Having undertaken Kriging interpolation a variety of methods and procedures exist to enable the quality of the results, or goodness of fit, to be evaluated. These include:

Residual plots: (sometimes referred to as error plots) and standard deviation maps; maps of residuals from trend analyses

Crossvalidation: this typically involves removing each observed data point one at a time (leaving the model otherwise unaltered) and then calculating the predicted values at these points. Best fit models should minimise residuals (often referred to as errors) in these predictions: minimising maximum residuals/errors; minimising total sum of squared residuals/errors; removing extreme residual values (outliers/invalid results)…. Some packages allow the validation results to be exported for further examination and statistical analysis

Jackknifing: see Efron (1982) and Efron and Tibshirani (1997) for more details. This is essentially a form of cross-validation achieved by statistically re-sampling the source dataset. Typically one or more subsets consisting of x% of data points are removed at random (without replacement) and statistics of interest calculated on these subsets, which are then compared to the global value. Note that the term bootstrapping, often used alongside jackknifing, refers to procedures involving re-sampling with replacement

Re-sampling the source material (field data): an expensive or impractical option in many cases, but a realistic option in others

Detailed modelling of related datasets (e.g. easy to measure variables)

Detailed modelling incorporating related datasets: look at possible stratification of the source dataset (e.g. using underlying geological information); explicitly model non-stationarity, if appropriate; explicitly incorporate boundaries/faults or similar linear or areal elements that may substantive affect the results

Comparison with independent data (e.g. satellite data or other aerial imagery)

Examination of the fit for possible artefacts and bull’s-eyes (a form of circular artefact) — these may be generated by the interpolation process and/or be a feature inherited from the underlying dataset