Numerical weather prediction: Difference between revisions

Revision as of 11:26, 17 August 2023

Revision as of 19:09, 23 August 2023

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An atmospheric 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|url=https://archive.org/details/mesoscalemeteoro00srro|url-access=limited|year=2002|publisher=[[Academic Press]]|isbn=978-0-12-554766-6|pages=[https://archive.org/details/mesoscalemeteoro00srro/page/n64 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 air [[velocity]] (wind) [[vector field]] of the atmosphere through time. Additional transport equations for pollutants and other [[aerosol]]s are included in some primitive-equation high-resolution models as well.<ref>{{cite book|last=Pielke|first=Roger A.|title=Mesoscale Meteorological Modeling|url=https://archive.org/details/mesoscalemeteoro00srro|url-access=limited|year=2002|publisher=[[Academic Press]]|isbn=978-0-12-554766-6|pages=[https://archive.org/details/mesoscalemeteoro00srro/page/n34 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|url=https://archive.org/details/mesoscalemeteoro00srro|url-access=limited|year=2002|publisher=[[Academic Press]]|isbn=978-0-12-554766-6|page=[https://archive.org/details/mesoscalemeteoro00srro/page/n81 65]}}</ref> Therefore, numerical methods obtain approximate solutions. Different models use different solution methods: some global models and almost all regional models use [[finite difference method]]s for all three spatial dimensions, while other global models and a few regional models use [[spectral method]]s for the horizontal dimensions and finite-difference methods in the vertical.<ref name="finite"/>

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]].<ref>{{cite book|last=Pielke|first=Roger A.|title=Mesoscale Meteorological Modeling|url=https://archive.org/details/mesoscalemeteoro00srro|url-access=limited|year=2002|publisher=[[Academic Press]]|isbn=978-0-12-554766-6|pages=[https://archive.org/details/mesoscalemeteoro00srro/page/n301 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 [[UKMET]] [[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|access-date=2011-02-24}}</ref> while the [[European Centre for Medium-Range Weather Forecasts]]' [[Integrated Forecast System]] and [[Environment Canada]]'s [[Global Environmental Multiscale Model]] both run out to ten 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|access-date=2011-02-24|isbn=978-0-12-354015-7}}</ref> and the [[Global Forecast System]] model run by the [[Environmental Modeling Center]] is run sixteen 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|journal=Famine Early Warning Systems and Remote Sensing Data|author=Brown, Molly E.|publisher=Springer|year=2008|access-date=2011-02-24|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>

== Parameterization ==

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The horizontal [[Domain of a function|___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]]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.<ref>{{cite book|url=https://books.google.com/books?id=6RQ3dnjE8lgC&pg=PA261|title=Numerical Weather and Climate Prediction|author=Warner, Thomas Tomkins |publisher=[[Cambridge University Press]]|year=2010|isbn=978-0-521-51389-0|page=259}}</ref>

The vertical coordinate is handled in various ways. Lewis Fry Richardson's 1922 model used 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|url=https://archive.org/details/emergencenumeric00lync|url-access=limited|year=2006|publisher=[[Cambridge University Press]]|isbn=978-0-521-85729-1|pages=[https://archive.org/details/emergencenumeric00lync/page/n55 45]–46|chapter=The Fundamental Equations}}</ref> This correlation between coordinate systems can be made since pressure decreases with height through the [[Earth's atmosphere]].<ref>{{cite book|author=Ahrens, C. Donald|page=10|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 first model used for operational forecasts, the single-layer barotropic model, used a single pressure coordinate at the 500-millibar (about {{convert|5500|m|ft|abbr=on}}) level,<ref name="Charney 1950">{{cite journal|last1=Charney|first1=Jule|last2=Fjørtoft|first2=Ragnar|last3=von Neumann|first3=John|title=Numerical Integration of the Barotropic Vorticity Equation|journal=Tellus|date=November 1950|volume=2|issue=4|bibcode=1950TellA1950Tell....2..237C |doi=10.3402/tellusa.v2i4.8607|author-link1=Jule Charney|author-link2=Ragnar Fjørtoft|author-link3=John von Neumann|pages=237|doi-access=free}}</ref> 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]] |access-date=2011-01-03 |author2=Gall, Robert |author3=Pyle, Matthew E. |pages=12–13 |date=February 2010 |url-status=dead |archive-url=https://web.archive.org/web/20110823082059/http://nldr.library.ucar.edu/collections/technotes/asset-000-000-000-845.pdf |archive-date=2011-08-23 }}</ref> This coordinate system receives its name from the [[independent variable]] <math>\sigma</math> used to [[nondimensionalization|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.<ref>{{cite book|last=Pielke|first=Roger A.|title=Mesoscale Meteorological Modeling|url=https://archive.org/details/mesoscalemeteoro00srro|url-access=limited|year=2002|publisher=[[Academic Press]]|isbn=978-0-12-554766-6|pages=[https://archive.org/details/mesoscalemeteoro00srro/page/n147 131]–132}}</ref>

==Model output statistics==