comparing horizontal and vertical space with number of residents, business and public service enterprises 

Hello colleague,

I have not directly worked on the subject of urban sprawl, but while working on poverty alleviation and sustainable development, I had the opportunity to study the Kachchi abadis (shanty towns) across the capital city of Islamabad.

In case you plan to conduct a survey, you could get most of the quantitative data from the district administration or city's development authority who keep track of rural-urban migration. For qualitative information, you could do some probing into the reasons.

In my case I found both push and pull factors. For example, lack of opportunities in the village, family disputes, loss of home due to natural disaster as well as searching for job/work opportunities, looking for better social services e.g. medical services, access to drinkable water, energy and space.

A particular phenomena was the Real Estate Mafia that would grab a piece of state land and bring people from the village to settle temporarily. After a certain period of time, the city administration is being pressurized to legalize the locality and then the Mafia will evict the poor residents against petty financial rewards and develop the area commercially. Hitting the jackpot at the cost of poor dwellers. You may find out a lot more by talking to settlers and also observing over a period of time as to how the whole phenomena take place.

I will be keen to know your results.

Best of success.

Hello khadija khan 

I am overwhelmed with your response and its heartening to know that you worked for the shanty towns in the capital city of Islamabad. yes for sure I will share my findings and results with all colleagues and i am still in early stage to quantify the urban sprawl in the karachi city. I would ask can i have access of your work regarding shanty towns of Islamabad. i will appreciate any feedback in this regard.

regards

Dear Sayed

I know its difficult to get and costly, but satellite date for time periods may be one of the best  ways to look into it.

Thanks Irshad. My work was part of a comprehensive research project on Sustainable Livelihood launched by Plan International, Pakistan in late 90s. There were two main exercises and two consolidated reports. If I may propose to check out with their Islamabad office and ask someone to look into the archives. At that time, Dr. Purnima was the Director, Pakistan. I am since travelling extensively and am not able to maintain track of publications. Best of success.

A simple way would be to calculate density. Around the city center, the density would be the highest, and then as you move away, the density will monotonically decrease. You can create different cutoff values for the sprawl, or your own definition of inner ring, outer ring, etc. 

dear tonmoy islam

i wonder what should be the standard cut off values in order to calculate the density for the urban sprawl

You may find this new paper useful: "How suitable is entropy as a measure of urban sprawl?" Landscape and Urban Planning184 (2019): 32-43.

From the abstract:

"Entropy has been one of the most often used metrics for the measurement of urban sprawl. However, its suitability in terms of requirements for measuring urban sprawl has not yet been examined sys- tematically. Therefore, our study examines the behavior and suitability of entropy as a measure of urban sprawl by applying it to seven simple model landscapes and six real-world case studies. We also investigate the influence of the choice of the city center and associated translocation of zones and assess entropy with regard to 13 suitability criteria for measures of urban sprawl. Our results show that entropy is, in many cases, not sensitive to important differences between spatial patterns of built-up areas that represent different levels of urban sprawl, e.g., dispersed vs. compact spatial arrangement of built-up areas. In addition, the value of entropy is strongly affected by changes in the choice of zones within a landscape. Finally, entropy does not meet several important suitability criteria for measuring urban sprawl; it only meets 5 out of 13 suitability criteria. We conclude that entropy is not suitable as a measure of urban sprawl. More suitable metrics of urban sprawl are available that should be used instead."

using remote sensing data/images combined with sophisticated software that analyses urban expansion through analyzing change in pixel color.

https://www.researchgate.net/publication/230738894_Peri-Urban_to_Urban_Landscape_Patterns_Elucidation_through_Spatial_Metrics

https://www.researchgate.net/publication/229826816_Empirical_patterns_of_the_influence_of_Spatial_Resolution_of_Remote_Sensing_Data_on_Landscape_Metrics