Weather forecast

Weather prediction is performed using the numerical model of the atmosphere evolution.The evolution equations are derived from the Navier Stokes equation for the adiabatic part but the are very much complicated by the change of phase of water, the radiation porocess and the boundary layer.The technique used operationally is described. Weather prediction is an initial value problem and accurate initial conditions need to be specified. Due to the small number of observations available (105 ) as compared to the dimension of the model state variable (107),the problem is largely underdetermined. Techniques of optimal control and inverse problems are used and have been adapted to the large dimension of our problem. our problem.The at mosphere is a chaotic system; the implication for weather prediction is discussed. Ensemble prediction is used operationally and the technique for generating initial conditions which lead to a numerical divergence of the subsequent forecasts is described.