地理研究 ›› 2020, Vol. 39 ›› Issue (11): 2607-2625.doi: 10.11821/dlyj020190794

• 论文 • 上一篇    下一篇

基于线性GSI二维半变异函数各向异性结构建模及估计研究——以DEM数据为例

高歆   

  1. 许昌学院城市与环境学院,许昌 461000
  • 收稿日期:2019-09-12 修回日期:2020-03-11 出版日期:2020-11-20 发布日期:2021-01-19
  • 基金资助:
    河南省高校人文社会科学研究一般项目(2021-ZDJH-0340);河南省高校人文社会科学研究一般项目(2020-ZZJH-426);辽宁省自然科学基金(2019-MS-342);河南省科技攻关项目(182102310924);河南省高等学校重点科研项目(21A170019)

Anisotropic modeling and estimation for a two-dimensional semi-variogram based on the linear GSI Model: Taking DEM data as an example

GAO Xin   

  1. College of Urban and Environmental Sciences, Xuchang University, Xuchang 461000, Henan, China
  • Received:2019-09-12 Revised:2020-03-11 Online:2020-11-20 Published:2021-01-19

摘要:

鉴于传统各向异性二维半变异函数各向同性化方法未充分考虑或无力精确描述其内部结构信息的缺陷,本研究通过引入线性广义尺度不变(GSI)模型,以DEM数据作为验证对象,对二维半变异函数各向异性结构信息进行多尺度建模,并采用旋转椭圆法、两步搜索作图法等方法对系统参数进行估计,最后以球状模型为例对理论半变异函数的估计精度,及其在空间数据插值中的应用效果进行对比研究。结果表明:各向异性普遍存在于地形数据的空间变异中,有证据表明,这种各向异性结构中处处显现出不同的变形特征,但是也存在着某种规则性的成分,如各向同性圆形或近圆形等值线,因此,在对坐标进行各向同性化处理时不适合采用“一刀切”的方式去处理;GSI系统参数皆能得到较高精度的估计,如决定系数R2普遍达到了0.99以上,间接证明了GSI模型对地形数据各向异性结构处理的有效性和适用性;通过理论模型估计和插值结果对比,线性GSI坐标转换法比传统坐标转换法有了明显的精度提升,并且展现出了较高的边缘信息恢复能力,但也表现出了一定的局限性和不稳定性。

关键词: 广义尺度不变性, 半变异函数, 各向异性, 数字高程模型, 坐标转换

Abstract:

Anisotropy has been found to widely exist in the nature, and also regarded as one of the several essential attributes of geographical phenomena and processes. Therefore, it needs some complex models and methods to analyze and explain these phenomena, and deal with such problems as the optimization and interpolation for discrete monitoring points, or the uncertainty analysis by stochastic simulation over the space for some regional variables. The traditional treatment on an anisotropic modeling in kriging interpolation based on coordinate transformation does not fully consider or cannot accurately describe the internal structures of a two-dimensional anisotropic semi-variogram. Therefore, this study introduced a model named as linear generalized scale invariance (GSI) to simulate the anisotropic information of a 2D semi-variogram by using DEM as input data, while the system parameters were estimated by using the rotating ellipse and two-step search mapping method, and the comparisons of the two methods including GSI and traditional coordinate transformation applied in the fittings to the spherical model and the corresponding kriging interpolation were also made. The results firstly showed that anisotropy is common and ubiquitous in the spatial variability for topographic data, and the complexity is characterized by a change for an anisotropic ration when the corresponding scale changes, i.e. the different deformation behaviors over the whole semi-variogram maintained. However, some evidences showed that there are some regular features like an isotropic component existing in the anisotropic mechanism, such as a circular scale or circular contour. When facing such a complex structure, simple and rough treatment is obviously not enough. Secondly, the related parameters in GSI model can be estimated with high accuracy, such as the values of R2, which are all almost over 0.99 for the six regions. This indirectly proved that the validity and applicability of GSI model in the treatment to the anisotropic structure. In addition, for the fittings of the theoretical spherical model, the GSI model showed huge advantage over the traditional transformation and isotropic methods. Finally, as the enhanced effect originated from application of the GSI model in the interpolation processes, the coordinate transformation based on the linear GSI model had better improvement in accuracy than the traditional coordinate transformation, as well as a high ability of edge information recovery, although it exhibited some limitations and instability due to its complex covariance structure.

Key words: generalized scale invariance, semi-variogram, anisotropy, DEM, coordinate transformation