A new adaptive grid technique is proposed, which can redistribute grid points according to the equivalence of area under the curve of the weight function. So the iteration in the traditional technique through a variational approach is unnecessary here, and the efficiency is improved greatly. The new technique is applied to Burgers equation with analytic solutions. The results show that different weight functions have different distribution of grid points, and variational weight functions with time have variational distribution of grid points. Because the new technique can redistribute more grid points in the high gradient solution regions in response to the numerical solution, it can capture the shock efficiently.

A two dimensional kinematic frontogenesis process is studied for examing the use of adaptive grids in numerical model. From the comparison of the numerical results using fixed and adaptive grids and those with exact solution, it is found the adaptive runs with 1/3 fewer grid points has the same accuracy, and it can catch the structure of front because of its excellent redistribution of grid points. The results also show the adaptive runs can increase more than 10 hours for the forecasting of extratropical cyclone with the same accuracy comparison to fixed grids. There is an optimum value for grid smoothness and the error increases as the grid orthogonality is considered.