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In this study, for feature extraction of seismic- and nonlinear trend terms of the nonlinear and nonstationary high-rate Global Navigation Satellite System (GNSS) seismic displacements, we present an adaptive complete ensemble empirical mode decomposition (CEEMD) method based on correlation coefficient. We also introduce an improved CEEMD (ICEEMD) based on multiway principal component analysis (MPCA), hereafter, ICEEMD-MPCA, denoising method for boosting the high-rate GNSS seismic displacements with/without nonlinear trend. The results show that the proposed method is suitable for extracting features of nonlinear and nonstationary high-rate GNSS seismic displacements. The ICEEMD-MPCA denoising method is able to obviously eliminate white noise at high frequencies, remove systematic errors, and effectively preserve the earthquake wave signals. The denoising method reflects that high-rate GNSS has millimeter-level accuracy in the vertical component and submillimeter-level accuracy in the horizontal component. To verify the performance characteristics of the feature extraction and denoising method, the focal mechanism inversion for the 2010 El Mayor–Cucapah earthquake is estimated using the high-rate GNSS data (5 Hz) and collocated strong motion data (50 and 200 Hz). The focal mechanism of the earthquake estimated using the denoised high-rate GNSS with/without nonlinear trend are more consistent with the teleseismic estimates than those estimated using the raw high-rate GNSS and strong motion data. For the GNSS observations, the inversion results are more affected by errors in low-frequency, which accumulate over time and display their signatures as trend in coseismic displacements. It can be concluded that with the adaptive CEEMD method and the ICEEMD-MPCA denoising method, high-rate GNSS at near-field stations only or combined with GNSS/strong-motion records can be applied to yield better information regarding the earthquake focal mechanism inversion, the lower bounds of earthquake magnitudes, and earthquake rupture parameters for small to moderate earthquakes.

In order to improve the possibility of correct interpretation of some geophysical phenomena such seismology, it is important to reduce systematic errors such as common mode error (CME) and multipath errors, and to improve the accuracy of high-rate (1–5 Hz) displacements. This paper focuses on accuracy enhancement and noise assessment of high-rate Global Navigation Satellite System (GNSS) position time series of regional network of GNSS stations. Complete ensemble empirical mode decomposition-based multiscale multiway principal component analysis (C-MSMPCA) denoising method is introduced to denoise the high-rate (1–5 Hz) GNSS position time series, whose performance was compared with those of modified sidereal filtering (MSF), stacking filtering, PCA and the recently developed multiscale multiway PCA (MSMPCA). It turns out that C-MSMPCA can significantly eliminate the high-frequency random noise and remove the low-frequency CME, and other systematic errors such as multipath errors. Furthermore, for denoising high-rate GNSS time series, C-MSMPCA is more precise than the other denoising methods. Irrespective of sampling rates and data processing strategies, C-MSMPCA can respectively reach the accuracy of submillimeter- and millimeter-levels on the horizontal and vertical components of high-rate GNSS displacements. Spectral analysis on the 1 Hz coordinate time series from the Sichuan GNSS Continuous Observing Network of China suggests that Gauss-Markov process is an adequate noise model for the noise characteristics of the filtered GNSS data using MSMPCA and C-MSMPCA. The CME magnitudes of MSMPCA are 2.61, 2.55, and 6.72 mm (east, north, and vertical), and those of C-MSMPCA are 2.69, 2.80, and 7.80 mm, respectively.

For many geoscience applications, the quality of digital elevation models (DEMs) is the first and foremost requirement. DEM quality generally depends on the interpolation procedure, especially in forested areas with complex terrain. However, classical interpolation methods do not always preserve terrain features, owing to their isotropic and local estimation nature. Therefore, this paper presents a feature-preserving interpolation method, where a structure tensor is integrated into the radial basis function to ensure its anisotropy. This method alleviates the influence of points located on different surface patches. The performance of the proposed method was compared with those of classical interpolation methods, including the inverse distance weighting (IDW), ordinary kriging (OK), topo to raster (ANUDEM), and natural neighbour (NN) methods. The performance of these methods was tested on benchmark data provided by the International Society for Photogrammetry and Remote Sensing (ISPRS) Commission, and on one private dataset. Both datasets were collected via the airborne light detection and ranging (LiDAR) technique. The results from both datasets demonstrate that from a quantitative perspective, the proposed method produces more accurate DEMs than the classical interpolation methods. Specifically, in terms of root mean square error (RMSE), the proposed method is at least 15.8% and 7.6% more accurate when applied to the ISPRS and private data, respectively. Moreover, the proposed method produces more visually appealing surfaces with a good trade-off between terrain feature retention and noise removal.

To suppress the influence of outliers on function estimation, we propose a least absolute deviation (LAD)-based robust support vector regression (SVR). Furthermore, an efficient algorithm based on the split-Bregman iteration is introduced to solve the optimization problem of the proposed algorithm. Both artificial and benchmark datasets are employed to compare the performance of the proposed algorithm with those of least squares SVR (LS-SVR), and two weighted versions of LS-SVR with the weight functions of Hampel and Logistic, respectively. Experiments demonstrate the superiority of the proposed algorithm.

A comparison between the Coupled Model Intercomparison Project Phase 5 (CMIP5) data and observations at 735 meteorological stations indicated that mean annual temperature (MAT) was underestimated about 1.8 °C while mean annual precipitation (MAP) was overestimated about 263 mm in general across the whole of China. A statistical analysis of China-CMIP5 data demonstrated that MAT exhibits spatial stationarity, while MAP exhibits spatial non-stationarity. MAT and MAP data from the China-CMIP5 dataset were downscaled by combining statistical approaches with a method for high accuracy surface modeling (HASM). A statistical transfer function (STF) of MAT was formulated using minimized residuals output by HASM with an ordinary least squares (OLS) linear equation that used latitude and elevation as independent variables, abbreviated as HASM-OLS. The STF of MAP under a BOX-COX transformation was derived as a combination of minimized residuals output by HASM with a geographically weight regression (GWR) using latitude, longitude, elevation and impact coefficient of aspect as independent variables, abbreviated as HASM-GB. Cross validation, using observational data from the 735 meteorological stations across China for the period 1976 to 2005, indicates that the largest uncertainty occurred on the Tibet plateau with mean absolute errors (MAEs) of MAT and MAP as high as 4.64 °C and 770.51 mm, respectively. The downscaling processes of HASM-OLS and HASM-GB generated MAEs of MAT and MAP that were 67.16% and 77.43% lower, respectively across the whole of China on average, and 88.48% and 97.09% lower for the Tibet plateau.

Separating ground from non-ground points is a challenging and essential task before the applications of airborne Light Detection And Ranging (LiDAR) data. The classical filters generally show good results on simple landscapes, but suffer from large filtering errors on complex landscapes with steep slopes and terrain discontinuities. To produce more satisfactory results over these landscapes, a scale-irrelevant and terrain-adaptive interpolation-based filter is presented in this paper. The contributions of the proposed method include a 1D spline-based algorithm for the collection of evenly distributed ground seeds as many as possible, a scale-irrelevant interpolation for estimating the heights of unclassified points and a terrain-adaptive elevation threshold to adapt to various terrain characteristics. The performance of the proposed method was first evaluated on the International Society Photogrammetry and Remote Sensing (ISPRS) benchmark dataset. Results show that the proposed method with the average total error of 2.70% and kappa coefficient of 90.84% outperforms the existing filtering algorithms developed in recent decade (2010–2020). The performance of the proposed method was further assessed on four high-density airborne LiDAR point clouds located in urban and forested sites and compared with four state-of-the-art filters including progressive morphological filter (PMF), cloth simulation filter (CSF), progressive TIN densification (PTD) and multiresolution hierarchical filter (MHF). Results demonstrate that the proposed method is averagely more accurate than the well-known filters in terms of total error and kappa coefficient, and much faster than PTD and MHF. Moreover, the proposed method produces more satisfactory DEMs than the classical methods.

A digital elevation model (DEM) derived from remote sensing data often suffers from outliers due to various reasons such as the physical limitation of sensors and low contrast of terrain textures. In order to reduce the effect of outliers on DEM construction, a robust algorithm of multiquadric (MQ) methodology based on M-estimators (MQ-M) was proposed. MQ-M adopts an adaptive weight function with three-parts. The weight function is null for large errors, one for small errors and quadric for others. A mathematical surface was employed to comparatively analyze the robustness of MQ-M, and its performance was compared with those of the classical MQ and a recently developed robust MQ method based on least absolute deviation (MQ-L). Numerical tests show that MQ-M is comparative to the classical MQ and superior to MQ-L when sample points follow normal and Laplace distributions, and under the presence of outliers the former is more accurate than the latter. A real-world example of DEM construction using stereo images indicates that compared with the classical interpolation methods, such as natural neighbor (NN), ordinary kriging (OK), ANUDEM, MQ-L and MQ, MQ-M has a better ability of preserving subtle terrain features. MQ-M replaces thin plate spline for reference DEM construction to assess the contribution to our recently developed multiresolution hierarchical classification method (MHC). Classifying the 15 groups of benchmark datasets provided by the ISPRS Commission demonstrates that MQ-M-based MHC is more accurate than MQ-L-based and TPS-based MHCs. MQ-M has high potential for DEM construction.

Ship-borne global navigation satellite system (GNSS) technique can overcome the weakness of satellite altimetry and tide gauge in measuring sea surface heights (SSHs) over coastal seas. Ship-borne GNSS technique can be used to calibrate SSHs determined by the satellite altimetry and tide gauge. The ship-borne GNSS data are processed with the single-epoch precise point positioning (PPP) method to estimate SSHs which are filtered by the Gaussian filter to weaken and/or remove effects of sea wind and wave field. Tidal corrections are also taken into consideration to improve SSHs. One crossover adjustment method is put forward to calculate the bias and drift along the ship route and assess the accuracy of SSHs. We processed the in-situ ship-borne GPS data over the offshore sea around Keelung to compute precisely SSHs with the single-epoch PPP. Statistical results of SSH differences of crossover points indicate that the root mean squares error of SSHs determined by the ship-borne GPS is up to level of 12.9 cm over the offshore sea ~30 km far away to land.

In order to improve the robustness of the classcial LSSVM when dealing with sample points in the presence of outliers, we have developed a robust weighted LSSVM (reweighted LSSVM) based on the least trimmed squares technique (LTS). The procedure of the reweighted LSSVM includes two stages, respectively used to increase the robustness and statistical efficiency of the estimator. In the first stage, LTS-based LSSVM (LSSVM-LTS) with C-steps was adopted to obtain robust simulation results at the cost of losing statistical efficiency to some extent. Thus, in the second stage, the results computed in the first stage were optimized with a weighted LSSVM to improve efficiency. Two groups of examples including numerical tests and real-world benchmark examples were respectively employed to compare the robustness of the reweighted LSSVM with those of the classical LSSVM, the weighted LSSVM and LSSVM-LTS. Numerical tests indicate that the reweighted LSSVM is comparable to the weighted LSSVM, and more accurate than the classical LSSVM and LSSVM-LTS when the contaminating proportion is small (i.e. 0.1 and 0.2), whereas with the increase of contaminating proportion, the reweighted LSSVM performs much better than other methods. The real-world exmaple of regressing seven benchmark datasets demonstrates that the reweighted LSSVM is always more accurate than other versions of LSSVM. In conclusion, the newly developed method can be considered as an alternative to function estimation, especially for sample points in the presence of outliers. A robust weighted LSSVM was presented.LTS-based LSSVM with C-steps was used to obtain robust results.A reweighted LSSVM was adopted to improve efficiency.The new estimator was validated with two groups of examples.

The General Circulation Models and Coupled Model Intercomparison Project Phase 5 (CMIP5) datasets used for the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC) painted future opportunities and challenges afforded by climate change with broad strokes. The model outputs incorporate substantial uncertainty due to the relatively coarse spatial scales and the complexity of the processes incorporated in these models and as a consequence, it is difficult to predict future trends and infrastructure needs in large countries like China at local and regional scales over the next century. The work reported in this article describes several statistical transfer functions that were used to downscale CMIP5 climate predictions in China. The original and new downscaled CMIP5 predictions are compared with observations from 735 meteorological stations scattered across China for the period 2006–2015 to show the various improvements achieved with downscaling. Comparing the three RCP scenarios (2.6, 4.5 and 8.5) during the period 2006–2015 with observations from 735 meteorological stations indicates that MAEs of mean annual temperature were 1.9 °C for China on average and that the actual temperature was under-estimated at 87% of the meteorological stations under all three scenarios. After the downscaling process using a High Accuracy Surface Modeling (HASM)-based method, the MAEs for mean annual temperature under the three scenarios were reduced to 0.62 °C for China on average. The MAEs of annual mean precipitation were 317.29, 315.24 and 315.49 mm under the RCP2.6, RCP4.5, and RCP8.5 scenarios, respectively for China on average and the actual precipitation was over-estimated by all three scenarios at approximately 75% of the meteorological stations. The HASM-based downscaling process meant that the MAEs for the three scenarios were reduced to 80–85 mm for China on average. The downscaled predictions are used to show how temperature and precipitation are likely to vary by region in China from 2011 to 2100. The downscaled results suggest that most of China will become warmer and wetter on average under all three scenarios over the next 30 years and provide improved information to guide the investments and actions that will be needed to improve climate change resilience across China's varied landscapes in the 21st century.

A new greedy-based multiquadric method (MQ-G) has been developed to perform LiDAR-derived ground data reduction by selecting a certain amount of significant terrain points from the raw dataset to keep the accuracy of the constructed DEMs as high as possible, while maximally retaining terrain features. In the process of MQ-G, the significant terrain points were selected with an iterative process. First, the points with the maximum and minimum elevations were selected as the initial significant points. Next, a smoothing MQ was employed to perform an interpolation with the selected critical points. Then, the importance of all candidate points was assessed by interpolation error (i.e. the absolute difference between the interpolated and actual elevations). Lastly, the most significant point in the current iteration was selected and used for point selection in the next iteration. The process was repeated until the number of selected points reached a pre-set level or no point was found to have the interpolation error exceeding a user-specified accuracy tolerance. In order to avoid the huge computing cost, a new technique was presented to quickly solve the systems of MQ equations in the global interpolation process, and then the global MQ was replaced with the local one when a certain amount of critical points were selected. Four study sites with different morphologies (i.e. flat, undulating, hilly and mountainous terrains) were respectively employed to comparatively analyze the performances of MQ-G and the classical data selection methods including maximum z-tolerance (Max-Z) and the random method for reducing LiDAR-derived ground datasets. Results show that irrespective of the number of selected critical points and terrain characteristics, MQ-G is always more accurate than the other methods for DEM construction. Moreover, MQ-G has a better ability of preserving terrain feature lines, especially for the undulating and hilly terrains.

We presented a multiresolution hierarchical classification (MHC) algorithm for differentiating ground from non-ground LiDAR point cloud based on point residuals from the interpolated raster surface. MHC includes three levels of hierarchy, with the simultaneous increase of cell resolution and residual threshold from the low to the high level of the hierarchy. At each level, the surface is iteratively interpolated towards the ground using thin plate spline (TPS) until no ground points are classified, and the classified ground points are used to update the surface in the next iteration. 15 groups of benchmark dataset, provided by the International Society for Photogrammetry and Remote Sensing (ISPRS) commission, were used to compare the performance of MHC with those of the 17 other publicized filtering methods. Results indicated that MHC with the average total error and average Cohen’s kappa coefficient of 4.11% and 86.27% performs better than all other filtering methods.

In order to avoid the ill-conditioning problem of thin plate spline (TPS), the orthogonal least squares (OLS) method was introduced, and a modified OLS (MOLS) was developed. The MOLS of TPS (TPS-M) can not only select significant points, termed knots, from large and dense sampling data sets, but also easily compute the weights of the knots in terms of back-substitution. For interpolating large sampling points, we developed a local TPS-M, where some neighbor sampling points around the point being estimated are selected for computation. Numerical tests indicate that irrespective of sampling noise level, the average performance of TPS-M can advantage with smoothing TPS. Under the same simulation accuracy, the computational time of TPS-M decreases with the increase of the number of sampling points. The smooth fitting results on lidar-derived noise data indicate that TPS-M has an obvious smoothing effect, which is on par with smoothing TPS. The example of constructing a series of large scale DEMs, located in Shandong province, China, was employed to comparatively analyze the estimation accuracies of the two versions of TPS and the classical interpolation methods including inverse distance weighting (IDW), ordinary kriging (OK) and universal kriging with the second-order drift function (UK). Results show that regardless of sampling interval and spatial resolution, TPS-M is more accurate than the classical interpolation methods, except for the smoothing TPS at the finest sampling interval of 20m, and the two versions of kriging at the spatial resolution of 15m. In conclusion, TPS-M, which avoids the ill-conditioning problem, is considered as a robust method for DEM construction.

In order to improve the computational speed of the method of surface modeling based on the theorem of surfaces (SMTS), a modified Gauss-Seidel (GS) method (MGS) was introduced and a MGS of SMTS (SMTS-MGS) has been developed. Numerical tests show that SMTS-MGS is more than twice as fast as SMTS-GS and much faster than the classical iterative methods provided by MATLAB 7.0. The computing time of SMTS-MGS is proportional to the first power of the total number of grid cells in the computational domain, whereas the classical SMTS computing time is proportional to the third power of the total number of grid cells. A real-world example of constructing a series of DEMs of Dongzhi tableland was employed to comparatively analyze the simulation accuracies of the two versions of SMTS including SMTS-MGS and the classical SMTS, and the well parameterized classical interpolation methods including the inverse distance weighted technique (IDW), kriging, thin plate spline (TPS), regularized TPS, TPS with tension, and ANUDEM Version 4.6.3, at spatial resolutions of 5, 12, 20, and 25m. The real-world example demonstrates that SMTS-MGS with the same accuracy as SMTS is approximately as accurate as the third-order TPS and much better than other classical interpolation methods at almost all spatial resolutions, except for ANUDEM at a spatial resolution of 5m. On average, SMTS-MGS provides the best results with a minimum of computing time.

We have presented a new method for generating grid-based digital elevation models (DEMs) based on Coons patch. A series of Gaussian synthetic surfaces with various surface complexities were employed to comparatively analyze the simulation accuracies of Coons patch and the classical interpolation methods, such as IDW, Natural neighbor, SPLINE and KRIGING. Results indicate that irrespective of terrain complexity, Coons patch is much more accurate than the classical interpolation methods, and the accuracy of Coons patch is about 327.30, 15.19, 3.66 and 40.07 times as high as the accuracies of IDW, Natural neighbor, SPLINE and KRIGING on average. A real-world test area was used to test the effect of sampling density on the simulation accuracy. The results indicate that Coons patch has a higher accuracy than the classical interpolation methods regardless of sampling density. In a word, Coons patch as an accurate interpolation method can be used for grid-based DEM construction.

A high accuracy and speed method (HASM) of surface modelling is developed to find a solution for error problem and to improve computation speed. A digital elevation model (DEM) is established on spatial resolution of 13.5 km x 13.5 km. Regression formulations among temperature, elevation and latitude are simulated in terms of data from 2766 weather observation stations scattered over the world by using the 13.5 km x 13.5 km DEM as auxiliary data. Three climate scenarios of HadCM3 are refined from spatial resolution of 405 km x 270 km to 13.5 km x 13.5 km in terms of the regression formulations. HASM is employed to simulate surfaces of mean annual bio-temperature, mean annual precipitation and potential evapotranspiration ratio during the periods from 1961 to 1990(T(1)), from 2010 to 2039 (T(2)), from 2040 to 2069 (T(3)), and from 2070 to 2099 (T(4)) on spatial resolution of 13.5 km x 13.5 km. Three scenarios of terrestrial ecosystems on global level are finally developed on the basis of the simulated climate surfaces. The scenarios show that all polar/nival, subpolar/alpine and cold ecosystem types would continuously shrink and all tropical types, except tropical rain forest in scenario A1Fi, would expand because of the climate warming. Especially at least 80% of moist tundra and 22% of nival area might disappear in period T(4) comparing with the ones in the period T(1). Tropical thorn woodland might increase by more than 97%. Subpolar/alpine moist tundra would be the most sensitive ecosystem type because its area would have the rapidest decreasing rate and its mean center would shift the longest distance towards west. Subpolar/alpine moist tundra might be able to serve as an indicator of climatic change. In general, climate change would lead to a continuous reduction of ecological diversity. (C) 2010 Elsevier B.V. All rights reserved.

The concept and the computation of terrain representation error (ETR) are investigated and total DEM error is presented as an accuracy index for DEM evaluation at a global level. A promising method of surface modelling based on the theorem of surfaces (SMTS) has been developed. A numerical test and a real-world example are employed to comparatively analyze the simulation accuracy of SMTS and the classical interpolation methods, including IDW, SPLINE and KRIGING performed in ARCGIS 9.1 in terms of sampling and interpolation errors and of total DEM error. The numerical test shows that SMTS is much more accurate than the classical interpolation methods and ETR has a worse influence on the accuracy of SMTS than those of the classical interpolation methods. In a real-world example, DEMs are constructed with SMTS as well as the three classical interpolation methods. The results indicate that, although SMTS is more accurate than the classical interpolation methods, a real-world test indicates that there is a large accuracy loss. Total DEM error composed of, not only sampling and interpolation errors, but also ETRs can be considered as a good accuracy measure for DEM evaluation at a global level. SMTS is an alternative method for DEM construction.

In addition to classical methods, namely kriging, Inverse Distance Weighting (IDW) and splines, which have been frequently used for interpolating the spatial patterns of soil properties, a relatively more accurate surface modelling technique is being developed in recent years, namely high accuracy surface modelling (HASM). It has been used in the numerical tests, DEM construction and the interpolation of climate and ecosystem changes. In this paper, HASM was applied to interpolate soil pH for assessing its feasibility of soil property interpolation in a red soil region of Jiangxi Province, China. Soil pH was measured on 150 samples of topsoil (0-20 cm) for the interpolation and comparing the performance of HASM, kriging. IDW and splines. The mean errors (MEs) of interpolations indicate little bias of interpolation for soil pH by the four techniques. HASM has less mean absolute error (MAE) and root mean square error (RMSE) than kriging, IDW and splines. HASM is still the most accurate one when we use the mean rank and the standard deviation of the ranks to avoid the outlier effects in assessing the prediction performance of the four methods. Therefore, HASM can be considered as an alternative and accurate method for interpolating soil properties. Further researches of HASM are needed to combine HASM with ancillary variables to improve the interpolation performance and develop a user-friendly algorithm that can be implemented in a GIS package. (C) 2009 Elsevier B.V. All rights reserved.