In the recent
years, a lot of thrust in this field has been to understand and analyse the
urban sprawl pattern. Various analysts have made considerable progress in
quantifying the urban sprawl pattern (Theobald, 2001; Lata et al., 2001; Torrens
and Alberti, 2000; Batty et al., 1999; Barnes et al., 2001). However, all these
studies have come up with different methodologies in quantifying sprawl. The
common approach is to consider the behaviour of builtup area and population
density over the spatial and temporal changes taking place and in most cases the
pattern of such sprawls is identified by visual interpretation methods.
Defining this
dynamic phenomenon with relative precision and accuracy for predicting the
future sprawl is indeed a great challenge to all working in this arena. One of
the basic and major challenge is quantification of such sprawl. Although
different sprawl types were identified and defined there has been an inadequacy
with respect to developing mathematical relationships to define them. Further as
if aggravating this problem, much of the work related to studying dynamics of
urban sprawl are not carried out in the developing countries, except a few.
Thus, giving very little relevance to correlate the available findings in the
context of developing countries. However, the negative impacts of such urban
sprawls in developing countries are more severe and intense compared to that of
developed countries. Typically, the developing countries are faced with an
unprecedented population growth and potentially threaten vast natural resources.
In such a scenario, it is definitely an exacting effort to study, characterise
and model the urban sprawl phenomenon in the context of developing countries.
This study is an attempt in understanding the urban sprawl phenomenon, pattern
recognition and modeling studies as well.
Urban sprawl
dynamics was analysed considering some of the causal factors. The rational
behind this is to identify such factors that play a significant role in the
process of urbanisation. The causal factors that were considered responsible for
sprawl were:
Population (POP99), 

a Population density (POPADEN) and b Population density (POPBDEN), 

Annual Population Growth Rate
(AGR) 

Distance from Mangalore (MANGDIST)
and 

Distance from Udupi (UDUPIDIST) 
Population has
been for long accepted as a key factor of urban sprawl. The percentage builtup
is the proportion of the builtup area to the total area of the village. The
a
population density (POPADEN) is the proportion of the population in every village
to the builtup area of that village. The b
population density (POPBDEN) is the proportion of population in every village
to the total area of that village. The b
population density is often referred as population density. Since the builtup
area plays an important role in the current study for the purpose of analyses,
the percentage builtup, a and b population densities are computed and analysed villagewise and categorised
as a subzone. The annual population growth rate (AGR) is computed from the
population data available from 1961 for all the villages. This growth rate is
used in predicting the population for 1999 and subsequent future populations.
The distance from the city centres, viz. Udupi and Mangalore to each village
was calculated. Thus, the effects of proximity of the cities on the urban sprawl
of these subzones were analysed. With these causal factors identified the modeling
studies were undertaken.
In order to explore the probable relationship of
percentage builtup (dependent variable) with causal factors of sprawl
(population, a and b population densities, etc.), regression analyses considering linear,
quadratic (order=2), and logarithmic (power law) were tried and the results are
tabulated in Annexure.
The regression
analyses revealed that the population shows linear relationship (y = a*x + b)
and plays a significant role in the sprawl phenomenon. The quadratic regression
analyses for second order were undertaken. All the causal factors were
considered and the regression was carried out for the square of causative
factors (e.g. When 'y' is the dependent variable and 'x' is the independent
variable, then a polynomial regression of second order will be of the form, y =
a*x^{2} + b*x + c). The quadratic regression analyses revealed that the
population b
density and distance from urban centre (Mangalore) have a significant role in
the sprawl phenomenon. The logarithmic (power law) regression analyses were also
undertaken. The same causal factors were considered and the regression was
carried out for the natural logarithmic of the causative factors (e.g. When 'y'
is the dependent variable and 'x' is the independent variable, then a
logarithmic regression will be of the form, log y = log a + b * log x; or y = a
* x^{b}). The logarithmic regression analyses revealed that the
population b density has significant role in the sprawl phenomenon.
The probable
relationships are
PCBUILT
= 0.000611*POP99 + 10.87149 (r = 0.5789)
............2
PCBUILT =
0.005651*(POPBDEN)^{2}  1.2*107*(POPBDEN) + 6.8950 (r = 0.6823)
.............3
PCBUILT =
1.7953*(MANGDIST)^{2} + 0.02593*(MANGDIST) + 36.8607 (r =
0.60).............4