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Semiparametric regression models for spatial prediction and uncertainty quantification of soil attributes

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Abstract

In many studies, the distribution of soil attributes depends on both spatial location and environmental factors, and prediction and process identification are performed using existing methods such as kriging. However, it is often too restrictive to model soil attributes as dependent on a known, parametric function of environmental factors, which kriging typically assumes. This paper investigates a semiparametric approach for identifying and modeling the nonlinear relationships of spatially dependent soil constituent levels with environmental variables and obtaining point and interval predictions over a spatial region. Frequentist and Bayesian versions of the proposed method are applied to measured soil nitrogen levels throughout Florida, USA and are compared to competing models, including frequentist and Bayesian kriging, based an array of point and interval measures of out-of-sample forecast quality. The semiparametric models outperformed competing models in all cases. Bayesian semiparametric models yielded the best predictive results and provided empirical coverage probability nearly equal to nominal.

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References

  • Banerjee S, Carlin B, Gelfand A (2003) Hierarchical modeling and analysis for spatial data. Chapman & Hall/CRC, Boca Raton

    Book  Google Scholar 

  • Bliss CM, Comerford NB, Graetz DA, Grunwald S, Stoppe AM (2014) Land use influence on carbon, nitrogen, and phosphorus in size fractions of sandy surface soils. Soil Sci J 178:654–661

    Article  Google Scholar 

  • Bliznyuk N, Ruppert D, Shoemaker C, Regis R, Wild S, Mugunthan P (2008) Bayesian calibration and uncertainty analysis for computationally expensive models using optimization and radial basis function approximation. J Comput Gr Stat 17(2):270–294

    Article  Google Scholar 

  • Bliznyuk N, Ruppert D, Shoemaker CA (2011) Efficient interpolation of computationally expensive posterior densities with variable parameter costs. J Comput Gr Stat 20(3):636–655

    Article  Google Scholar 

  • Bliznyuk N, Ruppert D, Shoemaker CA (2012) Local derivative-free approximation of computationally expensive posterior densities. J Comput Gr Stat 21(2):476–495

    Article  Google Scholar 

  • Bliznyuk N, Paciorek CJ, Schwartz J, Coull B (2014) Nonlinear predictive latent process models for integrating spatio-temporal exposure data from multiple sources. Ann Appl Stat 8(3):1538–1560

    Article  Google Scholar 

  • Buhmann MD (2003) Radial basis functions: theory and implementations. Cambridge Monogr Appl Comput Math 12:147–165

    Google Scholar 

  • Crainiceanu CM, Ruppert D, Wand MP (2005) Bayesian analysis for penalized spline regression using WinBUGS. J Stat Softw 14(14):1–24

    Article  Google Scholar 

  • Ding X, Zhou H, Lei X et al (2013) Hydrological and associated pollution load simulation and estimation for the Three Gorges Reservoir of China. Stoch Environ Res Risk Assess. 27:617. doi:10.1007/s00477-012-0627-4

    Article  Google Scholar 

  • Florida Fish and Wildlife Conservation Commission (FFWCC) (2003) Land cover/land use map of Florida derived from Landsat satellite imagery. 30 meter resolution. http://www.fgdl.org

  • Grunwald S, Thompson JA, Boettinger JL (2011) Digital soil mapping and modeling at continental scales—finding solutions for global issues. Soil Sci Soc Am J 75(4):1201–1213

    Article  Google Scholar 

  • Guan Y, Shao C, Gu Q et al (2016) Study of a comprehensive assessment method of the environmental quality of soil in industrial and mining gathering areas. Stoch Environ Res Risk Assess. 30:91

    Article  Google Scholar 

  • Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning, 2nd ed. Springer, New York

  • Kasiviswanathan KS, Sudheer KP (2013) Quantification of the predictive uncertainty of artificial neural network based river flow forecast models. Stoch Environ Res Risk Assess. 27:137. doi:10.1007/s00477-012-0600-2

    Article  Google Scholar 

  • Kaufman L, Rousseeuw PJ (2005) Finding groups in data: an introduction to cluster analysis. Wiley, New York

    Google Scholar 

  • Kim J, Grunwald S, Rivero RG (2014) Soil phosphorus and nitrogen predictions across spatial escalating scales in an aquatic ecosystem using remote sensing images. IEEE Trans Geosci Remote Sens J 52(10):6724–6737

    Article  Google Scholar 

  • Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models part I—a discussion of principles. J Hydrol 10(3):282–290

    Article  Google Scholar 

  • Natural Resources Conservation Service (NRCS) (2006) Soil Data Mart: Soil Survey Geographic Database, SSURGO. Map scale 1:24000. http://www.nrcs.usda.gov/wps/ portal/nrcs/detail/soils/survey/?cid = nrcs142p2_053627

  • Plummer M (2003) JAGS: A program for analysis of Bayesian graphical models using Gibbs sampling. http://mcmc-jags.sourceforge.net

  • Rabalais NN, Turner RE, Wiseman WJ (2002) Gulf of Mexico Hypoxia, A.K.A. “The Dead Zone”. Ann Rev Ecol Syst 33:235–263

    Article  Google Scholar 

  • R Core Team (2014) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. http://www.R-project.org/.Rabalais

  • Ruppert D, Wand MP, Carroll RJ (2003) Semiparametric regression. Cambridge University Press, New York

    Book  Google Scholar 

  • Seber GAF, Lee AJ (2003) Linear regression analysis. Wiley and Sons, Hoboken

    Book  Google Scholar 

  • Shmueli G (2010) To explain or to predict? Stat Sci 25(3):289–310

    Article  Google Scholar 

  • Su YS, Yajima M (2014) R2jags: A package for running jags from R. http://CRAN.R-project.org/package=R2jags

  • Sun Y, Bowman KP, Genton MG, Tokay A (2015) A Matern model of the spatial covariance structure of point rain rates. Stoch Env Res Risk Assess 29:411–416

    Article  Google Scholar 

  • Turner RE, Rabalais NN, Justic D (2006) Predicting summer hypoxia in the northern Gulf of Mexico: Riverine N, P, and Si loading. Mar Pollut Bull 52:139–148

    Article  CAS  Google Scholar 

  • Vasques GM, Grunwald S, Myers DB (2012) Associations between soil carbon and ecological landscape variables at escalating spatial scales in Florida, USA. Landsc Ecol J. 27:355–367. doi:10.1007/s10980-011-9702-3

    Article  Google Scholar 

  • Weese DJ, Heath KD, Dentinger M, Lau JA (2015) Long-term nitrogen addition causes the evolution of less-cooperative mutualists. Int J Org Evol. doi:10.1111/evo.12594

    Google Scholar 

  • Wood SN (2004) Stable and efficient multiple smoothing parameter estimation for generalized additive models. J Am Stat Assoc 99:673–686

    Article  Google Scholar 

  • Wood SN (2006) Generalized additive models: an introduction with R. Chapman & Hall/CRC, Boca Raton

    Google Scholar 

  • Wood SN (2011) Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. J Royal Stat Soc (B) 73(1):3–36

    Article  Google Scholar 

  • Wood SN, Goude Y, Shaw S (2015) Generalized additive models for large data sets. J Royal Stat Soc (C) 64(1):139–155

    Article  Google Scholar 

  • Xiong X, Grunwald S, Myers DB, Kim J, Harris WG, Comerford NB (2014a) Holistic environmental soil-landscape modeling of soil organic carbon. Environ Model Software J. 57:202–215

    Article  Google Scholar 

  • Xiong X, Grunwald S, Myers DB, Ross CW, Harris WG, Comerford NB (2014b) Interaction effects of climate and land use/land cover change on soil organic carbon sequestration. Sci Total Environ J. 493:974–982. doi:10.1016/j.scitotenv.2014.06.088

    Article  CAS  Google Scholar 

  • Xiong X, Grunwald S, Myers DB, Kim J, Harris WG, Bliznyuk N (2015) Assessing uncertainty in soil organic carbon modeling across a highly heterogeneous landscape. Geoderma 251:105–116

    Article  Google Scholar 

  • Yang Y, Christakos G (2015) Uncertainty assessment of heavy metal soil contamination mapping using spatiotemporal sequential indicator simulation with multi-temporal sampling points. Environ Monit Assess 187(9):1–15. doi:10.1007/s10661-015-4785-y

    Article  Google Scholar 

  • Ye M, Meyer PD, Lin Y et al (2010) Quantification of model uncertainty in environmental modeling. Stoch Environ Res Risk Assess. 24:807. doi:10.1007/s00477-010-0377-0

    Article  Google Scholar 

Download references

Acknowledgements

Bliznyuk’s effort was partially supported by National Institutes of Health grants U54GM111274 and R21AI119773. Data collection was funded by USDA-CSREES-NRI grant award 2007-35107-18368 ‘Rapid Assessment and Trajectory Modeling of Changes in Soil Carbon across a Southeastern Landscape’ (National Institute of Food and Agriculture (NIFA)—Agriculture and Food Research Initiative (AFRI)). This project is a Core Project of the North American Carbon Program. The authors would like to thank Aja Stoppe, Brenton D. Myers, Christopher Wade Ross, Elena Azuaje, Samiah Moustafa, Lisa Stanley, Adriana Comerford, and Anne Quidez for their hard work in field soil sampling and laboratory analyses. In addition, we like to thank Xiong Xiong, Christopher Wade Ross, Gustavo M. Vasques, and Brenton D. Myers for the preparation of geospatial environmental data using GIS methods. Other thanks go to: Dr. N.B. Comerford and Dr. W.G. Harris.

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Authors and Affiliations

  1. Department of Agricultural and Biological Engineering, University of Florida, Gainesville, FL, 32611, USA

    Hunter R. Merrill & Nikolay Bliznyuk

  2. Department of Soil and Water Science, University of Florida, Gainesville, FL, 32611, USA

    Sabine Grunwald

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  1. Hunter R. Merrill
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  2. Sabine Grunwald
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  3. Nikolay Bliznyuk
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Correspondence to Nikolay Bliznyuk.

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Merrill, H.R., Grunwald, S. & Bliznyuk, N. Semiparametric regression models for spatial prediction and uncertainty quantification of soil attributes. Stoch Environ Res Risk Assess 31, 2691–2703 (2017). https://doi.org/10.1007/s00477-016-1337-0

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