Surface modeling of DEMs based on a sequential adjustment method

A sequential adjustment (SA) method is employed to decrease the computational cost of high-accuracy surface modeling (HASM), and the SA of HASM (HASM-SA) is being developed. A mathematical surface was used to comparatively analyze the computing speed of SA and the classical iterative solvers provided by MATLAB 7.7 for solving the system of linear equations of HASM. Results indicate that SA is much faster than the classical iterative solvers. The computing time of HASM-SA is determined by not only the total number of grid cells but also the number of sampling points in the computational domain. A real-world example of surface modeling of digital elevation models (DEMs) with various resolutions shows that HASM-SA is averagely more accurate and much faster than the commonly used interpolation methods, such as inverse distance weighting (IDW), kriging, and three versions of spline, namely regularized spline (RSpline), thin-plate spline (TPS), and ANUDEM in terms of root mean square error (RMSE), mean absolute error (MAE), and mean error (ME). In particular, the ME of HASM-SA at different spatial resolutions is averagely smaller than those of IDW, kriging, RSpline, TPS, and ANUDEM by 85%, 83%, 83%, 53%, and 19%, respectively. The high speed and high accuracy of HASM-SA can be due to the absence of matrix inversion computation, combined with the perfect fundamental theorem of HASM.     

基于多重网格求解的土壤属性高精度曲面建模

高精度曲面建模(HASM)是近几年发展起来的可用于地理信息系统和生态建模的一种较高精度的曲面建模方法.本研究选择南方红壤丘陵区江西省吉安市辖区、吉安县和泰和县为研究区,采集150个表层土壤(0～20cm)样品,分别随机选取60、90和120个点作为模拟数据集,90、60和30个点作为验证数据集,基于多重网格(MG)作为...     

The smoothness of HASM

To smooth noises inherent in uniformly sampled dataset, the smoothness of high accuracy surface modeling (HASM) was explored, and a smoothing method of HASM (HASM-SM) was developed based on a penalized least squares method. The optimal smoothing parameter of HASM-SM was automatically obtained by means of the generalized cross-validation (GCV) method. For an efficient smoothing computation, discrete cosine transform was employed to solve the system of HASM-SM and to estimate the minimum GCV score, simultaneously. Two examples including a numerical test and a real-world example were employed to compare the smoothing ability of HASM-SM with that of GCV thin plate smoothing spline (TPS) and kriging. The numerical test indicated that the minimum GCV HASM-SM is averagely more accurate than TPS and kriging for noisy surface smoothing. The real-world example of smoothing a lidar-derived Digital Elevation Model (DEM) showed that HASM-SM has an obvious smoothing effect, which is on a par with TPS. In conclusion, HASM-SM provides an efficient tool for filtering noises in grid-based surfaces like remote sensing–derived images and DEMs.     

基于改进HASM方法的中国日照百分率的模拟

日照百分率作为研究日照时数及太阳辐射等的重要因素之一,其模拟结果的好坏,直接关系到相关领域的研究应用。而高精度曲面建模方法（HASM）是近几年发展起来的用于生态建模的高精度曲面模拟方法。首先对现有的HASM进行改进,给出建立在完整理论基础之上、精度更高的曲面建模方法,并记为HASM.MOD;以高斯合成曲面为数值试验对象,验证HASM与HASM.MOD的模拟精度;最后,根据全国1951-2010 年752 个气象站点的月平均日照百分率数据,运用HASM.MOD研究近60 年月平均日照百分率的分布状况,同时比较了HASM.MOD、HASM、Kriging 和IDW法的插值精度。数值试验和实例验证结果表明,HASM.MOD的模拟精度最高。用该方法所提供的日照百分率数据可作为基础地理数据供相关研究应用。     

高精度曲面建模方法研究进展与分类

高精度曲面建模方法(HASM)作为新一代的曲面模拟方法,经过20多年的发展,其理论体系不断完善,算法体系不断丰富,应用领域不断拓广。然而,目前HASM方法尚未建立科学的分类体系,仅依据求解算法为标准进行简单区分,忽视了HASM所研究问题本质上的差异,阻碍了HASM方法在相关领域的进一步应用。为此,本文在总结HASM方法发展过程的基础上,按照研究问题的本质特点,以输入数据的类型为依据,将HASM分为空间插值方法和空间数据融合方法。其中,HASM空间插值方法是根据离散采样点得到目标曲面,而HASM空间数据融合方法则是融合多源数据,并综合各个数据源优势而得到新曲面的过程。该分类科学、合理,为今后HASM方法的进一步应用提供了理论指导。最后本文叙述了应用两种HASM方法求解问题时的一般步骤,同时还对两种方法的发展前景进行了展望。     

SRTM resample with short distance‐low nugget kriging

The shuttle radar topography mission (SRTM), was flow on the space shuttle Endeavour in February 2000, with the objective of acquiring a digital elevation model of all land between 60° north latitude and 56° south latitude, using interferometric synthetic aperture radar (InSAR) techniques. The SRTM data are distributed at horizontal resolution of 1 arc‐second (～30 m) for areas within the USA and at 3 arc‐second (～90 m) resolution for the rest of the world. A resolution of 90 m can be considered suitable for the small or medium‐scale analysis, but it is too coarse for more detailed purposes. One alternative is to interpolate the SRTM data at a finer resolution; it will not increase the level of detail of the original digital elevation model (DEM), but it will lead to a surface where there is the coherence of angular properties (i.e. slope, aspect) between neighbouring pixels, which is an important characteristic when dealing with terrain analysis. This work intents to show how the proper adjustment of variogram and kriging parameters, namely the nugget effect and the maximum distance within which values are used in interpolation, can be set to achieve quality results on resampling SRTM data from 3” to 1”. We present for a test area in western USA, which includes different adjustment schemes (changes in nugget effect value and in the interpolation radius) and comparisons with the original 1” model of the area, with the national elevation dataset (NED) DEMs, and with other interpolation methods (splines and inverse distance weighted (IDW)). The basic concepts for using kriging to resample terrain data are: (i) working only with the immediate neighbourhood of the predicted point, due to the high spatial correlation of the topographic surface and omnidirectional behaviour of variogram in short distances; (ii) adding a very small random variation to the coordinates of the points prior to interpolation, to avoid punctual artifacts generated by predicted points with the same location than original data points and; (iii) using a small value of nugget effect, to avoid smoothing that can obliterate terrain features. Drainages derived from the surfaces interpolated by kriging and by splines have a good agreement with streams derived from the 1” NED, with correct identification of watersheds, even though a few differences occur in the positions of some rivers in flat areas. Although the 1” surfaces resampled by kriging and splines are very similar, we consider the results produced by kriging as superior, since the spline‐interpolated surface still presented some noise and linear artifacts, which were removed by kriging.     

1951-2010年中国季平均降水高精度曲面建模分析

利用1951-2010年中国711个气象观测站的月降水资料,对多年季平均降水根据中国农业气候类型进行分区模拟。针对中国降水特点,首先分析了影响各分区降水的地理、地形因素及局部地形因素,利用多项式回归和逐步回归的方法对各分区降水进行了趋势拟合;在此基础上,采用改进的高精度曲面建模(HASM)方法,对各模拟区域去掉趋势后的残差进行迭代修正,并比较验证了模拟效果。同时,为保证HASM在边界附近的模拟精度,根据区域内站点间的距离,对每一分区设置一个缓冲区,将HASM实际插值区域扩展为缓冲区内的部分。模拟结果表明:HASM方法的模拟精度在不同区域不同季节内均比经典的插值方法模拟精度高。利用上述方法分析了同一季节各分区降水的分布特点,并模拟了不同季节内多年平均降水的空间分布状况,模拟结果符合我国降水的实际分布特点。     

The Precision of C Stock Estimation in the Ludhikola Watershed Using Model-Based and Design-Based Approaches

In this study, two sampling protocols using a model-based and a design-based framework were juxtaposed to evaluate their precision in the estimation of C stock in the Ludikhola watershed, Nepal. The model-based approach exploits the spatial dependencies in the sampled variable and may therefore be attractive over the design-based approach as it reduces the substantial costs of survey and effort required in the latter. Scales of spatial variability for C stock which resulted in a grid resolution of 10,000 m² were determined using a reconnaissance variogram. Akaike information criterion was used for the selection of the best linear model of feature space for use in kriging with external drift (KED). Among the five tested covariates, distance, elevation, and aspect were statistically significant, with the best model of feature space accounting for 87.7% variability of C stock. An ANOVA established significance differences in mean C stocks (P = 0.00017). KED using the best model of feature space was found to be more precise, (9.89 ± 0.17) sqrt mg C/ha, than a pure-based approach of ordinary kriging and the design-based approach, (9.91 ± 0.8) sqrt mg C/ha. The confidence bounds of the two estimators showed that their confidence intervals will overlap 99.7% of the time, with both confidence intervals falling within the 95% confidence bounds of each other. There is less uncertainty around the mean C stock estimated using the model-based approach than the mean C stock estimated using the design-based approach. The model-based approach is a prospective option for the REDD framework.     

一种土壤属性制图的曲面建模方法(英文)

High accuracy surface modeling(HASM) is a method which can be applied to soil property interpolation.In this paper,we present a method of HASM combined geographic information for soil property interpolation(HASM-SP) to improve the accuracy.Based on soil types,land use types and parent rocks,HASM-SP was applied to interpolate soil available P,Li,pH,alkali-hydrolyzable N,total K and Cr in a typical red soil hilly region.To evaluate the performance of HASM-SP,we compared its performance with that of ordinary kriging(OK),ordinary kriging combined geographic information(OK-Geo) and stratified kriging(SK).The results showed that the methods combined with geographic information including HASM-SP and OK-Geo obtained a lower estimation bias.HASM-SP also showed less MAEs and RMSEs when it was compared with the other three methods(OK-Geo,OK and SK).Much more details were presented in the HASM-SP maps for soil properties due to the combination of different types of geographic information which gave abrupt boundary for the spatial varia-tion of soil properties.Therefore,HASM-SP can not only reduce prediction errors but also can be accordant with the distribution of geographic information,which make the spatial simula-tion of soil property more reasonable.HASM-SP has not only enriched the theory of high accuracy surface modeling of soil property,but also provided a scientific method for the ap-plication in resource management and environment planning.     

基于HASM的省级尺度气候与植被生态系统模拟分析

区域气候要素的空间模拟精度直接关系到区域气候-植被生态系统的模拟精度。针对这一问题,运用HASM方法对江西省气候要素进行空间模拟,而且与IDW、Kriging、Spline等传统经典方法模拟结果的对比分析表明,HASM方法的模拟精度最高。因此,在10年和30年时间尺度上,运用HASM方法分别完成江西过去60年的平均气温、平均降水和潜在蒸散的空间模拟,并采用Holdridge生命地带(HLZ)模型分别实现了江西不同时间尺度的HLZ生态系统时空变化模拟。模拟结果显示,在1961-2010年期间,20%左右的HLZ生态系统发生了变化,平均气温上升是HLZ生态系统发生变化的主要驱动因子。另外,在江西省出现的7种HLZ生态系统类型中,暖温带湿润森林类型受平均气温上升的影响最大。     

省尺度森林植被碳储量空间分布模拟不确定性分析——以江西省为例（英文）

Forest vegetation carbon patterns are significant for evaluating carbon emission and accumulation. Many methods were used to simulate patterns of forest vegetation carbon stock in previous studies, however, uncertainty apparently existed between results of different methods, even estimates of same method in different studies. Three previous methods, including Atmosphere-vegetation interaction model 2(AVIM2), Kriging, Satellite-data Based Approach(SBA), and a new method, High Accuracy Surface Modeling(HASM), were used to simulate forest vegetation carbon stock patterns in Jiangxi Province in China. Cross-validation was used to evaluate methods. The uncertainty and applicability of the four methods on provincial scale were analyzed and discussed. The results showed that HASM had the highest accuracy, which improved by 50.66%, 33.37% and 28.58%, compared with AVIM2, Kriging and SBA, respectively. Uncertainty of simulation of forest biomass carbon stock was mainly derived from modeling error, sampling error and statistical error of forest area. Total forest carbon stock, carbon density and forest area of Jiangxi were 288.62 Tg, 3.06 kg/m~2 and 94.32×109 m~2 simulated by HASM, respectively.     

An assessment of three satellite-based precipitation data sets as applied to the Thailand region

The study examines three satellite-based data sets to estimate long-term precipitation for the Thailand region: the Tropical Rainfall Mapping Mission (TRMM) 3B43, the Climate Prediction Centre morphing technique (CMORPH), and a locally developed regression model using the geostationary meteorological satellite (GMS) covering the Thailand region. Data for the first two sets were available at a spatial resolution of 0.25° × 0.25°, while the local regression model used data from the GMS at a resolution of 5 km × 5 km. The statistical regression model was developed by relating long-term monthly average precipitation from 27 rain gauge stations with concurrent satellite data in the visible and thermal infrared bands. The model was then tested against independent data from 27 rain gauge stations. Satellite/rain gauge ratios were estimated, and a smooth spline surface was used to correct the error from the model. Data from the three approaches were compared with a rain gauge network. The TRMM relation performed better than CMORPH, and the performance for GMS was comparable to TRMM with root mean square different and mean bias difference of 33.6 and 4.2%, respectively. The locally developed regression model was used to produce monthly and yearly total rainfall maps from the GMS data for the entire country.     

Deriving ground surface digital elevation models from LiDAR data with geostatistics

This paper focuses on two common problems encountered when using Light Detection And Ranging (LiDAR) data to derive digital elevation models (DEMs). Firstly, LiDAR measurements are obtained in an irregular configuration and on a point, rather than a pixel, basis. There is usually a need to interpolate from these point data to a regular grid so it is necessary to identify the approaches that make best use of the sample data to derive the most accurate DEM possible. Secondly, raw LiDAR data contain information on above‐surface features such as vegetation and buildings. It is often the desire to (digitally) remove these features and predict the surface elevations beneath them, thereby obtaining a DEM that does not contain any above‐surface features. This paper explores the use of geostatistical approaches for prediction in this situation. The approaches used are inverse distance weighting (IDW), ordinary kriging (OK) and kriging with a trend model (KT). It is concluded that, for the case studies presented, OK offers greater accuracy of prediction than IDW while KT demonstrates benefits over OK. The absolute differences are not large, but to make the most of the high quality LiDAR data KT seems the most appropriate technique in this case.     

基于GIS的新疆气温数据栅格化方法研究

以新疆99个气象台站1971-2010年年平均气温为数据源,采用多元回归结合空间插值的方法对新疆区域气温数据进行栅格化研究。建立了年平均气温与台站经纬度和海拔高度的多元回归模型,对于残差数据的插值采用了反距离权重法(IDW) 、普通克立格法 (Kriging)和样条函数法(Spline)3种目前应用广泛的空间插值方法,针对于这3种方法进行了基于MAE和RMSIE的交叉验证和对比分析,结果表明在新疆的年平均气温的GIS插值方案中,IDW方法精度总体要高于其他两种插值方法。     

Application of inverse path distance weighting for high-density spatial mapping of coastal water quality patterns

One of the primary goals of coastal water quality monitoring is to characterize spatial variation. Generally, this monitoring takes place at a limited number of fixed sampling points. The alternative sampling methodology explored in this paper involves high-density sampling from an on-board flow-through water analysis system (Dataflow). Dataflow (West Palm Beach, FL, USA) has the potential to provide better spatial resolution of water quality features because it generates many closely spaced (<10 m) measurements. Regardless of the measurement technique, parameter values at unsampled locations must be interpolated from nearby measurement points in order to generate a comprehensive picture of spatial variations. Standard Euclidean interpolations in coastal settings tend to yield inaccurate results because they extend through barriers in the landscape such as peninsulas, islands, and submerged banks. We recently developed a method for non-Euclidean interpolation by inverse path distance weighting (IPDW) in order to account for these barriers. The algorithms were implemented as part of an R package and made available from R repositories. The combination of IPDW with Dataflow provided more accurate estimates of salinity patterning relative to Euclidean inverse distance weighting (IDW). IPDW was notably more accurate than IDW in the presence of intense spatial gradients.     

自适应的IDW插值方法及其在气温场中的应用

反距离权重(Inverse Distance Weighting,IDW)插值通常采用距离搜索策略选择插值参考点,当采样点集分布不均匀时,距离搜索策略使得参考点聚集一侧影响插值精度。自然邻近关系具有良好的自适应分布特性,可有效地解决参考点分布不均匀问题。结合自然邻近关系,提出自适应的反距离权重(Adaptive-IDW,AIDW)插值方法。首先对采样数据构建初始Delaunay三角网,然后采用逐点插入法,将待插值点插入初始Delaunay三角网中,局部调整得到新的Delaunay三角网,以待插值点的一阶邻近点作为IDW插值的参考点,使参考点自适应均匀地分布在待插值点周围,再进行IDW插值计算。利用AIDW插值方法对Franke函数、全国气温观测数据进行插值实验,结果表明此方法具有较高的精度,且减少了“牛眼”现象。     

空间软数据及其插值方法研究进展

由于对地观测技术的迅速发展,空间数据的种类和数量增长迅猛,由空间数据反演得到的各种信息日趋膨胀,这些反演结果中的信息不少以软数据的形式出现。在实际应用中,这些软数据往往与空间插值的目标变量具有一定的相关性,甚至成为控制目标变量空间分布特征的重要因素。然而,由于这些数据通常表示为非数值形式,在计算和处理上存在着一定困难,以致被传统的插值方法所忽视,从而造成信息浪费。近来出现的空间软插值方法是一种利用空间软数据作为辅助信息并以改善插值效果的方法,能够较好的处理并利用软数据所隐含的信息,具有较好的应用发展前景。本文根据空间软数据的特点及其分类,系统综述了空间软插值方法及其应用领域。首先分析了空间数据软硬性质的根本区别,论述了软数据的分类和“硬化”方法,然后介绍空间插值模型中对空间软数据的集成方法和原理,最后对空间软插值方法及其应用研究领域进行了展望。     

DEM空间插值方法对土壤侵蚀模拟的影响研究——以USPED分析干热河谷典型冲沟为例

为探索不同空间插值方法得到的DEM如何影响土壤侵蚀模拟效果,本文选择金沙江干热河谷区典型冲沟为研究对象,利用野外测量高程数据,采用反距离加权(IDW)、析取克里格(DK)、局部多项式(LPI)和张力样条函数(ST)4种方法构建高精度DEM。基于USPED模型模拟冲沟的土壤侵蚀,对比不同空间插值方法的精度、土壤侵蚀的空间分布,采用相对差系数对比不同插值在土壤侵蚀研究中的相似性。结果表明：DEM空间插值的精度排序为ST相似文献   

小区域癌症数据典型空间插值方法比较研究

癌症已成为危害全球居民健康的重大民生问题,选取合适的空间插值方法分析小区域癌症数据的空间特征可对区域性癌症防控工作的有效开展提供依据。本研究以湖南省苏仙区2012和2016年以村为单位的肺癌死亡率数据为研究对象,以平均误差和均方根误差为评价指标,对反距离加权（IDW）、普通克里金（OK）、趋势面分析（TSA）、多元线性回归（MLR）与协同克里金（CK）五种典型空间插值方法进行精度效果对比及参数优选,并结合不同插值方法的优缺点,确定癌症数据的最优插值方法。结果表明：插值精度方面,CK法的均方根误差最小、插值精度最高,OK、IDW（幂值=1）和MLR次之,TSA（阶数=5）最低;插值效果方面,五种插值方法的实测值和预测值均显著相关,除CK外,其它四种方法均对死亡率低估程度较大,CK和OK插值结果的空间分布效果更好。同时考虑空间因素和影响因子的CK方法是小区域苏仙区2012年、2016年肺癌死亡率最优插值方法,应用该方法可对区域性癌症防控工作的有效开展提供最优的技术支撑。本论文的研究思路也可为小区域癌症数据空间插值方法及参数优选提供参考。     

不同时间尺度、季节的气温数据空间平稳特征及其对插值结果的影响

不同时间尺度、季节的气温数据表现出不同的空间平稳特征。为探讨分析空间平稳性对气温插值的影响规律,采用趋势线法对气温数据进行空间平稳性探索,并对比分析不同空间平稳性条件下,普通线性回归、普通克里格、回归克里格的气温插值精度及插值结果的空间分布特点。结果显示：冬季日均、月均气温与年均气温呈现空间非平稳,插值精度随时间序列的增长而提高,随着气温数据逐渐趋于稳定,精度提高的幅度逐渐下降;夏季日均、月均气温呈现空间平稳,随时间序列的增长,插值精度的提高并不显著;夏季日均气温各插值方法的插值精度普遍高于冬季日均气温。与普通克里格相比,回归克里格能有效提高空间非平稳数据的插值精度。时间序列的增长削弱了不同插值算法之间的插值精度差异和插值结果空间分布差异。