Spatiotemporal Risk Intensification from Encroachment on Underground Oil Pipelines: A Proximity-Based Indexing Approach

Spatiotemporal Risk Intensification from Encroachment on Underground Oil Pipelines: A Proximity-Based Indexing Approach | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Spatiotemporal Risk Intensification from Encroachment on Underground Oil Pipelines: A Proximity-Based Indexing Approach Fuseini Nyagsi Abdul Gafaru, Dzigbodi Adzo Doke, Samuel Jerry Cobbina This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7293238/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Rapid urbanisation and unplanned development in Africa have intensified encroachment on oil pipelines, heightening risks of leaks and environmental contamination. In Savelugu, fragmented governance and permit violations have eroded oil pipeline safety buffers. While frameworks like the U.S. PHMSA’s HCA offer static risk benchmarks, dynamic spatiotemporal assessments remain underdeveloped. This study developed and applied a Proximity-Based Risk Index (PBRI) to quantify encroachment trends along an oil pipeline, addressing gaps in synthesising proximity metrics with temporal risk intensification analyses. Multitemporal satellite imagery (2008–2024), pipeline vector data from Ghana’s BOST, and field-validated infrastructure coordinates were analysed using QGIS software. Euclidean distance metrics classified risk zones based on PHMSA’s PIR. Temporal trends were assessed via Mann–Kendall tests, Sen’s slope estimator, and Bai–Perron breakpoint analysis, while KDE mapped encroachment evolution. Infrastructure within HRZ surged by 545% and MRZ by 350% from 2008 to 2024. PBRI escalated from Low to Moderate, driven by declining mean proximity distances (HRZ: 31.34 m to 27.65 m). A significant positive monotonic trend (Kendall’s τ = 0.959, *p* < 0.0001) and Sen’s slope (0.268 units/year) confirmed accelerating risk. Structural breakpoints (2012, 2016, 2020) revealed phased intensification, correlating with urban expansion and regulatory shifts. KDE highlighted clustering along central and northern pipeline segments. These findings underscore urgent needs for enhanced land-use planning, periodic encroachment monitoring, community sensitisation on permit compliance, and GIS-enhanced regulatory enforcement. The PBRI’s methodology offers a replicable model for data-scarce regions. Future work should integrate socioeconomic surveys and real-time remote sensing to optimise risk mitigation. Underground oil pipeline spatiotemporal risk ProximityBased Risk Index urban planning Encroachment Savelugu Municipality Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1. Introduction Rapid urbanisation and unplanned spatial development have emerged as critical drivers of risk to underground oil and gas pipelines worldwide (Xu et al., 2025 ; Bouzouaid & Youcef, 2024 ). Oil pipelines, often extending through peri-urban and rural landscapes, are vulnerable to third-party encroachment that erodes safety buffers and exacerbates hazards such as leaks, explosions, and environmental contamination. Savelugu in Northern Ghana, a strategic node on the Tamale–Bolgatanga corridor, exemplifies this trend. The Municipality is hampered by fragmented planning and frequent permit violations. Yorgri et al. ( 2023 ) revealed that 82% of developers in the Municipality lack awareness of building permits, driving encroachment into buffer zones. Such dynamics mirror trends across Sub-Saharan Africa, where informal settlements increasingly encroach on hazardous zones due to governance gaps and housing shortages (WWF-Kenya & Civil Society Organisations, 2019). Underground oil pipelines pose distinct challenges. Their sub-surface location conceals growing proximities until adverse events reveal vulnerabilities. Internationally, frameworks like the U.S. Pipeline and Hazardous Materials Safety Administration’s (PHMSA) High Consequence Areas (HCAs) and Potential Impact Radius (PIR) calculations provide scientific benchmarks for risk zoning near hazardous pipelines (Cornell Law School, n.d.; PHMSA, 2020 ). Despite extensive literature on urban encroachment’s impacts on pipeline safety, critical gaps exist in operationalising spatiotemporal risk assessments. Existing studies in Ghana, including investigations into urban sprawl and flood risk in Kumasi (Abass, Buor, Afriyie, Dumedah, Segbefi, Guodaar, et al., 2020) or institutional deficits in Savelugu by Yorgri et al. ( 2023 ), provide valuable insights but fail to synthesise proximity metrics with temporal trend analyses to critical energy infrastructure such as oil pipelines. Consequently, decision-makers lack a composite metric that weights infrastructure density within risk buffers while capturing year-on-year intensification. This gap undermines proactive land-use planning and pipeline integrity management, especially where rapid urbanisation can outpace regulatory enforcement and field inspections. Research on composite risk indices demonstrates the value of integrating spatial proximity with consequence factors. Torretta, V. et al. ( 2014 ) introduced an index-based methodology for pipeline corridors by overlaying hazard, vulnerability, and exposure indices, producing a composite index that reflects both spatial adjacency and thematic vulnerability. The study guides planners toward corridors with minimal environmental and social impact. Building on this, Wang et al. ( 2024 ) developed a multi-source Pipeline Risk Index (PRI) in mountainous terrain that combined natural hazard, anthropogenic encroachment, and integrity components, illustrating the utility of weighted buffer analyses. In contrast, matrix-based approaches by Henselwood & Phillips ( 2006 ) simplified risk stratification through Likelihood × Consequence scoring, offering actionable segment-level prioritisation in Canadian networks. Complementary studies emphasise the spatial-statistical mapping of encroachment hotspots. Adebangbe et al. ( 2025 ) applied planar Getis-Ord Gi* and Kernel Density Estimation (KDE) to reveal chronic oil spill corridors in Nigeria, reinforcing KDE’s efficacy for hotspot detection. These geocomputation techniques, when combined with Euclidean distance metrics, form powerful tools for delineating and monitoring risk intensification zones around oil pipelines. Spatiotemporal trend analyses remain underutilised in pipeline risk research. The Mann–Kendall test and Sen’s slope estimator, widely adopted in hydrological and environmental studies, provide robust non-parametric means to detect monotonic trends and quantify median change rates without stringent distributional assumptions (Mann, 1945 ; Sen, 1968 ). Only a handful of pipeline studies, such as those using Bai–Perron breakpoint analysis (Bai & Perron, 1998 ), have explored structural shifts, leaving a methodological gap for integrating these statistical tools with proximity-based indices in African urban contexts (Nwilo, P. C. & Badejo, O. T., 2005). This study aims to (1) Apply a Proximity-Based Risk Index (PBRI) integrating Euclidean distance metrics and kernel density estimation, (2) quantify spatiotemporal encroachment trends in Savelugu Municipality using Mann-Kendall tests and Sen’s Slope estimator, and (3) identify structural breakpoints in risk accumulation via Bai-Perron analysis. The PBRI, by synthesising proximity weighting with spatiotemporal statistical analysis, advances pipeline risk assessment in two key ways: (1) it operationalises dynamic encroachment intensification metrics to anticipate evolving hazards, and (2) it offers a replicable framework for data-constrained African contexts through hybrid remote sensing. The findings will inform regulatory bodies, pipeline operators, and urban planners by pinpointing high-risk zones, quantifying escalation rates, and identifying critical hotspots for intervention. Ultimately, this research contributes to safeguarding energy infrastructure, enhancing community resilience, and guiding evidence-based land-use policies. Following this introduction, Section 2 details the study area and data sources, elaborating on the geospatial pre-processing. It also presents the analytical methods, including risk zoning classification, PBRI computation, trend detection, and hotspot mapping. Section 3 reports the results, highlighting temporal and spatial risk patterns. Section 4 discusses the results, addresses limitations, and proposes future research avenues. The paper concludes with a summary of key contributions and practical recommendations for stakeholders. 2. Materials and Methods 2.1 Study Area Savelugu Municipality (9.624° N, 0.828° W), situated in Ghana’s Northern Region (Fig. 1 ), is characterised by rapid urbanisation and unplanned spatial development. The municipality, with a population of 122,888 and an urbanisation rate of 62.9% (Ghana Statistical Service, 2014 ), faces intensifying pressure on land use, particularly along the Tamale–Bolgatanga corridor, a strategic transport route intersecting with oil pipeline infrastructure (Fig. 2 ). The terrain, predominantly flat with elevations of 150–800 feet, is prone to seasonal flooding in the northern zones (Hajaratu et al., 2022 ). 2.2 Data Collection Pipeline route data were acquired through geospatial demarcations provided by Ghana’s Bulk Oil Storage and Transportation Company Limited (BOST). Multitemporal satellite imagery of the study area was also procured from Google Earth Pro (version 7.3.6.10201 (64-bit)), encompassing cloud-free scenes for the years 2008, 2011, 2013, 2014, 2017, 2019, 2020, 2021, and 2024. Image selection adhered to temporal availability and spatial clarity criteria, with Fig. 3 providing a representative 2024 baseline of urban development patterns adjacent to the pipeline corridor. 2.3 Data Analysis 2.3.1 Data Preprocessing The multitemporal satellite imagery and spatial coordinates delineating the oil pipeline trajectories were integrated into Quantum Geographic Information System (QGIS) software (version 3.34.3-Prizren) to generate a raster and vector-based geodigital representation of the study area’s infrastructure and pipeline network layers. These datasets were georeferenced within QGIS using the World Geodetic System 1984 (WGS84) coordinate reference system (EPSG:4326) to ensure alignment with the pipeline vector layer. A systematic manual digitisation process was employed to identify critical infrastructure within the study area, including residential, educational, healthcare, governmental, commercial, and industrial structures. Each feature was assigned a unique geospatial identifier (GeoID) and stored as a point vector layer for all temporal years. 2.3.2 Infrastructure Proximity Computation To model proximity dynamics, the QGIS “Random Points on Lines” algorithm was executed on the pipeline vector layer, generating 1,000,000 equidistant sampling points along the pipeline corridor. Parameters were configured with a minimum inter-point distance of 0 meters to maximise spatial resolution. Subsequently, the “Distance to Nearest Hub (Points)” algorithm computed Euclidean distances between infrastructure points (origin layer) and pipeline sampling points (destination layer), deriving centroid-based proximity metrics. Yearly hub distance layers were synthesised, each containing infrastructure GeoIDs and their minimum linear distances to the pipeline network (in meters). Data integrity was ensured through iterative validation. A stratified random sample of infrastructure locations was cross-verified via Global Navigation Satellite System (GNSS) field surveys. Discrepancies between computed and observed distances exceeding 5 meters triggered algorithmic recalibration, achieving a final positional error tolerance of ± 2 meters across all layers. This hybrid approach harmonised automated geospatial processing with ground-truthing to mitigate systematic biases inherent in satellite-derived datasets. 2.3.3 Risk Zoning Classification High Consequence Areas (HCAs), as defined by PHMSA, represent zones where pipeline failures could result in severe consequences to human safety, property, or the environment (PHMSA, 2015 ). To operationalise HCA delineation in the study area, the Potential Impact Radius (PIR) framework was adopted, following the methodology outlined in 49 CFR § 192.903 (Title 49 of the Code of Federal Regulations (CFR), 2025 ). 49 CFR § 192.903 is a regulatory provision under the U.S. Code of Federal Regulations that defines key terms used in the integrity management of oil and gas transmission pipelines, including High Consequence Areas (HCAs) and the Potential Impact Radius (PIR), a calculated distance within which a pipeline rupture could cause significant harm to people or the environment. PIR defines the radial extent of potential hazard impact from a pipeline rupture and is calculated using the formula: $$\:\text{P}\text{I}\text{R}=0.69\times\:\sqrt{{\text{D}}^{2}\times\:\text{P}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(1\right)$$ where D is the pipeline diameter in inches and \(\:\text{P}\) is the Maximum Allowable Operating Pressure (MAOP) in pounds per square inch (psi). For this study, D and P were obtained from Ghana’s Bulk Oil Storage and Transportation Company Limited (BOST) technical specifications. The computed PIR value served as the foundational threshold for risk zonation. Three concentric risk zones were demarcated to quantify encroachment intensity: (1) High-Risk Zone (HRZ) for Infrastructure within the PIR boundary (≤ PIR), where pipeline breaches pose immediate threats of fatalities, severe injuries, or catastrophic environmental damage due to thermal radiation, toxic vapor dispersion, or blast overpressure (Moftakhari & AghaKouchak, 2019 ), (2) Moderate-Risk Zone (MRZ) for Infrastructure within 1–2 times the PIR (PRI–2*PIR), where secondary hazards such as structural damage, secondary fires, or lower-concentration inhalation risks prevail, and (3) Low-Risk Zone (LRZ) for Infrastructure beyond (> 2*PIR), primarily associated with long-term environmental contamination risks. 2.3.4 Proximity-Based Risk Index To synthesise multi-zone encroachment dynamics into a composite risk metric reflecting relative hazard severity, a Proximity-Based Risk Index (PBRI) was formulated. PBRI integrates infrastructure density within predefined risk zones while weighting closer infrastructure more heavily. This index, adapted in various risk assessment frameworks, is commonly used in environmental risk, epidemiology, and urban planning studies to quantify exposure or risk based on spatial clustering and distance decay effects (Omobhude & Chen, 2019 ). The PBRI was calculated as follows: $$\:\text{P}\text{B}\text{R}\text{I}=\frac{{\sum\:}_{\text{i}}^{\text{n}}({\text{W}}_{\text{i}}\times\:{\text{N}}_{<\text{d},\text{i}})}{{\text{N}}_{\text{t}\text{o}\text{t}\text{a}\text{l},\:\text{i}}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(2\right)$$ W i​ represents fixed weighting factors assigned to each risk zone (HRZ = 3, MRZ = 2, LRZ = 1). By weighting closer infrastructure more heavily, PBRI captures the disproportionate contribution of high-risk encroachment to the overall threat profile. Weighting values were derived from PHMSA’s consequence-based prioritisation framework, which assigns higher urgency to infrastructure in zones with immediate life-safety risks (PHMSA, 2020 ). \(\:{\text{N}}_{<\text{d},\text{i}}\) denotes the count of infrastructure units within zone i, (HRZ, MRZ, or LRZ) at time t, and \(\:{\text{N}}_{\text{t}\text{o}\text{t}\text{a}\text{l},\:\text{i}}\) ​ is the total infrastructure count across all zones at time t. 2.3.5 Trend Detection via Non-Parametric Methods To assess the presence of a monotonic trend in the PBRI time series from 2008 to 2024, the Mann–Kendall (MK) Test was employed. The MK Test is a non-parametric statistical test used to identify trends in a time series dataset. Developed by Mann, H. B. ( 1945 ), it is widely applied in environmental science, hydrology, and meteorology to assess whether there is a statistically significant monotonic (increasing or decreasing) trend in a data. In our study, we employed the Mann–Kendall (MK) test to check whether there has been any significant increase or decrease in the proximity risk metrics over the study period due to encroachment. $$\:\text{S}=\sum\:_{\text{i}-1}^{\text{n}-1}\sum\:_{\text{j}=\text{i}+1}^{\text{n}}\text{s}\text{g}\text{n}({\text{x}}_{\text{j}}-{\text{x}}_{\text{i}})\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(3\right)$$ $$\:{\tau\:}=\frac{\text{S}}{\frac{1}{2}\text{n}(\text{n}-1)}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(4\right)$$ Where \(\:{\text{x}}_{\text{j}}\) and \(\:{\text{x}}_{\text{i}}\) are sequential PRI scores, n is the length of the time series, and \(\:\text{s}\text{g}\text{n}\left(\right)\) is the signum function: $$\:\text{s}\text{g}\text{n}\left({\text{x}}_{\text{j}}-{\text{x}}_{\text{i}}\right)=\left\{\begin{array}{c}+1\\\:0\\\:-1\end{array}\:\:\begin{array}{c}\text{i}\text{f}\:{\text{x}}_{\text{j}}>{\text{x}}_{\text{i}}\:\\\:\text{i}\text{f}\:{\text{x}}_{\text{j}}={\text{x}}_{\text{i}}\\\:\text{i}\text{f}\:{\text{x}}_{\text{j}}<{\text{x}}_{\text{i}}\end{array}\right.\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(5\right)$$ The MK test statistic S and effect size τ were computed, with significance evaluated at the α = 0.05 level. This rank-based, distribution-free test obviates the need for residual normality and linearity assumptions inherent in parametric regression. Complementing the MK test, LOESS (locally weighted scatterplot smoothing) was applied to the PBRI series to visualise trend behaviour with a 95% confidence interval, guiding interpretation of temporal risk trajectories. 2.3.6 Slope Estimation To quantify the median rate of change in PBRI, Sen’s slope estimator (Theil–Sen robust method) was calculated as the median of all pairwise slopes between PBRI observations (year indices vs. PBRI values). The Sen’s Slope Estimator is a statistical technique used to estimate the slope of a trend line in bivariate data. It is particularly robust to outliers and does not assume normality of the residuals. This makes it a preferred method for analysing data where outliers or non-linearities could bias the results (Sen, 1968 ; Theil, H., 1950 ). $$\:{{\beta\:}}_{\text{i}\text{j}}=\frac{{\text{y}}_{\text{j}}-{\text{y}}_{\text{i}}}{{\text{x}}_{\text{j}}-{\text{x}}_{\text{i}}}\:\:\text{f}\text{o}\text{r}\:\text{a}\text{l}\text{l}\:\text{i}<\text{j}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(6\right)$$ $$\:{\beta\:}=\text{M}\text{e}\text{d}\text{i}\text{a}\text{n}\:\left({{\beta\:}}_{\text{i}\text{j}}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(7\right)$$ \(\:{{\beta\:}}_{\text{i}\text{j}}\) is the slope between all pairs of points, \(\:{\text{x}}_{\text{j}},{\text{x}}_{\text{i}}\) are time points and \(\:{\text{y}}_{\text{j}},{\text{y}}_{\text{i}}\) are observed PRI scores. The final Sen’s Slope (β) is the median of all pairwise slopes. 2.3.7 Structural Breakpoint Analysis To identify temporal inflection points in risk accumulation, the Bai–Perron multiple structural change procedure was implemented on the PBRI series using RStudio software (version 2023.12.1 Build 402). Structural Breakpoint Analysis is a statistical technique used to identify multiple structural changes (or breakpoints) within a time series or regression model. These breakpoints represent moments where the underlying relationship between variables undergoes significant change, such as changes in trend, mean, or variance (Bai & Perron, 1998 ; Bai & Perron, 2003 ). In our study, breakpoint candidates in the PBRI series were estimated via dynamic programming, minimising the residual sum of squares (RSS) for models with up to m breaks. Model selection leveraged the Bayesian Information Criterion (BIC), with optimal break number and dates selected under the null hypothesis of k breaks. $$\:\begin{array}{c}\text{m}\text{i}\text{n}\\\:{\text{t}}_{1,}{\text{t}}_{2}\dots\:\dots\:,{\text{t}}_{\text{m}}\end{array}\sum\:_{\text{j}=0}^{\text{m}}\text{R}\text{S}\text{S}({\text{t}}_{\text{j}},{\text{t}}_{\text{j}+1})\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(8\right)$$ Where m is the number of breakpoints, \(\:{\text{t}}_{\text{j}}\) is the \(\:\text{j}-\text{t}\text{h}\) breakpoint, \(\:{\text{t}}_{0}=0\) , and \(\:{\text{t}}_{\text{m}+\text{t}}=\text{n}\text{u}\text{m}\text{b}\text{e}\text{r}\:\text{o}\text{f}\:\text{o}\text{b}\text{s}\text{e}\text{r}\text{v}\text{a}\text{t}\text{i}\text{o}\text{n}\text{s}\) , and \(\:\text{R}\text{S}\text{S}\left({\text{t}}_{\text{j}},{\text{t}}_{\text{j}+1}\right)\) is the residual sum of squares (RSS) for observations from \(\:{\text{t}}_{\text{j}}+1\) to \(\:{\text{t}}_{\text{j}+1}\) . 2.3.9 Spatial Density Estimation Kernel Density Estimation (KDE) was applied to the point infrastructure layers for each temporal year to portray the spatiotemporal distribution of encroachment hotspots. KDE is a statistical technique used to estimate the density function of spatial data. It provides insight into how data points are distributed across a geographic space or multidimensional plane (Silverman, B. W, 1986 ). The goal of using KDE in our study is to model the intensity of observations (infrastructure encroachment) in space for spatial point patterns and distributions. Using a Gaussian kernel and bandwidth determined by Silverman’s rule of thumb (Harpole et al., 2014 ), continuous density rasters were generated in QGIS, enabling visualisation of clustering intensity along the pipeline corridor. $$\:\widehat{\text{f}}\left(\text{x}\right)=\frac{1}{\text{n}\text{h}}\sum\:_{\text{i}=1}^{\text{n}}\left({\varnothing}\frac{\text{x}-{\text{x}}_{\text{i}}}{\text{h}}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(9\right)$$ $$\:{\varnothing}\left(\text{u}\right)=\frac{1}{\sqrt{2{\pi\:}}}{\text{e}}^{-\frac{{\text{u}}^{2}}{2}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(10\right)$$ Where \(\:\widehat{\text{f}}\left(\text{x}\right)\) is the estimated density at location x, n is the number of data points, h is the bandwidth (smoothing parameter), \(\:{\varnothing}\left(\text{u}\right)\) is the standard Gaussian kernel, \(\:{\text{x}}_{\text{i}}\) ​ are the observed data points, and h is the bandwidth (smoothing parameter). 2.3.10 Descriptive Statistics For each risk zone and time slice, infrastructure counts \(\:\left({\text{N}}_{<\text{d},\text{t}}\right)\) for all risk zones and the total infrastructure \(\:\left({\text{N}}_{\text{t}\text{o}\text{t}\text{a}\text{l},\:\text{t}}\right)\) were tabulated. Summary metrics (arithmetic mean and standard deviation) of the minimum distances within HRZ and Encroachment Zone (EZ) were computed in RStudio (version 2023.12.1 Build 402) and cross-validated in Excel 2021 (Version 2108). 2.3.11 Encroachment Ratio To quantify relative encroachment intensity on the oil pipeline, Encroachment Ratio (ER), a metric used to quantify the extent to which one land use intrudes upon another, was used. $$\:{\text{E}\text{R}}_{\text{t}}^{<\text{d}}=\left(\frac{{\text{N}}_{<\text{d},\text{t}}}{{\text{N}}_{\text{t}\text{o}\text{t}\text{a}\text{l},\:\text{t}}}\right)\times\:100\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(11\right)$$ where \(\:{\text{N}}_{<\text{d},\text{t}}\) ​ denotes the infrastructure count within a zone distance \(\:\text{d}\) at year \(\:\text{t}\) , and \(\:{\text{N}}_{\text{t}\text{o}\text{t}\text{a}\text{l},\:\text{t}}\) is the total infrastructure count of our study area. 2.3.12 Encroachment Growth Rate We used Encroachment Growth Rate (EGR) calculations to express the year-on-year percentage change of infrastructure encroachment. EGR measures the rate at which encroachment (unwanted intrusion or expansion) increases over time within a specified boundary or domain. It is commonly used in environmental studies, urban planning, and land-use change analysis to quantify the expansion of human activities, settlements, or invasive species into natural or protected areas (Rowland, 2003 ). $$\:{\text{E}\text{G}\text{R}}_{\text{t}}^{<\text{d}}=\frac{{\text{N}}_{<\text{d},\text{t}}-{\text{N}}_{<\text{d},\text{t}-1}}{{\text{N}}_{<\text{d},\text{t}-1}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(12\right)$$ Where \(\:{\text{N}}_{<\text{d},\text{t}-1}\) is the count of infrastructure units within the same zone distance \(\:\text{d}\) in the previous year ( \(\:\text{t}-1\) ), \(\:{\text{N}}_{<\text{d},\text{t}}\) is the number of encroachment infrastructures within distance d at time t. 2.3.13 Cumulative Encroachment Index To integrate temporal encroachment pressure into a single normalised metric, the Cumulative Encroachment Index ( \(\:\text{C}\text{E}\text{I}\) ) at year t for zone distance \(\:\text{d}\) was computed as the arithmetic mean of annual ratios. \(\:\text{C}\text{E}\text{I}\) provides a normalised measure of encroachment intensity of human activities into natural or protected areas over time relative to the total area or available units. $$\:{\text{C}\text{E}\text{I}}_{\text{t}}^{<\text{d}}=\frac{1}{\text{t}}\sum\:_{\text{i}=1}^{\text{t}}\frac{{\text{N}}_{<\text{d},\text{i}}}{{\text{N}}_{\text{t}\text{o}\text{t}\text{a}\text{l},\:\text{i}}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(13\right)$$ Where \(\:{\text{C}\text{E}\text{I}}_{\text{t}}^{<\text{d}}\) is the Cumulative Encroachment Index up to time t for encroachments within distance d, t is the total time periods, \(\:{\text{N}}_{<\text{d},\text{i}}\) is the number of encroachment infrastructures within distance d at time i and \(\:{\text{N}}_{\text{t}\text{o}\text{t}\text{a}\text{l},\:\text{i}}\) is the total number of encroachment infrastructure at time i. 3. Results 3.1 Risk Zoning Classification The Potential Impact Radius (PIR) was calculated using the formula outlined in 49 CFR § 192.903. Incorporating the pipeline’s technical specifications, a diameter (D) of 8 inches and a maximum allowable operating pressure (P) of 1,200 psi, we achieved a PIR value of 58.28 meters. This PIR value delineated four concentric risk zones (Table 1 ). The HRZ threshold (50 meters) is conservatively set below the computed PIR (58.28 meters) to account for localised terrain variability and ensure alignment with the PHMSA’s precautionary buffer recommendations. Table 1 Risk zone classification framework based on Potential Impact Radius (PIR). Distance Range Zone Key Threats 10 kW/m² -Toxic vapour clouds (H₂S, benzene) 50–100 meters Moderate-Risk Zone (MRZ) Structural damage from blasts. -Secondary fires/heat exposure -Thermal radiation > 5 kW/m² -Inhalation hazards (lower concentrations) 100 meters Low-Risk Zone (LRZ) Long-term environmental contamination (soil/water) Table 2 Temporal analysis of infrastructure encroachment near underground oil pipelines in Savelugu Municipality, Ghana (2008–2024). The table presents: (1) Infrastructure counts by risk zone (High-Risk Zone [HRZ: 100m]); (2) Mean proximity distances (m) with standard deviations; (3) Encroachment Ratios (ER) by zone; and (4) annual Encroachment Growth Rates (EGR). Infrastructure Count Mean Distance to Pipeline (Metres) Standard Deviation (Metres) Encroachment Ratio (ER) (Percentage) Encroachment Growth Rate (EGR) (Percentage) Date HRZ EZ MRZ LRZ Total HRZ EZ HRZ EZ HRZ EZ MRZ LRZ Total HRZ EZ MRZ LRZ Total Feb-08 22 60 38 3,179 3,239 31.34 58.57 12.15 24.44 0.68 1.85 1.17 0.98 2.83 Nov-11 24 64 40 3,216 3,280 30.08 56.97 12.43 25.24 0.73 1.95 1.22 0.98 2.93 + 9.1 + 6.7 + 5.3 + 1.2 + 1.3 Dec-13 52 136 84 4,210 4,346 29.83 56.96 11.49 25.32 1.20 3.13 1.93 0.97 4.10 + 116.7 + 112.5 + 110.0 + 30.9 + 32.5 Dec-14 55 139 84 4,327 4,466 30.55 56.86 12.02 25.03 1.23 3.11 1.88 0.97 4.08 + 5.8 + 2.2 0 + 2.8 + 2.8 Oct-17 86 199 113 5,269 5,468 29.78 55.95 11.97 26.54 1.57 3.64 2.07 0.96 4.60 + 56.4 + 43.2 + 34.5 + 21.8 + 22.4 Nov-19 100 227 127 5,613 5,840 28.50 55.80 12.52 27.75 1.71 3.89 2.17 0.96 4.85 + 16.3 + 14.1 + 12.4 + 6.5 + 6.8 Nov-20 109 238 129 5,912 6,150 29.22 55.10 12.49 26.68 1.77 3.87 2.10 0.96 4.83 + 9.0 + 4.8 + 1.6 + 5.3 + 5.3 Nov-21 119 287 168 6,266 6,553 28.34 54.92 12.61 25.91 1.82 4.38 2.56 0.96 5.34 + 9.2 + 20.6 + 30.2 + 6.0 + 6.6 Apr-24 142 313 171 6,695 7,008 27.65 52.30 13.33 27.43 2.03 4.47 2.44 0.96 5.42 + 19.3 + 9.1 + 1.8 + 6.8 + 6.9 3.2 Descriptive Statistics Total infrastructure count of the study area exhibited progressive growth, quantified as 3,239 points (2008), 3,280 (2011), 4,210 (2013), 4,466 (2014), 5,468 (2017), 5,840 (2019), 6,150 (2020), 6,553 (2021), and 7,008 (2024). Annual counts of infrastructure units within each risk zone were tabulated for nine temporal snapshots (2008–2024). As reported in Table 2 , total infrastructure increased from 3,239 units in February 2008 to 7,008 units in April 2024. HRZ counts rose from 22 to 142 units, MRZ from 38 to 171, EZ from 60 to 313, and LRZ from 3,179 to 6,695 over the study period​. The cumulative infrastructure growth underscores spatial expansion across all proximity thresholds. Descriptive statistics for infrastructure distances to the pipeline within HRZ and EZ were computed. Between 2008 and 2024, the mean distance in HRZ decreased from 31.34 m to 27.65 m, while the EZ mean declined from 58.57 m to 52.30 m. 3.3 Encroachment Ratio, Growth Rate, and Index Metrics Encroachment Ratio (ER) values, representing the percentage of total infrastructure within HRZ, MRZ, and LRZ, are detailed in Table 2 . HRZ’s ER increased from 0.68% (Feb 2008) to 2.03% (Apr 2024); MRZ’s ER rose from 1.17–2.44%; LRZ's ER remained stable at approximately 0.96%. The aggregated ER for EZ escalated from 2.83–5.42% over the analysis period. Year-on-year Encroachment Growth Rates (EGR) for each zone are also reported in Table 2 . The largest singleinterval increases occurred between 2011 and 2013 (HRZ: +116.6 %; MRZ: +110.0 %; LRZ: +30.9 %; Total: +32.5 %). Subsequent intervals exhibited variable growth, with HRZ’s EGR ranging from + 5.7 % to + 56.3 %; MRZ from + 0.0 % to + 34.5 %; and LRZ from + 1.1 % to + 21.7 %. The Cumulative Encroachment Index (CEI), representing the mean of annual ER values up to each year, were calculated over the full study period. CEI values attained were 1.415 for HRZ, 1.950 for MRZ, and 0.966 for LRZ, reflecting cumulative proximity pressure​. 3.4 Proximity-Based Risk Index The ProximityBased Risk Index (PBRI), calculated as the weighted sum of zone-specific infrastructure counts normalised by total infrastructure, is shown in Table 3 . PBRI increased from 102.5 (Feb 2008) to 106.5 (Apr 2024). Risk level classifications transitioned from “Low” (PRI < 105) during 2008–2014 to “Moderate” (105 ≤ PRI < 107) from 2017 onward. Table 3 Temporal progression of the Proximity-Based Risk Index (PBRI) and associated risk classifications. Original Date PBRI Risk Level Feb-08 102.5 Low Nov-11 102.7 Low Dec-13 104.3 Low Dec-14 104.3 Low Oct-17 105.2 Moderate Nov-19 105.6 Moderate Nov-20 105.6 Moderate Nov-21 106.2 Moderate Apr-24 106.5 Moderate 3.5 Trend Detection Application of the Mann–Kendall test to the PBRI time series yielded a Kendall’s tau (τ) of 0.959 (p < 0.0001), indicating a statistically significant positive monotonic trend (Fig. 4 ) ​. LOESS smoothing overlaid on the PBRI series exhibits a narrow 95% confidence envelope, corroborating trend consistency. 3.6 Slope Estimation Sen’s slope estimator quantified the median annual increase in PBRI at 0.268 PRI units/year, with a 95% confidence interval of [0.215, 0.311] (p < 0.0001) (Fig. 5 )​. Over the 16-year span, this corresponds to an aggregate increase of approximately 4.29 PRI units. 3.7 Structural Breakpoint Analysis Using the Bai–Perron method, three significant breakpoints were identified at 2012, 2016, and 2020 in the PBRI series, partitioning data into four segments (Fig. 6 ) ​. Model selection via Bayesian Information Criterion yielded BIC = − 13.57 and residual sum of squares RSS = 0.06. Segment mean annual PBRI increases were 2008–2012: +0.18 units/year, 2012–2016: +0.35 units/year, 2016–2020: +0.25 units/year, and 2020–2024: +0.40 units/year. These segments correspond temporally to observed infrastructure count surges in HRZ and MRZ. 3.8 Kernel Density Estimation Heat Maps Kernel Density Estimation (KDE) heat maps were generated for each temporal layer using a Gaussian kernel with bandwidth determined by Silverman’s rule of thumb. Figure 7 displays density raster, illustrating spatiotemporal clustering of infrastructure points along the pipeline corridor for 2008, 2011, 2017, 2019, 2020, 2021, and 2024​. 4. Discussion This study quantified spatiotemporal risk intensification from urban encroachment on underground oil pipelines in Savelugu Municipality, Ghana, through a Proximity-Based Risk Index (PBRI). Key findings reveal a 545% increase in infrastructure within the High-Risk Zone (HRZ: <50 meters) and a 350% rise in the Moderate-Risk Zone (MRZ: 50–100 meters) between 2008 and 2024. The PBRI transitioned from "Low" (102.5) to "Moderate" (106.5) risk, driven by cumulative infrastructure growth and reduced mean proximity distances (HRZ: 31.34 m to 27.65 m; Encroachment Zone: 58.57 m to 52.30 m). Monotonic trend analysis (Mann–Kendall τ = 0.959, *p* < 0.0001) confirmed a statistically significant upward trajectory, with Sen’s slope estimating a median annual PBRI increase of 0.268 units (95% CI [0.215, 0.311]). Structural breakpoints in 2012, 2016, and 2020 delineated phases of accelerated risk accumulation linked to urbanisation surges and regulatory shifts. Kernel Density Estimation (KDE) further highlighted progressive infrastructure clustering along the pipeline corridor, exacerbating vulnerability. The observed trends align with Savelugu’s rapid urbanisation rate (62.9%) and governance gaps in land-use planning. As shown by (Yorgri et al., 2023 ), 82% of developers lacked awareness of building permits, enabling unchecked encroachment into pipeline buffer zones. The PBRI’s rise reflects the compounding effects of proximity-weighted infrastructure density, where closer developments disproportionately amplify hazard potential. Declining mean distances within HRZ and MRZ signify buffer erosion, mirroring patterns in Nigeria’s Niger Delta, where informal settlements encroach on pipelines (Jatto, 2024 ). The structural breakpoints: 2012, 2016, and 2020 correspond to critical socio-political and environmental events. The 2016–2020 deceleration (+ 0.25) coincides with Savelugu’s 2018 municipal status upgrade, which may have introduced tentative land-use regulations. However, the post-2020 resurgence in PBRI slopes (+ 0.40 units/year) likely reflects enforcement lapses and pandemic-induced rural–urban migration, underscoring the fragility of regulatory frameworks in rapidly urbanising contexts. KDE-derived hotspot migration underscores that encroachment is neither uniform nor static: central and northern corridor segments have experienced the most intense pressure, likely due to their superior road connectivity and proximity to commercial hubs. These spatial patterns highlight the “corridor effect,” whereby transport arteries spur informal settlement growth (Yakubu, 2021 ). These findings corroborate and extend studies of urban expansion impacts on critical infrastructure in Sub-Saharan contexts. Abass et al. ( 2020 ) documented how green space depletion in Kumasi heightened flood risks; similarly, our studies in Savelugu have shown that unplanned growth has eroded protective buffers around underground oil pipelines. (Jatto, 2024 ) observed that informal settlements in Nigeria’s Niger Delta reduced safe setback distances, paralleling the 11% contraction in our HRZ proximities. While these prior works focused on ecological or accident response outcomes, our study integrates spatiotemporal trend analyses, Sen’s slope, and Bai–Perron breakpoints, with proximity indices, thereby operationalising dynamic hazard evolution rather than static snapshots. Theoretically, this study advances pipeline risk modelling by integrating proximity metrics with spatiotemporal trend analysis. Unlike prior frameworks focusing on static hazard indices (Torretta, V. et al., 2014 ) or likelihood-consequence matrices (Henselwood & Phillips, 2006 ), our PBRI synthesises dynamic encroachment pressures through weighted distance decay and temporal trend detection. By weighting encroachment by distance decay and integrating non-parametric trend detection, the ProximityBased Risk Index (PBRI) encapsulates both intensity and velocity of hazard intensification. This dynamic framework could inform a revision of existing risk theory in linearinfrastructure contexts, emphasising the importance of breakpoints and trend acceleration phases. Practically, our findings carry several actionable implications. First, pipeline operators and municipal authorities must institutionalise periodic encroachment surveys, leveraging GIS and KDE analytics to update risk zones and prioritise high-pressure segments. Second, community sensitisation programs are urgent. Enhancing building permit awareness among the 82% of uninformed developers could curtail informal constructions near pipelines. Finally, integrating remote sensing with GNSS ground-truthing, as demonstrated in this study, offers a replicable protocol for other data-scarce municipalities. Three limitations of this study warrant consideration. First, reliance on cloud-free satellite imagery constrained temporal granularity, potentially underestimating short-term encroachment spikes. Second, socio-economic drivers of encroachment were inferred indirectly; household surveys could elucidate motivations behind permit violations. Third, the PBRI’s weighting scheme, while grounded in PHMSA guidelines, assumes uniform consequence severity across infrastructure types. A hospital within the HRZ may pose higher societal risks than a residential unit, yet the index treats them equally. Future studies should integrate participatory mapping and household-level surveys to understand the socioeconomic motives behind encroachment, enabling targeted behavioural interventions. Incorporating real‐time remote sensing, such as Unmanned Aerial Vehicles (UAV) imagery and machine‐learning–based built‐up detection, could automate encroachment monitoring and mitigate manual digitisation limitations. Comparative analyses across multiple municipalities would test the PBRI’s transferability and inform regionally calibrated policy frameworks. Finally, coupling proximity-based indices with pipeline integrity monitoring (e.g., SCADA alarms, inline inspection data) could yield a holistic risk dashboard, bridging spatial and operational perspectives for comprehensive pipeline safety management. Conclusion This study developed and applied a Proximity-Based Risk Index (PBRI) to assess the spatiotemporal intensification of infrastructure encroachment on an underground oil pipeline in Savelugu Municipality, Ghana. Using multitemporal satellite imagery, GIS-based proximity modelling, and statistical trend analysis, the research quantified changes in encroachment patterns from 2008 to 2024. Results revealed a 545% increase in infrastructure within the High-Risk Zone and a 350% rise within the Moderate-Risk Zone. The PBRI transitioned from a “Low” to a “Moderate” risk classification, with a statistically significant monotonic upward trend (τ = 0.959, p < 0.0001) and an annual growth rate of 0.268 units. These findings demonstrate a clear erosion of pipeline safety buffers over time, driven by unregulated urban expansion, land-use permit violations, and weak enforcement mechanisms. The identification of structural breakpoints in 2012, 2016, and 2020 underscores phases of intensified risk accumulation, corresponding with urbanisation surges and policy lapses. Spatial clustering of encroachment along the central and northern segments of the pipeline corridor further amplifies site-specific vulnerabilities. The study underscores the urgent need for integrated spatial planning, periodic GIS-based risk assessments, and targeted community sensitisation on development regulations. The PBRI framework offers a replicable and scalable approach for risk monitoring in data-constrained regions. Future research should incorporate household-level surveys and real-time remote sensing technologies to enhance the granularity and responsiveness of pipeline risk management strategies. Declarations Funding Statement: This research was supported by the West African Centre for Water, Irrigation and Sustainable Agriculture (WACWISA-UDS) as part of a Master's support of the Corresponding Author. Conflict of Interest Statement: The authors declare no conflict of interest. Author Contributions: Fuseini Nyagsi Abdul Gafaru : Conceptualisation, Data Collection, GIS Analysis, Writing – Original Draft Dzigbodi Adzo Doke : Supervision, Methodology Refinement, Writing – Review & Editing Samuel Jerry Cobbina : Data Validation, Statistical Analysis, Writing – Review & Editing Acknowledgements This research was supported by the West African Centre for Water, Irrigation and Sustainable Agriculture (WACWISA-UDS). Conflict of interest The authors declare no conflict of interest. Clinical trial number Not applicable. Author Contributions Fuseini Nyagsi Abdul Gafaru : Conceptualisation, Data Collection, GIS Analysis, Writing – Original Draft Dzigbodi Adzo Doke : Supervision, Methodology Refinement, Writing – Review & Editing Samuel Jerry Cobbina : Data Validation, Statistical Analysis, Writing – Review & Editing References Abass, K., Buor, D., Afriyie, K., Dumedah, G., Segbefi, A. Y., & Guodaar, L. (2020). Urban sprawl and green space depletion: Implications for flood incidence in Kumasi, Ghana. International Journal of Disaster Risk Reduction. Abass, K., Buor, D., Afriyie, K., Dumedah, G., Segbefi, A. Y., Guodaar, L., Garsonu, E. K., Adu-Gyamfi, S., Forkuor, D., Ofosu, A., Mohammed, A., & Gyasi, R. M. (2020). Urban sprawl and green space depletion: Implications for flood incidence in Kumasi, Ghana. International Journal of Disaster Risk Reduction, 51, 101915. https://doi.org/10.1016/j.ijdrr.2020.101915 Adebangbe, S. A., Dixon, D., & Barrett, B. (2025). 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OALib, 10(12), 1–18. https://doi.org/10.4236/oalib.1110296 Additional Declarations No competing interests reported. Supplementary Files Table2.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7293238","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":511916600,"identity":"adb52237-cac6-47fe-a55c-6daf17fdc4a5","order_by":0,"name":"Fuseini Nyagsi Abdul Gafaru","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyUlEQVRIiWNgGAWjYNACAxs5EHXgAQla0ozBWhJIsOZwYgOIIkqLuUTy45c/CpjT54cdfgi0xU5Ot4GAFssZaWbWPAZsuRtvpxkAtSQbmx0goMXgRoKZMYMBT+7G2QkgLQcStxHWkv7N8IeBRLrh7PQPxGrJMX7AY2CQIC+dQ6wtZ96UMfMYJBhukM4pOJBgQIxfjqdv/vjjz395+dnpmz98qLCTI6iFQSCBTQKsF6zSgJByEOA/wPwBRMs3EKN6FIyCUTAKRiQAABBRR6WisncKAAAAAElFTkSuQmCC","orcid":"","institution":"University for Development Studies","correspondingAuthor":true,"prefix":"","firstName":"Fuseini","middleName":"Nyagsi Abdul","lastName":"Gafaru","suffix":""},{"id":511916601,"identity":"21f350cc-9059-4e4a-9621-bf74cce40082","order_by":1,"name":"Dzigbodi Adzo Doke","email":"","orcid":"","institution":"University for Development Studies","correspondingAuthor":false,"prefix":"","firstName":"Dzigbodi","middleName":"Adzo","lastName":"Doke","suffix":""},{"id":511916602,"identity":"047b8500-31d9-4d21-9f1b-f5e4979c9c24","order_by":2,"name":"Samuel Jerry Cobbina","email":"","orcid":"","institution":"University for Development Studies","correspondingAuthor":false,"prefix":"","firstName":"Samuel","middleName":"Jerry","lastName":"Cobbina","suffix":""}],"badges":[],"createdAt":"2025-08-04 16:38:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7293238/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7293238/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":91107419,"identity":"942922c5-5878-4ec0-8291-61bfc332616f","added_by":"auto","created_at":"2025-09-11 15:49:14","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":403726,"visible":true,"origin":"","legend":"\u003cp\u003eMap of Savelugu Municipality, Ghana.\u003c/p\u003e","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-7293238/v1/c2d6baee2a982c1afa29b300.png"},{"id":91107420,"identity":"50d4d0e0-a61b-4a9b-b55d-e5494830ff6d","added_by":"auto","created_at":"2025-09-11 15:49:14","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1077341,"visible":true,"origin":"","legend":"\u003cp\u003eSpatial distribution of infrastructure encroachment near the underground oil pipeline.\u003c/p\u003e","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-7293238/v1/844ca5ada221703d309d051b.png"},{"id":91110090,"identity":"04040f2f-70e9-4078-be6c-eadadc70eae3","added_by":"auto","created_at":"2025-09-11 16:13:14","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":18987851,"visible":true,"origin":"","legend":"\u003cp\u003eHigh-resolution satellite image (2024) of the study area. Data source: Google Earth Pro (Version 7.3.6.10201).\u003c/p\u003e","description":"","filename":"Figure3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7293238/v1/04783b9c008ee35769fc5e1a.jpg"},{"id":91110089,"identity":"bc87d798-d215-4de3-8f47-24b22adec8b6","added_by":"auto","created_at":"2025-09-11 16:13:14","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":595202,"visible":true,"origin":"","legend":"\u003cp\u003eMann-Kendall trend test for monotonic change in PBR) values (2008-2024).\u003c/p\u003e","description":"","filename":"Figure4.png","url":"https://assets-eu.researchsquare.com/files/rs-7293238/v1/b1c5fd680fd821e8bb152cba.png"},{"id":91107423,"identity":"76238964-20d7-4c33-bf20-7349dc1b70a3","added_by":"auto","created_at":"2025-09-11 15:49:14","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":791594,"visible":true,"origin":"","legend":"\u003cp\u003eAnnual trend analysis of PRI values using Sen's slope estimator.\u003c/p\u003e","description":"","filename":"Figure5.png","url":"https://assets-eu.researchsquare.com/files/rs-7293238/v1/982b88b0a0d236f2cddcc1c4.png"},{"id":91108545,"identity":"eab4809f-48c1-47fe-80df-ad40f4126834","added_by":"auto","created_at":"2025-09-11 15:57:14","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":517872,"visible":true,"origin":"","legend":"\u003cp\u003eStructural breakpoint analysis of PBRI time series using the Bai-Perron method.\u003c/p\u003e","description":"","filename":"Figure6.png","url":"https://assets-eu.researchsquare.com/files/rs-7293238/v1/298945180fcb5f3e35e612c0.png"},{"id":91109097,"identity":"58948bfe-fef8-4468-9c5d-c517afa83865","added_by":"auto","created_at":"2025-09-11 16:05:14","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":3653059,"visible":true,"origin":"","legend":"\u003cp\u003eSpatiotemporal evolution of infrastructure encroachment near underground oil pipelines as revealed through Kernel Density Estimation (KDE) heat maps.\u003c/p\u003e","description":"","filename":"Figure7.png","url":"https://assets-eu.researchsquare.com/files/rs-7293238/v1/24b7ac0de522413d95404354.png"},{"id":99309359,"identity":"d2d03dbd-3702-4ba9-a376-4249c28c37ce","added_by":"auto","created_at":"2025-12-31 16:10:14","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":26793382,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7293238/v1/68d256dd-67ff-421e-b89e-df80d7e3ddc6.pdf"},{"id":91107428,"identity":"2c5166ea-7865-457b-9366-9dedfb9e3f15","added_by":"auto","created_at":"2025-09-11 15:49:14","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":17229,"visible":true,"origin":"","legend":"","description":"","filename":"Table2.docx","url":"https://assets-eu.researchsquare.com/files/rs-7293238/v1/16873276423e6698d5874f4f.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Spatiotemporal Risk Intensification from Encroachment on Underground Oil Pipelines: A Proximity-Based Indexing Approach","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eRapid urbanisation and unplanned spatial development have emerged as critical drivers of risk to underground oil and gas pipelines worldwide (Xu et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Bouzouaid \u0026amp; Youcef, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Oil pipelines, often extending through peri-urban and rural landscapes, are vulnerable to third-party encroachment that erodes safety buffers and exacerbates hazards such as leaks, explosions, and environmental contamination. Savelugu in Northern Ghana, a strategic node on the Tamale\u0026ndash;Bolgatanga corridor, exemplifies this trend. The Municipality is hampered by fragmented planning and frequent permit violations. Yorgri et al. (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) revealed that 82% of developers in the Municipality lack awareness of building permits, driving encroachment into buffer zones. Such dynamics mirror trends across Sub-Saharan Africa, where informal settlements increasingly encroach on hazardous zones due to governance gaps and housing shortages (WWF-Kenya \u0026amp; Civil Society Organisations, 2019). Underground oil pipelines pose distinct challenges. Their sub-surface location conceals growing proximities until adverse events reveal vulnerabilities. Internationally, frameworks like the U.S. Pipeline and Hazardous Materials Safety Administration\u0026rsquo;s (PHMSA) High Consequence Areas (HCAs) and Potential Impact Radius (PIR) calculations provide scientific benchmarks for risk zoning near hazardous pipelines (Cornell Law School, n.d.; PHMSA, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eDespite extensive literature on urban encroachment\u0026rsquo;s impacts on pipeline safety, critical gaps exist in operationalising spatiotemporal risk assessments. Existing studies in Ghana, including investigations into urban sprawl and flood risk in Kumasi (Abass, Buor, Afriyie, Dumedah, Segbefi, Guodaar, et al., 2020) or institutional deficits in Savelugu by Yorgri et al. (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), provide valuable insights but fail to synthesise proximity metrics with temporal trend analyses to critical energy infrastructure such as oil pipelines. Consequently, decision-makers lack a composite metric that weights infrastructure density within risk buffers while capturing year-on-year intensification. This gap undermines proactive land-use planning and pipeline integrity management, especially where rapid urbanisation can outpace regulatory enforcement and field inspections.\u003c/p\u003e\u003cp\u003eResearch on composite risk indices demonstrates the value of integrating spatial proximity with consequence factors. Torretta, V. et al. (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) introduced an index-based methodology for pipeline corridors by overlaying hazard, vulnerability, and exposure indices, producing a composite index that reflects both spatial adjacency and thematic vulnerability. The study guides planners toward corridors with minimal environmental and social impact. Building on this, Wang et al. (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) developed a multi-source Pipeline Risk Index (PRI) in mountainous terrain that combined natural hazard, anthropogenic encroachment, and integrity components, illustrating the utility of weighted buffer analyses. In contrast, matrix-based approaches by Henselwood \u0026amp; Phillips (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) simplified risk stratification through Likelihood \u0026times; Consequence scoring, offering actionable segment-level prioritisation in Canadian networks. Complementary studies emphasise the spatial-statistical mapping of encroachment hotspots. Adebangbe et al. (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) applied planar Getis-Ord Gi* and Kernel Density Estimation (KDE) to reveal chronic oil spill corridors in Nigeria, reinforcing KDE\u0026rsquo;s efficacy for hotspot detection. These geocomputation techniques, when combined with Euclidean distance metrics, form powerful tools for delineating and monitoring risk intensification zones around oil pipelines.\u003c/p\u003e\u003cp\u003eSpatiotemporal trend analyses remain underutilised in pipeline risk research. The Mann\u0026ndash;Kendall test and Sen\u0026rsquo;s slope estimator, widely adopted in hydrological and environmental studies, provide robust non-parametric means to detect monotonic trends and quantify median change rates without stringent distributional assumptions (Mann, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e1945\u003c/span\u003e; Sen, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e1968\u003c/span\u003e). Only a handful of pipeline studies, such as those using Bai\u0026ndash;Perron breakpoint analysis (Bai \u0026amp; Perron, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e1998\u003c/span\u003e), have explored structural shifts, leaving a methodological gap for integrating these statistical tools with proximity-based indices in African urban contexts (Nwilo, P. C. \u0026amp; Badejo, O. T., 2005).\u003c/p\u003e\u003cp\u003eThis study aims to (1) Apply a Proximity-Based Risk Index (PBRI) integrating Euclidean distance metrics and kernel density estimation, (2) quantify spatiotemporal encroachment trends in Savelugu Municipality using Mann-Kendall tests and Sen\u0026rsquo;s Slope estimator, and (3) identify structural breakpoints in risk accumulation via Bai-Perron analysis.\u003c/p\u003e\u003cp\u003eThe PBRI, by synthesising proximity weighting with spatiotemporal statistical analysis, advances pipeline risk assessment in two key ways: (1) it operationalises dynamic encroachment intensification metrics to anticipate evolving hazards, and (2) it offers a replicable framework for data-constrained African contexts through hybrid remote sensing. The findings will inform regulatory bodies, pipeline operators, and urban planners by pinpointing high-risk zones, quantifying escalation rates, and identifying critical hotspots for intervention. Ultimately, this research contributes to safeguarding energy infrastructure, enhancing community resilience, and guiding evidence-based land-use policies.\u003c/p\u003e\u003cp\u003eFollowing this introduction, Section 2 details the study area and data sources, elaborating on the geospatial pre-processing. It also presents the analytical methods, including risk zoning classification, PBRI computation, trend detection, and hotspot mapping. Section 3 reports the results, highlighting temporal and spatial risk patterns. Section 4 discusses the results, addresses limitations, and proposes future research avenues. The paper concludes with a summary of key contributions and practical recommendations for stakeholders.\u003c/p\u003e"},{"header":"2. Materials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Study Area\u003c/h2\u003e\u003cp\u003eSavelugu Municipality (9.624\u0026deg; N, 0.828\u0026deg; W), situated in Ghana\u0026rsquo;s Northern Region (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), is characterised by rapid urbanisation and unplanned spatial development. The municipality, with a population of 122,888 and an urbanisation rate of 62.9% (Ghana Statistical Service, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), faces intensifying pressure on land use, particularly along the Tamale\u0026ndash;Bolgatanga corridor, a strategic transport route intersecting with oil pipeline infrastructure (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The terrain, predominantly flat with elevations of 150\u0026ndash;800 feet, is prone to seasonal flooding in the northern zones (Hajaratu et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2 Data Collection\u003c/h2\u003e\u003cp\u003ePipeline route data were acquired through geospatial demarcations provided by Ghana\u0026rsquo;s Bulk Oil Storage and Transportation Company Limited (BOST). Multitemporal satellite imagery of the study area was also procured from Google Earth Pro (version 7.3.6.10201 (64-bit)), encompassing cloud-free scenes for the years 2008, 2011, 2013, 2014, 2017, 2019, 2020, 2021, and 2024. Image selection adhered to temporal availability and spatial clarity criteria, with Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e providing a representative 2024 baseline of urban development patterns adjacent to the pipeline corridor.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e2.3 Data Analysis\u003c/h2\u003e\u003cdiv id=\"Sec6\" class=\"Section3\"\u003e\u003ch2\u003e2.3.1 \u003cb\u003eData Preprocessing\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eThe multitemporal satellite imagery and spatial coordinates delineating the oil pipeline trajectories were integrated into Quantum Geographic Information System (QGIS) software (version 3.34.3-Prizren) to generate a raster and vector-based geodigital representation of the study area\u0026rsquo;s infrastructure and pipeline network layers. These datasets were georeferenced within QGIS using the World Geodetic System 1984 (WGS84) coordinate reference system (EPSG:4326) to ensure alignment with the pipeline vector layer. A systematic manual digitisation process was employed to identify critical infrastructure within the study area, including residential, educational, healthcare, governmental, commercial, and industrial structures. Each feature was assigned a unique geospatial identifier (GeoID) and stored as a point vector layer for all temporal years.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\u003ch2\u003e2.3.2 \u003cb\u003eInfrastructure Proximity Computation\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eTo model proximity dynamics, the QGIS \u0026ldquo;Random Points on Lines\u0026rdquo; algorithm was executed on the pipeline vector layer, generating 1,000,000 equidistant sampling points along the pipeline corridor. Parameters were configured with a minimum inter-point distance of 0 meters to maximise spatial resolution. Subsequently, the \u0026ldquo;Distance to Nearest Hub (Points)\u0026rdquo; algorithm computed Euclidean distances between infrastructure points (origin layer) and pipeline sampling points (destination layer), deriving centroid-based proximity metrics. Yearly hub distance layers were synthesised, each containing infrastructure GeoIDs and their minimum linear distances to the pipeline network (in meters).\u003c/p\u003e\u003cp\u003eData integrity was ensured through iterative validation. A stratified random sample of infrastructure locations was cross-verified via Global Navigation Satellite System (GNSS) field surveys. Discrepancies between computed and observed distances exceeding 5 meters triggered algorithmic recalibration, achieving a final positional error tolerance of \u0026plusmn;\u0026thinsp;2 meters across all layers. This hybrid approach harmonised automated geospatial processing with ground-truthing to mitigate systematic biases inherent in satellite-derived datasets.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section3\"\u003e\u003ch2\u003e2.3.3 \u003cb\u003eRisk Zoning Classification\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eHigh Consequence Areas (HCAs), as defined by PHMSA, represent zones where pipeline failures could result in severe consequences to human safety, property, or the environment (PHMSA, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). To operationalise HCA delineation in the study area, the Potential Impact Radius (PIR) framework was adopted, following the methodology outlined in 49 CFR \u0026sect;\u0026nbsp;192.903 (Title 49 of the Code of Federal Regulations (CFR), \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). 49 CFR \u0026sect;\u0026nbsp;192.903 is a regulatory provision under the U.S. Code of Federal Regulations that defines key terms used in the integrity management of oil and gas transmission pipelines, including High Consequence Areas (HCAs) and the Potential Impact Radius (PIR), a calculated distance within which a pipeline rupture could cause significant harm to people or the environment. PIR defines the radial extent of potential hazard impact from a pipeline rupture and is calculated using the formula:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:\\text{P}\\text{I}\\text{R}=0.69\\times\\:\\sqrt{{\\text{D}}^{2}\\times\\:\\text{P}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(1\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere D is the pipeline diameter in inches and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{P}\\)\u003c/span\u003e\u003c/span\u003e is the Maximum Allowable Operating Pressure (MAOP) in pounds per square inch (psi). For this study, D and P were obtained from Ghana\u0026rsquo;s Bulk Oil Storage and Transportation Company Limited (BOST) technical specifications.\u003c/p\u003e\u003cp\u003eThe computed PIR value served as the foundational threshold for risk zonation. Three concentric risk zones were demarcated to quantify encroachment intensity: (1) High-Risk Zone (HRZ) for Infrastructure within the PIR boundary (\u0026le;\u0026thinsp;PIR), where pipeline breaches pose immediate threats of fatalities, severe injuries, or catastrophic environmental damage due to thermal radiation, toxic vapor dispersion, or blast overpressure (Moftakhari \u0026amp; AghaKouchak, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), (2) Moderate-Risk Zone (MRZ) for Infrastructure within 1\u0026ndash;2 times the PIR (PRI\u0026ndash;2*PIR), where secondary hazards such as structural damage, secondary fires, or lower-concentration inhalation risks prevail, and (3) Low-Risk Zone (LRZ) for Infrastructure beyond (\u0026gt;\u0026thinsp;2*PIR), primarily associated with long-term environmental contamination risks.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section3\"\u003e\u003ch2\u003e2.3.4 \u003cb\u003eProximity-Based Risk Index\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eTo synthesise multi-zone encroachment dynamics into a composite risk metric reflecting relative hazard severity, a Proximity-Based Risk Index (PBRI) was formulated. PBRI integrates infrastructure density within predefined risk zones while weighting closer infrastructure more heavily. This index, adapted in various risk assessment frameworks, is commonly used in environmental risk, epidemiology, and urban planning studies to quantify exposure or risk based on spatial clustering and distance decay effects (Omobhude \u0026amp; Chen, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). The PBRI was calculated as follows:\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:\\text{P}\\text{B}\\text{R}\\text{I}=\\frac{{\\sum\\:}_{\\text{i}}^{\\text{n}}({\\text{W}}_{\\text{i}}\\times\\:{\\text{N}}_{\u0026lt;\\text{d},\\text{i}})}{{\\text{N}}_{\\text{t}\\text{o}\\text{t}\\text{a}\\text{l},\\:\\text{i}}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(2\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eW\u003csub\u003ei​\u003c/sub\u003e represents fixed weighting factors assigned to each risk zone (HRZ\u0026thinsp;=\u0026thinsp;3, MRZ\u0026thinsp;=\u0026thinsp;2, LRZ\u0026thinsp;=\u0026thinsp;1). By weighting closer infrastructure more heavily, PBRI captures the disproportionate contribution of high-risk encroachment to the overall threat profile. Weighting values were derived from PHMSA\u0026rsquo;s consequence-based prioritisation framework, which assigns higher urgency to infrastructure in zones with immediate life-safety risks (PHMSA, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{N}}_{\u0026lt;\\text{d},\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e denotes the count of infrastructure units within zone i, (HRZ, MRZ, or LRZ) at time t, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{N}}_{\\text{t}\\text{o}\\text{t}\\text{a}\\text{l},\\:\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e​ is the total infrastructure count across all zones at time t.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section3\"\u003e\u003ch2\u003e2.3.5 \u003cb\u003eTrend Detection via Non-Parametric Methods\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eTo assess the presence of a monotonic trend in the PBRI time series from 2008 to 2024, the Mann\u0026ndash;Kendall (MK) Test was employed. The MK Test is a non-parametric statistical test used to identify trends in a time series dataset. Developed by Mann, H. B. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e1945\u003c/span\u003e), it is widely applied in environmental science, hydrology, and meteorology to assess whether there is a statistically significant monotonic (increasing or decreasing) trend in a data. In our study, we employed the Mann\u0026ndash;Kendall (MK) test to check whether there has been any significant increase or decrease in the proximity risk metrics over the study period due to encroachment.\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:\\text{S}=\\sum\\:_{\\text{i}-1}^{\\text{n}-1}\\sum\\:_{\\text{j}=\\text{i}+1}^{\\text{n}}\\text{s}\\text{g}\\text{n}({\\text{x}}_{\\text{j}}-{\\text{x}}_{\\text{i}})\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(3\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$$\\:{\\tau\\:}=\\frac{\\text{S}}{\\frac{1}{2}\\text{n}(\\text{n}-1)}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(4\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{x}}_{\\text{j}}\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{x}}_{\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e are sequential PRI scores, n is the length of the time series, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{s}\\text{g}\\text{n}\\left(\\right)\\)\u003c/span\u003e\u003c/span\u003e is the signum function:\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$$\\:\\text{s}\\text{g}\\text{n}\\left({\\text{x}}_{\\text{j}}-{\\text{x}}_{\\text{i}}\\right)=\\left\\{\\begin{array}{c}+1\\\\\\:0\\\\\\:-1\\end{array}\\:\\:\\begin{array}{c}\\text{i}\\text{f}\\:{\\text{x}}_{\\text{j}}\u0026gt;{\\text{x}}_{\\text{i}}\\:\\\\\\:\\text{i}\\text{f}\\:{\\text{x}}_{\\text{j}}={\\text{x}}_{\\text{i}}\\\\\\:\\text{i}\\text{f}\\:{\\text{x}}_{\\text{j}}\u0026lt;{\\text{x}}_{\\text{i}}\\end{array}\\right.\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(5\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe MK test statistic S and effect size τ were computed, with significance evaluated at the α\u0026thinsp;=\u0026thinsp;0.05 level. This rank-based, distribution-free test obviates the need for residual normality and linearity assumptions inherent in parametric regression. Complementing the MK test, LOESS (locally weighted scatterplot smoothing) was applied to the PBRI series to visualise trend behaviour with a 95% confidence interval, guiding interpretation of temporal risk trajectories.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section3\"\u003e\u003ch2\u003e2.3.6 \u003cb\u003eSlope Estimation\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eTo quantify the median rate of change in PBRI, Sen\u0026rsquo;s slope estimator (Theil\u0026ndash;Sen robust method) was calculated as the median of all pairwise slopes between PBRI observations (year indices vs. PBRI values). The Sen\u0026rsquo;s Slope Estimator is a statistical technique used to estimate the slope of a trend line in bivariate data. It is particularly robust to outliers and does not assume normality of the residuals. This makes it a preferred method for analysing data where outliers or non-linearities could bias the results (Sen, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e1968\u003c/span\u003e; Theil, H., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e1950\u003c/span\u003e).\u003cdiv id=\"Equf\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equf\" name=\"EquationSource\"\u003e\n$$\\:{{\\beta\\:}}_{\\text{i}\\text{j}}=\\frac{{\\text{y}}_{\\text{j}}-{\\text{y}}_{\\text{i}}}{{\\text{x}}_{\\text{j}}-{\\text{x}}_{\\text{i}}}\\:\\:\\text{f}\\text{o}\\text{r}\\:\\text{a}\\text{l}\\text{l}\\:\\text{i}\u0026lt;\\text{j}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(6\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equg\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equg\" name=\"EquationSource\"\u003e\n$$\\:{\\beta\\:}=\\text{M}\\text{e}\\text{d}\\text{i}\\text{a}\\text{n}\\:\\left({{\\beta\\:}}_{\\text{i}\\text{j}}\\right)\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(7\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{\\beta\\:}}_{\\text{i}\\text{j}}\\)\u003c/span\u003e\u003c/span\u003e is the slope between all pairs of points, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{x}}_{\\text{j}},{\\text{x}}_{\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e are time points and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{y}}_{\\text{j}},{\\text{y}}_{\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e are observed PRI scores. The final Sen\u0026rsquo;s Slope (β) is the median of all pairwise slopes.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section3\"\u003e\u003ch2\u003e2.3.7 \u003cb\u003eStructural Breakpoint Analysis\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eTo identify temporal inflection points in risk accumulation, the Bai\u0026ndash;Perron multiple structural change procedure was implemented on the PBRI series using RStudio software (version 2023.12.1 Build 402). Structural Breakpoint Analysis is a statistical technique used to identify multiple structural changes (or breakpoints) within a time series or regression model. These breakpoints represent moments where the underlying relationship between variables undergoes significant change, such as changes in trend, mean, or variance (Bai \u0026amp; Perron, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Bai \u0026amp; Perron, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2003\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eIn our study, breakpoint candidates in the PBRI series were estimated via dynamic programming, minimising the residual sum of squares (RSS) for models with up to m breaks. Model selection leveraged the Bayesian Information Criterion (BIC), with optimal break number and dates selected under the null hypothesis of k breaks.\u003cdiv id=\"Equh\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equh\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}\\text{m}\\text{i}\\text{n}\\\\\\:{\\text{t}}_{1,}{\\text{t}}_{2}\\dots\\:\\dots\\:,{\\text{t}}_{\\text{m}}\\end{array}\\sum\\:_{\\text{j}=0}^{\\text{m}}\\text{R}\\text{S}\\text{S}({\\text{t}}_{\\text{j}},{\\text{t}}_{\\text{j}+1})\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(8\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere m is the number of breakpoints, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{t}}_{\\text{j}}\\)\u003c/span\u003e\u003c/span\u003e is the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{j}-\\text{t}\\text{h}\\)\u003c/span\u003e\u003c/span\u003e breakpoint, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{t}}_{0}=0\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{t}}_{\\text{m}+\\text{t}}=\\text{n}\\text{u}\\text{m}\\text{b}\\text{e}\\text{r}\\:\\text{o}\\text{f}\\:\\text{o}\\text{b}\\text{s}\\text{e}\\text{r}\\text{v}\\text{a}\\text{t}\\text{i}\\text{o}\\text{n}\\text{s}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{R}\\text{S}\\text{S}\\left({\\text{t}}_{\\text{j}},{\\text{t}}_{\\text{j}+1}\\right)\\)\u003c/span\u003e\u003c/span\u003e is the residual sum of squares (RSS) for observations from \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{t}}_{\\text{j}}+1\\)\u003c/span\u003e\u003c/span\u003e to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{t}}_{\\text{j}+1}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section3\"\u003e\u003ch2\u003e2.3.9 \u003cb\u003eSpatial Density Estimation\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eKernel Density Estimation (KDE) was applied to the point infrastructure layers for each temporal year to portray the spatiotemporal distribution of encroachment hotspots. KDE is a statistical technique used to estimate the density function of spatial data. It provides insight into how data points are distributed across a geographic space or multidimensional plane (Silverman, B. W, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e1986\u003c/span\u003e). The goal of using KDE in our study is to model the intensity of observations (infrastructure encroachment) in space for spatial point patterns and distributions.\u003c/p\u003e\u003cp\u003eUsing a Gaussian kernel and bandwidth determined by Silverman\u0026rsquo;s rule of thumb (Harpole et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), continuous density rasters were generated in QGIS, enabling visualisation of clustering intensity along the pipeline corridor.\u003cdiv id=\"Equi\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equi\" name=\"EquationSource\"\u003e\n$$\\:\\widehat{\\text{f}}\\left(\\text{x}\\right)=\\frac{1}{\\text{n}\\text{h}}\\sum\\:_{\\text{i}=1}^{\\text{n}}\\left({\\varnothing}\\frac{\\text{x}-{\\text{x}}_{\\text{i}}}{\\text{h}}\\right)\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(9\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equj\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equj\" name=\"EquationSource\"\u003e\n$$\\:{\\varnothing}\\left(\\text{u}\\right)=\\frac{1}{\\sqrt{2{\\pi\\:}}}{\\text{e}}^{-\\frac{{\\text{u}}^{2}}{2}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(10\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\widehat{\\text{f}}\\left(\\text{x}\\right)\\)\u003c/span\u003e\u003c/span\u003e is the estimated density at location x, n is the number of data points, h is the bandwidth (smoothing parameter), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\varnothing}\\left(\\text{u}\\right)\\)\u003c/span\u003e\u003c/span\u003e is the standard Gaussian kernel, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{x}}_{\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e​ are the observed data points, and h is the bandwidth (smoothing parameter).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section3\"\u003e\u003ch2\u003e2.3.10 \u003cb\u003eDescriptive Statistics\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eFor each risk zone and time slice, infrastructure counts \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left({\\text{N}}_{\u0026lt;\\text{d},\\text{t}}\\right)\\)\u003c/span\u003e\u003c/span\u003e for all risk zones and the total infrastructure \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left({\\text{N}}_{\\text{t}\\text{o}\\text{t}\\text{a}\\text{l},\\:\\text{t}}\\right)\\)\u003c/span\u003e\u003c/span\u003e were tabulated. Summary metrics (arithmetic mean and standard deviation) of the minimum distances within HRZ and Encroachment Zone (EZ) were computed in RStudio (version 2023.12.1 Build 402) and cross-validated in Excel 2021 (Version 2108).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec15\" class=\"Section3\"\u003e\u003ch2\u003e2.3.11 \u003cb\u003eEncroachment Ratio\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eTo quantify relative encroachment intensity on the oil pipeline, Encroachment Ratio (ER), a metric used to quantify the extent to which one land use intrudes upon another, was used.\u003cdiv id=\"Equk\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equk\" name=\"EquationSource\"\u003e\n$$\\:{\\text{E}\\text{R}}_{\\text{t}}^{\u0026lt;\\text{d}}=\\left(\\frac{{\\text{N}}_{\u0026lt;\\text{d},\\text{t}}}{{\\text{N}}_{\\text{t}\\text{o}\\text{t}\\text{a}\\text{l},\\:\\text{t}}}\\right)\\times\\:100\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(11\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{N}}_{\u0026lt;\\text{d},\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e​ denotes the infrastructure count within a zone distance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{d}\\)\u003c/span\u003e\u003c/span\u003e at year \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{t}\\)\u003c/span\u003e\u003c/span\u003e, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{N}}_{\\text{t}\\text{o}\\text{t}\\text{a}\\text{l},\\:\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e is the total infrastructure count of our study area.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec16\" class=\"Section3\"\u003e\u003ch2\u003e2.3.12 \u003cb\u003eEncroachment Growth Rate\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eWe used Encroachment Growth Rate (EGR) calculations to express the year-on-year percentage change of infrastructure encroachment. EGR measures the rate at which encroachment (unwanted intrusion or expansion) increases over time within a specified boundary or domain. It is commonly used in environmental studies, urban planning, and land-use change analysis to quantify the expansion of human activities, settlements, or invasive species into natural or protected areas (Rowland, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2003\u003c/span\u003e).\u003cdiv id=\"Equl\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equl\" name=\"EquationSource\"\u003e\n$$\\:{\\text{E}\\text{G}\\text{R}}_{\\text{t}}^{\u0026lt;\\text{d}}=\\frac{{\\text{N}}_{\u0026lt;\\text{d},\\text{t}}-{\\text{N}}_{\u0026lt;\\text{d},\\text{t}-1}}{{\\text{N}}_{\u0026lt;\\text{d},\\text{t}-1}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(12\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{N}}_{\u0026lt;\\text{d},\\text{t}-1}\\)\u003c/span\u003e\u003c/span\u003e is the count of infrastructure units within the same zone distance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{d}\\)\u003c/span\u003e\u003c/span\u003e in the previous year (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{t}-1\\)\u003c/span\u003e\u003c/span\u003e), \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{N}}_{\u0026lt;\\text{d},\\text{t}}\\)\u003c/span\u003e\u003c/span\u003e is the number of encroachment infrastructures within distance d at time t.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec17\" class=\"Section3\"\u003e\u003ch2\u003e2.3.13 \u003cb\u003eCumulative Encroachment Index\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eTo integrate temporal encroachment pressure into a single normalised metric, the Cumulative Encroachment Index (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{C}\\text{E}\\text{I}\\)\u003c/span\u003e\u003c/span\u003e) at year t for zone distance \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{d}\\)\u003c/span\u003e\u003c/span\u003e was computed as the arithmetic mean of annual ratios. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\text{C}\\text{E}\\text{I}\\)\u003c/span\u003e\u003c/span\u003e provides a normalised measure of encroachment intensity of human activities into natural or protected areas over time relative to the total area or available units.\u003cdiv id=\"Equm\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equm\" name=\"EquationSource\"\u003e\n$$\\:{\\text{C}\\text{E}\\text{I}}_{\\text{t}}^{\u0026lt;\\text{d}}=\\frac{1}{\\text{t}}\\sum\\:_{\\text{i}=1}^{\\text{t}}\\frac{{\\text{N}}_{\u0026lt;\\text{d},\\text{i}}}{{\\text{N}}_{\\text{t}\\text{o}\\text{t}\\text{a}\\text{l},\\:\\text{i}}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(13\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{C}\\text{E}\\text{I}}_{\\text{t}}^{\u0026lt;\\text{d}}\\)\u003c/span\u003e\u003c/span\u003e is the Cumulative Encroachment Index up to time t for encroachments within distance d, t is the total time periods, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{N}}_{\u0026lt;\\text{d},\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e is the number of encroachment infrastructures within distance d at time i and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{N}}_{\\text{t}\\text{o}\\text{t}\\text{a}\\text{l},\\:\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e is the total number of encroachment infrastructure at time i.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec19\" class=\"Section2\"\u003e\u003ch2\u003e3.1 \u003cb\u003eRisk Zoning Classification\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eThe Potential Impact Radius (PIR) was calculated using the formula outlined in 49 CFR \u0026sect;\u0026nbsp;192.903. Incorporating the pipeline\u0026rsquo;s technical specifications, a diameter (D) of 8 inches and a maximum allowable operating pressure (P) of 1,200 psi, we achieved a PIR value of 58.28 meters. This PIR value delineated four concentric risk zones (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The HRZ threshold (50 meters) is conservatively set below the computed PIR (58.28 meters) to account for localised terrain variability and ensure alignment with the PHMSA\u0026rsquo;s precautionary buffer recommendations.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eRisk zone classification framework based on Potential Impact Radius (PIR).\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDistance Range\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eZone\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eKey Threats\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;50 meters\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eHigh-Risk Zone (HRZ)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eImmediate fatalities or severe injuries.\u003c/p\u003e\u003cp\u003e-Thermal radiation\u0026thinsp;\u0026gt;\u0026thinsp;10 kW/m\u0026sup2;\u003c/p\u003e\u003cp\u003e-Toxic vapour clouds (H₂S, benzene)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e50\u0026ndash;100 meters\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModerate-Risk Zone (MRZ)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eStructural damage from blasts.\u003c/p\u003e\u003cp\u003e-Secondary fires/heat exposure\u003c/p\u003e\u003cp\u003e-Thermal radiation\u0026thinsp;\u0026gt;\u0026thinsp;5 kW/m\u0026sup2;\u003c/p\u003e\u003cp\u003e-Inhalation hazards (lower concentrations)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;100 meters\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eEncroachment Zone\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eCombined risks of HRZ\u0026thinsp;+\u0026thinsp;MRZ\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u0026gt;\u0026thinsp;100 meters\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eLow-Risk Zone (LRZ)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eLong-term environmental contamination (soil/water)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eTemporal analysis of infrastructure encroachment near underground oil pipelines in Savelugu Municipality, Ghana (2008\u0026ndash;2024). The table presents: (1) Infrastructure counts by risk zone (High-Risk Zone [HRZ: \u0026lt;50m], Moderate-Risk Zone [MRZ: 50-100m], Low-Risk Zone [LRZ: \u0026gt;100m]); (2) Mean proximity distances (m) with standard deviations; (3) Encroachment Ratios (ER) by zone; and (4) annual Encroachment Growth Rates (EGR).\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"21\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c15\" colnum=\"15\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c16\" colnum=\"16\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c17\" colnum=\"17\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c18\" colnum=\"18\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c19\" colnum=\"19\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c20\" colnum=\"20\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c21\" colnum=\"21\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003eInfrastructure Count\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e\u003cp\u003eMean Distance to Pipeline\u003c/p\u003e\u003cp\u003e(Metres)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e\u003cp\u003eStandard Deviation\u003c/p\u003e\u003cp\u003e(Metres)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"6\" nameend=\"c16\" namest=\"c11\"\u003e\u003cp\u003eEncroachment Ratio (ER)\u003c/p\u003e\u003cp\u003e(Percentage)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c21\" namest=\"c17\"\u003e\u003cp\u003eEncroachment Growth Rate (EGR)\u003c/p\u003e\u003cp\u003e(Percentage)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDate\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eHRZ\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eEZ\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMRZ\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eLRZ\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eTotal\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eHRZ\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003eEZ\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c9\"\u003e\u003cp\u003eHRZ\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c10\"\u003e\u003cp\u003eEZ\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c11\"\u003e\u003cp\u003eHRZ\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c12\"\u003e\u003cp\u003eEZ\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c13\"\u003e\u003cp\u003eMRZ\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c14\"\u003e\u003cp\u003eLRZ\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c15\"\u003e\u003cp\u003eTotal\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c17\" namest=\"c16\"\u003e\u003cp\u003eHRZ\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c18\"\u003e\u003cp\u003eEZ\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c19\"\u003e\u003cp\u003eMRZ\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c20\"\u003e\u003cp\u003eLRZ\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c21\"\u003e\u003cp\u003eTotal\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eFeb-08\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e38\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e3,179\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e3,239\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e31.34\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e58.57\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e12.15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e24.44\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0.68\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e1.85\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e1.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e2.83\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c17\" namest=\"c16\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c18\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c19\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c20\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c21\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eNov-11\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e24\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e64\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e3,216\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e3,280\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e30.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e56.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e12.43\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e25.24\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0.73\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e1.95\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e1.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.98\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e2.93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c17\" namest=\"c16\"\u003e\u003cp\u003e+\u0026thinsp;9.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c18\"\u003e\u003cp\u003e+\u0026thinsp;6.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c19\"\u003e\u003cp\u003e+\u0026thinsp;5.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c20\"\u003e\u003cp\u003e+\u0026thinsp;1.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c21\"\u003e\u003cp\u003e+\u0026thinsp;1.3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eDec-13\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e136\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e84\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e4,210\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e4,346\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e29.83\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e56.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e11.49\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e25.32\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e1.20\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e3.13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e1.93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e4.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c17\" namest=\"c16\"\u003e\u003cp\u003e+\u0026thinsp;116.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c18\"\u003e\u003cp\u003e+\u0026thinsp;112.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c19\"\u003e\u003cp\u003e+\u0026thinsp;110.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c20\"\u003e\u003cp\u003e+\u0026thinsp;30.9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c21\"\u003e\u003cp\u003e+\u0026thinsp;32.5\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eDec-14\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e139\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e84\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e4,327\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e4,466\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e30.55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e56.86\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e12.02\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e25.03\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e1.23\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e3.11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e1.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e4.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c17\" namest=\"c16\"\u003e\u003cp\u003e+\u0026thinsp;5.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c18\"\u003e\u003cp\u003e+\u0026thinsp;2.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c19\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c20\"\u003e\u003cp\u003e+\u0026thinsp;2.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c21\"\u003e\u003cp\u003e+\u0026thinsp;2.8\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eOct-17\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e86\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e199\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e113\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e5,269\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e5,468\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e29.78\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e55.95\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e11.97\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e26.54\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e1.57\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e3.64\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e2.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e4.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c17\" namest=\"c16\"\u003e\u003cp\u003e+\u0026thinsp;56.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c18\"\u003e\u003cp\u003e+\u0026thinsp;43.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c19\"\u003e\u003cp\u003e+\u0026thinsp;34.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c20\"\u003e\u003cp\u003e+\u0026thinsp;21.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c21\"\u003e\u003cp\u003e+\u0026thinsp;22.4\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eNov-19\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e100\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e227\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e127\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e5,613\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e5,840\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e28.50\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e55.80\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e12.52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e27.75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e1.71\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e3.89\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e2.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e4.85\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c17\" namest=\"c16\"\u003e\u003cp\u003e+\u0026thinsp;16.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c18\"\u003e\u003cp\u003e+\u0026thinsp;14.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c19\"\u003e\u003cp\u003e+\u0026thinsp;12.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c20\"\u003e\u003cp\u003e+\u0026thinsp;6.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c21\"\u003e\u003cp\u003e+\u0026thinsp;6.8\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eNov-20\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e109\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e238\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e129\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e5,912\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e6,150\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e29.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e55.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e12.49\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e26.68\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e1.77\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e3.87\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e2.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e4.83\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c17\" namest=\"c16\"\u003e\u003cp\u003e+\u0026thinsp;9.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c18\"\u003e\u003cp\u003e+\u0026thinsp;4.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c19\"\u003e\u003cp\u003e+\u0026thinsp;1.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c20\"\u003e\u003cp\u003e+\u0026thinsp;5.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c21\"\u003e\u003cp\u003e+\u0026thinsp;5.3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eNov-21\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e119\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e287\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e168\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e6,266\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e6,553\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e28.34\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e54.92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e12.61\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e25.91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e1.82\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e4.38\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e2.56\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e5.34\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c17\" namest=\"c16\"\u003e\u003cp\u003e+\u0026thinsp;9.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c18\"\u003e\u003cp\u003e+\u0026thinsp;20.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c19\"\u003e\u003cp\u003e+\u0026thinsp;30.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c20\"\u003e\u003cp\u003e+\u0026thinsp;6.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c21\"\u003e\u003cp\u003e+\u0026thinsp;6.6\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eApr-24\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e142\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e313\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e171\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e6,695\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e7,008\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e27.65\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e52.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e13.33\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e27.43\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e2.03\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e4.47\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e2.44\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e5.42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c17\" namest=\"c16\"\u003e\u003cp\u003e+\u0026thinsp;19.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c18\"\u003e\u003cp\u003e+\u0026thinsp;9.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c19\"\u003e\u003cp\u003e+\u0026thinsp;1.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c20\"\u003e\u003cp\u003e+\u0026thinsp;6.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c21\"\u003e\u003cp\u003e+\u0026thinsp;6.9\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec20\" class=\"Section2\"\u003e\u003ch2\u003e3.2 \u003cb\u003eDescriptive Statistics\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eTotal infrastructure count of the study area exhibited progressive growth, quantified as 3,239 points (2008), 3,280 (2011), 4,210 (2013), 4,466 (2014), 5,468 (2017), 5,840 (2019), 6,150 (2020), 6,553 (2021), and 7,008 (2024). Annual counts of infrastructure units within each risk zone were tabulated for nine temporal snapshots (2008\u0026ndash;2024). As reported in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, total infrastructure increased from 3,239 units in February 2008 to 7,008 units in April 2024. HRZ counts rose from 22 to 142 units, MRZ from 38 to 171, EZ from 60 to 313, and LRZ from 3,179 to 6,695 over the study period​. The cumulative infrastructure growth underscores spatial expansion across all proximity thresholds.\u003c/p\u003e\u003cp\u003eDescriptive statistics for infrastructure distances to the pipeline within HRZ and EZ were computed. Between 2008 and 2024, the mean distance in HRZ decreased from 31.34 m to 27.65 m, while the EZ mean declined from 58.57 m to 52.30 m.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec21\" class=\"Section2\"\u003e\u003ch2\u003e3.3 \u003cb\u003eEncroachment Ratio, Growth Rate, and Index Metrics\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eEncroachment Ratio (ER) values, representing the percentage of total infrastructure within HRZ, MRZ, and LRZ, are detailed in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. HRZ\u0026rsquo;s ER increased from 0.68% (Feb 2008) to 2.03% (Apr 2024); MRZ\u0026rsquo;s ER rose from 1.17\u0026ndash;2.44%; LRZ's ER remained stable at approximately 0.96%. The aggregated ER for EZ escalated from 2.83\u0026ndash;5.42% over the analysis period.\u003c/p\u003e\u003cp\u003eYear-on-year Encroachment Growth Rates (EGR) for each zone are also reported in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The largest singleinterval increases occurred between 2011 and 2013 (HRZ: +116.6 %; MRZ: +110.0 %; LRZ: +30.9 %; Total: +32.5 %). Subsequent intervals exhibited variable growth, with HRZ\u0026rsquo;s EGR ranging from +\u0026thinsp;5.7 % to +\u0026thinsp;56.3 %; MRZ from +\u0026thinsp;0.0 % to +\u0026thinsp;34.5 %; and LRZ from +\u0026thinsp;1.1 % to +\u0026thinsp;21.7 %.\u003c/p\u003e\u003cp\u003eThe Cumulative Encroachment Index (CEI), representing the mean of annual ER values up to each year, were calculated over the full study period. CEI values attained were 1.415 for HRZ, 1.950 for MRZ, and 0.966 for LRZ, reflecting cumulative proximity pressure​.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec22\" class=\"Section2\"\u003e\u003ch2\u003e3.4 \u003cb\u003eProximity-Based Risk Index\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eThe ProximityBased Risk Index (PBRI), calculated as the weighted sum of zone-specific infrastructure counts normalised by total infrastructure, is shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. PBRI increased from 102.5 (Feb 2008) to 106.5 (Apr 2024). Risk level classifications transitioned from \u0026ldquo;Low\u0026rdquo; (PRI\u0026thinsp;\u0026lt;\u0026thinsp;105) during 2008\u0026ndash;2014 to \u0026ldquo;Moderate\u0026rdquo; (105\u0026thinsp;\u0026le;\u0026thinsp;PRI\u0026thinsp;\u0026lt;\u0026thinsp;107) from 2017 onward.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eTemporal progression of the Proximity-Based Risk Index (PBRI) and associated risk classifications.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eOriginal Date\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePBRI\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRisk Level\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFeb-08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e102.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eLow\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNov-11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e102.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eLow\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDec-13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e104.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eLow\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDec-14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e104.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eLow\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eOct-17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e105.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eModerate\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNov-19\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e105.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eModerate\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNov-20\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e105.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eModerate\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNov-21\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e106.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eModerate\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eApr-24\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e106.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eModerate\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec23\" class=\"Section2\"\u003e\u003ch2\u003e3.5 \u003cb\u003eTrend Detection\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eApplication of the Mann\u0026ndash;Kendall test to the PBRI time series yielded a Kendall\u0026rsquo;s tau (τ) of 0.959 (p\u0026thinsp;\u0026lt;\u0026thinsp;0.0001), indicating a statistically significant positive monotonic trend (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) ​. LOESS smoothing overlaid on the PBRI series exhibits a narrow 95% confidence envelope, corroborating trend consistency.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec24\" class=\"Section2\"\u003e\u003ch2\u003e3.6 \u003cb\u003eSlope Estimation\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eSen\u0026rsquo;s slope estimator quantified the median annual increase in PBRI at 0.268 PRI units/year, with a 95% confidence interval of [0.215, 0.311] (p\u0026thinsp;\u0026lt;\u0026thinsp;0.0001) (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e)​. Over the 16-year span, this corresponds to an aggregate increase of approximately 4.29 PRI units.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec25\" class=\"Section2\"\u003e\u003ch2\u003e3.7 \u003cb\u003eStructural Breakpoint Analysis\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eUsing the Bai\u0026ndash;Perron method, three significant breakpoints were identified at 2012, 2016, and 2020 in the PBRI series, partitioning data into four segments (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) ​. Model selection via Bayesian Information Criterion yielded BIC = \u0026minus;\u0026thinsp;13.57 and residual sum of squares RSS\u0026thinsp;=\u0026thinsp;0.06. Segment mean annual PBRI increases were 2008\u0026ndash;2012: +0.18 units/year, 2012\u0026ndash;2016: +0.35 units/year, 2016\u0026ndash;2020: +0.25 units/year, and 2020\u0026ndash;2024: +0.40 units/year. These segments correspond temporally to observed infrastructure count surges in HRZ and MRZ.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec26\" class=\"Section2\"\u003e\u003ch2\u003e3.8 \u003cb\u003eKernel Density Estimation Heat Maps\u003c/b\u003e\u003c/h2\u003e\u003cp\u003eKernel Density Estimation (KDE) heat maps were generated for each temporal layer using a Gaussian kernel with bandwidth determined by Silverman\u0026rsquo;s rule of thumb. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e displays density raster, illustrating spatiotemporal clustering of infrastructure points along the pipeline corridor for 2008, 2011, 2017, 2019, 2020, 2021, and 2024​.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThis study quantified spatiotemporal risk intensification from urban encroachment on underground oil pipelines in Savelugu Municipality, Ghana, through a Proximity-Based Risk Index (PBRI). Key findings reveal a 545% increase in infrastructure within the High-Risk Zone (HRZ: \u0026lt;50 meters) and a 350% rise in the Moderate-Risk Zone (MRZ: 50\u0026ndash;100 meters) between 2008 and 2024. The PBRI transitioned from \"Low\" (102.5) to \"Moderate\" (106.5) risk, driven by cumulative infrastructure growth and reduced mean proximity distances (HRZ: 31.34 m to 27.65 m; Encroachment Zone: 58.57 m to 52.30 m). Monotonic trend analysis (Mann\u0026ndash;Kendall τ\u0026thinsp;=\u0026thinsp;0.959, *p* \u0026lt; 0.0001) confirmed a statistically significant upward trajectory, with Sen\u0026rsquo;s slope estimating a median annual PBRI increase of 0.268 units (95% CI [0.215, 0.311]). Structural breakpoints in 2012, 2016, and 2020 delineated phases of accelerated risk accumulation linked to urbanisation surges and regulatory shifts. Kernel Density Estimation (KDE) further highlighted progressive infrastructure clustering along the pipeline corridor, exacerbating vulnerability.\u003c/p\u003e\u003cp\u003eThe observed trends align with Savelugu\u0026rsquo;s rapid urbanisation rate (62.9%) and governance gaps in land-use planning. As shown by (Yorgri et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), 82% of developers lacked awareness of building permits, enabling unchecked encroachment into pipeline buffer zones. The PBRI\u0026rsquo;s rise reflects the compounding effects of proximity-weighted infrastructure density, where closer developments disproportionately amplify hazard potential. Declining mean distances within HRZ and MRZ signify buffer erosion, mirroring patterns in Nigeria\u0026rsquo;s Niger Delta, where informal settlements encroach on pipelines (Jatto, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The structural breakpoints: 2012, 2016, and 2020 correspond to critical socio-political and environmental events. The 2016\u0026ndash;2020 deceleration (+\u0026thinsp;0.25) coincides with Savelugu\u0026rsquo;s 2018 municipal status upgrade, which may have introduced tentative land-use regulations. However, the post-2020 resurgence in PBRI slopes (+\u0026thinsp;0.40 units/year) likely reflects enforcement lapses and pandemic-induced rural\u0026ndash;urban migration, underscoring the fragility of regulatory frameworks in rapidly urbanising contexts. KDE-derived hotspot migration underscores that encroachment is neither uniform nor static: central and northern corridor segments have experienced the most intense pressure, likely due to their superior road connectivity and proximity to commercial hubs. These spatial patterns highlight the \u0026ldquo;corridor effect,\u0026rdquo; whereby transport arteries spur informal settlement growth (Yakubu, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThese findings corroborate and extend studies of urban expansion impacts on critical infrastructure in Sub-Saharan contexts. Abass et al. (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) documented how green space depletion in Kumasi heightened flood risks; similarly, our studies in Savelugu have shown that unplanned growth has eroded protective buffers around underground oil pipelines. (Jatto, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) observed that informal settlements in Nigeria\u0026rsquo;s Niger Delta reduced safe setback distances, paralleling the 11% contraction in our HRZ proximities. While these prior works focused on ecological or accident response outcomes, our study integrates spatiotemporal trend analyses, Sen\u0026rsquo;s slope, and Bai\u0026ndash;Perron breakpoints, with proximity indices, thereby operationalising dynamic hazard evolution rather than static snapshots.\u003c/p\u003e\u003cp\u003eTheoretically, this study advances pipeline risk modelling by integrating proximity metrics with spatiotemporal trend analysis. Unlike prior frameworks focusing on static hazard indices (Torretta, V. et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) or likelihood-consequence matrices (Henselwood \u0026amp; Phillips, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), our PBRI synthesises dynamic encroachment pressures through weighted distance decay and temporal trend detection. By weighting encroachment by distance decay and integrating non-parametric trend detection, the ProximityBased Risk Index (PBRI) encapsulates both intensity and velocity of hazard intensification. This dynamic framework could inform a revision of existing risk theory in linearinfrastructure contexts, emphasising the importance of breakpoints and trend acceleration phases.\u003c/p\u003e\u003cp\u003ePractically, our findings carry several actionable implications. First, pipeline operators and municipal authorities must institutionalise periodic encroachment surveys, leveraging GIS and KDE analytics to update risk zones and prioritise high-pressure segments. Second, community sensitisation programs are urgent. Enhancing building permit awareness among the 82% of uninformed developers could curtail informal constructions near pipelines. Finally, integrating remote sensing with GNSS ground-truthing, as demonstrated in this study, offers a replicable protocol for other data-scarce municipalities.\u003c/p\u003e\u003cp\u003eThree limitations of this study warrant consideration. First, reliance on cloud-free satellite imagery constrained temporal granularity, potentially underestimating short-term encroachment spikes. Second, socio-economic drivers of encroachment were inferred indirectly; household surveys could elucidate motivations behind permit violations. Third, the PBRI\u0026rsquo;s weighting scheme, while grounded in PHMSA guidelines, assumes uniform consequence severity across infrastructure types. A hospital within the HRZ may pose higher societal risks than a residential unit, yet the index treats them equally.\u003c/p\u003e\u003cp\u003eFuture studies should integrate participatory mapping and household-level surveys to understand the socioeconomic motives behind encroachment, enabling targeted behavioural interventions. Incorporating real‐time remote sensing, such as Unmanned Aerial Vehicles (UAV) imagery and machine‐learning\u0026ndash;based built‐up detection, could automate encroachment monitoring and mitigate manual digitisation limitations. Comparative analyses across multiple municipalities would test the PBRI\u0026rsquo;s transferability and inform regionally calibrated policy frameworks. Finally, coupling proximity-based indices with pipeline integrity monitoring (e.g., SCADA alarms, inline inspection data) could yield a holistic risk dashboard, bridging spatial and operational perspectives for comprehensive pipeline safety management.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study developed and applied a Proximity-Based Risk Index (PBRI) to assess the spatiotemporal intensification of infrastructure encroachment on an underground oil pipeline in Savelugu Municipality, Ghana. Using multitemporal satellite imagery, GIS-based proximity modelling, and statistical trend analysis, the research quantified changes in encroachment patterns from 2008 to 2024. Results revealed a 545% increase in infrastructure within the High-Risk Zone and a 350% rise within the Moderate-Risk Zone. The PBRI transitioned from a \u0026ldquo;Low\u0026rdquo; to a \u0026ldquo;Moderate\u0026rdquo; risk classification, with a statistically significant monotonic upward trend (τ\u0026thinsp;=\u0026thinsp;0.959, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.0001) and an annual growth rate of 0.268 units.\u003c/p\u003e\u003cp\u003eThese findings demonstrate a clear erosion of pipeline safety buffers over time, driven by unregulated urban expansion, land-use permit violations, and weak enforcement mechanisms. The identification of structural breakpoints in 2012, 2016, and 2020 underscores phases of intensified risk accumulation, corresponding with urbanisation surges and policy lapses. Spatial clustering of encroachment along the central and northern segments of the pipeline corridor further amplifies site-specific vulnerabilities.\u003c/p\u003e\u003cp\u003eThe study underscores the urgent need for integrated spatial planning, periodic GIS-based risk assessments, and targeted community sensitisation on development regulations. The PBRI framework offers a replicable and scalable approach for risk monitoring in data-constrained regions. Future research should incorporate household-level surveys and real-time remote sensing technologies to enhance the granularity and responsiveness of pipeline risk management strategies.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding Statement:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research was supported by the West African Centre for Water, Irrigation and Sustainable Agriculture (WACWISA-UDS) as part of a Master's support of the Corresponding Author.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of Interest Statement:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no conflict of interest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contributions:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFuseini Nyagsi Abdul Gafaru\u003c/strong\u003e: Conceptualisation, Data Collection, GIS Analysis, Writing – Original Draft\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDzigbodi Adzo Doke\u003c/strong\u003e: Supervision, Methodology Refinement, Writing – Review \u0026amp; Editing\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSamuel Jerry Cobbina\u003c/strong\u003e: Data Validation, Statistical Analysis, Writing – Review \u0026amp; Editing\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research was supported by the West African Centre for Water, Irrigation and Sustainable Agriculture (WACWISA-UDS).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of interest\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no conflict of interest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eClinical trial number\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFuseini Nyagsi Abdul Gafaru\u003c/strong\u003e: Conceptualisation, Data Collection, GIS Analysis, Writing – Original Draft\u003cbr\u003e\u003cstrong\u003eDzigbodi Adzo Doke\u003c/strong\u003e: Supervision, Methodology Refinement, Writing – Review \u0026amp; Editing\u003cbr\u003e\u003cstrong\u003eSamuel Jerry Cobbina\u003c/strong\u003e: Data Validation, Statistical Analysis, Writing – Review \u0026amp; Editing\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAbass, K., Buor, D., Afriyie, K., Dumedah, G., Segbefi, A. 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Examining the Impact of Physical Development Practices and Control in the Savelugu Township. OALib, 10(12), 1\u0026ndash;18. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.4236/oalib.1110296\u003c/span\u003e\u003cspan address=\"10.4236/oalib.1110296\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Underground oil pipeline, spatiotemporal risk, ProximityBased Risk Index, urban planning, Encroachment, Savelugu Municipality","lastPublishedDoi":"10.21203/rs.3.rs-7293238/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7293238/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eRapid urbanisation and unplanned development in Africa have intensified encroachment on oil pipelines, heightening risks of leaks and environmental contamination. In Savelugu, fragmented governance and permit violations have eroded oil pipeline safety buffers. While frameworks like the U.S. PHMSA\u0026rsquo;s HCA offer static risk benchmarks, dynamic spatiotemporal assessments remain underdeveloped. This study developed and applied a Proximity-Based Risk Index (PBRI) to quantify encroachment trends along an oil pipeline, addressing gaps in synthesising proximity metrics with temporal risk intensification analyses. Multitemporal satellite imagery (2008\u0026ndash;2024), pipeline vector data from Ghana\u0026rsquo;s BOST, and field-validated infrastructure coordinates were analysed using QGIS software. Euclidean distance metrics classified risk zones based on PHMSA\u0026rsquo;s PIR. Temporal trends were assessed via Mann\u0026ndash;Kendall tests, Sen\u0026rsquo;s slope estimator, and Bai\u0026ndash;Perron breakpoint analysis, while KDE mapped encroachment evolution. Infrastructure within HRZ surged by 545% and MRZ by 350% from 2008 to 2024. PBRI escalated from Low to Moderate, driven by declining mean proximity distances (HRZ: 31.34 m to 27.65 m). A significant positive monotonic trend (Kendall\u0026rsquo;s τ\u0026thinsp;=\u0026thinsp;0.959, *p* \u0026lt; 0.0001) and Sen\u0026rsquo;s slope (0.268 units/year) confirmed accelerating risk. Structural breakpoints (2012, 2016, 2020) revealed phased intensification, correlating with urban expansion and regulatory shifts. KDE highlighted clustering along central and northern pipeline segments. These findings underscore urgent needs for enhanced land-use planning, periodic encroachment monitoring, community sensitisation on permit compliance, and GIS-enhanced regulatory enforcement. The PBRI\u0026rsquo;s methodology offers a replicable model for data-scarce regions. Future work should integrate socioeconomic surveys and real-time remote sensing to optimise risk mitigation.\u003c/p\u003e","manuscriptTitle":"Spatiotemporal Risk Intensification from Encroachment on Underground Oil Pipelines: A Proximity-Based Indexing Approach","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-11 15:49:09","doi":"10.21203/rs.3.rs-7293238/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"5d3d0a15-4a4b-459b-bb92-1d05e4bcc257","owner":[],"postedDate":"September 11th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-12-23T13:55:21+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-11 15:49:09","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7293238","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7293238","identity":"rs-7293238","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}