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We propose a fundamental theorem for eco-environmental surface modelling (FTEEM) in order to apply it into the fields of ecology and environmental science more easily after the fundamental theorem for Earth’s surface system modeling (FTESM). The Beijing-Tianjin-Hebei (BTH) region is taken as a case area to conduct empirical studies of algorithms for spatial upscaling, spatial downscaling, spatial interpolation, data fusion and model-data assimilation, which are based on high accuracy surface modelling (HASM), corresponding with corollaries of FTEEM. The case studies demonstrate how eco-environmental surface modelling is substantially improved when both extrinsic and intrinsic information are used along with an appropriate method of HASM. Compared with classic algorithms, the HASM-based algorithm for spatial upscaling reduced the root-mean-square error of the BTH elevation surface by 9 m. The HASM-based algorithm for spatial downscaling reduced the relative error of future scenarios of annual mean temperature by 16%. The HASM-based algorithm for spatial interpolation reduced the relative error of change trend of annual mean precipitation by 0.2%. The HASM-based algorithm for data fusion reduced the relative error of change trend of annual mean temperature by 70%. The HASM-based algorithm for model-data assimilation reduced the relative error of carbon stocks by 40%. We propose five theoretical challenges and three application problems of HASM that need to be addressed to improve FTEEM.

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.

To attenuate positional errors of LiDAR-derived datasets for constructing digital elevation models (DEMs), a feature-preserving point denoising algorithm (F-PDA) is developed in this paper. F-PDA i...

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.

Airborne light detection and ranging (lidar) is becoming a widely adopted technique for capturing elevation data, which are mainly used for creating digital terrain models (DTMs). However, the large size of lidar datasets poses a serious computational challenge to the promising radial basis function (RBF) interpolation method. In this work, to reduce the huge computational cost and improve the interpolation accuracy, random Fourier features are first introduced to approximate the Gaussian kernel of RBFs in feature space, then a random features-based weighted RBF interpolation method is developed. Based on randomized Fourier features, the nonlinear kernel-based training and evaluation of the RBF method is transformed into simple linear operations in feature space, and with the help of weighted ridge regression, the negative effect of the non-Gaussian distribution of lidar datasets on DTM production is reduced. In other words, the combination of randomized Fourier features and weighted ridge regression improves the efficiency and accuracy of the RBF interpolation method. Experiments on simulated datasets indicate that the proposed method performs better than the classical or random features-based RBF method for dealing with non-Gaussian distributed samples, with the former being slightly less accurate than the iterative RBF method due to the low-dimensional random features. However, the computational cost of the new method is much lower compared with the classical or iterative RBFs. Interpolation of airborne lidar-derived points demonstrates that the new method has a computational cost similar to the inverse distance weighting and triangulated irregular network (TIN) approaches, and is significantly faster than the ordinary kriging (OK) or thin plate spline (TPS) methods. Quantitatively, for interpolation of 644,433 points, the proposed method is approximately 833 and 21 times faster than OK and TPS, respectively. Moreover, the new method avoids the surface discontinuity artifacts presented by the OK, TPS, and TIN methods.

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.

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.

Surface modeling with very large data sets is challenging. An efficient method for modeling massive data sets using the high accuracy surface modeling method (HASM) is proposed, and HASM_Big is developed to handle very large data sets. A large data set is defined here as a large spatial domain with high resolution leading to a linear equation with matrix dimensions of hundreds of thousands. An augmented system approach is employed to solve the equality-constrained least squares problem (LSE) produced in HASM_Big, and a block row action method is applied to solve the corresponding very large matrix equations. A matrix partitioning method is used to avoid information redundancy among each block and thereby accelerate the model. Experiments including numerical tests and real-world applications are used to compare the performances of HASM_Big with its previous version, HASM. Results show that the memory storage and computing speed of HASM_Big are better than those of HASM. It is found that the computational cost of HASM_Big is linearly scalable, even with massive data sets. In conclusion, HASM_Big provides a powerful tool for surface modeling, especially when there are millions or more computing grid cells.

Light detection and ranging (lidar)-derived elevation data are commonly subjected to outliers due to the boundaries of occlusions, physical imperfections of sensors, and surface reflectance. Outliers have a serious negative effect on the accuracy of digital elevation models (DEMs). To decrease the impact of outliers on DEM construction, we propose a robust interpolation algorithm of multiquadric (MQ) based on a regularized least absolute deviation (LAD) technique. The objective function of the proposed method includes a regularization-based smoothing term and an LAD-based fitting term, respectively, used to smooth noisy samples and resist the influence of outliers. To solve the objective function of the proposed method, we develop a simple scheme based on the split-Bregman iteration algorithm. Results from simulated data sets indicate that when sample points are noisy or contaminated by outliers, the proposed method is more accurate than the classical MQ and two recently developed robust algorithms of MQ for surface modeling. Real-world examples of interpolating 1 private and 11 publicly available airborne lidar-derived data sets demonstrate that the proposed method averagely produces better results than two promising interpolation methods including regularized spline with tension (RST) and gridded data-based robust thin plate spline (RTPS). Specifically, the image of RTPS is too smooth to retain terrain details. Although RST can keep subtle terrain features, it is distorted by some misclassified object points (i.e., pseudooutliers). The proposed method obtains a good tradeoff between resisting the effect of outliers and preserving terrain features. Overall, the proposed method can be considered as an alternative for interpolating lidar-derived data sets potentially including outliers.

Due to the penetration ability of airborne light detection and ranging (lidar) into tree crowns, data pits commonly appear in lidar-derived canopy height models (CHMs). They have a seriously negative effect on the quality of tree detection and subsequent biophysical measurements. To construct a pit-free CHM, an algorithm based on robust locally weighted regression and robust z-score was presented to remove data pits. The significant advantage of the new algorithm is parameter-free, which makes it efficient and robust for practical applications. A numerical test and a real-world example were respectively employed to assess the performance of our method for CHM construction, and its results were compared with those of three classical methods including natural neighbor interpolation of the highest point method, mean and median filters. The numerical test demonstrates that our algorithm is more accurate than the other methods for generating pit-free CHMs under the presence of data pits. The real-world example shows that compared with the classical methods, our method has a better ability of data pit removal. Moreover, our method performs better than the other methods for deriving plot-level maximum tree height from CHMs. In a word, the new method shows high potential for pit-free CHM construction.

A more accurate Bayesian statistical technique together with a high accuracy surface modelling method (HASM) was used to improve the accuracy of temperature fields in the Beijing–Tianjin–Hebei (BTH) region, China. Bayesian statistical inference theory was first applied to fill missing daily values for meteorological stations on an annual scale. A mixed interpolator was then employed to simulate the annual mean temperature and was compared with other methods. The annual mean temperature was produced and the inter-decade change was investigated. The results show that the values filled by Bayesian statistical inference theory agree well with actual observations. A comparison with other interpolators shows that combining the Bayesian estimation method with the HASM gives better results than those of the other methods tested in this study. The construction of the annual mean temperature for 10 years shows the change interval and the spatial distribution of temperature in the BTH region. The annual temperature over 10 years changed from less than −1 °C in the northwest to more than 14 °C in the southeast. From 1981–1990 (T1) to 1991–2000 (T2) and T2 to 2001–2010 (T3) the temperature change was spatially stationary and varied mainly from −0.05 °C to 0.05 °C, except for some areas such as the southwest of Tangshan city and the south of Tianjin city where land cover and land use has exhibited large decadal variation during the past 30 years.

The HY-2A satellite is the first ocean dynamic environment monitoring satellite of China. Centimeter-level radial accuracy is a fundamental requirement for its scientific research and applications. To achieve this goal, we designed the strategies of precise orbit determination (POD) in detail. To achieve the relative optimal orbit for HY-2A, we carried out POD using DORIS-only, SLR-only, and DORIS + SLR tracking data, respectively. POD tests demonstrated that the consistency level of DORIS-only and SLR-only orbits with respect to the CNES orbits were about 1.81 cm and 3.34 cm in radial direction in the dynamic sense, respectively. We designed 6 cases of different weight combinations for DORIS and SLR data, and found that the optimal relative weight group was 0.2 mm/s for DORIS and 15.0 cm for SLR, and RMS of orbit differences with respect to the CNES orbits in radial direction and three-dimensional (3D) were 1.37 cm and 5.87 cm, respectively. These tests indicated that the relative radial and 3D accuracies computed using DORIS + SLR data with the optimal relative weight set were obviously higher than those computed using DORIS-only and SLR-only data, and satisfied the requirement of designed precision. The POD for HY-2A will provide the invaluable experience for the following HY-2B, HY-2C, and HY-2D satellites.

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.

The increasing availability of big spatial data demands large-scale surface modeling methods. To find a solution for large-scale surface modeling problem, based on previously developed high accuracy surface modeling (HASM) method, an extended high accuracy surface modeling method utilizing cloud computing is developed. The developed method was run on a Hadoop-based cloud computing environment comprising four computers and applied for China’s Poyang Lake basin digital elevation model construction. The experiments results indicate that the cloud computing-based method outperforms the general sequential method based on single computer significantly and attains three times speedups. Furthermore, the improved schedule algorithm for cloud computing-based HASM has further accelerated the computing speed.

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.

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.

A high accuracy surface modeling method (HASM) has been developed to provide a solution to many surface modeling problems such as DEM construction, surface estimation and spatial prediction. Although HASM is able to model surfaces with a higher accuracy, its low computing speed limits its popularity in constructing large scale surfaces. Hence, the research described in this article aims to improve the computing efficiency of HASM with a graphic processor unit (GPU) accelerated multi-grid method (HASM-GMG). HASM-GMG was tested with two types of surfaces: a Gauss synthetic surface and a real-world example. Results indicate that HASM-GMG can gain significant speedups compared with CPU-based HASM without acceleration on GPU. Moreover, both the accuracy and speed of HASM-GMG are superior to the classical interpolation methods including Kriging, Spline and IDW.

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.

Digital elevation model (DEM) source data are subject to both horizontal and vertical errors owing to improper instrument operation, physical limitations of sensors, and bad weather conditions. These factors may bring a negative effect on some DEM-based applications requiring low levels of positional errors. Although classical smoothing interpolation methods have the ability to handle vertical errors, they are prone to omit horizontal errors. Based on the statistical concept of the total least squares method, a total error-based multiquadric (MQ-T) method is proposed in this paper to reduce the effects of both horizontal and vertical errors in the context of DEM construction. In nature, the classical multiquadric (MQ) method is a vertical error regression procedure, whereas MQ-T is an orthogonal error regression model. Two examples, including a numerical test and a real-world example, are employed in a comparative performance analysis of MQ-T for surface modeling of DEMs. The numerical test indicates that...

The classification of airborne laser scanning ALS point clouds is a necessary step in the process of digital elevation model DEM construction. Motivated by the surface interpolation filtering scheme, a multi-resolution hierarchical classification MHC method was developed to perform classification in our previous research. However, similar to almost all filtering methods, MHC suffers from the problem of misclassifying off-terrain and ground points in complex landscapes with steep slopes and large discontinuities. To improve the classification accuracy in the above landscapes, the original MHC is improved in this article by adopting a region growing-based segmentation method to maximally capture the initial ground seeds of MHC. Furthermore, considering the high sensitivity of principle component analysis PCA to outliers, a robust PCA approach based on least trimmed squares LTS is proposed to estimate point normals. Fifteen groups of data sets provided by the International Society for Photogrammetry and Remote Sensing ISPRS Working Group III/3 are utilized to compare the performances of the improved and original MHCs. Results indicate that the improved MHC is more accurate than the original MHC, irrespective of accuracy measures. In addition, we also compare the results of our method with three new filtering methods developed in the years 2013 and 2014. It is found that regardless of landscapes i.e. urban and rural samples, the improved MHC is averagely more accurate than the three filtering methods in terms of type II error, and irrespective of accuracy measures i.e. types I, II and total errors, our method outperforms the three filtering methods for the rural samples. In short, the robust segmentation-based MHC demonstrates great potential to ALS-derived DEM construction in rural areas.

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.

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.

Changes in precipitation could have crucial influences on the regional water resources in arid regions such as Xinjiang. It is necessary to understand the intrinsic multi-scale variations of precipitation in different parts of Xinjiang in the context of climate change. In this study, based on precipitation data from 53 meteorological stations in Xinjiang during 1960–2012, we investigated the intrinsic multi-scale characteristics of precipitation variability using an adaptive method named ensemble empirical mode decomposition (EEMD). Obvious non-linear upward trends in precipitation were found in the north, south, east and the entire Xinjiang. Changes in precipitation in Xinjiang exhibited significant inter-annual scale (quasi-2 and quasi-6 years) and inter-decadal scale (quasi-12 and quasi-23 years). Moreover, the 2–3-year quasi-periodic fluctuation was dominant in regional precipitation and the inter-annual variation had a considerable effect on the regional-scale precipitation variation in Xinjiang. We also found that there were distinctive spatial differences in variation trends and turning points of precipitation in Xinjiang. The results of this study indicated that compared to traditional decomposition methods, the EEMD method, without using any a priori determined basis functions, could effectively extract the reliable multi-scale fluctuations and reveal the intrinsic oscillation properties of climate elements.

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.