Characteristics Analysis And Motion Expression Of Temporal-Spatial Field Data Based On Geometric Algebra

In recent years, sensor networks and remote sensing technology are widely used, and the global observing system is gradually improved and perfected. Temporal-spatial field data play a more and more important role in the continuous expression of geographical phenomena. The traditional analysis of temporal-spatial field involves only the scalar field data such as digital elevation model (DEM), remote sensing image and so on, but pays less attention to the vector field data. In addition, most temporal-spatial field analyses apply only to regularly arranged data, but lack the processing and analysis capabilities of irregular and massive field data. This paper introduces the Geometric Algebra which can construct a unified framework for expression and computing of temporal-spatial field data of different dimensions and different types. And then, the structure and movement characteristics extracting algorithms of temporal-spatial field data are implemented in the perspective of integration of dimension. At last, the accuracy, validity and geographical interpretation of mentioned algorithms are discussed through the typical case studies.(1) This paper expresses the basic characterization parameters of temporal-spatial field data and their relationship uniformly based on Clifford algebra. (2)The different dimension temporal-spatial field data and their characterization parameters are expressed in a unified form. (3)Algorithms of consistent structure are constructed to achieving the unified extraction of the characterization parameters in scalar field, vector field and multivector field. (4)Finally, the temporal-spatial evolution parameters of field data are express in the multidimensional-fused perspective.The adaptive template matching algorithm unify the traditional forms of template convolution by the classification and template matching of the original data's structure and evolution features through uniformly expressing of Euclidean transformation based on Rotor operator. The analysis results of the slope of sea surface topography and surface fluctuation characteristics based on altimetry data show that the method can effectively extract the geological structure of temporal-spatial field data. Feature template matching algorithm based on Clifford FFT (Fast Fourier Transform) realizes the extraction of Geo-oriented temporal-spatial field feature. Take the global sea surface altimetry data for example, this paper construct a features template of ENSO warm tongue and apply it to template matching algorithm. It Implement with the result of some significant characterization parameters which reflect the impact of ENSO (El Nino and Southern Oscillation) on the spatial pattern of variability of global sea surface.Through the segmentation of time and space based on space-time algebra, the segmentation of observer-view-dependent perspective can be achieved. For the evolution of a given geographical phenomena, this paper construct a series of Lorenz transformation to get the internal structure characters of temporal-spatial field data from different perspectives. With the algorithm, movement characteristics and evolution parameters of geographical phenomena can be effectively extracted. Apply the algorithm to altimeter data, the temporal-spatial evolution process of sea-level change in equatorial Pacific Ocean is simulated, what's more, the extracted movement parameters and the MEI (Multivariate ENSO Index) have good correspondence.