Identifying Geomorphological Changes of Coastal Cliffs through Point Cloud Registration from UAV Images

: Cliff monitoring is essential to stakeholders for their decision-making in maintaining a healthy coastal environment. Recently, photogrammetry-based technology has shown great successes in cliff monitoring. However, many methods to date require georeferencing efforts by either measuring geographic coordinates of the ground control points (GCPs) or using global navigation satellite system (GNSS)-enabled unmanned aerial vehicles (UAVs), signiﬁcantly increasing the implementation costs. In this study, we proposed an alternative cliff monitoring methodology that does not rely on any georeferencing efforts but can still yield reliable monitoring results. To this end, we treated 3D point clouds of the cliff from different periods as geometric datasets and further aligned them into the same coordinate system using a rigid registration protocol. We examined the performance of our approach through a few small-scale experiments on a rock sample as well as a full-scale ﬁeld validation on a coastal cliff. The ﬁndings of this study would be particularly valuable for underserved coastal communities, where high-end GPS devices and GIS specialists may not be easily accessible resources. quantifying indicate


Introduction
Monitoring coastal cliffs is essential for maintaining a healthy coastal ecosystem and is particularly crucial for the island of Guam. Being the largest island in the Marianas Chain in the Western Pacific, Guam has a coastline of 125.5 km and 59% of it is rocky coastlines characterized by steep cliffs and uplifted limestone terraces [1]. Due to the actions of the sea, strong winds, ground motions, and water surges [2], coastal cliffs are prone to erosion. For example, Typhoon Halong in 2002 struck Guam and led to erosion on the southeast shorelines; the 1993 Guam earthquake (magnitude of 7.8) also caused slides in coastal cliffs throughout the island [3]. Other natural impacts such as seasonal changes on rock thermal stress and/or cliff vegetation could also influence the cliff stability and cause geological hazards.
Cliff erosions could lead to sediments on coastal reefs and weaken the integrity of a local coastal ecosystem. One engineering approach to address this concern is to monitor the cliff erosion process using advanced technologies, based on which results can be delivered to the stakeholders for making timely decisions in managing a coastal zone. Traditionally, cartographic geological mapping [4,5] is the most popular method for surveying coastal erosion. However, this method is labor-intensive and prone to error due to mapping inaccuracy [6]. In addition, field deployments at inaccessible locations could be challenging and time-consuming. As such, terrestrial laser scanning (TLS)-based technology [7,8] has received increasing attention in coastal surveying for being able to achieve a non-contact and accurate solution through creating dense 3D point clouds of coastal areas. Nevertheless, the laser scanner could be costly, and inconvenient for field deployment due to its heavy the iterative closest point (ICP) algorithm [22,23] have been previously investigated in cliff monitoring [24][25][26][27][28], the roles of the ICP algorithm in these studies are limited as supplemental tools in improving point cloud alignment accuracy within the georeferencing framework. To the best knowledge of the author, there is no literature developing a completely non-georeferenced cliff monitoring methodology. The findings of this study would be particularly valuable for Guam and other underserved coastal communities, where high-end GPS devices and trained GIS professionals may not be easily accessible resources.
The rest of this manuscript is organized as follows: Section 2 illustrates the research methodology and explains the technical details; Section 3 demonstrates the soundness of the proposed method through a series of small-scale experiments; Section 4 validates the method using a full-scale coastal cliff; Section 5 further discusses applicability and limitations of our method; and Section 6 concludes the study.

Methodology
The research methodology, illustrated in Figure 1, contains three major components that include (a) image collection, (b) point cloud reconstruction, and (c) point cloud registration. Our method starts with the image collection of the cliff using UAVs. Then, UAV images are further processed by a series of computer vision algorithms, termed structure-from-motion with multi-view stereo (SfM-MVS), to reconstruct the point cloud of the cliff. Next, a new point cloud of the cliff can be obtained using the same procedure after the second field visit. Thereafter, these two point clouds are aligned into the same coordinate system through a protocol of rigid registration, which contains a few computational algorithms for point cloud alignment. Finally, the differential changes between two well-aligned point clouds can be extracted through computing the cloud-to-cloud distance. As a result, the geomorphological changes of the cliff can be identified. Each component in the research methodology is further explained in the rest of this section.
Remote Sens. 2021, 13, x FOR PEER REVIEW 3 of 17 together for uncovering the geomorphological changes caused by cliff erosion, significantly reducing the implementation cost. Although point cloud processing techniques such as the iterative closest point (ICP) algorithm [22,23] have been previously investigated in cliff monitoring [24][25][26][27][28], the roles of the ICP algorithm in these studies are limited as supplemental tools in improving point cloud alignment accuracy within the georeferencing framework. To the best knowledge of the author, there is no literature developing a completely non-georeferenced cliff monitoring methodology. The findings of this study would be particularly valuable for Guam and other underserved coastal communities, where high-end GPS devices and trained GIS professionals may not be easily accessible resources.
The rest of this manuscript is organized as follows: Section 2 illustrates the research methodology and explains the technical details; Section 3 demonstrates the soundness of the proposed method through a series of small-scale experiments; Section 4 validates the method using a full-scale coastal cliff; Section 5 further discusses applicability and limitations of our method; and Section 6 concludes the study.

Methodology
The research methodology, illustrated in Figure 1, contains three major components that include (a) image collection, (b) point cloud reconstruction, and (c) point cloud registration. Our method starts with the image collection of the cliff using UAVs. Then, UAV images are further processed by a series of computer vision algorithms, termed structurefrom-motion with multi-view stereo (SfM-MVS), to reconstruct the point cloud of the cliff. Next, a new point cloud of the cliff can be obtained using the same procedure after the second field visit. Thereafter, these two point clouds are aligned into the same coordinate system through a protocol of rigid registration, which contains a few computational algorithms for point cloud alignment. Finally, the differential changes between two wellaligned point clouds can be extracted through computing the cloud-to-cloud distance. As a result, the geomorphological changes of the cliff can be identified. Each component in the research methodology is further explained in the rest of this section.

Image Collection
A large volume of digital images of the target cliff are collected using UAVs (see Figure 1a). Many consumer-grade UAVs can fit such a role. The flight routes and camera parameters (e.g., ISO, shutter speed, image resolution, and camera shooting interval) can be predefined through built-in flight operation apps. UAV images are intended to cover Remote Sens. 2021, 13, 3152 4 of 17 the cliff with different camera positions and angles. Adjacent images shall have enough overlapping for matching feature points that will be explained in Section 2.2.

Point Cloud Reconstruction
UAV images are processed by SfM-MVS for creating a 3D point cloud of the cliff (see Figure 1b). SfM-MVS is a well-established photogrammetry workflow that has been widely applied to coastal surveying [29], civil infrastructure inspection [30], river bathymetry extraction [31], and historic building preservation [32]. To this end, feature points (i.e., tie points, key points), which are small image patches that contain unique intensity distributions, are detected from each UAV image. Because feature points are invariant against image translation, rotation, and scaling, feature points with similar intensity distributions can be consistently tracked and matched across multiple UAV images. Some of the wellknown features are scale-invariant feature transform (SIFT) [33], Shi-Tomasi [34], features from accelerated segment test (FAST) [35], Harris-Stephens [36], binary robust invariant scalable keypoints (BRISK) [37], and speeded up robust features (SURF) [38].
Next, feature points across different UAV images are matched based on their levels of similarities in intensity distributions. A geometric transformation matrix is also estimated in this stage to describe the relations between matched feature pairs (i.e., correspondences) of two adjacent UAV images. Based on the transformation matrix, incorrect matching results (i.e., outliers) can be eliminated.
Thereafter, SfM algorithms are adopted to estimate both extrinsic parameters (e.g., locations and orientations) and intrinsic parameters (e.g., focal length and pixel sensor size) of the camera. The 3D geometry of the cliff scene is also calculated in this stage. Then, camera positions and angles are further refined through bundle-adjustment algorithms to reduce reprojection errors in MVS. Next, multiple-view UAV images and their corresponding camera parameters are utilized for reconstructing the sparse 3D point cloud of the cliff. Users can also examine the quality of reconstruction errors in the sparse point cloud, and if needed, may change the parameters of the algorithms to re-create the sparse point cloud. Finally, pixels are back-projected to all UAV images to create an RGB-colored dense point cloud, which represents the 3D surface of the cliff. The detailed reviews of SfM-MVS are summarized in [39][40][41].

Point Cloud Registration
To uncover the geomorphological changes of the cliff, two dense point clouds at different periods are aligned together using the protocol of rigid registration (Figure 1c). The protocol can find geometric similarities of two point clouds and applies rotation, scaling, and translation to rigidly align one point cloud to another. This procedure further contains three steps that include (1) scaling one point cloud to a real-world length unit; (2) rough alignment of two point clouds based on manually selected correspondences; and (3) fine alignment of two point clouds using the automated ICP algorithm. Each step is further explained as follows.
As shown in Figure 1c, point cloud A is first scaled to the correct real-world unit using a scaling factor, which is the ratio of the distance between two existing points measured from the cliff site in the real world over the distance of the same two points from the point cloud. The point cloud after scaling is considered as the reference point cloud which will not move for the rest of the registration procedure.
Then, point cloud B (denoted as the floating point cloud) is roughly aligned to the reference point cloud (i.e., point cloud A) through manually finding correspondences. Correspondences are points that appear at similar locations in both reference and floating point clouds. Selections of correspondences are flexible as long as they can be visually identified. Based on correspondences, a geometric transformation matrix can be estimated, allowing the floating point cloud to be rigidly translated, rotated, and scaled for matching the reference point cloud.
Due to the manual selection of correspondences, errors are inevitably introduced during rough alignment. Such errors can be further reduced through fine registration. Here we adopt the ICP algorithm to further optimize the transformation matrix. The ICP algorithm starts with an initial guess of the rigid body transform of two point clouds, and iteratively improves the transformation matrix through repeatedly finding correspondences with minimum errors. The last row of Figure 1c illustrates comparisons of two point clouds at each stage of the registration.
The rough alignment can effectively align two point clouds together but small misalignments may exist. Fine alignment, on the other hand, is capable of adjusting small misalignments but may not work well if the initial misalignment of two point clouds is large. By successively adopting these two alignments in the correct order, the misalignments between two point clouds can be gradually reduced.

Test Configuration
A series of small-scale tests on a rock sample was performed with the purposes of (1) reconstructing dense 3D point clouds from the test sample under different lighting and surface texture conditions; and (2) detecting, localizing, and quantifying differential features of the rock sample under geometric changes. To this end, a rock sample was collected from Tumon Bay in Guam in June 2020. The longest diameter of the sample is about 13.5 cm, as shown in figure (a) in Table 1. Five test cases were established to mimic different testing environments. The third column of Table 1 elaborates the different lighting conditions and geometric changes for each test case. The rock sample in Case A had a darker texture due to the high moisture content after the sample was collected from the beach. Images of Cases B to E were taken a few days later; hence, the sample has a brighter surface texture. Correspondences are points that appear at similar locations in both reference and floating point clouds. Selections of correspondences are flexible as long as they can be visually identified. Based on correspondences, a geometric transformation matrix can be estimated, allowing the floating point cloud to be rigidly translated, rotated, and scaled for matching the reference point cloud. Due to the manual selection of correspondences, errors are inevitably introduced during rough alignment. Such errors can be further reduced through fine registration. Here we adopt the ICP algorithm to further optimize the transformation matrix. The ICP algorithm starts with an initial guess of the rigid body transform of two point clouds, and iteratively improves the transformation matrix through repeatedly finding correspondences with minimum errors. The last row of Figure 1c illustrates comparisons of two point clouds at each stage of the registration.
The rough alignment can effectively align two point clouds together but small misalignments may exist. Fine alignment, on the other hand, is capable of adjusting small misalignments but may not work well if the initial misalignment of two point clouds is large. By successively adopting these two alignments in the correct order, the misalignments between two point clouds can be gradually reduced.

Test Configuration
A series of small-scale tests on a rock sample was performed with the purposes of (1) reconstructing dense 3D point clouds from the test sample under different lighting and surface texture conditions; and (2) detecting, localizing, and quantifying differential features of the rock sample under geometric changes. To this end, a rock sample was collected from Tumon Bay in Guam in June 2020. The longest diameter of the sample is about 13.5 cm, as shown in figure (a) in Table 1. Five test cases were established to mimic different testing environments. The third column of Table 1 elaborates the different lighting conditions and geometric changes for each test case. The rock sample in Case A had a darker texture due to the high moisture content after the sample was collected from the beach. Images of Cases B to E were taken a few days later; hence, the sample has a brighter surface texture. Correspondences are points that appear at similar locations in both reference and floating point clouds. Selections of correspondences are flexible as long as they can be visually identified. Based on correspondences, a geometric transformation matrix can be estimated, allowing the floating point cloud to be rigidly translated, rotated, and scaled for matching the reference point cloud. Due to the manual selection of correspondences, errors are inevitably introduced during rough alignment. Such errors can be further reduced through fine registration. Here we adopt the ICP algorithm to further optimize the transformation matrix. The ICP algorithm starts with an initial guess of the rigid body transform of two point clouds, and iteratively improves the transformation matrix through repeatedly finding correspondences with minimum errors. The last row of Figure 1c illustrates comparisons of two point clouds at each stage of the registration.
The rough alignment can effectively align two point clouds together but small misalignments may exist. Fine alignment, on the other hand, is capable of adjusting small misalignments but may not work well if the initial misalignment of two point clouds is large. By successively adopting these two alignments in the correct order, the misalignments between two point clouds can be gradually reduced.

Test Configuration
A series of small-scale tests on a rock sample was performed with the purposes of (1) reconstructing dense 3D point clouds from the test sample under different lighting and surface texture conditions; and (2) detecting, localizing, and quantifying differential features of the rock sample under geometric changes. To this end, a rock sample was collected from Tumon Bay in Guam in June 2020. The longest diameter of the sample is about 13.5 cm, as shown in figure (a) in Table 1. Five test cases were established to mimic different testing environments. The third column of Table 1 elaborates the different lighting conditions and geometric changes for each test case. The rock sample in Case A had a darker texture due to the high moisture content after the sample was collected from the beach. Images of Cases B to E were taken a few days later; hence, the sample has a brighter surface texture.  Correspondences are points that appear at similar locations in both reference and floating point clouds. Selections of correspondences are flexible as long as they can be visually identified. Based on correspondences, a geometric transformation matrix can be estimated, allowing the floating point cloud to be rigidly translated, rotated, and scaled for matching the reference point cloud.
Due to the manual selection of correspondences, errors are inevitably introduced during rough alignment. Such errors can be further reduced through fine registration. Here we adopt the ICP algorithm to further optimize the transformation matrix. The ICP algorithm starts with an initial guess of the rigid body transform of two point clouds, and iteratively improves the transformation matrix through repeatedly finding correspondences with minimum errors. The last row of Figure 1c illustrates comparisons of two point clouds at each stage of the registration.
The rough alignment can effectively align two point clouds together but small misalignments may exist. Fine alignment, on the other hand, is capable of adjusting small misalignments but may not work well if the initial misalignment of two point clouds is large. By successively adopting these two alignments in the correct order, the misalignments between two point clouds can be gradually reduced.

Test Configuration
A series of small-scale tests on a rock sample was performed with the purposes of (1) reconstructing dense 3D point clouds from the test sample under different lighting and surface texture conditions; and (2) detecting, localizing, and quantifying differential features of the rock sample under geometric changes. To this end, a rock sample was collected from Tumon Bay in Guam in June 2020. The longest diameter of the sample is about 13.5 cm, as shown in figure (a) in Table 1. Five test cases were established to mimic different testing environments. The third column of Table 1 elaborates the different lighting conditions and geometric changes for each test case. The rock sample in Case A had a darker texture due to the high moisture content after the sample was collected from the beach. Images of Cases B to E were taken a few days later; hence, the sample has a brighter surface texture.  Correspondences are points that appear at similar locations in both reference and floating point clouds. Selections of correspondences are flexible as long as they can be visually identified. Based on correspondences, a geometric transformation matrix can be estimated, allowing the floating point cloud to be rigidly translated, rotated, and scaled for matching the reference point cloud.
Due to the manual selection of correspondences, errors are inevitably introduced during rough alignment. Such errors can be further reduced through fine registration. Here we adopt the ICP algorithm to further optimize the transformation matrix. The ICP algorithm starts with an initial guess of the rigid body transform of two point clouds, and iteratively improves the transformation matrix through repeatedly finding correspondences with minimum errors. The last row of Figure 1c illustrates comparisons of two point clouds at each stage of the registration.
The rough alignment can effectively align two point clouds together but small misalignments may exist. Fine alignment, on the other hand, is capable of adjusting small misalignments but may not work well if the initial misalignment of two point clouds is large. By successively adopting these two alignments in the correct order, the misalignments between two point clouds can be gradually reduced.

Test Configuration
A series of small-scale tests on a rock sample was performed with the purposes of (1) reconstructing dense 3D point clouds from the test sample under different lighting and surface texture conditions; and (2) detecting, localizing, and quantifying differential features of the rock sample under geometric changes. To this end, a rock sample was collected from Tumon Bay in Guam in June 2020. The longest diameter of the sample is about 13.5 cm, as shown in figure (a) in Table 1. Five test cases were established to mimic different testing environments. The third column of Table 1 elaborates the different lighting conditions and geometric changes for each test case. The rock sample in Case A had a darker texture due to the high moisture content after the sample was collected from the beach. Images of Cases B to E were taken a few days later; hence, the sample has a brighter surface texture.  To mimic the landscape changes that one would see in a cliff, some geometric features of the rock sample were intentionally changed in Cases C, D, and E (see the fourth column of Table 1). Briefly, in Case C, three small stones denoted S1, S2, and S3 were placed on the top of the rock sample (see Figure 2a). In Case D, instead of adding stones, a thin layer of the rock sample were intentionally changed in Cases C, D, and E (see the fourth column of Table 1). Briefly, in Case C, three small stones denoted S1, S2, and S3 were placed on the top of the rock sample (see Figure 2a). In Case D, instead of adding stones, a thin layer of salt particles was added on the top of the sample (see Figure 2b). Thereafter, such a layer was removed, and a new layer of salt particles was added to a different location of the sample in Case E (see Figure 2c). A consumer-grade digital camera (Sony Alpha 6400 with the E PZ 16-50 mm Lens) was adopted for image collection. The auto mode was selected to allow the camera to define its preferred shooting parameters. The distance between the lens and the rock sample varied from 20 to 40 cm during image collection. Images were shot with a resolution of 6000 pixels by 4000 pixels. In Cases A to E, 199, 86, 70, 67, and 98 images were collected, respectively.

Point Cloud Reconstruction
The 3D point clouds of the sample were reconstructed using the off-the-shelf software Agisoft Metashape (version 1.6.2) [42] installed on a mobile workstation (Lenovo ThinkPad P72 with 16 GB of RAM and a 2.2 GHz CPU). Here, we use Case A as an example to illustrate the workflow.   To mimic the landscape changes that one would see in a cliff, some geometric features of the rock sample were intentionally changed in Cases C, D, and E (see the fourth column of Table 1). Briefly, in Case C, three small stones denoted S1, S2, and S3 were placed on the top of the rock sample (see Figure 2a). In Case D, instead of adding stones, a thin layer of salt particles was added on the top of the sample (see Figure 2b). Thereafter, such a layer was removed, and a new layer of salt particles was added to a different location of the sample in Case E (see Figure 2c).
A consumer-grade digital camera (Sony Alpha 6400 with the E PZ 16-50 mm Lens) was adopted for image collection. The auto mode was selected to allow the camera to define its preferred shooting parameters. The distance between the lens and the rock sample varied from 20 to 40 cm during image collection. Images were shot with a resolution of 6000 pixels by 4000 pixels. In Cases A to E, 199, 86, 70, 67, and 98 images were collected, respectively.

Point Cloud Reconstruction
The 3D point clouds of the sample were reconstructed using the off-the-shelf software Agisoft Metashape (version 1.6.2) [42] installed on a mobile workstation (Lenovo ThinkPad P72 with 16 GB of RAM and a 2.2 GHz CPU). Here, we use Case A as an example to illustrate the workflow.

Case E Light
Outdoor lighting condition; the sample was placed in the shadow A thin layer of salt particles was added to a different location (see Figure 2c) To mimic the landscape changes that one would see in a cliff, some geometric features of the rock sample were intentionally changed in Cases C, D, and E (see the fourth column of Table 1). Briefly, in Case C, three small stones denoted S1, S2, and S3 were placed on the top of the rock sample (see Figure 2a). In Case D, instead of adding stones, a thin layer of salt particles was added on the top of the sample (see Figure 2b). Thereafter, such a layer was removed, and a new layer of salt particles was added to a different location of the sample in Case E (see Figure 2c). A consumer-grade digital camera (Sony Alpha 6400 with the E PZ 16-50 mm Lens) was adopted for image collection. The auto mode was selected to allow the camera to define its preferred shooting parameters. The distance between the lens and the rock sample varied from 20 to 40 cm during image collection. Images were shot with a resolution of 6000 pixels by 4000 pixels. In Cases A to E, 199, 86, 70, 67, and 98 images were collected, respectively.

Point Cloud Reconstruction
The 3D point clouds of the sample were reconstructed using the off-the-shelf software Agisoft Metashape (version 1.6.2) [42] installed on a mobile workstation (Lenovo ThinkPad P72 with 16 GB of RAM and a 2.2 GHz CPU). Here, we use Case A as an example to illustrate the workflow.     (Figure 4b,c). This is because the sample was in an outdoor environment for the former test cases. Additionally, notice that the dense point cloud in Case A (Figure 3d) has a slightly darker color than Cases C and D  Figure 4b,c). This is caused by the fact that Case A has a higher moisture content, despite all three test cases being under indoor lighting conditions. Figure 4 shows the 3D reconstruction results of Cases B to E. The dense point clouds of the sample have different surface colors due to changes in lighting conditions. For instance, the dense point clouds have a lighter color representation in Cases B and E ( Figure  4a,d) compared with dense point clouds in Cases C and D (Figure 4b,c). This is because the sample was in an outdoor environment for the former test cases. Additionally, notice that the dense point cloud in Case A (Figure 3d) has a slightly darker color than Cases C and D (Figure 4b,c). This is caused by the fact that Case A has a higher moisture content, despite all three test cases being under indoor lighting conditions.

Point Cloud Registration
To align dense point clouds together, we adopt open-source software, CloudCompare (version 2.10.2) [43], and first scale the point cloud in Case A with the real-world unit. To do this, two points (#4332244 and #3697936 in Figure 5a) were selected in the unscaled point cloud. The distance between these two points was measured as 7.753 from Cloud-Compare. Notice that there is no real-world dimension associated with this distance. Next, the locations of these two points were identified in the rock sample and the corresponding distance was measured as 10.5 cm. This further led to a scaling factor of 10.5 cm/7.753 = 1.354 cm/1. Thereafter, the initial point cloud was scaled up by multiplying 1.354 to the coordinates of each point. The new point cloud, after scaling, is treated as the reference point cloud. Figure 5b illustrates the comparison of the point clouds before and after scaling. Next, a point cloud from a new test case is aligned to the reference point cloud. We use Case C as an example here for illustration. First, rough registration was performed using four correspondences (A0-R0, A1-R1, A2-R2, and A3-R3 in Figure 5c) from both point clouds. Thereafter, fine registration was conducted through the ICP algorithm. Point clouds from Case B, D, and E were aligned with the point cloud in Case A using the same

Point Cloud Registration
To align dense point clouds together, we adopt open-source software, CloudCompare (version 2.10.2) [43], and first scale the point cloud in Case A with the real-world unit. To do this, two points (#4332244 and #3697936 in Figure 5a) were selected in the unscaled point cloud. The distance between these two points was measured as 7.753 from CloudCompare. Notice that there is no real-world dimension associated with this distance. Next, the locations of these two points were identified in the rock sample and the corresponding distance was measured as 10.5 cm. This further led to a scaling factor of 10.5 cm/7.753 = 1.354 cm/1. Thereafter, the initial point cloud was scaled up by multiplying 1.354 to the coordinates of each point. The new point cloud, after scaling, is treated as the reference point cloud. Figure 5b illustrates the comparison of the point clouds before and after scaling. Figure 4 shows the 3D reconstruction results of Cases B to E. The dense point clouds of the sample have different surface colors due to changes in lighting conditions. For instance, the dense point clouds have a lighter color representation in Cases B and E ( Figure  4a,d) compared with dense point clouds in Cases C and D (Figure 4b,c). This is because the sample was in an outdoor environment for the former test cases. Additionally, notice that the dense point cloud in Case A (Figure 3d) has a slightly darker color than Cases C and D (Figure 4b,c). This is caused by the fact that Case A has a higher moisture content, despite all three test cases being under indoor lighting conditions.

Point Cloud Registration
To align dense point clouds together, we adopt open-source software, CloudCompare (version 2.10.2) [43], and first scale the point cloud in Case A with the real-world unit. To do this, two points (#4332244 and #3697936 in Figure 5a) were selected in the unscaled point cloud. The distance between these two points was measured as 7.753 from Cloud-Compare. Notice that there is no real-world dimension associated with this distance. Next, the locations of these two points were identified in the rock sample and the corresponding distance was measured as 10.5 cm. This further led to a scaling factor of 10.5 cm/7.753 = 1.354 cm/1. Thereafter, the initial point cloud was scaled up by multiplying 1.354 to the coordinates of each point. The new point cloud, after scaling, is treated as the reference point cloud. Figure 5b illustrates the comparison of the point clouds before and after scaling. Next, a point cloud from a new test case is aligned to the reference point cloud. We use Case C as an example here for illustration. First, rough registration was performed using four correspondences (A0-R0, A1-R1, A2-R2, and A3-R3 in Figure 5c) from both point clouds. Thereafter, fine registration was conducted through the ICP algorithm. Point clouds from Case B, D, and E were aligned with the point cloud in Case A using the same Next, a point cloud from a new test case is aligned to the reference point cloud. We use Case C as an example here for illustration. First, rough registration was performed using four correspondences (A0-R0, A1-R1, A2-R2, and A3-R3 in Figure 5c) from both point clouds. Thereafter, fine registration was conducted through the ICP algorithm. Point clouds from Case B, D, and E were aligned with the point cloud in Case A using the same procedure, but the procedures of these alignments are not shown in this manuscript due to the length constraint.

Point Cloud Comparison
Once point clouds of Case B to E are aligned with the reference point cloud in Case A, the differential features can be identified through computing cloud-to-cloud distance in CloudCompare. The cloud-to-cloud distance between Case A-B and Case A-C are illustrated in Figure 6. As shown in the figure, the test sample in Case B experienced no geometric change but was under a different lighting condition. As a result, the cloudto-cloud distance between Case B and reference point cloud (i.e., Case A) is extremely small (0.07 cm in Figure 6a,b), indicating two point clouds match well with each other. The three stones in Case C can be identified from the cloud-to-cloud distance as shown in Figure 6d,e. The locations of stones agree well with the ground truth measurements in Figure 6f. Furthermore, the height of S1, S2, and S3 can be roughly quantified as 0.4, 0.3, and 0.7 cm. procedure, but the procedures of these alignments are not shown in this manuscript due to the length constraint.

Point Cloud Comparison
Once point clouds of Case B to E are aligned with the reference point cloud in Case A, the differential features can be identified through computing cloud-to-cloud distance in CloudCompare. The cloud-to-cloud distance between Case A-B and Case A-C are illustrated in Figure 6. As shown in the figure, the test sample in Case B experienced no geometric change but was under a different lighting condition. As a result, the cloud-tocloud distance between Case B and reference point cloud (i.e., Case A) is extremely small (0.07 cm in Figure 6a,b), indicating two point clouds match well with each other. The three stones in Case C can be identified from the cloud-to-cloud distance as shown in Figure  6d,e. The locations of stones agree well with the ground truth measurements in Figure 6f. Furthermore, the height of S1, S2, and S3 can be roughly quantified as 0.4, 0.3, and 0.7 cm. The cloud-to-cloud distances between Case A-D and Case A-E are shown in Figure  7. As can be seen in the first and second columns of the figure, salt particles in the test samples in Cases D and E can be identified. The cloud-to-cloud distance in log scale has better demonstrations on finding the boundary of the particles; while the result in linear scale is more suitable for quantifying the thickness of the salt layer. Results indicate that the proposed method can reliably find geometric changes that occurred in the test sample, regardless of changes in the lighting conditions, as seen in Cases D and E. The cloud-to-cloud distances between Case A-D and Case A-E are shown in Figure 7. As can be seen in the first and second columns of the figure, salt particles in the test samples in Cases D and E can be identified. The cloud-to-cloud distance in log scale has better demonstrations on finding the boundary of the particles; while the result in linear scale is more suitable for quantifying the thickness of the salt layer. Results indicate that the proposed method can reliably find geometric changes that occurred in the test sample, regardless of changes in the lighting conditions, as seen in Cases D and E.

Site Description
A cliff at Tagachang Beach in Guam is selected as the testbed for field validation. Tagachang Beach is located on the east side of the island. Showing in Figure 8d, the cliff starts at the south end of the beach and extends to the south. A small portion of the cliff is selected in this study (see the white circle in Figure 8d). Figure 9 illustrates the testbed from different views. The target cliff is about 30 m high measured from the cliff bottom and has a relatively flat top surface covered by vegetation (Figure 9a). Both north and east sides of the target cliff are steep rock surfaces (Figure 9b,c). A rock slide can be observed on the east vertical plane of the cliff due to the previous erosion (Figure 9d).

Site Description
A cliff at Tagachang Beach in Guam is selected as the testbed for field validation. Tagachang Beach is located on the east side of the island. Showing in Figure 8d, the cliff starts at the south end of the beach and extends to the south. A small portion of the cliff is selected in this study (see the white circle in Figure 8d). Figure 9 illustrates the testbed from different views. The target cliff is about 30 m high measured from the cliff bottom and has a relatively flat top surface covered by vegetation (Figure 9a). Both north and east sides of the target cliff are steep rock surfaces (Figure 9b,c). A rock slide can be observed on the east vertical plane of the cliff due to the previous erosion (Figure 9d).

Site Description
A cliff at Tagachang Beach in Guam is selected as the testbed for field validation. Tagachang Beach is located on the east side of the island. Showing in Figure 8d, the cliff starts at the south end of the beach and extends to the south. A small portion of the cliff is selected in this study (see the white circle in Figure 8d). Figure 9 illustrates the testbed from different views. The target cliff is about 30 m high measured from the cliff bottom and has a relatively flat top surface covered by vegetation (Figure 9a). Both north and east sides of the target cliff are steep rock surfaces (Figure 9b,c). A rock slide can be observed on the east vertical plane of the cliff due to the previous erosion (Figure 9d).

UAV Operation, Data Collection, and Point Cloud Reconstruction
Two visits were carried out on 25 June and 11 July 2020, respectively. The east side of the cliff was inaccessible due to high tides during both visits. Hence, the deployment work was performed at the north side of the cliff (i.e., see the deployment area in Figure  8d). Two off-the-shelf UAVs, the DJI Air (SZ DJI Technology Co., Ltd, Shenzhen, China) and DJI Phantom 4 Pro + V2.0 (DJI Phantom 4, hereafter, SZ DJI Technology Co., Ltd, Shenzhen, China), were adopted as tools for image collection.
To evenly capture the testbed under different camera positions, two image collection strategies were proposed. The first strategy was to take a series of images under a preprogrammed flight route to scan the cliff from the top. This was achieved by operating the DJI Air through an off-the-shelf smartphone app, Pix4Dcapture (version 4.10.0) [44], installed on an iPhone 11. A double-grid mapping mission was created in the app. The altitude of the flight was defined as 90.2 m with front and side overlapping of 90% and 75%, respectively, based on which the app calculated the UAV locations for shooting each image. As a result, 83 images were collected by the DJI Air for both field visits with an image resolution of 4056 pixels by 3040 pixels. The UAV camera angle was selected as 80 degrees.
For the second image collection strategy, images were captured by the DJI Phantom 4 through an intelligent mode, named point of interest (POI), using the smartphone app DJI Go 4 (version 4.3.36) [45]. The app was preinstalled in the all-in-one DJI remote controller. The POI mode allowed the UAV to fly along a circular path horizontally with a predefined center point and a radius. The center point was defined at the cliff's top (see the white cross in Figure 9a), and the radius was selected as 62 m. Then, multiple POI flights were performed under altitudes of 25 m to 45 m. Images were automatically collected by the onboard UAV camera using a camera shooting interval of 2 seconds with an image resolution of 4864 pixels by 3648 pixels. In total, 284 and 251 images were collected in the field visits of 25 June and 11 July, respectively. Figure 10a,c show the sample UAV images from the DJI Phantom 4 under the POI mode for both field visits. Figure 10b,d show the camera positions where the backgrounds are sparse point clouds of the testbed. As can be seen in the figures, the DJI Air follows flight missions of a 3-by-3 grid to cover the top of the cliff area. The DJI Phantom 4 is operated in POI mode to mainly scan the east and north sides of the cliff from four different altitudes.

UAV Operation, Data Collection, and Point Cloud Reconstruction
Two visits were carried out on 25 June and 11 July 2020, respectively. The east side of the cliff was inaccessible due to high tides during both visits. Hence, the deployment work was performed at the north side of the cliff (i.e., see the deployment area in Figure 8d). Two off-the-shelf UAVs, the DJI Air (SZ DJI Technology Co., Ltd, Shenzhen, China) and DJI Phantom 4 Pro + V2.0 (DJI Phantom 4, hereafter, SZ DJI Technology Co., Ltd, Shenzhen, China), were adopted as tools for image collection.
To evenly capture the testbed under different camera positions, two image collection strategies were proposed. The first strategy was to take a series of images under a preprogrammed flight route to scan the cliff from the top. This was achieved by operating the DJI Air through an off-the-shelf smartphone app, Pix4Dcapture (version 4.10.0) [44], installed on an iPhone 11. A double-grid mapping mission was created in the app. The altitude of the flight was defined as 90.2 m with front and side overlapping of 90% and 75%, respectively, based on which the app calculated the UAV locations for shooting each image. As a result, 83 images were collected by the DJI Air for both field visits with an image resolution of 4056 pixels by 3040 pixels. The UAV camera angle was selected as 80 degrees.
For the second image collection strategy, images were captured by the DJI Phantom 4 through an intelligent mode, named point of interest (POI), using the smartphone app DJI Go 4 (version 4.3.36) [45]. The app was preinstalled in the all-in-one DJI remote controller. The POI mode allowed the UAV to fly along a circular path horizontally with a predefined center point and a radius. The center point was defined at the cliff's top (see the white cross in Figure 9a), and the radius was selected as 62 m. Then, multiple POI flights were performed under altitudes of 25 m to 45 m. Images were automatically collected by the onboard UAV camera using a camera shooting interval of 2 seconds with an image resolution of 4864 pixels by 3648 pixels. In total, 284 and 251 images were collected in the field visits of 25 June and 11 July, respectively. Figure 10a,c show the sample UAV images from the DJI Phantom 4 under the POI mode for both field visits. Figure 10b,d show the camera positions where the backgrounds are sparse point clouds of the testbed. As can be seen in the figures, the DJI Air follows flight missions of a 3-by-3 grid to cover the top of the cliff area. The DJI Phantom 4 is operated in POI mode to mainly scan the east and north sides of the cliff from four different altitudes.
Based on the collected UAV images from the DJI Air and Phantom 4, the dense point clouds of two field visits are reconstructed using Agisoft Metashape on a workstation (Dell XPS 8930-7814BLK-PUS with 32 GB of RAM and a 3.0 GHz CPU). Figure 11 illustrates the dense point clouds from both field visits where point clouds outside the scope of the testbed are truncated. The point cloud in the 25 June visit contains 48.5 million points, while the point cloud on 11 July contains 55.8 million points.
in the field visits of 25 June and 11 July, respectively. Figure 10a,c show the sample UAV images from the DJI Phantom 4 under the POI mode for both field visits. Figure 10b,d show the camera positions where the backgrounds are sparse point clouds of the testbed. As can be seen in the figures, the DJI Air follows flight missions of a 3-by-3 grid to cover the top of the cliff area. The DJI Phantom 4 is operated in POI mode to mainly scan the east and north sides of the cliff from four different altitudes.

Point Cloud Registration
To align the point clouds, we first scale the point cloud into a correct real-world unit in CloudCompare. To this end, we treat the point cloud in the second visit on 11 July as the reference point cloud. During this visit, three markers (M1, M2, and M3) were placed in the testbed as seen in Figure 12d. M1 and M2 were X marks made by the blue paint tape, while M3 was the UAV landing pad. The distances between the three markers were taken by a measuring tape (see the second column in Table 2). Next, the markers were visually identified from the dense point cloud (Figure 12a-c). The distances between three markers in the point cloud were also measured (see the third column in Table 2). Finally, three scaling factors were calculated, based on which the average scaling factor of 1.054 m was applied for scaling the point cloud in the second visit.

Point Cloud Registration
To align the point clouds, we first scale the point cloud into a correct real-world unit in CloudCompare. To this end, we treat the point cloud in the second visit on 11 July as the reference point cloud. During this visit, three markers (M1, M2, and M3) were placed in the testbed as seen in Figure 12d. M1 and M2 were X marks made by the blue paint tape, while M3 was the UAV landing pad. The distances between the three markers were taken by a measuring tape (see the second column in Table 2). Next, the markers were visually identified from the dense point cloud (Figure 12a-c). The distances between three markers in the point cloud were also measured (see the third column in Table 2). Finally, three scaling factors were calculated, based on which the average scaling factor of 1.054 m was applied for scaling the point cloud in the second visit.
Thereafter, the scaled point cloud in the first visit was aligned to the reference point cloud through the registration protocol. Figure 11 demonstrates the selections of correspondences (A1-R1, A2-R2, A3-R3, and A4-R4) from both point clouds for rough alignment. Next, the point cloud in the first visit was further aligned by the automated ICP algorithm. Figure 13 shows the comparison of point clouds under different views of the cliff from two visits during the registration procedure. The point cloud from the 25 June visit is rendered in blue. As can be seen in Figure 13b,e,h, small misalignments can be observed after rough alignment. Such misalignments can be minimized after fine alignment is performed (Figure 13c,f,i). tape, while M3 was the UAV landing pad. The distances between the three markers were taken by a measuring tape (see the second column in Table 2). Next, the markers were visually identified from the dense point cloud (Figure 12a-c). The distances between three markers in the point cloud were also measured (see the third column in Table 2). Finally, three scaling factors were calculated, based on which the average scaling factor of 1.054 m was applied for scaling the point cloud in the second visit.    Thereafter, the scaled point cloud in the first visit was aligned to the reference point cloud through the registration protocol. Figure 11 demonstrates the selections of correspondences (A1-R1, A2-R2, A3-R3, and A4-R4) from both point clouds for rough alignment. Next, the point cloud in the first visit was further aligned by the automated ICP algorithm. Figure 13 shows the comparison of point clouds under different views of the cliff from two visits during the registration procedure. The point cloud from the 25 June visit is rendered in blue. As can be seen in Figure 13b,e,h, small misalignments can be observed after rough alignment. Such misalignments can be minimized after fine alignment is performed (Figure 13c,f,i).

Cliff Monitoring
The cloud-to-cloud distance is computed in CloudCompare and the results are shown in Figure 14. As can be seen from the figure, the majority of the cliff area is covered in green, indicating the discrepancies between two point clouds are about or less than 1.47 cm (read from the figure). However, scattered yellow and red spots can be also found from the results. The cloud-to-cloud distances for these locations span from 19 cm (yellow) to 2.47 m (red), showing significant discrepancies that occurred in the point clouds from two field visits.

Cliff Monitoring
The cloud-to-cloud distance is computed in CloudCompare and the results are shown in Figure 14. As can be seen from the figure, the majority of the cliff area is covered in green, indicating the discrepancies between two point clouds are about or less than 1.47 cm (read from the figure). However, scattered yellow and red spots can be also found from the results. The cloud-to-cloud distances for these locations span from 19 cm (yellow) to 2.47 m (red), showing significant discrepancies that occurred in the point clouds from two field visits. Remote Sens. 2021, 13, x FOR PEER REVIEW 13 of 17 To further investigate such discrepancies, two locations (Patch A and B) are identified from the bird's-eye view in Figure 14a. Patch A contains a steep cliff face covered by scattered vegetation as shown in Figure 15b; Patch B locates at the flat top of the cliff filled by vegetation ( Figure 15d). As observed from the figures, the cloud-to-cloud distances are large in the area of vegetation (yellow spots in Figure 15a,c) and become smaller around the cliff rock face (e.g., the green area in Figure 15a). This is because the SfM-MVS algorithm has difficulties reconstructing thin structures such as plants [41], leading to reconstruction errors to the point clouds. To reduce the errors caused by vegetation, we truncate the cloud-to-cloud distance result in Figure 14 by only reserving the steep cliff faces on the east and north sides. The new results of cloud-to-cloud distance are shown in Figure 16. As a result, the maximum cloud-to-cloud distance has been reduced from 2.47 m in Figure 14 to 0.66 m in Figure 16. Red spots can be still observed from the figures, mainly caused by the scattered vegetation on the cliff faces. We further inquiry three cloud-to-cloud distances from typical cliff faces and the results range from 0.7 cm to 2.2 cm. Considering the size of the entire cliff (about 30 m in height), such differences are negligible. To further investigate such discrepancies, two locations (Patch A and B) are identified from the bird's-eye view in Figure 14a. Patch A contains a steep cliff face covered by scattered vegetation as shown in Figure 15b; Patch B locates at the flat top of the cliff filled by vegetation (Figure 15d). As observed from the figures, the cloud-to-cloud distances are large in the area of vegetation (yellow spots in Figure 15a,c) and become smaller around the cliff rock face (e.g., the green area in Figure 15a). This is because the SfM-MVS algorithm has difficulties reconstructing thin structures such as plants [41], leading to reconstruction errors to the point clouds. To further investigate such discrepancies, two locations (Patch A and B) are identified from the bird's-eye view in Figure 14a. Patch A contains a steep cliff face covered by scattered vegetation as shown in Figure 15b; Patch B locates at the flat top of the cliff filled by vegetation ( Figure 15d). As observed from the figures, the cloud-to-cloud distances are large in the area of vegetation (yellow spots in Figure 15a,c) and become smaller around the cliff rock face (e.g., the green area in Figure 15a). This is because the SfM-MVS algorithm has difficulties reconstructing thin structures such as plants [41], leading to reconstruction errors to the point clouds. To reduce the errors caused by vegetation, we truncate the cloud-to-cloud distance result in Figure 14 by only reserving the steep cliff faces on the east and north sides. The new results of cloud-to-cloud distance are shown in Figure 16. As a result, the maximum cloud-to-cloud distance has been reduced from 2.47 m in Figure 14 to 0.66 m in Figure 16. Red spots can be still observed from the figures, mainly caused by the scattered vegetation on the cliff faces. We further inquiry three cloud-to-cloud distances from typical cliff faces and the results range from 0.7 cm to 2.2 cm. Considering the size of the entire cliff (about 30 m in height), such differences are negligible. To reduce the errors caused by vegetation, we truncate the cloud-to-cloud distance result in Figure 14 by only reserving the steep cliff faces on the east and north sides. The new results of cloud-to-cloud distance are shown in Figure 16. As a result, the maximum cloud-to-cloud distance has been reduced from 2.47 m in Figure 14 to 0.66 m in Figure 16. Red spots can be still observed from the figures, mainly caused by the scattered vegetation on the cliff faces. We further inquiry three cloud-to-cloud distances from typical cliff faces and the results range from 0.7 cm to 2.

Discussions
We validated the proposed method through a few small-scale experiments using a rock sample. Although SfM-MVS is a well-established workflow for reconstructing point clouds, few studies in the literature focused on the robustness of SfM-MVS against different lighting conditions and surface textures in the context of coastal cliffs. The small-scale validation in this study serves as the mean for addressing such concerns. The lighting conditions and surface textures (see the second and third columns in Table 1) would simulate the different weather conditions of a cliff one could see in the field. For instance, the lighting conditions of the cliff site would change across different periods of the day; the surface texture of rock may become dark after rain or a typhoon. The geometric changes in small-scale validation include abrupt changes, such as adding stones (Case C); or gradual changes, such as adding salt particle layers (Cases D and E). These changes mimic the geomorphological changes of the cliff. For the erosion behavior of the cliff, instead of adding contents, landscape features of the cliff would be removed. In this case, point clouds in Case C, D, and E can be considered as the initial models, while the point cloud in Case A shall be the new model after erosion.
Results from the small-scale validation demonstrated the effectiveness of our method in detecting, identifying, and quantifying geometric changes in the rock sample, regardless of variations in lighting conditions and surface texture. Although the cliff in the field validation of this study did not experience visible erosion due to a short inspection interval, the findings in the small-scale validation would serve as the basis for the success of our method in monitoring cliff erosion over the long term.
In terms of correspondence selection, four pairs of correspondences are selected on the top of the test sample in small-scale validation showing in Figure 5. Selecting correspondences from other locations of the rock sample is also feasible. Since correspondence selection only serves as the mean for rough alignment, errors that occurred in this

Discussion
We validated the proposed method through a few small-scale experiments using a rock sample. Although SfM-MVS is a well-established workflow for reconstructing point clouds, few studies in the literature focused on the robustness of SfM-MVS against different lighting conditions and surface textures in the context of coastal cliffs. The small-scale validation in this study serves as the mean for addressing such concerns. The lighting conditions and surface textures (see the second and third columns in Table 1) would simulate the different weather conditions of a cliff one could see in the field. For instance, the lighting conditions of the cliff site would change across different periods of the day; the surface texture of rock may become dark after rain or a typhoon. The geometric changes in small-scale validation include abrupt changes, such as adding stones (Case C); or gradual changes, such as adding salt particle layers (Cases D and E). These changes mimic the geomorphological changes of the cliff. For the erosion behavior of the cliff, instead of adding contents, landscape features of the cliff would be removed. In this case, point clouds in Case C, D, and E can be considered as the initial models, while the point cloud in Case A shall be the new model after erosion.
Results from the small-scale validation demonstrated the effectiveness of our method in detecting, identifying, and quantifying geometric changes in the rock sample, regardless of variations in lighting conditions and surface texture. Although the cliff in the field validation of this study did not experience visible erosion due to a short inspection interval, the findings in the small-scale validation would serve as the basis for the success of our method in monitoring cliff erosion over the long term.
In terms of correspondence selection, four pairs of correspondences are selected on the top of the test sample in small-scale validation showing in Figure 5. Selecting correspondences from other locations of the rock sample is also feasible. Since correspondence selection only serves as the mean for rough alignment, errors that occurred in this regis-tration stage can be further reduced during fine alignment and would not affect the final registration result.
One difference between small-scale and field validations is that extra errors are induced in the field validation due to vegetation in the cliff area. Vegetation fully covers the top surface of the cliff and appears in scattered patterns at the vertical cliff faces. Estimating the locations of true rock surfaces in these areas from the point cloud could be very challenging as the surfaces are barely visible from UAV images. However, the false-positive results can be easily identified through visual inspections between cloud-to-cloud distance and ground truth measurements (see Figure 15).
Since the nature of our method is a non-georeferenced approach, the point cloud generated by our method is not intended to contain any geographic information. Although most consumer-grade UAVs (including the ones in this study) provide geotagged images, such UAV images are not suitable for georeferencing due to the low accuracy of GIS coordinates. Secondly, the point cloud produced by our method cannot be directly linked to georeferenced datasets (e.g., geotagged maps, point clouds, or models). However, if a georeferenced point cloud of a cliff exists in the past, one can align a newly collected non-georeferenced point cloud from our method to the existing georeferenced one through the registration method established in this study. In terms of geomorphological changes, our method assumes that only a small portion of the cliff experiences erosion while the remainder of the cliff remains unchanged during inspections, which could be commonly found in coastal surveying [46]. Investigating dramatic geomorphological changes of a cliff due to severe erosions is out of the scope of this study.

Conclusions
Monitoring cliff erosion is essential for maintaining a healthy coastal ecosystem. The usage of photogrammetry-based workflows and UAVs have been proven effective in monitoring coastal cliffs. To date, many photogrammetry-based methods rely on georeferencing frameworks for point cloud alignments. Despite the successes reported in these studies, georeferencing efforts significantly increase the project cost through securing high-end GPS equipment, hiring GIS specialists, and/or relying on GNSS-enabled UAVs. This may hinder the usage of photogrammetry technology for monitoring cliffs on a routine basis, particularly in underserved coastal communities where expensive hardware and trained GIS specialists are limited resources.
In this study, we proposed a novel photogrammetry-based approach for identifying geomorphological changes of coastal cliffs that does not rely on any georeferencing efforts. The SfM-MVS algorithms were adopted in reconstructing 3D dense point clouds of the cliff. Then, a rigid registration protocol was established to gradually align two point clouds at different periods together to uncover the differential changes caused by cliff erosion. Our method has been examined by a series of small-scale experiments on a rock sample. Results indicated the proposed method can detect, localize, and quantify small changes that occurred in the rock sample, regardless of variations in lighting and surface texture conditions. Thereafter, we further validated our method on a full-scale coastal cliff in Guam. Point clouds from two field visits were reconstructed and aligned together to find the differential features caused by geomorphological changes. The findings of this study are highly impactful for being able to offer a low-cost and flexible cliff monitoring methodology to government agencies and stakeholders for their decision-making in coastal zone management.
Funding: This study is based on work supported by the seed grant through the National Science Foundation project Guam EPSCoR (Grant No. 1457769) in the United States. However, any opinions, findings, and conclusions, or recommendations expressed in this study are those of the author and do not necessarily reflect the views of the National Science Foundation or Guam EPSCoR.

Data Availability Statement:
The data presented in this study are available from the author upon reasonable request.