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第12行： + − 【终稿】由热致模式作出的主要假设是，[[热风]]的大小可以改变，但方向不随高度变化，因此大气的斜压性可以用位势高度面和它们之间的平均热风来模拟。<ref>{{cite book|last= Gates|first=W. Lawrence|title=Results Of Numerical Forecasting With The Barotropic And Thermotropic Atmospheric Models|date=August 1955|publisher=Air Force Cambridge Research Laboratories|location=[[Hanscom Air Force Base]]|url=http://handle.dtic.mil/100.2/AD101943}}</ref><ref>{{cite journal |last=Thompson|first=P. D.|author2=W. Lawrence Gates|title=A Test of Numerical Prediction Methods Based on the Barotropic and Two-Parameter Baroclinic Models|journal=[[Journal of the Atmospheric Sciences|Journal of Meteorology]]| date=April 1956 |volume=13|issue=2|pages=127–141 |doi= 10.1175/1520-0469(1956)013<0127:ATONPM>2.0.CO;2 |issn=1520-0469|bibcode = 1956JAtS...13..127T |doi-access=free}}</ref>+ − '''Barotropic''' models assume the atmosphere is nearly [[barotropic]], which means that the direction and speed of the [[geostrophic wind]] are independent of height. In other words, no vertical [[wind shear]] of the geostrophic wind. It also implies that thickness contours (a proxy for temperature) are parallel to upper level height contours. In this type of atmosphere, [[high-pressure area|high]] and [[low-pressure area|low pressure area]]s are centers of warm and cold temperature anomalies. Warm-core highs (such as the [[subtropical ridge]] and Bermuda-Azores high) and [[cold-core low]]s have strengthening winds with height, with the reverse true for cold-core highs (shallow arctic highs) and warm-core lows (such as [[tropical cyclone]]s).<ref>{{cite book|title=Atmospheric Science: An Introductory Survey|author1=Wallace, John M. |author2=Peter V. Hobbs |name-list-style=amp |year=1977|isbn=978-0-12-732950-5|publisher=Academic Press, Inc.|pages=384–385}}</ref> A barotropic model tries to solve a simplified form of [[atmospheric dynamics]] based on the assumption that the atmosphere is in [[geostrophic balance]]; that is, that the [[Rossby number]] of the air in the atmosphere is small.<ref>{{cite book|last=Marshall|first=John|title=Atmosphere, ocean, and climate dynamics : an introductory text|year=2008|publisher=Elsevier Academic Press|location=Amsterdam|isbn=978-0-12-558691-7|author2=Plumb, R. Alan|pages=109–12|chapter=Balanced flow}}</ref> If the assumption is made that the atmosphere is [[divergence-free]], the [[curl (mathematics)|curl]] of the [[Euler equations (fluid dynamics)|Euler equations]] reduces into the [[barotropic vorticity equation]]. This latter equation can be solved over a single layer of the atmosphere. Since the atmosphere at a height of approximately {{convert|5.5|km|mi}} is mostly divergence-free, the barotropic model best approximates the state of the atmosphere at a [[geopotential height]] corresponding to that altitude, which corresponds to the atmosphere's {{convert|500|mb|inHg|abbr=on}} pressure surface.<ref name="Charney 1950" /><!-- also solved as a stream function, need to find a reference for that --> − Barotropic models assume the atmosphere is nearly barotropic, which means that the direction and speed of the geostrophic wind are independent of height. In other words, no vertical wind shear of the geostrophic wind. It also implies that thickness contours (a proxy for temperature) are parallel to upper level height contours. In this type of atmosphere, high and low pressure areas are centers of warm and cold temperature anomalies. Warm-core highs (such as the subtropical ridge and Bermuda-Azores high) and cold-core lows have strengthening winds with height, with the reverse true for cold-core highs (shallow arctic highs) and warm-core lows (such as tropical cyclones). A barotropic model tries to solve a simplified form of atmospheric dynamics based on the assumption that the atmosphere is in geostrophic balance; that is, that the Rossby number of the air in the atmosphere is small. If the assumption is made that the atmosphere is divergence-free, the curl of the Euler equations reduces into the barotropic vorticity equation. This latter equation can be solved over a single layer of the atmosphere. Since the atmosphere at a height of approximately 5.5 kilometres (3.4 mi) is mostly divergence-free, the barotropic model best approximates the state of the atmosphere at a geopotential height corresponding to that altitude, which corresponds to the atmosphere's pressure surface.+ − 正压模式假设大气接近正压，这意味着地转风的方向和速度与高度无关。换句话说，没有地转风的垂直风切变。这也意味着厚度等值线(代表温度)是平行于上层高度等值线。在这种类型的大气中，高压区和低压区是暖温和冷温异常的中心。温核高压(如副热带嵴线和百慕大-亚速尔群岛高压)和冷核低压具有随高度增强的风力，而冷核高压(北极浅层高压)和温核低压(如热带气旋)则相反。正压模式试图解决一个简化形式的大气动力学的基础上的假设，大气是地转平衡，即大气中的空气罗斯比数量很小。如果假设大气是无散度的，则欧拉方程的旋度降为正压涡度方程。后一个方程可以在一层大气上求解。由于大气在大约高度处基本上是无辐散的，正压模式最接近大气在相应于高度的位势高度处的状态，也就是相应于大气压力表面的状态。 − 【终稿】正压模式假定大气接近正压，这意味着地转风的方向和速度与高度无关，即地转风无垂直切变。这也意味着温度的厚度等值线平行于上层高度等值线。在这种类型的大气中，高压区和低压区是冷暖温度异常的中心。暖心高压（如亚热带脊线和百慕大-亚速尔高压）和冷心低压具有随高度增强的风力，而冷心高压（北极浅层高压）和暖心低压（如热带气旋）则相反。正压模式试图基于大气处于地转平衡的假设（即空气中的罗斯比数小）来解决简化形式的大气动力学问题。如果假设大气无散度，则欧拉方程的旋度简化为正压涡度方程，后者可以在一层大气上求解。由于大气在大约5.5 千米（3.4 英里）处几乎无旋度，正压模式最接近大气在对应海拔处的位势高度时的状态，该海拔与大气压力面有关。+ + − [[Primitive equations#Vertical pressure.2C Cartesian tangential plane|'''Hydrostatic''' model]]s filter out vertically moving [[acoustic wave]]s from the vertical momentum equation, which significantly increases the time step used within the model's run. This is known as the [[hydrostatic equilibrium|hydrostatic approximation]]. Hydrostatic models use either pressure or [[sigma coordinate system|sigma-pressure]] vertical coordinates. Pressure coordinates intersect topography while sigma coordinates follow the contour of the land. Its hydrostatic assumption is reasonable as long as horizontal grid resolution is not small, which is a scale where the hydrostatic assumption fails. Models which use the entire vertical momentum equation are known as '''nonhydrostatic'''. A nonhydrostatic model can be solved anelastically, meaning it solves the complete [[continuity equation]] for air assuming it is incompressible, or elastically, meaning it solves the complete continuity equation for air and is fully compressible. Nonhydrostatic models use altitude or sigma altitude for their vertical coordinates. Altitude coordinates can intersect land while sigma-altitude coordinates follow the contours of the land.<ref>{{cite book|url=https://books.google.com/books?id=41qztAEACAAJ|pages=138–143|title=Fundamentals of atmospheric modeling|author=Jacobson, Mark Zachary|year=2005|publisher=Cambridge University Press|isbn=978-0-521-83970-9}}</ref>+ − − Hydrostatic models filter out vertically moving acoustic waves from the vertical momentum equation, which significantly increases the time step used within the model's run. This is known as the hydrostatic approximation. Hydrostatic models use either pressure or sigma-pressure vertical coordinates. Pressure coordinates intersect topography while sigma coordinates follow the contour of the land. Its hydrostatic assumption is reasonable as long as horizontal grid resolution is not small, which is a scale where the hydrostatic assumption fails. Models which use the entire vertical momentum equation are known as nonhydrostatic. A nonhydrostatic model can be solved anelastically, meaning it solves the complete continuity equation for air assuming it is incompressible, or elastically, meaning it solves the complete continuity equation for air and is fully compressible. Nonhydrostatic models use altitude or sigma altitude for their vertical coordinates. Altitude coordinates can intersect land while sigma-altitude coordinates follow the contours of the land. − − 流体静力学模型从垂直动量方程中过滤出垂直移动声波的方程，显著地增加了模型运行中使用的时间步长。这就是流体静力学近似。流体静力学模型使用压力或 sigma 压力的垂直坐标。压力坐标与地形相交，而 sigma 坐标跟随地形等高线。只要水平网格分辨率不小，其静力学假设是合理的，这是静力学假设失效的尺度。使用整个垂直动量方程的模型称为非静力学模型。非流体静力学模型可以用分弹性方法求解，这意味着它可以求解空气的完全连续性方程，前提是它是不可压缩的，或者是弹性的，这意味着它可以求解空气的完全连续性方程，并且是完全可压缩的。非静力学模型使用高度或西格玛高度作为其垂直坐标。高度坐标可以与地面相交，而 sigma 高度坐标则跟随地面的等高线。 − − 【终稿】流体静力学模式从垂直动量方恒中过滤出垂直运动的声波，这显著地增加了模型运行中使用的时间步长，这就是流体静力学近似。流体静力学模式使用压力或sigma 压力作为垂直坐标。压力坐标与地形相交，而sigma 坐标随地形等高线变化。只要水平网格分辨率不小，该模式的流体静力学假设便是合理的。使用整个垂直动量方程的模式称为非流体静力学模式，它既可以滞弹性求解，这意味着它求解了不可压缩空气的完整的连续性方程；也可以弹性求解，这意味着它求解了完全可压缩空气的完整的连续性方程。非静力学假设使用海拔高度或sigma 高度作为其垂直坐标。海拔高度可以和地形相交，而sigma 高度坐标随地面等高线改变。 − − == History 历史 == − [[File:Two women operating ENIAC.gif|thumb|280px|The ENIAC main control panel at the [[Moore School of Electrical Engineering]]|链接=Special:FilePath/Two_women_operating_ENIAC.gif]] − {{Main|History of numerical weather prediction}} − The [[history of numerical weather prediction]] began in the 1920s through the efforts of [[Lewis Fry Richardson]] who utilized procedures developed by [[Vilhelm Bjerknes]].<ref name="Lynch JCP">{{cite journal|last=Lynch|author-link=Peter Lynch (meteorologist)|first=Peter|title=The origins of computer weather prediction and climate modeling|journal=[[Journal of Computational Physics]]|date=2008-03-20|volume=227|issue=7|pages=3431–44|doi= 10.1016/j.jcp.2007.02.034 |url=http://www.rsmas.miami.edu/personal/miskandarani/Courses/MPO662/Lynch,Peter/OriginsCompWF.JCP227.pdf|access-date= 2010-12-23 |bibcode=2008JCoPh.227.3431L|archive-url=https://web.archive.org/web/20100708191309/http://www.rsmas.miami.edu/personal/miskandarani/Courses/MPO662/Lynch,Peter/OriginsCompWF.JCP227.pdf|archive-date=2010-07-08|url-status=dead}}</ref><ref name="Lynch Ch1">{{cite book|last=Lynch |first= Peter |title=The Emergence of Numerical Weather Prediction|year=2006|publisher=[[Cambridge University Press]]|isbn=978-0-521-85729-1|pages=1–27 |chapter= Weather Prediction by Numerical Process}}</ref> It was not until the advent of the computer and [[computer simulation]] that computation time was reduced to less than the forecast period itself. [[ENIAC]] created the first computer forecasts in 1950,<ref name="Charney 1950">{{cite journal|last1= Charney|first1=Jule|last2=Fjörtoft|first2=Ragnar|last3=von Neumann|first3=John|title=Numerical Integration of the Barotropic Vorticity Equation|journal= Tellus|date=November 1950|volume=2|issue=4|doi=10.3402/tellusa.v2i4.8607|author-link1=Jule Charney|author-link3=John von Neumann|bibcode= 1950TellA...2..237C |pages=237–254|doi-access=free}}</ref><ref>{{cite book|title=Storm Watchers|page=[https://archive.org/details/stormwatcherstur00cox_df1/page/208 208]|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/208}}</ref> and more powerful computers later increased the size of initial datasets and included more complicated versions of the equations of motion.<ref name="Harper BAMS">{{cite journal|last=Harper|first=Kristine|author2=Uccellini, Louis W.|author3= Kalnay, Eugenia|author4= Carey, Kenneth|author5= Morone, Lauren|title=2007: 50th Anniversary of Operational Numerical Weather Prediction|journal=[[Bulletin of the American Meteorological Society]]|date=May 2007|volume=88|issue=5|pages=639–650|doi=10.1175/BAMS-88-5-639 |bibcode=2007BAMS...88..639H |doi-access=free}}</ref> In 1966, [[West Germany]] and the United States began producing operational forecasts based on [[primitive equations|primitive-equation]] models, followed by the United Kingdom in 1972 and Australia in 1977.<ref name="Lynch JCP"/><ref name="Leslie BOM">{{cite journal|last=Leslie|first=L.M.|author2=Dietachmeyer, G.S.|title=Real-time limited area numerical weather prediction in Australia: a historical perspective|journal=Australian Meteorological Magazine|date=December 1992|volume=41|issue=SP|pages=61–77|url=http://www.bom.gov.au/amoj/docs/1992/leslie2.pdf|access-date=2011-01-03|publisher=[[Bureau of Meteorology]]}}</ref> The development of global [[Forecasting#Categories of forecasting methods|forecasting models]] led to the first climate models.<ref name="Phillips"/><ref name="Cox210"/> The development of limited area (regional) models facilitated advances in forecasting the tracks of [[tropical cyclone]] as well as [[air quality]] in the 1970s and 1980s.<ref name="Shuman W&F">{{cite journal|last=Shuman|first=Frederick G.|author-link=Frederick Gale Shuman|title=History of Numerical Weather Prediction at the National Meteorological Center|journal=[[Weather and Forecasting]]|date=September 1989|volume=4|issue=3|pages=286–296|doi= 10.1175/1520-0434(1989)004<0286:HONWPA>2.0.CO;2 |issn=1520-0434|bibcode=1989WtFor...4..286S|doi-access=free}}</ref><ref name="Steyn, D. G. 1991 241–242">{{cite book|title=Air pollution modeling and its application VIII, Volume 8|author=Steyn, D. G.|publisher=Birkhäuser|year=1991|pages=241–242|isbn= 978-0-306-43828-8}}</ref> − − The history of numerical weather prediction began in the 1920s through the efforts of Lewis Fry Richardson who utilized procedures developed by Vilhelm Bjerknes. It was not until the advent of the computer and computer simulation that computation time was reduced to less than the forecast period itself. ENIAC created the first computer forecasts in 1950, and more powerful computers later increased the size of initial datasets and included more complicated versions of the equations of motion. 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. The development of global forecasting models led to the first climate models. The development of limited area (regional) models facilitated advances in forecasting the tracks of tropical cyclone as well as air quality in the 1970s and 1980s. − − 数值天气预报的历史始于20世纪20年代，这得益于 Lewis Fry Richardson 的努力，他运用了威廉·皮耶克尼斯的方法。直到计算机和计算机模拟时代的到来，计算时间才减少到低于预测期本身。1950年 ENIAC 发明了第一台计算机预测系统，后来功能更强大的计算机增加了初始数据集的规模，并包含了更复杂的运动方程预测系统。1966年，西德和美国开始根据原始方程模型制作业务预报，1972年联合王国和1977年澳大利亚紧随其后。全球预报模型的发展导致了第一个气候模型的诞生。在20世纪70年代和80年代，有限区域(区域)模型的发展促进了热带气旋轨道和空气质量预报的进步。 − − 【终稿】数值天气预报的历史起于20世纪20年代，这得益于 Lewis Fry Richardson 使用了 Vihelm Bjerknes 开发的方法的成果。直到计算机和计算机模拟时代的到来，计算时间才降低到少于被预测时段。ENIAC 在1950年发明了第一台计算机预测系统，之后功能更强大的计算机增加了初始数据集的规模，并包含了更复杂的运动方程的版本。1966年，西德和美国开始根据原始方程模式制作业务预测系统，1972年英国和1977年澳大利亚紧随其后。全球预报模式的发展导致了第一个气候模式的诞生。在20世纪70年代和20世纪80年代，有限区域（区域性）模式的发展推动了热带气旋轨道和空气质量预报的进步。 − Because the output of forecast models based on atmospheric dynamics requires corrections near ground level, model output statistics (MOS) were developed in the 1970s and 1980s for individual forecast points (locations). Even with the increasing power of supercomputers, the forecast skill of numerical weather models only extends to about two weeks into the future, since the density and quality of observations—together with the chaotic nature of the partial differential equations used to calculate the forecast—introduce errors which double every five days.Weickmann, Klaus, Jeff Whitaker, Andres Roubicek and Catherine Smith (2001-12-01). The Use of Ensemble Forecasts to Produce Improved Medium Range (3–15 days) Weather Forecasts. Climate Diagnostics Center. Retrieved 2007-02-16. The use of model ensemble forecasts since the 1990s helps to define the forecast uncertainty and extend weather forecasting farther into the future than otherwise possible.+ − − 由于基于大气动力学的预报模式的输出需要近地面水平的修正，因此在20世纪70年代和80年代发展了单个预报点(位置)的模式输出统计学(MOS)。即使超级计算机的能力越来越强，数值天气模式的预报技巧也只能延伸到未来两周左右，因为观测的密度和质量ーー以及用于计算预报的偏微分方程的混沌性ーー带来了每五天翻一番的误差。Weickmann，Klaus，Jeff Whitaker，Andres Roubicek 和 Catherine Smith (2001-12-01)。利用集合天气预报制作经改进的中期(3-15天)天气预报。气候诊断中心。检索2007-02-16。自20世纪90年代以来，模式集合预报的使用有助于确定预报的不确定性，并且比其他方式可能延长未来一个天气预报。 − 【终稿】由于基于大气动力学的预报模式的输出结果需要近地面处的修正，因此20世纪70年代和20世纪80年代开发了单个预报位点的模式输出统计（MOS）。尽管超级计算机的能力不断提升，数值天气模式的预报仅能延伸到未来两周左右，这是因为观测点的密度和质量以及被用来预测的偏微分方程的混沌本质都会引入每五天加倍的误差。自20世纪90年代以来，模式集合预报的使用帮助确定了不确定性，并且预测时段比其他可能的方式都要长。 − ==Initialization 初始化== − {{transcluded section|source=Numerical weather prediction}} − {{#section-h:Numerical weather prediction|Initialization}} − 【更正】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 conditions is called ''initialization''. On land, terrain maps available at resolutions down to 1 kilometer (0.6 mi) globally are used to help model atmospheric circulations within regions of rugged topography, in order to better depict features such as downslope winds, mountain waves and related cloudiness that affects incoming solar radiation. The main inputs from country-based weather services are observations from devices (called radiosondes) in weather balloons that measure various atmospheric parameters and transmits them to a fixed receiver, as well as from weather satellites. The World Meteorological Organization acts to standardize the instrumentation, observing practices and timing of these observations worldwide. Stations either report hourly in METAR reports, or every six hours in SYNOP reports. 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. The data are then used in the model as the starting point for a forecast.+ + − 【终稿】大气是流动的。因此，数值天气预报的思想是对给定时间的流体状态进行采样，并使用流体动力学和热力学方程来估计未来某个时间的流体状态。将观测数据输入模型以生成初始条件的过程称为初始化。在陆地上，全球分辨率低至1公里（0.6英里）的地形图用于帮助模拟崎岖地形区域内的大气环流，以便更好地描述影响入射太阳辐射的下坡风、过山波和相关云量等特征。基于国家的气象服务的主要输入是来自气象气球上的设备（称为无线电探空仪）的观测，这些设备测量各种大气参数并将其传输到固定接收器，以及来自气象卫星的观测。世界气象组织（World Meteorological Organization）在全球范围内对仪器、观测实践和观测时间进行标准化。观测站在METAR报告中每小时报告一次，或者在SYNOP报告中每六小时报告一次。这些观测数据的间隔不规则，因此通过数据同化和客观分析方法进行处理，以实现质量控制并在模型数学算法可用的位置获取数值，使得最后在模式中被用作预测的起点。 − 【更正】A variety of methods are used to gather observational data for use in numerical models. Sites launch radiosondes in weather balloons which rise through the troposphere and well into the stratosphere. Information from weather satellites is used where traditional data sources are not available. Commerce provides pilot reports along aircraft routes and ship reports along shipping routes. Research projects use reconnaissance aircraft to fly in and around weather systems of interest, such as tropical cyclones. 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 from three to seven days into the future over the downstream continent. Sea ice began to be initialized in forecast models in 1971. 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.+ − 【终稿】有许多方法可以收集数值模型的观测数据。这些站点通过从对流层上升到平流层的气象气球来发射无线电探空仪。在传统数据源不可用的情况下，则可以使用气象卫星提供的信息。商务部提供飞机航线上的飞行员报告和航运航线上的船舶报告。研究项目使用侦察机在关注的天气系统内和周围飞行，如热带气旋。在寒冷季节，侦察机也会飞越公海，进入一些对预报制导造成重大不确定性、预计在未来三到七天内对下游大陆产生重大影响的系统中。1971年，海冰开始在预报模型中得到初始化。1972年，由于海洋表面温度在调节太平洋高纬度地区天气方面的作用，将其纳入模型初始化的工作也开始进行。 − + − + − − − thumb|Supercomputers are capable of running highly complex models to help scientists better understand Earth's climate. − − 超级计算机能够运行高度复杂的模型，以帮助科学家更好地了解地球的气候。 − − 【终稿】超级计算机能够运行高度复杂的模型，从而帮助科学家更好地理解地球的气候。 − − 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=978-0-12-554766-6|pages=48–49}}</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=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|author=Sunderam, V. S. |author2=G. Dick van Albada |author3=Peter M. A. Sloot |author4=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 |author2=Norbert Kreitz |author3=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" /> the [[European Centre for Medium-Range Weather Forecasts]] model is run out to 10 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 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}}</ref> − − 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. 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. Time steps for global models are on the order of tens of minutes, while time steps for regional models are between one and four minutes. The global models are run at varying times into the future. The UKMET Unified model is run six days into the future, the European Centre for Medium-Range Weather Forecasts model is run out to 10 days into the future, while the Global Forecast System model run by the Environmental Modeling Center is run 16 days into the future. − − 模型是一种计算机程序，可以在给定的地点和高度为未来时间生成气象信息。在任何模型中都有一组方程，被称为原始方程组方程，用来预测未来的大气状态。这些方程由分析数据初始化，并确定变化率。这些变化率可以预测未来一小段时间内大气层的状态，每一个时间增量称为时间步长。然后将这些方程式应用到这种新的大气状态，以发现新的变化速率，而这些新的变化速率预测了未来更远时间的大气层。重复时间步进，直到解到达预期的预测时间。在模型中选择的时间步长与计算网格中点之间的距离有关，选择这个时间步长是为了保持数值稳定性。全球模型的时间步长约为数十分钟，而区域模型的时间步长约为1至4分钟。全球模型在未来的不同时间运行。统一模型在未来6天内运行，欧洲中期天气预报中心模型在未来10天内运行，而由环境建模中心运行的全球预报系统模型在未来16天内运行。 − 【终稿】模式指的是一种可以在给定的位置和海拔高度生成未来气象信息的一种计算机程序。任何模型中都有一套称为“原始方程组”的方程组，用于预测未来的大气状态。这些方程组依据分析数据初始化，并确定变化速率。这些变化速率可以预测未来一小段时间的大气状态，每一个时间增量被称为一个时间步长。然后这些方程组被用于新的大气状态，得到新的变化速率，新的变化速率接着被用于预测再往后的大气状态。不断推进时间步，直到方程组的解到达了想要的预测时间。模式内时间步长的选择与计算网格间距有关，需要确保数值稳定性。全球模式的时间步长约为数十分钟，而区域模式则为1到4分钟。全球模式预测时段各有不同。UKMET联合模式可预测未来6天，欧洲中心的中程天气预测模式（European Centre for Medium-Range Weather Forecasts model）可预测未来10天，而环境建模中心（Environmental Modeling Center）的全球预测系统模式（Global Forest System model）可以预测未来16天。+ − The equations used are nonlinear partial differential equations which are impossible to solve exactly through analytical methods, with the exception of a few idealized cases. 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. The visual output produced by a model solution is known as a prognostic chart, or prog. − − 所用的方程是非线性偏微分方程，除了少数理想化的情况外，不可能用解析方法精确求解。因此，数值方法可以得到近似解。不同的模型使用不同的求解方法: 一些全球模型使用谱方法求解水平维度，而差分方法求解垂直维度，而区域模型和其他全球模型通常使用三维有限差分方法。模型解决方案产生的可视化输出被称为预测图，或 prog。
无编辑摘要
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 [[Baroclinity|baroclinicity]] in the atmosphere can be simulated using the {{convert|500|mb|inHg|adj=on |abbr=on |lk=on}} and {{convert|1000|mb|inHg|adj=on|abbr=on}} [[geopotential height]] surfaces and the average thermal wind between them.
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 [[Baroclinity|baroclinicity]] in the atmosphere can be simulated using the {{convert|500|mb|inHg|adj=on |abbr=on |lk=on}} and {{convert|1000|mb|inHg|adj=on|abbr=on}} [[geopotential height]] surfaces and the average thermal wind between them.
由热致模式作出的主要假设是，[[热风]]的大小可以改变，但方向不随高度变化，因此大气的斜压性可以用位势高度面和它们之间的平均热风来模拟。<ref>{{cite book|last= Gates|first=W. Lawrence|title=Results Of Numerical Forecasting With The Barotropic And Thermotropic Atmospheric Models|date=August 1955|publisher=Air Force Cambridge Research Laboratories|location=[[Hanscom Air Force Base]]|url=http://handle.dtic.mil/100.2/AD101943}}</ref><ref>{{cite journal |last=Thompson|first=P. D.|author2=W. Lawrence Gates|title=A Test of Numerical Prediction Methods Based on the Barotropic and Two-Parameter Baroclinic Models|journal=[[Journal of the Atmospheric Sciences|Journal of Meteorology]]| date=April 1956 |volume=13|issue=2|pages=127–141 |doi= 10.1175/1520-0469(1956)013<0127:ATONPM>2.0.CO;2 |issn=1520-0469|bibcode = 1956JAtS...13..127T |doi-access=free}}</ref>
'''正压 Barotropic'''模式假定大气接近正压，这意味着地转风的方向和速度与高度无关，即地转风无垂直切变。这也意味着温度的厚度等值线平行于上层高度等值线。在这种类型的大气中，高压区和低压区是冷暖温度异常的中心。暖心高压（如亚热带脊线和百慕大-亚速尔高压）和冷心低压具有随高度增强的风力，而冷心高压（北极浅层高压）和暖心低压（如热带气旋）则相反。<ref>{{cite book|title=Atmospheric Science: An Introductory Survey|author1=Wallace, John M. |author2=Peter V. Hobbs |name-list-style=amp |year=1977|isbn=978-0-12-732950-5|publisher=Academic Press, Inc.|pages=384–385}}</ref>正压模式试图基于大气处于地转平衡的假设（即空气中的罗斯比数小）来解决简化形式的大气动力学问题。<ref>{{cite book|last=Marshall|first=John|title=Atmosphere, ocean, and climate dynamics : an introductory text|year=2008|publisher=Elsevier Academic Press|location=Amsterdam|isbn=978-0-12-558691-7|author2=Plumb, R. Alan|pages=109–12|chapter=Balanced flow}}</ref>如果假设大气无散度，则欧拉方程的旋度简化为正压涡度方程，后者可以在一层大气上求解。由于大气在大约5.5 千米（3.4 英里）处几乎无旋度，正压模式最接近大气在对应海拔处的位势高度时的状态，该海拔与大气压力面有关。<ref name="Charney 1950" />
'''流体静力学 Hydrostatic'''模式从垂直动量方恒中过滤出垂直运动的声波，这显著地增加了模型运行中使用的时间步长，这就是流体静力学近似。流体静力学模式使用压力或sigma压力作为垂直坐标。压力坐标与地形相交，而sigma坐标随地形等高线变化。只要水平网格分辨率不小，该模式的流体静力学假设便是合理的。使用整个垂直动量方程的模式称为 '''非流体静力学模式 nonhydrostatic model'''，它既可以滞弹性求解，这意味着它求解了不可压缩空气的完整的连续性方程；也可以弹性求解，这意味着它求解了完全可压缩空气的完整的连续性方程。非静力学假设使用海拔高度或sigma高度作为其垂直坐标。海拔高度可以和地形相交，而sigma 高度坐标随地面等高线改变。<ref>{{cite book|url=https://books.google.com/books?id=41qztAEACAAJ|pages=138–143|title=Fundamentals of atmospheric modeling|author=Jacobson, Mark Zachary|year=2005|publisher=Cambridge University Press|isbn=978-0-521-83970-9}}</ref>
==历史 ==
[[File:Two women operating ENIAC.gif|thumb|280px|The ENIAC main control panel at the [[Moore School of Electrical Engineering]]]]
数值天气预报的历史起于20世纪20年代，这得益于 Lewis Fry Richardson 使用了 Vihelm Bjerknes 开发的方法的成果。<ref name="Lynch JCP">{{cite journal|last=Lynch|author-link=Peter Lynch (meteorologist)|first=Peter|title=The origins of computer weather prediction and climate modeling|journal=[[Journal of Computational Physics]]|date=2008-03-20|volume=227|issue=7|pages=3431–44|doi= 10.1016/j.jcp.2007.02.034 |url=http://www.rsmas.miami.edu/personal/miskandarani/Courses/MPO662/Lynch,Peter/OriginsCompWF.JCP227.pdf|access-date= 2010-12-23 |bibcode=2008JCoPh.227.3431L|archive-url=https://web.archive.org/web/20100708191309/http://www.rsmas.miami.edu/personal/miskandarani/Courses/MPO662/Lynch,Peter/OriginsCompWF.JCP227.pdf|archive-date=2010-07-08|url-status=dead}}</ref><ref name="Lynch Ch1">{{cite book|last=Lynch |first= Peter |title=The Emergence of Numerical Weather Prediction|year=2006|publisher=[[Cambridge University Press]]|isbn=978-0-521-85729-1|pages=1–27 |chapter= Weather Prediction by Numerical Process}}</ref>直到计算机和计算机模拟时代的到来，计算时间才降低到少于被预测时段。ENIAC 在1950年发明了第一台计算机预测系统，<ref name="Charney 1950">{{cite journal|last1= Charney|first1=Jule|last2=Fjörtoft|first2=Ragnar|last3=von Neumann|first3=John|title=Numerical Integration of the Barotropic Vorticity Equation|journal= Tellus|date=November 1950|volume=2|issue=4|doi=10.3402/tellusa.v2i4.8607|author-link1=Jule Charney|author-link3=John von Neumann|bibcode= 1950TellA...2..237C |pages=237–254|doi-access=free}}</ref><ref>{{cite book|title=Storm Watchers|page=[https://archive.org/details/stormwatcherstur00cox_df1/page/208 208]|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/208}}</ref>之后功能更强大的计算机增加了初始数据集的规模，并包含了更复杂的运动方程的版本。<ref name="Harper BAMS">{{cite journal|last=Harper|first=Kristine|author2=Uccellini, Louis W.|author3= Kalnay, Eugenia|author4= Carey, Kenneth|author5= Morone, Lauren|title=2007: 50th Anniversary of Operational Numerical Weather Prediction|journal=[[Bulletin of the American Meteorological Society]]|date=May 2007|volume=88|issue=5|pages=639–650|doi=10.1175/BAMS-88-5-639 |bibcode=2007BAMS...88..639H |doi-access=free}}</ref>1966年，西德和美国开始根据原始方程模式制作业务预测系统，1972年英国和1977年澳大利亚紧随其后。<ref name="Lynch JCP"/><ref name="Leslie BOM">{{cite journal|last=Leslie|first=L.M.|author2=Dietachmeyer, G.S.|title=Real-time limited area numerical weather prediction in Australia: a historical perspective|journal=Australian Meteorological Magazine|date=December 1992|volume=41|issue=SP|pages=61–77|url=http://www.bom.gov.au/amoj/docs/1992/leslie2.pdf|access-date=2011-01-03|publisher=[[Bureau of Meteorology]]}}</ref> The development of global [[Forecasting#Categories of forecasting methods|forecasting models]] led to the first climate models.<ref name="Phillips"/><ref name="Cox210"/>全球预报模式的发展导致了第一个气候模式的诞生。在20世纪70年代和20世纪80年代，有限区域（区域性）模式的发展推动了热带气旋轨道和空气质量预报的进步。<ref name="Shuman W&F">{{cite journal|last=Shuman|first=Frederick G.|author-link=Frederick Gale Shuman|title=History of Numerical Weather Prediction at the National Meteorological Center|journal=[[Weather and Forecasting]]|date=September 1989|volume=4|issue=3|pages=286–296|doi= 10.1175/1520-0434(1989)004<0286:HONWPA>2.0.CO;2 |issn=1520-0434|bibcode=1989WtFor...4..286S|doi-access=free}}</ref><ref name="Steyn, D. G. 1991 241–242">{{cite book|title=Air pollution modeling and its application VIII, Volume 8|author=Steyn, D. G.|publisher=Birkhäuser|year=1991|pages=241–242|isbn= 978-0-306-43828-8}}</ref>
Because the output of forecast models based on [[atmospheric dynamics]] requires corrections near ground level, [[model output statistics]] (MOS) were developed in the 1970s and 1980s for individual ''forecast points'' (locations).<ref name="MOS" /><ref name="L. Best, D. L. and S. P. Pryor 1983 1–90">{{cite book|title=Air Weather Service Model Output Statistics Systems|author1=L. Best, D. L. |author2=S. P. Pryor |name-list-style=amp |year=1983|pages=1–90|publisher=Air Force Global Weather Central}}</ref> Even with the increasing power of supercomputers, the [[forecast skill]] of numerical weather models only extends to about two weeks into the future, since the density and quality of observations—together with the [[Chaos theory|chaotic]] nature of the [[partial differential equation]]s used to calculate the forecast—introduce errors which double every five days.<ref name="Cox">{{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><ref name="Klaus">Weickmann, Klaus, Jeff Whitaker, Andres Roubicek and Catherine Smith (2001-12-01). [http://www.cdc.noaa.gov/spotlight/12012001/ The Use of Ensemble Forecasts to Produce Improved Medium Range (3–15 days) Weather Forecasts.] [[Climate Diagnostics Center]]. Retrieved 2007-02-16.</ref> The use of model ensemble forecasts since the 1990s helps to define the forecast uncertainty and extend [[weather forecasting]] farther into the future than otherwise possible.<ref name="Toth">{{cite journal|last=Toth|first=Zoltan|author2=Kalnay, Eugenia|title=Ensemble Forecasting at NCEP and the Breeding Method |journal=[[Monthly Weather Review]]|date=December 1997|volume=125|issue=12|pages=3297–3319|doi=10.1175/1520-0493(1997)125<3297:EFANAT>2.0.CO;2|issn=1520-0493|bibcode=1997MWRv..125.3297T|author-link2=Eugenia Kalnay|citeseerx=10.1.1.324.3941}}</ref><ref name="ECens">{{cite web|url=http://ecmwf.int/products/forecasts/guide/The_Ensemble_Prediction_System_EPS_1.html |title=The Ensemble Prediction System (EPS) |publisher=[[ECMWF]] |access-date=2011-01-05 |archive-url=https://web.archive.org/web/20110125125209/http://ecmwf.int/products/forecasts/guide/The_Ensemble_Prediction_System_EPS_1.html |archive-date=25 January 2011 |url-status=dead }}</ref><ref name="RMS">{{cite journal|title=The ECMWF Ensemble Prediction System: Methodology and validation|journal=Quarterly Journal of the Royal Meteorological Society|date=January 1996|volume=122|issue=529|pages=73–119|author1=Molteni, F. |author2=Buizza, R. |author3=Palmer, T.N. |author4=Petroliagis, T. |doi=10.1002/qj.49712252905|bibcode=1996QJRMS.122...73M}}</ref>
Because the output of forecast models based on [[atmospheric dynamics]] requires corrections near ground level, [[model output statistics]] (MOS) were developed in the 1970s and 1980s for individual ''forecast points'' (locations).<ref name="MOS" /><ref name="L. Best, D. L. and S. P. Pryor 1983 1–90">{{cite book|title=Air Weather Service Model Output Statistics Systems|author1=L. Best, D. L. |author2=S. P. Pryor |name-list-style=amp |year=1983|pages=1–90|publisher=Air Force Global Weather Central}}</ref> Even with the increasing power of supercomputers, the [[forecast skill]] of numerical weather models only extends to about two weeks into the future, since the density and quality of observations—together with the [[Chaos theory|chaotic]] nature of the [[partial differential equation]]s used to calculate the forecast—introduce errors which double every five days.<ref name="Cox">{{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><ref name="Klaus">Weickmann, Klaus, Jeff Whitaker, Andres Roubicek and Catherine Smith (2001-12-01). [http://www.cdc.noaa.gov/spotlight/12012001/ The Use of Ensemble Forecasts to Produce Improved Medium Range (3–15 days) Weather Forecasts.] [[Climate Diagnostics Center]]. Retrieved 2007-02-16.</ref> The use of model ensemble forecasts since the 1990s helps to define the forecast uncertainty and extend [[weather forecasting]] farther into the future than otherwise possible.<ref name="Toth">{{cite journal|last=Toth|first=Zoltan|author2=Kalnay, Eugenia|title=Ensemble Forecasting at NCEP and the Breeding Method |journal=[[Monthly Weather Review]]|date=December 1997|volume=125|issue=12|pages=3297–3319|doi=10.1175/1520-0493(1997)125<3297:EFANAT>2.0.CO;2|issn=1520-0493|bibcode=1997MWRv..125.3297T|author-link2=Eugenia Kalnay|citeseerx=10.1.1.324.3941}}</ref><ref name="ECens">{{cite web|url=http://ecmwf.int/products/forecasts/guide/The_Ensemble_Prediction_System_EPS_1.html |title=The Ensemble Prediction System (EPS) |publisher=[[ECMWF]] |access-date=2011-01-05 |archive-url=https://web.archive.org/web/20110125125209/http://ecmwf.int/products/forecasts/guide/The_Ensemble_Prediction_System_EPS_1.html |archive-date=25 January 2011 |url-status=dead }}</ref><ref name="RMS">{{cite journal|title=The ECMWF Ensemble Prediction System: Methodology and validation|journal=Quarterly Journal of the Royal Meteorological Society|date=January 1996|volume=122|issue=529|pages=73–119|author1=Molteni, F. |author2=Buizza, R. |author3=Palmer, T.N. |author4=Petroliagis, T. |doi=10.1002/qj.49712252905|bibcode=1996QJRMS.122...73M}}</ref>
由于基于大气动力学的预报模式的输出结果需要近地面处的修正，因此20世纪70年代和20世纪80年代开发了单个预报位点的模式输出统计（MOS）。尽管超级计算机的能力不断提升，数值天气模式的预报仅能延伸到未来两周左右，这是因为观测点的密度和质量以及被用来预测的偏微分方程的混沌本质都会引入每五天加倍的误差。自20世纪90年代以来，模式集合预报的使用帮助确定了不确定性，并且预测时段比其他可能的方式都要长。
==初始化==
大气是流动的。因此，数值天气预报的思想是对给定时间的流体状态进行采样，并使用流体动力学和热力学方程来估计未来某个时间的流体状态。将观测数据输入模型以生成初始条件的过程称为初始化。在陆地上，全球分辨率低至1公里（0.6英里）的地形图用于帮助模拟崎岖地形区域内的大气环流，以便更好地描述影响入射太阳辐射的下坡风、过山波和相关云量等特征。基于国家的气象服务的主要输入是来自气象气球上的设备（称为无线电探空仪）的观测，这些设备测量各种大气参数并将其传输到固定接收器，以及来自气象卫星的观测。世界气象组织（World Meteorological Organization）在全球范围内对仪器、观测实践和观测时间进行标准化。观测站在METAR报告中每小时报告一次，或者在SYNOP报告中每六小时报告一次。这些观测数据的间隔不规则，因此通过数据同化和客观分析方法进行处理，以实现质量控制并在模型数学算法可用的位置获取数值，使得最后在模式中被用作预测的起点。
有许多方法可以收集数值模型的观测数据。这些站点通过从对流层上升到平流层的气象气球来发射无线电探空仪。在传统数据源不可用的情况下，则可以使用气象卫星提供的信息。商务部提供飞机航线上的飞行员报告和航运航线上的船舶报告。研究项目使用侦察机在关注的天气系统内和周围飞行，如热带气旋。在寒冷季节，侦察机也会飞越公海，进入一些对预报制导造成重大不确定性、预计在未来三到七天内对下游大陆产生重大影响的系统中。1971年，海冰开始在预报模型中得到初始化。1972年，由于海洋表面温度在调节太平洋高纬度地区天气方面的作用，将其纳入模型初始化的工作也开始进行。
==Computation 计算==
==计算==
[[File:NAM 500 MB.PNG|thumb|An example of 500 [[millibar|mbar]] [[geopotential height]] prediction from a numerical weather prediction model.|链接=Special:FilePath/NAM_500_MB.PNG]]
[[File:NAM 500 MB.PNG|thumb|An example of 500 [[millibar|mbar]] [[geopotential height]] prediction from a numerical weather prediction model.|链接=Special:FilePath/NAM_500_MB.PNG]]
[[File:Supercomputing the Climate.ogv|thumb|Supercomputers are capable of running highly complex models to help scientists better understand Earth's climate.|链接=Special:FilePath/Supercomputing_the_Climate.ogv]]
[[File:Supercomputing the Climate.ogv|thumb|超级计算机能够运行高度复杂的模型，从而帮助科学家更好地理解地球的气候。]]
模式指的是一种可以在给定的位置和海拔高度生成未来气象信息的一种计算机程序。任何模型中都有一套称为“原始方程组”的方程组，用于预测未来的大气状态。这些方程组依据分析数据初始化，并确定变化速率。这些变化速率可以预测未来一小段时间的大气状态，每一个时间增量被称为一个时间步长。然后这些方程组被用于新的大气状态，得到新的变化速率，新的变化速率接着被用于预测再往后的大气状态。<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>不断推进时间步，直到方程组的解到达了想要的预测时间。模式内时间步长的选择与计算网格间距有关，需要确保数值稳定性。<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>全球模式的时间步长约为数十分钟，<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|author=Sunderam, V. S. |author2=G. Dick van Albada |author3=Peter M. A. Sloot |author4=J. J. Dongarra|year=2005|publisher=Springer|isbn=978-3-540-26032-5}}</ref>而区域模式则为1到4分钟。<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 |author2=Norbert Kreitz |author3=European Centre for Medium Range Weather Forecasts|year=2001|publisher=World Scientific|isbn=978-981-02-4761-4}}</ref>全球模式预测时段各有不同。UKMET联合模式可预测未来6天，<ref name="models" />欧洲中心的中程天气预测模式 European Centre for Medium-Range Weather Forecasts model可预测未来10天，<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>而环境建模中心 Environmental Modeling Center的全球预测系统模式 Global Forest System model可以预测未来16天。<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}}</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|pages=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 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=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 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|pages=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 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=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>
【终稿】 由于使用的方程组是非线性的偏微分方程组，除了少数理想情况外无法用解析方法得到准确解，因此使用数值方法来获得近似解。不同的模式使用不同的求解方法：一些全球模式在水平维度使用谱方法求解，在垂直维度使用有限差分方法求解；而另一些全球模式以及区域模式则在三个维度都使用有限差分方法求解。模式的结果可视化通常称为预测图，或简称为“prog”。
【终稿】 由于使用的方程组是非线性的偏微分方程组，除了少数理想情况外无法用解析方法得到准确解，因此使用数值方法来获得近似解。不同的模式使用不同的求解方法：一些全球模式在水平维度使用谱方法求解，在垂直维度使用有限差分方法求解；而另一些全球模式以及区域模式则在三个维度都使用有限差分方法求解。模式的结果可视化通常称为预测图，或简称为“prog”。