![AtmosphericModelSchematic](https://upload.wikimedia.org/wikipedia/commons/7/73/AtmosphericModelSchematic.png)
Numerical weather prediction (NWP) uses
mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
s of the atmosphere and oceans to
predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of
computer simulation
Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be dete ...
in the 1950s that numerical weather predictions produced realistic results. A number of global and regional forecast models are run in different countries worldwide, using current weather observations relayed from
radiosonde
A radiosonde is a battery-powered telemetry instrument carried into the atmosphere usually by a weather balloon that measures various atmospheric parameters and transmits them by radio to a ground receiver. Modern radiosondes measure or calcula ...
s,
weather satellites
A weather satellite or meteorological satellite is a type of Earth observation satellite that is primarily used to monitor the weather and climate of the Earth. Satellites can be polar orbiting (covering the entire Earth asynchronously), or geo ...
and other observing systems as inputs.
Mathematical models based on the same physical principles can be used to generate either short-term weather forecasts or longer-term climate predictions; the latter are widely applied for understanding and projecting
climate change
In common usage, climate change describes global warming—the ongoing increase in global average temperature—and its effects on Earth's climate system. Climate change in a broader sense also includes previous long-term changes to E ...
. The improvements made to regional models have allowed for significant improvements in
tropical cyclone track and
air quality
Air pollution is the contamination of air due to the presence of substances in the atmosphere that are harmful to the health of humans and other living beings, or cause damage to the climate or to materials. There are many different types ...
forecasts; however, atmospheric models perform poorly at handling processes that occur in a relatively constricted area, such as
wildfire
A wildfire, forest fire, bushfire, wildland fire or rural fire is an unplanned, uncontrolled and unpredictable fire in an area of Combustibility and flammability, combustible vegetation. Depending on the type of vegetation present, a wildfire ...
s.
Manipulating the vast datasets and performing the complex calculations necessary to modern numerical weather prediction requires some of the most powerful
supercomputer
A supercomputer is a computer with a high level of performance as compared to a general-purpose computer. The performance of a supercomputer is commonly measured in floating-point operations per second ( FLOPS) instead of million instructions ...
s in the world. Even with the increasing power of supercomputers, the
forecast skill In the fields of forecasting and prediction, forecast skill or prediction skill is any measure of the accuracy and/or degree of association of prediction to an observation or estimate of the actual value of what is being predicted (formally, the pre ...
of numerical weather models extends to only about six days. Factors affecting the accuracy of numerical predictions include the density and quality of observations used as input to the forecasts, along with deficiencies in the numerical models themselves. Post-processing techniques such as
model output statistics In weather forecasting, model output statistics (MOS) is a multiple linear regression technique in which predictands, often near-surface quantities (such as two-meter-above-ground-level air temperature, horizontal visibility, and wind direction, ...
(MOS) have been developed to improve the handling of errors in numerical predictions.
A more fundamental problem lies in the
chaotic
Chaotic was originally a Danish trading card game. It expanded to an online game in America which then became a television program based on the game. The program was able to be seen on 4Kids TV (Fox affiliates, nationwide), Jetix, The CW4Kid ...
nature of the
partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function.
The function is often thought of as an "unknown" to be sol ...
s that govern the atmosphere. It is impossible to solve these equations exactly, and small errors grow with time (doubling about every five days). Present understanding is that this chaotic behavior limits accurate forecasts to about 14 days even with accurate input data and a flawless model. In addition, the partial differential equations used in the model need to be supplemented with
parameterizations for
solar radiation
Solar irradiance is the power per unit area (surface power density) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument.
Solar irradiance is measured in watts per square metre (W/m ...
,
moist processes __NOTOC__
Moist, describing the presence of moisture, may refer to:
Music
* Moist (band), a Canadian alternative rock band
* "Moist", a song by Janet Jackson from her 2004 album '' Damita Jo''
People
* Lewis Moist (1881–1940), British Olympic ...
(clouds and
precipitation
In meteorology, precipitation is any product of the condensation of atmospheric water vapor that falls under gravitational pull from clouds. The main forms of precipitation include drizzle, rain, sleet, snow, ice pellets, graupel and hail. ...
),
heat exchange
Heat Exchange was a Canadian rock band who had evolved out of a late 1960s, blues quartet. They had a hit in Canada in 1972 with "Can You Tell Me". Nearly five decades later they would finally have their album released.
Background
They started o ...
, soil, vegetation, surface water, and the effects of terrain. In an effort to quantify the large amount of inherent uncertainty remaining in numerical predictions,
ensemble forecasts have been used since the 1990s to help gauge the confidence in the forecast, and to obtain useful results farther into the future than otherwise possible. This approach analyzes multiple forecasts created with an individual forecast model or multiple models.
History
![Two women operating ENIAC](https://upload.wikimedia.org/wikipedia/commons/3/3b/Two_women_operating_ENIAC.gif)
The
history of numerical weather prediction
The history of numerical weather prediction considers how current weather conditions as input into mathematical models of the atmosphere and oceans to weather forecasting, predict the weather and future sea state (the process of numerical weather ...
began in the 1920s through the efforts of
Lewis Fry Richardson
Lewis Fry Richardson, FRS (11 October 1881 – 30 September 1953) was an English mathematician, physicist, meteorologist, psychologist, and pacifist who pioneered modern mathematical techniques of weather forecasting, and the application of si ...
, who used procedures originally developed by
Vilhelm Bjerknes
Vilhelm Friman Koren Bjerknes ( , ; 14 March 1862 – 9 April 1951) 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 num ...
to produce by hand a six-hour forecast for the state of the atmosphere over two points in central Europe, taking at least six weeks to do so.
It was not until the advent of the computer and
computer simulation
Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be dete ...
s that computation time was reduced to less than the forecast period itself. The
ENIAC
ENIAC (; Electronic Numerical Integrator and Computer) was the first programmable, electronic, general-purpose digital computer, completed in 1945. There were other computers that had these features, but the ENIAC had all of them in one packa ...
was used to create the first weather forecasts via computer in 1950, based on a highly simplified approximation to the atmospheric governing equations.
In 1954,
Carl-Gustav Rossby
Carl-Gustaf Arvid Rossby ( 28 December 1898 – 19 August 1957) was a Swedish-born American meteorologist who first explained the large-scale motions of the atmosphere in terms of fluid mechanics. He identified and characterized both the jet ...
's group at the
Swedish Meteorological and Hydrological Institute
The Swedish Meteorological and Hydrological Institute ( sv, Sveriges meteorologiska och hydrologiska institut, abbreviated SMHI) is a Government agency in Sweden and operates under the Ministry of the Environment. SMHI has expertise within the ...
used the same model to produce the first operational forecast (i.e., a routine prediction for practical use).
Operational numerical weather prediction in the United States began in 1955 under the Joint Numerical Weather Prediction Unit (JNWPU), a joint project by the
U.S. Air Force
The United States Air Force (USAF) is the air service branch of the United States Armed Forces, and is one of the eight uniformed services of the United States. Originally created on 1 August 1907, as a part of the United States Army Signal ...
,
Navy
A navy, naval force, or maritime force is the branch of a nation's armed forces principally designated for naval warfare, naval and amphibious warfare; namely, lake-borne, riverine, littoral zone, littoral, or ocean-borne combat operations and ...
and
Weather Bureau
The National Weather Service (NWS) is an agency of the United States federal government that is tasked with providing weather forecasts, warnings of hazardous weather, and other weather-related products to organizations and the public for the p ...
. In 1956,
Norman Phillips developed a mathematical model which could realistically depict monthly and seasonal patterns in the troposphere; this became the first successful
climate model
Numerical climate models use quantitative methods to simulate the interactions of the important drivers of climate, including atmosphere, oceans, land surface and ice. They are used for a variety of purposes from study of the dynamics of the cl ...
.
Following Phillips' work, several groups began working to create
general circulation model
A general circulation model (GCM) is a type of climate model. It employs a mathematical model of the general circulation of a planetary atmosphere or ocean. It uses the Navier–Stokes equations on a rotating sphere with thermodynamic terms f ...
s.
The first general circulation climate model that combined both oceanic and atmospheric processes was developed in the late 1960s at the
NOAA
The National Oceanic and Atmospheric Administration (abbreviated as NOAA ) is an United States scientific and regulatory agency within the United States Department of Commerce that forecasts weather, monitors oceanic and atmospheric conditio ...
Geophysical Fluid Dynamics Laboratory
The Geophysical Fluid Dynamics Laboratory (GFDL) is a laboratory in the National Oceanic and Atmospheric Administration (NOAA) Office of Oceanic and Atmospheric Research (OAR). The current director is Dr. Venkatachalam Ramaswamy. It is one of se ...
.
As computers have become more powerful, the size of the initial data sets has increased and
newer atmospheric models have been developed to take advantage of the added available computing power. These newer models include more physical processes in the simplifications of the
equations of motion
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.''Encyclopaedia of Physics'' (second Edition), R.G. Lerner, G.L. Trigg, VHC Publishers, 1991, ISBN (Ver ...
in numerical simulations of the atmosphere.
In 1966,
West Germany
West Germany is the colloquial term used to indicate the Federal Republic of Germany (FRG; german: Bundesrepublik Deutschland , BRD) between its formation on 23 May 1949 and the German reunification through the accession of East Germany on 3 O ...
and the United States began producing operational forecasts based on
primitive-equation models, followed by the United Kingdom in 1972 and Australia in 1977.
The development of limited area (regional) models facilitated advances in forecasting the tracks of
tropical cyclone
A tropical cyclone is a rapidly rotating storm system characterized by a low-pressure center, a closed low-level atmospheric circulation, strong winds, and a spiral arrangement of thunderstorms that produce heavy rain and squalls. Depend ...
s as well as
air quality
Air pollution is the contamination of air due to the presence of substances in the atmosphere that are harmful to the health of humans and other living beings, or cause damage to the climate or to materials. There are many different types ...
in the 1970s and 1980s.
By the early 1980s models began to include the interactions of soil and vegetation with the atmosphere, which led to more realistic forecasts.
The output of forecast models based on
atmospheric dynamics
Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not ...
is unable to resolve some details of the weather near the Earth's surface. As such, a statistical relationship between the output of a numerical weather model and the ensuing conditions at the ground was developed in the 1970s and 1980s, known as
model output statistics In weather forecasting, model output statistics (MOS) is a multiple linear regression technique in which predictands, often near-surface quantities (such as two-meter-above-ground-level air temperature, horizontal visibility, and wind direction, ...
(MOS).
Starting in the 1990s, model ensemble forecasts have been used to help define the forecast uncertainty and to extend the window in which numerical weather forecasting is viable farther into the future than otherwise possible.
Initialization
![Lockheed WP-3D Orion](https://upload.wikimedia.org/wikipedia/commons/6/69/Lockheed_WP-3D_Orion.jpg)
The
atmosphere
An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A s ...
is a
fluid
In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...
. 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
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...
and
thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...
to estimate the state of the fluid at some time in the future. The process of entering observation data into the model to generate
initial conditions
In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted ''t'' = 0). For ...
is called ''initialization''. On land, terrain maps available at resolutions down to globally are used to help model atmospheric circulations within regions of rugged topography, in order to better depict features such as downslope winds,
mountain wave
In meteorology, lee waves are atmospheric stationary waves. The most common form is mountain waves, which are atmospheric internal gravity waves. These were discovered in 1933 by two German glider pilots, Hans Deutschmann and Wolf Hirth, above t ...
s and related cloudiness that affects incoming solar radiation. The main inputs from country-based weather services are observations from devices (called
radiosonde
A radiosonde is a battery-powered telemetry instrument carried into the atmosphere usually by a weather balloon that measures various atmospheric parameters and transmits them by radio to a ground receiver. Modern radiosondes measure or calcula ...
s) in weather balloons that measure various atmospheric parameters and transmits them to a fixed receiver, as well as from
weather satellite
A weather satellite or meteorological satellite is a type of Earth observation satellite that is primarily used to monitor the weather and climate of the Earth. Satellites can be polar orbiting (covering the entire Earth asynchronously), or ge ...
s. The
World Meteorological Organization
The World Meteorological Organization (WMO) is a specialized agency of the United Nations responsible for promoting international cooperation on atmospheric science, climatology, hydrology and geophysics.
The WMO originated from the Internati ...
acts to standardize the instrumentation, observing practices and timing of these observations worldwide. Stations either report hourly in
METAR
METAR is a format for reporting weather information. A METAR weather report is predominantly used by aircraft pilots, and by meteorologists, who use aggregated METAR information to assist in weather forecasting.
Raw METAR is the most common form ...
reports, or every six hours in
SYNOP
SYNOP (surface synoptic observations) is a numerical code (called FM-12 by WMO) used for reporting weather observations made by manned and automated weather stations. SYNOP reports are typically sent every six hours by Deutscher Wetterdienst on ...
reports. These observations are irregularly spaced, so they are processed by
data assimilation
Data assimilation is a mathematical discipline that seeks to optimally combine theory (usually in the form of a numerical model) with observations. There may be a number of different goals sought – for example, to determine the optimal state es ...
and objective analysis methods, which perform quality control and obtain values at locations usable by the model's mathematical algorithms.
The data are then used in the model as the starting point for a forecast.
A variety of methods are used to gather observational data for use in numerical models. Sites launch radiosondes in weather balloons which rise through the
troposphere
The troposphere is the first and lowest layer of the atmosphere of the Earth, and contains 75% of the total mass of the planetary atmosphere, 99% of the total mass of water vapour and aerosols, and is where most weather phenomena occur. From ...
and well into the
stratosphere
The stratosphere () is the second layer of the atmosphere of the Earth, located above the troposphere and below the mesosphere. The stratosphere is an atmospheric layer composed of stratified temperature layers, with the warm layers of air ...
. Information from weather satellites is used where traditional data sources are not available. Commerce provides
pilot report
A pilot report or PIREP is a report of actual flight or ground conditions encountered by an aircraft. Reports commonly include information about atmospheric conditions (like temperature, icing, turbulence) or airport conditions (like runway con ...
s along aircraft routes and ship reports along shipping routes. Research projects use
reconnaissance aircraft
A reconnaissance aircraft (colloquially, a spy plane) is a military aircraft designed or adapted to perform aerial reconnaissance with roles including collection of imagery intelligence (including using photography), signals intelligence, as ...
to fly in and around weather systems of interest, such as
tropical cyclone
A tropical cyclone is a rapidly rotating storm system characterized by a low-pressure center, a closed low-level atmospheric circulation, strong winds, and a spiral arrangement of thunderstorms that produce heavy rain and squalls. Depend ...
s.
Reconnaissance aircraft are also flown over the open oceans during the cold season into systems which cause significant uncertainty in forecast guidance, or are expected to be of high impact from three to seven days into the future over the downstream continent. Sea ice began to be initialized in forecast models in 1971. Efforts to involve
sea surface temperature
Sea surface temperature (SST), or ocean surface temperature, is the ocean temperature close to the surface. The exact meaning of ''surface'' varies according to the measurement method used, but it is between and below the sea surface. Air mass ...
in model initialization began in 1972 due to its role in modulating weather in higher latitudes of the Pacific.
Computation
![GFS 850 MB](https://upload.wikimedia.org/wikipedia/commons/d/d9/GFS_850_MB.PNG)
An atmospheric model is a computer program that produces
meteorological
Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not ...
information for future times at given locations and altitudes. Within any modern model is a set of equations, known as the
primitive equations
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 equ ...
, used to predict the future state of the atmosphere. These equations—along with the
ideal gas law
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stat ...
—are used to evolve the
density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
,
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
, and
potential temperature
The potential temperature of a parcel of fluid at pressure P is the temperature that the parcel would attain if adiabatically brought to a standard reference pressure P_, usually . The potential temperature is denoted \theta and, for a gas well-a ...
scalar field
In mathematics and physics, a scalar field is a function (mathematics), function associating a single number to every point (geometry), point in a space (mathematics), space – possibly physical space. The scalar may either be a pure Scalar ( ...
s and the air
velocity
Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
(wind)
vector field of the atmosphere through time. Additional transport equations for pollutants and other
aerosol
An aerosol is a suspension (chemistry), suspension of fine solid particles or liquid Drop (liquid), droplets in air or another gas. Aerosols can be natural or Human impact on the environment, anthropogenic. Examples of natural aerosols are fog o ...
s are included in some primitive-equation high-resolution models as well. The equations used are
nonlinear
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
partial differential equations which are impossible to solve exactly through analytical methods,
with the exception of a few idealized cases. Therefore, numerical methods obtain approximate solutions. Different models use different solution methods: some global models and almost all regional models use
finite difference method
In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are di ...
s for all three spatial dimensions, while other global models and a few regional models use
spectral method
Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations. The idea is to write the solution of the differential equation as a sum of certain " basis functio ...
s for the horizontal dimensions and finite-difference methods in the vertical.
These equations are initialized from the analysis data and rates of change are determined. These rates of change predict the state of the atmosphere a short time into the future; the time increment for this prediction is called a ''time step''. This future atmospheric state is then used as the starting point for another application of the predictive equations to find new rates of change, and these new rates of change predict the atmosphere at a yet further time step into the future. This time stepping is repeated until the solution reaches the desired forecast time. The length of the time step chosen within the model is related to the distance between the points on the computational grid, and is chosen to maintain
numerical stability
In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorit ...
. Time steps for global models are on the order of tens of minutes, while time steps for regional models are between one and four minutes. The global models are run at varying times into the future. The
UKMET
The Meteorological Office, abbreviated as the Met Office, is the United Kingdom's national weather service. It is an executive agency and trading fund of the Department for Business, Energy and Industrial Strategy and is led by CEO Penelope ...
Unified Model The Unified Model is a numerical weather prediction and climate modeling software suite originally developed by the United Kingdom Met Office, and now both used and further developed by many weather-forecasting agencies around the world. The Unifi ...
is run six days into the future,
while the
European Centre for Medium-Range Weather Forecasts
The European Centre for Medium-Range Weather Forecasts (ECMWF) is an independent intergovernmental organisation supported by most of the nations of Europe. It is based at three sites: Shinfield Park, Reading, United Kingdom; Bologna, Italy; an ...
'
Integrated Forecast System The Integrated Forecasting System (IFS) is a global numerical weather prediction system jointly developed and maintained by the European Centre for Medium-Range Weather Forecasts (ECMWF) based in Reading, England, and Météo-France based in Toulous ...
and
Environment Canada
Environment and Climate Change Canada (ECCC; french: Environnement et Changement climatique Canada),Environment and Climate Change Canada is the applied title under the Federal Identity Program; the legal title is Department of the Environment ( ...
's
Global Environmental Multiscale Model
The Global Environmental Multiscale Model (GEM), often known as the CMC model in North America, is an integrated forecasting and data assimilation system developed in the Recherche en Prévision Numérique (RPN), Meteorological Research Branch (MR ...
both run out to ten days into the future, and the
Global Forecast System
The Global Forecast System (GFS) is a global numerical weather prediction system containing a global computer model and variational analysis run by the United States' National Weather Service (NWS).
Operation
The mathematical model is run f ...
model run by the
Environmental Modeling Center
The Environmental Modeling Center (EMC) is a United States Government agency, which improves numerical weather, marine and climate predictions at the National Centers for Environmental Prediction (NCEP), through a broad program of research in dat ...
is run sixteen days into the future. The visual output produced by a model solution is known as a
prognostic chart A prognostic chart is a map displaying the likely weather forecast for a future time. Such charts generated by atmospheric models as output from numerical weather prediction and contain a variety of information such as temperature, wind, precipitat ...
, or ''prog''.
Parameterization
![GoldenMedows](https://upload.wikimedia.org/wikipedia/commons/3/3c/GoldenMedows.jpg)
Some meteorological processes are too small-scale or too complex to be explicitly included in numerical weather prediction models. ''
Parameterization
In mathematics, and more specifically in geometry, parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, de ...
'' is a procedure for representing these processes by relating them to variables on the scales that the model resolves. For example, the gridboxes in weather and climate models have sides that are between and in length. A typical
cumulus cloud
Cumulus clouds are clouds which have flat bases and are often described as "puffy", "cotton-like" or "fluffy" in appearance. Their name derives from the Latin ''cumulo-'', meaning ''heap'' or ''pile''. Cumulus clouds are low-level clouds, gener ...
has a scale of less than , and would require a grid even finer than this to be represented physically by the equations of fluid motion. Therefore, the processes that such
cloud
In meteorology, a cloud is an aerosol consisting of a visible mass of miniature liquid droplets, frozen crystals, or other particles suspended in the atmosphere of a planetary body or similar space. Water or various other chemicals may co ...
s represent are parameterized, by processes of various sophistication. In the earliest models, if a column of air within a model gridbox was conditionally unstable (essentially, the bottom was warmer and moister than the top) and the water vapor content at any point within the column became saturated then it would be overturned (the warm, moist air would begin rising), and the air in that vertical column mixed. More sophisticated schemes recognize that only some portions of the box might
convect and that
entrainment
Entrainment may refer to:
* Air entrainment, the intentional creation of tiny air bubbles in concrete
* Brainwave entrainment, the practice of entraining one's brainwaves to a desired frequency
* Entrainment (biomusicology), the synchronization o ...
and other processes occur. Weather models that have gridboxes with sizes between can explicitly represent convective clouds, although they need to parameterize
cloud microphysics
Cloud physics is the study of the physical processes that lead to the formation, growth and precipitation of atmospheric clouds. These aerosols are found in the troposphere, stratosphere, and mesosphere, which collectively make up the greatest ...
which occur at a smaller scale. The formation of large-scale (
stratus
Stratus may refer to:
Weather
*Stratus cloud, a cloud type
**Nimbostratus cloud, a cloud type
**Stratocumulus cloud, a cloud type
**Altostratus cloud, a cloud type
**Altostratus undulatus cloud, a cloud type
**Cirrostratus cloud, a cloud type
Mus ...
-type) clouds is more physically based; they form when the
relative humidity
Humidity is the concentration of water vapor present in the air. Water vapor, the gaseous state of water, is generally invisible to the human eye. Humidity indicates the likelihood for precipitation, dew, or fog to be present.
Humidity depe ...
reaches some prescribed value. The
cloud fraction Cloud fraction is the percentage of each pixel in satellite imagery or each gridbox in a weather or climate model that is covered with cloud
In meteorology, a cloud is an aerosol consisting of a visible mass of miniature liquid droplets, ...
can be related to this critical value of relative humidity.
The amount of solar radiation reaching the ground, as well as the formation of cloud droplets occur on the molecular scale, and so they must be parameterized before they can be included in the model.
Atmospheric drag
In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding flu ...
produced by mountains must also be parameterized, as the limitations in the resolution of
elevation
The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface (see Geodetic datum § Vert ...
contours produce significant underestimates of the drag. This method of parameterization is also done for the surface flux of energy between the ocean and the atmosphere, in order to determine realistic sea surface temperatures and type of sea ice found near the ocean's surface. Sun angle as well as the impact of multiple cloud layers is taken into account. Soil type, vegetation type, and soil moisture all determine how much radiation goes into warming and how much moisture is drawn up into the adjacent atmosphere, and thus it is important to parameterize their contribution to these processes. Within air quality models, parameterizations take into account atmospheric emissions from multiple relatively tiny sources (e.g. roads, fields, factories) within specific grid boxes.
Domains
![Sigma-z-coordinates](https://upload.wikimedia.org/wikipedia/commons/a/a1/Sigma-z-coordinates.svg)
The horizontal
domain of a model is either ''global'', covering the entire Earth, or ''regional'', covering only part of the Earth. Regional models (also known as ''limited-area'' models, or LAMs) allow for the use of finer grid spacing than global models because the available computational resources are focused on a specific area instead of being spread over the globe. This allows regional models to resolve explicitly smaller-scale meteorological phenomena that cannot be represented on the coarser grid of a global model. Regional models use a global model to specify conditions at the edge of their domain (
boundary condition
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to th ...
s) in order to allow systems from outside the regional model domain to move into its area. Uncertainty and errors within regional models are introduced by the global model used for the boundary conditions of the edge of the regional model, as well as errors attributable to the regional model itself.
The vertical coordinate is handled in various ways. Lewis Fry Richardson's 1922 model used geometric height (
) as the vertical coordinate. Later models substituted the geometric
coordinate with a pressure coordinate system, in which the
geopotential height
Geopotential height or geopotential altitude is a vertical coordinate referenced to Earth's mean sea level, an adjustment to geometric height (altitude above mean sea level) that accounts for the variation of gravity with latitude and altitude. Thu ...
s of constant-pressure surfaces become
dependent variable
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand ...
s, greatly simplifying the primitive equations.
This correlation between coordinate systems can be made since pressure decreases with height through the
Earth's atmosphere
The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing for ...
. The first model used for operational forecasts, the single-layer barotropic model, used a single pressure coordinate at the 500-millibar (about ) level,
and thus was essentially two-dimensional. High-resolution models—also called ''mesoscale models''—such as the
Weather Research and Forecasting model tend to use normalized pressure coordinates referred to as
sigma coordinates. This coordinate system receives its name from the
independent variable
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand ...
used to
scale atmospheric pressures with respect to the pressure at the surface, and in some cases also with the pressure at the top of the domain.
Model output statistics
Because forecast models based upon the equations for atmospheric dynamics do not perfectly determine weather conditions, statistical methods have been developed to attempt to correct the forecasts. Statistical models were created based upon the three-dimensional fields produced by numerical weather models, surface observations and the climatological conditions for specific locations. These statistical models are collectively referred to as
model output statistics In weather forecasting, model output statistics (MOS) is a multiple linear regression technique in which predictands, often near-surface quantities (such as two-meter-above-ground-level air temperature, horizontal visibility, and wind direction, ...
(MOS), and were developed by the
National Weather Service
The National Weather Service (NWS) is an Government agency, agency of the Federal government of the United States, United States federal government that is tasked with providing weather forecasts, warnings of hazardous weather, and other weathe ...
for their suite of weather forecasting models in the late 1960s.
Model output statistics differ from the ''perfect prog'' technique, which assumes that the output of numerical weather prediction guidance is perfect. MOS can correct for local effects that cannot be resolved by the model due to insufficient grid resolution, as well as model biases. Because MOS is run after its respective global or regional model, its production is known as post-processing. Forecast parameters within MOS include maximum and minimum temperatures, percentage chance of rain within a several hour period, precipitation amount expected, chance that the precipitation will be frozen in nature, chance for thunderstorms, cloudiness, and surface winds.
Ensembles
![WRF rita spread2](https://upload.wikimedia.org/wikipedia/commons/d/d5/WRF_rita_spread2.jpg)
In 1963,
Edward Lorenz
Edward Norton Lorenz (May 23, 1917 – April 16, 2008) was an American mathematician and meteorologist who established the theoretical basis of weather and climate predictability, as well as the basis for computer-aided atmospheric physics and me ...
discovered the
chaotic nature of the
fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...
equations involved in weather forecasting.
Extremely small errors in temperature, winds, or other initial inputs given to numerical models will amplify and double every five days,
making it impossible for long-range forecasts—those made more than two weeks in advance—to predict the state of the atmosphere with any degree of
forecast skill In the fields of forecasting and prediction, forecast skill or prediction skill is any measure of the accuracy and/or degree of association of prediction to an observation or estimate of the actual value of what is being predicted (formally, the pre ...
. Furthermore, existing observation networks have poor coverage in some regions (for example, over large bodies of water such as the Pacific Ocean), which introduces uncertainty into the true initial state of the atmosphere. While a set of equations, known as the
Liouville equations
:''For Liouville's equation in dynamical systems, see Liouville's theorem (Hamiltonian).''
: ''For Liouville's equation in quantum mechanics, see Von Neumann equation.''
: ''For Liouville's equation in Euclidean space, see Liouville–Bratu–Gel ...
, exists to determine the initial uncertainty in the model initialization, the equations are too complex to run in real-time, even with the use of supercomputers.
These uncertainties limit forecast model accuracy to about five or six days into the future.
Edward Epstein recognized in 1969 that the atmosphere could not be completely described with a single forecast run due to inherent uncertainty, and proposed using an
ensemble
Ensemble may refer to:
Art
* Architectural ensemble
* ''Ensemble'' (album), Kendji Girac 2015 album
* Ensemble (band), a project of Olivier Alary
* Ensemble cast (drama, comedy)
* Ensemble (musical theatre), also known as the chorus
* ''En ...
of
stochastic
Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselv ...
Monte Carlo simulations
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be determi ...
to produce
means
Means may refer to:
* Means LLC, an anti-capitalist media worker cooperative
* Means (band), a Christian hardcore band from Regina, Saskatchewan
* Means, Kentucky, a town in the US
* Means (surname)
* Means Johnston Jr. (1916–1989), US Navy adm ...
and
variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers ...
s for the state of the atmosphere. Although this early example of an ensemble showed skill, in 1974
Cecil Leith showed that they produced adequate forecasts only when the ensemble
probability distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon i ...
was a representative sample of the probability distribution in the atmosphere.
Since the 1990s, ''ensemble forecasts'' have been used operationally (as routine forecasts) to account for the stochastic nature of weather processes – that is, to resolve their inherent uncertainty. This method involves analyzing multiple forecasts created with an individual forecast model by using different physical
parametrizations or varying initial conditions.
Starting in 1992 with
ensemble forecasts prepared by the
European Centre for Medium-Range Weather Forecasts
The European Centre for Medium-Range Weather Forecasts (ECMWF) is an independent intergovernmental organisation supported by most of the nations of Europe. It is based at three sites: Shinfield Park, Reading, United Kingdom; Bologna, Italy; an ...
(ECMWF) and the
National Centers for Environmental Prediction
The United States National Centers for Environmental Prediction (NCEP) delivers national and global weather, water, climate and space weather guidance, forecasts, warnings and analyses to its Partners and External User Communities. These prod ...
, model ensemble forecasts have been used to help define the forecast uncertainty and to extend the window in which numerical weather forecasting is viable farther into the future than otherwise possible.
The ECMWF model, the Ensemble Prediction System,
uses
singular vectors to simulate the initial
probability density
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can ...
, while the NCEP ensemble, the Global Ensemble Forecasting System, uses a technique known as
vector breeding.
The UK
Met Office
The Meteorological Office, abbreviated as the Met Office, is the United Kingdom's national weather service. It is an executive agency and trading fund of the Department for Business, Energy and Industrial Strategy and is led by CEO Penelope E ...
runs global and regional ensemble forecasts where perturbations to initial conditions are used by 24 ensemble members in the Met Office Global and Regional Ensemble Prediction System (MOGREPS) to produce 24 different forecasts.
In a single model-based approach, the ensemble forecast is usually evaluated in terms of an average of the individual forecasts concerning one forecast variable, as well as the degree of agreement between various forecasts within the ensemble system, as represented by their overall spread. Ensemble spread is diagnosed through tools such as
spaghetti diagrams, which show the dispersion of one quantity on prognostic charts for specific time steps in the future. Another tool where ensemble spread is used is a
meteogram
A meteogram, also known as a meteorogram, is a graphical presentation of one or more meteorological variables with respect to time, whether observed or forecast, for a particular location. Where forecast data is used, the meteogram will typically ...
, which shows the dispersion in the forecast of one quantity for one specific location. It is common for the ensemble spread to be too small to include the weather that actually occurs, which can lead to forecasters misdiagnosing model uncertainty;
this problem becomes particularly severe for forecasts of the weather about ten days in advance. When ensemble spread is small and the forecast solutions are consistent within multiple model runs, forecasters perceive more confidence in the ensemble mean, and the forecast in general.
Despite this perception, a ''spread-skill relationship'' is often weak or not found, as spread-error
correlations
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formal ...
are normally less than 0.6, and only under special circumstances range between 0.6–0.7.
In the same way that many forecasts from a single model can be used to form an ensemble, multiple models may also be combined to produce an ensemble forecast. This approach is called ''multi-model ensemble forecasting'', and it has been shown to improve forecasts when compared to a single model-based approach. Models within a multi-model ensemble can be adjusted for their various biases, which is a process known as ''superensemble forecasting''. This type of forecast significantly reduces errors in model output.
Applications
Air quality modeling
Air quality forecasting attempts to predict when the concentrations of pollutants will attain levels that are hazardous to public health. The concentration of pollutants in the atmosphere is determined by their ''transport'', or
mean
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set.
For a data set, the ''arithme ...
velocity of movement through the atmosphere, their
diffusion
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
,
chemical transformation
A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some references add that chemical substance cannot be separated into its constituent elements by physical separation methods, i.e., wi ...
, and ground
deposition. In addition to pollutant source and terrain information, these models require data about the state of the
fluid flow
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...
in the atmosphere to determine its transport and diffusion.
Meteorological conditions such as
thermal inversion
In meteorology, an inversion is a deviation from the normal change of an atmospheric property with altitude. It almost always refers to an inversion of the air temperature lapse rate, in which case it is called a temperature inversion. N ...
s can prevent surface air from rising, trapping pollutants near the surface, which makes accurate forecasts of such events crucial for air quality modeling. Urban air quality models require a very fine computational mesh, requiring the use of high-resolution mesoscale weather models; in spite of this, the quality of numerical weather guidance is the main uncertainty in air quality forecasts.
Climate modeling
A General Circulation Model (GCM) is a
mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
that can be used in computer simulations of the global circulation of a planetary
atmosphere
An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A s ...
or ocean. An atmospheric general circulation model (AGCM) is essentially the same as a global numerical weather prediction model, and some (such as the one used in the UK Unified Model) can be configured for both short-term weather forecasts and longer-term climate predictions. Along with
sea ice
Sea ice arises as seawater freezes. Because ice is less dense than water, it floats on the ocean's surface (as does fresh water ice, which has an even lower density). Sea ice covers about 7% of the Earth's surface and about 12% of the world's oce ...
and land-surface components, AGCMs and oceanic GCMs (OGCM) are key components of global climate models, and are widely applied for understanding the
climate
Climate is the long-term weather pattern in an area, typically averaged over 30 years. More rigorously, it is the mean and variability of meteorological variables over a time spanning from months to millions of years. Some of the meteorologic ...
and projecting
climate change
In common usage, climate change describes global warming—the ongoing increase in global average temperature—and its effects on Earth's climate system. Climate change in a broader sense also includes previous long-term changes to E ...
. For aspects of climate change, a range of man-made chemical emission scenarios can be fed into the climate models to see how an enhanced
greenhouse effect
The greenhouse effect is a process that occurs when energy from a planet's host star goes through the planet's atmosphere and heats the planet's surface, but greenhouse gases in the atmosphere prevent some of the heat from returning directly ...
would modify the Earth's climate. Versions designed for climate applications with time scales of decades to centuries were originally created in 1969 by
Syukuro Manabe
is a Japanese-American meteorologist and climatologist who pioneered the use of computers to simulate global climate change and natural climate variations. He was awarded the 2021 Nobel Prize in Physics jointly with Klaus Hasselmann and Giorg ...
and
Kirk Bryan at the
Geophysical Fluid Dynamics Laboratory
The Geophysical Fluid Dynamics Laboratory (GFDL) is a laboratory in the National Oceanic and Atmospheric Administration (NOAA) Office of Oceanic and Atmospheric Research (OAR). The current director is Dr. Venkatachalam Ramaswamy. It is one of se ...
in
Princeton, New Jersey
Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...
. When run for multiple decades, computational limitations mean that the models must use a coarse grid that leaves smaller-scale interactions unresolved.
Ocean surface modeling
![NOAA Wavewatch III Sample Forecast](https://upload.wikimedia.org/wikipedia/commons/c/c0/NOAA_Wavewatch_III_Sample_Forecast.gif)
The transfer of energy between the wind blowing over the surface of an ocean and the ocean's upper layer is an important element in wave dynamics. The
spectral wave transport equation is used to describe the change in wave spectrum over changing topography. It simulates wave generation, wave movement (propagation within a fluid),
wave shoaling
In fluid dynamics, wave shoaling is the effect by which surface waves, entering shallower water, change in wave height. It is caused by the fact that the group velocity, which is also the wave-energy transport velocity, changes with water depth ...
,
refraction
In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
, energy transfer between waves, and wave dissipation. Since surface winds are the primary forcing mechanism in the spectral wave transport equation, ocean wave models use information produced by numerical weather prediction models as inputs to determine how much energy is transferred from the atmosphere into the layer at the surface of the ocean. Along with dissipation of energy through
whitecaps and
resonance
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscillatin ...
between waves, surface winds from numerical weather models allow for more accurate predictions of the state of the sea surface.
Tropical cyclone forecasting
Tropical cyclone forecasting also relies on data provided by numerical weather models. Three main classes of
tropical cyclone guidance models exist: Statistical models are based on an analysis of storm behavior using climatology, and correlate a storm's position and date to produce a forecast that is not based on the physics of the atmosphere at the time. Dynamical models are numerical models that solve the governing equations of fluid flow in the atmosphere; they are based on the same principles as other limited-area numerical weather prediction models but may include special computational techniques such as refined spatial domains that move along with the cyclone. Models that use elements of both approaches are called statistical-dynamical models.
In 1978, the first
hurricane-tracking model based on
atmospheric dynamics
Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not ...
—the movable fine-mesh (MFM) model—began operating.
Within the field of
tropical cyclone track forecasting
Tropical cyclone track forecasting involves predicting where a tropical cyclone is going to track over the next five days, every 6 to 12 hours. The history of tropical cyclone track forecasting has evolved from a single-station approach to a ...
, despite the ever-improving dynamical model guidance which occurred with increased computational power, it was not until the 1980s when numerical weather prediction showed
skill
A skill is the learned ability to act with determined results with good execution often within a given amount of time, energy, or both. Skills can often be divided into domain-general and domain-specific skills. For example, in the domain of wo ...
, and until the 1990s when it consistently outperformed
statistical
Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industria ...
or simple dynamical models. Predictions of the intensity of a tropical cyclone based on numerical weather prediction continue to be a challenge, since statistical methods continue to show higher skill over dynamical guidance.
Wildfire modeling
![Propagation model wildfire (English)](https://upload.wikimedia.org/wikipedia/commons/c/c9/Propagation_model_wildfire_%28English%29.svg)
On a molecular scale, there are two main competing reaction processes involved in the degradation of
cellulose
Cellulose is an organic compound with the formula , a polysaccharide consisting of a linear chain of several hundred to many thousands of β(1→4) linked D-glucose units. Cellulose is an important structural component of the primary cell wall ...
, or wood fuels, in
wildfire
A wildfire, forest fire, bushfire, wildland fire or rural fire is an unplanned, uncontrolled and unpredictable fire in an area of Combustibility and flammability, combustible vegetation. Depending on the type of vegetation present, a wildfire ...
s. When there is a low amount of moisture in a cellulose fiber,
volatilization
Volatilization is the process whereby a dissolved sample is vaporised. In atomic spectroscopy this is usually a two-step process. The analyte is turned into small droplets in a nebuliser which are entrained in a gas flow which is in turn volatilis ...
of the fuel occurs; this process will generate intermediate gaseous products that will ultimately be the source of
combustion
Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combusti ...
. When moisture is present—or when enough heat is being carried away from the fiber,
charring Charring is a chemical process of incomplete combustion of certain solids when subjected to high heat. Heat distillation removes water vapour and volatile organic compounds ( syngas) from the matrix. The residual black carbon material is char, as d ...
occurs. The
chemical kinetics
Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with chemical thermodynamics, which deals with the direction in wh ...
of both reactions indicate that there is a point at which the level of moisture is low enough—and/or heating rates high enough—for combustion processes to become self-sufficient. Consequently, changes in wind speed, direction, moisture, temperature, or
lapse rate
The lapse rate is the rate at which an atmospheric variable, normally temperature in Earth's atmosphere, falls with altitude. ''Lapse rate'' arises from the word ''lapse'', in the sense of a gradual fall. In dry air, the adiabatic lapse rate is ...
at different levels of the atmosphere can have a significant impact on the behavior and growth of a wildfire. Since the wildfire acts as a heat source to the atmospheric flow, the wildfire can modify local
advection
In the field of physics, engineering, and earth sciences, advection is the transport of a substance or quantity by bulk motion of a fluid. The properties of that substance are carried with it. Generally the majority of the advected substance is al ...
patterns, introducing a
feedback loop
Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The system can then be said to ''feed back'' into itself. The notion of cause-and-effect has to be handled c ...
between the fire and the atmosphere.
A simplified two-dimensional model for the spread of wildfires that used
convection
Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convec ...
to represent the effects of wind and terrain, as well as
radiative heat transfer
Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. Thermal radiation is generated when heat from the movement of charges in the material (electrons and protons in common forms of matter) is ...
as the dominant method of heat transport led to
reaction–diffusion system
Reaction–diffusion systems are mathematical models which correspond to several physical phenomena. The most common is the change in space and time of the concentration of one or more chemical substances: local chemical reactions in which the s ...
s of
partial differential equation
In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function.
The function is often thought of as an "unknown" to be sol ...
s.
More complex models join numerical weather models or
computational fluid dynamics
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 th ...
models with a wildfire component which allow the feedback effects between the fire and the atmosphere to be estimated.
The additional complexity in the latter class of models translates to a corresponding increase in their computer power requirements. In fact, a full three-dimensional treatment of
combustion
Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combusti ...
via
direct numerical simulation
A direct numerical simulation (DNS)Here the origin of the term ''direct numerical simulation'' (see e.g. p. 385 in ) owes to the fact that, at that time, there were considered to be just two principal ways of getting ''theoretical'' results r ...
at scales relevant for atmospheric modeling is not currently practical because of the excessive computational cost such a simulation would require. Numerical weather models have limited forecast skill at spatial resolutions under , forcing complex wildfire models to parameterize the fire in order to calculate how the winds will be modified locally by the wildfire, and to use those modified winds to determine the rate at which the fire will spread locally.
See also
*
Atmospheric physics
Within the atmospheric sciences, atmospheric physics is the application of physics to the study of the atmosphere. Atmospheric physicists attempt to model Earth's atmosphere and the atmospheres of the other planets using fluid flow equations, che ...
*
Atmospheric thermodynamics Atmospheric thermodynamics is the study of heat-to-work transformations (and their reverse) that take place in the earth's atmosphere and manifest as weather or climate. Atmospheric thermodynamics use the laws of classical thermodynamics, to descr ...
*
Tropical cyclone forecast model
A tropical cyclone forecast model is a computer program that uses meteorological data to forecast aspects of the future state of tropical cyclones. There are three types of models: statistical, dynamical, or combined statistical-dynamic. Dyna ...
*
Types of atmospheric models
References
Further reading
*
*
*
*
*
*From Turbulence to sCl
External links
NOAA Supercomputer upgradeAir Resources LaboratoryFleet Numerical Meteorology and Oceanography CenterEuropean Centre for Medium-Range Weather ForecastsUK Met Office
{{DEFAULTSORT:Numerical Weather Prediction
Computational science
Numerical climate and weather models
Applied mathematics
Weather prediction
Computational fields of study