A Trial to Reduce Truncation Errors of the Pressure Gradient Force in the Sigma Coordinate Systems

[摘要] Large truncation errors are frequently found in the calculation of the pressure gradient force in the sigma coordinate systems for the domain with steep slopes. It is pointed out that the errors result from the use of hydrostatic equation in the calculation of pressure gradient force. Thus we propose the use of not the first order but the higher order approximation of the geopotential height in the calculation of the pressure gradient force. We adopt here a polynomial function of log p to represent the geopotential height Φ on each pressure level. The pressure gradient force between the two adjacent grid points i and i+ 1 is represented as the difference between the two geopotentials Φi and Φi+1 which are given by the polynomial functions on the same pressure level. It is found that the errors in the calculation of the pressure gradient force by this method are considerably smaller than that shown by previous workers.

[学科分类] 大气科学