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Satellite global digital elevation models (GDEMs) suffer from positive biases in urban areas due to building artifacts. While various machine learning (ML)-based methods have been proposed to remove these biases, their generalizability is limited by spatial heterogeneity and redundancy in prediction factors across different regions. Therefore, to investigate the spatial heterogeneity of prediction factors and address the problem of factor redundancy in ML-based model prediction, this paper proposes an explainable artificial intelligence framework (XAI) for correcting urban GDEMs using the SHapley additive explanation (SHAP)-random forest (RF) algorithm. The performance of the proposed model for correcting the 30-m COPDEM (COPDEM30) was demonstrated in New York City. The results were compared with the first global Forests-And-Buildings removed DEM (FABDEM) and three classical RF-based models without considering spatial heterogeneity and (or) factor optimization. The results indicate that each factor contributes differently to the correction of COPDEM30 across the regions, showing distinct regional characteristics and spatial heterogeneity. The constructed model is more applicable to regions with similar features to the training regions. In comparison to the three traditional RF-based models in areas with training points, the proposed method obtains the high accuracy. Specifically, while the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) values of the classical RF models ranged between 2.601 m and 2.724 m, and 1.686 m and 1.785 m, respectively, the proposed method achieves an RMSE of 2.258 m and an MAE of 1.436 m. Moreover, the proposed method reduces the RMSE (MAE) of the original COPDEM30 from 7.652 m (4.858 m) to 3.797 m (2.404 m), when applied to an area without providing training points. In summary, the XAI framework based on SHAP-RF can effectively quantify the contribution of prediction factors on GDEM correction, both globally and locally, which is conducive to the construction and improvement of the prediction factor system for urban GDEM correction in different regions. It also provides a reference for improving the performance of ML-based spatial prediction in geosciences.

To remove vegetation bias (VB) from the global DEMs (GDEMs), an artificial neural network (ANN)-based method with the consideration of elevation spatial autocorrelation is developed in this paper. Three study sites with different forest types (evergreen, mixed evergreen-deciduous, and deciduous) are employed to evaluate the performance of the proposed model on three popular 30-m GDEMs, including SRTM1, AW3D30, and COPDEM30. Taking LiDAR DTM as the ground truth, the accuracy of the GDEMs before and after VB correction is assessed, as well as two existing GDEMs including MERIT and FABDEM. Results show that all the original GDEMs significantly overestimate the LiDAR DTM in the three forest types, with the largest biases of 21.5 m for SRTM1, 26.3 m for AW3D30, and 27.18 m for COPDEM30. Taking data randomly sampled from the corrected area as the training points, the proposed model reduces the mean errors (root mean square errors) of the three GDEMs by 98.8%−99.9% (55.1%−75.8%) in the three forests. When training data have the same forest type as the corrected GDEM but under different local situations, the proposed model lowers the GDEM errors by at least 76.9% (44.1%). Furthermore, our corrected GDEMs consistently outperform the existing GDEMs for the two cases.

Over the past decades, plenty of filtering algorithms have been presented to distinguish ground and non-ground points from airborne LiDAR point clouds. However, with the existing methods, it is difficult to derive satisfactory filtering results on rugged terrains with dense vegetation due to the low-level penetration ability of laser pulses. Therefore, a multi-level interpolation-based filter is developed in this paper. The novelty of the algorithm lies within its usage of multi-scale morphological operations and robust z-score to correctly select ground seeds as more as possible, and a terrain-adaptive residual threshold to adapt to various terrain characteristics. Rural samples provided by International Society for Photogrammetry and Remote Sensing (ISPRS) were employed to assess the performance of the proposed method and its results were compared with 15 filtering algorithms developed in recent 5 years (2015-2019). Results show that the proposed method with the optimized parameters produces the best accuracy with the average total error and kappa coefficient of 1.89% and 87.88%, respectively. We further filtered high-density point clouds in six forested areas with different vegetation covers and terrain slopes. Results demonstrate that the proposed algorithm is more accurate than the well-known filtering methods including morphological-based filter, progressive TIN densification filter (PTD), improved PTD and cloth simulation filter, with the average total error decreased by 26.2%, 19.9%, 3.8% and 40.4%, respectively. Moreover, the DEMs of the proposed method have lower average root mean square errors than the four classical filters. Therefore, the proposed method can be considered as an effective ground filtering algorithm for airborne LiDAR point clouds in forested areas.

The high noise levels of high-rate Global Navigation Satellite System (GNSS) solutions limit their seismological applications, including capturing earthquake-induced coseismic displacements. In this study, we developed a new adaptive denoising approach for high-rate GNSS observations to improve the precision of seismic displacements and preserve seismic waveforms in GNSS coseismic signals. The performance of the proposed method was evaluated using high-rate (5 Hz) GNSS data acquired from the moderate EI Mayor-Cucapah earthquake (Mw 7.2) on 4 April 2010 and the small Brawley seismic swarm (Mw 4.6-5.5) on 26 August 2012. The performance of the proposed method was compared with those of modified sidereal filtering, Stacking filtering, and MSF plus Stacking. The comparison showed that the proposed method is more precise than other widely used method. It can significantly remove high-frequency white noise and low-frequency colored noise caused by CME, multipath errors, and/or other unmodeled systematic errors in high-rate GNSS displacements. The results were also compared with collocated strong motion data (50 and 200 Hz). The high precision of the proposed method was mainly afforded by the high performance of complete ensemble empirical mode decomposition, which was used to decompose the GNSS signal into different frequency modes. However, the normalized autocorrelation function and correlation coefficients used to determine the noise-dominated high-frequency modes and the “wavelet-like” soft-threshold used for direct denoising of the noise-dominated high-frequency modes also contributed. Despite the high noise levels of GNSS solutions, especially regarding the vertical displacement components, some small-amplitude details, which are usually only detectable by seismic instruments, could be observed in the denoised displacements in this study. The results reported herein indicate that the proposed method significantly improves the precision and reliability of GNSS displacements and the effectiveness of seismic signal detection, which is particularly critical for the measurement of earthquake-induced coseismic displacements.

[This corrects the article DOI: 10.1371/journal.pone.0176954.].

Airborne light detection and ranging (LiDAR) technology has become the mainstream data source in geosciences and environmental sciences. Point cloud filtering is a prerequisite for almost all LiDAR-based applications. However, it is challenging to select a suitable filtering algorithm for handling high-density point clouds over complex landscapes. Therefore, to determine an appropriate filter on a specific environment, this paper comparatively assessed the performance of five representative filtering algorithms on six study sites with different terrain characteristics, where three plots are located in urban areas and three in forest areas. The representative filtering methods include simple morphological filter (SMRF), multiresolution hierarchical filter (MHF), slope-based filter (SBF), progressive TIN densification (PTD) and segmentation-based filter (SegBF). Results demonstrate that SMRF performs the best in urban areas, and compared to MHF, SBF, PTD and SegBF, the total error of SMRF is reduced by 1.38%, 48.21%, 48.25% and 31.03%, respectively. MHF outperforms the others in forest areas, and compared to SMRF, SBF, PTD and SegBF, the total error of MHF is reduced by 1.98%, 35.87%, 45.11% and 9.42%, respectively. Moreover, both SMRF and MHF keep a good balance between type I and II errors, which makes the produced DEMs much similar to the references. Overall, SMRF and MHF are recommended for urban and forest areas, respectively, and MHF averagely performs slightly better than SMRF on all areas with respect to kappa coefficient.

Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) inherently suffers from various errors. Many previous works employed Geoscience Laser Altimeter System onboard the Ice, Cloud, and land Elevation Satellite (ICESat/GLAS) data to assess and enhance SRTM DEM accuracy. Nevertheless, data coregistration between the two datasets was commonly neglected in their studies. In this paper, an automated and simple three dimensional (3D) coregistration method (3CM) was introduced to align the 3-arc-second SRTM (SRTM3) DEM and ICESat/GLAS data over Jiangxi province, China. Then, accuracy evaluation of the SRTM3 DEM using ICESat/GLAS data with and without data coregistration was performed on different classes of terrain factors and different land uses, with the purpose of evaluating the importance of data coregistration. Results show that after data coregistration, the root mean square error (RMSE) and mean bias of the SRTM3 DEM are reduced by 14.4% and 97.1%, respectively. Without data coregistration, terrain aspects with a sine-like shape are strongly related to SRTM3 DEM errors; nevertheless, this relationship disappears after data coregistration. Among the six land uses, SRTM3 DEM produces the lowest accuracy in forest areas. Finally, by incorporating land uses, terrain factors and ICESat/GLAS data into the correction models, the SRTM3 DEM was enhanced using multiple linear regression (MLR), back propagation neural network (BPNN), generalized regression NN (GRNN), and random forest (RF), respectively. Results exhibit that the four enhancement models with data coregistration obviously outperform themselves without the coregistration. Among the four models, RF produces the best result, and its RMSE is about 3.1%, 2.7% and 11.3% lower than those of MLR, BPNN, and GRNN, respectively. Moreover, 146 Global Navigation Satellite System (GNSS) points over Ganzhou city of Jiangxi province were used to assess the accuracy of the RF-derived SRTM3 DEM. It is found that the DEM quality is improved and has a similar error magnitude to that relative to the ICESat/GLASS data.

Light detection and ranging (LiDAR) technique is currently one of the most important tools for collecting elevation points with a high density in the context of digital elevation model (DEM) construction. However, the high density data always leads to serious time and memory consumption problems in data processing. In this paper, we have developed a thin plate spline (TPS)-based feature-preserving (TPS-F) method for LiDAR-derived ground data reduction by selecting a certain amount of significant terrain points and by extracting geomorphological features from the raw dataset to maintain the accuracy of constructed DEMs as high as possible, while maximally keeping terrain features. We employed four study sites with different topographies (i.e., flat, undulating, hilly and mountainous terrains) to analyze the performance of TPS-F for LiDAR data reduction in the context of DEM construction. These results were compared with those of the TPS-based algorithm without features (TPS-W) and two classical data selection methods including maximum z-tolerance (Max-Z) and the random method. Results show that irrespective of terrain characteristic, the two versions of TPS-based approaches (i.e., TPS-F and TPS-W) are always more accurate than the classical methods in terms of error range and root means square error. Moreover, in terms of streamline matching rate (SMR), TPS-F has a better ability of preserving geomorphological features, especially for the mountainous terrain. For example, the average SMR of TPS-F is 89.2% in the mountainous area, while those of TPS-W, max-Z and the random method are 56.6%, 34.7% and 35.3%, respectively.

Remote-sensing-derived elevation data sets often suffer from noise and outliers due to various reasons, such as the physical limitations of sensors, multiple reflectance, occlusions and low contrast of texture. Outliers generally have a seriously negative effect on DEM construction. Some interpolation methods like ordinary kriging (OK) are capable of smoothing noise inherent in sample points, but are sensitive to outliers. In this paper, a robust algorithm of multiquadric method (MQ) based on an Improved Huber loss function (MQ-IH) has been developed to decrease the impact of outliers on DEM construction. Theoretically, the improved Huber loss function is null for outliers, quadratic for small errors, and linear for others. Simulated data sets drawn from a mathematical surface with different error distributions were employed to analyze the robustness of MQ-IH. Results indicate that MQ-IH obtains a good balance between efficiency and robustness. Namely, the performance of MQ-IH is comparative to those of the classical MQ and MQ based on the Classical Huber loss function (MQ-CH) when sample points follow a normal distribution, and the former outperforms the latter two when sample points are subject to outliers. For example, for the Cauchy error distribution with the location parameter of 0 and scale parameter of 1, the root mean square errors (RMSEs) of MQ-CH and the classical MQ are 0.3916 and 1.4591, respectively, whereas that of MQ-IH is 0.3698. The performance of MQ-IH is further evaluated by qualitative and quantitative analysis through a real-world example of DEM construction with the stereo-images-derived elevation points. Results demonstrate that compared with the classical interpolation methods, including natural neighbor (NN), OK and ANUDEM (a program that calculates regular grid digital elevation models (DEMs) with sensible shape and drainage structure from arbitrarily large topographic data sets), and two versions of MQ, including the classical MQ and MQ-CH, MQ-IH has a better ability of maximally reducing the impact of outliers, while faithfully preserving terrain features. Theoretically, MQ-IH is not a promising interpolation method, and some side effects can be found from its simulation results. For example, the contours of MQ-IH are coarser than ANUDEM in some locations of the real-world study site, and its hill shade may not strictly agree with the real-world surface at rough terrain. Furthermore, the computing cost of MQ-IH is much bigger than that of the classical interpolation methods. However, compared with the classical interpolation methods, MQ-IH has significant potential for interpolating remote-sensing-derived elevation data sets.

A fast and robust interpolation filter based on finite difference TPS has been proposed in this paper. The proposed method employs discrete cosine transform to efficiently solve the linear system of TPS equations in case of gridded data, and by a pre-defined weight function with respect to simulation residuals to reduce the effect of outliers and misclassified non-ground points on the accuracy of reference ground surface construction. Fifteen groups of benchmark datasets, provided by the International Society for Photogrammetry and Remote Sensing (ISPRS) commission, were employed to compare the performance of the proposed method with that of the multi-resolution hierarchical classification method (MHC). Results indicate that with respect to kappa coefficient and total error, the proposed method is averagely more accurate than MHC. Specifically, the proposed method is 1.03 and 1.32 times as accurate as MHC in terms of kappa coefficient and total errors. More importantly, the proposed method is averagely more than 8 times faster than MHC. In comparison with some recently developed methods, the proposed algorithm also achieves a good performance.

Airborne light detection and ranging (LiDAR) datasets with a large volume pose a great challenge to the traditional interpolation methods for the production of digital terrain models (DTMs). Thus, a fast, global interpolation method based on thin plate spline (TPS) is proposed in this paper. In the methodology, a weighted version of finite difference TPS is first developed to deal with the problem of missing data in the grid-based surface construction. Then, the interpolation matrix of the weighted TPS is deduced and found to be largely sparse. Furthermore, the values and positions of each nonzero element in the matrix are analytically determined. Finally, to make full use of the sparseness of the interpolation matrix, the linear system is solved with an iterative manner. These make the new method not only fast, but also require less random-access memory. Tests on six simulated datasets indicate that compared to recently developed discrete cosine transformation (DCT)-based TPS, the proposed method has a higher speed and accuracy, lower memory requirement, and less sensitivity to the smoothing parameter. Real-world examples on 10 public and 1 private dataset demonstrate that compared to the DCT-based TPS and the locally weighted interpolation methods, such as linear, natural neighbor (NN), inverse distance weighting (IDW), and ordinary kriging (OK), the proposed method produces visually good surfaces, which overcome the problems of peak-cutting, coarseness, and discontinuity of the aforementioned interpolators. More importantly, the proposed method has a similar performance to the simple interpolation methods (e.g., IDW and NN) with respect to computing time and memory cost, and significantly outperforms OK. Overall, the proposed method with low memory requirement and computing cost offers great potential for the derivation of DTMs from large-scale LiDAR datasets.

High accuracy surface modeling method (HASM) has the capacity of constructing a surface with a higher accuracy than classical methods. However, surface construction with HASM requires a large amount of computing time due to the intensive computing arising from solving the large linear systems. An effective linear system solving method is essential to cutting down the computing time so that HASM could be applied in constructing large scale surface with high resolution. This paper aims to study the performances of seven linear system solution methods, including HASM-GS, HASM-MGS, HASM-DSPM, HASM-CG, HASM-PCG, HASM-GCG and HASM-GPCG, thus providing a guideline for choosing the right method for HASM under different situations of computing environment. These seven methods were tested against a real-world DEM surface in the Boyang lake basin, which owns a complex topography. Three performance metrics were used, including convergence rates, computing time and consumed memory size. We found that to attain the same accuracy HASM-DSPM method consumed the least memory, HASM-GCG and HASM-GPCG needed less computing time than other methods and HASM-PCG had the fastest convergent rate. This study could provide valuable suggestions for HASM users to make a wise choice of linear system solving method for different surface construction applications.

To overcome the huge volume problem of light detection and ranging (LiDAR) data for the derivation of digital terrain models (DTMs), a least squares compactly supported radial basis function (CSRBF) interpolation method is proposed in this paper. The proposed method has a limited support radius and fewer RBF centers than the sample points, selected by a newly developed surface variation-based algorithm. Those make the linear system of the proposed method not only much sparser but also efficiently solvable. Tests on a synthetic dataset demonstrate that the proposed method is comparable to the smoothing RBF, and far superior to the exact RBF. Moreover, the first is much faster than the others. The proposed method with the RBF centers selected by the surface variation-based algorithm obviously outperforms that with the random selection of equal number. Real-world examples on one private and ten public datasets show that the surfaces of simple interpolation methods including inverse distance weighting, natural neighbor, linear and bicubic suffer from the problems of roughness, peak-cutting, discontinuity and subtle terrain feature loss, respectively. By contrast, the proposed method produces visually appealing results, keeping a good tradeoff between noise removal and terrain feature preservation. Additionally, the new method compares favorably with ordinary kriging (OK) for the generation of high-resolution DTMs in terms of interpolation accuracy, yet the former is much more robust to spatial resolution variation and terrain characteristics than the latter. More importantly, our method is about 4 times faster than OK. In conclusion, the proposed method has high potential for the interpolation of a large LiDAR dataset, especially when both interpolation accuracy and computational cost are taken into account.

Data pits commonly appear in lidar-derived canopy height models (CHMs) owing to the penetration ability of airborne light detection and ranging (lidar) into tree crowns. They have a seriously negative effect on the quality of tree detection and subsequent biophysical measurements. In this study, we propose an algorithm based on robust locally weighted regression and robust z-scores for the construction of a pit-free CHM. A significant advantage of the new algorithm is that it is parameter free, which makes it efficient and robust for practical applications. Simulated and airborne lidar-derived data sets are employed to assess the performance of the new method for CHM construction, and its results are compared to those of three classical methods, namely the natural neighbor (NN) interpolation of the highest point method (HPM), mean filter, and median filter. The results from the simulated data set demonstrate that our algorithm is more accurate compared to the three classical methods for generating pit-free CHMs in the presence of data pits. CHM construction using the lidar-derived data set shows that, compared to the classical methods, the new method has a better ability to remove data pits as well as preserving the edges, shapes, and structures of canopy gaps and crowns. Moreover, the proposed method performs better compared to the classical methods in deriving plot-level maximum tree heights from CHMs. Thus, the new method shows high potential for pit-free CHM construction.