**Generating an accessibility map**

Now we need to reclassify the two accessibility maps. At the moment they are just simple distance maps, so the closer each cell is to a road or a river, the lower the value. But, for accessibility, we need precisely the opposite. We can obtain this using White et al’s (1997) local accessibility equation:

(from White et al 1997)

where D is the euclidean distance from the cell to the nearest cell in the network, and δj is the coefficient expressing the importance of accessibility for the desirability of the cell for land activity j; aj is then inserted as a coefficient in equation 2 (see above).

To produce the coefficients, we need to reclassify the accessibility map

**summary(distroad_null)**

**Min. 0**

** 1st Qu. 424**

** Median 1118**

** Mean 1966**

** 3rd Qu. 2326**

** Max. 13710**

** NA’s 600147**

**roadsco <- reclassify(distroad_null,c(-Inf,100,1,100,300,0.9,300,800,0.8, 800,1500,0.7,1500,2500,0.6,2500,5000,0.5,5000,8000,0.4,8000,10000,0.3,10000,12000,0.2,12000,Inf,0.1))**

This gives a reasonably dispersed distance effect with a halving distance of 2.5km.

**accessibility <- 1+((distroad_null/roadsco)^-1)**

**plot(accessibility)
**

Works fine. Note that areas where roads already exist (distance 0) take unmeasurably large values, (Inf) (and therefore appear white). This should be no particular problem, it will just mean that all urban cells will try to sit on top of roads. Since roads are not explicitly modelled, this isn’t a problem.

If we wanted the maximum value in this map to be 2, the same as at distance 1, we can set it with a map calculation:

**funacc <- function(x) { x[x>2] <- 2; return(x) }**

** acc<-calc(accessibility, funacc)**

Thus every cell which had a value greater than 2 gets a value of 2.

**model_accessibility <- accessibility ** #change the name to match the others we will use for the Transition Potential computation.