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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.
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.
Within any modern model is a set of equations, known as the primitive equations, used to predict the future state of the atmosphere. [61] These equations—along with the ideal gas law—are used to evolve the density, pressure, and potential temperature scalar fields and the velocity vector field of the atmosphere through
The equations relate the properties of a two-dimensional fluid layer uniformly warmed from below and cooled from above. In particular, the equations describe the rate of change of three quantities with respect to time: x is proportional to the rate of convection, y to the horizontal temperature variation, and z to the vertical temperature ...
Within any modern model is a set of equations, known as the primitive equations, used to predict the future state of the atmosphere. [21] 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
Prognostic equation - in the context of physical (and especially geophysical) simulation, a prognostic equation predicts the value of variables for some time in the future on the basis of the values at the current or previous times.
Linear prediction is a mathematical operation where future values of a discrete-time signal are estimated as a linear function of previous samples. In digital signal processing , linear prediction is often called linear predictive coding (LPC) and can thus be viewed as a subset of filter theory .
Similarly, a differential equation is said to be linear if it can be written with linear differential operators, but it can still have nonlinear expressions in it. In a mathematical programming model, if the objective functions and constraints are represented entirely by linear equations , then the model is regarded as a linear model.