A technique is presented as a means of treating problems in meteorology by numerical prediction on a fine scale. The method involves solution of numerical equations on a grid of data points in the usual way. Then, results from that forecast are used for the boundary conditions of a more dense but smaller-size grid network placed within the original one. Successively smaller grids are introduced so that the final grid size is as small as desired. Twenty-four hour forecasts have been made with a 2-level baroclinic model using a grid spacing reduced from 655 km to 327 km, to 163 km, and finally to 81 km. For an initial test, the method is applied to a developing cyclone just off the East Coast of the United States. During the 24-hr period of forecast, this cyclone developed from an incipient stage to a mature occluding system. The results of the numerical forecasts show that the method may be used successfully. Abstract A technique is presented as a means of treating problems in meteorology by numerical prediction on a fine scale. The method involves solution of numerical equations on a grid of data points in the usual way. Then, results from that forecast are used for the boundary conditions of a more dense but smaller-size grid network placed within the original one. Successively smaller grids are introduced so that the final grid size is as small as desired. Twenty-four hour forecasts have been made with a 2-level baroclinic model using a grid spacing reduced from 655 km to 327 km, to 163 km, and finally to 81 km. For an initial test, the method is applied to a developing cyclone just off the East Coast of the United States. During the 24-hr period of forecast, this cyclone developed from an incipient stage to a mature occluding system. The results of the numerical forecasts show that the method may be used successfully.