Editing Weather forecasting (section)

== Numerical weather prediction ==
[[File:NAM 500 MB.PNG|thumb|An example of 500 [[millibar|mbar]] [[geopotential height]] and absolute [[vorticity]] prediction from a numerical weather prediction model]]
{{Main|Numerical weather prediction}}

The basic idea of numerical weather prediction is to sample the state of the fluid at a given time and use the equations of [[fluid dynamics]] and [[thermodynamics]] to estimate the state of the fluid at some time in the future. The main inputs from country-based weather services are [[Surface weather observation|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>[[National Climatic Data Center]]. [http://www.ncdc.noaa.gov/oa/climate/conversion/swometardecoder.html "Key to METAR Surface Weather Observations"] {{Webarchive|url=https://web.archive.org/web/20021101221848/http://www0.ncdc.noaa.gov/oa/climate/conversion/swometardecoder.html |date=November 1, 2002 }}. Retrieved March 9, 2008.</ref> or every six hours in [[SYNOP]] reports.<ref>[[UNISYS]]. [http://weather.unisys.com/wxp/Appendices/Formats/SYNOP.html "SYNOP Data Format (FM-12): Surface Synoptic Observations"]. {{webarchive|url=https://web.archive.org/web/20071230100059/http://weather.unisys.com/wxp/Appendices/Formats/SYNOP.html |date=December 30, 2007 }} Retrieved May 25, 2008.</ref> Sites launch [[radiosonde]]s, which rise through the depth of the [[troposphere]] and well into the [[stratosphere]].<ref>Gaffen, Dian J. (June 7, 2007). [https://web.archive.org/web/20070607142822/http://www.aero.jussieu.fr/~sparc/News12/Radiosondes.html "Radiosonde Observations and Their Use in SPARC-Related Investigations"]. Retrieved May 25, 2008.</ref> Data from [[weather satellite]]s are used in areas where traditional data sources are not available.<ref>[[NASA]]. [http://wwwghcc.msfc.nasa.gov/GOES/globalir.html "Interactive Global Composite Weather Satellite Images"] {{webarchive|url=https://web.archive.org/web/20080531175530/http://wwwghcc.msfc.nasa.gov/GOES/globalir.html |date=May 31, 2008 }}. Retrieved May 25, 2008.</ref><ref>[[NOAA]]. [http://www.goes.noaa.gov/ECIR4.html Goes Eastern US Sector Infrared Image] {{Webarchive|url=https://web.archive.org/web/20080523192007/http://www.goes.noaa.gov/ECIR4.html |date=May 23, 2008 }}. Retrieved May 25, 2008.</ref><ref>[[Met Office]]. [https://archive.today/20070705213142/http://www.metoffice.gov.uk/research/nwp/satellite/ "Satellite applications"]. Retrieved May 25, 2008.</ref> Compared with similar data from radiosondes, the satellite data has the advantage of global coverage, but at a lower accuracy and resolution.<ref>Tony Reale. [http://cimss.ssec.wisc.edu/itwg/itsc/itsc12/presentations/1a4_T.Reale.ppt "ATOVS Sounding Products (ITSVC-12)"] {{Webarchive|url=https://web.archive.org/web/20080910142825/http://cimss.ssec.wisc.edu/itwg/itsc/itsc12/presentations/1a4_T.Reale.ppt |date=September 10, 2008 }}. Retrieved May 25, 2008.</ref> [[Weather radar|Meteorological radar]] provide information on precipitation location and intensity, which can be used to estimate precipitation accumulations over time.<ref>{{Cite web|url=http://www.csu.edu.au/special/bushfire99/papers/treloar/|date=July 1999|archive-url=https://web.archive.org/web/20090607174157/http://www.csu.edu.au/special/bushfire99/papers/treloar/|archive-date=June 7, 2009|title=The use of accumulated rainfall maps from weather radar systems to assist wildfire detection reconnaissance|author=Andrew Treloar and Peter Brookhouse|url-status=dead}}</ref> Additionally, if a [[Pulse-Doppler radar|pulse Doppler]] [[weather radar]] is used then wind speed and direction can be determined.<ref>University of Washington. [http://www.artsci.washington.edu/news/WinterSpring03/Forecast.htm "An improving forecast"]. Retrieved April 15, 2007 {{webarchive|url=https://web.archive.org/web/20071024112614/http://www.artsci.washington.edu/news/WinterSpring03/Forecast.htm |date=October 24, 2007 }}</ref> These methods, however, leave an in-situ observational gap in the lower atmosphere (from 100 m to 6&nbsp;km above ground level). To reduce this gap, in the late 1990s [[weather drone]]s started to be considered for obtaining data from those altitudes. Research has been growing significantly since the 2010s, and weather-drone data may in future be added to numerical weather models.<ref>{{Cite journal |last1=Pinto |first1=James O. |last2=O’Sullivan |first2=Debbie |last3=Taylor |first3=Stewart |last4=Elston |first4=Jack |last5=Baker |first5=C. B. |last6=Hotz |first6=David |last7=Marshall |first7=Curtis |last8=Jacob |first8=Jamey |last9=Barfuss |first9=Konrad |last10=Piguet |first10=Bruno |last11=Roberts |first11=Greg |last12=Omanovic |first12=Nadja |last13=Fengler |first13=Martin |last14=Jensen |first14=Anders A. |last15=Steiner |first15=Matthias |date=November 1, 2021 |title=The Status and Future of Small Uncrewed Aircraft Systems (UAS) in Operational Meteorology |journal=Bulletin of the American Meteorological Society |language=EN |volume=102 |issue=11 |pages=E2121–E2136 |doi=10.1175/BAMS-D-20-0138.1 |bibcode=2021BAMS..102E2121P |s2cid=237750279 |issn=0003-0007|doi-access=free |url=https://hal-meteofrance.archives-ouvertes.fr/meteo-03450993/file/%5B15200477%20-%20Bulletin%20of%20the%20American%20Meteorological%20Society%5D%20The%20Status%20and%20Future%20of%20Small%20Uncrewed%20Aircraft%20Systems%20%28UAS%29%20in%20Operational%20Meteorology-1.pdf }}</ref><ref>{{Cite web |date=November 14, 2022 |title=Workshop on Use of Unmanned Aerial Vehicles (UAV) for Operational Meteorology |url=https://library.wmo.int/doc_num.php?explnum_id=9951 |access-date=November 14, 2022 |website=World Meteorological Organization |archive-date=October 20, 2022 |archive-url=https://web.archive.org/web/20221020192146/https://library.wmo.int/doc_num.php?explnum_id=9951 |url-status=live }}</ref>

[[File:2005-09-22-10PM CDT Hurricane Rita 3 day path.png|thumb|Modern weather predictions aid in timely evacuations and potentially save lives and prevent property damage]]
Commerce provides [[pilot report]]s along aircraft routes,<ref>Ballish, Bradley A. and V. Krishna Kumar (May 23, 2008). [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"] {{Webarchive|url=https://web.archive.org/web/20110721055504/http://amdar.noaa.gov/docs/bams_ballish_kumar.pdf |date=July 21, 2011 }}. Retrieved May 25, 2008.</ref> and ship reports along 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|year=2011|url=http://www.hurricanehunters.com/|title=The Hurricane Hunters|publisher=[[Hurricane Hunters|53rd Weather Reconnaissance Squadron]]|access-date=March 30, 2006|archive-date=May 30, 2012|archive-url=https://web.archive.org/web/20120530232904/http://www.hurricanehunters.com/|url-status=live}}</ref><ref name="SunHerald">{{cite news|author=Lee, Christopher|date=October 8, 2007|title=Drone, Sensors May Open Path Into Eye of Storm|url=https://www.washingtonpost.com/wp-dyn/content/article/2007/10/07/AR2007100700971_pf.html|newspaper=The Washington Post|access-date=February 22, 2008|archive-date=November 11, 2012|archive-url=https://web.archive.org/web/20121111093844/http://www.washingtonpost.com/wp-dyn/content/article/2007/10/07/AR2007100700971_pf.html|url-status=live}}</ref> Reconnaissance aircraft are also flown over the open oceans during the cold season into systems that cause significant uncertainty in forecast guidance, or are expected to be of high impact three–seven days into the future over the downstream continent.<ref>{{cite web |date=January 12, 2010 |url=http://www.noaanews.noaa.gov/stories2010/20100112_plane.html |title=NOAA Dispatches High-Tech Research Plane to Improve Winter Storm Forecasts |publisher=[[National Oceanic and Atmospheric Administration]] |access-date=December 22, 2010 |archive-date=January 3, 2011 |archive-url=https://web.archive.org/web/20110103152316/http://www.noaanews.noaa.gov/stories2010/20100112_plane.html |url-status=live }}</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.<ref>[[University Corporation for Atmospheric Research]] (August 14, 2007). [https://web.archive.org/web/20070814044336/http://www.mmm.ucar.edu/wrf/WG4/wrfvar/wrfvar-tutorial.htm "The WRF Variational Data Assimilation System (WRF-Var)"]. Retrieved May 25, 2008.</ref> Commonly, the set of equations used to predict the physics and dynamics of the atmosphere are called [[primitive equations]]. These are initialized from the analysis data and rates of change are determined. The rates of change predict the state of the atmosphere a short time into the future. The equations are then applied to this new atmospheric state to find new rates of change, which predict the atmosphere at a yet further time into the future. This ''time stepping'' procedure is continually repeated until the solution reaches the desired forecast time.

The length of the time step 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=978-0-12-554766-6|pages=285–287}}</ref> Time steps for global models are on the order of tens of minutes,<ref>{{cite book|url=https://books.google.com/books?id=JZikIbXzipwC&pg=PA131|page=132|title=Computational Science – ICCS 2005: 5th International Conference, Atlanta, GA, USA, May 22–25, 2005, Proceedings, Part 1|author1=Sunderam, V. S. |author2=van Albada, G. Dick |author3=Peter, M. A. |author4=Sloot, J. J. Dongarra |year=2005 |publisher=Springer |isbn=978-3-540-26032-5}}</ref> while time steps for regional models are between one and four minutes.<ref>{{cite book|url=https://books.google.com/books?id=UV6PnF2z5_wC&pg=PA276|page=276|title=Developments in teracomputing: proceedings of the ninth ECMWF Workshop on the Use of High Performance Computing in Meteorology|author=Zwieflhofer, Walter; Kreitz, Norbert; European Centre for Medium Range Weather Forecasts |year=2001 |publisher=World Scientific |isbn=978-981-02-4761-4}}</ref> The global models are run at varying times into the future. The [[Met Office]]'s [[Unified Model]] is run six days into the future,<ref name="models">{{cite book|pages=295–296|url=https://books.google.com/books?id=6gFiunmKWWAC&pg=PA297|title=Global Perspectives on Tropical Cyclones: From Science to Mitigation|author1=Chan, Johnny C. L. |author2=Jeffrey D. Kepert |name-list-style=amp |year=2010|publisher=World Scientific|isbn=978-981-4293-47-1}}</ref> the [[European Centre for Medium-Range Weather Forecasts]] model is run out to 10&nbsp;days into the future,<ref>{{cite book|url=https://books.google.com/books?id=fhW5oDv3EPsC&pg=PA474|page=480|author=Holton, James R.|title=An introduction to dynamic meteorology, Volume 1|year=2004|publisher=Academic Press |isbn=978-0-12-354015-7 }}</ref> while the [[Global Forecast System]] model run by the [[Environmental Modeling Center]] is run 16&nbsp;days into the future.<ref>{{cite book|url=https://books.google.com/books?id=mTZvR3R6YdkC&pg=PA121|page=121|title=Famine early warning systems and remote sensing data|author=Brown, Molly E.|publisher=Springer|year=2008 |isbn=978-3-540-75367-4|bibcode=2008fews.book.....B}}</ref> 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=978-0-495-11558-8|year=2008|publisher=Cengage Learning|title=Essentials of meteorology: an invitation to the atmosphere|url=https://books.google.com/books?id=2Yn29IFukbgC&pg=PA244}}</ref> The raw output is often modified before being presented as the forecast. This can be in the form of statistical techniques to remove known [[bias]]es in the model, or of adjustment to take into account consensus among other numerical weather forecasts.<ref>Daniel Andersson (2007). [http://his.diva-portal.org/smash/record.jsf?pid=diva2%3A2675&dswid=-1516 "Improved accuracy of surrogate models using output postprocessing"] {{Webarchive|url=https://web.archive.org/web/20171012045146/http://his.diva-portal.org/smash/record.jsf?pid=diva2%3A2675&dswid=-1516 |date=October 12, 2017 }}. Retrieved May 25, 2008.</ref> MOS or model output statistics is a technique used to interpret numerical model output and produce site-specific guidance. This guidance is presented in coded numerical form, and can be obtained for nearly all National Weather Service reporting stations in the United States. As proposed by [[Edward Lorenz]] in 1963, long range forecasts, those made at a range of two weeks or more cannot definitively predict the state of the atmosphere, owing to the [[chaos theory|chaotic nature]] of the [[fluid dynamics]] equations involved. In numerical models, extremely small errors in initial values double roughly every five days for variables such as temperature and wind velocity.<ref>{{cite book|title=Storm Watchers|pages=[https://archive.org/details/stormwatcherstur00cox_df1/page/222 222–224]|year=2002|author=Cox, John D.|publisher=John Wiley & Sons, Inc.|isbn=978-0-471-38108-2|url=https://archive.org/details/stormwatcherstur00cox_df1/page/222}}</ref>

Essentially, a model is a computer program that produces [[meteorological]] information for future times at given locations and altitudes. Within any modern 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=978-0-12-554766-6|pages=48–49}}</ref> These equations—along with the [[ideal gas law]]—are used to evolve the [[density]], [[pressure]], and [[potential temperature]] [[scalar field]]s and the [[velocity]] [[vector field]] of the atmosphere through time. Additional transport equations for pollutants and other [[aerosol]]s are included in some primitive-equation mesoscale models as well.<ref>{{cite book|last=Pielke|first=Roger A.|title=Mesoscale Meteorological Modeling|year=2002|publisher=[[Academic Press]]|isbn=978-0-12-554766-6|pages=18–19}}</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=https://books.google.com/books?id=SH8R_flZBGIC&pg=PA165|title=Finite difference schemes and partial differential equations|author=Strikwerda, John C.|pages=165–170|year=2004|publisher=SIAM|isbn=978-0-89871-567-5}}</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=978-0-12-554766-6|page=65}}</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 and other global models usually use finite-difference methods in all three dimensions.<ref name="finite"/>