Once I had to spatially interpolate climate data. I had conducted a thorough literature review first on the various interpolation methods, and then on related software. Ultimately, I came up with the conclusion that a hybrid interpolator would be better in miming the generating process of my data (trend surface analysis + residual krigging + conditional simulations). Since such an interpolator is not -to my knowledge- readily available, I ended up switching between GIS and Stata/Mata to derive the interpolated values in multiple steps. It was time consuming but the resultant values behave according to the theory I envision.

Yes, and this has been accomplished in the SpaceStat software (biomedware.com). Two approaches are implemented. The first is in the methods "Scale conversion/Interpolation). Given set(s) of input data and destination geographies, the technique will automatically select an appropriate method of upscaling, downscaling or sidescaling. The other approach is in the kriging method itself, where the appropriate variogram model form is automatically selected, and then automatically fitted. Should you have time-dynamic data (e.g. a space-time geography), the interpolation is automatically accomplished through time.

This is an interesting question. I have not met a tool like this. I think it is so difficult to design a tool like this because the variable of users' demand depends on several variables such as data, preference, and domain tasks. In that, data may change over time and at locations; preference depends on each user; tasks depend on different domains, and change over time as well as at locations. For example, the spatial interpolation method applying for data of fields such as flood water, pollutant in the air based on the view of the continuous variation over time is different from the method based on the view of a process of stop at each time point. I consider that the problem can be solved with a limitation of the characteristics of variables.

This is quite a complex topic. I'm oversimplifying, but in my mind the choice of an interpolation method boils down to (1) characteristics of the data (e.g., continuous and categorical data require very different interpolation techniques), (2) skill level of the analyst (e.g., analysts unfamiliar with interpolation techniques that require decision making -- even things as simple as picking exponents in IDW -- cannot be expected to make decisions that are as sound as those made by experienced analysts), and (3) the ability to communicate all aspects of the interpolation results to the analyst, including both the interpolated values and the confidence that should be placed in the interpolated values. I see no reason why you couldn't develop an expert system interface that walked analysts through a series of questions addressing these topics, and based on their responses, picked an appropriate interpolation technique. However, I think such a system would only be useful for relative novices; experts are going to have their own preferences as to how they want to perform interpolations.

I run a number of finite difference models that require daily climate grids so I built a geodatabase that has code to populate daily fields of point feature classes, then run a python script (arcpy) that interpolates grids. In the script you can change the type of interpolation and parameters however you like. You need ArcGIS and Spatial Analyst.

Knowledge of the methods of interpolation with knowledge of the field in which it will be used. They are essential.

sometimes it has a single person but often several specialists.