Lessons for Sustainable Urban Development: Interplay of Construction, Groundwater Withdrawal, and Land Subsidence at Battersea, London

: The capacity of aquifers to store water and the stability of infrastructure can each be adversely inﬂuenced by variations in groundwater levels and subsequent land subsidence. Along the south bank of the River Thames, the Battersea neighbourhood of London is renovating a vast 42-acre (over 8 million sq ft) former industrial brownﬁeld site to become host to a community of homes, shops, bars, restaurants, cafes, ofﬁces, and over 19 acres of public space. For this renovation, between 2016 and 2020, a signiﬁcant number of bearing piles and secant wall piles, with diameters ranging from 450 mm to 2000 mm and depths of up to 60 m, were erected inside the Battersea Power Station. Additionally, there was considerable groundwater removal that caused the water level to drop by 2.55 ± 0.4 m/year between 2016 and 2020, as shown by Environment Agency data. The study reported here used Sentinel-1 C-band radar images and the persistent scatterer interferometric synthetic aperture radar (PSInSAR) methodology to analyse the associated land movement for Battersea, London, during this period. The average land subsidence was found to occur at the rate of − 6.8 ± 1.6 mm/year, which was attributed to large groundwater withdrawals and underground pile construction for the renovation work. Thus, this study underscores the critical interdependence between civil engineering construction, groundwater management, and land subsidence. It emphasises the need for holistic planning and sustainable development practices to mitigate the adverse effects of construction on groundwater resources and land stability. By considering the Sustainable Development Goals (SDGs) outlined by the United Nations, particularly Goal 11 (Sustainable Cities and Communities) and Goal 6 (Clean Water and Sanitation), city planners and stakeholders can proactively address these interrelated challenges.


Introduction
Land subsidence, the gradual sinking or lowering of the Earth's surface, is a significant concern in urban areas worldwide [1][2][3]. Factors such as excessive groundwater withdrawal and extensive piling work during construction can contribute to land subsidence, leading to negative consequences such as damage to infrastructure, environmental impacts, and threats to human safety [4][5][6][7]. Piling work involves the installation of piles, which are deep foundations that provide support to structures. Piles can transfer loads to more stable layers of soil, improving the stability of the constructed structure. However, excessive piling work can exacerbate subsidence issues [8][9][10]. Unchecked and unplanned groundwater abstraction can result in a significant decline in aquifer levels [11], leading to compaction  [51] This research aims to investigate the effects of land subsidence, piling work, and groundwater abstraction on the stability of Battersea, London, using PSInSAR techniques to monitor subsidence and provide recommendations for future urban development in the area. This research contributes novelty by investigating the interplay between construction activities, groundwater withdrawal, and land subsidence in the context of urban development, shedding light on their interconnected impacts. Furthermore, it highlights the importance of considering the Sustainable Development Goals (SDGs) as a framework for addressing these challenges and achieving sustainable and resilient cities. Additionally, the application of statistical tests to evaluate the correlations between subsidence and groundwater withdrawal provides a fresh perspective on understanding their relationship.
The main objectives of this research are to (a) investigate the spatial distribution and magnitude of land subsidence in Battersea using InSAR data; (b) determine the correlation between excessive groundwater withdrawal and observed land subsidence patterns; (c) analyse the relationship between extensive piling work during construction and land subsidence patterns; and (d) provide recommendations for mitigating subsidence risks, such as sustainable groundwater management practices or improved construction techniques.

Study Area
Battersea is a district located in Southwest London, England, and is part of the London Borough of Wandsworth ( Figure 1). It is situated on the south bank of the River Thames and is~2.9 miles (4.6 km) southwest of Charing Cross [52][53][54]. Battersea is a primarily residential area, but it has experienced significant development and regeneration in recent years [55]. This has involved rapid urbanisation and development, with several highprofile projects such as the Battersea Power Station redevelopment and the construction of new residential and commercial buildings [56]. One of the most iconic landmarks in Battersea is the Battersea Power Station, a decommissioned coal-fired power station that has become an architectural symbol of London [57]. The power station is currently undergoing significant redevelopment, which includes the construction of new residential, commercial, and cultural spaces [56]. Battersea is also known for its parks, notably Battersea Park, which is a 200-acre (83-hectare) green space featuring gardens, sports facilities, a boating lake, and a children's zoo [55]. The park offers a serene and aesthetically pleasing environment for both residents and visitors, reflecting the growing significance of recreational spaces that contribute to the overall liveability of cities and align with the goals outlined by the United Nations Sustainable Development Goals (SDGs).
Remote Sens. 2023, 15, x FOR PEER REVIEW 5 of 18 groundwater resources and addressing the possible consequences of construction activities on land subsidence in the area. By considering the intricate geological composition described above, valuable insights can be gained into the hydrogeological characteristics of Battersea to make informed assessments regarding the potential impacts of groundwater extraction on land subsidence. This knowledge contributes to a comprehensive understanding of the complexities involved and aids in ensuring sustainable groundwater management practices aligned with the goals of urban development and the United Nations Sustainable Development Goals.  Understanding the geological composition of Battersea and its correlation with the Greater London region is crucial for studying the potential impacts of groundwater extraction on land subsidence. The sedimentary layers and stratigraphy within the London Basin, which encompasses Battersea, play a significant role in hydrogeology [58]. The geological formations, such as the London Clay Formation, the Lambeth Group, the Thanet Sand Formation, and the Chalk Group, dictate the permeability and confinement of aquifers [14]. This information is pertinent for evaluating the relationship between groundwater extraction and land subsidence, providing insights into the potential risks and implications associated with the utilisation of the Chalk aquifer, a vital groundwater resource for the entire Southeast region.
The hydrogeology of the Battersea area in London is characterised by its unique geological composition and diverse groundwater systems. Figure 2, which shows a borehole cross section of Battersea Power Station, represents the local geology. Located along the River Thames, Battersea is underlain by a complex series of sedimentary layers, primarily composed of alternating layers of gravel, clay, sand, and silt. These strata, deposited over millions of years, are part of the Thames Group, consisting of the Lambeth Group, the Thames Gravel Aquifer, and the London Clay Formation. The Thames Gravel Aquifer, an unconfined aquifer, is the primary source of groundwater in the region. This permeable layer, consisting of gravel and sand, allows for water infiltration and storage, supporting the local ecosystem and supplying water for domestic and industrial use. The London Clay Formation, on the other hand, acts as an impermeable barrier, restricting the vertical movement of groundwater, thus influencing local groundwater flow patterns. Furthermore, the Battersea area's hydrogeology is significantly impacted by the River Thames, which plays a vital role in controlling groundwater levels and the interaction between surface water and groundwater resources [59].

Land Subsidence
Land displacement information was obtained using the PSInSAR method [61] using the ENVI SARscape v5.4software [62]. Typically, the PSInSAR approach requires a minimum of 20 or more SAR image pairs to produce a trustworthy result [63]. We used a set of 99 Sentinel-1 C-band images, captured from October 2016 to October 2020 over Battersea, London, and employed for calculating land displacement. The data used are summarised in Table 2, while the methodology is summarised in Figure 3.  The geology of Battersea is crucial for evaluating land subsidence risks, as the area's hydrogeology and aquifer behaviour are influenced by the properties of these geological formations. Comprehending the local geology is crucial for efficiently managing groundwater resources and addressing the possible consequences of construction activities on land subsidence in the area. By considering the intricate geological composition described above, valuable insights can be gained into the hydrogeological characteristics of Battersea to make informed assessments regarding the potential impacts of groundwater extraction on land subsidence. This knowledge contributes to a comprehensive understanding of the complexities involved and aids in ensuring sustainable groundwater management practices aligned with the goals of urban development and the United Nations Sustainable Development Goals.

Land Subsidence
Land displacement information was obtained using the PSInSAR method [61] using the ENVI SARscape v5.4software [62]. Typically, the PSInSAR approach requires a minimum of 20 or more SAR image pairs to produce a trustworthy result [63]. We used a set of 99 Sentinel-1 C-band images, captured from October 2016 to October 2020 over Battersea, London, and employed for calculating land displacement. The data used are summarised in Table 2, while the methodology is summarised in Figure 3. term trends and dynamics associated with these factors, enhancing the reliability and relevance of the findings. The SARscape module facilitates PSInSAR processing of SAR data using a multi-step, semi-automatic process [64]. The first step involves selecting a master image, to which all the other slave images are co-registered. The master image is chosen based on the stack's smallest average baseline, guaranteeing an ideal spatio-temporal position compared to the slave images. This process enhances coherence and data co-registration, as minimal baselines exhibit reduced sensitivity to volume de-correlation [62]. Upon co-registration, interferograms are generated from master-slave pairs, and flattening is accomplished by implementing a reference digital elevation model (SRTM DEM V4).
SARscape divides the entire study area into overlapping subsets for PSInSAR analysis if the area surpasses a predefined threshold. Each subset is independently analysed, with each having its own reference point. This step is undertaken to improve atmospheric estimation accuracy, and in the end, all separate areas are merged. The predetermined threshold area is known as the "Area for Single Reference Point (sq km)" [62]. In this study, the threshold was set at 25 km 2 , resulting in 238 subsets. The permanent scatterers' density, which is used for deriving land motion measurements, depends on the coherence threshold chosen for the PSInSAR analysis. A higher coherence threshold leads to superior quality and a smaller number of PS points, and vice versa. As a result, an optimum balance between the quality and quantity of PS points should be achieved when selecting the coherence threshold. The first inversion step was conducted to obtain coherence, displacement velocity, and residual topography, which were subsequently used for flattening complex interferograms. Then, a second inversion step addressed atmospheric phase components of linear model products originating from the first inversion. Ultimately, geocoding was executed to display average (linear) velocity and displacement time-series maps for the observation period.  water extraction that occurred during the renovation and redevelopment of Battersea, allowing for a comprehensive analysis of their impacts. Additionally, consistent Sentinel InSAR (interferometric synthetic aperture radar) data and groundwater data from the Environment Agency (EA) were available for this period, facilitating a robust examination of the interdependencies between land subsidence, piling work, and groundwater levels. By utilising data from this timeframe, the study ensures a thorough evaluation of the long-term trends and dynamics associated with these factors, enhancing the reliability and relevance of the findings.
The SARscape module facilitates PSInSAR processing of SAR data using a multi-step, semi-automatic process [64]. The first step involves selecting a master image, to which all the other slave images are co-registered. The master image is chosen based on the stack's smallest average baseline, guaranteeing an ideal spatio-temporal position compared to the slave images. This process enhances coherence and data co-registration, as minimal baselines exhibit reduced sensitivity to volume de-correlation [62]. Upon co-registration, interferograms are generated from master-slave pairs, and flattening is accomplished by implementing a reference digital elevation model (SRTM DEM V4).
SARscape divides the entire study area into overlapping subsets for PSInSAR analysis if the area surpasses a predefined threshold. Each subset is independently analysed, with each having its own reference point. This step is undertaken to improve atmospheric estimation accuracy, and in the end, all separate areas are merged. The predetermined threshold area is known as the "Area for Single Reference Point (sq km)" [62]. In this study, the threshold was set at 25 km 2 , resulting in 238 subsets. The permanent scatterers' density, which is used for deriving land motion measurements, depends on the coherence threshold chosen for the PSInSAR analysis. A higher coherence threshold leads to superior quality and a smaller number of PS points, and vice versa. As a result, an optimum balance between the quality and quantity of PS points should be achieved when selecting the coherence threshold. The first inversion step was conducted to obtain coherence, displacement velocity, and residual topography, which were subsequently used for flattening complex interferograms. Then, a second inversion step addressed atmospheric phase components of linear model products originating from the first inversion. Ultimately, geocoding was executed to display average (linear) velocity and displacement time-series maps for the observation period.

Groundwater Variation
The groundwater variation data for the Battersea chalk borehole were obtained from the England and Wales Environment Agency [65]. The correlation between groundwater withdrawal and observed land subsidence patterns was investigated. The units for land displacement (mm/year) and groundwater levels (mAOD) are different, and thus, comparing the absolute values is not meaningful. Instead, the focus was on analysing the trends of both variables to understand the relationship between them. The methodology used is explained below:

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The time-series dataset for groundwater levels and subsidence in the Battersea area were aligned for the same time periods. To align the time periods, the missing values were filled using ARIMA (autoregressive integrated moving average) [66], which combines three components: autoregression (AR), differencing (I), and moving average (MA).

•
The data were normalised for both variables (groundwater level and subsidence) by converting the values into relative changes or percentage changes. This made the trends of both variables more comparable without being affected by the difference in units.

•
The moving average was calculated for both variables to smooth the time-series data and highlight the underlying trends.

•
Cross-correlation analysis [67]: The cross-correlation function was computed between the normalised time-series data for groundwater levels and subsidence rates. This Based on the results of the trend analysis, cross-correlation analysis, and Granger causality test, the relationship between the temporal trends of groundwater levels and subsidence in the Battersea area was interpreted.
By focusing on the trends of both variables and normalising the data, a robust analysis of the relationship between the temporal distribution of groundwater levels and subsidence in the Battersea area was conducted.

Construction Work Assessment
Our study delved into the construction projects taking place in the Battersea area, with a specific focus on projects like the Northern Line Extension and the associated piling work. To gain comprehensive insights, we collected detailed information regarding various aspects of these construction projects. In terms of foundation depth, we examined the depths to which the foundations were laid during the construction activities. This information allowed us to understand the extent to which the underlying soil layers were impacted by the construction process. Furthermore, we investigated the piling techniques employed in the projects by sheet piling and Martello piling. These details provided us with a deeper understanding of the construction processes and their potential influence on the surrounding environment.
With the gathered information, we then proceeded to examine the relationship between the piling work undertaken and the land subsidence patterns observed in the InSAR data. By conducting analysis of the geospatial and temporal correlation between the construction activities and the detected land subsidence, we aimed to identify any potential causal links or associations. This comprehensive investigation allowed us to assess the impact of the construction projects, particularly the piling work, on the observed land subsidence patterns in the Battersea area. By integrating detailed information about the construction activities and analysing their relationship with the InSAR data, we aimed to gain valuable insights into the interplay between construction processes, piling techniques, and resulting land subsidence.

Trend Analysis
Because the units for land displacement and groundwater levels are different, comparing the absolute values is futile. Instead, we focus on analysing the trends of both variables to understand the relationship between them. For this analysis, a model is created in the R programming language, and the approach used is described below: Data collection and preparation: We obtain a time-series dataset for groundwater levels and subsidence in the Battersea area and align the time periods for both variables.
Normalisation: Then, data for both variables are normalised by converting the values into relative changes or percentage changes. This will make the trends of both variables more comparable without being affected by the difference in units.
Trend analysis: A moving average is calculated for both variables to smoothen the time-series data and highlight the underlying trends. The moving averages for groundwater levels and subsidence rates over time are plotted to visualise their trends and observe any apparent relationship between the two variables.
Cross-correlation analysis: The cross-correlation function is computed between the normalised time series data for groundwater levels and subsidence rates. This will help assess the strength and direction of the relationship between the two variables, as well as the time lag between them if there is any. Granger causality test: Finally, a Granger causality test is performed to determine whether changes in groundwater levels can predict changes in subsidence rates or vice versa. This test will help establish a causal relationship between the two variables.

Land Subsidence
The processed InSAR data revealed the spatial distribution and magnitude of land subsidence in Battersea, London (Figure 4). The subsidence statistics are summarised in Table 3. An average subsidence of −6.8 ± 1.6 mm/year was observed at Battersea from 2016 to 2020 and can be attributed to several factors, which may have occurred individually or in combination. These include groundwater withdrawal, underground construction activities, and tunnelling activities. The study area has two tunnels underneath it, viz., the Tideway and the Northern Line Extension [14,70,71].  The Northern Line Extension (NLE) is a significant infrastructure project in London that extends the existing Northern Line from Kennington to Battersea [71]. The project aims to improve transportation in the region, support the ongoing redevelopment of the Vauxhall, Nine Elms, and Battersea areas, and promote economic growth. The construction of the Northern Line Extension began in 2015, and the new stations were initially expected to open in 2020 [72]. However, due to various delays and challenges, the expected opening has been pushed back. Most of the construction work was conducted between 2016 and 2020, the time-period observed in this study. Figure 5 shows section A-A' passing along the Northern Line Extension. The subsidence variation along the section A-A' for each year shows maximum displacement near the location of the NLE. This high-  This ground settlement has been caused by NLE construction activities, such as tunnelling and excavation, which can alter stress distribution in the overlying soil and rock layers. It is essential to consistently examine and track subsidence patterns during and post-construction to guarantee long-term infrastructure stability. Additionally, the intricate geology and hydrogeology of Battersea, including clay formations like the London Clay, could contribute to ground subsidence. It is necessary to comprehensively study and manage the behaviour of these formations under the added stress from construction activities to reduce land subsidence risks. Moreover, extracting groundwater from the Chalk aquifer or other shallow aquifers in Battersea could cause ground settlement due to reduced pore water pressure in soil layers. Proper monitoring and management of groundwater abstraction are critical for mitigating these land subsidence risks.
Significant subsidence in Battersea could potentially damage infrastructure such as buildings, roads, and utilities and jeopardise the safety and stability of the NLE and nearby structures [73]. Consequently, it is crucial to continuously monitor subsidence rates and patterns for the long-term safety and functionality of the infrastructure. To tackle land subsidence issues in Battersea and along the NLE, it is necessary to apply appropriate mitigation measures. Techniques like InSAR and other remote sensing methods can continuously observe land subsidence, while construction methods and groundwater management practices are adjusted to minimise ground surface impacts. Effective management of subsidence risks in the area requires collaboration among stakeholders, including engineers, geologists, and local authorities [3,63,74].
By leveraging remote sensing techniques, both retrospectively as a source of valuable lessons and currently during ongoing projects, it is possible to bolster the alignment of urban planning and delivery with the United Nations Sustainable Development Goals (SDGs). This entails employing non-invasive sensing approaches to holistically assess the broader ramifications on factors such as liveability, ecosystem health, and urban connectivity, thus fostering sustainable urban development under SDG 11 (Sustainable Cities and Communities).  The Northern Line Extension (NLE) is a significant infrastructure project in London that extends the existing Northern Line from Kennington to Battersea [71]. The project aims to improve transportation in the region, support the ongoing redevelopment of the Vauxhall, Nine Elms, and Battersea areas, and promote economic growth. The construction of the Northern Line Extension began in 2015, and the new stations were initially expected to open in 2020 [72]. However, due to various delays and challenges, the expected opening has been pushed back. Most of the construction work was conducted between 2016 and 2020, the time-period observed in this study. Figure 5 shows section A-A passing along the Northern Line Extension. The subsidence variation along the section A-A for each year shows maximum displacement near the location of the NLE. This highlights that subsidence is highly influenced by underground construction activity, with the maximum subsidence near the NLE site on the order of 75 mm ( Figure 5).
This ground settlement has been caused by NLE construction activities, such as tunnelling and excavation, which can alter stress distribution in the overlying soil and rock layers. It is essential to consistently examine and track subsidence patterns during and post-construction to guarantee long-term infrastructure stability. Additionally, the intricate geology and hydrogeology of Battersea, including clay formations like the London Clay, could contribute to ground subsidence. It is necessary to comprehensively study and manage the behaviour of these formations under the added stress from construction activities to reduce land subsidence risks. Moreover, extracting groundwater from the Chalk aquifer or other shallow aquifers in Battersea could cause ground settlement due to reduced pore water pressure in soil layers. Proper monitoring and management of groundwater abstraction are critical for mitigating these land subsidence risks.
Significant subsidence in Battersea could potentially damage infrastructure such as buildings, roads, and utilities and jeopardise the safety and stability of the NLE and nearby structures [73]. Consequently, it is crucial to continuously monitor subsidence rates and patterns for the long-term safety and functionality of the infrastructure. To tackle land subsidence issues in Battersea and along the NLE, it is necessary to apply appropriate mitigation measures. Techniques like InSAR and other remote sensing methods can continuously observe land subsidence, while construction methods and groundwater management practices are adjusted to minimise ground surface impacts. Effective management of subsidence risks in the area requires collaboration among stakeholders, including engineers, geologists, and local authorities [3,63,74].
By leveraging remote sensing techniques, both retrospectively as a source of valuable lessons and currently during ongoing projects, it is possible to bolster the alignment of urban planning and delivery with the United Nations Sustainable Development Goals (SDGs). This entails employing non-invasive sensing approaches to holistically assess the broader ramifications on factors such as liveability, ecosystem health, and urban connectivity, thus fostering sustainable urban development under SDG 11 (Sustainable Cities and Communities). Figure 6 shows the variation of land subsidence and groundwater in the Battersea area. The groundwater variation is shown by the blue line, and the values are represented on the left-hand vertical axis. The groundwater level is in mAOD (meters above ordnance datum) and varies between −18 and −30 mAOD. The negative values represent the groundwater level being below the reference point, which is the ordnance datum. In the United Kingdom, the ordnance datum is the mean sea level at Newlyn in Cornwall. This can happen due to various factors such as local geological conditions, groundwater extraction, or natural fluctuations in groundwater levels. In some cases, a negative groundwater level could be associated with potential issues such as land subsidence or the need for more sustainable water management practices. The subsidence variation is shown by the red line, and the values are represented on right-hand vertical axis. The subsidence varies between −0.5 mm and −13 mm over the observed time period. The negative values indicate that the ground is moving away from the sensor and so indicate that land subsidence is occurring.

Correlation with Groundwater
Clearly, both the groundwater and ground-surface levels are decreasing, but the units for land displacement (mm/year) and groundwater levels (mAOD) are different; thus, comparing the absolute values is not meaningful. Instead, we focus on analysing the trends of both variables to understand the relationship between them in subsequent sections.

Cross-Correlation Analysis
Cross-correlation is a measure of similarity between two time series as a function of the time lag applied to one of them. It helps to identify how much one time series influences another at various time lags. The cross-correlation between two time series at different lags is shown in Figure 7, utilising the ACF (autocorrelation function) versus the lag plot for cross-correlation analysis. From this, the relationship between the two time series at different time lags can be visualised. Figure 6 indicates a strong correlation between groundwater and subsidence, especially around the lag of 0-2. An ACF value of 0.4 indicates that an increase (or decrease) in groundwater will bring about a corresponding decrease (or increase) in subsidence. As the lag increases, we can see a negative correlation, which indicates that with an increase in lag (difference in the observation period of the two phenomena), the dependence of one variable on other decreases, and other factors might become more dominant in affecting these phenomena. The lag with the highest cross-correlation value is the lag at which the two time series are most strongly related. This lag can provide insights into the timing or lead-lag relationship between the two time series. Thus, it can be concluded that for Battersea, there is a direct effect of groundwater withdrawal on land subsidence. datum) and varies between −18 and −30 mAOD. The negative values represent the groundwater level being below the reference point, which is the ordnance datum. In the United Kingdom, the ordnance datum is the mean sea level at Newlyn in Cornwall. This can happen due to various factors such as local geological conditions, groundwater extraction, or natural fluctuations in groundwater levels. In some cases, a negative groundwater level could be associated with potential issues such as land subsidence or the need for more sustainable water management practices. The subsidence variation is shown by the red line, and the values are represented on right-hand vertical axis. The subsidence varies between −0.5 mm and −13 mm over the observed time period. The negative values indicate that the ground is moving away from the sensor and so indicate that land subsidence is occurring. Clearly, both the groundwater and ground-surface levels are decreasing, but the units for land displacement (mm/year) and groundwater levels (mAOD) are different; thus, comparing the absolute values is not meaningful. Instead, we focus on analysing the trends of both variables to understand the relationship between them in subsequent sections.

Cross-Correlation Analysis
Cross-correlation is a measure of similarity between two time series as a function of the time lag applied to one of them. It helps to identify how much one time series influences another at various time lags. The cross-correlation between two time series at different lags is shown in Figure 7, utilising the ACF (autocorrelation function) versus the lag plot for cross-correlation analysis. From this, the relationship between the two time series at different time lags can be visualised. Figure 6 indicates a strong correlation between groundwater and subsidence, especially around the lag of 0-2. An ACF value of 0.4 indicates that an increase (or decrease) in groundwater will bring about a corresponding decrease (or increase) in subsidence. As the lag increases, we can see a negative correlation, which indicates that with an increase in lag (difference in the observation period of the two phenomena), the dependence of one variable on other decreases, and other factors might become more dominant in affecting these phenomena. The lag with the highest cross-correlation value is the lag at which the two time series are most strongly related. This lag can provide insights into the timing or lead-lag relationship between the two time series. Thus, it can be concluded that for Battersea, there is a direct effect of groundwater withdrawal on land subsidence.

The Granger Causality Test
The Granger causality test is used to determine if one time series (groundwater levels) can predict or "Granger-cause" another time series (land subsidence). In this study, we have used two models: Model 1: Groundwater (moving average) is explained by its own values and the values of subsidence (moving average).

The Granger Causality Test
The Granger causality test is used to determine if one time series (groundwater levels) can predict or "Granger-cause" another time series (land subsidence). In this study, we have used two models: Model 1: Groundwater (moving average) is explained by its own values and the values of subsidence (moving average).
Model 2: Groundwater (moving average) is explained only by its own values.
The test compares the two models to determine if including the values of groundwater in Model 1 provides a better explanation of the variation in subsidence compared to Model 2, where only the lagged values of groundwater are included. This test aims to demonstrate the interconnected nature of groundwater and subsidence and their potential influence on each other within the study area.
The result of the Granger causality test is given in the form of an F-statistic and its corresponding p-value [68]. Table 4 shows the F-statistic is 6.5242, and the p-value is 0.01477 (indicated by the '*' symbol, which means it is significant at the 0.01 level). Because the p-value is less than 0.05 (a common threshold for statistical significance), we can reject the null hypothesis that subsidence does not Granger-cause groundwater. This means that there is evidence to suggest that past values of subsidence have a predictive power in explaining the variation in groundwater (and vice versa). Including the lagged values of subsidence in the model significantly improves the model's ability to predict groundwater compared to using only the lagged values of groundwater. Furthermore, the positive correlation between the moving average plot of subsidence and groundwater (Figure 8), highlights the strong interdependence of the two phenomena on each other. correlation between the moving average plot of subsidence and groundwater (Figure 8), highlights the strong interdependence of the two phenomena on each other.

Correlation of Subsidence with Construction (Piling) Work
Several underground construction activities took place at and nearby the Battersea area during our observation time period [58,60]. Two of the notable projects were the Battersea Power Station redevelopment [57] and the Northern Line Extension [14]. Piling work was a crucial part of the construction process for these developments, as it involved installing deep foundations to support the weight of the new buildings and infrastructure. Long, slender column piles made of materials such as concrete, steel, or timber were driven or drilled into the ground to transfer the load of the structure to the underlying soil or rock layers. The Northern Line Extension project was proposed in 2010, and after a

Correlation of Subsidence with Construction (Piling) Work
Several underground construction activities took place at and nearby the Battersea area during our observation time period [58,60]. Two of the notable projects were the Battersea Power Station redevelopment [57] and the Northern Line Extension [14]. Piling work was a crucial part of the construction process for these developments, as it involved installing deep foundations to support the weight of the new buildings and infrastructure. Long, slender column piles made of materials such as concrete, steel, or timber were driven or drilled into the ground to transfer the load of the structure to the underlying soil or rock layers. The Northern Line Extension project was proposed in 2010, and after a series of consultations and approvals, the United Kingdom Secretary of State for Transport granted planning permission in November 2014. The construction work on the Northern Line Extension began in 2015 and involved tunnelling and station building; it also involved piling work to ensure the stability and safety of the new infrastructure [75,76]. Figures 4 and 5 clearly show the impact of NLE on the subsidence profile of the area.
Construction projects like the Battersea Power Station redevelopment and the Northern Line Extension can have an impact on groundwater during the construction phase, particularly when they involve excavation, tunnelling, or piling work [14,56,57,72,77]. These activities can potentially disrupt the natural flow of groundwater or change the distribution of groundwater in the area. During construction, it may be necessary to manage groundwater levels to ensure the safety and stability of the structures being built. This can involve dewatering, which is the process of extracting groundwater from the construction site to lower the water table temporarily and create a dry, stable environment for construction. Dewatering can affect groundwater levels in the immediate vicinity of the construction site, but it is generally a temporary measure and unlikely to have a long-term impact on the overall groundwater quantity in the area. Moreover, construction projects in the United Kingdom, especially large-scale ones like the Battersea Power Station redevelopment and the Northern Line Extension, are subject to stringent environmental regulations and assessments. These assessments aim to identify potential impacts on the environment, including groundwater, and outline measures to minimise and mitigate those impacts.
Furthermore, advanced construction techniques and monitoring systems are employed to ensure the stability of the structures being built and to minimise any adverse impacts on the surrounding environment. For example, the tunnelling work for the Northern Line Extension utilised tunnel-boring machines (TBMs) that are designed to minimise ground movement and reduce the risk of subsidence. In addition, extensive monitoring systems were put in place to detect any signs of ground movement during and after construction. It is also worth noting that environmental regulations and assessments are in place to ensure that the potential risks associated with land subsidence are carefully considered and mitigated during the planning, design, and construction phases of these projects.
In conclusion, while the Battersea Power Station redevelopment and the Northern Line Extension projects have the potential to cause land subsidence, and indeed our study detects such movement, this is expected. The risks are typically well-managed through comprehensive geotechnical investigations, advanced construction techniques, and adherence to environmental regulations. It is important, however, that construction practices adhere to environmental regulations and best practices to minimise any potential adverse effects on groundwater resources.

Conclusions
This study aimed to investigate land subsidence in Battersea, London, using interferometric synthetic aperture radar (InSAR) techniques. The results revealed the spatial distribution and magnitude of land subsidence in the area and identified correlations with potential contributing factors, such as excessive groundwater withdrawal and extensive piling work during construction.
The implications of these findings highlight the need for sustainable groundwater management practices, improved construction techniques, and informed urban planning and infrastructure management in Battersea. By addressing the issue of land subsidence proactively, local authorities, urban planners, and engineers can minimise the risk of damage to infrastructure, protect the environment, and ensure the safety and well-being of the community.
The study also emphasises the importance of ongoing research to better understand the long-term trends and impacts of land subsidence in Battersea and other urban areas facing similar challenges. Expanding the analysis to other regions and assessing the effectiveness of various mitigation strategies can contribute to a broader understanding of land subsidence and its implications for urban planning and development worldwide.
In summary, this study demonstrates the value of using InSAR techniques to investigate land subsidence in urban areas like Battersea, London, and provides a solid foundation for future research and the development of effective mitigation strategies.