## Description

Defining the spatial distribution of hydrologic data is an important aspect in many water-resources investigations. Estimating values of a particular parameter in areas where no known data exist may be accomplished by employing an interpolation technique. Several techniques are available, each producing results of varying degrees of accuracy. Six interpolation techniques were compared in this study for estimating the transmissivity distribution for San Antonio Creek valley in Santa Barbara County, California. The interpolation techniques considered in this study were nearest neighbor, inverse distance squared weighting, least squares, Laplace, Laplace plus splines and kriging. The basis of comparison was a transmissivity distribution produced by a calibrated two-dimensional steady-state ground-water flow model. A hypothetical fault was introduced to determine the accuracy of each method when a discontinuity exists. Methods of analysis included verification of ten known values suppressed and subsequently estimated by each technique and whole-dataset analysis. The verification procedure included an error analysis, use of scatterplots and simple regression. Scatterplots and simple regression were also used in the whole-dataset analysis, as well as a qualitative analysis consisting of comparisons of transmissivity distribution, contours of the difference between real and estimated transmissivities and contoured water-level elevations generated by using each estimated and the real transmissivity distribution in the model. The error analysis for the verification data indicated that Laplace plus splines had the best overall average error, 67 percent. Kriging interpolation produced the most estimates with errors less than ten percent, an arbitrary criterion of acceptability. However, other kriged values had errors much higher than those of Laplace plus splines. Scatterplots showed that least squares produced the best fit about the real equals estimated line with Laplace plus splines also producing a good fit. Nearest neighbor interpolation produced the worst plot, with much scatter about the real equals estimated line. Simple regression analysis indicated the Laplace plus splines had the highest correlation coefficient and coefficient of determination and lowest sum of squared deviations and standard deviation about the regression line. Least squares interpolation produced results similar to those of Laplace plus splines. Nearest neighbor produced the worst results. Scatterplots for whole datasets for both the with- and without-fault data showed that Laplace plus splines provided the best fit about the real equals estimated line. Laplace interpolation also produced a good fit. In this case, however, least squares produced the worst fit, with many outliers. In general, simple regression for whole datasets supported the scatterplot analysis. For the without-fault case, Laplace plus splines produced the highest correlation coefficient and coefficient of determination and lowest sum of squared deviations and standard deviation about the regression line. Laplace interpolation, however, produced slightly better values for the with-fault case. Least squares provided the worst results. The qualitative analysis provided similar results. Laplace plus splines and Laplace interpolation techniques produced the most accurate results in estimating transmissivity values in the San Antonio Creek valley. Kriging, inverse distance squared weighting and nearest neighbor can produce satisfactory results when data are abundant and uniform. Least squares interpolation has a tendency to produce values that increase without limit near the basin boundary.