Date of submission: 12

5.7 Transition Potentials

After selecting the transition sub-model it was required to select explanatory variables, which are the factors driving the change. Urban sprawl has been acknowledged to be the outcome of a number of complex factors, though attempts have been made to model this previously (Parker et al, 2003). Although a number of different factors have been input into models in past research, variables have frequently included factors related to

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  Previous sprawl and
  

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  Distance to roads
  

In order to feed the previous sprawl in as an explanatory variable the decrease in NDVI in epoch 1 was used as an input to create a Euclidean distance from disturbance layer.

These maps could now be selected within LCM to test their respective explanatory power in driving change. The test is based on contingency table analysis and the quantitative measure of association used is Cramer’s V. A high Cramer’s V indicates that the potential explanatory value of the variable is good, but this doesn’t guarantee a strong performance (Clark Labs, 2009). Values of 0.4 or higher are regarded as good while anything over 0.15 is useful. The explanatory variables used were selected and tested with the results as below:

The distance from previous disturbance showed a high Cramer’s V value, which suggests that this variable is strongly associated with change. The value for distance from roads was perhaps lower than would have been expected. However, given how roads have been discussed as a factor in sprawl and have been used in models in the past it was decided to keep this variable in the model.

After the sub-model had been selected and explanatory variables input and tested, the choice of model needed to be decided upon. The MLP is the recommended option within the Land Change Modeler program and this option was selected for use in this study.

The MLP launches in an automatic training mode. When the model is executed the MLP creates a random sample of cells that have experienced a transition from Austin to a decrease in NDVI as well as an additional set of random samples for pixels which persisted. Thus the neural network is fed with examples of the two cases, one transition class and one persistent class. Using the samples the MLP develops a multivariate function that can predict transition potential based on the values at any location for the two explanatory variables, by using half of the samples to train and the other half to test how well it is doing. The model builds a neural network between the explanatory variables (distance from sprawl and distance from roads) and the transition and persistence classes. This web of connections between the neurons is applied as a set of weights which structure the multivariate function. As it analyses the pixels in the training data the model gauges error and adjusts weights. As it continues to train it gets better and the accuracy and precision can improve. These are measured by the accuracy rate and Root Mean Square (RMS) value in the model.

The transition from Austin to decrease in NDVI sub model was run in order to create the transition potential map. The MLP achieved an accuracy rate of 94.06 % and a RMS value of 0.23. The model was run using the default training parameters, as advised by Clark Labs.

Once the model had successfully run and achieved the desired number of iterations to train the data and required accuracy rate, the transition potential map was created. This map marks the probability that a pixel will transition from Austin to a decrease in NDVI.

It is evident from the map above that sprawl is expected across the study area. The impact of distance from roads cannot be clearly seen and in the transition the distance from previous sprawl has appeared to have come out as the stronger factor, as suggested by the higher Cramer’s V value.