Abstract: According to the two sources of errors in NWP,two kinds of inverse problems are put forward,then some numerical expriments of ideal fields are performed on these two inverse problems using a nonlinear advective-diffusion equation and its adjoint equation.The result shows that this method for solving the inverse problems is fairly effective.It can determine the initial spatial state of meteorological elements (or the error corrective term of model equation) through the time-varition information involved in the observational data.This method can be used to obtain significant results whether the observation is over-determined or underdetermined.