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The output of forecast models based on [[atmospheric dynamics]] 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]] (MOS).<ref name="MOS"/><ref>{{cite book|title=Air Weather Service Model Output Statistics Systems|author1=Best, D. L. |author2=Pryor, S. P. |year=1983|pages=1–90|publisher=Air Force Global Weather Central}}</ref> 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.<ref name="Toth"/><ref name="ECens"/><ref name="RMS"/>
==Data collection and initialization==
[[File:Lockheed WP-3D Orion.jpg|280px|thumb|right|Weather reconnaissance aircraft, such as this [[WP-3D Orion]], provide data that is then used in numerical weather forecasts.|alt=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 process of entering observation data into the model to generate [[initial value problem|initial conditions]] is called ''initialization''. On land, terrain maps available at resolutions down to {{convert|1|km|mi|1|sp=us}} globally are used to help model atmospheric circulations within regions of rugged topography, in order to better depict features such as downslope winds, [[Lee wave|mountain wave]]s and related cloudiness that affects incoming solar radiation.<ref>{{cite book|url=https://books.google.com/books?id=lMXSpRwKNO8C&pg=PA56|title=Parameterization schemes: keys to understanding numerical weather prediction models|author=Stensrud, David J.|page=56|year=2007|publisher=Cambridge University Press|isbn=978-0-521-86540-1}}</ref> The main inputs from country-based weather services are observations from devices (called [[radiosonde]]s) in weather balloons that measure various atmospheric parameters and transmits them to a fixed receiver, as well as from [[weather satellite]]s. 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]]|access-date=2011-02-11|author=[[National Climatic Data Center]]|date=2008-08-20|archive-date=2002-11-01|archive-url=https://web.archive.org/web/20021101221848/http://www0.ncdc.noaa.gov/oa/climate/conversion/swometardecoder.html|url-status=dead}}</ref> or every six hours in [[SYNOP]] reports.<ref>{{cite web|title=SYNOP Data Format (FM-12): Surface Synoptic Observations|publisher=[[UNISYS]]|archive-url=https://web.archive.org/web/20071230100059/http://weather.unisys.com/wxp/Appendices/Formats/SYNOP.html|archive-date=2007-12-30|date=2008-05-25|url=http://weather.unisys.com/wxp/Appendices/Formats/SYNOP.html}}</ref> These observations are irregularly spaced, so they 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.<ref name="Krishnamurti Annu Rev FM">{{cite journal|last=Krishnamurti|first=T. N.|title=Numerical Weather Prediction|journal=[[Annual Reviews (publisher)|Annual Review of Fluid Mechanics]]|date=January 1995|volume=27|issue=1|pages=195–225|doi=10.1146/annurev.fl.27.010195.001211|bibcode=1995AnRFM..27..195K|s2cid=122230747 }}</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]]|archive-url=https://web.archive.org/web/20070814044336/http://www.mmm.ucar.edu/wrf/WG4/wrfvar/wrfvar-tutorial.htm|archive-date=2007-08-14|date=2007-08-14|url=http://www.mmm.ucar.edu/wrf/WG4/wrfvar/wrfvar-tutorial.htm}}</ref>
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