Potential

The POTENTIAL module of FUTURES determines the probable location of land change using a suitability map.

Current Implementation

Currently, the POTENTIAL sub-model is implemented using a set of coefficients that relate a selection of site suitability factors to the probability of a place becoming developed. This is implemented using the parameter table in combination with maps of those site suitability factors (mapped predictors).

In past analysis, the coefficients have been obtained by conducting some form of logistic regression. If a multilevel model is used, the coefficients may vary by county. Logistic regression is conducted by the user in a statistical software of choice, but code for running the analysis in R is in the file POTENTIAL.R. This code demonstrates model selection using the best model and multilevel logistic regression. Note that this code was designed to allow automation of this sub-model, which has numerous caveats.

Data needs

1. Maps of all variables expected to influence the probability of development
2. Development pressure (see development pressure tool)
3. Map of “change” for a given time period (this serves as the model response variable)
4. Index for regions representing “levels”

5.  Random points: some points falling in areas that changed, some falling in areas that remain undeveloped - Intersect point file with all predictor variables including development pressure, response variable, and index. These will serve as sample points for regression analysis.
   

Development pressure

The development pressure variable plays a special role in the model, allowing for a feedback between predicted change and change in subsequent steps. For each patch-building interation a new landscape pattern is generated, which in turn is processed by one of the three development pressure approaches, which is then supplied as a parameter for the multi-level statistical model, which ultimately generates the next potential surface.

There are multiple options for calculating development pressure in the model.

1. Occurrence: simple count of the number of developed cells within the specified window size
2. k/d^alpha
3. k * exp (-2*d/alpha) where k is a scaling factor, alpha is the coefficient controlling the influence of distance

In previous modeling efforts, we have chosen the "best" value for alpha during the model selection process.

New module r.futures.devpressure was implemented. Unlike the older C code, this implementation is memory efficient, possibly even faster because it minimizes distance computation. Please see #2 and #3.

Alternatives

1. Rule based model
2. Statistical model: logistic regression, multilevel logistic regression (using single best model, model averaging,...)
3. User inputs suitability surface (turn off development pressure feedback)
4. Bayesian networks
5. Others?