URBAN SPRAWL AT ITS BRIM: SHANNON'S ENTROPY ANALYSIS




Shannon's Entropy is calculated to check the urban sprawl and spare capacity (Yeh and Li 2001,Sudhira etal(2003),S.Sekhar (2005).
Shannon's Entropy is calculated using the following formulae.
Hn = -? Pi *logpi
Where Hn = the entropy
Pi= the proportion of the variable in the ith grid
n = the total number of grids
Minimum and the hypothetical value of entropy is zero while the maximum value is
log n.
Entropy of built up area of each grid is found to be very high which is nearer to log n .
Entropy results are tabulated as below.

Variable

Entropy1968

-∑pi ln pi

Entropy 2002

-∑pi ln pi

n

logn

Built up area

5.401

5.410

281

5.638

Entropy Values of MSA 1968 and 2002
Entropy calculations reveal that builtup area distribution is highly dispersed indicating the presence of urban sprawl and spare capacity. There is no substantial change of entropy between the years 1968 and 2002, if not become slightly worse.