The Spatio-temporal Unified Expression Of Xinanjiang Watershed Model Based On Clifford Algebra

Multidimensional unified GIS platform which is based on geometric algebra broke the limitations in analysis of dynamic models in the existing GIS.It can express and simulate spatial-temporal process of geographic phenomena. Hydrological model simulate the reallocation of rainfall in time and space, which has significant spatial and temporal variations is compatible with Euler and Lagrange sports concept. The spatial-temporal unified data model based on geometric algebra can express and compute multi-dimensional geometric objects and geographic processes spatial-temporal unified way. It can express hydrological processes with complex spatial-temporal variation. To analysis the spatial-temporal elements in the Xinanjiang Watershed Model and then express them in spatial-temporal unified ways is an important way to achive seamless integration of GIS and hydrological model.Taking the Xinanjiang Watershed Model for the prototype, the author explored the main space-time elements and their expression in the model,and classified the temporal and spatial elements according to their continuous and discrete characteristics. And analyzed the expression and transformation of the spatial and temporal elements when the model is running, taking advantage of the space-time Clifford algebra unified expression, finally established the basic framework of expression and analysis of hydrological model under the framework of the unified space-time. The main research contents and innovation are as follows:(1) Summarized the processing method of space and time in the four-level’s calculation of the model,and analyzed the parameters and elements of their semantic relationships in the Xinanjiang Watershed Model. And expressed changes in the elements of time and space in the Xinanjiang Watershed Model from two perspectives:the spatial and temporal distribution of rainfall, evaporation process, runoff process and surface to the point calculation of the convergence process.(2) Based on the space-time unified expression framework of geometric algebra, the author expressed the space-time elements of the rainfall, evaporation, runoff, and convergence process of the Xinanjiang Watershed Model in a space-time unified way. And transformed the expression of rainfall, evaporation process into the construction and calculation of the four-dimensional space-time body object in the Minkowski space-time which is composed of e1, e2, e3, e4. (3) Expressed rainfall process based on the Voronoi interpolation of geometric algebra relying on the space discrete system of rainfall in existing Xinanjiang Watershed Model. And established the outer product of the expression of precipitation process using existing empirical parameter.(4) Constructed the continuous hydrological processe expression based on Clifford integral for the elimination of inconsistencies of space and time caused by the Voronoi interpolation, and proved the consistency of the expression of discrete expression in the expression and calculation.(5) Based on the Realization of a space-time unified expression and calculation of the the rainfall, evaporation and runoff process and their coupled characteristics. The author completed the calculation of the total flow process in the drainage outlet after the surface to point calculation of the slope flow process.In the model of this article, precipitation, evaporation process is the input of the model, runoff and convergence process is also similar to the four-dimensional space-time body, their sizes of the volume and change can characterize the evolution of the elements in different space-time point. Thus making the calculation simplicity and relative independent. The establishment of the hydrological model based on the the space-time unified expression of Clifford algebra, expressed the element of basin space and hydrological processes in space-time unified spatial and temporal way on the level of generalization of space and time. Taking into account of hydrological processes under the the influence of variety of factors, It can express and calculate the hydrological processes of space-time continuum distribution in a more intuitional and accurate way.