赵明伟
, 岳天祥
ZHAO Mingwei, YUE Tianxiang
版权声明: 2016 地理科学进展 《地理科学进展》杂志 版权所有
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作者简介:
作者简介：赵明伟(1986-),男,山东莱芜人,博士,讲师,主要研究方向为高精度曲面建模与环境生态信息学,E-mail: zhaomw@lreis.ac.cn。
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摘要
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。
关键词：
Abstract
High accuracy surface modeling (HASM) is a new generation of surface simulation method. After 20 years of development, its theoretical basis has continuously improved, the algorithm is enriched, and the application field is expanding. However, a scientific classification system of HASM methods has not been established and this has prevented further application of HASM in various fields. To solve this problem, this article first summarizes the development process of HASM, then according to the nature of given research problems, HASM is divided into spatial interpolation and spatial data fusion methods based on the type of input data. The HASM spatial interpolation method generates target surface according to discrete sampling points. The HASM spatial data fusion method is the fusion of multi-source data that integrates the advantages of each data source to obtain a new surface. This classification provides a theoretical guidance for the further application of HASM. The article also introduces the general steps of solving spatial simulation problems using the two HASM methods, and the development prospect of the two methods is discussed.
Keywords：
地面观测数据精度虽高,但离散的地面观测点无法计算区域尺度上的各种参数,因此空间插值方法是解决该问题的重要途径。以往的曲面建模方法或是基于地统计学理论,或是基于邻域相关性假设,或是弹性力学机制,而并非从曲面自身的要素出发考虑,在建模中没有考虑曲面的内蕴因素对曲面重建的约束作用,因此,在曲面拟合过程中难以控制建模误差。
基于曲面论的高精度曲面建模方法(HASM)是近几年发展起来的一种新的可用于空间插值和预测的方法(Yue, 2011)。基于Evans(1980)的研究,坡面、坡向和曲率是反映局部规律的重要变量,岳天祥等(1990)首先完成了基于曲线论的冰斗形态的数学模型,用来探测地球曲面系统的变化(Yue et al, 2002)。根据微分几何理论,空间曲线由曲率和挠率决定;曲面由第一类基本量和第二类基本量决定(Toponogov et al, 2006)。因此,曲面建模技术应更多地考虑曲面自身的决定因素。基于此,岳天祥等(2001, 2003)发展了基于曲面论的高精度曲面建模方法(HASM)。自2004年起,高精度曲面建模(HASM)理论体系日益完善,并解决了地理信息系统中的经典曲面建模的误差问题(Yue et al, 2007; Yue, Chen et al, 2010; Yue, Wang, 2010; Yue et al, 2012)。数值试验和实例验证都表明,HASM模拟精度高于经典的插值方法(Yue et al, 2007; Shi et al, 2009; Yue, Chen et al, 2010; Zhao et al, 2013)。
基于离散数据点进行空间插值,尽管HASM方法的精度显著优于经典插值方法,然而,许多问题仅仅依赖空间插值还是难以解决的。例如采样点过于稀疏、目标曲面剧烈变化等。遥感手段可以获取区域尺度上的观测数据,为解决上述问题提供了数据源,但是目前遥感数据的精度还有待进一步提高。相关学者对遥感数据的融合和增强进行了研究,提出了多种遥感数据融合模型。如利用不同时相的影像数据进行配准生成DEM(Schultz et al, 1999; Palubinskas et al, 2010; Okano et al, 2011);利用ASTER DEMs、GTOPO30、数字地图数据、地面测量数据等多源数据实现SRTM DEM空值区域的填补(游松财等, 2005; 凌峰等, 2006; Luedeling et al, 2007; Reuter et al, 2007);也有学者采用时间、区域基本一致的不同DEM进行融合(Karkee et al, 2008)。从融合方法看,主要方法有自一致性技术(Schultz et al, 1999)、快速傅里叶变换(Karkee, 2008; 陈传法等, 2010)、稀疏表示(Papasaika et al, 2011)、卡尔曼滤波(Slatton et al, 2002)等。这些方法基于不同来源DEM数据进行融合,其精度受限于原始DEM数据的精度,因而难以得到本质上的改善。岳天祥等(1990)提出基于HASM方法实现地面观测数据和卫星遥感数据的融合思想,将地面观测数据的精度优势和卫星遥感数据覆盖区域的特点结合起来,得到既能覆盖研究区域、又能显著提高精度的表面模型,这是HASM关于数据融合的思想的初始阶段。
基于这种思想,Zhao M W等(2014)对中国森林植被碳储量空间分布进行模拟,表明无论是在精度还是空间分布特征上,HASM方法的融合结果都显著优于直接采用离散采样点进行空间插值的结果。显然,已经不能将HASM仅仅看作是一种空间插值方法,如何定义HASM方法成为一个亟需解决的问题。
HASM从提出至今,应用领域不断拓广,但针对不同问题,HASM方法的应用并不是完全相同的。由于没有科学的定义和分类指导,这种差异造成了一种混乱,使得用户在解决具体问题时,难以准确快速的确定应用方案,这对HASM方法自身的发展也是不利的。本文在总结HASM发展过程的基础上,对其进行科学定义和分类,论述了分类后的HASM方法的求解过程,并讨论了HASM方法在后续发展过程中应重点考虑的问题。
HASM的发展可以分为四个阶段。其中第一阶段(1986-2001年),基于空间曲率理论认为空间曲面由其曲率决定。坡度和曲率是曲面分析中的重要变量(Evans, 1980),事实上,基于曲面论基本定理,曲面由其坡度和曲率唯一决定(Spivak, 1999)。基于此,岳天祥等(1990)构建了冰斗模型,并随后应用到地球表面变化探测的相关研究中(Yue et al, 2002)。第二阶段(2002-2007年),HASM的研究围绕曲面论基本定理展开,重点解决了曲面模拟的误差问题(Yue, 2011)。地球表面可以表达为(Kerimov, 2009)：z=f(x, y),其中z是在位置(x, y)的曲面属性。对于曲面方程z=f(x, y),构建了迭代HASM方程,将曲面模拟问题转化为对称正定的大型稀疏线性方程组问题(Yue et al, 2007)。第三阶段(2008-2011年),基于曲面论的HASM方法重点研究该方法的计算效率和内存需求问题。由于需要构建覆盖研究区域每个格网属性值的大型线性方程组,HASM方法求解计算时间消耗较大。为加速求解HASM,先后发展了多重网格HASM算法(HASM-MG)(Yue et al, 2008; Yue, Zhao et al, 2013)、HASM自适应算法(HASM-AM)(Yue, Chen et al, 2010),HASM平差算法(HASM-AC)(Yue, Wang, 2010),以及HASM预处理共轭梯度算法(赵娜等, 2012)等。其中多重网格算法是基于误差平滑理论和粗网格校正理论,是求解偏微分方程组最快的数值算法;HASM自适应算法的基本思想是在迭代计算过程中对误差超过一定阈值的网格进行标记继续迭代计算,而满足精度要求的格网点则不再参与新的迭代计算过程,以达到加速整体收敛计算的目的。第四阶段(2012年以来),将高斯—柯达西方程组引入HASM理论体系中(Yue, Zhao, Ramsey et al, 2013; Zhao, Yue, 2014),高斯—柯达西方程组作为迭代停止的一个依据,避免了之前人为主观设定迭代次数的缺陷,使HASM在理论上更加完美。同时,在算法方面也对HASM平差算法、HASM预处理共轭梯度算法等进行优化(赵明伟等, 2013; 赵明伟,岳天祥,赵娜, 2014),提高了上述HASM算法的解算速度和模拟精度。同时还引入HASM并行算法与基于MPI的并行策略(Zhao et al, 2015),将研究区域按照一定的划分策略分割成子区域进行计算,大大提高了HASM解决大区域、高分辨率问题的能力。
HASM的各个阶段按其发展顺序,模拟精度依次提高,且HASM 4在计算速度上与前三个阶段相比,有了很大的改善(岳天祥等, 2007)。数值试验表明,HASM方法的模拟精度比在GIS、CAD领域广泛使用的经典插值方法(反距离权重法(IDW)、克里金法(Kriging)、样条法(Spline)等)提高了多个数量级(Yue et al, 2007)。对HASM模型精度大幅度提高的理论分析表明,HASM能解决数值模拟中的峰值削平现象,且模拟精度对采样点之间的距离并不十分敏感(岳天祥等, 2007)。HASM模型的整个计算过程可分为偏微分方程组的离散、采样方程的建立及代数方程组的求解三个阶段(Yue, 2011)。即：HASM基于曲面论基本定理,将曲面所满足的微分方程组进行离散,然后结合采样点信息对离散后的代数系统进行求解。
在应用方面,HASM方法已经成功应用于数字高程模型(DEM)构建及相关卫星DEM数据产品的空缺值填补研究(Yue et al, 2007; Chen et al, 2010, Chen et al, 2012; Yue et al, 2012; Chen, Li et al, 2013; Chen, Yue et al, 2013);同时还应用于土壤属性要素、土壤污染物等的空间分布模拟(Shi et al, 2009, 2011, 2012),气候要素(气温、降水、辐射等)的时空变化模拟与分析(Yue, Zhao, Yang et al, 2013; Yue, Zhao, Ramsey et al, 2013; Zhao N, Yue T X, 2014; Zhao N, Yue T X, ; Zhao M W et al, 2014; 赵娜等, 2014)。近年来,HASM方法在碳源汇及全球变化领域也得到成功应用,如卫星反演XCO2数据的空缺值填补(Yue et al, 2015)、森林植被碳储量空间分布模拟(Zhao M W et al, 2014)、草地生物量空间分布模拟(赵明伟等, 2014)、基于Lidar点云数据的小流域尺度上的树高模拟(Wang Y F et al, 2015)等。这些研究采取一定的精度验证方案,都表明HASM方法的精度显著优于经典插值方法。同时部分研究(Zhao M W et al, 2014)结合具体的研究对象,还验证了HASM方法的研究结果在空间分布特征上更符合具体研究对象的分布规律。
如前文所述,最初,HASM方法本质属于空间插值方法,即根据给定的离散采样点数据插值计算得到研究区域的空间曲面。但是在后续发展中,HASM方法开始将卫星遥感数据或生态模型的输出结果(称为驱动场)与地面采样点数据(称为优化控制条件)相结合,取二者之长生成一种新的曲面,显然这已经不属于空间插值的范畴了。为此,根据所研究问题性质的不同,本文将HASM方法分为空间插值方法和空间数据融合方法。
(1) HASM空间插值
HASM空间插值是指通过HASM方法,将空间中离散的测量点转为连续的数据曲面(图1)。其对数据的要求明确为空间中离散的测量点,不包含除测量点以外的其他数据源。需要特别指出的是,在早期HASM研究中为了提高计算速度,将离散采样点使用普通插值方法得到的初始插值曲面也作为输入,这里的初始插值曲面来源于离散采样点,因此仍属于空间插值。
HASM空间插值的应用范围与常规插值方法一致,其中目前已经成熟应用的领域主要包括DEM构建(Yue et al, 2007; Chen et al, 2010; Chen, Li et al, 2013; Chen, Yue et al, 2013)、土壤要素空间插值(Shi et al, 2011)、气候数据插值(赵娜等, 2013; 赵娜等, 2014)、生物量空间插值(赵明伟, 岳天祥, 孙晓芳等, 2014)等,大量研究表明HASM方法在上述领域中的插值精度优于常规插值方法。
在针对具体问题的应用中,基于HASM的空间变量插值方法又分为以下两种思路：①直接对空间变量进行空间插值,得到连续的空间变化曲面,例如DEM构建、土壤要素空间插值等;②构建插值变量与其他变量(如高程、空间位置等)的回归关系并生成插值变量的趋势面,然后计算离散点观测值与趋势面值的差值,对差值进行空间插值,最后将残差曲面与趋势面叠加得到最终变量的插值结果,相关研究表明这种思路对于气候要素的空间插值具有更高的插值精度(Zhao N, Yue T X, 2014)。
(2) HASM空间数据融合
HASM空间数据融合是指通过HASM方法,将同一变量的多种数据集融合在一起,生成一种新的数据集。融合的数据集一般包括两类,即点状数据和面状数据。其中点状数据集为地面观测值,代表了数据集的精度,称作优化控制条件;面状数据来自卫星遥感或者其他模型的输出,代表了数据集的范围,称作驱动场。而HASM融合后的结果数据集是面状数据,它将地面优化控制条件的精度优势和驱动场的范围优势结合起来,最终生成一种精度相对较高、又能覆盖整个研究范围的数据曲面(图2)。
HASM空间数据融合方法的提出,是为了使卫星遥感观测(反演)的面状数据和地面站点观测的点状数据实现无缝结合,使得数据融合结果既能覆盖整个研究区域,又能将地面观测站点的精度优势融合到结果中。HASM空间数据融合方法在地理学、生态学等领域具有很大的应用潜力,目前已经得到初步应用的有植被碳储量模拟(Zhao M W et al, 2014)和大气XCO2浓度模拟(Yue et al, 2015)等。
根据HASM概念模型,HASM空间插值方法和HASM空间数据融合方法的根本区别是前者不需要提供驱动场,但是两者的计算过程基本一致,因此在本小节综合介绍HASM方法的基本原理和计算过程,对于两种方法的区别则在过程中予以说明。
根据曲面论基本定理(Somasundaram, 2005),当曲面的第一基本量E, F, G,第二基本量L, M, N满足对称性,且E, F, G为正定时,E, F, G, L, M, N满足Gauss-Codazii方程组,全微分方程组(1)在初始条件
式中：第一基本量和第二基本量,以及克式符号
考虑高斯方程组(1),本文对该方程组中的
式中：
式中：
基于最小二乘优化理论,HASM最终转化为求解下述最小二乘问题：
式中：
最优化问题,即式(6)等价于：
式中：
式(7)为一大型线性方程组表达式,即HASM计算最终转化为大型线性方程组的求解。由于线性方程组阶数较大,直接求解法已经不适用,一般需要采用迭代法进行线性方程组的求解,例如高斯—赛尔德迭代法,预处理共轭梯度迭代法等(赵娜等, 2012)。大型线性方程组计算出满足精度的解后,将解向量的元素值对应相应的空间位置,即得到研究目标变量的空间分布曲面。
在实际应用中,根据所研究问题的性质确定是采用HASM空间插值方法还是HASM空间数据融合方法。明确所需方法后,可按照如下步骤进行建模求解：
(1) 根据计算区域面积和计算结果分辨率,构建系数矩阵A, B, C;根据采样点信息,构建系数矩阵S和向量v。
(2) 构建大型稀疏线性方程组,参数
(3) 求解大型稀疏线性方程组,对求解结果进行精度判定,如果满足精度条件则将结果输出,否则进行外迭代,即更新方程右端向量,重新求解大型稀疏线性方程组。
(4) 求解结果满足精度条件,将结果输出到外部文件中。
对于HASM空间插值方法和空间数据融合方法,其区别在于当进行第一次迭代求解时,HASM空间插值方法的右端向量(式(2))是0值,即空间插值对于未知点的计算仅仅是依靠有限的空间采样点。而空间数据融合方法进行计算时,右端项是非0值,具体数值由驱动场计算得出,第一基本量和第二基本量的组合将驱动场的趋势信息传递给HASM方法。因此,对于空间数据融合,HASM不仅考虑了采样点,还同时将驱动场计算在内,实现了采样点状数据和驱动面状数据的有效融合。
(1) 结果空间分辨率设定
HASM方法计算结果的空间分辨率由优化控制点决定,其中优化控制点所代表的范围决定了计算结果空间分辨率的下限,而具体的分辨率设置则同时需要参考优化控制点的分布密度等因素。这里所讲的优化控制点所代表的范围是针对特殊问题而言,例如在温室气体卫星反演数据产品中,SCIMACHY发布的XCO2有效数据点代表的空间范围是0.5°×0.5°,因此在对该数据点进行空间插值时,插值结果空间分辨率应不高于0.5°。对其他问题而言,优化控制点所代表的范围就是地理空间中的一个点,例如DEM构建中的采样点,此时理论上计算结果的分辨率可以尽可能高,具体设置时根据优化控制点在研究区域中的分布密度决定。
(2) 曲面理论和空间统计理论的结合
HASM的理论基础是曲面论基本定理,该定理指出,曲面的形状由第一基本量和第二基本量唯一决定。但是,由于地理研究对象在自然空间中的分布并不一定符合标准的数学曲面,同时,由于人工采集过程中不可避免引入的误差,优化控制点可能会带有较大的误差。因此在采用HASM方法进行计算分析时必须考虑这种不一致性和误差,此时可以考虑引入空间统计学的相关理论。
此外,以往的HASM研究过于重视数学理论的推导,相对忽视研究对象本身的地理学特性,例如绝大部分研究属性在空间中的分布并不是光滑的数学曲面,对于该类问题该如何处理,仍需要考虑。
(3) HASM区域算法的发展
本文提出的发展高精度的区域HASM算法是基于如下几个方面的考虑：首先,HASM全局算法巨大的内存占用和时间消耗,例如,要计算覆盖中国大陆区域的1 km分辨率的某种变量,计算规模大约为4000×5000,则需要求解的线性方程组阶数为2×107,这一计算量是非常大的,必然带来较大的时间消耗。其次,对于研究规模较大的问题,利用全局算法进行计算可能并不合理。因为考虑到研究变量的空间异质性,变量在空间中的分布可能是不同区域对应不同曲面形态的情况,此时HASM区域算法更加合理。虽然当前基于MPI的并行HASM方法能够快速计算大区域、高分辨率的问题(Zhao et al, 2015),但其应用仍然受到一定的限制,表现在当采样点稀疏且分布不均时,采用棋盘式数据分割方法效果较差;即便优化区域分割方案,当采样点特别稀疏时,单个区域的计算可能也难以开展。因此,根据研究对象在空间中的分布特征,设计区域化的HASM求解方法,是解决HASM计算效率的重要途径。
此外,HASM在计算过程中对于采样点赋一个权重,目前该权重是默认统一的。而实际上,一个采样点的影响范围应该是有限的,并受曲面本身形态的影响,因此,在后续研究中应该构建一个可变权重的采样点设置方案。
HASM方法发展至今,在算法和理论两方面都取得了长足的发展。但随着该方法在更多领域中的应用,其理论缺陷也开始显现,最为明显的就是关于HASM方法的定义不明确。由于定义的不确定造成了关于该方法应用的一些混乱,也制约了该方法的进一步发展。
本文在总结HASM发展历程的基础上,重点阐述了HASM方法的科学分类。根据研究问题性质的不同,将HASM方法分为HASM空间插值方法和HASM空间数据融合方法。前者是基于给定的离散采样点模拟区域曲面;后者则是融合场数据和离散点数据各自的优势,优化原始场数据,提高其精度的方法。
HASM方法的科学分类解决了HASM是否属于空间插值方法的疑惑,为今后HASM方法的科学应用提供方法指导。两种方法的计算机理不同,其研究和要解决的问题也不同。同时,针对这两类方法,本文还讨论了今后发展中应重点解决的问题,为HASM完整理论体系的发展方向提供有益借鉴。
The authors have declared that no competing interests exist.
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<p> 为了克服两种向全球开放的、不同数据源（ASTER和SRTM）DEM的获取技术缺陷，以甘肃省东部董志塬某测区为例，研究两种来源DEM的有效融合方案。首先，借助快速傅里叶变换（FFT）将ASTER和SRTM 的DEM数据由空域转换到频域； 然后，分别基于高通和低通滤波器进行滤波处理，并将滤波后的频域相加； 最后，基于FFT逆变换将融合后的频域转换到空域，实现DEM数据的有效融合。误差分析表明： 融合后的DEM最小、最大误差较融合前的均有明显降低，中误差也有降低趋势，误差绝对值大于30 m的网格点数占全部网格数的比例均有所下降。</p>
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<p> 为了克服两种向全球开放的、不同数据源（ASTER和SRTM）DEM的获取技术缺陷，以甘肃省东部董志塬某测区为例，研究两种来源DEM的有效融合方案。首先，借助快速傅里叶变换（FFT）将ASTER和SRTM 的DEM数据由空域转换到频域； 然后，分别基于高通和低通滤波器进行滤波处理，并将滤波后的频域相加； 最后，基于FFT逆变换将融合后的频域转换到空域，实现DEM数据的有效融合。误差分析表明： 融合后的DEM最小、最大误差较融合前的均有明显降低，中误差也有降低趋势，误差绝对值大于30 m的网格点数占全部网格数的比例均有所下降。</p>
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提出了利用ASTER数据,通 过分析两种数据高程差异的空间分布特点,从而进行SRTM无效区域填充的方法.该方法首先对ASTER数据进行预处理,然后计算两种DEM数据的高程差 异,并利用ASTER数据的地形因子,通过协同克里金方法对高程差异进行空间插值,得到SRTM无效区域内两种数据的高程差异,并在此基础上对ASTER 数据进行变换,从而对SRTM无效区域进行填充.计算结果表明该方法可以提高填充结果的精度,是一种有效的SRTM无效区域填充方法.
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<p>本文对中国地区SRTM90m分辨率的数字高程数据的空值区域做了提取和分析，在此基础上尝试了4种内插填补的方法，并对各种处理方法的过程及结果做了比较，从而确定先从SRTM90m数据中直接提取等高线，再内插生成DEM，用内插出来的值填补原始数据的方法在目前较为适用。此外本文还提出了一些后期处理方法以完善数据。</p>
Comparison of patching methods of SRTM 90 m DEM voids in China [J].https://doi.org/10.3969/j.issn.1007-6301.2005.06.010 URL Magsci [本文引用: 1] 摘要
<p>本文对中国地区SRTM90m分辨率的数字高程数据的空值区域做了提取和分析，在此基础上尝试了4种内插填补的方法，并对各种处理方法的过程及结果做了比较，从而确定先从SRTM90m数据中直接提取等高线，再内插生成DEM，用内插出来的值填补原始数据的方法在目前较为适用。此外本文还提出了一些后期处理方法以完善数据。</p>
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为了解决高精度曲面建模方法的速度问题,在大量数值实验的基础 上,将模拟迭代方程HASM3改进为HASM4.分析结果表明,HASM4的CPU时间较HASM3有了大幅度的减少,而且随着计算域栅格总数的增加,这 种减少幅度呈负幂指数规律;同时,随着计算规模的增大,HASM4达到收敛所需的迭代次数较HASM3达到收敛所需的迭代次数呈直线下降趋势.HASM4 减少了模型计算量,提高了模型的运行速度,其模拟精度与HASM3相比也有一定幅度的提高.
High accuracy surface modelling: HASM4 [J].https://doi.org/10.3969/j.issn.1006-8961.2007.02.027 URL [本文引用: 8] 摘要
为了解决高精度曲面建模方法的速度问题,在大量数值实验的基础 上,将模拟迭代方程HASM3改进为HASM4.分析结果表明,HASM4的CPU时间较HASM3有了大幅度的减少,而且随着计算域栅格总数的增加,这 种减少幅度呈负幂指数规律;同时,随着计算规模的增大,HASM4达到收敛所需的迭代次数较HASM3达到收敛所需的迭代次数呈直线下降趋势.HASM4 减少了模型计算量,提高了模型的运行速度,其模拟精度与HASM3相比也有一定幅度的提高.
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草地生态系统是陆地生态系统中分布最广泛的生态系统类型之一，草地生物量的精确估算一直是陆地生态学研究的重点问题。针对目前草地生物量估算方法的不确定性问题，提出了不依赖于遥感植被指数，而是通过分析草地生物量影响因素的方法去构建草地生物量估算模型。根据年积温（> 0℃）和湿润度指标将研究区域划分为4种潜在植被类型，即微温干旱温带半荒漠类、微温微干温带典型草原类、微温微润草甸草原类和微温湿润森林草原类，然后对每一种潜在植被类型的草地生物量分析其内在影响因素，研究结果发现，微温干旱温带半荒漠类的草地生物量与年积温存在较好的线性关系，微温微干温带典型草原类的草地生物量可以用表层土壤粘粒含量的二次多项式来模拟，后两种潜在植被类型的草地生物量则随着潜在NPP的变化呈现先减小后增大的变化趋势。对4种潜在植被类型区域分别建立草地生物量与其影响因素之间的回归关系确定研究区域草地生物量的趋势面，结合HASM模型实现研究区域草地生物量的高精度模拟，结果显示上述4种潜在植被类型区的草地平均生物量分别为76.62、110.94 、142.69 、184.40 g/m<sup>2</sup>。
High accuracy simulation of aboveground biomass in northern China based on IOCSG [J].https://doi.org/10.5846/stxb201301050031 URL Magsci [本文引用: 10] 摘要
草地生态系统是陆地生态系统中分布最广泛的生态系统类型之一，草地生物量的精确估算一直是陆地生态学研究的重点问题。针对目前草地生物量估算方法的不确定性问题，提出了不依赖于遥感植被指数，而是通过分析草地生物量影响因素的方法去构建草地生物量估算模型。根据年积温（> 0℃）和湿润度指标将研究区域划分为4种潜在植被类型，即微温干旱温带半荒漠类、微温微干温带典型草原类、微温微润草甸草原类和微温湿润森林草原类，然后对每一种潜在植被类型的草地生物量分析其内在影响因素，研究结果发现，微温干旱温带半荒漠类的草地生物量与年积温存在较好的线性关系，微温微干温带典型草原类的草地生物量可以用表层土壤粘粒含量的二次多项式来模拟，后两种潜在植被类型的草地生物量则随着潜在NPP的变化呈现先减小后增大的变化趋势。对4种潜在植被类型区域分别建立草地生物量与其影响因素之间的回归关系确定研究区域草地生物量的趋势面，结合HASM模型实现研究区域草地生物量的高精度模拟，结果显示上述4种潜在植被类型区的草地平均生物量分别为76.62、110.94 、142.69 、184.40 g/m<sup>2</sup>。
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高精度曲面建模(HASM)可以显著提高空间曲面模拟的精度,但是计算速度低限制了该模型的进一步应用。为了提高HASM模型的计算效率,本文对HASM-AD算法作了改进,通过在计算过程中为采样点添加索引,避免了计算过程中对采样点信息的重复查找操作;同时,在遍历独立计算单元时实时计算第一类、第二类基本量及克式符号,避免了全局存储上述变量所需要的额外内存消耗。数值试验表明,由于将全局线性方程组求解问题转化为局部独立计算单元(5×5栅格)内的方程组求解,改进的HASM-AD算法显著提高了计算效率,同时降低了模型运行过程中的内存消耗。最后,本文以全国陆地降水空间分布模拟分析作为实例,验证改进的HASM-AD算法模拟精度及计算效率,模拟结果表明,改进的HASM-AD算法模拟结果精度优于其他HASM算法(以HASM-PCG为例),并且计算效率优势更为明显,实现全国10km分辨率的降水分布模拟耗时仅为4s。表明改进的HASM-AD算法提高了计算速度,并且适于大尺度的空间变量模拟应用。
Application analysis of the improved HASM-AD in the spatial variable simulation [J].https://doi.org/10.3724/SP.J.1047.2013.00655 URL Magsci [本文引用: 2] 摘要
高精度曲面建模(HASM)可以显著提高空间曲面模拟的精度,但是计算速度低限制了该模型的进一步应用。为了提高HASM模型的计算效率,本文对HASM-AD算法作了改进,通过在计算过程中为采样点添加索引,避免了计算过程中对采样点信息的重复查找操作;同时,在遍历独立计算单元时实时计算第一类、第二类基本量及克式符号,避免了全局存储上述变量所需要的额外内存消耗。数值试验表明,由于将全局线性方程组求解问题转化为局部独立计算单元(5×5栅格)内的方程组求解,改进的HASM-AD算法显著提高了计算效率,同时降低了模型运行过程中的内存消耗。最后,本文以全国陆地降水空间分布模拟分析作为实例,验证改进的HASM-AD算法模拟精度及计算效率,模拟结果表明,改进的HASM-AD算法模拟结果精度优于其他HASM算法(以HASM-PCG为例),并且计算效率优势更为明显,实现全国10km分辨率的降水分布模拟耗时仅为4s。表明改进的HASM-AD算法提高了计算速度,并且适于大尺度的空间变量模拟应用。
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高精度曲面建模优化方案 [J].https://doi.org/10.11834/jig.20140215 URL Magsci [本文引用: 1] 摘要
<b>目的 </b>为了进一步提高高精度曲面建模（HASM）方法的模拟精度和计算速度，进而拓宽该模型的应用领域，提出了新的HASM模型算法。<b>方法 </b> 采用新的差分格式计算HASM高斯方程中的一阶偏导数，以HASM预处理共轭梯度算法为例分析改进的差分格式对HASM的优化效果。<b>结果 </b> 数值实验表明：在计算耗时及内存需求不变的情况下，采用新的差分格式的HASM算法可以显著提高单次迭代的模拟精度，同时能够降低关键采样点缺失对模拟结果精度的影响。进一步研究发现，当HASM采用新差分格式与原始差分格式（中心差分）交替迭代时，能够快速降低模拟结果的误差。<b>结论 </b> 本文算法当达到指定的精度条时能够显著减小计算耗时，同时还能降低关键采样点缺失对模拟结果的影响。
HASM optimization based on the improved difference scheme [J].https://doi.org/10.11834/jig.20140215 URL Magsci [本文引用: 1] 摘要
<b>目的 </b>为了进一步提高高精度曲面建模（HASM）方法的模拟精度和计算速度，进而拓宽该模型的应用领域，提出了新的HASM模型算法。<b>方法 </b> 采用新的差分格式计算HASM高斯方程中的一阶偏导数，以HASM预处理共轭梯度算法为例分析改进的差分格式对HASM的优化效果。<b>结果 </b> 数值实验表明：在计算耗时及内存需求不变的情况下，采用新的差分格式的HASM算法可以显著提高单次迭代的模拟精度，同时能够降低关键采样点缺失对模拟结果精度的影响。进一步研究发现，当HASM采用新差分格式与原始差分格式（中心差分）交替迭代时，能够快速降低模拟结果的误差。<b>结论 </b> 本文算法当达到指定的精度条时能够显著减小计算耗时，同时还能降低关键采样点缺失对模拟结果的影响。
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| [11] |
高精度曲面建模的一种快速算法 [J].https://doi.org/10.3724/SP.J.1047.2012.00281 URL Magsci [本文引用: 2] 摘要
高精度曲面建模(HASM)是一种全新的曲面建模方法,其整个过程可分为偏微分方程的离散、采样方程建立和代数方程组求解3个阶段。目前所采用的求解对称正定方程组的方法主要是共轭梯度法。为了解决HASM的计算速度问题,本文给出了2种新的预处理共轭梯度算法,分别为不完全Cholesky分解共轭梯度法和对称逐步超松弛预处理共轭梯度法。实验表明,不完全Cholesky分解共轭梯度法收敛速度最快,且这2种预处理方法均比其他方法具有更快的收敛速度。
Fast methods for high accuracy surface moldeling [J].https://doi.org/10.3724/SP.J.1047.2012.00281 URL Magsci [本文引用: 2] 摘要
高精度曲面建模(HASM)是一种全新的曲面建模方法,其整个过程可分为偏微分方程的离散、采样方程建立和代数方程组求解3个阶段。目前所采用的求解对称正定方程组的方法主要是共轭梯度法。为了解决HASM的计算速度问题,本文给出了2种新的预处理共轭梯度算法,分别为不完全Cholesky分解共轭梯度法和对称逐步超松弛预处理共轭梯度法。实验表明,不完全Cholesky分解共轭梯度法收敛速度最快,且这2种预处理方法均比其他方法具有更快的收敛速度。
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| [12] |
1951-2010年中国季平均降水高精度曲面建模分析 [J].https://doi.org/10.11820/dlkxjz.2013.01.005 URL Magsci [本文引用: 1] 摘要
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。
Surface modeling of seasonal mean precipitation in China during 1951-2010 [J].https://doi.org/10.11820/dlkxjz.2013.01.005 URL Magsci [本文引用: 1] 摘要
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。
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基于改进的HASM方法的中国日照百分率的模拟研究 [J].https://doi.org/10.11821/dlyj201407010 URL Magsci [本文引用: 2] 摘要
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。
Surface modeling of sunshine percentage in China based on a modified version of HASM [J].https://doi.org/10.11821/dlyj201407010 URL Magsci [本文引用: 2] 摘要
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。
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| [14] |
Surface modeling of DEMs based on a sequential adjustment method [J].https://doi.org/10.1080/13658816.2012.704037 URL [本文引用: 2] 摘要
surface modeling; DEM; interpolation; accuracy; digital elevation models; artificial neural-networks; high-speed method; high-accuracy; spatial interpolation; density; construction; uncertainty; generation; rainfall
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| [15] |
A method of DEM construction and related error analysis [J].https://doi.org/10.1016/j.cageo.2009.12.001 URL 摘要
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.
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| [16] |
The smoothness of HASM [J].https://doi.org/10.1080/13658816.2013.787146 URL [本文引用: 2] 摘要
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鈥揹erived images and DEMs.
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| [17] |
A high speed method of SMTS [J].https://doi.org/10.1016/j.cageo.2011.08.012 URL [本文引用: 1] 摘要
In order to improve the computational speed of the method of surface modeling based on the theorem of surfaces (SMTS), a modified Gauss鈥揝eidel (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.
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An integrated system of terrain analysis and slope mapping [J]. |
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Spatial interpolation of monthly mean climate data for China [J].https://doi.org/10.1002/joc.1187 URL 摘要
Spline interpolation techniques are used to develop a gridded climate database for China at a resolution of 0.01掳 in latitude and longitude. A digital elevation model (DEM) was developed at the same resolution to improve the accuracy of interpolation based upon the general spatial dependence of climate on topography. Climate data for the period 1971-2000 from meteorological stations in China were used to develop thin-plate smoothing spline surfaces for monthly mean temperature and precipitation. A regularly gridded climate database was produced by coupling the spline surfaces with the underlying DEM. The summary statistics show interpolation errors for monthly temperatures varying within 0.42-0.83 掳C and 8-13% for monthly precipitation. These estimates are superior to results produced by methods commonly used in China. The fine-resolution spatial climate database has many potential applications in natural resource management. For example, it can be used as a baseline for climate change studies, in which potential distributions of flora and fauna can be predicted under the impact of climate change and priority areas for biodiversity conservation can be identified.
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Improving quality of public domain digital elevation models through data fusion [J].https://doi.org/10.1016/j.biosystemseng.2008.09.010 URL [本文引用: 1] 摘要
Digital Elevation Model (DEM) fusion was investigated for improving the overall accuracy of DEMs.: Shuttle Radar Topographic Mission (SRTM) DEM and Advanced Spaceborne Thermal Emission and Reflection (ASTER) DEM. The ASTER relative DEM was co-registered to the SRTM co-ordinates and converted to an absolute DEM by shifting the histogram to the average elevation of the SRTM DEM. The voids in the DEMs were filled through an technique using the slope and aspect from the other DEM and the elevation of surrounding pixels. Finally, the DEMs were converted to the frequency domain and an ideal low-pass filter with a cut-off frequency of 0.024 m-1 was applied to the ASTER DEM and a high-pass filter with the same cut-off frequency was applied to the SRTM DEM to filter out errors in the respective frequency ranges. The filtered DEM spectra were then summed in the frequency domain before being converted back to the spatial domain. This approach was tested in a 6000 ha test site with fairly complex topography located in the central region of Nepal. The fused DEM had a 42% improvement in Root Mean Squared Error (RMSE). The approach showed promise for improving DEM accuracy and completeness while maintaining the highest resolution of the input DEMs. This approach increased the reliability and applicability of public domain DEMs produced by Optical and Radar remote sensing technologies.
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F-approximation of the earth’s surface topography [J].https://doi.org/10.1134/S1069351309080114 URL [本文引用: 1] 摘要
At the present time, the development and implementation of the new methods of describing the relief (topography) of the Earthís surface is a highly urgent task. It is referred to the construction of the substantially more powerful and more flexible methods of the analytical description of the topography of the Earthís surface: such linear analytical approximations, which are constructed according to the data on the heights of points on the Earthís surface on a sufficiently large set of points in the territory with a sufficiently large area, and which are used for this entire area for the solution of a large set of problems of geodesy, geomorphology and geophysics (in particular, for calculation of the values of topographic corrections in the observed gravity forces). Earlier, on the basis of the method of linear integral representations of V.N. Strakhov, the general theoretical concepts of the F-approximation of the relief of the Earthís surface were developed in the rectangular and spherical coordinates [Strakhov et al., 1999]. In the present paper the special features of the F-approximation of the relief of the Earthís surface are considered in more detail for the relatively small territories, i.e., with the use of the rectangular coordinates, the obtained analytical expressions, and, also, the results of validation on the model and the real topographic materials are presented..
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Filling the voids in the SRTM elevation model: A TIN-based delta surface approach [J].https://doi.org/10.1016/j.isprsjprs.2007.05.004 URL Magsci [本文引用: 1] 摘要
<h2 class="secHeading" id="section_abstract">Abstract</h2><p id="">The Digital Elevation Model (DEM) derived from NASA's Shuttle Radar Topography Mission is the most accurate near-global elevation model that is publicly available. However, it contains many data voids, mostly in mountainous terrain. This problem is particularly severe in the rugged Oman Mountains. This study presents a method to fill these voids using a fill surface derived from Russian military maps. For this we developed a new method, which is based on Triangular Irregular Networks (TINs). For each void, we extracted points around the edge of the void from the SRTM DEM and the fill surface. TINs were calculated from these points and converted to a base surface for each dataset. The fill base surface was subtracted from the fill surface, and the result added to the SRTM base surface. The fill surface could then seamlessly be merged with the SRTM DEM. For validation, we compared the resulting DEM to the original SRTM surface, to the fill DEM and to a surface calculated by the International Center for Tropical Agriculture (CIAT) from the SRTM data. We calculated the differences between measured GPS positions and the respective surfaces for 187,500 points throughout the mountain range (ΔGPS). Comparison of the means and standard deviations of these values showed that for the void areas, the fill surface was most accurate, with a standard deviation of the ΔGPS from the mean ΔGPS of 69 m, and only little accuracy was lost by merging it to the SRTM surface (standard deviation of 76 m). The CIAT model was much less accurate in these areas (standard deviation of 128 m).</p><p id="">The results show that our method is capable of transferring the relative vertical accuracy of a fill surface to the void areas in the SRTM model, without introducing uncertainties about the absolute elevation of the fill surface. It is well suited for datasets with varying altitude biases, which is a common problem of older topographic information.</p>
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Resolution enhancement of ASTER digital elevation model [C]// |
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Image acquisition geometry analysis for the fusion of optical and radar remote sensing data [J].https://doi.org/10.1080/19479832.2010.484152 URL [本文引用: 1] 摘要
Fusion of optical and radar remote sensing data is becoming an actual topic of discussion recently in various application areas though the results are not always satisfactory. In this article, we analyse some disturbing aspects of fusing orthoimages from sensors having different acquisition geometries. These aspects arise due to errors in digital elevation models (DEM), used for image orthorectification, and the existence of 3-D objects in the scene which are not accounted in the DEM. We analyse how these effects influence the ground displacement in orthoimages produced from optical and radar data. Further, we propose sensor formations with acquisition geometry parameters which allow to minimise or compensate for ground displacements in different orthoimages due to the above-mentioned effects and to produce good prerequisites for the following fusion for specific application areas, e.g. matching, filling data gaps, classification, etc. To demonstrate the potential of the proposed approach, two pairs of op...
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Fusion of digital elevation models using sparse representations [M] |
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An evaluation of void filling interpolation methods for SRTM data [J].https://doi.org/10.1080/13658810601169899 URL [本文引用: 1] 摘要
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聽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.
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Error detection and DEM fusion using self-consistency [C]// |
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Surface modelling of soil pH [J].https://doi.org/10.1016/j.geoderma.2009.01.020 URL [本文引用: 2] 摘要
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.
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| [29] |
Surface modelling of soil properties based on land use information [J].https://doi.org/10.1016/j.geoderma.2011.03.007 [本文引用: 2] 摘要
High accuracy surface modelling (HASM) is a spatial interpolation technique based on the fundamental theorem of surfaces. This study proposed a modified HASM method based on the incorporation of ancillary land use information (HASM_LU) for improved interpolation of soil properties. To assess its feasibility, a total of 150 samples were collected in different land use types (woodlands, croplands and grasslands) of a typical red soil region in the middle part of Jiangxi Province, China. Observations on soil pH, alkali-hydrolyzable N (AN), total C, N, K, Al, Ca, Mg and Zn were interpolated. To evaluate the performance of HASM_LU, it was compared with four other interpolators: HASM, ordinary kriging with land use information (OK_LU), stratified kriging (SK) and regression-kriging using a generalized linear model (RK_GLM). To do so, predicted and measured values were compared using the mean error (ME), mean absolute error (MAE), root mean square error (RMSE) and prediction efficiency (PE). The results have shown that HASM_LU generally performs better than HASM, OK_LU, SK and RK_GLM with a lower estimation bias, MAE and RMSE as well as greater PE. In particular, the RMSE of HASM_LU for AN was smaller than that of HASM by 33.4%; that of OK_LU, 1.6%; that of SK, 41.5%; and that of RK_GLM, 67.6%. The largest difference in PE occurred when comparing HASM_LU with HASM for N (57.95%), with OK_LU (7.18%) for K, with SK (125.16%) for Zn and with RK_GLM (100.21%) for AN. The HASM_LU maps of soil properties present more details and more accurate spatial patterns. The good performance of HASM_LU can be attributed to the adequate surface modelling ability of HASM, combined with incorporation of information on abrupt spatial boundaries introduced by land use.
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| [30] |
Development of a surface modeling method for mapping soil properties [J].https://doi.org/10.1007/s11442-012-0960-z Magsci 摘要
Abstract<br/><p class="a-plus-plus">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 variation 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 simulation 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 application in resource management and environment planning.</p><br/>
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Multiscale fusion of InSAR data for hydrological applications [C]// |
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Differential geometry: A first course [M]. |
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A comprehensive introduction to differential geometry [M]. |
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Differential geometry of curves and surfaces: A concise guide [M]. |
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Change trend of monthly precipitation in China with an improved surface modeling method [J].https://doi.org/10.1007/s12665-014-4012-0 URL [本文引用: 1] 摘要
In this paper, a combination of a novel interpolation method and a local regression method was employed to improve the estimation accuracy of monthly precipitation over China. After the normalized processing and Box-Cox transformation of the data, we used the geographically weighted regression (GWR) method to describe the spatial precipitation trend, and then interpolated the residual by using a modified high accuracy surface modeling method (HASM-PRE). A high quality database of monthly precipitation with a resolution of 1聽km 2 was constructed based on the meteorological stations. Results showed that wet years and dry years appear alternatively, and trend analysis of precipitation data series from 1981 to 2010 showed that the probability of years with extreme precipitation has increased in recent years. Precipitation in winter is rather uncertain and more dynamic from year to year compared to precipitation in summer.
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| [36] |
Improving the accuracy of the height-diameter equation using the classified factors method [J].https://doi.org/10.1007/s12665-015-4168-2 URL 摘要
The height–diameter relationship model is crucial in the estimation of forest stand volume, biomass and carbon storage, etc. To improve prediction accuracy, the classified factors method for height–diameter relationship modeling was developed based on the classified height method. The data set contained 959 tree samples obtained from 28 plots measured by topographic factors (aspect, slope position and altitude). The Chapman–Richards equation was used to build models. Classification methods have improved fitting performance and prediction accuracy compared to the classical method. The classified height method has the best fitting performance because it has the highest determination coefficient ( R 2 02=020.927) and the lowest root mean square error (RMSE02=021.548), whereas the classified factors method has the highest prediction accuracy because it has the lowest mean absolute error (MAE02=021.137) and mean relative error (MRE02=020.109).
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| [37] |
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| [38] |
An adaptive method of high accuracy surface modeling and its application to simulating elevation surfaces [J].https://doi.org/10.1111/j.1467-9671.2010.01213.x URL [本文引用: 2] 摘要
中国科学院机构知识库(中国科学院机构知识库网格（CAS IR GRID）)以发展机构知识能力和知识管理能力为目标，快速实现对本机构知识资产的收集、长期保存、合理传播利用，积极建设对知识内容进行捕获、转化、传播、利用和审计的能力，逐步建设包括知识内容分析、关系分析和能力审计在内的知识服务能力，开展综合知识管理。
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| [39] |
A high-accuracy method for filling SRTM voids and its verification [J].https://doi.org/10.1080/01431161.2011.621465 URL [本文引用: 2] 摘要
ABSTRACT A new method for filling voids is developed by improving the approach to high- accuracy surface modelling (HASM), which is based on the first fundamental coefficients and the second fundamental coefficients of surfaces. The first fundamental coefficients are used to calculate the lengths of curves, angles of tangent vectors, areas of regions and geodesics on the surface. The second fundamental coefficients reflect the local warping of the surface, namely its deviation from the tangent plane at the point under consideration, which can be observed from outside the Earth. Nine regions with different landform complexities in hilly, plateau and mountainous areas are selected for testing the performance of HASM by comparing those ones of the classic methods such as triangulated irregular network (TIN), inverse distance weighted interpolation (IDW), advanced Spline method (ANUDEM), Spline and Kriging. The results demonstrated that the HASM void filling always has the highest accuracy regardless of the landform complexity, void area and auxiliary data.
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| [40] |
A curve-theorem based approach for change detection and its application to Yellow River Delta [J].https://doi.org/10.1080/01431160110106041 URL [本文引用: 2] 摘要
A curve-theorem based approach is proposed and is used to handle NDVI data. The curve-theorem based approach includes a general index and two nonlinear transformations and . It is applied to Landsat MSS images of the Yellow River Delta, taken on 1 December, 1976 and 3 December, 1988. Results show that can describe the general situation of vegetation cover change in the Yellow River Delta and is sensitive to environmental change in rivers and sea, while is sensitive to environmental change in industrial and urban areas.
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| [41] |
A new method of surface modeling and its application to DEM construction [J].https://doi.org/10.1016/j.geomorph.2007.02.006 URL 摘要
A new method of surface modelling based on the fundamental theorem of surfaces (SMTS) is presented. Eight different test surfaces are employed to comparatively analyze the simulation errors of SMTS and the classical methods of surface modeling in GIS, including TLI (triangulated irregular network with linear interpolation), SPLINE, IDW (inverse distance weighted) and KRIGING. Numerical tests show that SMTS is much more accurate than the classical methods. SMTS theoretically gives a solution to the error problem that has long troubled DEM construction. As a real-world example, SMTS is used to construct a DEM of the Da-Fo-Si coal mine in Shaan-Xi Province, China. Its root mean square error (RMSE) is compared with those of DEMs constructed by the four classical methods. The results show that although SMTS also has a higher accuracy in the real-world example, the improvement of accuracy is less distinct than that expected from the numerical tests. The accuracy loss seems to be caused by location differences between sampling points and the central points of lattices of the simulated surfaces. Two alternative ways are proposed to solve this problem.
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| [42] |
Adjustment computation of HASM: A high-accuracy and high-speed method [J].https://doi.org/10.1080/13658810903569580 URL [本文引用: 2] 摘要
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 0.402km02×020.502km 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 600002×026000 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.
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| [43] |
A high-accuracy method for filling voids on remotely sensed XCO2 surfaces and its verification [J].https://doi.org/10.1016/j.jclepro.2014.08.080 URL [本文引用: 2] 摘要
The method for high accuracy surface modeling (HASM), inverse distance weighting (IDW) and ordinary Kriging (OK) are used to fill voids on XCO 2 surfaces of GOSAT and SCIAMACHY. Inner voids and boundary voids are artificially made by cleaning out the downloaded data, where there are no voids, in different latitude belts of the northern hemisphere and the southern hemisphere at random. The cleaned-out data in the artificial voids are selected as the ‘true’ values for verification. The results demonstrated that HASM always has the highest accuracy compared with the classical methods of IDW and OK, whether voids are inner ones or boundary ones, data sets are from GOSAT or from SCIAMACHY, and the void areas are larger or smaller. HASM is an alternative approach to filling voids on XCO 2 surfaces from the satellites.
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| [44] |
A multi-grid method of high accuracy surface modeling and its validation [J].https://doi.org/10.1111/tgis.12019 URL [本文引用: 2] 摘要
Abstract A method of high accuracy surface modeling (HASM) has been constructed to find a solution for error problems that had long troubled surface modeling in geographical information systems (GIS). It is found that when a preconditioned conjugate gradient (PCG) algorithm is used to solve the large sparse linear system, which HASM can be transferred into, HASM performs best in terms of simulation compared with all other algorithms. But its computing speed is not fast enough for all applications. A multi-grid method is introduced into HASM to try to shorten its computing time. Both numerical and real-world tests demonstrate that there is a range of stop error (SE). The multi-grid method of HASM (HASM-MG) greatly increases computing speed when SEs are within this range, compared with the PCG algorithm of HASM (HASM-PCG). HASM-MG is suitable for applications with a need for less accuracy and a shorter computing time. HASM-PCG is appropriate for issues needing higher accuracy. HASM-MG performs better than HASM-PCG in flat areas, while HASM-PCG does better in complex terrainm in terms of accuracy and computing time.
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| [45] |
Climate change trend in China, with improved accuracy [J].https://doi.org/10.1007/s10584-013-0785-5 URL Magsci [本文引用: 1] 摘要
We have found that a spatial interpolation of mean annual temperature (MAT) in China can be accomplished using a global ordinary least squares regression model since the relationship between temperature and its environmental determinants is constant. Therefore the estimation of MAT does not very across space and thus exhibits spatial stationarity. The interpolation of mean annual precipitation (MAP), however, is more complex and changes spatially as a function of topographic variation. Therefore, MAP shows spatial non-stationarity and must be estimated with a geographically weighted regression. A statistical transfer function (STF) of MAT was formulated using minimized residuals output from a high accuracy and high speed method for surface modeling (HASM) with an ordinary least squares (OLS) linear equation that uses latitude and elevation as independent variables, abbreviated as HASM-OLS. The STF of MAP under a BOX-COX transformation is derived as a combination of minimized residuals output by HASM with a geographically weighted regression (GWR) using latitude, longitude, elevation, impact coefficient of aspect and sky view factor as independent variables, abbreviated as HASM-GWR-BC. In terms of HASM-OLS and HASM-GWR-BC, MAT had an increasing trend since the 1960s in China, with an especially accelerated increasing trend since 1980. Overall, our data show that MAT has increased by 1.44 A degrees C since the 1960s. The warming rates increase from the south to north in China, except in the Qinghai-Xizang plateau. Specifically, the 2,100 A degrees C A center dot d contour line of annual accumulated temperature (AAT) of a parts per thousand yen10 A degrees C shifted northwestward 255 km in the Heilongjiang province since the 1960s. MAP in Qinghai-Xizang plateau and in arid region had a continuously increasing trend. In the other 7 regions of China, MAP shows both increasing and decreasing trends. On average, China became wetter from the 1960s to the 1990s, but drier from the 1990s to 2000s. The Qinghai-Xizang Plateau and Northern China experienced more climatic extremes than Southern China since the 1960s.
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| [46] |
Combining LPJ-GUESS and HASM to simulate the spatial distribution of forest vegetation carbon stock in China [J].https://doi.org/10.1007/s11442-014-1086-2 URL [本文引用: 1] 摘要
<p>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 manifests that the carbon storage of the two regions do increase clearly. The results of this research show that the large-scale reforestation in the last decades in China attains a significant carbon sink.</p>
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| [47] |
Parallel algorithm of a modified surface modeling method and its application in digital elevation model construction [J].https://doi.org/10.1007/s12665-015-4177-1 URL [本文引用: 2] 摘要
High accuracy surface modeling (HASM) has been proved to be a superior method for surface simulation compared to classical interpolation methods. However, the fact that HASM is time consuming combined with its dependence on its driving field restricts its application in large area problems. This research develops a modified HASM which can get rid of the driving field in the surface simulation, and the parallel version of the modified HASM is also proposed with the purpose of improving its computational efficiency. Light detection and ranging (LIDAR) data are used as an optimum constraint to construct digital elevation model (DEM). Tests show that the modified HASM can perform surface simulation successfully without the driving field. And it also shows that the simulation accuracy of the modified HASM is almost the same as the old HASM and the classical interpolation methods when the sampling rate is larger than 0.5 %, while the modified HASM shows significantly increased simulation accuracy as the sampling rate decreases. This characteristic indicates that the modified HASM no longer relies on the driving field in the surface simulation. And it also improves the simulation accuracy compared to the old HASM and the classical interpolation methods. Tests of parallel efficiency show that the master-slave mode used in the parallel algorithm obtains a satisfactory result, indicating that the HASM can be applied to surface simulation of large area problems. And it also shows that the modified HASM would have great potential where applied in high-resolution DEM and digital surface model (DSM) construction from LIDAR data.
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| [48] |
A modification of HASM for interpolating precipitation in China [J].https://doi.org/10.1007/s00704-013-0952-7 URL 摘要
Based on the spatial distribution of precipitation in China, this study gives a modification of High Accuracy Surface Modeling (HASM) method for improving interpolation of precipitation. To assess the feasibility of this modified model, namely, HASM-PRE, we use precipitation data measured at 712 stations for the period 1951鈥2010, using 605 stations for function development and reserving 107 for validation tests. The performance of HASM-PRE is compared with those of HASM and other classical methods: kriging, inverse distance weighted (IDW) method and spline. Results show that HASM-PRE has less root mean square error (RMSE) and mean absolute error (MAE) than the other techniques tested in this study. The precipitation map obtained from HASM-PRE is better than that obtained using other methods. Therefore, HASM-PRE can be seen as an alternative to the popular interpolation techniques, particularly if we focus on simulation accuracy. In addition, the effective way to combine the strengths of both human expert and differential geometry in this study can be applied for calculating precipitation for other areas in other temporal scales. For better improvement, HASM-PRE can be combined with ancillary variables and implemented in parallel environments.
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| [49] |
An improved version of a high accuracy surface modeling method [J].https://doi.org/10.1007/s13137-013-0051-z URL [本文引用: 1] 摘要
A method of surface modeling, high accuracy surface modeling (HASM), which is based on the fundamental theorem of surface theory, is modified. The earlier version of HASM is theoretically incomplete a
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| [50] |
Sensitivity studies of a high accuracy surface modeling method [J].https://doi.org/10.1007/s11430-014-4926-0 URL 摘要
The sensitivities of the initial value and the sampling information to the accuracy of a high accuracy surface modeling (HASM) are investigated and the implementations of this new modeling method are modified and enhanced. Based on the fundamental theorem of surface theory, HASM is developed to correct the error produced in geographical information system and ecological modeling process. However, the earlier version of HASM is theoretically incomplete and its initial value must be produced by other surface modeling methods, such as spline, which limit its promotion. In other words, we must use other interpolators to drive HASM. According to the fundamental theorem of surface theory, we modify HASM, namely HASM.MOD, by adding another important nonlinear equation to make it independent of other methods and, at the same time, have a complete and solid theory foundation. Two mathematic surfaces and monthly mean temperature of 1951-2010 are used to validate the effectiveness of the new method. Experiments show that the modified version of HASM is insensitive to the selection of initial value which is particular important for HASM. We analyze the sensitivities of sampling error and sampling ratio to the simulation accuracy of HASM.MOD. It is found that sampling information plays an important role in the simulation accuracy of HASM.MOD. Another feature of the modified version of HASM is that it is theoretically perfect as it considers the third equation of the surface theory which reflects the local warping of the surface. The modified HASM may be useful with a wide range of spatial interpolation as it would no longer rely on other interpolation methods.
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