Re-tooling of regression kriging in R for improved digital mapping of soil properties

Regression analysis and kriging are popular spatial estimation methods often used in soil science to provide soil information at different spatial resolutions and extent. Attempts have been made to combine them into a method known as regression kriging (RK). With the increasing acceptance of digital soil mapping paradigm, utilization of spatial estimation method such as RK is bound to rise. Although RK is versatile and popular, its current format has deficiencies which can hinder the quality of estimated soil properties. One of the deficiencies of RK is the failure of its regression model to recognize that natural soil occurs in groups with unique response characteristics to soil forming factors. Ideally, these groups should be represented as a family of curves when modelling the landscape. However, the current applications tend to use average models which either block/control the grouping effects or do not statistically recognize them. In this paper, mixed-effects modelling technique is shown for ingenious recognition of soil groupings and consequent improvement of RK accuracy. Mixed-effects modelling allows for simultaneous regression estimation for individual models in a group and for different groups in the landscape. Its implementation in RK has been illustrated using executable scripts in R. It gives better mapping accuracy and reliable maps than the current application in RK. The new RK and its easy implementation in R software are anticipated to provide potential for wide application and eventual contribution to improved soil mapping and application of DSM.

[1]  Yu Liu,et al.  An Efficient Algorithm for Raster-to-Vector Data Conversion , 2008, Ann. GIS.

[2]  N. Batjes,et al.  ISRIC-WISE Harmonized Global Soil Profile Dataset (Ver. 3.1) , 2008 .

[3]  Alfred E. Hartemink,et al.  Digital soil mapping: bridging research, environmental application, and operation , 2010 .

[4]  G. Heuvelink,et al.  Bayesian Maximum Entropy prediction of soil categories using a traditional soil map as soft information , 2008 .

[5]  P. Scull,et al.  The application of classification tree analysis to soil type prediction in a desert landscape , 2005 .

[6]  D. R. Nielsen,et al.  Spatial and Temporal Statistics - Sampling Field Soils and Their Vegetation , 2003 .

[7]  J. Ware,et al.  Random-effects models for longitudinal data. , 1982, Biometrics.

[8]  R. J. Pike,et al.  Automated classifications of topography from DEMs by an unsupervised nested-means algorithm and a three-part geometric signature , 2007 .

[9]  Michael Edward Hohn,et al.  An Introduction to Applied Geostatistics: by Edward H. Isaaks and R. Mohan Srivastava, 1989, Oxford University Press, New York, 561 p., ISBN 0-19-505012-6, ISBN 0-19-505013-4 (paperback), $55.00 cloth, $35.00 paper (US) , 1991 .

[10]  Gerard B. M. Heuvelink,et al.  About regression-kriging: From equations to case studies , 2007, Comput. Geosci..

[11]  B. Minasny,et al.  Nonlinear mixed effect modelling for improved estimation of water retention and infiltration parameters , 2006 .

[12]  Isaac Barshad,et al.  Factors Affecting Clay Formation , 1957 .

[13]  C. T. Omuto,et al.  Estimating water infiltration and retention characteristics using a computer program in R , 2009, Comput. Geosci..

[14]  B. Diekkrüger,et al.  Geostatistical co-regionalization of soil hydraulic properties in a micro-scale catchment using terrain attributes , 2006 .

[15]  M. Velbel,et al.  Rates and time scales of clay-mineral formation by weathering in saprolitic regoliths of the southern Appalachians from geochemical mass balance , 2005 .

[16]  Philippe Lagacherie,et al.  Digital soil mapping : an introductory perspective , 2007 .

[17]  V. Carey,et al.  Mixed-Effects Models in S and S-Plus , 2001 .

[18]  R. L. Hay,et al.  Rate of clay formation and mineral alteration in a 4000-year-old volcanic ash soil on Saint Vincent, B.W.I , 1960 .

[19]  R. Lark,et al.  On spatial prediction of soil properties in the presence of a spatial trend: the empirical best linear unbiased predictor (E‐BLUP) with REML , 2006 .

[20]  Renzo Rosso,et al.  Statistics, Probability and Reliability for Civil and Environmental Engineers , 1997 .

[21]  Carol A. Gotway,et al.  Fitting semivariogram models by weighted least squares short note , 1991 .

[22]  B. Minasny,et al.  On digital soil mapping , 2003 .

[23]  Budiman Minasny,et al.  On digital soil mapping , 2003 .

[24]  J. Faraway.  Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models , 2005 .

[25]  D. Myers,et al.  Extension of spatial information, Bayesian kriging and updating of prior variogram parameters , 1995 .

[26]  F. Carré,et al.  Quantitative mapping of soil types based on regression kriging of taxonomic distances with landform and land cover attributes , 2002 .

[27]  A-Xing Zhu,et al.  Soil Mapping Using GIS, Expert Knowledge, and Fuzzy Logic , 2001 .

[28]  R. Bilonick.  An Introduction to Applied Geostatistics , 1989 .

[29]  G. K. Eagleson,et al.  Transformations for Smooth Regression Models with Multiplicative Errors , 1997 .

[30]  A. McBratney,et al.  Further results on prediction of soil properties from terrain attributes: heterotopic cokriging and regression-kriging , 1995 .