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== Initialization ==
==Initialization==
[[Image:GOES 8 Spac0255.jpg|right|thumb|[[GOES|GOES-8]], a United States weather satellite.]]
[[Image:Lockheed WP-3D Orion.jpg|thumb|right|320p|A [[WP-3D Orion]] weather reconnaissance aircraft in flight]]
The basic idea of Atmospheric models 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. The main inputs from country-based weather services are surface observations from automated [[weather station]]s at ground level over land and from weather buoys at sea. Sites launch [[radiosonde]]s, which rise through the depth of the [[troposphere]] and well into the [[stratosphere]]. Data from [[weather satellite]]s are used in areas of where traditional data sources are not available. Commerce provides [[pilot report]]s along aircraft routes, and ship reports along their shipping routes. Research flights using [[weather reconnaissance|reconnaissance aircraft]] fly in and around weather systems of interest such as [[tropical cyclone]]s.<ref name="Hurricane Hunters">{{cite web|author=403rd Wing|url=http://www.hurricanehunters.com|title=The Hurricane Hunters|publisher=[[Hurricane Hunters|53rd Weather Reconnaissance Squadron]]|accessdate=2006-03-30}}</ref><ref name="SunHerald">{{cite news|author=Lee, Christopher|title=Drone, Sensors May Open Path Into Eye of Storm|url=http://www.washingtonpost.com/wp-dyn/content/article/2007/10/07/AR2007100700971_pf.html|publisher=The Washington Post|accessdate=2008-02-22}}</ref> 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 3–7 days into the future over the downstream continent.<ref>{{cite web|url=http://www.noaanews.noaa.gov/stories2010/20100112_plane.html|title=NOAA Dispatches High-Tech Research Plane to Improve Winter Storm Forecasts|date=2010-11-12|accessdate=2010-12-22|author=[[National Oceanic and Atmospheric Administration]]}}</ref> Models are ''initialized'' using this observed data. 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.
The [[atmosphere]] is a [[fluid]]. As such, the idea of numerical weather prediction is to sample the state of the fluid at a given time and use the equations of [[fluid dynamics]] and [[thermodynamics]] to estimate the state of the fluid at some time in the future. The main inputs from country-based weather services are surface observations from automated [[weather station]]s at ground level over land and from weather buoys at sea. The [[World Meteorological Organization]] acts to standardize the instrumentation, observing practices and timing of these observations worldwide. Stations either report hourly in [[METAR]] reports,<ref>{{cite web|title=Key to METAR Surface Weather Observations|url=http://www.ncdc.noaa.gov/oa/climate/conversion/swometardecoder.html|publisher=[[National Oceanic and Atmospheric Administration]]|accessdate=2011-02-11|author=[[National Climatic Data Center]]|date=2008-08-20}}</ref> or every six hours in [[SYNOP]] reports.<ref>{{cite web|title=SYNOP Data Format (FM-12): Surface Synoptic Observations|publisher=[[UNISYS]]|accessdate=2011-02-11|archiveurl=http://web.archive.org/web/20071230100059/http://weather.unisys.com/wxp/Appendices/Formats/SYNOP.html|archivedate=2007-12-30|date=2008-05-25}}</ref> Models are ''initialized'' using this observed data. 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. The grid used for global models is [[geodesic grid|geodesic]] or [[icosahedron|icosahedral]], spaced by latitude, longitude, and elevation.<ref>{{cite book|url=http://books.google.com/books?id=BQ_7vh5SrHQC&pg=PA224&dq=geodesic+grid+numerical+weather+prediction+book&hl=en&ei=EdwlTdPyE4OKlwffn4TlAQ&sa=X&oi=book_result&ct=result&resnum=3&ved=0CDEQ6AEwAg#v=onepage&q=geodesic%20grid%20numerical%20weather%20prediction%20book&f=false|page=224|title=Parallel computational fluid dynamics: parallel computings and its applications : proceedings of the Parallel CFD 2006 Conference, Busan city, Korea (May 15–18, 2006)|author=Kwon, J. H.|year=2007|accessdate=2011-01-06|publisher=Elsevier|ISBN=9780444530356}}</ref> The data are then used in the model as the starting point for a forecast.<ref>{{cite web|title=The WRF Variational Data Assimilation System (WRF-Var)|publisher=[[University Corporation for Atmospheric Research]]|accessdate=2011-02-11|archiveurl=http://web.archive.org/web/20070814044336/http://www.mmm.ucar.edu/wrf/WG4/wrfvar/wrfvar-tutorial.htm|archivedate=2007-08-14|date=2007-08-14}}</ref>
A variety of methods are used to gather observational data for use in numerical models. Sites launch [[radiosonde]]s, which rise through the [[troposphere]] and well into the [[stratosphere]].<ref>{{cite web|last=Gaffen|first=Dian J.|title=Radiosonde Observations and Their Use in SPARC-Related Investigations|accessdate=2011-02-11|archiveurl=http://web.archive.org/web/20070607142822/http://www.aero.jussieu.fr/~sparc/News12/Radiosondes.html|archivedate=2007-06-07|date=2007-06-07}}</ref> Information from [[weather satellite]]s is used where traditional data sources are not available. Commerce provides [[pilot report]]s along aircraft routes<ref>Ballish, Bradley A. and V. Krishna Kumar (2008-05-23). [http://amdar.noaa.gov/docs/bams_ballish_kumar.pdf Investigation of Systematic Differences in Aircraft and Radiosonde Temperatures with Implications for NWP and Climate Studies.] Retrieved 2008-05-25.</ref> and ship reports along shipping routes. Research projects use [[weather reconnaissance|reconnaissance aircraft]] to fly in and around weather systems of interest, such as [[tropical cyclone]]s.<ref name="Hurricane Hunters">{{cite web|year=2011|author=403rd Wing|url=http://www.hurricanehunters.com|title=The Hurricane Hunters|publisher=[[Hurricane Hunters|53rd Weather Reconnaissance Squadron]]|accessdate=2006-03-30}}</ref><ref name="SunHerald">{{cite journal|author=Lee, Christopher|title=Drone, Sensors May Open Path Into Eye of Storm|url=http://www.washingtonpost.com/wp-dyn/content/article/2007/10/07/AR2007100700971_pf.html|journal=The Washington Post|accessdate=2008-02-22|date=2007-10-08}}</ref> 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 3–7&nbsp;days into the future over the downstream continent.<ref>{{cite web|url=http://www.noaanews.noaa.gov/stories2010/20100112_plane.html|title=NOAA Dispatches High-Tech Research Plane to Improve Winter Storm Forecasts|date=2010-11-12|accessdate=2010-12-22|author=[[National Oceanic and Atmospheric Administration]]}}</ref> Sea ice began to be initialized in forecast models in 1971.<ref>{{cite book|url=http://books.google.com/books?id=lMXSpRwKNO8C&pg=PA137&dq=sea+ice+use+numerical+weather+prediction+book&hl=en&ei=wIkoTYfsOcT6lwfX36mjAQ&sa=X&oi=book_result&ct=result&resnum=6&ved=0CEgQ6AEwBQ#v=onepage&q=sea%20ice%20use%20numerical%20weather%20prediction%20book&f=false|author=Stensrud, David J.|page=137|title=Parameterization schemes: keys to understanding numerical weather prediction models|publisher=[[Cambridge University Press]]|year=2007|accessdate=2011-01-08|ISBN=9780521865401}}</ref> Efforts to involve [[sea surface temperature]] in model initialization began in 1972 due to its role in modulating weather in higher latitudes of the Pacific.<ref>{{cite book|url=http://books.google.com/books?id=SV04AAAAIAAJ&pg=PA38&dq=sea+surface+temperature+importance+use+numerical+weather+prediction+book&hl=en&ei=IYwoTZ7QJ4Odlgenrqm8AQ&sa=X&oi=book_result&ct=result&resnum=8&ved=0CFIQ6AEwBw#v=onepage&q=sea%20surface%20temperature%20importance%20use%20numerical%20weather%20prediction%20book&f=false|pages=49–50|title=The Global Climate|author=Houghton, John Theodore|publisher=Cambridge University Press archive|year=1985|accessdate=2011-01-08|ISBN=9780521312561}}</ref>

==Computation==
[[Image:GFS 850 MB.PNG|right|260px|thumb|A prognostic chart of the 96-hour forecast of 850 [[millibar|mbar]] [[geopotential height]] and [[temperature]] from the [[Global Forecast System]]]]

{{Main|Atmospheric model}}
Essentially, a model is a computer program that produces [[meteorological]] information for future times at given locations and altitudes. Within any model is a set of equations, known as the [[primitive equations]], used to predict the future state of the atmosphere.<ref>{{cite book|last=Pielke|first=Roger A.|title=Mesoscale Meteorological Modeling|year=2002|publisher=[[Academic Press]]|isbn=0125547668|pages=48–49|accessdate=2011-01-02}}</ref> 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, with each time increment known as a time step. The equations are then applied to this new atmospheric state to find new rates of change, and these new rates of change predict the atmosphere at a yet further time into the future. ''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]].<ref>{{cite book|last=Pielke|first=Roger A.|title=Mesoscale Meteorological Modeling|year=2002|publisher=[[Academic Press]]|isbn=0125547668|pages=285–287|accessdate=2011-01-02}}</ref> Time steps for global models are on the order of tens of minutes,<ref>{{cite book|url=http://books.google.com/books?id=JZikIbXzipwC&pg=PA131&lpg=PA131&dq=time+step+numerical+weather+prediction&source=bl&ots=KoeMxpt3_J&sig=7DEG9Sjy6-8O9BVJtNuLnWOBrBo&hl=en&ei=9xshTem6C8GB8gaGzq3fDQ&sa=X&oi=book_result&ct=result&resnum=7&sqi=2&ved=0CEIQ6AEwBg#v=onepage&q=time%20step%20numerical%20weather%20prediction&f=false|page=132|title=|author=Sunderam, V. S., G. Dick van Albada, Peter M. A. Sloot, J. J. Dongarra|title=Computational Science – ICCS 2005: 5th International Conference, Atlanta, GA, USA, May 22–25, 2005, Proceedings, Part 1|year=2005|accessdate=2011-01-02|publisher=Springer|ISBN=9783540260325}}</ref> while time steps for regional models are between one and four minutes.<ref>{{cite book|url=http://books.google.com/books?id=UV6PnF2z5_wC&pg=PA276&dq=time+step+WRF+weather&hl=en&ei=iCAhTejVDMOBlAfz6-WcDA&sa=X&oi=book_result&ct=result&resnum=2&ved=0CDIQ6AEwAQ#v=onepage&q=time%20step%20WRF%20weather&f=false|page=276|title=Developments in teracomputing: proceedings of the ninth ECMWF Workshop on the Use of High Performance Computing in Meteorology|author=Zwieflhofer, Walter, Norbert Kreitz, European Centre for Medium Range Weather Forecasts|year=2001|accessdate=2011-01-02|publisher=World Scientific|ISBN=9789810247614}}</ref>

The equations used are [[nonlinear system|nonlinear]] partial differential equations which are impossible to solve exactly through analytical methods,<ref name="finite">{{cite book|url=http://books.google.com/books?id=SH8R_flZBGIC&pg=PA165&lpg=PA165&dq=numerical+weather+prediction+partial+differential+equations+book&source=bl&ots=C_jqWj-tu6&sig=kY2D6joPnrFWh9qC3oI0u4BMdoI&hl=en&ei=uBMeTa3EHIH78AaS-_DSDQ&sa=X&oi=book_result&ct=result&resnum=6&ved=0CDwQ6AEwBQ#v=onepage&q=numerical%20weather%20prediction%20partial%20differential%20equations%20book&f=false|title=Finite difference schemes and partial differential equations|author=Strikwerda, John C.|pages=165–170|year=2004|publisher=SIAM|ISBN=9780898715675|accessdate=2010-12-31}}</ref> with the exception of a few idealized cases.<ref>{{cite book|last=Pielke|first=Roger A.|title=Mesoscale Meteorological Modeling|year=2002|publisher=[[Academic Press]]|isbn=0125547668|pages=65|accessdate=2011-01-02}}</ref> Therefore, numerical methods obtain approximate solutions. Different models use different solution methods: some global models use [[spectral method]]s for the horizontal dimensions and [[finite difference method]]s for the vertical dimension, while regional models and other global models usually use finite-difference methods in all three dimensions.<ref name="finite"/> The visual output produced by a model solution is known as a prognostic chart, or ''prog''.<ref>{{cite book|author=Ahrens, C. Donald|page=244|ISBN=9780495115588|year=2008|publisher=Cengage Learning|title=Essentials of meteorology: an invitation to the atmosphere|url=http://books.google.com/books?id=2Yn29IFukbgC&pg=PA244&lpg=PA244&dq=regional+weather+forecast+model+characteristics+book&source=bl&ots=iBxiwg0atz&sig=dj58_uKk0k3ef8RxnjbZb76QZ74&hl=en&ei=JyQeTfWZK8H7lweXgYXkCw&sa=X&oi=book_result&ct=result&resnum=6&ved=0CDkQ6AEwBQ#v=onepage&q&f=false|accessdate=2011-02-11}}</ref>

==Domains==
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, or LAMs. Regional models use finer grid spacing to resolve explicitly smaller-scale meteorological phenomena, since their smaller domain decreases computational demands. Regional models use a compatible global model for initial conditions of the edge of their domain. Uncertainty and errors within LAMs are introduced by the global model used for the boundary conditions of the edge of the regional model, as well as within the creation of the boundary conditions for the LAMs itself.<ref>{{cite book|url=http://books.google.com/books?id=6RQ3dnjE8lgC&pg=PA261&dq=use+of+ensemble+forecasts+book&hl=en&ei=nqIgTcuJLMX_lgeOn8m8DA&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC4Q6AEwAA#v=onepage&q=use%20of%20ensemble%20forecasts%20book&f=false|title=Numerical Weather and Climate Prediction|author=Warner, Thomas Tomkins |publisher=[[Cambridge University Press]]|year=2010|ISBN=9780521513890|page=259|accessdate=2011-02-11}}</ref>

The vertical coordinate is handled in various ways. Some models, such as Richardson's 1922 model, use geometric height (<math>z</math>) as the vertical coordinate. Later models substituted the geometric <math>z</math> coordinate with a pressure coordinate system, in which the [[geopotential height]]s of constant-pressure surfaces become [[dependent variable]]s, greatly simplifying the primitive equations.<ref name="Lynch Ch2">{{cite book|last=Lynch|first=Peter|title=The Emergence of Numerical Weather Prediction|year=2006|publisher=[[Cambridge University Press]]|isbn=9780521857291|pages=45–46|chapter=The Fundamental Equations}}</ref> This follows since pressure decreases with height through the [[Earth's atmosphere]].<ref>{{cite book|author=Ahrens, C. Donald|page=10|ISBN=9780495115588|year=2008|publisher=Cengage Learning|title=Essentials of meteorology: an invitation to the atmosphere|url=http://books.google.com/books?id=2Yn29IFukbgC&pg=PA244&lpg=PA244&dq=regional+weather+forecast+model+characteristics+book&source=bl&ots=iBxiwg0atz&sig=dj58_uKk0k3ef8RxnjbZb76QZ74&hl=en&ei=JyQeTfWZK8H7lweXgYXkCw&sa=X&oi=book_result&ct=result&resnum=6&ved=0CDkQ6AEwBQ#v=onepage&q&f=false|accessdate=2011-02-11}}</ref> The first model used for operational forecasts, the single-layer barotropic model, used a single pressure coordinate at the {{convert|500|mbar|inHg|adj=on}} level,<ref name="Charney 1950"/> 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''.<ref>{{cite web|last=Janjic |first=Zavisa|title=Scientific Documentation for the NMM Solver|url=http://nldr.library.ucar.edu/collections/technotes/asset-000-000-000-845.pdf|publisher=[[National Center for Atmospheric Research]]|accessdate=2011-01-03|coauthors=Gall, Robert; Pyle, Matthew E.|pages=12–13|month=February|year=2010}}</ref> This coordinate system receives that name since the [[independent variable]] <math>\sigma</math> is used to represent a pressure level (<math>p</math>) [[nondimensionalization|scaled]] with the surface pressure (<math>p_0</math>) and in some cases the pressure at the top of the domain (<math>p_T</math>).<ref>Pielke, pp. 131–132</ref>

==Model output statistics==
{{Main article|Model output statistics}}
Because forecast models based upon the equations for atmospheric dynamics do not perfectly determine weather conditions near the ground, statistical corrections were developed to attempt to resolve this problem. 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]] (MOS),<ref>{{cite book|url=http://books.google.com/books?id=blEMoIKX_0IC&pg=PA188&dq=model+output+statistics+book&hl=en&ei=8KxVTcGPH4j2gAe_isnwDA&sa=X&oi=book_result&ct=result&resnum=3&ved=0CEgQ6AEwAg#v=onepage&q=model%20output%20statistics%20book&f=false|page=189|title=When nature strikes: weather disasters and the law|author=Baum, Marsha L.|publisher=Greenwood Publishing Group|date=2007|ISBN=9780275221294|accessdate=2011-02-11}}</ref> and were developed by the [[National Weather Service]] for their suite of weather forecasting models by 1976.<ref>{{cite book|title=Model output statistics forecast guidance|author=Harry Hughes|publisher=United States Air Force Environmental Technical Applications Center|date=1976|pages=1–16}}</ref> The [[United States Air Force]] developed its own set of MOS based upon their dynamical weather model by 1983.<ref>{{cite book|title=Air Weather Service Model Output Statistics Systems|author=L. Best, D. L. and S. P. Pryor|date=1983|pages=1–90|publisher=Air Force Global Weather Central}}</ref>

Model output statistics differ from the ''perfect prog'' technique, which assumes that the output of numerical weather prediction guidance is perfect.<ref>{{cite book|url=http://books.google.com/books?id=QwzHZ-wV-BAC&pg=PA1144&dq=model+output+statistics+book&hl=en&ei=8KxVTcGPH4j2gAe_isnwDA&sa=X&oi=book_result&ct=result&resnum=6&ved=0CFgQ6AEwBQ#v=onepage&q=model%20output%20statistics%20book&f=false|page=1144|title=Fog and boundary layer clouds: fog visibility and forecasting|author=Gultepe, Ismail|publisher=Springer|date=2007|ISBN=9783764384180|accessdate=2011-02-11}}</ref> MOS can correct for local effects that cannot be resolved by the model due to insufficient grid resolution, as well as model biases. 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.<ref>{{cite book|url=http://books.google.com/books?id=Xs9LiGpNX-AC&pg=PA171&dq=model+output+statistics+book&hl=en&ei=3bJVTbOJG8iSgQfJ9v3dDA&sa=X&oi=book_result&ct=result&resnum=6&ved=0CFQQ6AEwBTgK#v=onepage&q=model%20output%20statistics%20book&f=false|page=172|author=Barry, Roger Graham and Richard J. Chorley|title=Atmosphere, weather, and climate|publisher=Psychology Press|date=2003|accessdate=2011-02-11|ISBN=9780415271714}}</ref>


== Applications ==
===Climate modeling===
{{See also|Global climate model}}
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]].<ref>{{cite journal|last=Phillips|first=Norman A.|title=The general circulation of the atmosphere: a numerical experiment|journal=Quarterly Journal of the [[Royal Meteorological Society]]|year=1956|month=April|volume=82|issue=352|pages=123–154|accessdate=2010-12-31}}</ref><ref>{{cite book|title=Storm Watchers|page=210|year=2002|author=Cox, John D.|publisher=John Wiley & Sons, Inc.|ISBN=047138108X}}</ref> Following Phillips's work, several groups began working to create [[general circulation model]]s.<ref name="Lynch Ch10"/> The first general circulation climate model that combined both oceanic and atmospheric processes was developed in the late 1960s at the [[NOAA]] [[Geophysical Fluid Dynamics Laboratory]].<ref>{{cite web|url=http://celebrating200years.noaa.gov/breakthroughs/climate_model/welcome.html|title=The First Climate Model|author=[[National Oceanic and Atmospheric Administration]]|date=2008-05-22|accessdate=2011-01-08}}</ref> By the early 1980s, the United States' [[National Center for Atmospheric Research]] had developed the Community Atmosphere Model; this model has been continuously refined into the 2000s.<ref>{{cite web|last=Collins|first=William D. |title=Description of the NCAR Community Atmosphere Model (CAM 3.0)|url=http://www.cesm.ucar.edu/models/atm-cam/docs/description/description.pdf|publisher=[[University Corporation for Atmospheric Research]]|accessdate=2011-01-03|coauthors=et al.|month=June|year=2004}}</ref> In 1986, efforts began to initialize and model soil and vegetation types, which led to more realistic forecasts.<ref>{{cite journal|url=http://www.geog.ucla.edu/~yxue/pdf/1996jgr.pdf|title=Impact of vegetation properties on U. S. summer weather prediction|page=7419|author=Xue, Yongkang and Michael J. Fennessey|journal=[[Journal of Geophysical Research]]|volume=101|number=D3|date=1996-03-20|accessdate=2011-01-06|publisher=[[American Geophysical Union]]}}</ref> Coupled ocean-atmosphere climate models such as the [[Hadley Centre for Climate Prediction and Research]]'s [[HadCM3]] model are currently being used as inputs for [[climate change]] studies.<ref name="Lynch Ch10">{{cite book|last=Lynch|first=Peter|title=The Emergence of Numerical Weather Prediction|year=2006|publisher=[[Cambridge University Press]]|isbn=9780521857291|pages=206–208|chapter=The ENIAC Integrations}}</ref>

===Limited area modeling===
{{seealso|Tropical cyclone forecast model}}
[[Air quality]] forecasts depend on Atmospheric models to provide [[fluid flow]] information for tracking the movement of a pollutant.<ref>{{cite journal|last=Baklanov|first=Alexander|coauthors=Alix Rasmussen, Barbara Fay, Erik Berge, Sandro Finardi|title=Potential and Shortcomings of Numerical Weather Prediction Models in Providing Meteorological Data for Urban Air Pollution Forecasting|journal=Water, Air and Soil Pollution: Focus|year=2002|month=September|volume=2|issue=5|pages=43–60|doi=10.1023/A:1021394126149|accessdate=2011-02-13}}</ref> The Urban Airshed Model, a regional forecast model for the effects of [[air pollution]] and [[acid rain]], was developed by a private company in the USA in 1970. Development of this model was taken over by the [[Environmental Protection Agency]] and improved in the mid to late 1970s using results from a regional air pollution study. While developed in [[California]], this model was later used in other areas of [[North America]], [[Europe]] and [[Asia]] during the 1980s.<ref>{{cite book|title=Air pollution modeling and its application VIII, Volume 8|author=Steyn, D. G.|publisher=Birkhäuser|year=1991|pages=241–242|ISBN=9780306438288}}</ref>

In 1978, the first [[tropical cyclone forecast model|hurricane-tracking model]] based on [[Atmospheric dynamics#Dynamic meteorology|atmospheric dynamics]] – the movable fine-mesh (MFM) model – began operating .<ref name="Shuman W&F"/> Within the field of [[tropical cyclone track forecasting]], despite the ever-improving dynamical model guidance which occurred with increased computational power, it was not until the decade of the 1980s when numerical weather prediction showed [[Forecast skill|skill]], and until the 1990s when it consistently outperformed [[statistical model|statistical]] or simple dynamical models.<ref>{{cite web|url=http://www.nhc.noaa.gov/verification/verify6.shtml|publisher=[[National Hurricane Center]]|date=2010-04-20|accessdate=2011-01-02|author=[[James Franklin (meteorologist)|Franklin, James]]|title=National Hurricane Center Forecast Verification}}</ref> However, predictions of the intensity of a tropical cyclone based on numerical weather predictions continues to be a challenge, since statical methods continue to show higher skill over dynamical guidance.<ref>{{cite journal|last=Rappaport|first=Edward N.|coauthors=James L. Franklin, Lixion A. Avila, Stephen R. Baig, John L. Beven II, Eric S. Blake, Christopher A. Burr, Jiann-Gwo Jiing, Christopher A. Juckins, Richard D. Knabb, Christopher W. Landsea, Michelle Mainelli, Max Mayfield, Colin J. McAdie, Richard J. Pasch, Christopher Sisko, Stacy R. Stewart, Ahsha N. Tribble|title=Advances and Challenges at the National Hurricane Center|journal=[[Weather and Forecasting]]|year=2009|month=April|volume=24|issue=2|pages=395–419|doi=10.1175/2008WAF2222128.1}}</ref>


== Global models ==
== Global models ==

Revision as of 11:56, 15 February 2011

A 96-hour forecast of 850 mbar geopotential height and temperature from the Global Forecast System

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 regional (limited-area), covering only part of the Earth.

= 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.

History

Until the end of the 19th century, weather prediction was entirely subjective and based on empirical rules, with only limited understanding of the physical mechanisms behind weather processes. In 1901 Cleveland Abbe, founder of the United States Weather Bureau, proposed that the atmosphere is governed by the same principles of thermodynamics and hydrodynamics that were studied in the previous century.[1] In 1904, Vilhelm Bjerknes derived a two-step procedure for model-based weather forecasting. First, a diagnostic step is used to process data to generate initial conditions, which are then advanced in time by a prognostic step that solves the initial value problem.[2] He also identified seven variables that defined the state of the atmosphere at a given point: pressure, temperature, density, humidity, and the three components of the velocity vector. Bjerknes pointed out that equations based on mass continuity, conservation of momentum, the first and second laws of thermodynamics, and the ideal gas law could be used to estimate the state of the atmosphere in the future through numerical methods.[3] These equations form the basis of the primitive equations used in present-day weather models.[4]

In 1922, Lewis Fry Richardson published the first attempt at forecasting the weather numerically. Using a hydrostatic variation of Bjerknes's primitive equations,[2] Richardson produced by hand a 6-hour forecast for the state of the atmosphere over two points in central Europe, taking at least six weeks to do so.[3] His forecast calculated that the change in surface pressure would be 145 millibars (4.3 inHg), an unrealistic value incorrect by two orders of magnitude. The large error was caused by an imbalance in the pressure and wind velocity fields used as the initial conditions in his analysis.[2]

The ENIAC main control panel at the Moore School of Electrical Engineering

The first successful numerical prediction was performed using the ENIAC digital computer in 1950 by a team composed of American meteorologists Jule Charney, Philip Thompson, Larry Gates, and Norwegian meteorologist Ragnar Fjörtoft and applied mathematician John von Neumann. They used a simplified form of atmospheric dynamics based on solving the barotropic vorticity equation over a single layer of the atmosphere, by computing the geopotential height of the atmosphere's 500 millibars (15 inHg) pressure surface.[5] This simplification greatly reduced demands on computer time and memory, so the computations could be performed on the relatively primitive computers of the day.[6] When news of the first weather forecast by ENIAC was received by Richardson in 1950, he remarked that the results were an "enormous scientific advance."[2] The first calculations for a 24 hour forecast took ENIAC nearly 24 hours to produce,[2] but Charney's group noted that most of that time was spent in "manual operations", and expressed hope that forecasts of the weather before it occurs would soon be realized.[5]

In September 1954, Carl-Gustav Rossby's group at the Swedish Meteorological and Hydrological Institute produced the first operational forecast (i.e. routine predictions for practical use) based on the barotropic equation.[7] 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, Navy, and Weather Bureau.[8] The JNWPU model was originally a three-layer barotropic model, also developed by Charney.[9] In 1956, the JNWPU switched to a two-layer thermotropic model developed by Thompson and Gates.[9] The main assumption made by the thermotropic model is that while the magnitude of the thermal wind may change, its direction does not change with respect to height, and thus the baroclinicity in the atmosphere can be simulated using the 500 mb (15 inHg) and 1,000 mb (30 inHg) geopotential height surfaces and the average thermal wind between them.[10][11] However, due to the low skill showed by the thermotropic model, the JNWPU reverted to the single-layer barotropic model in 1958.[2] The first real-time forecasts made by Australia's Bureau of Meteorology in 1969 were also based on the single-layer barotropic model.[12]

An example of 500 mbar geopotential height prediction from a numerical weather prediction model

Later models used more complete equations for atmospheric dynamics and thermodynamics. In 1959, Karl-Heinz Hinkelmann produced the first reasonable primitive equation forecast, 37 years after Richardson's failed attempt. Hinkelmann did so by removing small oscillations from the numerical model during initialization. In 1966, West Germany and the United States began producing operational forecasts based on primitive-equation models, followed by the United Kingdom in 1972 and Australia in 1977.[2][12] Later additions to primitive equation models allowed additional insight into different weather phenomena. In the United States, solar radiation effects were added to the primitive equation model in 1967; moisture effects and latent heat were added in 1968; and feedback effects from rain on convection were incorporated in 1971. The first operational regional model, the limited-area fine-mesh (LFM) model, was also introduced in 1971.[9] Three years later, the first global forecast model was introduced.[9]


Initialization

A WP-3D Orion weather reconnaissance aircraft in flight

The atmosphere is a fluid. As such, the idea of numerical weather prediction is to sample the state of the fluid at a given time and use the equations of fluid dynamics and thermodynamics to estimate the state of the fluid at some time in the future. The main inputs from country-based weather services are surface observations from automated weather stations at ground level over land and from weather buoys at sea. The World Meteorological Organization acts to standardize the instrumentation, observing practices and timing of these observations worldwide. Stations either report hourly in METAR reports,[13] or every six hours in SYNOP reports.[14] Models are initialized using this observed data. 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. The grid used for global models is geodesic or icosahedral, spaced by latitude, longitude, and elevation.[15] The data are then used in the model as the starting point for a forecast.[16]

A variety of methods are used to gather observational data for use in numerical models. Sites launch radiosondes, which rise through the troposphere and well into the stratosphere.[17] Information from weather satellites is used where traditional data sources are not available. Commerce provides pilot reports along aircraft routes[18] and ship reports along shipping routes. Research projects use reconnaissance aircraft to fly in and around weather systems of interest, such as tropical cyclones.[19][20] 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 3–7 days into the future over the downstream continent.[21] Sea ice began to be initialized in forecast models in 1971.[22] Efforts to involve sea surface temperature in model initialization began in 1972 due to its role in modulating weather in higher latitudes of the Pacific.[23]

Computation

A prognostic chart of the 96-hour forecast of 850 mbar geopotential height and temperature from the Global Forecast System
Main article: Atmospheric model

Essentially, a model is a computer program that produces meteorological information for future times at given locations and altitudes. Within any model is a set of equations, known as the primitive equations, used to predict the future state of the atmosphere.[24] 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, with each time increment known as a time step. The equations are then applied to this new atmospheric state to find new rates of change, and these new rates of change predict the atmosphere at a yet further time into the future. 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.[25] Time steps for global models are on the order of tens of minutes,[26] while time steps for regional models are between one and four minutes.[27]

The equations used are nonlinear partial differential equations which are impossible to solve exactly through analytical methods,[28] with the exception of a few idealized cases.[29] 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 finite-difference methods in all three dimensions.[28] The visual output produced by a model solution is known as a prognostic chart, or prog.[30]

Domains

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, or LAMs. Regional models use finer grid spacing to resolve explicitly smaller-scale meteorological phenomena, since their smaller domain decreases computational demands. Regional models use a compatible global model for initial conditions of the edge of their domain. Uncertainty and errors within LAMs are introduced by the global model used for the boundary conditions of the edge of the regional model, as well as within the creation of the boundary conditions for the LAMs itself.[31]

The vertical coordinate is handled in various ways. Some models, such as Richardson's 1922 model, use geometric height () as the vertical coordinate. Later models substituted the geometric coordinate with a pressure coordinate system, in which the geopotential heights of constant-pressure surfaces become dependent variables, greatly simplifying the primitive equations.[32] This follows since pressure decreases with height through the Earth's atmosphere.[33] The first model used for operational forecasts, the single-layer barotropic model, used a single pressure coordinate at the 500-millibar (15 inHg) level,[5] 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.[34] This coordinate system receives that name since the independent variable is used to represent a pressure level () scaled with the surface pressure () and in some cases the pressure at the top of the domain ().[35]

Model output statistics

Main article: Model output statistics

Because forecast models based upon the equations for atmospheric dynamics do not perfectly determine weather conditions near the ground, statistical corrections were developed to attempt to resolve this problem. 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 (MOS),[36] and were developed by the National Weather Service for their suite of weather forecasting models by 1976.[37] The United States Air Force developed its own set of MOS based upon their dynamical weather model by 1983.[38]

Model output statistics differ from the perfect prog technique, which assumes that the output of numerical weather prediction guidance is perfect.[39] MOS can correct for local effects that cannot be resolved by the model due to insufficient grid resolution, as well as model biases. 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.[40]


Applications

Climate modeling

See also: Global climate model

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.[41][42] Following Phillips's work, several groups began working to create general circulation models.[43] The first general circulation climate model that combined both oceanic and atmospheric processes was developed in the late 1960s at the NOAA Geophysical Fluid Dynamics Laboratory.[44] By the early 1980s, the United States' National Center for Atmospheric Research had developed the Community Atmosphere Model; this model has been continuously refined into the 2000s.[45] In 1986, efforts began to initialize and model soil and vegetation types, which led to more realistic forecasts.[46] Coupled ocean-atmosphere climate models such as the Hadley Centre for Climate Prediction and Research's HadCM3 model are currently being used as inputs for climate change studies.[43]

Limited area modeling

See also: Tropical cyclone forecast model

Air quality forecasts depend on Atmospheric models to provide fluid flow information for tracking the movement of a pollutant.[47] The Urban Airshed Model, a regional forecast model for the effects of air pollution and acid rain, was developed by a private company in the USA in 1970. Development of this model was taken over by the Environmental Protection Agency and improved in the mid to late 1970s using results from a regional air pollution study. While developed in California, this model was later used in other areas of North America, Europe and Asia during the 1980s.[48]

In 1978, the first hurricane-tracking model based on atmospheric dynamics – the movable fine-mesh (MFM) model – began operating .[9] Within the field of tropical cyclone track forecasting, despite the ever-improving dynamical model guidance which occurred with increased computational power, it was not until the decade of the 1980s when numerical weather prediction showed skill, and until the 1990s when it consistently outperformed statistical or simple dynamical models.[49] However, predictions of the intensity of a tropical cyclone based on numerical weather predictions continues to be a challenge, since statical methods continue to show higher skill over dynamical guidance.[50]

Global models

Some of the better known global numerical models are:

Regional models

Some of the better known regional numerical models are:

  • 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 hundreds of kilometers - now supported in the public domain RAMS source code available under the GNU General Public License
  • MM5 The Fifth Generation Penn State/NCAR Mesoscale Model MM5 Source Code download
  • 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. The source code of ARPS is freely available.
  • 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 (ALADIN Community web pages)
  • COSMO The COSMO Model, formerly known as LM, aLMo or LAMI, is a limited-area non-hydrostatic model developed within the framework of the Consortium for Small-Scale Modelling (Germany, Switzerland, Italy, Greece, Poland, Romania, and Russia).[51]
  1. COSMO The COSMO Model (formerly known as LM, aLMo or LAMI) is a limited-area non-hydrostatic model for operational numerical weather prediction, regional climate modelling, environmental prediction (aerosols, pollen and atmospheric chemistry) and research (idealised case studies). A first NWP version was originally developed by the German Weather Service. It is now further developed by the Consortium for Small-Scale Modelling (www.cosmo-model.org, Germany, Switzerland, Italy, Greece, Poland, Romania, and Russia), the Climate Limited-area Modelling (CLM)-Community (www.clm-community.eu) and other research institutes.[1]

See also

References

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  37. ^ Harry Hughes (1976). Model output statistics forecast guidance. United States Air Force Environmental Technical Applications Center. pp. 1–16.
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  51. ^ Consortium on Small Scale Modelling. Consortium for Small-scale Modeling. Retrieved on 2008-01-13.
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