1. Introduction

2. Conceptualising Urban Growth from a Morphological Perspective

2.1. Spreading Pancake

Proximity to the city centre influences urban growth and form. Accessibility to the centre (regarding travel time) is crucial for residents because this part of the metropolitan area has high concentrations of urban services and jobs (livelihoods) they need to access. Therefore, locations near the centre experience more intense growth than the edges [18,30]. However, over time, as population, economic activities and demand for space grow, space at and around the centre gets exhausted, and growth spreads horizontally to the urban fringe in a manner akin to a spreading pancake [28] (see Figure 2(a)). Reminiscent of von Thünen’s 1826 agricultural land use model and the monocentric bid-rent model popularised by William Alonso, Richard Muth and Edwin Mills in the 1960s and 1970s, the spreading pancake model assumes the existence of a dominant central city that drives outward urban growth in concentric waves across a metropolitan area [18,31]. Thus, based on the spreading pancake hypothesis, locations at the Densu Delta Ramsar site that are closer to Accra, the central city, are expected to experience more significant amounts of physical growth than locations that are farther from the city.

Figure 2. Patterns of Horizontal Urban Growth. Source: Authors’ construct

Figure 2. Patterns of Horizontal Urban Growth. Source: Authors’ construct

3. Materials and Methods

3.1. The Study Setting

The 5,893-hectare Densu Delta wetlands were designated a Ramsar site in 1992 [36]. Located between latitudes 5°29'45"N and 5°34'20"N and longitudes 0°15'33"W and 0°23'16"W, the site straddles the Ga South and Weija-Gbawe Municipalities in the Greater Accra Region (see Figure 3). The Gulf of Guinea also bounds it in the south and the Weija Lake (an artificial lake created by constructing the Weija Dam on the Densu River) in the northwest. The eastern half of the protected site, where the core wetlands are located, is generally flat and low-lying, with an elevation of less than 5m above sea level. However, the eastern half is primarily hilly, rising to 100m above sea level.

Figure 3. Physical Features of Densu Delta Ramsar Site. Source: Authors’ construct

Figure 3. Physical Features of Densu Delta Ramsar Site. Source: Authors’ construct

The wetland ecosystem within the protected area includes a delta formed by the Densu River, lagoons, salt pans, freshwater marshes and scrubs, and streams [37]. During the dry season, water flow from the Densu River to the wetlands is interrupted by the Weija Dam, located approximately 11 km upstream [38]. However, during the rainy season, excess water from the dam is discharged downstream, and this, together with an increased volume of water from surrounding streams and surface runoff, causes the delta and the lagoons to overflow their banks, leading to flooding in low-lying communities such as Gbegbeyise and Glefe. The seasonal flooding also brings detritus, nutrients and pollution [39]. The vegetation at the site comprises about 136 plant species made up of 50 flowering plant families, including mangroves, reeds and sedges [37]. The site also serves as a habitat for about 35,000 birds belonging to 57 species; reptiles such as snakes, lizards and turtles; mammals; marine and freshwater fish and shellfish species; and other invertebrates [37,40].

Notable communities within the protected area are Bortianor, Kokrobite, Oshieyie, Aplaku, Tetegu, Gbegbeyise and Glefe, all existing before the Ramsar site designation. Spillovers from the growth of Accra have resulted in rapid population growth in these and other peri-urban communities. For instance, available census data show that the combined population of the above communities was only 3,669 in 1970 but increased dramatically to 28,216 in 2000 and 87,852 in 2010. Similarly, the combined population of four communities close to the protected area—Malam, McCarthy Hill, Mpoase and Oblogo—increased from 3,954 to 50,530 between 1970 and 2010, respectively.

The main economic activities at the protected area before its Ramsar site designation included fishing, crop farming and salt winning [37]. However, crop farming is currently limited while industrial and commercial activities have become predominant. The rapid growth in population and non-farm economic activities has accelerated the construction of residential and other buildings, leading to significant loss and degradation of the wetlands.

3.2. Study Methodology

The aim of the study, which commenced in 2023, is to analyse the magnitude, speed and morphological patterns of urban growth at the Densu Delta Ramsar site. it also analyses the extent to which this growth has been driven by proximal factors such as the presence of the city of Accra, road network, and nearby village magnets. To achieve this, satellite images were acquired and analysed using various geospatial and statistical techniques, which were supplemented by ground truthing and limited interviews by the researcher during visits to the study area.

3.2.1. Land Use/Land Cover Analysis

The loss of the Ramsar site to urban growth was preliminarily assessed though spatio-temporal analysis of land use/land cover (LULC) data. The LULC analysis spanned a 20-year period, from 2003 to 2023. The choice of this period was informed by the fact that most of the urban growth at the site occurred during this period.

Data were obtained from the United States Geological Survey’s (USGS’s) Landsat images [41]. Data for 2003, 2008 and 2013 were obtained from Landsat 7 images while data for 2018 and 2023 were from Landsat 8 and Landsat 9, respectively (Table 1). With the aid of version 3.34 of the QGIS software, the images were processed and classified using the supervised classification method. The classes were vegetation (including reeds, shrubs, grass and croplands), water (including rivers, streams, lagoons, ponds and salt pans), bare land (scraped surfaces, sandy surfaces, etc) and built-up areas (including buildings, roads and other artificially constructed physical structures).

3.2.2. Using Geospatial Technology to Compute ABCRs

The study used ABCRs (aggregate building coverage ratios) to measure and analyse the magnitude, speed and pattern of physical urban growth at the study site between 2013-2023. ABCR is a modified version of building coverage ratio (BCR). BCR, also known as site coverage, is a zoning concept used to regulate the intensity of urban land use. It is defined as the ratio of the coverage area of the building(s) or other physical structures erected on a single plot to the total plot size when viewed vertically from the sky [42,43]. Similarly, the term ABCR is used in this study to refer to the ratio of the aggregated coverage area of all building(s) erected in a sector to the total sector area. A sector comprises multiple plots.

Generation of data for the computation of ABCRs was done using the ArcGIS (version 10.8.2) software to digitise the coverages of all existing buildings at the study site based on high-resolution satellite images extracted from the Google Earth application for the years 2013, 2018 and 2023. The same software and images were used to digitally divide the site into ‘sectors’ using roads, streams and other physical barriers as boundaries. This is illustrated in Figure 4.

Figure 4. Building coverages in a sector. Source: Authors’ construct

Figure 4. Building coverages in a sector. Source: Authors’ construct

Based on the digitised data (in the form of shapefiles), sector and building coverage areas were electronically computed in ArcGIS, which in turn allowed the ABCR of each sector to be computed as:

$$ABCR=\left(\frac{\sum _{i=1}^n{A}_i}{B}\right)\times 100$$

(1)

where

A_i = Coverage area of building i (in m²)

B = Sector area (in m²)

0 ≤ ABCR ≤ 100

3.2.3. Variable Description

The main variables used for data generation and analysis included ABCRs, changes in ABCRs and proximity to the three urban growth drivers—Accra, arterial roads, and village magnets. The major arterial, a segment of the N1 highway connecting Accra to the southwestern part of the country and Abidjan (Cote d’Ivoire), forms the northern boundary of the Ramsar site. In contrast, the minor arterial is a 15.8-kilometre paved secondary road connecting communities at the site to the N1 highway. The pre-existing peri-urban localities serving as village magnets include Kokrobite, Oshiyie, Bortianor, Aplaku, Glefe and Gbegbeyise (see Figure 5).

Figure 5. Map of Densu Ramsar Site Showing Urban Growth Drivers. Source: Authors’ construct

Figure 5. Map of Densu Ramsar Site Showing Urban Growth Drivers. Source: Authors’ construct

In addition to the growth drivers, the possible effects of natural features on urban growth were controlled for. These include steep terrain and nearness to marshy areas, both of which were assumed to inhibit growth (see Table 2).

Table 2. Description of Variables.

Table 2. Description of Variables.

Variable Name	Description/Measurement	Variable Type
Outcome variables:
ABCR13	ABCR in 2013	Continuous
ABCR18	ABCR in 2018	Continuous
ABCR23	ABCR in 2023	Continuous
CHNGE1	Absolute change in ABCR, 2013-2018	Continuous
CHNGE2	Absolute change in ABCR, 2018-2023	Continuous
CHNGE3	Absolute change in ABCR, 2013-2023	Continuous
Predictors:
ACC	Distance from Accra (km) squared	Continuous
VILL	Located within 1 km of a village magnet	Dichotomous (Yes = 1, No = 0)
ROAD1	Located within 1 km of a major arterial road	Dichotomous (Yes = 1, No = 0)
ROAD2	Located within 1 km of a minor arterial road	Dichotomous (Yes = 1, No = 0)
WET	Located within 1 km of the wetland core	Dichotomous (Yes = 1, No = 0)
ELEV	Elevation exceeding 50m above sea level	Dichotomous (Yes = 1, No = 0)

Source: Author’s construct.

3.2.4. Statistical analytic Techniques

With the sectors serving as units of analysis, the study employed tables, graphs, maps and other descriptive statistical tools to analyse the magnitude, patterns and trend/rate of physical growth based on the outcome variables listed in Table 2. To test the spreading pancake, ribbon development, and village magnet hypotheses, multivariate regression techniques were employed to establish the statistical significance of the growth drivers on the outcome variables. This began with fitting an ordinary least square (OLS) multiple linear regression model, which is of the form:

$$Y=\alpha +{\beta }_1{X}_1+{\beta }_2{X}_2+{\beta }_3{X}_3+\dots +{\beta }_k{X}_k+ϵ$$

(2)

where

Y = outcome variable;${\mathit{X}}_{\mathit{i}}=$ predictors; $\mathit{\alpha }$ = intercept;${\mathit{\beta }}_{\mathit{i}}=$ coefficient of ${\mathit{X}}_{\mathit{i}}$; $\mathit{ϵ}$ = error term

Various diagnostic procedures were conducted to check for five multiple linear regression assumptions: normality, linearity, non-multicollinearity, multivariate normality, homoscedasticity and absence of autocorrelation. A Jarque-Bera normality test showed that the predictor ACC violated the normality assumption, and this was resolved by squaring the variable (renamed as ACC2). There were no serious violations of the linearity assumption.

Multicollinearity tests using scatterplots, correlation coefficients and variance inflation factors (VIFs) showed that the variables ACC2 and WET were highly correlated with a Pearson correlation coefficient of –0.73, while the remaining predictors showed very low multicollinearity. Hence ACC2 was retained while WET was dropped.

Although Jarque-Bera tests for normality showed some violation of the multivariate normality assumption, visual examinations of kernel density histograms showed the extent of violation was minimal. Besides, non-normality of residuals does not seriously affect the F-statistic regression coefficients and other related hypothesis-testing procedures in terms of significance and power [44].

Visual inspection of scatterplots of residuals against fitted values of the outcome variables and formal Breusch-Pagan/Cook-Weisberg tests showed no severe violation of the homoscedasticity assumption. However, as expected, a visual inspection of choropleth maps of ABCRs and ABCR changes revealed some clustering in the distribution of these variables, implying a possible spatial autocorrelation. A formal diagnosis was conducted using Moan’s tests. Moran’ I, which is based on spatial weighting, defined as:

$$\frac{n}{W}\ast \frac{{\sum }_i{\sum }_j{w}_{ij(x_i-\overline{x})(x_j-\overline{x})}}{{\sum }_i{(x_i-\overline{x})}^2}$$

(3)

where:

n is the number of spatial units indexed by i and j

x is the variable of interest with $\overline{x}$ being the arithmetic mean of x

w is a matrix of spatial weights

W is the sum of all w_ij

A joint Moran test based on contiguity and inverse distance weighting matrices showed no statistically significant spatial dependence in three outcome variables—CHANGE1, CHANGE2 and CHANGE3 (see Table 3). Therefore, the OLS linear regression method was maintained for these variables, with the model being specified as:

$$\mathrm{C}\mathrm{H}\mathrm{A}\mathrm{N}\mathrm{G}\mathrm{E}1={\alpha }_1+{\beta }_{11}\mathrm{A}\mathrm{C}\mathrm{C}2+{\beta }_{12}\mathrm{R}\mathrm{O}\mathrm{A}\mathrm{D}1+{\beta }_{13}\mathrm{R}\mathrm{O}\mathrm{A}\mathrm{D}2+{\beta }_{14}\mathrm{V}\mathrm{I}\mathrm{L}\mathrm{L}+{\beta }_{15}\mathrm{W}\mathrm{E}\mathrm{T}+{\beta }_{16}\mathrm{E}\mathrm{L}\mathrm{E}\mathrm{V}+{ϵ}_1$$

(4a)

$$\mathrm{C}\mathrm{H}\mathrm{A}\mathrm{N}\mathrm{G}\mathrm{E}2={\alpha }_2+{\beta }_{21}\mathrm{A}\mathrm{C}\mathrm{C}2+{\beta }_{22}\mathrm{R}\mathrm{O}\mathrm{A}\mathrm{D}1+{\beta }_{23}\mathrm{R}\mathrm{O}\mathrm{A}\mathrm{D}2+{\beta }_2\mathrm{V}\mathrm{I}\mathrm{L}\mathrm{L}+{\beta }_{25}\mathrm{W}\mathrm{E}\mathrm{T}+{\beta }_{26}\mathrm{E}\mathrm{L}\mathrm{E}\mathrm{V}+{ϵ}_2$$

(4b)

$$\mathrm{C}\mathrm{H}\mathrm{A}\mathrm{N}\mathrm{G}\mathrm{E}3={\alpha }_3+{\beta }_{31}\mathrm{A}\mathrm{C}\mathrm{C}2+{\beta }_{32}\mathrm{R}\mathrm{A}\mathrm{D}1+{\beta }_{33}\mathrm{R}\mathrm{O}\mathrm{A}\mathrm{D}2+{\beta }_{34}\mathrm{V}\mathrm{L}\mathrm{L}+{\beta }_{35}\mathrm{W}\mathrm{E}\mathrm{T}+{\beta }_{36}\mathrm{E}\mathrm{L}\mathrm{E}\mathrm{V}+{ϵ}_3$$

(4c)

However, for the outcome variables ABCR12, ABCR17 and ABCR22, serious spatial autocorrelation problems were found (see Table 3). This was resolved by using spatial autoregressive (SAR) models in place of OLS regression models.

The SAR model is of the form:

$$Y=\alpha +{\sum }_{i=1}^k{\beta }_i{X}_i+\lambda Wy+{(I-\rho W)}^{-1}ϵ$$

(5)

where

Y is the outcome variable; $\mathit{\alpha }$ is the intercept; ${\mathit{X}}_i$ are predictors; ${\mathit{\beta }}_i$ are coefficients $X_i$; $\mathit{W}\mathit{y}$ is a spatial lag of Y based on weighting matrix $\mathit{w}$ with $\mathit{\lambda }$ as its coefficient; and${(\mathit{I}-\mathit{\rho }\mathit{W})}^{-1}\mathit{ϵ}$ represents a spatial lag of the autoregressive error term $\mathit{ϵ}$ with $\mathit{\rho }$ rho being autocorrelation parameter and I being an identity matrix.

Thus, based on the variables under consideration, the SAR model was specified for each of the three outcome variables (ABCR12, ABCR17 and ABCR22) as:

$$\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{R}12={\alpha }_1+{\beta }_{11}\mathrm{A}\mathrm{C}\mathrm{C}2+{\beta }_{12}\mathrm{R}\mathrm{O}\mathrm{A}\mathrm{D}1+{\beta }_{13}\mathrm{R}\mathrm{O}\mathrm{A}\mathrm{D}2+{\beta }_{14}\mathrm{V}\mathrm{I}\mathrm{L}\mathrm{L}+{\beta }_{15}\mathrm{W}\mathrm{E}\mathrm{T}+{\beta }_{16}\mathrm{E}\mathrm{L}\mathrm{E}\mathrm{V}+{\lambda }_1{W}_{ABCR12}+{(I-{\rho }_{1}W)}^{-1}{ϵ}_1$$

(6a)

$$\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{R}17={\alpha }_2+{\beta }_{21}\mathrm{A}\mathrm{C}\mathrm{C}2+{\beta }_{22}\mathrm{R}\mathrm{O}\mathrm{A}\mathrm{D}1+{\beta }_{23}\mathrm{R}\mathrm{O}\mathrm{A}\mathrm{D}2+{\beta }_{24}\mathrm{V}\mathrm{I}\mathrm{L}\mathrm{L}+{\beta }_{25}\mathrm{W}\mathrm{E}\mathrm{T}+{\beta }_{26}\mathrm{E}\mathrm{L}\mathrm{E}\mathrm{V}+{\lambda }_2{W}_{ABCR17}+{(I-{\rho }_{2}W)}^{-1}{ϵ}_2$$

(6b)

$$\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{R}22={\alpha }_3+{\beta }_{31}\mathrm{A}\mathrm{C}\mathrm{C}2+{\beta }_{32}\mathrm{R}\mathrm{O}\mathrm{A}\mathrm{D}1+{\beta }_{33}\mathrm{R}\mathrm{O}\mathrm{A}\mathrm{D}2+{\beta }_{34}\mathrm{V}\mathrm{I}\mathrm{L}\mathrm{L}+{\beta }_{35}\mathrm{W}\mathrm{E}\mathrm{T}+{\beta }_{36}\mathrm{E}\mathrm{L}\mathrm{E}\mathrm{V}+{\lambda }_3{W}_{ABCR22}+{(I-{\rho }_{3}W)}^{-1}{ϵ}_3$$

(6c)

The generalised spatial two-stage least squares (GS2SLS) estimator, robust to violations of the assumption of normally distributed residuals [45], was used to fit the SAR model.

3.2.5. Ground Truthing and Interviews

In addition to generating geospatial data from satellite images, the study involved ground truthing and key informant interviews. The ground truthing exercise involved the research team paying visits to the study site to relate the remotely sensed data with features on the ground. The visits, which were necessary to aid data interpretation, offered the team the opportunity to directly observe the state of the wetlands, the nature of buildings constructed, and other human activities taking place at the site, as well as identify the use of the structures constructed at the site. In all, the uses of 163 randomly selected completed buildings were identified.

The key informant interviews were conducted with purposively selected officials of four key state agencies responsible for protecting wetlands against uncontrolled urban growth: Environmental Protection Agency, Wildlife Division of the Forestry Commission, Water Resource Commission, and the Ga South Municipal Assembly. The interviews focused on reasons for physical development at the study site despite its official status as a protected Ramsar site.

4. Results

4.1. Land Cover Depletion at the RAMSAR site

Results of the LULC analysis show a dramatic transformation of the Densu Delta Ramsar site over the last 20 years. As Figure 6 and Figure 7 show, all the four landcover classes have undergone either an increase or a reduction in size, with vegetation and built-up area showing the most remarkable changes. For instance, while the built-up area more than tripled between 2003-2023, vegetation declined by 77% during the same period. Apart from vegetation, there were also considerable declines in the area occupied by bare land and water (see Figure 7).

Change detection analysis reveals that, between 2003 and 2023, all the four land cover classes lost and gained land from each other (see Figure 8). As expected, the largest change, amounting to 1,912 hectares, was from vegetation to built-up area, followed by bare land to built-up area (789 hectares). Overall, the built-up area gained 2,907.4 hectares and lost only 28.24 hectares while vegetation gained only 2,77.3 hectares and lost 2,214.2 hectares. Also, water lost 493.7 hectares and gained only 81.5 hectares. In summary, most of the natural landcover (vegetation and water) at the Ramsar site has been lost to urban growth (built-up area), which has serious implications for environmental sustainability.

Figure 8. Landcover Change Detection between 2003 and 2023. Source: Authors’ construct

Figure 8. Landcover Change Detection between 2003 and 2023. Source: Authors’ construct

4.2. Magnitude and Trend Of Building Coverage

The preceding sub-section has shed light on the extent to which natural landcover has been indiscriminately built up during the last 20 years. This and subsequent sections provide a close-view analysis of the magnitude and spatial patterns of building construction, which makes up most of the built-up area, and how these have changed over the last 10 years (2013-2023).

The data show considerable growth in the number of buildings and building coverage between 2013-2023. In 2013, the site had 43,243 buildings, which increased to 45,659 in 2018 and 46,850 in 2023, representing an overall increase of 8.3% between 2013-2023. As Figure 9 shows, this translated into growth in total building coverage (land take) from 626.8 hectares (or 10.6% of the total area of the study site) in 2013 to 789.6 hectares (or 13.4%) and 855.3 hectares (or 14.5%) in 2018 and 2023, respectively. It also means that building coverage growth rate rose from 32.6 hectares per annum between 2013-2018 to 13.15 hectares per annum between 2018-2023. At the 2018-2023 growth rate, the total building coverage is projected to reach 986.8 hectares by 2032 if measures are not taken to slow physical development.

Figure 9. Total Building Coverage, 2013-2032. Source: Authors’ construct.

Figure 9. Total Building Coverage, 2013-2032. Source: Authors’ construct.

The field data show that the buildings constructed at the site were predominantly residential structures. Out of the 163 randomly selected buildings directly observed on the field as part of the ground-truthing, as many as 144 (or 88%) were residential structures. In comparison, the remaining 12% included churches and mosques, school buildings and commercial buildings. Also, building construction occurred on both dry ground and at locations where the landscape is low-lying, waterlogged and highly flood-prone. For instance, at Glefe, one of the flood-prone communities, land was being reclaimed from Lagoons and marshes for building construction.

4.3. Spatial Pattern of Building Coverage

Visual examination of the spatial distribution of buildings shows that, between 2013-2023, building construction was more concentrated at specific locations than others. Locations with exceptionally high concentrations included the eastern edge of the study site, which happens to be closest to Accra. High concentrations were also recorded around Glefe, Gbegbeyise and the other village magnets and along the arterial roads. Areas of low concentration included the southwestern portion of the site and areas immediately surrounding the wetland core (see Figure 10).

Figure 10. Spatial Pattern of Buildings, 2013-2023.Source: Authors’ construct.

Figure 10. Spatial Pattern of Buildings, 2013-2023.Source: Authors’ construct.

The spatial patterns of building coverage described above were confirmed by analysis of ABCR patterns. From 2013 to 2023, ABCRs were persistently high in sectors within the corridors of the major and minor arterial roads, except those located along the Kokrobite-Tuba Junction stretch of the minor arterial, where there was little building construction (see Figure 11). For instance, in 2023, seven (7) out of the ten sectors with the highest ABCRs (ranging from 29.3 to 53.1) either abutted or were located within one kilometre of a major or minor arterial. In addition, the ABCRs of sectors located within the immediate environs of the six village magnets were relatively high, with the top three sectors (with ABCRs of 37.6, 50.0 and 53.1, respectively) being located within the Glefe-Gbegbeyise enclave. Overall, sectors along the eastern boundary of the study site (i.e. those closest to Accra) recorded a mean ABCR of 30.5 in 2023, compared to the overall mean of 21.5.

Figure 11. Spatial Pattern of ABCRs, 2013-2023.Source: Authors’ construct.

Figure 11. Spatial Pattern of ABCRs, 2013-2023.Source: Authors’ construct.

4.4. Growth in Building Coverage

Between 2013 and 2023, about 92.2% of the 102 sectors recorded positive growth in ABCR, while the remaining 7.8% recorded either zero or negative growth. However, most of the growth occurred between 2013-2018, during which period the average sector recorded an ABCR change of 27.9%, compared to the 2018-2023 period, when the corresponding change was only 8.1%. This was because the rate of building construction slowed down during the latter period.

As Figure 12 shows, the absolute increase was more significant in sectors located along the segment of the major arterial east of Old Barrier and the Old Barrier-Kokrobite stretch of the minor arterial, as well as those located around village magnets or near Accra. The fact that sectors with the highest ABCRs in 2013 recorded the most significant increase in ABCR means that, between 2013-2023, already built-up sectors experienced considerable consolidation and in-fill development in building construction.

Figure 12. Absolute Change in ABCR, 2013-2023.Source: Authors’ construct.

Figure 12. Absolute Change in ABCR, 2013-2023.Source: Authors’ construct.

While the spatial distribution of absolute ABCR change showed clear patterns, relative ABCR change was substantially uniform, with 67 out of the 102 sectors recording a 25-50% increase. As Figure 13 shows, there was a slight spatial variation in percentage growth in ABCR between 2013 and 2023, except in the western end of the study site and areas along the Old Barrier-Tuba Junction stretch of the major arterial where nine sectors recorded between -35.3% and 0.8% change. The relatively slow pace of ABCR growth in the western end of the study site could partly be attributed to the hilly terrain. This part of the study area also included a 40-hectare protected farmland (near the village of Tuba), forming part of the Tuba Irrigation Scheme. It is also significant to note that Glefe, Gbegbeyise and Tetegu communities, together with their immediate environs, where the landscape is low-lying, waterlogged and highly flood-prone, experienced almost the same amount of relative ABCR growth as other locations.

Figure 13. Percentage Change in ABCRs.Source: Authors’ construct.

Figure 13. Percentage Change in ABCRs.Source: Authors’ construct.

4.5. Statistical Significance of the Effects of Growth Drivers

Data presented under the preceding sub-sections suggest, rather descriptively, that the hypothesised growth drivers (i.e. proximity to Accra, arterial roads and village magnets) influenced the spatial pattern and growth of building coverage at the study site. This sub-section presents the results of OLS regression and SAR models to ascertain the statistical significance of these revelations. As indicated earlier, the SAR technique was used to assess the effects of the growth drivers on the spatial distribution of ABCRs, while OLS regression was used to assess their effects on ABCR changes.

4.5.1. Effects on the Spatial Distribution of ABCRs (SAR Models)

The results in Table 4 show that ACC2, VILL and ROAD1 significantly influenced the spatial patterns of ABCRs throughout the period 2013-2023. For instance, ABCRs were higher in sectors close to Accra (ACC2) than those located farther away from the city. In other words, as suggested by the spreading pancake hypothesis, the SAR models show that distance from Accra negatively impacted ABCR values, after accounting for spatial autocorrelation and the effects of other growth drivers. Similarly, sectors located within 1km of a village magnet (VILL) or the N1 highway (ROAD1) recorded higher ABCRs than those located elsewhere. That is, in consonance with the village magnet and ribbon development hypotheses, proximity to the five village magnets and the N1 highway positively impacted ABCRs, even after accounting for spatial autocorrelation and proximity to Accra. However, the effects of ROAD2 and ELEV were found to be statistically insignificant as their p-values exceeded the 5% alpha level.

Table 4. Spatial Autoregressive (SAR) Models of ABCR.

Table 4. Spatial Autoregressive (SAR) Models of ABCR.

Predictors	Model 1 (y = ABCR12)			Model 2 (y = ABCR17)			Model 3 (y = ABCR22)
	Coefficient	Std. err.		Coefficient	Std. err.		Coefficient	Std. err.
$Alpha\left({\alpha }_i\right)$	13.086***	2.297		18.448***	2.772		20.662***	3.008
ACC2	-0.020***	0.008		-0.032***	0.009		-0.037***	0.010
VILL	3.886*	2.084		5.343**	2.420		5.835**	2.599
ROAD1	4.539***	1.732		4.681**	1.976		4.864**	2.115
ROAD2	-1.305	1.777		-1.707	2.102		-1.617	2.275
ELEV	-0.965	1.560		-2.057	1.780		-2.399	1.905
$Lambda{(\lambda }_i)$	0.283**	0.139		0.270**	0.136		0.257*	0.137
$Rho{(\rho }_{i)}$	0.444*	0.253		0.428	0.275		0.429	0.279
Wald test of spatial terms [chi2(2)]	17.1***	--		13.5***	--		12.4***	--
Pseudo R2	0.289	--		0.379	--		0.406	--
Wald chi2(6)	37.650***	--		55.020***	--		60.210***	--
Number of observations	102			102			102

* p≤0.10; ** p≤0.05; *** p≤0.01; Source: Authors’ construct.

4.5.2. Effects on ABCR Change (OLS Regression)

Table 5 shows the influence of ACC2, VILL, ROAD1 and ROAD2 on changes in ABCR between 2013-2018 (Model 1), 2018-2023 (Model 2) and 2013-2023 (Model 3) after controlling for terrain and base-year ABCRs. It shows a significant negative relationship between ABCR change and distance from Accra (ACC2) in all three periods. That is, in line with the spreading pancake hypothesis, sectors closer to Accra registered higher amounts of absolute growth in ABCR than those located farther away. During the period 2018-2023, sectors located within 1km of the N1 highway (ROAD1) registered lower amounts of absolute growth in ABCR than those located more than 1km away. This was probably because sectors within the immediate vicinity of the highway were nearing the point of saturation, so building construction had slowed down there. The data also show that sectors with elevations (ELEV) exceeding 50m above sea level registered lower absolute growth in ABCR than those on lower grounds. However, proximity to the village magnets (VILL) and the minor arterial (ROAD2) had no statistically significant influence on ABCR change.

Table 5. Ordinary Least Square (OLS) Regression Models of ABCR Change.

Table 5. Ordinary Least Square (OLS) Regression Models of ABCR Change.

Predictors	Model 1 (y = CHANGE1)			Model 2 (y = CHANGE2)			Model 3 (y = CHANGE3)
	Coefficient	Std. err.		Coefficient	Std. err.		Coefficient	Std. err.
${\alpha }_i$	4.865***	0.910		1.058***	0.251		6.518***	1.139
ACC2	-0.011***	0.003		-0.003***	0.001		-0.016***	0.003
VILL	0.693	0.742		0.028	0.190		0.862	0.929
ROAD1	-0.873	0.612		-0.321**	0.153		-1.137	0.766
ROAD2	0.179	0.589		0.280*	0.150		0.453	0.737
ELEV	-1.255***	0.493		-0.329***	0.126		-1.656***	0.617
ABCR13	0.101***	0.035		--	--		0.156***	0.044
ABCR18	--	--		0.067***	0.008		--	--
R2	0.4892	--		0.7434	--		0.5482	--
Adjusted R2	0.4570	--		0.7272	--		0.5196	--
F-test (6, 95)	15.17	--		45.87	--		19.21	--
p-value	0.000	--		0.000	--		0.000	--
No. of observations	102	--		102	--		102	--

* p≤0.10; ** p≤0.05; *** p≤0.01; Source: Authors’ construct.

5. Discussion

6. Conclusions

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