Comparing the efficiency of ordinary kriging and cokriging to estimate the Atterberg limits spatially using some soil physical properties

Abstract The spatial distribution of the Atterberg limits can be used to distinguish the consistency and behaviour of a soil and its engineering properties, which strongly depends on the water content of the soil and types of silts and clays in the soil. By spatial modeling, and comparing the results of ordinary kriging with the cokriging approach, this study aims to find correlations between the Atterberg limits and the selected physical soil parameters in order to examine how effective they are in generating an understanding of the dynamics of a physical soil system. In 156 soil samples, the Atterberg limits and soil moisture conditions were determined, and auxiliary functions were selected by application of cokriging using correlation analysis and regression equations obtained by the residual maximum likelihood (REML). These techniques were evaluated by the results of the mean absolute error (MAE) and the mean squared error (MSE). Cokriging analysis was found to be more effective at estimating the liquid limit (WLL) and the plastic limit (WPL) than kriging analysis and with smaller error values. On the other hand, the kriging approach, which had smaller MAE and MSE values, was more effective at estimating the plasticity index (WPI) values than the cokriging method. Unlike the REML regression equations, the field capacity (FC) value was the more suitable parameter for the cokriging estimates. When the necessary labour and time were considered for determining the Atterberg limits, both kriging and cokriging were found to be applicable for estimation of these limits.

[1]  C. Smith,et al.  Shrinkage and Atterberg limits in relation to other properties of principal soil types in Israel , 1985 .

[2]  D. Hillel.  Environmental soil physics , 1998 .

[3]  P. Goovaerts.  Geostatistics in soil science: state-of-the-art and perspectives , 1999 .

[4]  Joseph E. Bowles,et al.  Engineering Properties of Soils and Their Measurement , 1978 .

[5]  E. Jong,et al.  ESTIMATING THE ATTERBERG LIMITS OF SOUTHERN SASKATCHEWAN SOILS FROM TEXTURE AND CARBON CONTENTS , 1990 .

[6]  J. W. Biggar,et al.  Spatial Variability of Field-Measured Infiltration Rate1 , 1981 .

[7]  Alan L. Flint,et al.  Multivariate Geostatistïcal Analysis of Ground‐Water Contamination: A Case History , 1993 .

[8]  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 .

[9]  Geoffrey M. Laslett,et al.  Kriging and Splines: An Empirical Comparison of their Predictive Performance in Some Applications , 1994 .

[10]  W. V. Dooremolen,et al.  Cokriging Point Data on Moisture Deficit , 1988 .

[11]  G. Bouyoucos.  A Recalibration of the Hydrometer Method for Making Mechanical Analysis of Soils1 , 1951 .

[12]  I. Baillie,et al.  Soil Survey Staff 1999, Soil Taxonomy , 2006 .

[13]  W. B. Russell,et al.  SPATIAL DISTRIBUTION OF SOIL PARTICLE SIZE AND AGGREGATE STABILITY INDEX IN A CLAY SOIL , 1990 .

[14]  A. Warrick,et al.  Estimating Soil Water Content Using Cokriging1 , 1987 .

[15]  L. Zelazny,et al.  Relationship of Map Unit Variability to Shrink–Swell Indicators , 2000 .

[16]  B. Balla,et al.  Soil compactibility in relation to physical and organic properties at 156 sites in UK , 2000 .

[17]  J. Lester,et al.  Geostatistical analysis of sampling uncertainty at the Tollesbury Managed Retreat site in Blackwater Estuary, Essex, UK: Kriging and cokriging approach to minimise sampling density , 1998 .

[18]  A. Castrignanò,et al.  ESTIMATING SOIL WATER CONTENT USING COKRIGING , 1990 .

[19]  C. Dirksen,et al.  Hydraulic Conductivity and Diffusivity: Laboratory Methods , 2018, SSSA Book Series.

[20]  A. Martínez-cob,et al.  Multivariate geostatistical analysis of evapotranspiration and precipitation in mountainous terrain , 1996 .

[21]  E. Mapfumo,et al.  Guidelines for safe trafficking and cultivation, and resistance–density–moisture relations of three disturbed soils from Alberta , 1998 .

[22]  L. D. Baver.  The Atterberg Consistency Constants: Factors Affecting their Values and a New Concept of their Significance1 , 1930 .

[23]  R. Reese.  Geostatistics for Environmental Scientists , 2001 .

[24]  A. Stein,et al.  Universal kriging and cokriging as a regression procedure. , 1991 .

[25]  W. Busscher.  Fundamentals of Soil Behavior , 1994 .

[26]  C. Gotway,et al.  Comparison of kriging and inverse-distance methods for mapping soil parameters , 1996 .

[27]  S. Erşahin.  Comparing Ordinary Kriging and Cokriging to Estimate Infiltration Rate , 2003 .

[28]  Pierre Goovaerts,et al.  Using elevation to aid the geostatistical mapping of rainfall erosivity , 1999 .

[29]  L. A. Richards.  Diagnosis and Improvement of Saline and Alkali Soils , 1954 .

[30]  John Triantafilis,et al.  Five Geostatistical Models to Predict Soil Salinity from Electromagnetic Induction Data Across Irrigated Cotton , 2001 .

[31]  R. Mcbride.  A Re-Examination of Alternative Test Procedures for Soil Consistency Limit Determination: II. A Simulated Desorption Procedure , 1989 .

[32]  S. Yates,et al.  Use of pseudo-crossvariograms and cokriging to improve estimates of soil solute concentrations , 1997 .

[33]  R. Webster,et al.  Optimal interpolation and isarithmic mapping of soil properties. II. Block kriging. , 1980 .

[34]  G. Uehara,et al.  Application of Geostatistics to Spatial Studies of Soil Properties , 1986 .

[35]  H B Seed,et al.  Fundamental Aspects of the Atterberg Limits , 1966 .

[36]  R. Lal,et al.  Comparison of methods for estimating maximum soil water content for optimum workability , 2003 .

[37]  Marc Voltz,et al.  A comparison of kriging, cubic splines and classification for predicting soil properties from sample information , 1990 .

[38]  D. R. Nielsen,et al.  The Use of Cokriging with Limited Field Soil Observations 1 , 1983 .

[39]  C. Rogers,et al.  Liquid limit and the temperature sensitivity of clays , 1998 .

[40]  E. Youngs,et al.  Fundamentals of Soil Physics. , 1982 .

[41]  R. T. Odell,et al.  Relationships of Atterberg limits to some other properties of Illinois soils. , 1960 .

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

[43]  Sudhakar M. Rao,et al.  Liquid Limit of Montmorillonite Soils , 1986 .

[44]  Donald E. Myers,et al.  Estimation of the Spatial Distribution of Soil Chemicals Using Pseudo-Cross-Variograms , 1992 .