page_title: Atmospheric model
section_title: Computation
hierarchical_section_title: Atmospheric model / Computation
caption_attribution_description: English: 500 mb geopotential height forecast by the United States numerical weather prediction model NAM. Also an example of an Omega Block.
context_page_description: An atmospheric model is a mathematical model constructed around the full set of primitive dynamical equations which govern atmospheric motions. It can supplement these equations with parameterizations for turbulent diffusion, radiation, moist processes, heat exchange, soil, vegetation, surface water, the kinematic effects of terrain, and convection. Most atmospheric models are numerical, i.e. they discretize equations of motion. They can predict microscale phenomena such as tornadoes and boundary layer eddies, sub-microscale turbulent flow over buildings, as well as synoptic and global flows. The horizontal domain of a model is either global, covering the entire Earth, or regional, covering only part of the Earth. The different types of models run are thermotropic, barotropic, hydrostatic, and nonhydrostatic. Some of the model types make assumptions about the atmosphere which lengthens the time steps used and increases computational speed.
  Forecasts are computed using mathematical equations for the physics and dynamics of the atmosphere. These equations are nonlinear and are impossible to solve exactly. Therefore, numerical methods obtain approximate solutions.
context_section_description: A model is a computer program that produces meteorological information for future times at given locations and altitudes.   Within any model is a set of equations, known as the primitive equations, used to predict the future state of the atmosphere.  These equations are initialized from the analysis data and rates of change are determined.  These rates of change predict the state of the atmosphere a short time into the future, with each time increment known as a time step.  The equations are then applied to this new atmospheric state to find new rates of change, and these new rates of change predict the atmosphere at a yet further time into the future.  Time stepping is repeated until the solution reaches the desired forecast time.  The length of the time step chosen within the model is related to the distance between the points on the computational grid, and is chosen to maintain numerical stability.  Time steps for global models are on the order of tens of minutes, while time steps for regional models are between one and four minutes.  The global models are run at varying times into the future.  The UKMET Unified model is run six days into the future, the European Centre for Medium-Range Weather Forecasts model is run out to 10 days into the future, while the Global Forecast System model run by the Environmental Modeling Center is run 16 days into the future.
  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 use spectral methods for the horizontal dimensions and finite difference methods for the vertical dimension, while regional models and other global models usually use finite-difference methods in all three dimensions.  The visual output produced by a model solution is known as a prognostic chart, or prog.
caption: An example of 500 mbar geopotential height prediction from a numerical weather prediction model.
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