Urban sprawl in Mangalore and Udupi regions of Karnataka, India is modeled and analyzed using GIS and other techniques. Shannon's entropy and landscape metrics are used to analyze patterns and structures of urban growth. Regression analysis is performed to quantify relationships between factors like population, density, and distance from cities, and the extent of built-up areas. Non-linear models provide better predictions of cumulative effects of variables on urbanization compared to linear models. This methodology can effectively model and analyze urban sprawl dynamics.

1. Urban sprawl: metrics, dynamics and
modelling using GIS
By
Pankaj Kumar
120040112

2. Urban Sprawl

3. • It is a global phenomenon mainly driven by population growth and large scale migration
• Provide information of rate of growth, pattern and extent of sprawl to provide basic
amenities
• Techniques of cellular automata (CA) are used for modelling the phenomenon
• Data used : Multispectral LISS satellite data
• Classification is done using MLC
• Areas: Built-up of residential and commercial localities,
agricultural lands and open, and water bodies. Mangalore,
Udupi region in Karnataka state was chosen
INTRODUCTION

4. Methodology:

5. Patterns and Composite structures are analysed using Shannon’s entropy and landscape matrices.
Entropy is best understood as a measure of uncertainty.
Shannon Entropy: It is chosen because it provides compression of any sequence which consist of
independent no. of variables which are identically distributed random variables.
Hn= -∑Pi loge (Pi) Pi is the Proportion of the variable in the ith zone where n the Total number
of zones, values closer to log n indicates that the distribution is very dispersed. Larger entropy
reveals sprawl location.

6. Patchiness:
It is the measurement of the density of
patches of all types or number of
clusters within the n×n window. Greater
the patchiness more heterogeneous the
landscape.
Landscape Matrix

7. Map density:
It defines values are computed by
dividing number of built up pixels to
the total number of pixels in a kernel.
This enabled in identifying different
urban growth centres and subsequently
correlating the results with Shannon’s
entropy for identifying the regions of
high dispersion.

8. Factors playing role in urbanisation:
1. Population
2. Population Density(α, β)
3. Annual Population Growth
4. Distance from Mangalore
5. Distance from Udupi
Regression equations are used to quantify the relationships between the variables
and the built-up. Three types of regressions are used:
1. Linear Regression Analysis
2. Quadratic Regression Analysis
3. Logarithmic Regression Analysis
Individual effects of factors is taken and then
cumulative effects is taken

9. Results: Individual Effect

10. Cumulative Effect of variables Actual Effect Predicted

11. Conclusion:
• Non-linear models give better results than linear models
• Higher degree/order of polynomial increases the computational time, hence only certain degree of
polynomial is taken
• Method of moments can be used to decrease computational time over MLC