When might one choose to use the Spline interpolation method?

Choosing to use the Spline interpolation method is particularly advantageous when a high level of precision in representing existing data values is essential. Spline interpolation employs piecewise polynomial functions that not only fit the data points accurately but also provide a smooth approximation of the surface between those points. This method is especially effective in maintaining the integrity of the data by closely adhering to the given values, which is crucial in scenarios such as geophysical studies, environmental modeling, or any application where precise representation of the data is required for analysis or decision-making.

In contrast, while smoothing out peaks and valleys, creating quickly interpolated surfaces, or enhancing visual representation can all be important tasks in GIS, these may not rely as heavily on the mathematical precision provided by Spline interpolation. Other methods might be more suited for those purposes, particularly if results do not demand strict adherence to the original data points or where speed is a priority over accuracy.