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Weather reconnaissance aircraft, such as this WP-3D Orion, provide data that is then used in numerical weather forecasts.. The atmosphere is a fluid.As such, the idea of numerical weather prediction is to sample the state of the fluid at a given time and use the equations of fluid dynamics and thermodynamics to estimate the state of the fluid at some time in the future.
The primitive equations are a set of nonlinear partial differential equations that are used to approximate global atmospheric flow and are used in most atmospheric models. They consist of three main sets of balance equations: A continuity equation: Representing the conservation of mass.
Lorenz system. A sample solution in the Lorenz attractor when ρ = 28, σ = 10, and β = 8 3 . The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions.
The Semi-Lagrangian scheme (SLS) is a numerical method that is widely used in numerical weather prediction models for the integration of the equations governing atmospheric motion. A Lagrangian description of a system (such as the atmosphere) focuses on following individual air parcels along their trajectories as opposed to the Eulerian ...
Atmospheric model. In atmospheric science, 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 (clouds and precipitation), heat exchange, soil ...
Vilhelm Friman Koren Bjerknes ForMemRS [1] (/ ˈbjɜːrknɪs / BYURK-niss, Norwegian: [ˈbjæ̂rkneːs]; 14 March 1862 – 9 April 1951 [1][3][4][5][6]) was a Norwegian physicist and meteorologist who did much to found the modern practice of weather forecasting. He formulated the primitive equations that are still in use in numerical weather ...
Climate models are systems of differential equations based on the basic laws of physics, fluid motion, and chemistry. Scientists divide the planet into a 3-dimensional grid and apply the basic equations to those grids. Atmospheric models calculate winds, heat transfer, radiation, relative humidity, and surface hydrology within each grid and ...
In the 1950s, the first successful programs for numerical weather forecasting utilized that equation. In modern numerical weather forecasting models and general circulation models (GCMs), vorticity may be one of the predicted variables, in which case the corresponding time-dependent equation is a prognostic equation.