Adjustment computation of HASM: a high-accuracy and high-speed method

We developed a method for high-accuracy surface modeling (HASM) in terms of the fundamental theorem of surfaces, which has theoretically found a solution for error problems. However, the computing speed of HASM was too slow to be widely applied in practice. Thus, adjustment computation of HASM (HASM-AC) is developed in this article. For comparatively testing HASM-AC accuracy, a mathematical surface is first selected so that the true value is able to be predetermined to avoid uncontrollable data errors. The numerical test indicates that HASM-AC has the highest accuracy and its accuracy is 20.67, 15.67, and 14.67 times higher than the inverse distance weighting (IDW), kriging, and spline, respectively. Then, a 0.4 km × 0.5 km rectangular area is used to test the effects of different spatial resolutions and sampling intervals on accuracy. This real-world test demonstrates that HASM-AC accuracy increases at a much better and stable pace as the spatial resolution becomes finer and sampling intervals get shorter, compared to the classic methods. Finally, the computing speed is tested in an area with 6000 × 6000 grid cells where Qinghai, Gansu, and Sichuan provinces meet. The computing speed of HASM-AC is 11, 8, and 563 times faster than IDW, spline, and kriging, respectively, which makes HASM-AC able to process data in a huge size and make real-time visualization realizable. In short, HASM-AC performs best in both the numerical and real-world tests.     

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。     

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...     

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。     

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。     

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。     

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.     

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.     

中国表层土壤全氮的空间模拟分析

基于第二次全国土壤普查5336个典型土壤剖面数据,分析表土全氮(A层)与环境因素的相关关系,利用多元回归模型和HASM模型结合的方法模拟中国国家尺度上表层土壤全氮的空间分布格局。结果表明:对350个检验点模拟结果的平均绝对误差和平均相对误差为0.67g·kg^-1和61.06%,与普通克里格法相比分别降低了0.05g·kg^-1和17.53%;对样点分布较少的西北地区的模拟结果也更符合实际情况。多元回归模型和HASM模型结合的方法考虑了环境因素的影响,可作为目前模拟大尺度土壤性质空间分布相对有效的方法。     

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.     

气象要素空间插值方法优化

在区域水土平衡模型的研究中 ,空间插值可提供每个计算栅格的气象要素资料。本文运用反距离加权法 (IDW )和梯度距离反比法 (GIDW ) ,对 196 1～ 2 0 0 0年甘肃省及其周围85个气象站点的多年平均温度与降雨量进行了内插。交叉验证结果表明 :对于IDW和GIDW ,二者温度插值的平均绝对误差 (MAE)分别为 2 2 8℃和 0 73℃ ,平均相对误差(MRE)分别为 2 9 0 2 %和 9 4 1% ,降雨插值的MAE值依次为 5 5 2mm和 4 90mm ,MRE值分别为 19 4 3%和 17 80 % ,GIDW明显优于IDW。需要指出的是 :对于降雨 ,当其经纬度和海拔高程的复相关系数大于 0 80时 ,GIDW插值结果优于IDW ;否则相反     

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。     

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。     

An evaluation of void‐filling interpolation methods for SRTM data

The Digital Elevation Model that has been derived from the February 2000 Shuttle Radar Topography Mission (SRTM) has been one of the most important publicly available new spatial data sets in recent years. However, the ‘finished’ grade version of the data (also referred to as Version 2) still contains data voids (some 836,000 km²)—and other anomalies—that prevent immediate use in many applications. These voids can be filled using a range of interpolation algorithms in conjunction with other sources of elevation data, but there is little guidance on the most appropriate void‐filling method. This paper describes: (i) a method to fill voids using a variety of interpolators, (ii) a method to determine the most appropriate void‐filling algorithms using a classification of the voids based on their size and a typology of their surrounding terrain; and (iii) the classification of the most appropriate algorithm for each of the 3,339,913 voids in the SRTM data. Based on a sample of 1304 artificial but realistic voids across six terrain types and eight void size classes, we found that the choice of void‐filling algorithm is dependent on both the size and terrain type of the void. Contrary to some previous findings, the best methods can be generalised as: kriging or inverse distance weighting interpolation for small and medium size voids in relatively flat low‐lying areas; spline interpolation for small and medium‐sized voids in high‐altitude and dissected terrain; triangular irregular network or inverse distance weighting interpolation for large voids in very flat areas, and an advanced spline method (ANUDEM) for large voids in other terrains.     

The scale effects of the spatial autocorrelation measurement: aggregation level and spatial resolution

The scale effects of the spatial autocorrelation (SA) measurement has been explored for decades. However, the effects of the data aggregation levels and spatial resolution on the SA measurement are often confused. Whether the two types of scale effects are the same is still unclear and requires further investigation. We retrieved the land surface temperature (LST) from Landsat 8 images in 30 capital cities of China. By aggregating the LST images, we observed a decrease in the SA of the LST as the data aggregation level increased; this relationship can be fitted well with a negative logarithmic function. We derived an indicator to measure the scale effects intensity of SA, which was negatively correlated with the spatial complexity of LST. Both aggregating images and the increasing spatial resolution induce weaker SA, but the effect of the former was stronger. The aggregating images negatively affected the SA degree regardless of the spatial resolutions of the original images. The SA degrees of the aggregated images were far below those of the real-life images. This study suggests that the scale effects caused by aggregation levels and spatial resolutions are different, and cautions should be taken when applying relevant conclusions derived from aggregating images.     

基于地学信息的土壤属性高精度曲面建模

目前土壤属性的曲面建模面临两大问题,一是缺乏足够多的采样点进行模拟,二是采样点的土壤属性与环境变量间存在非线性关系。高精度曲面建模(HASM)方法在如何融合地学信息对土壤属性进行空间插值,尚需深入研究。本文提出高精度曲面建模与地学信息相结合的土壤属性空间插值方法(High accuracy surface modeling for soil properties, HASM-SP),分别基于研究区的土壤类型、土地利用类型和母岩类型,模拟了江西省典型红壤丘陵区土壤的速效磷(AP)、锂(Li)、pH、碱解氮(AN)、全钾(K) 和铬(Cr) 6 种土壤属性的空间分布。将HASM-SP与普通克立格(OK)、OK与地学信息相结合的方法(OK-Geo) 和分层克立格(SK) 相对比,结果表明：结合地学信息可以使插值方法(HASM-SP和OK-Geo) 模拟结果的平均误差更趋近于0;相对于其他3 种方法,HASM-SP具有较小的平均绝对误差和均方根误差。从模拟的空间分布图上来看,HASM-SP获得了由于地学要素类型突变导致的土壤属性空间变异的细节信息。因此,基于地学信息的土壤属性高精度曲面建模方法(HASM-SP) 与传统插值方法相比,不仅提高了土壤属性空间分布的模拟精度,还能更好地刻画突变边界处土壤属性的空间变异,使土壤属性分布图更好地符合地学规律和实际情况。HASM-SP的提出对于丰富土壤属性的高精度曲面建模理论具有重要意义,并为土壤管理、精准农业的实施以及区域环境规划等提供科学依据。     

Spatial interpolation of marine environment data using P-MSN

ABSTRACT

When a marine study area is large, the environmental variables often present spatially stratified non-homogeneity, violating the spatial second-order stationary assumption. The stratified non-homogeneous surface can be divided into several stationary strata with different means or variances, but still with close relationships between neighboring strata. To give the best linear-unbiased estimator for those environmental variables, an interpolated version of the mean of the surface with stratified non-homogeneity (MSN) method called point mean of the surface with stratified non-homogeneity (P-MSN) was derived. P-MSN distinguishes the spatial mean and variogram in different strata and borrows information from neighboring strata to improve the interpolation precision near the strata boundary. This paper also introduces the implementation of this method, and its performance is demonstrated in two case studies, one using ocean color remote sensing data, and the other using marine environment monitoring data. The predictions of P-MSN were compared with ordinary kriging, stratified kriging, kriging with an external drift, and empirical Bayesian kriging, the most frequently used methods that can handle some extent of spatial non-homogeneity. The results illustrated that for spatially stratified non-homogeneous environmental variables, P-MSN outperforms other methods by simultaneously improving interpolation precision and avoiding artificially abrupt changes along the strata boundaries.     

Combining LPJ-GUESS and HASM to simulate the spatial distribution of forest vegetation carbon stock in China简

It is very important in accurately estimating the forests＇ carbon stock and spatial distribution in the regional scale because they possess a great rate in the carbon stock of the terrestrial ecosystem. Yet the current estimation of forest carbon stock in the regional scale mainly depends on the forest inventory data, and the whole process consumes too much labor, money and time. And meanwhile it has many negative influences on the forest carbon storage updating. In order to figure out these problems, this paper, based on High Accuracy Surface Modeling （HASM）, proposes a forest vegetation carbon storage simulation method. This new method employs the output of LPJ-GUESS model as initial values of HASM and uses the inventory data as sample points of HASM to simulate the distribution of forest carbon storage in China. This study also adopts the seventh forest resources statistics of China as the data source to generate sample points, and it also works as the simulation accuracy test. The HASM simulation shows that the total forest carbon storage of China is 9.2405 Pg, while the calculated value based on forest resources statistics are 7.8115 Pg. The forest resources statistics is taken based on a forest canopy closure, and the result of HASM is much more suitable to the real forest carbon storage. The simulation result also indicates that the southwestern mountain region and the northeastern forests are the important forest carbon reservoirs in China, and they account for 39.82% and 20.46% of the country＇s total forest vegetation carbon stock respectively. Compared with the former value （1975-1995）, it mani- fests that the carbon storage of the two regions do increase clearly. The results of this re- search show that the large-scale reforestation in the last decades in China attains a signifi- cant carbon sink.     

基于HASM的中国森林植被碳储量空间分布模拟

当前区域尺度上森林碳储量估算主要依据森林资源清查数据,整个过程不仅消耗大量人力、物力,而且十分耗时,严重影响了森林碳储量估算的时效性。针对这一问题,本文提出了基于HASM的森林植被碳储量模拟方法,该方法以全球植被动态模型LPJ-Guess 输出的植被碳储量为驱动场,以森林清查样地数据为精度控制点,模拟生成中国陆地森林碳储量分布情况。研究以第7 次中国森林资源清查数据作为精度控制点数据源,同时作为本文模拟方法的精度验证。结果表明,中国森林碳储量为9.2405 Pg,考虑到森林资源清查是基于一定的郁闭度进行的,因此HASM模拟的结果与根据森林资源清查结果计算得出的7.8115 Pg 相比更符合实际情况,西南山区和东北林区是中国森林最主要的碳库,其碳储量分别占中国森林植被碳储量的39.82%和20.46%。同时与之前(1975-1995 年) 相比具有较大幅度的增长,表明近几十年来中国坚持大规模植树造林的碳汇效果显著。同时也表明基于HASM的森林植被碳储量空间分布模拟方法是有效的,模拟结果合理且精度较高,表明该方法在全球尺度上森林植被碳储量模拟及其它生态系统中碳储量模拟中具有应用潜力。