Assessing Spatiotemporal Built-up Dynamics in Chiang Mai City, Thailand using Entropy approach


 The rates of urban dynamics affecting by industrialization, urban agglomeration, and large-scale migration turn its behaviour from monocentric to polycentric metropolitan resulting in unprecedented urban growth. Therefore, the present study incorporated an entropy-based approach to measure the degree of compactness and dispersiveness of urban development in Chiang Mai City. The Object-based machine learning was deployed for the image classifications with an overall accuracy above the minimum requirements (i.e., 90%) and kappa statistic of agreement above 0.85. The study reveals that Chiang Mai city has undergone urban development outskirts from the urban centre (CBD) and north and south-west direction from the CBD. A considerable increase in urban demographic and physical urban patches was observed in last 1998 to 2018. The research emphasized the significant role of Shannon Entropy to analyze the built-up growth supplemented by Remote Sensing and Geographic Information System (GIS) in respective zones and geographical directions.


Introduction
Migrating from rural to urban area is one of the primary sources of urban expansion, which re ects either increase in population and land size or urban patches . Additionally, urban growth is considered as an indicator that characterized socio-economic development, whereas it also reveals the impacts of anthropogenic activities on the natural environment (Badlani et al., 2017b).
Developing land use for different unique purposes or converting natural landscapes to impervious surfaces, for instance, creates a negative in uence on the urban ecosystem (Hamedianfar & Shafri, 2015). In this context, monitoring urban sprawl, infrastructure growth, or planning and management for long term is necessary to involve a primary information on the amount of built-up and land use pattern.
This enables planners to propose for maintaining smooth and to balance the developmental activities in the region (Jat et al., 2007). Hence, it supports for the decision maker and policymaker to prioritize on monitoring the land use and sustaining natural resources, biodiversity, and climate change from negative consequences.
Chiang Mai is the third largest city in North of Thailand with rapid socio-economics development and physical increase in urban growth was observed with ever increase in population and being center for business development in recent year (B. Setiawan B. & Rahmi, 2002). The primary factor of urban growth is service center for urban agglomeration, rural urban development, absorption of immigration toward the largest cities of Thailand and availability of social and public service facilities Rahmi, 2002, Srinurak andMishima, 2014). In this context, several studies have employed for modelling and monitoring of urban development under the aspects of engineering, economic and environment in Chiang Mai City (Brian McGrath et al., 2017;Sangawongse, 2006;Thitimakorn, 2013). Those studies used classi cation techniques [i.e. maximum likelihood classi cation, object based image classi cation, and other supervised classi cation (Brian McGrath et al., 2017) for examining urban sprawl studies. However, in the context of classi cation, Object Based Image Analysis (OBIA) used spatial and spectral informations for categorization of pixels in correlation with surrounding pixels based on shape, spectral and texture, improving accuracy of the classi cation. Addition to the OBIA, Shannon Entropy Index (SEI) was used to calculate the diversity of land use pattern at local (Rahman, 2016) and regional levels . In geographical concept, the entropy for spatial analysis is de ned as spatial entropy that enable in partitioning the area into various zones for analyzing the geographical features (Cabral et al., 2013). Therefore, the built-up pattern in the Chiang Mai city was selected to implement based on the application of the OBIA and the SEI.
Remotely sensed data is an e cient database resource to extract a piece of various information's regarding urban management and sustainable planning (Kadhim et al., 2016) through space and time. It provides an enhancement in terms of spatial, temporal, radiometric, and spectral resolution (Hamedianfar & Shafri, 2015), large area coverage (Badlani et al., 2017a), cost effective, detection of landscape dynamics at subpixel level (Hamedianfar & Shafri, 2015;Raziq et al., 2016), and availability of multi-time series archival data. Previous study applied ASTER (Jianwen and Bagan, 2005), IKONOS (Zhang and Wang, 2003), SPOT 5 (Lu et al., 2012), RADARSAT-1 and ENVISAT SAR (Xu, 2007), Sentinel (Abdulhakim Mohamed, 2019) and Landsat (Alam et al., 2019) to monitor urban changes at separate regions. Among various sensors, Landsat was commonly used to analyze urban sprawl and performed built-up pattern at provincial level with considerable accuracy, because of free charge, a long temporal resolution from 1972, spatial resolution of 30 m, and large swath area (Bhatti and Tripathi, 2014;Nautiyal et al., 2019;Ramachandra et al., 2012). The Landsat series consists of sensor with a various spatial resolution that can be used for different applications such as Operation Land Imagery (OLI) with Multi Spectral Sensor (MSS) for land use monitoring (Amalisana and Hernina, 2017;Badlani et al., 2017b;Phiri and Morgenroth, 2017), ice ow mapping (Fahnestock et al., 2016) and the thermal infrared band (TIR) for active re detections (Schroeder et al., 2016). In this study, Landsat imagery between 1988 and 2018 was applied for characterizing built-up changes in Chiang Mai city.
Overall, the study aimed at (i) classifying built-up and non-built-up using OBIA techniques from the Landsat imagery, (ii) computing Shannon Entropy Index for each zone, and (iii) understanding urban expansion in zone and geographical direction. The Chiang Mai city in Thailand was selected as a case study for examining the dynamics growth of built-up patches. This research also enables to support comprehensive development control strategy and policy documentation for future sustainable urban planning without haphazard urban sprawl.

Study site
Chiang Mai (18°47'N lat and 098°59'E long) is the largest city with an area of 22,800 km 2 , comprises of seven administrative districts, named Muang, Mae Rim, Hang Dong, Saraphi, Sansai, Sankamphaeng and Doi Saket (Sangawongse, 2006) (presented in Figure 1). The city is situated on the ood plain of Ping Mai River Basin with Doi Suthep-Pui range to the west and the curvilinear ridge of Doi-lang Ka-Khun Tan mountain range toward East (Thitimakorn, 2013). The average annual temperature is 25.6˚C with an annual rainfall of 1,184 mm. The general elevation of the study area ranges from 280 m to 335 m above mean sea level. In the past decade, the study area observed with the rapid expansion in built-up area and population as per O cial Statistics Registration Systems of Thailand in 2018 (Plecher, 2019;Prurapark and Asavaritikrai, 2020). According to Srinurak and Mishima (2014), the Thailand government had considered Chiang Mai City as the multicenter to the north of Thailand being center of Lan Na (independent state) before it merged to a part of Thailand. Chiang Mai is exacerbating toward Urban Heat Island (UHI) due to high construction activities, clustered impervious surfaces (Srivanit and Hokao, 2012) and juxtaposition for new incoming immigrants lead to formation of outward peri-urban (Tubtim, 2012).
Therefore, this study may demonstrate the urban density information using SEI on impervious surface in respective zone and direction.

Data used
Landsat 5 Thematic Mapper (TM) and Landsat 8 Operational Land Imagery (OLI) were selected to evaluate the long-term trend analysis of urban dynamics during 1998-2018 period. The classi ed land use land cover maps are geographically projected to the UTM 47 North zone with WGS84 datum. The satellite imagery was corrected radio-metrically, geometrically and atmospherically by removing the effects of sun angle, noise and atmospheric noise reproducing the actual surface re ectance values. The details of date of acquisition, rows and path of satellite imagery is shown in Table 1 and their band speci cation are stated more in details by (Gyeltshen et al., 2020).

Image Processing
The Object-Based Image Analysis (OBIA), also known as Object-oriented classi cation techniques, was applied widely to extract a variety of pixel information as well as to classify the spectral and spatial relationship of an identical object based on its contextual, tonal and shape (Gupta & Bhadauria, 2014). Several studies proved that the OBIA conveys a boundless potential in the classi cation and extraction of built-up patches for further analysis Shafri 2015, Amalisana andHernina 2017). It was widely used other than normal classi cation techniques such as: supervised or unsupervised classi cation namely, maximum likelihood classi cation, parallelepiped classi cation and minimum distance classi cation method (Ahadnejad et al., 2009). In this study, the object-based classi cation is followed by two steps (i.e., segmentation of image into discrete objects and assemblage of each object in different classes).
It is considered that multi-resolution segmentation is the pivotal component of Object-based image classi cation (Hossain and Chen, 2019). It groups the number of pixels into object or feature based on the spatial and spectral characteristics of an image (Blaschke et al., 2004). The current research maintains threshold scales values of 50 and classi ed the image into six classes; forest, urban, vegetation, barren land, fallow land, and waterbodies. Besides, the false color composite (FCC) band 4, 3, 2 for Landsat 5 TM and band 5, 4, 3 for Landsat 8 OLI color composite information were used to interpret features in the satellite imagery. Since the study emphasized on built-up and non-built-up growth, the six classes have been further reclassi ed into built-up and non-built-up category by merging urban into builtup and rest of the land use into non-built-up areas.
Finally, the most profound and popular techniques for accessing the accuracy of the classi cation is Kappa Index of Agreement (KIA) which is based on confusion matrix. It requires ground truth data (training data) to determine the accuracy of classi ed map. Since, ground truth data are time consuming due to large extent and expansive, high-resolution satellite imagery, google image and existing classi ed imagery suit the requirement of eld data collection. Hence, the current research picked up random training samples from the high resolution google earth image to compute confusion matrix and determine the kappa coe cient along with user and producer accuracy. Mathematically, the Kappa Coe cient can be computed using equation (4).

Shannon Entropy
A technique was developed by Shannon in 1948 which measure the degree of compactness and divergence of any geographical feature. It plays a signi cant role in information theory measuring information, prefer ability, and uncertainty (Burgin, 2003). Das Chatterjee et al., (2016), has also demonstrated the effective used of entropy metric-based approach in integration with geographic information system for urban sprawl modelling and monitoring. Besides, it is suitable for the measurement of built-up spatially and temporally with the help of concentric buffering and spatial geographical direction approach (Shukla and Jain, 2019). The mathematical formula to compute the Shannon entropy is shown in Equation (2) below: The above equation can be further restructured using the following equation by removing (-) ve values: Where H n , represent the Shannon Entropy, n for number of zones in the concentric buffering or directional pattern and P i for ratio of built-up within the zone to total built-up within the zone. The values of Shannon entropy ranges from 0 to log (n), (i.e., for concentric buffering, n=10 and for directional approach, n=8 was identi ed). Furthermore, H n approaching toward log (n), determine the high rate of dispersion or divergence with less density of built-up in the area whereas, H n tending toward zero indicate urban haphazard due to compact built-up and less urban growth (Aburas et al., 2018;Shukla and Jain, 2019). In this study, a spatial distribution and variability of geographical features in respective geographical direction and zone was implemented with the assistance of Shannon entropy under the approaches of concentric buffering and geographical direction. An analysis of 5 km interval from CBD (loop) toward edge of the study area (i.e. Zone 1-Zone 10) was employed based on compactness and depressiveness following the Burgess Theorem in 1924 (Aburas et al., 2018). In addition, 8 different directions (i.e., E, NE, N, NW, W, SW, S, and SE) were divided to determine the built-up growth in respective geographical direction.

Relative Entropy
The normalization of SEI values in between 0 to 1 is called relative entropy (Thomas, 1981) which can be calculated using equation (4).  Table 2 with Kappa co-e cient of three years, respectively. From the explored result, a strong agreement of statistic between the raster was observed that OBIA can be used for the classi cation of imagery for dynamical assessment of urban built-up. As indicated in (Deka et al., 2011), the overall accuracy of the classi cation above 85% is acceptable. Therefore, the current adopted classi cation using OBIA obtained above the minimum accuracy requirement.

Spatiotemporal pattern of built-up dynamic based on concentric circle
The main principle behinds subdividing the area in concentric circle is to evaluate the degree of urban growth within the zone according to Burgess theorem which state that the urban expansion start from centre of business district (loop) toward edges (Aburas et al., 2018). Multi-ring concentric circle with equal distance in whole direction, therefore, facilitate an analysis of spatial distributions of built-up from centre toward edge of the study area. The study area, hence, was subdivided into 10 sub-zone to compute the entropy values of each zone for analysing the degree of built-up compactness and divergence for the respective zones. The 5 km intervals were maintained for creating concentric buffer from the loop (CBD) stretching outskirt of 50 km toward the edge of study area. The location of CBD was collected using handle GPS from Chiang Mai City. Additionally, the built-up feature of each zone was further extracted to compute the Shannon entropy values.
In comparison with 1998, the built-up pattern mostly occurred in the centre loop under zone 1, while the built-up in corresponding two years (i.e., 2008 and 2018) speeded a development toward the edges of the study area (Figure 3).  Table 3. According to (Aburas et al., 2018;Deka et al., 2011;Shukla and Jain, 2019), the values of Shannon entropy range from 0 -log(n), where n represents the number of concentric circle (i.e. log (10) = 2.3026). The H n values, therefore, range from 0 -2.3026.
From  , 0.722, 0.87, and 0.892, respectively). This revealed that the city experienced with scattered impervious surface and distributed with diversi ed economic development (Jat et al., 2008;Ozturk, 2017). It also indicates that the development in patches (building footprints) on the landscape had been observed with an increase in entropy values for the last 20 years in the study area (Shukla and Jain, 2019). In addition, the urban growth patches in 1998 were less dispersed than the patterns of 2008 and 2018 as a demonstration to uniform developmental activities in whole direction. However, the growth pattern in different geographical directions was further discussed in next section using geographical direction technique for urban growth analysis.
Regression analysis was performed between the driving factor (population) and Entropy values of the patches. A high correlation between population and Shannon entropy was observed with strong correlation coe cient of 0.9. The archival population data of Chiang Mai City was retrieved from macro trends website (United Nations, 2020).

Quanti cation of built-up at different geographical direction
Built-up analysis on spatial and geographical direction were evaluated and quanti ed based on concentric circular buffering technique surrounding the Centre Business District (CBD) serving as a centre point of developmental activities (Aburas et al., 2018). Hence, the Chiang Mai City was divided into 8 major geographical directions ( Figure 5) to further quantify the spatial distribution of urban patches into realistic evaluation which support circular buffering analysis. Table 5 demonstrate that the area of impervious footprint of built-up reveal a vertical distribution throughout the study area. Based on the directional approach, the dispersed patches obtained from concentric buffering approach are mostly occurs along the north direction with 115.3 km 2 in three consecutive years followed by S-W direction with an area of 79 km 2 .
The area and entropy values in each direction is computed in Table 5. Most of the developmental activities were occurred from 1998 to 2008 followed by 2018 in north direction, where least developmental activities are observed in W and N-W directions. Furthermore, it was also demonstrated that Chiang Mai City experienced hefty developmental activities, which indicate rapid increase in population density (Brian McGrath et al., 2017;B. B. Setiawan and Rahmi, 2002) From Table 6, a high R(H n ) was observed in the case of geographical directional analysis in addition to the concentric buffering approach. The rate of dispersion is high as most of the entropy values tend toward upper limits (i.e., 0.5). However, small entropy value was observed at the Centre Loop, West and North-West directions where least development activities were occurred in the beginning of 1998's ( Figure  6). In addition, along West and North-West direction, the developmental activities were interrupted due to topographical and geological phenomena. The observed values are mostly above the threshold of builtup patches for depressiveness in three years (i.e., 0.5). From this analysis, patches at W and N-W geographical direction shown to be lower values since least development activities was occurred in 1998 in core area (i.e., loop). On the contrary, due to topographical and geological reason, which composed of mountain ridges and fault line, least development activities are happened in that W and N-W direction.
According to Setiawan and Rahmi, (2002), the author emphasized on statistical measure with other contributing factors such as population, land values and economic scale in Chiang Mai City for land-use change. In addition, Brain McGrath et al., (2017) has analysed the built-up dynamic using area statistics to demonstrate the land use change, patch dynamic and type of landform existed in Chiang Mai City.
They also employed SLEUTH model for determining the urban growth and land use dynamics. However, these researches have not demonstrated the level of urban growth or sprawl happen in which zones and geographic directions, respectively. Therefore, the emphasization on entropy-based approach provide indepth understanding on the level of urban growths in respective zones and geographical directions in terms of compactness and dispersive nature of urban patches which gives the clear picture on how and where to implement the developmental activities in equitable and sustainable manner. Hence, the research enable to provide the fundamental information's on built-up pattern in Chiang Mai which support the urban planner, designer and local authorities to propose accordingly to implement based on the innovative approach indicated above for future developmental activities.

Conclusions
The study emphasized OBIA based GIS approach for classi cation of remote sensing data and statistical model to monitor the time series analysis on built-up growth in the Chiang Mai city. driving factor (population) and Shannon entropy which is dependent on population. It was observed with high positive correlation of 0.9 between the entropy and population data.
Through directional approach, it was observed with high dispersive developmental activities mostly occurs in north direction followed by S-W direction and less entropy values with compact development were observed in W and N-W direction since the clustered developmental activities was mostly happen before 1998 in the loop of Chiang Mai city. The study concludes that Chiang Mai City is diverging toward the edge of the study area with diversi ed built-up growth increasing every year. Thus, this study will enable an individual, working under government sector, NGO and other related focal person under planning and strategy section to come up with innovative policies and development control strategy for sustaining the developmental activities in all direction without urban sprawl. Since the classi cation of land use using OBIA in this paper obtained considerable accuracy above the minimum requirement, the future land use/built-up prediction will be carried out using Markov Chain (MC) Analysis or any method that best suit the requirement of the study.

Declarations Con ict of Interests
The author declares no con ict of interests for this publication.