Estimation of Ground Vertical Displacement in Landslide Prone Areas Using PS-InSAR. A Case Study of Bududa, Uganda

Estimation of ground displacement in landslide susceptible regions is very critical to understanding how landslides develop. The knowledge of ground displacement rates and magnitudes helps plan for the safety of the people and infrastructure. The early detection of landslides in Bududa is still a challenge due to the limited technology, hard to access, and a need for an affordable technique that can monitor a wide area continuously. In recent studies, the use of Persistent Scatterer Interferometry Synthetic Aperture Radar (PS-InSAR) has provided vital information on landslide monitoring through the measurement of ground displacement. In this study, Synthetic Aperture Radar (SAR) band C series of Sentinel 1-A and 1-B Satellite images were acquired between 2019 and 2020 along ascending and descending orbit paths. The Line of Sight Sight (LOS) displacement was determined for both satellite tracks, and then the LOS displacement was projected to the vertical direction. The PS-InSAR derived vertical displacement was then compared with GPS vertical displacement magnitudes over three GPS stations in the area. It was observed that vertical displacement velocity reached 20 cm/yr in Mountain Elgon. This displacement rate showed that there are points in the region that are highly unstable. The displacement velocity and magnitude in Bududa reached 6 cm/yr and 13 cm in two years. This rate and magnitude showed that Bududa is highly unstable compared with displacement velocities and magnitudes in landslide susceptible areas globally. The displacement was generally subsidence over the observation period. The vertical displacement estimated by PS-InSAR was comparable with GPS based on the estimated RMSE. The vertical enced by slope, rainfall and soil texture. Displacement could be estimated in three dimensions using PS-InSAR in the future if sufficient SAR images in ascending and descending tracks are made available with significantly different geometries. This would add to the knowledge of displacement patterns in the east and north directions at a large spatial scale.


Introduction
Landslides are one of the most devasting natural disasters in the world. They are responsible for the destruction of property, the environment and human life.
Landslides happen after the slope fails; this could be through debris flow, mudflows, human activity or rock falls. Landslide can also occur through different movements, for example, spreads, falls, topples, slides or flows. The combination of all these factors to cause movement is not uncommon [1]. On the other hand, the landslide triggering factors majorly include rainfall, river overflow, earthquakes, volcanic eruptions and slope undercuts.
The measurement of ground displacement is crucial in the monitoring of landslides [2]. It is essential because it gives insight into how landslides form and build before a failure happens. Monitoring surface displacement over a large area is vital to identify unstable areas potentially at risk of landslides. However, this process has challenges to achieve due to the landslide formation process's complex nature [3]. Landslide inventories today require documentation of the rate at which slopes are sliding hence making the need for information on displacement critical [4] [5].
The Interferometric Synthetic Aperture Radar (InSAR) technique has been widely applied in monitoring ground displacement in landslide susceptible areas due to its ability to cover large areas. It has a high spatial and temporal resolution, and it works all day, both at night and day and through all weather conditions. Furthermore, the traditional InSAR technique estimates ground displacement in the order of dm/yr [6]- [11]. Whereas the more advanced InSAR algorithms which are based on a stack of SAR images, that is, the small baseline subset (SBAS) InSAR and Persistent Scatterers (PS) can determine even slower displacement reaching mm/yr. The PS is an advanced InSAR technique that can estimate ground displacement at millimetre level [12]. Conventional InSAR can estimate surface displacement, but it is affected by temporal decorrelation due to vegetation. The temporal decorrelation limits the application of conventional InSAR measurement of surface displacement of natural terrains. Conventional InSAR is additionally affected by phase delay that results from atmospheric constituents. These atmospheric constituents are difficult to remove from interferograms, especially when conventional InSAR is used [13]. After the removal of atmospheric and topographic errors from the interferograms, the differential interferograms comprise only the residual phase that results from surface deformation [14]. The PS-InSAR technique has been proven to estimate surface displacement in landslide-prone areas [15]- [28].
Bududa has been observed to experience significant displacement in the vertical direction compared to the horizontal. In the absence of a technique that estimates displacement reliably in all directions and at many points. A technique that estimates displacements reliably in the vertical direction and at many points should be considered. InSAR is such a technique that estimates ground displacement in the vertical direction more reliably than the horizontal and at more points than GPS. This advantage is attributed to the ascending and descending trajectory of the SAR satellites [29]. InSAR, however, does not directly measure displacement in the vertical direction but the Line of Sight (LOS); therefore, it requires projection of the LOS displacement to the vertical direction [30]. Several algorithms have been developed to ensure that the projection to both the vertical and horizontal directions is reliable enough to achieve accuracy comparable to Global Positioning Systems (GPS) and Levelling [28] [30]. In this study, we employ a technique where a combination of ascending and descending satellite tracks of significantly different geometrical properties are used to derive vertical displacement [30]. We here, however, put emphasis on the vertical displacement that is well estimated by InSAR and used PS-InSAR to derive displacement points in the vertical, which points are more comparable with GPS points in contrast to if we had used Small Baseline Subset (SBAS) advanced In-SAR algorithm. However, this approach is affected by several factors beyond the technical limitation of the formulae used. These include the number of ascending and descending satellites available, atmospheric and topographic artefacts.
We use a significant number of ascending and descending satellites with suitable geometrical properties. Use high temporal imagery with short baseline lengths and a Digital Elevation Model (DEM) of a fair resolution. We then compare the retrieved vertical displacement with GPS measurements to assess InSAR derived vertical displacements' reliability. Additionally, derived vertical displacement is compared with slope, rainfall and soil characteristics to determine the influence of these on ground displacement.

Study Area
This study was undertaken in Bududa district because of the frequency of landslides A about a quarter of the study area is protected and covered by Mountain Elgon national park. The District has about twenty-four (24) small rivers flowing through it from the Mountain Elgon peak, through the cultivated and degraded habited slopes and valleys to river Manafwa and draining into Lake Kyoga, as shown in Figure 1.
The District has high altitude variation ranging from 1250 to 2850 m. The altitude rises in the east to 3000 and 4000 m at the peak of the Mountain, as shown in Figure 1. The District generally has steep slopes. The District's population growth rate is high compared to the national approximated at 3.8%, which has led to increased deforestation and soil degradation.

InSAR Datasets
The Copernicus Sentinel-1 C band Synthetic Aperture Radar (SAR) images from the European Commission (EC) and European Space Agency (ESA) initiative were used in the study. The Sentinel-1A and -1B twin spaceborne satellite images were used.
Particularly, the Sentinel-1 Terrain Observation with Progressive Scan (TOPS) mode was used because it covers a wide area and the revisit period is short (12 days globally and 6 days in Europe). The TOPS mode imagery is well suited for InSAR applications, according to [32]. TOPS mode obtains data in three sub-swaths which cover 250 km, and the ground range cell size is 5 × 20 m. TOPs mode attains uniform distributed target ambiguity ratio and signal-to-noise ratio electronically steering the radar beam backwards to forwards in an azimuth direction.
Additionally, it steers the beam in a range direction like in normal ScanSAR mode [33]. Each sub-swath comprises bursts, where each burst is an independent Single Look Complex (SLC) image. The bursts in each sub-swath are arranged in an azimuth-time domain, having black lines separating these bursts.
Furthermore, Sentinel-1 data is free and can be accessed via different data hubs, for example, Copernicus Open Access Hub. Data processing has to be done on the Sentinel data sets before the application of PS-InSAR. The data processing mainly involves extraction of the sub-swath covering the area studied, a process called TOPS splitting. The removal of black strips is done, which separates the bursts by moving a window averaging filter through the bursts, a process called TOPS deburst [32].

PS-InSAR Processing Methodology
The topographic contribution to each interferogram's radar phase was eliminated using the Shuttle Radar Topography Mission (SRTM) 3-arcsecond digital elevation model [34]. The interferograms were then geocoded to align them in the correct geographical position for interpretation purposes. The initial selection of PS points was based on noise characteristics and amplitude analysis, as discussed by [35]- [41]. These PSs can only be estimated after eliminating atmospheric artefacts, DEM errors, deformation due to terrain and orbital ramps. Because we need targets with low geometric and temporal decorrelation, pixels with stable amplitudes should be selected.
A subset of pixels from the Persistent Scatterer Candidates (PSC) was selected as final PSs after determining the phase stability. The Amplitude Dispersion Index (D A ) was used to select the amplitude stable pixels [39] [42] [43].
where, A σ is the temporal deviation and A µ the temporal mean for each pixel. For low values of the Amplitude Dispersion Index, reaching 0.25, the amplitude and phase dispersion were in good agreement [39]. For Persistent Scatterer Candidates in phase analysis, the Amplitude Dispersion Index was used, where a threshold of 0.4 was used to select a large number of pixels. Given a PSC (x) in the i th interferogram that has been corrected for topographic errors, the interferometric phase can be computed as [12] [44]: where, The temporal coherence (γ) of the PSCs was then computed to finally estimate phase noise in the interferograms using Equation (3) [12] [44].
where x γ is the temporal coherence, N is the number of interferograms, int, , The final Persistent Scatterers (PS) was selected from the PSCs using the Amplitude Dispersion Index and temporal coherence. To achieve this, the Persistent Scatterer probability was calculated for the PSC. Finally, PSs dominated by scatterers in pixels neighbouring and those persistent in some particular interferograms were rejected. The pixels that remained were selected as the final Persistent Scatterers for surface displacement estimation [44]. The interferometric phase difference between adjacent PS pixels would at times be greater than π due to spatially uncorrelated component of the look angle error.
Before phase unwrapping, the look angle error contribution from the slave and master images was estimated. The 3D phase unwrapping technique was used to unwrap the wrapped phase, as shown in Figure 4. The 3D unwrapping took To ensure that the phase unwrapping was accurate, the displacement between a PS pixel and one of the neighbouring PS had to be less than half the antenna wavelength. The LOS displacement was then extracted for the ascending and descending satellite tracks. The vertical displacement was finally estimated using Equation (4). Ascending and descending tracks with different incidence and azimuth angles provides different perspectives on ground movement, and this is a base to extract vertical deformation from InSAR processing [45]. The vertical velocities and time-series were recovered, assuming that there was no movement in the west-east direction [45]. Only two of the three components could be retrieved. The PS-InSAR LOS displacement of the ascending and descending tracks was decomposed into east-west and vertical components. It was assumed that the north-south deformation was negligible. This is due to the near-polar orbits that SAR satellites have, this produces low sensitivity to the north-south deformation component. The InSAR LOS velocity for the ascending and descending tracks were first transformed into the same reference frame using a stable reference area before the decomposition process. The LOS velocity was decomposed into the horizontal and vertical deformation components based on the local incidence angle of the satellite using Equation (4). The Vertical deformation velocities and timeseries for all the estimated PSs were extracted. Emphasis was put on the vertical deformation that was estimated reliably as discussed earlier in the introduction section.
where asc v and dsc v the velocity of the ascending and descending tracks, asc θ and dsc θ local incidence angles of the ascending and descending tracks, asc α and dsc α satellite heading in the ascending and descending tracks ver v and hor v the velocity in the vertical and horizontal directions.

InSAR-Derived Mean Velocity Maps
The mean vertical velocity map was determined for the whole of Mountain Elgon, as shown in Figure 5. It exploits the advantage of InSAR where displacements can be determined over a larger area compared to other ground displacement measurement techniques like GPS. The results showed that the vertical displacement velocity in Mountain Elgon reached 20 cm/yr, a high displacement posing a danger to surrounding communities.
It was not possible to estimate Ground displacement using PS-InSAR in the heavily vegetated areas of Bududa due to high temporal decorrelation, as shown in  It was observed that areas that experienced landslides had high vertical displacement velocity compared to those that did not. Areas with ground cracks also experienced higher vertical displacement velocity. Areas that are at high elevation in all the transects experienced high vertical displacement velocity; however, the transects in the east had the highest rates compared to the transects in the west and the dome in the centre. In the carbonatite dome located in Bukigai, areas that had cultivated slopes and slopes above 8.53˚ experienced higher displacement velocity. It means that vertical displacement velocity can show areas that are susceptible to landslides.

InSAR-Derived Vertical Displacement Time Series
The knowledge of the vertical ground displacement velocity alone is not sufficient to assess how unstable areas are. There is a need to extract and analyse approximately 100 years [45]. These points were observed to receive higher rainfall due to the local microclimate, which contributed to high water run-off.
All the points, at gentle, medium and steep slopes experienced subsidence as is shown in Figures 6(a)  is more than 30% according to [46], and it varies less than 20% over above 12 cm     Additionally, many streams radiate from almost all directions; these have been responsible for landslides that result from flash floods. However, the development of these kinds of landslides cannot be done by solely monitoring ground displacement. Other measures like streamflow and water levels should be monitored.

InSAR-Derived and GPS Vertical Displacement Time Series
The InSAR derived vertical displacements were compared with GPS displacements at P3, P6 and P11 in Bududa, Bushika and Bulucheke. These points had experienced landslides in the past, they had GPS monuments installed and vertical displacement determined through the PS-InSAR technique. This was done to determine how comparable and reliable vertical displacements determined by PS-InSAR are.
GPS data has high reliability in the x, y and z directions but has a low spatial resolution. On the other hand, PS-InSAR has a high spatial, temporal resolution.
Still, measurements are in the Line of Sight (LOS), necessitating ascending and descending satellite tracks to estimate vertical displacement. In this study, the PS-InSAR LOS displacement is projected to the vertical direction using Equation (4). This displacement is compared with vertical displacement derived from campaign GPS measurements at these 3 points.
According to the Root Mean Square Error (RMSE) error between PS-InSAR and GPS, there is a relative agreement between the vertical displacement estimated by the two techniques, as is shown in Figures 11(a)  Even if InSAR has some advantages over GPS, like high spatial coverage, GPS stations will still be essential in displacement measurement and cannot be substituted by InSAR technology. InSAR still provides displacement in two directions. We assume a zero north-south deformation, which is true in many situations compared to GPS that estimates displacement with sufficient reliability in three directions. GPS data is still part of many applications where InSAR has been used to derive ground velocities. Furthermore, GPS data is still used in many circumstances to estimate ground strain in disaster-stricken areas. Yet, InSAR has not been incorporated in strain analysis due to the limitation of not reliably determining displacement in all directions, which will not be the case in the future according to current research trends in InSAR technology.

InSAR-Derived Vertical Displacement, Rainfall and Soil Properties
InSAR derived vertical displacement was further correlated with rainfall received at the three sampled points. It was observed that the correlation between vertical ground displacement and rainfall in Bududa was strong, as is shown in Figures   12(a)-(c), which was R 2 of 0.9572, 0.9844 and 0.9821 in BUDU, BUSH and BULU. It implies that when rainfall is high, the vertical ground displacement will also be high. The incremental movement of soil is affected by driving and resisting forces affected by absorbed and drained water at multiple scales and rates.
When rainfall penetrates the bedrock, rock slabs are split or pulverised through mechanical weathering; hence ground displacement occurs. Dense vegetation    table to a shallow depth, and the rising water table results from surface infiltra-tion into unsaturated soils than deep percolation. The extreme case will be when the water rises until it reaches the surface, implying that it is entirely saturated.
The saturation of soil increases the pore pressure significantly. Soil saturation forces the soil particles apart, reducing inter soil particle friction, cohesion, shear strength and resisting forces. Given the low drainage rates, field capacity and saturation of the sampled soils as observed in Figures 14(a)-(c) it is the reason the sampled points exhibited high displacement magnitudes.
The soil texture at the sampled points contained clay above 30%, as is shown in Figures 13(a)-(c). The high clay content was observed up to 200 cm depths but with layering, especially at BUSH and BULU compared to BUDU. The points where clay layering occurred acted as stagnation points. Water that managed to infiltrate the upper layers was restricted from quickly moving through these clay layers, causing an increase in the soil's weight at such points. The weight of water above the clay layer considering the steep slopes caused high displacement velocity and magnitudes at such points.
The soils experience meagre drainage rates due to the high clay content shown in Figure 14

Discussion
Ground vertical displacement velocity and magnitude were determined using the PS-InSAR. Vertical displacement was highest at slope ranges between 32˚ and 60˚ followed by slopes between 10˚ and 31˚ and most minor between 0˚ and 9˚. It showed that a change in slope largely drove displacement. The vertical displacement was also highly correlated with rainfall, which showed that the main triggering factor for displacement was rainfall. The soils were observed to have a very high clay content than silt and sand, contributing to low drainage rate, field capacity, saturation, and bulk density. These physical properties of the soil contributed high displacement rates and magnitudes in Bududa.

Conclusions and Recommendations
The Mountain Elgon region experienced high vertical displacement velocity reaching 20 cm/yr. Still, this high displacement velocity was outside the study area of Bududa, which experienced vertical displacement velocity reaching 6 cm/yr. The Vertical displacement velocity in Bududa reaching 6 cm/yr and magnitudes of 13 cm in two years shows that the area is unstable. The ground displacement estimated by PS-InSAR was comparable with that from GPS, which implied that InSAR could provide reliable displacement estimates of unstable areas. Bududa had high displacement magnitudes and velocity, evidenced by developed cracks and landslide scars. The points that were downslope and had slopes between 0˚ and 9˚ experienced low displacement velocity and magnitudes compared to the points in the upper slopes 32˚ to 60˚.
Additionally, the points at the middle slopes 10˚ to 31˚ generally had higher displacement than normal. The Bushika, Nusu ridge and Bukalasi Transects experienced the highest displacement velocity and magnitude. The high displacement was due to horizon stratification and water stagnation at the lower horizons. Nusu Ridge and Bukalasi transect experienced higher displacement velocity except at the peak of Mountain Elgon. The higher displacement at the other transects was due to increased population, over-cultivation, terracing and steep concave slopes. Areas in Bududa transect and Bukigai carbonatite transect that did not experience high displacement were located at the lower slopes. They had soils permeable to water and plant roots experiencing little run-off erosion. The soils in the Bukigai carbonatite dome that experienced low displacement also had soils weathered to depths reaching 40 m derived from magnetite and hematite minerals rich in iron. These were stable due to the calcium carbonate cementing minerals.
Ground displacement in Bududa was highly correlated with rainfall. It implied that ground displacement in Bududa is majorly triggered by precipitation. It is due to the high rainfall amounts that are received in Bududa. The high rainfall amounts given the soil types, texture and slopes acted as an accelerator of ground displacement. The soils in Bududa had high clay content above 30% a condition that favours land displacement. It was also observed that soil type did not have a significant impact on ground displacement as soil texture. Furthermore, soils in these transects had low drainage rates, field capacity, saturation and bulk density that caused water to flow less through the soil profiles, causing stagnation when they came into contact with higher clay layers. are most affected by displacement due to exposed ground slopes. Vertical estimation of displacement using PS-InSAR is only reliable with over 20 ascending and descending used.