Editing Numerical weather prediction (section)

== Parameterization ==
[[File:GoldenMedows.jpg|thumb|right|Field of [[cumulus cloud]]s, which are parameterized since they are too small to be explicitly included within numerical weather prediction]]
{{Main|Parametrization (atmospheric modeling)}}
Some meteorological processes are too small-scale or too complex to be explicitly included in numerical weather prediction models. ''[[Parametrization (atmospheric modeling)|Parameterization]]'' 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 {{convert|5|km|mi|0|sp=us}} and {{convert|300|km|mi|-2|sp=us}} in length. A typical [[cumulus cloud]] has a scale of less than {{convert|1|km|mi|1|sp=us}}, 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]]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 [[convection|convect]] and that [[Entrainment (meteorology)|entrainment]] and other processes occur. Weather models that have gridboxes with sizes between {{convert|5|and|25|km|mi|0|sp=us}} can explicitly represent convective clouds, although they need to parameterize [[cloud microphysics]] which occur at a smaller scale.<ref>{{cite journal|url=http://ams.confex.com/ams/pdfpapers/126017.pdf|title=3.7 Improving Precipitation Forecasts by the Operational Nonhydrostatic Mesoscale Model with the Kain-Fritsch Convective Parameterization and Cloud Microphysics|author1=Narita, Masami  |author2=Shiro Ohmori |name-list-style=amp |date=2007-08-06|access-date=2011-02-15|journal=12th Conference on Mesoscale Processes}}</ref> The formation of large-scale ([[stratus cloud|stratus]]-type) clouds is more physically based; they form when the [[relative humidity]] reaches some prescribed value. The [[cloud fraction]] can be related to this critical value of relative humidity.<ref>{{cite web|url=http://www.atmos.washington.edu/~dargan/591/diag_cloud.tech.pdf |pages=4–5 |title=The Diagnostic Cloud Parameterization Scheme |author=Frierson, Dargan |publisher=[[University of Washington]] |date=2000-09-14 |access-date=2011-02-15 |url-status=dead |archive-url=https://web.archive.org/web/20110401013742/http://www.atmos.washington.edu/~dargan/591/diag_cloud.tech.pdf |archive-date=2011-04-01 }}</ref>

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. [[Drag (physics)|Atmospheric drag]] produced by mountains must also be parameterized, as the limitations in the resolution of [[elevation]] contours produce significant underestimates of the drag.<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=6|year=2007|publisher=Cambridge University Press|isbn=978-0-521-86540-1}}</ref> 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.<ref>{{cite book|page=188|title=A climate modelling primer|author1=McGuffie, K.  |author2=A. Henderson-Sellers |name-list-style=amp |publisher=John Wiley and Sons|year=2005|isbn=978-0-470-85751-9}}</ref> Sun angle as well as the impact of multiple cloud layers is taken into account.<ref>{{cite book|url=https://books.google.com/books?id=vdg5BgBmMkQC&pg=PA226|author1=Melʹnikova, Irina N.  |author2=Alexander V. Vasilyev |name-list-style=amp |pages=226–228|title=Short-wave solar radiation in the earth's atmosphere: calculation, observation, interpretation|year=2005|publisher=Springer|isbn=978-3-540-21452-6}}</ref> 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.<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.|pages=12–14|year=2007|publisher=Cambridge University Press|isbn=978-0-521-86540-1}}</ref> Within air quality models, parameterizations take into account atmospheric emissions from multiple relatively tiny sources (e.g. roads, fields, factories) within specific grid boxes.<ref>{{cite book|url=https://books.google.com/books?id=wh-Xf0WZQlMC&pg=PA11|pages=11–12|title=Meteorological and Air Quality Models for Urban Areas|author=Baklanov, Alexander, Sue Grimmond, Alexander Mahura|access-date=2011-02-24|year=2009|publisher=Springer|isbn=978-3-642-00297-7}}</ref>