Abstract:A conceivable BIcubic Numerical Model(BINM) is studied,which is used to fit the cubic curve function(spline) and the Coons Bicubic Surface.It is like fitting the three-dimension curved surface with a set of bicubic surface patches at the horizontal and vertical directions,on which many atmospheric physical quantity fields are all cubic continuous.So BINM is a new numerical model used to fit n bicubic surfaces in the mathematic R~n-space and the n squares of atmospheric quantity fields in the atmosphere,getting their all cubic continuous fields with their derivative,square derivative quotients.One of BINM's main mathematical characteristics is that the special differential quotients of the basic system of equations have their analytical solutions for the atmospheric kinematics,if the synoptic systems can be embodied by the "bicubic surface" of mathematics.Different from the finite-difference(linear) model and the truncated spectral model,which have their special and wave-number truncation error correspondingly,BINM has its special fitting error only. A computing case is given with a linear advection equation on the spherical coordinates,which is an air pressure field at sea level in a limited area,and got successfully its 6 hour forecast field with a time step of 12 seconds(1800 steps).So, it is concluded that BINM's mathematical truss can adapt to the physical packages of the atmosphere;BINM may be the third kind of meteorological numerical forecast model and may be superior to our linear model and spectral model.
