Numerical weather prediction uses current weather conditions as input into mathematical models of the atmosphere to predict the weather. Although the first efforts to accomplish this were done in the 1920s, it wasn't until the advent of the computer and computer simulation that it was feasible to do in realtime. Manipulating the huge datasets and performing the complex calculations necessary to do this on a resolution fine enough to make the results useful requires the use of some of the most powerful supercomputers in the world. A number of forecast models, both global and regional in scale, are run to help create forecasts for nations worldwide. Use of model ensemble forecasts helps to define the forecast uncertainty and extend weather forecasting farther into the future than would otherwise be possible.
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The atmosphere is a fluid. The basic 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.
British mathematician Lewis Fry Richardson first proposed numerical weather prediction in 1922. Richardson attempted to perform a numerical forecast but it was not successful. The first successful numerical prediction was performed in 1950 by a team composed of the American meteorologists Jule Charney, Philip Thompson, Larry Gates, and Norwegian meteorologist Ragnar Fjörtoft and applied mathematician John von Neumann, using the ENIAC digital computer. They used a simplified form of atmospheric dynamics based on the barotropic vorticity equation. This simplification greatly reduced demands on computer time and memory, so that the computations could be performed on the relatively primitive computers available at the time. Later models used more complete equations for atmospheric dynamics and thermodynamics.
Operational numerical weather prediction (i.e., routine predictions for practical use) began in 1955 under a joint project by the U.S. Air Force, Navy, and Weather Bureau.^{[1]}
A model, in this context, is a computer program that produces meteorological information for future times at given positions and altitudes. The horizontal domain of a model is either global, covering the entire Earth, or regional , covering only part of the Earth. Regional models also are known as limitedarea models.
The 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. 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 finitedifference methods in all three dimensions. Regional models also can use finer grids to explicitly resolve smallerscale meteorological phenomena, since they do not have to solve equations for the whole globe.
Models are initialized using observed data from radiosondes, weather satellites, and surface weather observations. The irregularlyspaced observations are processed by data assimilation and objective analysis methods, which perform quality control and obtain values at locations usable by the model's mathematical algorithms (usually an evenlyspaced grid). The data are then used in the model as the starting point for a forecast. Commonly, the set of equations used is known as the primitive equations. These equations are initialized from the analysis data and rates of change are determined. The rates of change predict the state of the atmosphere a short time into the future. 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. This time stepping procedure is continually repeated until the solution reaches the desired forecast time. The length of the time step is related to the distance between the points on the computational grid. Time steps for global climate models may be on the order of tens of minutes, while time steps for regional models may be a few seconds to a few minutes.
As proposed by Edward Lorenz in 1963, it is impossible to definitively predict the state of the atmosphere, owing to the chaotic nature of the fluid dynamics equations involved. Furthermore, existing observation networks have limited spatial and temporal resolution, especially over large bodies of water such as the Pacific Ocean, which introduces uncertainty into the true initial state of the atmosphere. To account for this uncertainty, stochastic or "ensemble" forecasting is used, involving multiple forecasts created with different model systems, different physical parametrizations, or varying initial conditions. The ensemble forecast is usually evaluated in terms of the ensemble mean of a forecast variable, and the ensemble spread, which represents the degree of agreement between various forecasts in the ensemble system, known as ensemble members. A common misconception is that low spread amongst ensemble members necessarily implies more confidence in the ensemble mean. Although a spreadskill relationship sometimes exists, the relationship between ensemble spread and skill varies substantially depending on such factors as the forecast model and the region for which the forecast is made.

Numerical weather prediction is the way weather forecasts are made. This is done using computer models of the atmosphere. Such models describe the current weather conditions, and how they change over time using equations. Using the current weather conditions, the equations can be solved, or approximated to tell what the weather will be like in the near future. The relevant physical parameters, such as pressure, temperature, the direction and the sped of the wind are taken to be functions of time. These are modelled with a system of partial differential equations. This is a dynamic system that is solved numerically. Most of these equations are implemented using FORTRAN. The equations are approximated. Since this takes a lot of computing power or time, supercomputers are used for this task, most of the time.
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The atmosphere is modelled as a fluid. The basic idea of numerical weather prediction is to sample the state of the fluid at a given time. The equations of fluid dynamics and thermodynamics can then be used to estimate the state of the fluid at some time in the future.
The results are usually too inaccurate to be used for predicting the weather at any place. For this reason, meteorologists ('weather men') check the values, and compare them to historical data. In other words, they use the data to help produce the weather forecast.
Model Output Statistics is a statistical model that was developed in the 1960s and 1970s. It uses regression analysis for a fully automated forecast. With it, historical data is analysed automatically. One of its applications is called Direct Model Output. MOS uses both historical data and statistical modeling. Predictions beyond about six hours are unreliable.
Another wellknown model is called Global Forecast System (GFS), which is run by the US weather service, NOAA. It gives a forecast four times a day. Since the information is free, the GFS is often used, especially by smaller weather stations.
The atmosphere is a chaotic system. A small change of the input values does not necessarily lead to a small change of the output. This is due to the equations of fluid dynamics that are involved. These equations involved are solved or approximated once with the parameters that were observed. This is done several times more, with parameters that are based on the observed values, but which have been changed slightly. Because the computing power is limited, the "resolution" of such a model is more coarse. Once all the calculations are finished, they are compared to one another. Calculated results that are "similar" indicate that the prognosis is relatively good. In some cases, this means that it is possible to accurately predict the weather for a time of about ten days; in other cases a prediction over even a few days may be difficult.
