Kriging on highly skewed data for DTPA-extractable soil Zn with auxiliary information for pH and organic carbon B J. Wu 1 , W.A. Norvell * , R.M. Welch U.S. Plant, Soil and Nutrition Laboratory, USDA-ARS and Cornell Univ., Tower Road, Ithaca, NY 14853, USA Received 4 March 2004; received in revised form 28 October 2005; accepted 9 November 2005 Available online 4 January 2006 Abstract Knowledge of the distribution of crop-available trace elements in soils is limited by the sparseness of georeferenced data and the inherent variability of the more-labile forms of these elements. Cokriging with auxiliary variables can sometimes improve estimates for a less densely sampled primary variable, while skewed data can often be made more suitable for geostatistical modeling by appropriate transformation. Benefits from data transformation and cokriging in predicting Zn(DTPA) (an estimate of plant-available Zn, extracted from soil by the chelating agent diethylenetriaminepentaacetic acid) were assessed using a georeferenced set of data from northern North Dakota. Soil organic carbon (OC) and pH were used as auxiliary variables for cokriging. Data for Zn(DTPA), OC and pH were available for 587 locations. The statistical distribution of the data for Zn(DTPA) was highly skewed (approximately log-normal). Three methods of data transformation (computation of logarithms, conversion to standardized rank order and assignment of normal scores) were carried out prior to kriging or cokriging to reduce skewness. For comparisons of predictive success, the Zn(DTPA) data were partitioned into a predictor set of 293 sites and a testing set of 294 sites, according to a stratified randomized approach. Data for Zn(DTPA) in the testing set were reserved for testing estimates based on the predictor set. Cokriging on Zn(DTPA), using OC or pH as auxiliary variables, was consistently more effective than kriging on Zn(DTPA) alone. Cokriging with OC and pH together provided additional benefit. Data transformation generally improved kriged estimates, especially for low concentrations of Zn(DTPA) (e.g., b 0.5 mg kg  1 ), which are important because they are indicative of soils containing inadequate Zn for optimal crop growth. Differences among normal score cokriging, log-normal cokriging and rank- ordered cokriging were relatively small. Published by Elsevier B.V. Keywords: Skewed distribution; Transformation; Zinc availability; Ordinary kriging; Log-normal; Rank order; Normal score; Cokriging; Auxiliary variables 0016-7061/$ - see front matter. Published by Elsevier B.V. doi:10.1016/j.geoderma.2005.11.002 Abbreviations: OK, ordinary kriging; OCK, ordinary cokriging; S.D., standard deviation; Zn(DTPA), DTPA-extractable (available) Zn in soils; OC, organic carbon; LG, logarithmic transform; RK, rank order transformation; NS, normal score transformation; cdf, cumulative distribution function; ME, mean error; RMSE, root mean square error. B Mention of proprietary product or vendors does not imply approval or recommendation by the U.S. Department of Agriculture. * Corresponding author. Fax: +1 607 255 1132. E-mail address: WAN1@cornell.edu (W.A. Norvell). 1 Current address: Department of Resources and Environment, Zhejiang Univ., Hangzhou, 310029, China. Geoderma 134 (2006) 187 – 199 www.elsevier.com/locate/geoderma