Basics of Akaike's Information Criterion in GIS/Hydrology

I have been asked to use the AIC to assess the relative fitness of various terrain wetness index (TWI) methods for predicting soil moisture in a specific study site.

The TWI is calculated from a single digital elevation model (DEM) by calculating the slope of terrain local to a pixel (by one of several methods), by calculating the flow from one pixel to zero or more neighbours (by one of several methods) and then calculating the upstream contributing area. From these one calculates the index using:

$$\ln \left(\frac{a}{tan(b)} \right)$$

where $a$ is the upslope contributing area and $b$ is the slope in radians.

Most of of the slope and flow methods are not parameterised, except by the raster itself. The exceptions are, for example, the Hjerdt slope methods, which have a vertical drop parameter and the Holmgren flow method which takes an exponent.

I have field measurements against which I can compare my TWI indices.

So my question is basic: how can one perform the AIC using these inputs in R? Though I am not a statistician, I understand the basic goals and rationale for the AIC, but I'm not sure how to actually use it with this type of input.

Along the way, it would be helpful to me to understand, what constitutes a model or a parameter in this case? These raster methods are essentially operators on matrices, so I'm not sure how to think of them as models.

• +1 You might consider re-interpreting your task as one of identifying and applying an appropriate measure of agreement between predicted and measured soil moisture to various TWI procedures as applied to data from the site. AIC, even if it could be interpreted in this context, would not necessarily be hydrologically relevant. After all, what does anybody care about the number of parameters used (at least within reasonable limits) when the objective is to make reliable predictions? – whuber Sep 26 '17 at 17:21
• @whuber Thanks for your comment. My intuition is to say, "why bother?" – Rob Skelly Sep 26 '17 at 17:48