 A global forecast model is a weather forecasting model which initializes and forecasts the weather throughout the Earth 's troposphere . It is a computer program that produces meteorological information for future times at given locations and altitudes . Within any modern model is a set of equations , known as the primitive equations , used to predict the future state of the atmosphere . These equations — along with the ideal gas law — are used to evolve the density , pressure , and potential temperature scalar fields and the flow velocity vector field of the atmosphere through time . Additional transport equations for pollutants and other aerosols are included in some primitive @-@ equation high @-@ resolution models as well . The equations used are nonlinear partial differential equations which are impossible to solve exactly through analytical methods , with the exception of a few idealized cases . Therefore , numerical methods obtain approximate solutions . Different models use different solution methods : some global models and almost all regional models use finite difference methods for all three spatial dimensions , while other global models and a few regional models use spectral methods for the horizontal dimensions and finite @-@ difference methods in the vertical . 
