estimates. Specifically, we used the Century ecosystem model to estimate changes in SOC stocks for US croplands during the 1990s, addressing uncertainties in model inputs, structure and scaling of results from point locations to regions and the entire country. Overall, SOC stocks increased in US croplands by 14.6 Tg C yr -1 from 1990 to 1995 and 17.5 Tg C yr -1 during 1995 to 2000, and uncertainties were ± 22% and ± 16% for the two time periods, respectively. Uncertainties were inversely related to spatial scale, with median uncertainties at the regional scale estimated at ± 118% and ± 114% during the early and latter part of 1990s, and even higher at the site scale with estimates at ± 739% and ± 674% for the time periods, respectively. This relationship appeared to be driven by the amount of the SOC stock change; changes in stocks that exceeded 200 Gg C yr -1 represented a threshold where uncertainties were always lower than ±100%. Consequently, the amount of uncertainty in estimates derived from process-based models will partly depend on the level of SOC accumulation or loss. In general, the majority of uncertainty was associated with model structure in this application, and so attaining higher levels of precision in the estimates will largely depend on improving the model algorithms and parameterization, as well as increasing the number of measurement sites used to evaluate the structural uncertainty.

Geographic information systems (GIS) organize spatial data in multiple two-dimensional arrays called layers. In many applications, a response of interest is observed on a set of sites in the landscape, and it is of interest to build a regression model from the GIS layers to predict the response at unsampled sites. Model selection in this context then consists not only of selecting appropriate layers, but also of choosing appropriate neighborhoods within those layers. We formalize this problem as a linear model and propose the use of Lasso to simultaneously select variables, choose neighborhoods, and estimate parameters. Spatially dependent errors are accounted for using generalized least squares and spatial smoothness in selected coefficients is incorporated through use of a priori spatial covariance structure. This leads to a modification of the Lasso procedure, called spatial Lasso. The spatial Lasso can be implemented by a fast algorithm and it performs well in numerical examples, including an applicat...

Vegetation indices derived from remote sensing data provide information about the variability in stature, growth and vigor of the vegetation across a region, and have been used to model plant processes. For example, the Enhanced Vegetation Index (EVI) provides a measure of greenness of the vegetation that can be used to predict net primary production. However, ecosystem models relying on remote sensing data for EVI or other vegetation indices are limited by the time series of the satellite data record. Our objective was to develop a statistical model to predict EVI in order to extend the time series for modeling applications. To explain the functional behavior of the seasonal EVI curves, a two-stage multiple regression fitting procedure within a semi-parametric mixed effect (SPME) model framework was used. First, a linear mixed effect (LME) model was fitted to the EVI with climate indexes, crop and irrigation information as predictor variables. Second, Penalized B-splines were used to explain the behavior of the smooth residuals, which result from a smooth model fit to the smooth EVI data curve, in order to describe the uncertainty of the EVI curve. Individual models were fit within individual Major Land Resources Areas (MLRAs). Predicted seasonal EVI, derived from our regression equations, showed a strong agreement with the observed EVI and was able to capture the site by site and year by year variation in the EVI curve. Out-of-sample prediction produced excellent results for a majority of the sites, except for sites without clear seasonal patterns, which may have resulted from cloud contamination and/or snow cover. Therefore, given the appropriate climate, crop, and irrigation information, the proposed approach can be used to predict seasonal EVI curves for extending the time series into the past and future.