Terrain analysis is essential for modeling environmental systems [1
]. The variability of landforms is frequently used to understand, map or model geomorphological, hydrological, and biological processes [4
]. Elevation has a strong relationship with terrestrial temperature, vegetation type, and with the potential energy accumulated on a slope. The aspect and derived products, such as Northernness and Easternness attributes, can be linked to the potential solar irradiation on terrain. The Slope gradient, for example, controls the overland and subsurface flow velocity and runoff rate. Similarly, curvatures are associated with acceleration and dispersion of water and sediment flows, which impacts the erosion and soil water content [8
The public availability of elevation data with global coverage, such as the digital elevation model (DEM) derived from NASA’s Shuttle Radar Topography Mission (SRTM DEM, [9
]) and the digital surface model from the Advanced Land Observing Satellite (AW3D30 DSM, [10
]), has promoted the exploration of topographic features in different contexts using processing tools available in several geographic information systems (GIS) [4
]. However, despite the popularization of many global elevation datasets, it is important to pay attention to their quality when used for modelling purposes, as the acquisition mean and other production aspects can significantly impact the outputs [13
]. In addition, analyzing big geospatial datasets can pose some limitations to traditional GIS. This becomes more critical with the availability of new digital datasets, which are providing better temporal and spatial resolutions due to advances in sensor technologies [15
The Global Multi-resolution Terrain Elevation Data 2010 [16
] and the global suit of terrain attributes [2
] are examples of datasets that were produced using large computational tasks for mapping the global extent and in different spatial resolutions, which demanded optimized processing architectures. In general, high performance architectures are based on splitting the data in smaller subsets (tiles) to take the advantage of distributed computing operations. Recently, with the advent and popularization of cloud-based interfaces for processing big geospatial data, e.g., Google Earth Engine [17
], the Pangeo software packages [18
], and Actinia REST service [19
], computational tasks applied to terrain analysis could be scaled and customized directly by the user.
Earth Engine (GEE) is a cloud-based platform developed by Google that supports the global-scale analysis of big catalogs of Earth Observation data [17
]. It has been used to map global forest change in the 21st century [20
], Earth’s surface water change [21
], global urban areas [11
], wildfire progression [22
], global bare surface change [23
], and others. In this sense, GEE becomes compelling not because the distributed processing tasks are executed on the server-side of Google, but also due to the increasing availability of many global geospatial datasets that could be explored in topographic mapping. There exist several available topographical data within GEE, such as the global SRTM DEM, AW3D30 DSM, Global 30 Arc-Second Elevation data (GTOPO30 DEM, [24
]), and others. Thus, GEE characteristics could permit the customization of high-performance terrain analysis with minimal user input and any computational processing on the user side. In fact, GEE provides three algorithms for calculating slope, illumination, and aspect of terrain, but lacks in providing calculation methods of other terrain information, such as the curvatures and landscape characterization.
In addition, a common obstacle of global terrain analysis in common GIS is the need for projecting DEMs onto projected coordinate systems, which ensures the elevation data is equally spaced on a plane square grid [25
]. This step is complicated because it is difficult to define a projected system that minimizes terrain distortions over a global extent [26
]. Moreover, as many available global DEMs are referenced by geographical coordinate systems and some researchers continue to apply square-grid algorithms to them, the algorithms should consider the geometry and specificity of global spheroidal DEMs [25
]. This aspect is important because the application of square-grid methods to spheroidal equal angular DEMs leads to substantial computational errors in models of morphometric variables [25
In this paper, we aimed at describing and making available a user-friendly processing algorithm for performing terrain analysis in GEE. This algorithm takes advantage of GEE’s high-performance architecture for making the computational analysis scalable, adapted to customized needs, and requiring minimal user input. For this, the proposed package takes advantage of a calculation method adapted for spheroidal elevation grids, which favors the global-scale analysis of different DEM resolutions without projecting elevation data.
3. Results and Discussion
The statistical analysis revealed a significant correlation (p
< 0.01) of the TAGEE outputs with equivalent terrain attributes calculated from GEE and SAGA GIS (Table 2
). The slope estimated over a near-global extent reached a correlation of 0.98 (error of 2%) between TAGEE and functions of GEE, while the aspect resulted in a Pearson’s r
of 0.89 (13% of error). The lower correlation of aspect can be associated to its dimension nature, i.e., a circular variable, as well as to the differences of calculation methods between TAGEE and GEE. Despite the small differences, TAGEE revealed the same spatial patterns and allowed the estimation of additional attributes at the global scale, such as the Northernness, horizontal and vertical curvatures (Figure 3
A–C, respectively). The main mountain ranges of the Earth, such as the Rocky Mountains in North America, Andes in South America, Alps in Europe, Himalayas, and Tibetan plateau in Asia, etc., present the highest curvatures calculated by TAGEE. Conversely, the plains and flat surfaces had the lowest estimates for both curvatures. The degree of orientation to North (Figure 3
A) also depict the main landforms of the Earth.
TAGEE was developed in GEE to take advantage of the high-performance computing of the platform. As the cloud-based interfaces have created much enthusiasm and engagement in the remote sensing and geospatial fields, many processing algorithms have been adapted to make substantive progress on global challenges involving the processing of big geospatial data [30
]. Within this framework, TAGEE supports the development of customized terrain analysis with different elevation data across large geographical extents.
When TAGEE outputs were compared to those from SAGA GIS (Table 2
), the statistical evaluation resulted in a significant and high correlation for the slope, horizontal and vertical curvatures of terrain (Pearson’s r
of 0.98, with an error difference of 3 and 4%). Aspects from TAGEE and SAGA GIS had an inferior correlation coefficient, but the result was higher than the aspect from the algorithm of GEE. The region of Mount Ararat was also used to visually compare the slope, horizontal and vertical curvatures, calculated from both TAGEE and SAGA GIS (Figure 4
). The 3D visualizations revealed a high similarity between both maps, but some small differences can be visualized by the color intensity. This is the case of the slope of the Mount Ararat calculated by TAGEE (Figure 4
A), which had a higher intensity compared to the slope of SAGA GIS (Figure 4
B). A slightly higher intensity for the vertical curvature calculated by SAGA GIS was also evident on an edge of the Mount Ararat (Figure 4
F). Despite being small, these visual differences confirm the relative error of both methods (Table 2
). In addition, the spatial patterns of aspect, slope, and curvatures from TAGEE presented a high correspondence with the terrain maps of Mount Ararat available in [8
], reinforcing the confidence of the TAGEE calculation method.
In this work, the TAGEE algorithm was developed to consider spheroidal geometries in its calculation method. This approach diverges from the techniques available in traditional GIS, where TAGEE considers the great circle distances of the DEM defined by Latitude and Longitude positions. Common GIS software, such as SAGA GIS, requires the projection of the DEM to ensure the elevation data have the same pixel size. However, as identified by [25
], some researchers continue to apply square-grid algorithms to spheroidal equal angular DEMs, which can lead to substantial computational errors in models of morphometric variables. The small relative errors between TAGEE and GEE or SAGA GIS could be linked to the differences in their calculation methods.
Finally, some limitations of TAGEE can also be noted. Only local morphometric variables can be calculated by the package, which includes flux and form attributes. Non-local attributes, such as specific catchment area, were not implemented due to the absence of a general analytical theory, which is still little developed [29
], and due to the recursion processing that is still challenging within GEE [17
]. Furthermore, a novel method became available to handle major problems of terrain analysis, which includes the approximation of DEM, generalization and denoising, and the computation of morphometric variables. The universal spectral analytical method based on high-order orthogonal expansions using the Chebyshev polynomials were developed by [31
] to handle the aforementioned issues into an integrated framework, but was not implemented in this work.