Assessment of Urban Green Open Spaces of Micro- and Meso-Level Zones, Based on the Growth Pattern: Case of Patna City

Abstract

India’s urban population increase is creating pressure on the urban green open spaces. The overall city-level per capita open space is considered as a benchmark of the open space. The open space of Patna is 2.43 sq m per capita, but at the community level or ward level, there is a lacuna. So, there is a significant gap in open space distribution at the city level and the micro level, that is, ward or block level. An assessment was carried out on three parameters, i.e., quantity, accessibility, and quality. Open space, catchment area, and vegetation cover were used as independent variables, and population density and ward area as dependent variables, to understand the distribution at the ward level, that is, community level. Distribution was analyzed by Pearson correlation between the independent and dependent variables within three parameters. The open space distribution between three meso-level areas based on the growth pattern was analyzed with the help of linear regression and R-squared tests to compare the distribution between the areas. The result shows that Patna has poor distribution in the old and new areas. The developed areas in between have good distribution at the micro level and meso level. Patna has 2.3 sq m per capita as per the proposed open space plan and projected population of 2030, which is less than the standard 3.16 sq m/capita at the community level and 3.66 sq m/capita at the district level.

1. Introduction

Urban green open spaces play a significant role in any city development as they provides an opportunity for physical activity, social interaction, and enjoyment of nature, and offer a unique environmental setting within the urban area and, most notably, the urban ecology [1]. Different disciplines have used various definitions from their professional concept for urban green open spaces, such as horticultural green land system, urban green land system, ecological green land system, and urban green space, green open space, and urban green open space [2,3]. All open spaces which are publicly accessible are referred to as public open spaces, including green or civic. Moreover, in many definitions, urban green space is all types of public or private open spaces in urban areas that are entirely or mostly covered with vegetation [4,5]. Urban green open spaces, as per Wang [3], are considered vegetation-covered public areas used for social interaction and physical activity. As urban green spaces have multiple definitions, in this paper, the definition of urban green open space can be understood as urban open spaces having vegetation and accessible to the public. It refers to the human-built environment, such as an urban park, garden, or any green space, and serves for community needs, social interaction, and joint activities [6]. It is combination of the term urban green space, which comprises areas covered with vegetation, and public open space, which is a publicly accessible part of urban land and contributes to the urban landscape [3,5,6]. It constitutes the most crucial component of urban spaces as it comprises parks, forests, playgrounds, riparian areas such as riverbanks, lakes, green promenades, trails, and nature conservation areas [2,7,8]. It helps mitigate the heat island effect in urban areas with the help of evapotranspiration and shading effects [9,10]. It helps in improving air quality, flood control, and reducing noise pollution [11,12]. The urban green open space can also refer to an urban open space. It has a similar definition in terms of uses, but it is limited to the areas with green cover in the urban open space that is publicly accessible [5,6].

Urban green open spaces provide many functions in an urban context that benefit people’s quality of life [13]. Despite knowing the importance and benefits, such as physical, psychological, social, environmental, and economic benefits [14], urban green open spaces there will be a shortage due to rapid urbanization and an increase in the population [14]. Urban green open spaces are very vulnerable due to the sudden loss of vegetation cover and change in vegetation in the built-up areas in Indian cities [15,16]. This built-up area is increasing and will be continue to increase at a rapid pace. The problem can be seen with the help of demographic change projection for the future. This says that the urban population is projected to increase by 18.5% from 35% in 2020 to 53.5% in 2050 [17], which tells that more than half of the population will live in urban areas by 2050 in India (see

Table 1. India Population Projection by United Nations [17].

Year	Population	Density (P/km2)	Urban Population (%)	Urban Population
2010	1,234,281,170	415	30.8%	380,744,554
2020	1,380,004,385	464	35.0%	483,098,640
2030	1,503,642,322	506	40.4%	607,341,981
2040	1,592,691,513	536	46.7%	744,380,367
2050	1,693,176,033	551	53.5%	876,613,025

). This change will affect the urban agglomeration and increase the population density from 464 people/km² in 2010 to 550 people/km² in 2050. The number of cities with a population of at least a million in India increased from 35 in 2001 to 53 in 2011, and there will be six cities with a population over 10 million and more than 100 cities with a population of at least a million by 2030 [18]. By 2050, India will be the most populous country in the world [17].

These demographic changes have resulted in a significant decrease in green spaces across many cities in India and they are further decreasing with growing urbanization and population increase [19]. The loss of green spaces and environmental degradation are likely to increase due to an increase in population and density. There is a lack of per capita availability of urban green open spaces in most Indian cities [20]. Indian megacities such as Bangalore, Hyderabad, and Kolkata have lost many open spaces, urban wetlands, and water bodies because of urban sprawl [16,20]. It has been observed that this pressure of urbanization and population increase is greater on the older cities and settlements. As per the study by Rao and Kumar, the old core area of a city has less open space because of population pressure compared to the new areas. Additionally, it is not adequately distributed [21,22]. The open space standard should be fulfilled on different levels, such as community, district, and city levels, as per Urban and Regional Development Plans Formulation and Implementation (URDPFI) guidelines in India [23]. However, the open space assessment is per capita, not focusing on the distribution in all levels in Indian cities [24]. A lot of qualitative and quantitative research has been carried out to assess urban green open spaces in cities such as Nagpur, Bhopal, Delhi, Kolkata, and Bangalore [8,16,22,25]. As per Senik [26], a qualitative evaluation has been carried out for the open green space planning approach. Ahirrao carried out an assessment, and the qualitative approach has been assessed based on perception and was limited only to the parks of Nagpur [8]. In India, quantification and distribution of UGS have not been fully incorporated in urban planning due to a lack of detailed assessment [27]. A limited study has been carried out on the quantitative change in urban green space with urbanization. In addition, the study shows the urban green change based on remote sensing with an assessment based on the green cover LULC change [16]. A very limited study was carried out to assess the urban green open space as per the definition given in the paper. Moreover, no assessment study has been carried out in Indian cities on urban green open space based on the growth pattern and the identified parameters. The assessment of only the green cover will not give the actual picture as some urban green open spaces can fall into private or restricted areas. Moreover, they might not be accessible to the public for social interaction and physical activities, as defined in this paper. A quantitative and qualitative assessment study of urban green open spaces has yet to be carried out based on the city’s growth pattern, especially for older and tier 2 metro cities. This study is required to understand the open space distribution of an Indian city at different levels (micro and meso level) and assess the distribution with respect to the city’s growth.

The main aim of this research is to assess the open space at the micro and meso level of a city based on the growth pattern.

To assess urban green open space, it is required to understand the standards related to urban green open space and assessment parameters in India and abroad. As per the Urban Green Guideline 2014 by the Government of India, classification is carried out based on hierarchy and uses, which are reserved forest, protected forest, national park, district park, playground, green belt buffer, and green strip. As per the URDPFI guideline, the city should have 31.6 hectares of open space per a population of one lakh for the community level, which will be 3.16 m²/capita, and 183 hectares of open space per a population of five lakh for the district level, which will be 3.66 m²/capita. In addition, the metropolitan city should have 20–25% green areas, including recreational space, organized green space, and other common open spaces, including vacant land, open spaces including flood plains, etc. [23].

India and many Asian countries follow the quantitative assessment standard, which is the per capita green space, unlike other European, Australian, and American countries that also follow accessibility and quality for their assessment [24]. In Britain, as per the National Playing Field Association (NPFA), it is 24 m² per capita, and in the USA as per the National Recreation Park Association standard, 40 m² per capita is required. As per LEED-ND, more than 20 m²/capita or 1.25 hectares/1000 residents within 250 m should be provided. The WHO standard recommends 9 m²/capita.

As per a study by Dhanpal in 2014, regarding the per capita green space in major cities in India, only a few have been able to provide more per capita green space than the international standard. Jaipur (20 m²/capita), Gandhinagar (147 m²/capita), Chandigarh (54.45 m²/capita), and Bangalore (17.79 m²/capita) are among the few cities which have higher than standard open space requirements [19].

In terms of the assessment parameters, as in India, open space assessment is carried out on a quantity basis that is derived from population and area concerning open space [7,23,28]. However, when we compare with other European, Australian, and American countries they also assess the open space based on quantity, that is, per capita open space [19,20,23,24], and also accessibility, that is, the catchment area of the open space [19,24], and the served population and the quality, that is, the healthy vegetation cover [24,25]. The problem of lack of availability of open space is not limited to the tier 1 megacities such as Bangalore, Hyderabad, Kolkata, and Delhi, as it is also seen in tier 2 metro cities, and Patna is not an exception [13,20,21,22].

The Patna Municipal Corporation area has a population of 1,684,222, and an area of 108.164 km² which has risen 48.97% from 1991 to 2001 and 32.53% from 2001 to 2011 [18]. In the study carried out by Asraf and Ghose in 2015, the urban green space was reduced to 16.28 km² in 2014 from 50.4 km² in 1993 [13]. This study showed the green cover, which also included private land. Patna has lost many green spaces and water bodies in the past few decades because of encroachment and urban sprawl [13,21]. As per the existing master plan, the per capita green space is 2.43 m² per capita [28]. This 2.43 m² per capita open space shows the overall open space of Patna; at the micro level, we can see fewer open spaces in the core city area compared to the new areas [21], which means some areas will have less than 2.43 m² per capita of open space. Patna City in context with open space is shown in Figure 1.

As per a study by Kumar, the distribution of open space is missing for Patna City. Additionally, as per Rao and Kumar, their study shows that the core city area of older cities such as Patna and Bhopal has less open space because of population pressure than outgrowth or new areas [21,22].

This this research suggests that because of increasing population pressure and urbanization, the open space standard is lower in the core city area or the old city area compared to the new development [21,22]. However, this research does not explain whether the changes are proportional to the change in the city’s growth pattern, and there is a need to understand the lack on the micro level (ward-wise) and meso level (zone-wise). In addition, the assessment parameter for the urban green open spaces especially in Indian cities is very limited to a quantitative approach, as per the study by Maharina [24] and other European and Australian countries, in which the open space assessment has to be carried out based on quantity, quality, and accessibility.

Based on the need for study, previous literature study, and the aim of this research, in this paper, we are trying to answer two questions based on the identified parameters:

• What is the urban green open space distribution in Patna City?
• Is urban green open space distribution based on the city’s growth pattern?

2. Study Area

The study area selected is Patna City within Patna Municipal Corporation. Patna is the capital of the state of Bihar of India, and it is located at 25°37′ north latitude and 85°10′ east longitude on the south bank of the River Ganges. Rivers Sone and Punpun also surround it. It has a humid subtropical climate with extremely hot summer in May and June, followed by the monsoon in July and August. It is also a sacred place for Sikhs for being the birthplace of the last Guru Govind Singh. Patna City is one of the oldest cities in India, whose history goes back to 600 BC [29], and it is the 19th largest urban agglomeration in India, having a population of 1,684,222 [18] and an area of 108.75 square km with a population density of 15,488 people per square kilometer. The study was carried out in three areas based on the city’s growth pattern at the meso level and ward-wise at the micro level (see Figure 2). The growth pattern is based on the city’s growth from the 18th century after the extension from the fort city of Shershah Suri. Then, the extension of 1912 of the south of the city, and then the extension towards the west [29]. Overlapping the growth pattern as per the British map and master plan zoning map within the study area, the meso-level zone is considered. The three areas are given names as per the growth pattern; the older area is Area 1, then Area 2, and the new area is Area 3. These areas are also demarcated based on the zones given in the Patna Master Plan 2031. Area 1, which is the old area, is demarcated as a special area, Area 2 is the special zone excluding the special area, and Area 3 excludes the special zone and is demarcated as Zone 2 within the Patna Municipal Corporation boundary in the Patna Master Plan (for a detailed study area map, see Figure 2).

The Patna Municipal Corporation areas have 75 wards. At the time of the last census in 2011, the total ward number was 72. However, now it is 75 as ward number 22 is further divided into 22, 22A, 22B, and 22C, and the census data have not been updated since then. For this study population, data were divided as per the area proportionate to ward 22, to understand the distribution for these wards.

3. Material and Methods

The data used in the study are secondary data from various sources such as population data, ward boundary data, Patna Master Plan, and Landsat 8 image for NDVI from USGS EarthExplorer. The details of the data collected and the source are given in

Table 2. Materials used and their sources.

Data	Source
Open space map, 2021	Patna Master Plan 2031
Study area land use and boundary, 2019	Existing land use plan of Patna, Patna Master Plan 2031
Population data, 2011	Census of India 2011
Area of open space, special area, land use	Georeferenced Arc Map software
Landsat 8 remote sensing image, 2022	USGS EarthExplorer

.

There is a lack of census data, as the last census was in 2011, so the ward-wise data used for the correlation are from 2011, and the open space data are as per the latest master plan.

3.1. Methods

We have selected Patna based on three zones within the Patna Municipal Corporation (PMC) boundary, which also show the evolution pattern of the city. As per a report by the Institute of Human Development, the growth of Patna shows a growth pattern starting from the Patna City area (currently Patna City in the special area) on the eastern side, then towards the south (currently in the special zone), and a little bit towards the west, and then towards the west (currently Zone 2) [28,29]. The old city area in the city master plan has been earmarked as a special area, and Zone 1 (special zone) includes the special area [28]. This demarcation has been taken based on the current zones as per the Patna Master Plan 2031 [28]. The study area is restricted to the Patna Municipal Corporation boundary for the availability of ward-wise (for micro-level analysis) data, e.g., ward area and population data.

All three areas were selected and analyzed based on the assessment parameter, e.g., quantity, accessibility, and quality [19,24], taken from the literature study, and to find the relationship between the variables of those parameters within the individual areas and then between the three meso-level areas. This is to find out, based on the growth pattern, how the urban green open space is distributed within the individual areas (ward-wise) and different meso-level areas and to know how urban green open spaces are changing, based on the growth pattern identified along with the current zones within Patna Municipal Corporation.

3.2. Parameters

Quantity is taken based on the area of open space and per capita open space, which is normally derived from the open space area, the population of the area, and the total area [24,28]. The Green Space Scotland research report shows that green space within 5 min of walking is a strong indicator for good quality of health and life [30], and shows how many people can access green space with the help of population data and area [19,25]. Quality depends on biodiversity, green cover, and vegetation [19,25]. In this case, the healthy vegetation is NDVI value 0.3 and above, representing the tree canopy cover [31]. The parameters, variables, and tools used are given in

Table 3. Parameters, independent and dependent variables for assessment.

Quantity Urban Green Open Space (Independent Variable) Area (Dependent Variable) Population Density (Dependent Variable)	Correlation (r) between the independent and dependent variables (Independent variables: open space, catchment area, and vegetation cover; and dependent variables are ward area and population density)	Geographically weighted regression (R-squared value, AICc, sigma, bandwidth, and effective number)
2. Accessibility b. Accessible Area (Independent Variable) Area (Dependent Variable) Population Density (Dependent Variable)
3. Quality c. Healthy Vegetation (Independent Variable) Area (Dependent Variable) Population Density (Dependent Variable)
	Strength and significance of the variables (result = distribution of open space within the wards)	Will determine the area with best fit within the given variables (result = distribution within the three meso areas)

.

Based on the literature, the selected parameters for the assessment of the urban green space of the study area are:

• Quantity.
• Accessibility.
• Quality.

For analysis, two methods were used:

• The first is the Pearson correlation which determines the strength and significance of the variables and analyzes the open space distribution [32,33] in relation to the area and population.
• The second method is geographically weighted regression; it is a statistical approach to explore spatial non-stationarity of the regression relationship in spatial data analysis. It is determined by the variance in the dependent variable, which can be explained by the independent variable in spatial data form, and this helps in determining the adequate fit of the model, which helps in analyzing the parameters of different meso-level areas and the best fit within the given variables through spatial data [34].

4. Results

From the georeferenced Patna municipal boundary and open space map of the Patna Master Plan on ArcGIS, the parameters and variables to calculate the per capita open space, ward density, total open space, and the NDVI mapping with the Landsat 8 image (July 2022) to know the vegetation cover are given in

Table 4. Urban green space of Patna (variable data as per 2011 census population data).

	Area 1	Area 2	Area 3
Total Area (km2)	22.3	32.2	53.15
Total Urban Green Open Space (km2)	2.3	2	2.6
Total Ward Density (People/km2)	29,573	11,137	12,556
Total Vegetation Cover (km2)	0.84 (3.7%)	2.5 (7.7%)	7.4 (13.9%)
Open Space Per Capita (km2)	3.45	5.6	3.95
Served Population	485,182	246,299	321,920

.

One of the limitations of the study is that the population data were from 2011, as the new census for 2021 was not yet available from the Government of India. Additionally, acquiring the micro-level population data (ward level) was also not feasible as the number of wards as per the census in 2001 was 42, which has changed to 75 wards as per the latest 2021 data, and the ward boundaries and area have been changed since then. So, the regression and quantitative analysis were carried out on the basis of 2011 population data. However, to obtain the result of the current and future years, the assumption of population data was taken on the basis of the population projection of 2030 by the City Development Plan, only for the overall three areas of the meso level. The micro-level regression analysis was not possible because of the limitation in projecting the ward-level population due to the difference in the number of wards and area boundaries within the decade (2001–2011). For the meso-level analysis based on the quantity and accessibility, the city-level population projection data could be used. As per the City Development Plan 2010 and Patna Master Plan, the population of Patna will reach thirty lakh according to the linear method, so the growth percentage from 2011 to 2030 is 78.2% [35]. For the different study areas, population projection is given in

Table 5. Study area population forecast for 2021 and 2030 based on City Development Plan 2010 and Patna Master plan 2031.

	2011	2021 (@39% Growth)	2030 (@78.2% Growth)
Area 1	657,212	913,525	1,167,837
Area 2	358,035	497,668	637,302
Area 3	666,202	926,020	1,185,839

.

Based on the population projection as per Table 5,

Table 6. Urban green space of Patna (variable data for projected population of 2021 as per CDP 2010).

2021	Area 1	Area 2	Area 3
Total Area (km2)	22.3	32.2	53.15
Total Urban Green Open Space (km2)	2.3	2	2.6
Total Ward Density (People/km2)	40,965	15,445	17,422
Open Space Per Capita (m2)	2.5	4.01	2.8
Served Population	637,825	359,405	418,128

and

Table 7. Urban green space of Patna (variable data for projected population of 2030 as per CDP 2010).

2030	Area 1	Area 2	Area 3
Total Area (km2)	22.3	32.2	53.15
Total Urban Green Open Space (km2)	2.3	2	2.6
Total Ward Density (People/km2)	52,369	19,791	22,311
Open Space Per Capita (m2)	1.96	3.13	2.19
Served Population	811,719	459,151	535,464

, the per capita open space and served population based on the proposed open space map as per the Patna Master Plan 2031 were calculated.

As per data extracted from the secondary sources, the variables used in the study are total urban green open space, total area, population density, healthy vegetation cover, and open space per capita. The following data reveal that the special area has more than double the population density than the other two. However, it has mostly similar per capita open space compared to Area 3. Zone 2 has comparatively more per capita open space than the other two (Table 5). As per the projected population in Table 6 and Table 7, Area 2 (4.01 m²/capita) had a good amount of open space compared to Area 1 (2.5 m²/capita) and Area 3 (2.8 m²/capita) in 2021, but it has close to the standard open space for recreational use, that is, 3.13 m²/capita, for the 2030 projected population. Areas 1 and 3 have less than the standard open space requirement for recreational use for the projected population (see Table 6 and Table 7).

In terms of accessibility, more populations have access in Area 1 than Areas 2 and 3. The served population in Area 1 is 485,182 (73.82%), that of Area 2 is 246,299 (68.8%), and that of Area 3 is 32,1920 (48.3%). For the projected population of 2030, Area 2 serves 72%, then Area 1 serves 69%, and, finally, Area 3 serves 45% of the population. The served population is calculated by the following formula:

(Served Population = Population Density × Catchment Area).

The healthy vegetation cover was derived from remote sensing data of Landsat 8 in July 2022 with the help of the normalized difference vegetation index (NDVI). For the Landsat 8 image, band 4 and band 5 were used in the NDVI. The formula for the NDVI is:

(NDVI = Band 5 − Band 4/Band 5 + Band 4).

The healthy vegetation range was taken as 0.3 and above in supervised classification. As per the data from supervised classification, Area 3 has more vegetation than Areas 1 and 2.

This is for an overall understanding of the different meso-level areas based on different parameters. Now, the micro-level analysis at the ward level of all three meso levels is given, and the correlation between the variables for the given parameters is given in Table 8, Table 9 and Table 10.

4.1. Quantitative Analysis

This part of the analysis shows the correlation with the variables. We have used Pearson correlation analysis to check the correlation between variables and also the strength of the correlation. As discussed previously for selecting parameters, the independent variable is open space and the dependent variables are ward area and population density.

Ward area has a positive relationship in Zones 1, 2, and 3, with the open space having r = 0.58, 0.89, 0.45, respectively, whereas population density has a negative relationship with open space with r = −0.497, −0.615, −0.45, respectively (see Table 8). This shows that the open space area increases as the ward area increases, but it decreases as the population density increases. Open space’s negative relationship with population density shows that, in wards where the population is larger, the open space is smaller, so this has to improve. By comparing with the strength in the variables, in Zone 2, the strength of “r” is higher in both cases, then Zone 1, and then Zone 3. On the map (Figure 3), it is visible that many areas have less than the city-level per capita amount of open space, i.e., 2.4 m²/capita, especially in Area 3.

Table 8. Quantitative and correlation analysis of different Zones.

	Between Ward Area (km2) and Urban Green Space	Between Ward Population Density (Thousands/km2) and Urban Green Space
Area 1 (special Area)
	Pearson Coefficient r = 0.586351	Pearson Coefficient r = −0.4673
Area 2 (Special zone- Special Area)
	Pearson Coefficient r = 0.898147	Pearson Coefficient r = −0.61522
Area 3 (Zone 2)
	Pearson Coefficient r = 0.459012211	Pearson Coefficient r = −0.45053642

Table 8. Quantitative and correlation analysis of different Zones.

	Between Ward Area (km2) and Urban Green Space	Between Ward Population Density (Thousands/km2) and Urban Green Space
Area 1 (special Area)
	Pearson Coefficient r = 0.586351	Pearson Coefficient r = −0.4673
Area 2 (Special zone- Special Area)
	Pearson Coefficient r = 0.898147	Pearson Coefficient r = −0.61522
Area 3 (Zone 2)
	Pearson Coefficient r = 0.459012211	Pearson Coefficient r = −0.45053642

Figure 3. Map of Per Capita ward-wise distribution of Patna. (Source: Census Of India—Population data, Patna Municipal Corporation ward boundary and corporation boundary and area, Master Plan 2031—open space location, map generated in ArcMap 10.4.1).

Figure 3. Map of Per Capita ward-wise distribution of Patna. (Source: Census Of India—Population data, Patna Municipal Corporation ward boundary and corporation boundary and area, Master Plan 2031—open space location, map generated in ArcMap 10.4.1).

4.2. Accessibility Analysis

In terms of accessibility, ward area has a positive correlation in Area 1, Area 2, and Area 3, having r = 0.62, 0.96, and 0.51, respectively. Area 2 shows the high strength of open space catchment in the relationship with the ward area, followed by Area 1 and then Area 3. However, it shows a negative relationship with population density, i.e., Area 1 = −0.55, Area 2 = −0.72, and Area 3 = −0.37 (see Table 9). This shows that the density is higher in these areas and, compared to the density, the catchment area is smaller. Out of all three, Area 2 shows a stronger negative correlation than that of Area 1 and then Area 3. In Figure 4, we can see that the majority of areas in Area 3 have less than 50% of the served population.

Table 9. Accessibility and correlation analysis of different Zones.

	Between Ward Area (km2) and Total Catchment Area (km2)	Between Population Density (Thousand/km2) and Total Catchment Area (km2)
Area 1 (special Area)
	Pearson Coefficient r = 0.626062	Pearson Coefficient r = −0.55338
Area 2 (Special zone- Special Area)
	Pearson Coefficient r = 0.96672	Pearson Coefficient r = −0.72694
Area 3 (Zone 2)
	Pearson Coefficient r = 0.511082697	Pearson Coefficient r = −0.37575257

Table 9. Accessibility and correlation analysis of different Zones.

	Between Ward Area (km2) and Total Catchment Area (km2)	Between Population Density (Thousand/km2) and Total Catchment Area (km2)
Area 1 (special Area)
	Pearson Coefficient r = 0.626062	Pearson Coefficient r = −0.55338
Area 2 (Special zone- Special Area)
	Pearson Coefficient r = 0.96672	Pearson Coefficient r = −0.72694
Area 3 (Zone 2)
	Pearson Coefficient r = 0.511082697	Pearson Coefficient r = −0.37575257

Figure 4. Map of ward-wise Served population of Patna. (Source: Census Of India—Population data, Patna Municipal Corporation ward boundary and corporation boundary and area, Master Plan 2031—open space location, map generated in ArcMap 10.4.1).

Figure 4. Map of ward-wise Served population of Patna. (Source: Census Of India—Population data, Patna Municipal Corporation ward boundary and corporation boundary and area, Master Plan 2031—open space location, map generated in ArcMap 10.4.1).

4.3. Qualitative Analysis

Vegetation cover shows a positive relationship with ward area, with r = 0.3, 0.95, 0.76 for Area 1, Area 2, and Area 3, respectively (Table 10). However, with ward-wise population density, there is a negative correlation in all the areas. Open space shows a positive correlation. Comparing all three zones, the vegetation cover is better in Area 2 in terms of ward area and open space area as it shows a strong correlation with these two (Table 10 and Figure 5).

Table 10. Qualitative and correlation analysis of different Zones.

	Relationship between Ward Area and Vegetation Area	Relationship between Population Density (People/km2) and Vegetation Area	Relationship between Open Spaces and Vegetation Area
Area 1
	r = 0.31125	r = −0.38009	r = 0.648153
Area 2
	r = 0.95334	r = −0.67001	r = 0.801145
Area 3
	r = 0.768879936	r = −0.621144752	r = 0.760933681

Table 10. Qualitative and correlation analysis of different Zones.

	Relationship between Ward Area and Vegetation Area	Relationship between Population Density (People/km2) and Vegetation Area	Relationship between Open Spaces and Vegetation Area
Area 1
	r = 0.31125	r = −0.38009	r = 0.648153
Area 2
	r = 0.95334	r = −0.67001	r = 0.801145
Area 3
	r = 0.768879936	r = −0.621144752	r = 0.760933681

Figure 5. Map of ward-wise healthy vegetation distribution of Patna. (Source: USGS—Landsat Image, Patna Municipal Corporation ward Boundary and Corporation Boundary, Map Generated in ArcMap 10.4.1).

Figure 5. Map of ward-wise healthy vegetation distribution of Patna. (Source: USGS—Landsat Image, Patna Municipal Corporation ward Boundary and Corporation Boundary, Map Generated in ArcMap 10.4.1).

4.4. Geographically Weighted Regression Analysis

Geographically weighted regression was carried out to see the model best fitting the variables (Table 11, Figure 6, Figure 7 and Figure 8)). If we compare all the areas, Area 2 has the better fit with R-square = 0.77 in quantity, 0.93 in accessibility, and 0.90 in quality, and AICc is lower in Area 2 compared to the others. Then comes Area 1 having R-square = 0.34 in quantity and 0.67 in accessibility, but in quality, it is 0.7, which is less than Area 3 which has R-square = 0.97.

This shows that Area 2 has a better distribution of open space, based on the given variables, than Area 1 and then Area 3. Between Area 1 and Area 3, Area 1 scores more in quantity and accessibility than Area 3, but it has less vegetation cover, which pertains to quality.

Table 11. Geographically weighted Regression Analysis of different zones and parameters, input data for Area 1 (as per

Table A1. Table showing ward-wise population data and open space as per Patna Master Plan used for quantitative analysis of urban green open spaces of Area 1.

Area 1 Ward Area and Population				Open Space (m2)
Ward Number	Ward Area (sq km) (yi)	Area 1 Ward Population	Population Density (People/sq km) (yii)	Park and Playground	Open Space Buffer	Forest	Water Body Buffer	Bioconservation	Total Open Space (x)
27	0.88	9442.5	10,730.11	11,093	245,000		0	0	256,093
28	0.55	8002	14,549.09	6615			0	0	6615
36	0.6	26,640	44,400	0			0	0	0
37	0.42	14,317	34,088.1	3445			0	0	3445
38	0.49	14,870	30,346.94	0			0	0	0
39	0.24	10,949	45,620.83	7058			0	0	7058
40	0.3	15,133	50,443.33	4541			0	0	4541
41	0.92	18,645	20,266.3	55,086			0	0	55,086
42	0.64	21,087	32,948.44	18,785			0	0	18,785
43	0.97	21,752	22,424.74	23,011			0	0	23,011
47	1.53	28,966	18,932.03	0			192,417	0	192,417
48	0.82	21,599	26,340.24	250,168			0	0	250,168
49	0.62	21,438	34,577.42	26,347			0	72,818	99,165
50	0.61	24,863	40,759.02	0			0	0	0
51	0.55	28,148	51,178.18	0			0	0	0
52	0.5	24,906	49,812	0			0	0	0
53	0.67	23,172	34,585.07	24,482			0	0	24,482
54	1.25	25,983	20,786.4	0			107,240	0	107,240
56	0.40366	1050	2601.199	0			333	0	333
57	0.59	22,429	38,015.25	0			47,173	0	47,173
58	0.71	34,166	48,121.13	17,275			0	0	17,275
59	0.68	26,308	38,688.24	0			0	0	0
60	0.52	23,843	45,851.92	0			0	0	0
62	0.23	7646.76	33,246.78	8474			0	0	8474
63	0.33	18,048	54,690.91	0			0	0	0
64	0.23	16,545	71,934.78	0			4442	0	4442
65	0.52	21,589	41,517.31	0			0	125,294	125,294
66	0.78	18,636	23,892.31	0			43,898	205,935	249,833
67	0.65	27,132	41,741.54	12,575			0	82,280	94,855
69	0.5	16,618	33,236	0			19,764	48,046	67,810
70	0.78	25,563	32,773.08	0		73,780	66,341	103,499	243,620
71	1.05	23,818	22,683.81	0			18,208	188,117	206,325
72	1.69	13,908	8229.586	0			2945	147,562	150,507
Total =	22.22366	657,212.3		468,955	245,000	73,780	502,761	973,551	2,264,047

(yⁱ) and (yⁱⁱ) are the dependent variable and (x) is independent variable.

,

Table A2. Table showing ward-wise open space catchment used for accessibility analysis of urban green open spaces of Area 1.

	Catchment Area (km2)							Vegetation Cover (m2)
Ward Number	Park and Playground Catchment	Open Space Buffer Catchment	Forest Catchment	Water Body Buffer Catchment	Bioconservation Catchment	Overlap	Total Catchment Area (x)	Vegetation Area
27	0.581515	0.769467				0.54	0.810982	150,974.8
28	0.212547	0.102783				0.1	0.21533	7870.677
36	0.031331						0.031331	10,149.51
37	0.398518	0.285463				0.28	0.403981	23,077.77
38	0.246699	0.105255				0.1	0.251954
39	0.238429	0.054541				0.05	0.24297	2980.985
40	0.297839						0.297839	900
41	0.902682						0.902682	94,967.74
42	0.516568						0.516568	18,316.94
43	0.860044			0.018706		0.018706	0.860044	6432.311
47	0.31513			1.5111		0.311256	1.514974	25,183.17
48	0.820696			0.254632		0.254632	0.820696	166,015.8
49	0.610762			0.001762	0.072818	0.001762	0.68358	34,164.42
50	0.280128			0.403702			0.68383	1228.865
51	0.077841			0.108815			0.186656	7945.054
52	0.288402						0.288402	10,012.4
53	0.623077			0.044065		0.031743	0.635399	28,992.08
54	0.055071			1.17471		0.042045	1.187736	4171.736
56	0.087962			0.40366		0.072737	0.418885	3324.926
57	0.030061			0.548167		0.030061	0.548167	20,470.94
58	0.438195			0.194239		0.117962	0.514472	6366.479
59							0	2884.272
60				0.021382			0.021382	22,857.77
62	0.219939			0.169934		0.120957	0.268916	616.2033
63	0.005754			0.107144		0.005365	0.107533
64				0.178609			0.178609	576.3495
65				0.131857	0.125294	0.05465	0.202501	806.1628
66	0.005526			0.355726	0.205935	0.149665	0.417522	12,002.32
67	0.33767			0.127623	0.08228	0.127623	0.41995	1840.573
69	0.153426		0.042381	0.239114	0.048046	0.18	0.302967	28,353.28
70			0.412054	0.371065	0.103499	0.34	0.546618	80,635.9
71			0.309792	0.410574	0.188117	0.22	0.688483	26,776.33
72				0.244294	0.147562	0.035579	0.356277	36,861.86
Total=	8.635812	1.317509	0.764227	7.02088	0.973551	3.184743	15.52724	837,757

and

Table A3. Table showing ward-wise data of served population and per capita open space based on the provided data of urban green open spaces of Area 1.

Ward Number	Park and Playground Served Population	Open Space Buffer Served Population	Forest Served Population	Water Body Buffer Served Population	Bioconservation Served Population	Open Space Served Population	Per Capita Open Space
27	6239.722	8256.468	0	0	0	8701.929	27.12131
28	3092.366	1495.399	0	0	0	3132.856	0.826668
36	1391.096	0	0	0	0	1391.096	0
37	13,584.72	9730.89	0	0	0	13,770.94	0.240623
38	7486.559	3194.167	0	0	0	7646.033	0
39	10,877.33	2488.206	0	0	0	11,084.49	0.644625
40	15,023.99	0	0	0	0	15,023.99	0.300073
41	18,294.03	0	0	0	0	18,294.03	2.954465
42	17,020.11	0	0	0	0	17,020.11	0.890833
43	19,286.27	0	0	419.4772	0	19,286.27	1.05788
47	5966.049	0	0	28,608.18	0	28,681.53	6.642857
48	21,617.33	0	0	6707.069	0	21,617.33	11.58239
49	21,118.57	0	0	60.92541	2517.859	23,636.43	4.625665
50	11,417.74	0	0	16,454.5	0	27,872.24	0
51	3983.761	0	0	5568.954	0	9552.715	0
52	14,365.88	0	0	0	0	14,365.88	0
53	21,549.16	0	0	1523.991	0	21,975.32	1.056534
54	1144.728	0	0	24,417.99	0	24,688.76	4.127314
56	228.8067	0	0	1050	0	1089.603	0.317143
57	1142.777	0	0	20,838.71	0	20,838.71	2.103215
58	21,086.44	0	0	9347	0	24,756.97	0.50562
59	0	0	0	0	0	0	0
60	0	0	0	980.4058	0	980.4058	0
62	7312.264	0	0	5649.759	0	8940.592	1.108182
63	314.6915	0	0	5859.803	0	5881.078	0
64	0	0	0	12848.2	0	12,848.2	0.26848
65	0	0	0	5474.348	5201.87	8407.296	5.803604
66	132.0289	0	0	8499.115	4920.262	9975.564	13.40593
67	14,094.87	0	0	5327.18	3434.494	17,529.36	3.496056
69	5099.267	0	1408.575	7947.193	1596.857	10,069.41	4.080515
70	0	0	13,504.28	12160.94	3391.981	17,914.35	9.53018
71	0	0	7027.263	9313.382	4267.21	15,617.42	8.662566
72	0	0	0	2010.438	1214.374	2932.012	10.82161
Total =	26,2870.6	25,165.13	21,940.12	191,067.6	26,544.91	445,522.9

), Area 2 (as per

Table A4. Table showing ward-wise population data and open space as per Patna Master Plan used for quantitative analysis of urban green open spaces of Area 2.

Area 2 Ward Area and Population				Open Space (m2)
Ward Number	Ward Area (sq km) (yi)	Area 2 Ward Population	Population Density (People/sq km) (yii)	Park and Playground	Open Space Buffer	Forest	Water Body Buffer	Total Open Space (x)
29	1.47	24,863	16,913.61		285,690.3			285,690.3
30	2.04	21,291.21	10,436.87		52,732.3			52,732.3
31	1.38	39,768	28,817.39					0
32	1.07	25,516	23,846.73					0
33	0.66	17,564	26,612.12		21,022.9			21,022.9
34	0.98	17,294	17,646.94		162,245.5		6188.531	168,434.1
35	0.79	18,996	24,045.57		5810.078			5810.078
44	1.89	22,333	11,816.4		110,753.6			110,753.6
45	1.23	27,381	22,260.98		7234.069		400.9238	7634.993
46	2.46	31,876	12,957.72		38,427.81		41,676.61	80,104.42
55	2.42	17,394	7187.603	66,345	17,397.76	153,972.2	10,834.92	248,549.9
56	9.2	23,943.78	2602.585		643,801.6	188,565.2		832,366.9
61	2.91	31,205	10,723.37			1547.791	31,492.33	33,040.12
62	0.65	15,535	23,900		18,205.05			18,205.05
68	2.51	16,396	6532.271		51,581.13	79,464.3	5045.266	136,090.7
72	0.487	6679.68	13,715.98		2741.123			2741.123
Total	32.147	358,035.7		66,345	1,417,643	423,549.5	95,638.57	2,003,176

(yⁱ) and (yⁱⁱ) are the dependent variable and (x) is independent variable.

,

Table A5. Table showing ward-wise open space catchment used for accessibility analysis of urban green open spaces of Area 2.

	Catchment Area (Km2)						Vegetation Cover
Ward Number	Park and Playground Catchment	Open Space Buffer Catchment	Forest Catchment	Water Body Buffer Catchment	Overlap	Total Catchment Area (x)	Vegetation Area (m2)
29		0.64				0.64	107,748.9
30		0.95				0.95	229,646.7
31		0.19		0.006	0.000875	0.195125	26,830.01
32		0.44			0	0.44	19,341.02
33		0.6		0.009	0.009363	0.599637	6552.699
34		0.97		0.52	0.512695	0.977305	13,547.44
35		0.4		0.09	0	0.49	26,982.64
44		1.66			0	1.66	22,935.5
45		1.01		0.42	0.279834	1.150166	6014.755
46		2		1.09	0.784902	2.305098	213,985.5
55	0.71	1.05	0.58	0.54	0.896123	1.983877	66,019
56		5.87	1.56	0.01	1.075522	6.364478	990,637.8
61		0.8	0.49	1.78	0.406194	2.663806	454,782.3
62		0.27	0.27	0.12	0.093846	0.566154	17,635.53
68		1.26	1.03	0.35	0.558424	2.081576	273,871.7
72		0.18	0.05		0.021973	0.208027	28,431.55
Total	0.71	18.29	3.98	4.935		23.27525	2,504,963

and

Table A6. Table showing ward-wise data of served population and per capita open space based on the provided data of urban green open spaces of Area 2.

Ward Number	Park and Playground Served Population	Open Space Buffer Served Population	Forest Served Population	Water Body Buffer Served Population	Open Space Served Population	Per Capita Open Space (m2/Capita)
29		10,824.71	0	0	10,824.71	11.49058
30		9915.027	0	0	9915.027	2.476716
31		5475.304	0	172.9043	5622.993	0
32		10,492.56	0	0	10,492.56	0
33		15,967.27	0	239.5091	15,957.61	1.196931
34		17,117.53	0	9176.408	17,246.44	9.739452
35		9618.228	0	2164.101	11,782.33	0.305858
44		19,615.23	0	0	19,615.23	4.959192
45		22,483.59	0	9349.61	25,603.82	0.278843
46		25,915.45	0	14,123.92	29,868.82	2.513001
55	5103.198	7546.983	4168.81	3881.306	14,259.32	14.2894
56		15,277.18	4060.033	26.02585	16,564.1	34.76338
61		8578.694	5254.45	19,087.59	28,564.97	1.058808
62		6453	6453	2868	13,531.08	1.171873
68		8230.661	6728.239	2286.295	13,597.42	8.300238
72		2468.876	685.7988	0	2853.293	0.410367
Total	5103.198	195,980.3	27,350.33	63,375.67	246,299.7

), and Area 3 (as per

Table A7. Table showing ward-wise population data and open space as per Patna Master Plan used for quantitative analysis of urban green open spaces of Area 3.

Area 3 Ward Area and Population				Open Space (Sqm)
Ward Number	Ward Area(sq km) (yi)	Area 3 Ward Population	Population Density (yii)	Park and Playground	Open Space Buffer	Forest	Water Body Buffer	Total Open Space (x)
2	2.915	33,230	11,399.66					0
3	5.6201	37,524	6676.75					0
4	3.5808	22,509	6286.025		422,446			422,446
5	2.1972	37,704	17,160.02		29,934			29,934
6	1.2132	15,277	12,592.32					0
7	1.5315	30,131	19,674.18					0
8	2.1305	22,634	10,623.8		42,425			42425
9	3.7435	11,653	3112.862	110,951	943,058			1,054,009
10	1.5524	23,387	15,065.06					0
11	4.541	27,265	6004.184		34,034.7			34,034.7
12	0.6901	19,098	27,674.25		5774			5774
13	0.4795	16,978	35,407.72		1391.63			1391.63
14	0.7676	19,434	25,317.87					0
30	1.7261	17,999	10,427.55		69,355.3			69,355.3
15	0.7491	18,147	24,225.07		20,430.1			20,430.1
20	0.6129	16,752	27,332.35		20,145.8			20,145.8
18	0.408	13,877	34,012.25					0
19	0.6036	19,848	32,882.7		922.112			922.112
24	0.6397	16,299	25,479.13		65,108			65,108
25	0.6106	11,522	18,869.96					0
26	0.535	20,515	38,345.79		21,115.9			21,115.9
27	0.9246	9928	10,737.62	13,730				13,730
22	1.3237	28,045	21,186.82		62,603.9		16623.6	79,227.5
23	0.3883	8769	22,583.05		5211.09			5211.09
21	2.2643	23,146	10,222.14		105,067		11,920.6	116,987.6
28	0.4583	6607	14,416.32		84,675.2			84,675.2
1	5.2961	35,074	6622.609		229,034		26221.8	255,255.8
17	0.4463	18,672	41,837.33					0
16	0.3736	11,962	32,018.2					0
22B, 22C	4.7322	72,216	15,260.56		213,780	65497		279,277
Total =	53.0548	666,202		124,681	2,376,512	65,497	54,766	2,621,456

(yⁱ) and (yⁱⁱ) are the dependent variable and (x) is independent variable.

,

Table A8. Table showing ward-wise open space catchment used for accessibility analysis of urban green open spaces of Area 3.

	Catchment Area (Km2)						Vegetation Cover
Ward Number	Park and Playground Catchment	Open Space Buffer Catchment	Forest Catchment	Water Body Buffer Catchment	Overlap	Total Catchment Area (x)	Vegetation Area (m2)
2		0.017195				0.017195	237,730
3		0.490215				0.490215	1,345,210
4		2.95946				2.95946	1,083,580
5		1.03535				1.03535	157,515
6						0	10,185.8
7		0.331357				0.331357	2052.7
8		1.37148				1.37148	144,890
9	1.14995	2.12736			0.208817	3.068493	1,810,240
10	0.028518	0.137937			0.013039	0.153416	98,840.9
11		0.650747				0.650747	860,126
12		0.425443				0.425443	9135.17
13		0.28028				0.28028	20,092.6
14		0.212072				0.212072	90,828
30		0.578561				0.578561	173,556
15	0.075982	0.576644			0.074247	0.578379	136,950
20	0.097228	0.564403			0.057168	0.604463	19,487.3
18						0	0
19		0.392958				0.392958	1005.96
24	0.015735	0.6397			0.015735	0.6397	12,959.9
25		0.398528				0.398528	37,410
26	0.187895	0.5274		0.000047	0.180277	0.535065	3154.96
27	0.327106	0.20887		0.002277	0.107248	0.431005	72,543.2
22		1.23964		0.772256	0.772256	1.23964	10,410.8
23		0.38833				0.38833	3564.66
21	0.043327	1.3611		0.511859	0.362411	1.553875	197,170
28		0.4473		0.165399	0.165399	0.4473	39,192.8
1		2.10279		1.22448	1.1895	2.13777	424,203
17						0	2986.89
16						0	7245.05
22B, 22C		3.43584	1.02	0.40128	1.7	3.15712	473,596
Total =	1.925741	22.90096	1.02	3.077598	4.846097	24.0782	7,341,432

and

Table A9. Table showing ward-wise data of serving population and per capita open space based on the provided data of urban green open spaces of Area 3.

Ward Number	Park and Playground Served Population	Open Space Buffer Served Population	Forest Served Population	Water Body Buffer Served Population	Open Space Served Population	Per Capita Open Space (m2/Capita)
2	0	196.0171	0	0	196.0171	0
3	0	3273.043	0	0	3273.043	0
4	0	18,603.24	0	0	18,603.24	18.76787
5	0	17,766.63	0	0	17,766.63	0.793921
6	0	0	0	0	0	0
7	0	6519.176	0	0	6519.176	0
8	0	14,570.33	0	0	14,570.33	1.874393
9	3579.636	6622.179	0	0	9551.796	90.44958
10	429.6254	2078.029	0	0	2311.221	0
11	0	3907.205	0	0	3907.205	1.248293
12	0	11,773.82	0	0	11,773.82	0.302335
13	0	9924.075	0	0	9924.075	0.081967
14	0	5369.212	0	0	5369.212	0
30	0	6032.976	0	0	6032.976	3.853286
15	1840.669	13,969.24	0	0	14,011.27	1.125811
20	2657.47	15,426.46	0	0	16,521.4	1.202591
18	0	0	0	0	0	0
19	0	12,921.52	0	0	12,921.52	0.046459
24	400.9141	16,299	0	0	16,299	3.994601
25	0	7520.209	0	0	7520.209	0
26	7204.983	20,223.57	0	1.802252	20,517.49	1.029291
27	3512.339	2242.766	0	24.44955	4627.966	1.382957
22	0	26,264.04	0	16,361.65	26,264.04	2.825013
23	0	8769.677	0	0	8769.677	0.594263
21	442.8948	13,913.36	0	5232.296	15,883.93	5.054333
28	0	6448.42	0	2384.445	6448.42	12.81598
1	0	13,925.96	0	8109.252	14,157.62	7.277636
17	0	0	0	0	0	0
16	0	0	0	0	0	0
22B, 22C	0	52,432.83	15,565.77	6123.756	48,179.4	3.867245
Total =	20,068.53	316,993	15,565.77	38,237.65	321,920.7

).

Geographically Weighted Regression—Quantity (Open Space): Map shown in Figure 6
Area 1		Area 2		Area 3
Results
Bandwidth	10,100.65439	Bandwidth	123,110.6601	Bandwidth	75,571.71323
Residual Squares	139,117,335,143.2	Residual Squares	128,119,257,522.7	Residual Squares	946,650,475,913.7
Effective Number	3.872741	Effective Number	3.00729	Effective Number	3.01298
Sigma	69,109.98734	Sigma	99,301.85037	Sigma	187,291.1977
AICc	835.781489	AICc	421.915098	AICc	820.004354
R2	0.404624	R2	0.804623	R2	0.239661
R2 Adjusted	0.345903	R2 Adjusted	0.774438	R2 Adjusted	0.182946
Geographically Weighted Regression—Accessibility (Catchment): Map shown in Figure 7
Area 1		Area 2		Area 3
Results
Bandwidth	4689.309348	Bandwidth	123,110.6601	Bandwidth	3068.400882
Residual Squares	1,002,111,364,037.7	Residual Squares	1,854,515,780,024.8	Residual Squares	7,105,404,734,163.7
Effective Number	5.719825	Effective Number	3.00729	Effective Number	9.253491
Sigma	191,661.2964	Sigma	377,802.9991	Sigma	585,223.6892
AICc	905.090156	AICc	464.673776	AICc	894.366594
R2	0.726975	R2	0.946812	R2	0.703599
R2 Adjusted	0.679738	R2 Adjusted	0.938594	R2 Adjusted	0.585684
Geographically Weighted Regression—Quality (Green Cover): Map shown in Figure 8
Area 1		Area 2		Area 3
Results
Bandwidth	2799.333134	Bandwidth	123,110.6601	Bandwidth	2559.388547
Residual Squares	10,877,730,087	Residual Squares	73,669,178,831	Residual Squares	69,658,099,629
Effective Number	10.909455	Effective Number	4.00948	Effective Number	12.486928
Sigma	22,190.44066	Sigma	78,383.36368	Sigma	63,067.35923
AICc	771.841591	AICc	417.433007	AICc	768.628262
R2	0.792999	R2	0.92553	R2	0.987895
R2 Adjusted	0.700142	R2 Adjusted	0.906839	R2 Adjusted	0.979955

Table 11. Geographically weighted Regression Analysis of different zones and parameters, input data for Area 1 (as per Table A1, Table A2 and Table A3), Area 2 (as per Table A4, Table A5 and Table A6), and Area 3 (as per Table A7, Table A8 and Table A9).

Geographically Weighted Regression—Quantity (Open Space): Map shown in Figure 6
Area 1		Area 2		Area 3
Results
Bandwidth	10,100.65439	Bandwidth	123,110.6601	Bandwidth	75,571.71323
Residual Squares	139,117,335,143.2	Residual Squares	128,119,257,522.7	Residual Squares	946,650,475,913.7
Effective Number	3.872741	Effective Number	3.00729	Effective Number	3.01298
Sigma	69,109.98734	Sigma	99,301.85037	Sigma	187,291.1977
AICc	835.781489	AICc	421.915098	AICc	820.004354
R2	0.404624	R2	0.804623	R2	0.239661
R2 Adjusted	0.345903	R2 Adjusted	0.774438	R2 Adjusted	0.182946
Geographically Weighted Regression—Accessibility (Catchment): Map shown in Figure 7
Area 1		Area 2		Area 3
Results
Bandwidth	4689.309348	Bandwidth	123,110.6601	Bandwidth	3068.400882
Residual Squares	1,002,111,364,037.7	Residual Squares	1,854,515,780,024.8	Residual Squares	7,105,404,734,163.7
Effective Number	5.719825	Effective Number	3.00729	Effective Number	9.253491
Sigma	191,661.2964	Sigma	377,802.9991	Sigma	585,223.6892
AICc	905.090156	AICc	464.673776	AICc	894.366594
R2	0.726975	R2	0.946812	R2	0.703599
R2 Adjusted	0.679738	R2 Adjusted	0.938594	R2 Adjusted	0.585684
Geographically Weighted Regression—Quality (Green Cover): Map shown in Figure 8
Area 1		Area 2		Area 3
Results
Bandwidth	2799.333134	Bandwidth	123,110.6601	Bandwidth	2559.388547
Residual Squares	10,877,730,087	Residual Squares	73,669,178,831	Residual Squares	69,658,099,629
Effective Number	10.909455	Effective Number	4.00948	Effective Number	12.486928
Sigma	22,190.44066	Sigma	78,383.36368	Sigma	63,067.35923
AICc	771.841591	AICc	417.433007	AICc	768.628262
R2	0.792999	R2	0.92553	R2	0.987895
R2 Adjusted	0.700142	R2 Adjusted	0.906839	R2 Adjusted	0.979955

Figure 6. Geographically Weighted Regression map of open space (Census Of India—Population data, Patna Municipal Corporation ward Boundary and Corporation Boundary and area, Master Plan 2031—Open space location, Map Generated in ArcMap 10.4.1).

Figure 6. Geographically Weighted Regression map of open space (Census Of India—Population data, Patna Municipal Corporation ward Boundary and Corporation Boundary and area, Master Plan 2031—Open space location, Map Generated in ArcMap 10.4.1).

Figure 7. Geographically Weighted Regression map of Catchment (Census Of India—Population data, Patna Municipal Corporation ward Boundary and Corporation Boundary and area, Master Plan 2031—Open space location, Map Generated in ArcMap 10.4.1).

Figure 7. Geographically Weighted Regression map of Catchment (Census Of India—Population data, Patna Municipal Corporation ward Boundary and Corporation Boundary and area, Master Plan 2031—Open space location, Map Generated in ArcMap 10.4.1).

Figure 8. Geographically Weighted Regression map of green cover (Census Of India—Population data, Patna Municipal Corporation ward Boundary and Corporation Boundary and area, Master Plan 2031—Open space location, Map Generated in ArcMap 10.4.1).

Figure 8. Geographically Weighted Regression map of green cover (Census Of India—Population data, Patna Municipal Corporation ward Boundary and Corporation Boundary and area, Master Plan 2031—Open space location, Map Generated in ArcMap 10.4.1).

5. Discussion

With the help of the identified parameters quantity, accessibility, and quality and the independent variables, i.e., open space, catchment area, and vegetation cover, the dependent variables of the ward and population density for all the independent variables were analyzed using Pearson correlation and geographically weighted regression analysis. The result shows that within the three areas identified based on the growth pattern, Area 1 is the old area, and Area 2 and Area 3 are the new areas within the Patna Municipal Corporation boundary. Area 2 has a better distribution than the other two areas, with r = 0.89 for quantity and r = 0.96 for accessibility in relation to area. Area 1, as the oldest, has higher density but shows a positive relationship between the area and open space distribution with r = 0.58, and accessibility’s relationship with area is positive at r = 0.62, which is better than the new Area 3 with r = 0.45 and 0.51, respectively. In all the parameters, the relationship of area to population density shows a negative correlation, which shows a lacuna of open space with respect to the population density. Area 3 has a very poor distribution compared to the other two areas in quantity and accessibility, but in terms of vegetation cover it has a good distribution with r = 0.76 in terms of the relationship with ward area and r = 0.76 with open space, which shows that the vegetative cover increases with ward area and also increases with the open space, which means good vegetative cover in the open spaces.

It is observed that in Area 1 (see Table 4) there is 3.7% total vegetative cover, in which eight wards have less than 1 m²/capita, which serves a population of 0.98 lakh people out of 6.5 lakh, and 13 wards are below the URDPFI guideline of 3.16 m²/capita, serving a population of 1.69 lakh. In Area 2, there is 7.7% vegetation cover, in which eight wards are below the standard level of 3.16 m²/capita with a served population of 1.38 lakh out of 3.58 lakh. In Area 3, there is 13.9% vegetation cover, which is the highest among all the areas. It has five wards which have a population with less than 1 m²/capita with a served population of 0.61 lakh and 12 wards that have less than the standard open space with a served population of 1.61 lakh out of 6.66 lakh. As per the projected population (Table 5), the per capita open space for the served population will be less than the standard guideline of 3.16 m²/capita in terms of recreational open space, especially in Area 1, having 1.96 m²/capita, and Area 3, having 2.19 m²/capita (see Table 6 and Table 7).

As per the Pearson correlation, the open space distribution among the areas can be ranked. In quantity, Area 2 has a good distribution, then next is Area 1, then Area 3. In accessibility, Area 2 is also better than Area 1 and then Area 3. In quality, Area 2 is better than Area 3, then Area 1, having much less vegetative cover, is last. In population density, all the areas have a negative correlation.

As per geographically weighted regression and fitting, the independent variables: open space, open space catchment, and vegetation cover, and dependent variables: ward area and population density. The R-square value of Area 2 is R² = 0.8, 0.94, 0.92 for quantity, accessibility, and quality, which is higher than the Area 1 with R² = 0.40, 0.72, 0.79 and Area 3 with R² = 0.23, 0.70, 0.98 for quantity, accessibility, and quality, respectively. In addition, AICc and sigma square show that Area 2, which has a smaller value for these two, suggests a better fit compared to the other two.

The result shows that as per geographically weighted regression analysis, Area 2 also has a better distribution than Area 1 and then Area 3. So, both the analyses show that the area identified as per the growth pattern and the master plan zoning of the proposed open space distribution does not support the relationship of the new area with more open space in terms of the availability of land. Instead, the intermediate growth zone has a better distribution than the old and new areas.

The geographically weighted regression map shows that in Area 1, 13 wards have a standard deviation of −0.5 to −1.5 compared to Area 2. In Area 3, six wards have a negative standard deviation from the mean open space area. Area 2 has four wards with a negative standard deviation. Area 2 is equally distributed (see Figure 6). In terms of accessibility, the model shows a good fit in terms of predicted vs. observed catchments, especially in Area 1 and Area 2 (see Table 11, Figure 7). In terms of quality, that is, the green cover, Area 3 has a good fit as per the predicted and observed green cover. Then comes Area 2 and, finally, Area 1 (see Figure 8). Although Area 3 has a good green cover, as per the geographically weighted regression map, it has more gray and blue colors in wards, representing negative green cover in many of the wards, which shows that it is not appropriately distributed based on the variables.

Related ward-wise (micro-level) and zone-wise (meso-level) data used for the analysis, such as per capita open space, catchment area, served population, and vegetation cover, are given in Appendix A, Appendix B, Appendix C. The open space map and catchment area map are in Appendix A for Area 1 (Figure A1), Appendix B for Area 2 (Figure A2), and Appendix C for Area 3 (Figure A3) for reference.

As per the study, the newer area also faces a shortage in urban green open space both in terms of quantity and accessibility compared to the older areas, which shows the issue at the policy level of the planning. The policy should be in terms of the quantity (per capita open space of the micro level), accessibility (urban green open space serving the population), and quality in terms of vegetation cover to maintain the overall quality of the urban landscape, especially in the newer area. As per the quantitative analysis, most of the area still needs to reach the required standard of per capita urban green open space as specified by URDPFI. For a historic city such as Patna, with space crunch, or the core city area such as Area 1 in this study, the alternative potential urban green open spaces have to be identified. The potential urban green open spaces, such as road verges, railway verges, spaces under flyovers, spaces along canals or open drains, other urban green space systems, etc., should be included as urban green open spaces in the development plan. A green open space conservation plan should be implemented where there is a shortage. Encroachment in these spaces should also be monitored as it will lead to a further reduction in the number of urban green open spaces.

Green spaces act as carbon sequesters [36,37]. Urban planning effort should be made to save these green areas which are also carbon reservoirs. The conservation of these urban green open spaces will also support the aim of missions such as the National Mission of Green India and National Mission on Sustainable Habitat to enhance carbon sink potential in urban areas [38]. As per the result, green cover is greater in the newer areas as compared to the older area, and an increase in the urban green open spaces will also increase the carbon sink potential of the city [39]. In newer areas, more open spaces are present, which should be conserved and managed. The conservation of open spaces and making them more accessible will fulfill Sustainable Development Goals 11 and 13 of the United Nations.

6. Conclusions

This study has tried to understand the open space distribution at the micro and meso levels with respect to its quantity, quality, and accessibility based on the growth pattern of the city. This is the first time the assessment of urban green open space with the identified parameters of quantity, quality, and accessibility has been carried out based on the growth pattern of the city. The study tried to answer the research question given in the Introduction section for the study area of Patna Municipal Corporation.

The distribution, as per Table 8, Table 9 and Table 10, of the Pearson correlation of all the zones has a positive relationship with the ward area and open space, which shows that the open space is distributed as per the ward area sizes. However, the strength of Area 1 (r = 0.58) and Area 3 (r = 0.45) is lower, which means that many open spaces are not well distributed in these zones as per the ward area. Compared to the other zones, Area 2 has r = 0.89, which is a comparatively high value showing that most of the areas are well distributed based on the ward area. However, not all the zones are well distributed as per the population density and they show a negative correlation. This means that the open spaces are not distributed according to population density. This answers the first research question.

The distribution pattern does not depend only on the growth pattern of the city, as we can see that the intermediate meso area with r = 0.89 and r² = 0.8 (Area 2) has more distributed open space than the newer (r = 0.45, r² =0.23) and older area (r = 0.58, r² = 0.40). However, the vegetation cover is greater in the new areas than in the older areas because of the availability of vacant land. Additionally, the vegetation cover depends on the new area and the land use, as more vegetation cover is found in the public semi-public land use than the other land uses, and this answers the second question.

All three areas’ open space distribution has negative relation with the population density although it has positive relation with the area. In addition, the intermediate growth area, that is, Area 2, has good accessibility, distribution of open space, and vegetative cover distribution, compared to the other areas. The open space distribution and accessibility distribution are poorer in the new areas (Area 3) compared to the older area (Area 1). As per the population data of 2011, the open space per capita is 4.1 m²/capita. However, as per the projection by the City Development Plan 2030, the population will reach 30 lakh so there will be only 2.33 m²/capita of open space, which is again less than the open space standard by URDPFI.

There is a need to identify the potential green open space in Patna City, especially in the older area, other than the formal green open spaces such as parks and playgrounds for public use. As per Rupprecht, it is observed that parks no longer seem up to the task of meeting residents’ green space needs [40]. It is suggested that informal green spaces (IGSs) exist even when development pressure is high. So, the identification of the potential green space is needed in the city to meet the public space demand [41]. The open space has to be identified at micro and meso levels to have proper accessibility for proper distribution.

This study has been limited to the historic city of Patna as an example facing population explosion issues, and the urban green open spaces identified as per the city’s master plan. The future scope of this research can include the study of other tier 2 cities or cities having urban population expansion issues based on the given parameters. Research can also be carried out for the other types of informal urban green open spaces such as street verges, railway verges, and others, which have potential as urban green open spaces of Patna City or other cities. The growth patterns taken for this study are based on the historical evolution to obtain clear demarcation based on a previous map and article [29] as it is a historical city, and for the current study, the ward-level population and ward-level area were required which would not have been possible in the LULC change boundary using remote sensing. However, for newer cities, the evolution can be taken for decadal change based on remote sensing data with LULC change or nighttime light data [42,43].