An Overall Optimization Model Of The Spherical Grid Based On The Optimal Transformation Theory

With the rapid development of computer technology and the continuous improvement of atmospheric science theory,the study about high-precision atmospheric numerical simulation has become one of the hotspots in global environmental change research.The spherical icosahedral grid provides a basic framework for the global atmospheric model research owing to the absence of grid aggregation or expansion.Nonetheless,the sphere which is a form of manifold makes the geometric features of grid,such as cell area and shape,deform to different degrees with the increasing subdivision level and have complex distribution,which affects the accuracy of atmospheric numerical simulation.In this case,optimizing and improving the grid quality has become one of the urgent problems to be solved to ensure the accuracy and stability of global atmospheric simulation and prediction.However,the most of the existing methods tend to optimize a certain index of the grid quality,such as the distance between two midpoints of spherical grid,the distance between grid center and mass center and so on,ignoring other geometric features of the grid,such as grid area,the edge length of grid and so on.Therefore,the optimal transformation theory is introduced to our method,and a model is proposed for the overall optimization of the spherical icosahedral grid.The specific process is as follows: firstly,the correlation of several quantitative indicators in the grid quality evaluation standard-“Goodchild criterion” is calculated,and the independent comprehensive evaluation factors of spherical grid quality are extracted.Then,the correlation between grid quality and numerical simulation accuracy is analyzed,and the influence weight of grid geometry characteristics on numerical simulation accuracy is determined.Finally,an overall optimization model of spherical icosahedral hexagonal grid is established based on the optimal transformation theory under the weights.The main work and achievements are as follows:(1)The comprehensive evaluation factors of spherical icosahedral hexagonal grid quality are extracted.Firstly,nine quantifiable indicators are selected from the“Goodchild criterion” to calculate a correlation coefficient matrix of these quantized results.Then,two comprehensive evaluation factors are extracted from the factor load matrix.These two factors have independent index connotation,which can not only completely cover the connotation of “Goodchild criterion”,but also reduce information overlap,and improve the reliability and credibility of grid quality evaluation.(2)The influence weights of grid geometric features on numerical simulation accuracy are quantified.Firstly,two representative indicators are selected from the comprehensive evaluation factors of grid quality.Then,the influence weights of these two indicators are calculated by the correlation coefficient between the quantitative indicators and the simulation error of the basic numerical model and their information entropy.It is a basis that is used to set the constraint conditions for the overall optimization of spherical grid.(3)The overall optimization model of spherical icosahedral grid is constructed.Firstly,the optimal transformation theory is introduced to design the core algorithm of grid area optimization.Then,the convergence condition of the grid optimization model is determined according to the influence weight of the grid geometric characteristics on the numerical simulation accuracy.Finally,an optimization result is obtained.Compared with other grids,the standard deviation of area,edge length and compactness of the optimized grid are reduced by at least 37 times,2.65 times and 1.58 times respectively,while the distance between two midpoints of spherical grid is preserved to the greatest extent.(4)A system of optimized global icosahedral hexagonal grid is designed.Firstly,a system is designed.Then,the accuracy and stability of the atmospheric numerical simulation with the proposed optimized grid are verified.Specifically,the average error and maximum error of the partial differential operator and the test model based on the optimized grid are all smaller than those of the comparison grids,and also the long-time simulation for the test is stable.It is expected to provide a kind of high-quality spherical grid for global atmospheric numerical simulation and guarantee the high precision and stability of simulation.