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Kriging with Generalized Covariances¹

ABSTRACT

Electrical conductivities (EC) of saturated paste extracts of 225 soil samples collected from depths of 30 to 60 cm along five transects were determined. The field was irrigated using a two-line source sprinkler system that applied two different qualities of irrigation water. The sampling interval along each transect was 1 m. Forty-five soil samples were collected from each transect, with each transect separated by 10 m. The mean and four directional experimental variograms of the EC were computed. The east-west (0°) directional variogram showed a structure with a range of 19 m. The raw data showed a skewed distribution with two outliers. One hundred eleven of the total data points were used to check for the presence of a drift and to determine the best generalized covariance function. The best general drift, calculated with mean squares, was found to be of order one. Structural analysis confirmed that the best drift order was one, and the best generalized covariance fit had linear and cubic terms. The best fit covariance function had a mean square error (MSE) of 0.187 and a correlation coefficient of 0.98 from the jackknifing. The cross-validation of the best covariance fit was performed by removing each data point and estimating from the remaining data (MSE = 0.164). If the difference between the measured and estimated points was greater than twice the standard deviation, that point was considered to be an outlier. The results of cross-validation, when 111 data points were used, showed no outliers. The scatter diagram of the estimated values and reduced error showed no correlation (r = –0.0035). On the other hand, a high correlation (r = 0.93) was found between the estimated and the true values. The best covariance function with a drift of order one was used to estimate 225 measured values, as well as an additional 1260 values over the entire field with a grid size of 1 x 1.25 m. This technique allowed detailed information to be obtained from a limited number of data points with dependability.

¹ Contribution from Dep. of Land, Air and Water Resources, Univ. of California, Davis. This research was supported by the Kearney Foundation of Soil Science.

² Post Graduate Researcher, Professors from Dep. of Land, Air and Water Resources, Univ. of California, Davis, CA 95616, and Professor, Dep. of Mathematics, Univ. of Arizona, Tucson, AZ 85721, respectively.

Received for publication January 13, 1987.