Numerical weather prediction in the context of Fortran

Weather forecasting or weather prediction is the application of science and technology to predict the conditions of the atmosphere for a given location and time. People have attempted to predict the weather informally for thousands of years and formally since the 19th century.

Weather forecasts are made by collecting quantitative data about the current state of the atmosphere, land, and ocean and using meteorology to project how the atmosphere will change at a given place. Once calculated manually based mainly upon changes in barometric pressure, current weather conditions, and sky conditions or cloud cover, weather forecasting now relies on computer-based models that take many atmospheric factors into account. Human input is still required to pick the best possible model to base the forecast upon, which involves pattern recognition skills, teleconnections, knowledge of model performance, and knowledge of model biases.

A model is an informative representation of an object, person, or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin modulus, 'a measure'.

Models can be divided into physical models (e.g. a ship model or a fashion model) and abstract models (e.g. a set of mathematical equations describing the workings of the atmosphere for the purpose of weather forecasting). Abstract or conceptual models are central to philosophy of science.

In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.

The term is closely associated with the work of the mathematician and meteorologist Edward Norton Lorenz. He noted that the butterfly effect is derived from the example of the details of a tornado (the exact time of formation, the exact path taken) being influenced by minor perturbations such as a distant butterfly flapping its wings several weeks earlier. Lorenz originally used a seagull causing a storm but was persuaded to make it more poetic with the use of a butterfly and tornado by 1972. He discovered the effect when he observed runs of his weather model with initial condition data that were rounded in a seemingly inconsequential manner. He noted that the weather model would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome.

A weather radar, also called weather surveillance radar (WSR) and Doppler weather radar, is a type of radar used to locate precipitation, calculate its motion, and estimate its type (rain, snow, hail etc.). Modern weather radars are mostly pulse-Doppler radars, capable of detecting the motion of rain droplets in addition to the intensity of the precipitation. Both types of data can be analyzed to determine the structure of storms and their potential to cause severe weather.

During World War II, radar operators discovered that weather was causing echoes on their screens, masking potential enemy targets. Techniques were developed to filter them, but scientists began to study the phenomenon. Soon after the war, surplus radars were used to detect precipitation. Since then, weather radar has evolved and is used by national weather services, research departments in universities, and in television stations' weather departments. Raw images are routinely processed by specialized software to make short term forecasts of future positions and intensities of rain, snow, hail, and other weather phenomena. Radar output is even incorporated into numerical weather prediction models to improve analyses and forecasts.

A weather balloon, also known as a sounding balloon, is a balloon (specifically a type of high-altitude balloon) that carries instruments to the stratosphere to send back information on atmospheric pressure, temperature, humidity and wind speed by means of a small, expendable measuring device called a radiosonde. To obtain wind data, they can be tracked by radar, radio direction finding, or navigation systems (such as the satellite-based Global Positioning System, GPS). Balloons meant to stay at a constant altitude for long periods are known as transosondes. Weather balloons that do not carry an instrument pack are used to determine upper-level winds and the height of cloud layers. For such balloons, a theodolite or total station is used to track the balloon's azimuth and elevation, which are then converted to estimated wind speed and direction and/or cloud height, as applicable.

Weather balloons are launched around the world for observations used to diagnose current conditions as well as by human forecasters and computer models for weather forecasting. Between 900 and 1,300 locations around the globe do routine releases, typically two or four times daily.

Nowcasting is weather forecasting on a very short term mesoscale period of up to 2 hours, according to the World Meteorological Organization, and up to six hours, according to other authors in the field. This forecast is an extrapolation in time of known weather parameters, including those obtained by means of remote sensing, using techniques that take into account a possible evolution of the air mass. This type of forecast therefore includes details that cannot be solved by numerical weather prediction (NWP) models running over longer forecast periods.

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, 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 other planetary body), or regional (limited-area), covering only part of the Earth. Atmospheric models also differ in how they compute vertical fluid motions; some types of models are thermotropic, barotropic, hydrostatic, and non-hydrostatic. These model types are differentiated by their assumptions about the atmosphere, which must balance computational speed with the model's fidelity to the atmosphere it is simulating.

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. For specific locations, model output statistics use climate information, output from numerical weather prediction, and current surface weather observations to develop statistical relationships which account for model bias and resolution issues.

MetOp (Meteorological Operational satellite) is a series of three polar-orbiting meteorological satellites developed by the European Space Agency (ESA) and operated by the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT). The satellites form the space segment component of the overall EUMETSAT Polar System (EPS), which in turn is the European half of the EUMETSAT / NOAA Initial Joint Polar System (IJPS). The satellites carry a payload comprising 11 scientific instruments and two which support Cospas-Sarsat Search and Rescue services. In order to provide data continuity between MetOp and NOAA Polar Operational Environmental Satellites (POES), several instruments are carried on both fleets of satellites.

MetOp-A, launched on 19 October 2006, was Europe's first polar orbiting satellite used for operational meteorology. With respect to its primary mission of providing data for Numerical Weather Prediction, studies have shown that MetOp-A data was measured as having the largest impact of any individual satellite platform on reducing 24-hour forecasting errors, and accounted for about 25% of the total impact on global forecast error reduction across all data sources. A 2023 report updated this estimate stating that the primary MetOp satellite has decreased in relative terms since 2011 from 24.5% to 11.15% in the FSOI metric.

The Weather Research and Forecasting (WRF) Model (/ˈwɔːrf/) is a numerical weather prediction (NWP) system designed to serve both atmospheric research and operational forecasting needs, developed in the United States. NWP refers to the simulation and prediction of the atmosphere with a computer model, and WRF is a set of software for this. WRF features two dynamical (computational) cores (or solvers), a data assimilation system, and a software architecture allowing for parallel computation and system extensibility. The model serves a wide range of meteorological applications across scales ranging from meters to thousands of kilometers.

The effort to develop WRF began in the latter part of the 1990s and was a collaborative partnership principally among the National Center for Atmospheric Research (NCAR), the National Oceanic and Atmospheric Administration (represented by the National Centers for Environmental Prediction (NCEP) and the (then) Forecast Systems Laboratory (FSL)), the Air Force Weather Agency (AFWA), the Naval Research Laboratory (NRL), the University of Oklahoma (OU), and the Federal Aviation Administration (FAA). The bulk of the work on the model has been performed or supported by NCAR, NOAA, and AFWA.

Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid (liquids and gases) with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed analytical or empirical analysis of a particular problem can be used for comparison. A final validation is often performed using full-scale testing, such as flight tests.

CFD is applied to a range of research and engineering problems in multiple fields of study and industries, including aerodynamics and aerospace analysis, hypersonics, weather simulation, natural science and environmental engineering, industrial system design and analysis, biological engineering, fluid flows and heat transfer, engine and combustion analysis, and visual effects for film and games.

Vilhelm Friman Koren Bjerknes (/ˈbjɜːrknɪs/ BYURK-niss, Norwegian: [ˈʋɪlˌhɛlm ˈbjæɾknɛs]; 14 March 1862 – 9 April 1951) was a Norwegian geophysicist and meteorologist who did much to lay the foundation of the modern practice of weather forecasting. He formulated the primitive equations that are still in use in numerical weather prediction and climate modeling. He founded the so-called Bergen School of Meteorology, which was successful in advancing weather prediction and meteorology in the early 20th century.

In models of radiative transfer, the two-stream approximation is a discrete ordinate approximation in which radiation propagating along only two discrete directions is considered. In other words, the two-stream approximation assumes the intensity is constant with angle in the upward hemisphere, with a different constant value in the downward hemisphere. It was first used by Arthur Schuster in 1905. The two ordinates are chosen such that the model captures the essence of radiative transport in light scattering atmospheres. A practical benefit of the approach is that it reduces the computational cost of integrating the radiative transfer equation. The two-stream approximation is commonly used in parameterizations of radiative transport in global circulation models and in weather forecasting models, such as the WRF. There are a large number of applications of the two-stream approximation, including variants such as the Kubelka-Munk approximation. It is the simplest approximation that can be used to explain common observations inexplicable by single-scattering arguments, such as the brightness and color of the clear sky, the brightness of clouds, the whiteness of a glass of milk, and the darkening of sand upon wetting. The two-stream approximation comes in many variants, such as the Quadrature, and Hemispheric constant models. Mathematical descriptions of the two-stream approximation are given in several books. The two-stream approximation is separate from the Eddington approximation (and its derivatives such as Delta-Eddington), which instead assumes that the intensity is linear in the cosine of the incidence angle (from +1 to -1), with no discontinuity at the horizon.