Terrain Correction Research Articles

A comparative analysis of different terrain correction methods based on Landsat-8 OLI data

The topographic effect has long been recognized as one of problems for quantitative remote sensing. The paper compares the correction results of OLI data based on C model, Cosine model, SCS model, Minnaert model and pixel-based Minnaert Correction Method. The visual inspection, statistical analysis and regression analysis of images were used to analyze the results before and after correction of image. The results show that the C model has a better correction effect. The Cosine model and SCS model were significantly overcorrected. However, C model, Minnaert model and slope-based Minnaert model weakened the influence of terrain. By comparative analysis, the C correction method was optimal model for OLI image.

The Potential Scattering Model for Oil Palm Phenology Based on Spaceborne X‐, C‐, and L‐Band Polarimetric SAR Imaging

Information about oil palm phenology is required for oil palm plantation management, but using spaceborne polarimetric radar imagery remains challenging. However, spaceborne polarimetric radar on X‐, C‐, and L‐band is promising on structure vegetation and cloud area. This study investigates the scattering model of oil palm phenology based on spaceborne X‐, C‐, and L‐band polarimetric Synthetic Aperture Radar (SAR) imaging. The X‐, C‐, and L‐band polarimetric SAR are derived from spaceborne of TerraSAR‐X, Sentinel‐1A, and ALOS PALSAR 2. Study area is located in oil palm plantations, Asahan District, North Sumatra, Indonesia. The methodology includes data collection, preprocessing, radiometric calibration, speckle filtering, terrain correction, extraction of scattering value, and development of scattering model of oil palm phenology. The results showed different scattering characteristics for the X‐, C‐, and L‐band polarimetric SAR of oil palm for age and found the potential of the scattering model for oil palm phenology based on the X‐band on HH polarization that showed a nonlinear model with R2 = 0.65. The C‐band on VH and VV polarization showed a nonlinear model with R2 = 0.56 and R2 = 0.89. The L‐band on HV and HH polarization showed a logarithmic model with R2 = 0.50 and R2 = 0.51. In this case, the most potential of the scattering model of oil palm phenology based onR2is using C‐band on VV polarization. However, the scattering model based on X‐, C‐, and L‐band is potentially to be used and applied to identify the phenology of oil palm in Indonesia, which is the main parameter in yield estimation. For the future phenology model needs to improve accuracy by integrating multisensors, including different wavelengths on optical and microwave sensors and more in situ data.

ОПРЕДЕЛЕНИЕ ОПТИМАЛЬНЫХ ПАРАМЕТРОВ ДЛЯ ВЫЧИСЛЕНИЯ ПОПРАВОК ЗА РЕЛЬЕФ НА ОСНОВЕ ЦИФРОВЫХ МОДЕЛЕЙ РЕЛЬЕФА МЕСТНОСТИ (НА ПРИМЕРЕ ВОСТОЧНОГО ЗАБАЙКАЛЬЯ)

The study of corrections for the influence of terrain is a very popular and significant procedure in the production of high-precision gravimetric work. The results of such studies allow us to determine the optimal parameters for calculating terrain corrections, which helps to reduce the error in calculating the anomaly of the force of gravity in the Buge reduction and, accordingly, leads to an increase in the quality of the interpreted material. Therefore, the improvement of the methodology for calculating corrections for terrain is of particular interest for gravity exploration today and is a very relevant direction in high-precision surveying. Thus, in this article, the purpose of the study is to determine the optimal parameters for calculating terrain corrections for during high-precision gravimetric surveying. The degree of elaboration of the study indicates a number of unresolved issues, which are to some extent disclosed by the authors as a result of calculations and analysis of digital grids, graphs and other data involved in calculating terraincorrections. The article discusses the actual materials and methods for determining corrections for the influence of terrain, obtained during the production of high-precision field gravimetric work on one of the objects of the Trans-baikal Territory. In the course of the study, the results of determining the terraincorrections are presented, comparisons of the corrections in different zones are made, their quantitative indicators are analyzed, and statistics are provided. With the help of mathematical modeling, matrices (grids) of calculated parameters are constructed. The results of the study are clearly demonstrated in the diagrams and in the final tables, which indicates the reliability of the study performed. On the basis of the conducted research, conclusions are drawn and recommendations are made for the method of calculating corrections for the influence of terrain

Rapid wind–terrain correction for wildfire simulations

Modelling the propagation of wildfires requires an accurate wind field to correctly predict the behaviour of the fire. Although numerical weather prediction models produce reliable and accurate mesoscale forecasts, these are typically either available at a spatial resolution many times greater than the typical resolution of a wildfire model or a spot forecast that must be spatially interpolated to the area of the modelled wildfire. Due to this, these forecasts may not account for fine-scale terrain interactions with the wind and must be downscaled to a higher spatial resolution before use in a wildfire model. These downscaling methods are typically computationally intensive, limiting their use for situations where rapid predictions are required. Despite this, a three-dimensional mass balancing method is commonly used in wildfire prediction as a preprocessing step. In this study we show that this mass balancing method can be reduced to a two-dimensional approach, greatly reducing the complexity and computational time required for the model. The two-dimensional method is compared with the existing three-dimensional method and experimentally measured datasets. Furthermore, a combination of rapid numerical solution techniques and modern computational processors allow these wind–terrain correction methods to be directly incorporated into wildfire propagation models.

Two-Dimensional magnetotelluric modelling based on the numerical manifold method

As a numerical method based on the Galerkin variation, the numerical manifold method (NMM) adopts a dual covering system, which is convenient for constructing high-order manifold elements and performing adaptive analysis. In this paper, the NMM is used to simulate the electromagnetic response based on the structure of the undulating terrain existing in actual geophysical exploration. The relevant system equations are derived, and a penalty function method is proposed for dealing with boundary conditions. The simulation results validate the effectiveness and accuracy of this method. Through the simulation of ground barriers and ridge models, the effect of undulating terrain on the apparent resistivity and phase is investigated, which is potentially useful for examining the complex geoelectric model characteristics as well as for terrain correction of the detection results.

Improving Landsat Multispectral Scanner (MSS) geolocation by least-squares-adjustment based time-series co-registration

The Landsat Multispectral Scanner (MSS) data sensed by the Landsat 1–5 satellites make up a significant portion of the early Landsat data record. However, accurate MSS image geolocation has been difficult to achieve systematically due to a number of factors associated primarily with the older sensor and satellite technology. As of August 2019, only 49% of the Landsat MSS archive could be processed at the highest-level L1TP (precision and terrain corrected) level, and the remainder were processed as L1GS (systematically corrected) with inaccurate geolocation and no terrain correction. This paper presents a methodology to improve the geolocation of MSS time series. The methodology uses an area- and feature-based least-squares matching scale-space algorithm, with a time series registration implementation, that we developed previously using Landsat-8 and Sentinel-2 imagery. The methodology requires that at least three L1TP images in the time series acquired over a given path/row are available. A linear combination of a polynomial transformation and multiple radially symmetric radial-basis-functions (RBFs) to model local uncorrected terrain relief effects present in the L1GS images are used. The processing is automated and applied in two passes. The first pass screens L1TP images to select the well-aligned ones that are used as references. The second pass registers the target images, including the L1GS images and any misaligned L1TP images, to all the reference L1TP images. The transformation coefficients for each registered target image are derived by least-squares adjustment using densely-matched tie-points between the target and the reference images. The methodology is demonstrated using 12 months of Landsat-4 MSS images at four Landsat path/row locations that contain agricultural, mountainous, and coastal regions, including a total of 43 L1TP and 31 L1GS images. There were sufficient tie-points to characterize the degree of misregistration of 14 L1GS images that had significant mean misregistration shifts ranging from 7.33 to 17.42 60 m pixels. In addition, at one site, two L1TP images were found to be misaligned and have mean misregistration shifts of 1.27 and 2.20 60 m pixels. The methodology provides sub-pixel registration accuracy - after registration, the mean misregistration shifts for the 14 L1GS and two misaligned L1TP images varied from only 0.10 to 0.41 60 m pixels. The methodology does not use a digital elevation model, and examples illustrate that although the RBF transformations can compensate terrain relief distortion effects, larger (~0.5 to 1.0 pixel) misregistration errors can remain in areas with highly variable terrain relief. Results are also provided for Landsat-1 MSS imagery to demonstrate the applicability of the methodology to even the earliest part of the Landsat record. Detailed qualitative and quantitative results are presented and indicate the potential of the methodology to improve the geolocation of the Landsat MSS data record that is discussed with recommendations for future research.

Use of Sentinel-1 Data in Flood Mapping in the Buna River Area

Floods are one of the disasters that cause many human lives and property. In Albania, most floods are associated with periods of heavy rainfall. In recent years, Synthetic Aperture Radar (SAR) sensors, which provide reliable data in all weather conditions and day and night, have been favored because they eliminate the limitations of optical images.
 In this study, a flood occurred in the Buna River region in March 2018, was mapped using SAR Sentinel-1 data. The aim of this study is to investigate the potential of flood mapping using SAR images using different methodologies. Sentinel-1A / B SAR images of the study area were obtained from the European Space Agency (ESA).
 Preprocessing steps, which include trajectory correction, calibration, speckle filtering, and terrain correction, have been applied to the images. RGB composition and the calibrated threshold technique have been applied to SAR images to detect flooded areas and the results are discussed here.

UAV-Based Terrain Modeling under Vegetation in the Chinese Loess Plateau: A Deep Learning and Terrain Correction Ensemble Framework

Accurate topographic mapping is a critical task for various environmental applications because elevation affects hydrodynamics and vegetation distributions. UAV photogrammetry is popular in terrain modelling because of its lower cost compared to laser scanning. However, this method is restricted in vegetation area with a complex terrain, due to reduced ground visibility and lack of robust and automatic filtering algorithms. To solve this problem, this work proposed an ensemble method of deep learning and terrain correction. First, image matching point cloud was generated by UAV photogrammetry. Second, vegetation points were identified based on U-net deep learning network. After that, ground elevation was corrected by estimating vegetation height to generate the digital terrain model (DTM). Two scenarios, namely, discrete and continuous vegetation areas were considered. The vegetation points in the discrete area were directly removed and then interpolated, and terrain correction was applied for the points in the continuous areas. Case studies were conducted in three different landforms in the loess plateau of China, and accuracy assessment indicated that the overall accuracy of vegetation detection was 95.0%, and the MSE (Mean Square Error) of final DTM (Digital Terrain Model) was 0.024 m.

Comparing Sentinel-1 Surface Water Mapping Algorithms and Radiometric Terrain Correction Processing in Southeast Asia Utilizing Google Earth Engine

Satellite remote sensing plays an important role in the monitoring of surface water for historical analysis and near real-time applications. Due to its cloud penetrating capability, many studies have focused on providing efficient and high quality methods for surface water mapping using Synthetic Aperture Radar (SAR). However, few studies have explored the effects of SAR pre-processing steps used and the subsequent results as inputs into surface water mapping algorithms. This study leverages the Google Earth Engine to compare two unsupervised histogram-based thresholding surface water mapping algorithms utilizing two distinct pre-processed Sentinel-1 SAR datasets, specifically one with and one without terrain correction. The resulting surface water maps from the four different collections were validated with user-interpreted samples from high-resolution Planet Scope data. It was found that the overall accuracy from the four collections ranged from 92% to 95% with Cohen’s Kappa coefficients ranging from 0.7999 to 0.8427. The thresholding algorithm that samples a histogram based on water edge information performed best with a maximum accuracy of 95%. While the accuracies varied between methods it was found that there is no statistical significant difference between the errors of the different collections. Furthermore, the surface water maps generated from the terrain corrected data resulted in a intersection over union metrics of 95.8%–96.4%, showing greater spatial agreement, as compared to 92.3%–93.1% intersection over union using the non-terrain corrected data. Overall, it was found that algorithms using terrain correction yield higher overall accuracy and yielded a greater spatial agreement between methods. However, differences between the approaches presented in this paper were not found to be significant suggesting both methods are valid for generating accurate surface water maps. High accuracy surface water maps are critical to disaster planning and response efforts, thus results from this study can help inform SAR data users on the pre-processing steps needed and its effects as inputs on algorithms for surface water mapping applications.

Archaeological Investigation at the Urartian Sites of Bastam Castle Using Magnetics Method

Archaeological Investigation at the Urartian Sites of Bastam Castle Using Magnetics Method

ANALISIS DATA GAYA BERAT DI DAERAH BENDAN DUWUR SEMARANG

This study was about the gravity in the area of ​​Bendan Duwur, Gajah Mungkur, Semarang. The method used in this research was gravity. The following steps in this activity were: calculating the value of Reader Gravity (gobs), Free Air Correction (FAC), Free Air Anomaly (FAA), Bouguer Correction (BC), Simple Bouguer Anomaly (SBA), Terrain Correction (TC), and Complete Bouguer Anomaly (CBA). The results of this research were listed as the Duwur bendan area, which can be seen from the shape of the points contained in the CBA, which is the smallest mGal value, 2.78 and the largest was 14.14. This can be assessed as an anomaly value, blue was the lowest value while pink the highest value, and yellow was the medium category. Based on the results of gravity measurements in the Bendan Duwur area, Semarang, the smallest mGal value was recognized by the TC compared to the gobs, FAC, FAA, and BC values. TC was producing 0.24 and the highest value was 1.13. The largest correction value was the FAC, the lowest value of mGal was 16.14, while the highest value of mGal was 26.33. Adapters for the Bendan Duwur soil structure based on CBA including the underground category generated were directly related to tectonic activity, but were more related to geology that requires special sedimentation and anthropogenic activities such as water needed.

Synthetic Aperture Radar (SAR) image processing for operational space-based agriculture mapping

ABSTRACT Few countries are using space-based Synthetic Aperture Radar (SAR) to operationally produce national-scale maps of their agricultural landscapes. For the past ten years, Canada has integrated C-band SAR with optical satellite data to map what crops are grown in every field, for the entire country. While the advantages of SAR are well understood, the barriers to its operational use include the lack of familiarity with SAR data by agricultural end-user agencies and the lack of a ‘blueprint’ on how to implement an operational SAR-based mapping system. This research reviewed order of operations for SAR data processing and how order choice affects processing time and classification outcomes. Additionally this research assessed the impact of speckle filtering by testing three filter types (adaptive, multi-temporal and multi-resolution) at varying window sizes for three study sites with different average field sizes. The Touzi multi-resolution filter achieved the highest overall classification accuracies for all three sites with varying window sizes, and with only a small (< 2%) difference in accuracy relative to the Gamma Maximum A Posteriori (MAP) adaptive filter which had similar window sizes across sites. As such, the assessment of order of operations for noise reduction and terrain correction was completed using the Gamma MAP adaptive filter. This research found there was no difference in classification accuracies regardless of whether noise reduction was applied before or after terrain correction. However, implementing the terrain correction as the first operation resulted in a 10 to 50% increase in processing time. This is an important consideration when designing and delivering operational systems, especially for large geographies like Canada where hundreds of SAR images are required. These findings will encourage country-wide, regional and global food monitoring initiatives to consider SAR sensors as an important source of data to operationally map agricultural production.

Development of an Automated Tool for Delineation of Flood Footprints from SAR Imagery for Rapid Disaster Response: A Case Study

Floods are one of the most common natural disasters. In recent times, microwave synthetic aperture radar (SAR) satellite images have been used widely for mapping flood affected areas due to its all-weather capability and acquisition during day and night. Here, in this paper, an automated algorithm is proposed to delineate flood extent from SAR images without any human intervention. The algorithm consists of pre-processing steps like applying orbit file, calibrate to sigma naught, speckle filtering, terrain correction and linear to decibel conversion. The water layer is delineated using multi-segmentation and Otsu’s thresholding technique. Further, flood layer is extracted by postprocessing steps using majority filter, applying permanent water body mask and eliminating hill shadows. The algorithm is tested on a significant number of satellite images covering floods in India, which are having diverse terrain and flooding patterns. In this paper, the steps involved in delineating flood from SAR image of VH polarization from SENTINEL-1 satellite covering chronic flood-prone stretch of part of Ganga River in Bihar state is presented. Accuracy assessment is carried out with the flood layer derived from RADARSAT SAR HV polarized data acquired on the same day and an accuracy of about 96% is obtained. The total processing time taken for the extraction of the flood layer is 9 min. This automation process is beneficial for the generation of rapid flood inundation maps, with high accuracy, which is helpful for flood monitoring and relief management during a disaster.

New gravity data and 3-D density model constraints on the Ivrea Geophysical Body (Western Alps)

SUMMARY We provide a high-resolution image of the Ivrea Geophysical Body (IGB) in the Western Alps with new gravity data and 3-D density modelling, integrated with surface geological observations and laboratory analyses of rock properties. The IGB is a sliver of Adriatic lower lithosphere that is located at shallow depths along the inner arc of the Western Alps, and associated with dense rocks that are exposed in the Ivrea-Verbano Zone (IVZ). The IGB is known for its high seismic velocity anomaly at shallow crustal depths and a pronounced positive gravity anomaly. Here, we investigate the IGB at a finer spatial scale, merging geophysical and geological observations. We compile existing gravity data and we add 207 new relative gravity measurements, approaching an optimal spatial coverage of 1 data point per 4–9 km2 across the IVZ. A compilation of tectonic maps and rock laboratory analyses together with a mineral properties database is used to produce a novel surface rock-density map of the IVZ. The density map is incorporated into the gravity anomaly computation routine, from which we defined the Niggli gravity anomaly. This accounts for Bouguer Plate and terrain correction, both considering the in situ surface rock densities, deviating from the 2670 kg m–3 value commonly used in such computations. We then develop a 3-D single-interface crustal density model, which represents the density distribution of the IGB, including the above Niggli-correction. We retrieve an optimal fit to the observations by using a 400 kg m–3 density contrast across the model interface, which reaches as shallow as 1 km depth below sea level. The model sensitivity tests suggest that the ∼300–500 kg m–3 density contrast range is still plausible, and consequently locates the shallowest parts of the interface at 0 km and at 2 km depth below sea level, for the lowest and the highest density contrast, respectively. The former model requires a sharp density discontinuity, the latter may feature a vertical transition of densities on the order of few kilometres. Compared with previous studies, the model geometry reaches shallower depths and suggests that the width of the anomaly is larger, ∼20 km in west–east direction and steeply E–SE dipping. Regarding the possible rock types composing the IGB, both regional geology and standard background crustal structure considerations are taken into account. These exclude both felsic rocks and high-pressure metamorphic rocks as suitable candidates, and point towards ultramafic or mantle peridotite type rocks composing the bulk of the IGB.

Identification of Subsurface Structures of Geothermal Potential Area in East of Mount Lawu Using The Gravity Method

&lt;p&gt;Information about the eastern side subsurface stones of Mount Lawu regarding geothermal potential is limited. This research was conducted to provide information regarding geothermal potential in those area by using the gravity method. We did a 18 sites of gravity surveys in eastern flank of Mount Lawu where located in Magetan regency, Ngawi regency and Sragen regency, East Java. The principle of this method is to measure the earth's gravity field, then the value of gravity is corrected by some gravity corrections, i.e. height, tide, drift, normal gravity, free-air, Bouguer and terrain corrections. The Complete Bouguer Anomaly (CBA) shows the formation that related to the rock formation in the subsurface of Mount Lawu. Based on CBA modelling we found that in the eastern flank of Mount Lawu contains of tuff and breccia of volcanic rocks, breccia Jabolarangan and tuff Jabolarangan, lava andesite, igneous rock (pumice), and sedimentary rocks in the form of sandstone and clay. We found a fault structure on six tracks of a research area. Otherwise, we estimated that there is a geothermal potential on the southeast side of the research area&lt;/p&gt;

Towards an International Height Reference System: insights from the Colorado geoid experiment using AUSGeoid computation methods

We apply the AUSGeoid data processing and computation methodologies to data provided for the International Height Reference System (IHRS) Colorado experiment as part of the International Association of Geodesy Joint Working Groups 0.1.2 and 2.2.2. This experiment is undertaken to test a range of different geoid computation methods from international research groups with a view to standardising these methods to form a set of conventions that can be established as an IHRS. The IHRS can realise an International Height Reference Frame to be used to study physical changes on and within the Earth. The Colorado experiment study site is much more mountainous (maximum height 4401 m) than the mostly flat Australian continent (maximum height 2228 m), and the available data over Colorado are different from Australian data (e.g. much more extensive airborne gravity coverage). Hence, we have tested and applied several modifications to the AUSGeoid approach, which had been tailored to the Australian situation. This includes different methods for the computation of terrain corrections, the gridding of terrestrial gravity data, the treatment of long-wavelength errors in the gravity anomaly grid and the combination of terrestrial and airborne data. A new method that has not previously been tested is the application of a spherical harmonic high-pass filter to residual anomalies. The results indicate that the AUSGeoid methods can successfully be used to compute a high accuracy geoid in challenging mountainous conditions. Modifications to the AUSGeoid approach lead to root-mean-square differences between geoid models up to ~ 0.028 m and agreement with GNSS-levelling data to ~ 0.044 m, but the benefits of these modifications cannot be rigorously assessed due to the limitation of the GNSS-levelling accuracy over the computation area.

Predicting biomass dynamics at the national extent from digital aerial photogrammetry

The demand for precise mapping and monitoring of forest resources, such as above ground biomass (AGB), has increased rapidly. National accounting and monitoring of AGB requires regularly updated information based on consistent methods. While remote sensing technologies such as airborne laser scanning (ALS) and digital aerial photogrammetry (DAP) have been shown to deliver the necessary 3D spatial data for AGB mapping, the capacity of repeat acquisition, remotely sensed, vegetation structure data for AGB monitoring has received less attention. Here, we use vegetation height models (VHMs) derived from repeat acquisition DAP data (with ALS terrain correction) to map and monitor woody AGB dynamics across Switzerland over 35 years (1983-2017 inclusive), using a linear least-squares regression approach. We demonstrate a consistent relationship between canopy height derived from DAP and field-based NFI measures of woody AGB across four inventory periods. Over the environmentally heterogeneous area of Switzerland, our models have a comparable predictive performance (R2 = 0.54) to previous work predicting AGB based on ALS metrics. Pearson correlation coefficients between measured and predicted changes in woody AGB over time increased with shorter time gaps (< 2 years) between image capture and field-based measurements, ranging between 0.76 and 0.34. A close temporal match between field surveys and remote sensing data acquisition is thus key to reliable mapping and monitoring of AGB dynamics, especially in areas where forest management and natural disturbances trigger relatively fast canopy dynamics. We show that VHMs derived from repeat DAP capture constitute a cost effective and reliable approach to map and monitor changes in woody AGB at a national extent and can provide an important information source for national carbon accounting and monitoring of ecosystem service provisioning.

High accuracy gravity terrain correction by Optimally Selecting Sectors algorithm based on Hammer charts method

High accuracy gravity terrain correction by Optimally Selecting Sectors algorithm based on Hammer charts method

Refinement of a gravimetric geoid model for Japan using GOCE and an updated regional gravity field model

We developed a refined gravimetric geoid model for Japan on a 1 × 1.5 arc-minute (2 km) grid from a GOCE-based satellite-only global geopotential model and a regional gravity field model updated in this study. First, we have constructed a regional gravity field model for Japan using updated gravity datasets together with a residual terrain model: 323,431 land gravity data, 77,389 shipborne marine gravity data, and Sandwell’s v28.1 altimetry-derived global marine gravity model. Then, the geoid was determined with the gravity field model. The methodology for gravimetric geoid determination was based on the remove–compute–restore technique with Helmert’s second method of condensation of topography (Stokes–Helmert scheme). Here, the hybrid Meissl–Molodensky modified spheroidal Stokes kernel was employed to minimize the truncation error under an appropriate combination of different kinds of gravity data. In addition, a high-resolution GSI-DEM on a 0.4 × 0.4 arc-second (10 m) grid, together with the SRTM-DEM on a 7.5 × 11.25 arc-second (250 m) grid, was utilized for precisely applying terrain correction to the regional gravity field model. Consequently, we created a gravimetric geoid model for Japan, consistent with 971 GNSS/leveling geoid heights distributed over the four main islands of Japan with a standard deviation of 5.7 cm, showing a considerable improvement by 2.3 cm over the previous model (JGEOID2008). However, there remain some areas with large discrepancies between the computed and GNSS/leveling geoid heights in northern Japan (Hokkaido), mountainous areas in central Japan, and some coastal regions. Since terrestrial gravity data are especially sparse in these areas, we speculated that the largeness of the geoid discrepancies there could be partly attributed to the insufficient coverage and accuracy of gravity data. The Geospatial Information Authority of Japan has started airborne gravity surveys to be covered over the Japanese Islands, and in future, we plan to develop a geoid model for Japan further accurately by incorporating airborne gravity data to come.

Efficient spatial-spectral computation of local planar gravimetric terrain corrections from high-resolution digital elevation models

SUMMARY Computation of gravimetric terrain corrections (TCs) is a numerical challenge, especially when using very high-resolution (say, ∼30 m or less) digital elevation models (DEMs). TC computations can use spatial or/and spectral techniques: Spatial domain methods are more exact but can be very time-consuming; the discrete/fast Fourier transform (D/FFT) implementation of a binomial expansion is efficient, but fails to achieve a convergent solution for terrain slopes &amp;gt;45°. We show that this condition must be satisfied for each and every computation-roving point pair in the whole integration domain, not just at or near the computation points. A combination of spatial and spectral methods has been advocated by some through dividing the integration domain into inner and outer zones, where the TC is computed from the superposition of analytical mass-prism integration and the D/FFT. However, there remain two unresolved issues with this combined approach: (1) deciding upon a radius that best separates the inner and outer zones and (2) analytical mass-prism integration in the inner zone remains time-consuming, particularly for high-resolution DEMs. This paper provides a solution by proposing: (1) three methods to define the radius separating the inner and outer zones and (2) a numerical solution for near-zone TC computations based on the trapezoidal and Simpson's rules that is sufficiently accurate w.r.t. the exact analytical solution, but which can reduce the computation time by almost 50 per cent.