Kriging Fitted Hat Plot Modeling

One approach to constructing a kriging model involves fitting a variogram and applying it for spatial interpolation at unobserved locations. This procedure can be visualized through a kriging fitted hat plot, which illustrates predicted values across the spatial domain based on the kriging model's output. While effective, alternative variogram fitting techniques—such as manual fitting, weighted least squares, or maximum likelihood estimation—can also be integrated into kriging workflows. In Python, this might involve using libraries like `scikit-learn` or `gstools` to implement variogram modeling with functions like `Variogram.fit()` followed by kriging interpolation using `Krige.predict()`. The choice of fitting method should be carefully evaluated based on data characteristics (e.g., spatial autocorrelation, stationarity) and analysis objectives. Notably, kriging represents one of multiple spatial interpolation methods—including inverse distance weighting and spline interpolation—available for geostatistical analysis.