Definitions

# Numerical weather prediction

Numerical weather prediction uses current weather conditions as input into mathematical models of the atmosphere to predict the weather. 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. Use of model ensemble forecasts helps to define the forecast uncertainty and extend weather forecasting farther into the future than would otherwise be possible.

## Physical overview

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.

## History

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.

## Definition of a forecast model

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 limited-area 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. Global models often use spectral methods for the horizontal dimensions and finite difference methods for the vertical dimension, while regional models usually use finite-difference methods in all three dimensions. Regional models also can use finer grids to explicitly resolve smaller-scale 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 irregularly-spaced 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 evenly-spaced 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.

### Global models

Some of the better known global numerical models are:

### Regional models

Some of the better known regional numerical models are:

• WRF The Weather Research and Forecasting Model was developed cooperatively by NCEP and the meteorological research community. WRF has several configurations, including:

* WRF-NMM The WRF Nonhydrostatic Mesoscale Model is the primary short-term weather forecast model for the U.S., replacing the Eta model.
* AR-WRF Advanced Research WRF developed primarily at the U.S. National Center for Atmospheric Research (NCAR)

• NAM The term North American Mesoscale model refers to whatever regional model NCEP operates over the North American domain. NCEP began using this designation system in January 2005. Between January 2005 and May 2006 the Eta model (began in Yugoslavia (now Serbia) during the 1970s by Zaviša Janjić and Fedor Mesinger) used this designation. Beginning in May 2006, NCEP began to use the WRF-NMM as the operational NAM.
• RAMS the Regional Atmospheric Modeling System developed at Colorado State University for numerical simulations of atmospheric meteorology and other environmental phenomena on scales from meters to 100's of kilometers - now supported in the public domain.
• MM5 the Fifth Generation Penn State/NCAR Mesoscale Model
• ARPS the Advanced Region Prediction System developed at the University of Oklahoma is a comprehensive multi-scale nonhydrostatic simulation and prediction system that can be used for regional-scale weather prediction up to the tornado-scale simulation and prediction. Advanced radar data assimilation for thunderstorm prediction is a key part of the system.
• HIRLAM High Resolution Limited Area Model
• GEM-LAM Global Environmental Multiscale Limited Area Model, the high resolution (2.5 km) GEM by the Meteorological Service of Canada (MSC)
• ALADIN The high-resolution limited-area hydrostatic and non-hydrostatic model developed and operated by several European and North African countries under the leadership of Météo-France
• COSMO The COSMO Model, formerly known as LM, Lokal-Modell, aLMo or LAMI, is a limited-area non hydrostatic model developed within the framework of the Consortium for Small-Scale Modeling (Germany, Switzerland, Italy, Poland, Greece, and Romania).

## Ensembles

As proposed by Dr. 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 spread-skill 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.