6
个编辑
更改
跳到导航
跳到搜索
第9行：
第9行： − 【终稿】大气模式是围绕控制大气运动的一整套原始的动力学方程所建立的数学模型。它可以通过湍流扩散、辐射额、湿过程（云和降水）、热交换、土壤、植被、地表水、地形的动力学效应和对流等的参数化来补充这些方程。大多数大气模式是基于数值方法的，即将运动方程离散化。它们可以预测微尺度的现象，例如龙卷风、边界层的涡旋、流经建筑物上方的亚微尺度湍流，以及天气气流、全球气流。模式的水平区域全球性的，覆盖整个地球，也可以是区域性的（有限区域的），只覆盖部分地球。模式运行的不同类型包括热致的、正压的、流体静力学的和非流体静力学的。部分类型的模式对大气进行了一些假设，从而加长了时间步长并提高计算速度。+ 第19行：
第19行： − + 第26行：
第26行： − '''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 -->+ − + + + + + 第36行：
第40行： − 流体静力学模型从垂直动量方程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。+ + + − + − − 第49行：
第53行： − + + + 第55行：
第61行： − + + + − + 第80行：
第88行： − +
无编辑摘要
大气模式是围绕控制大气运动的一整套原始动力学方程建立的数学模式。它可以用湍流扩散、辐射、湿过程(云和降水)、热交换、土壤、植被、地表水、地形的运动学效应和对流等参数化来补充这些方程。大多数大气模型都是数字化的，例如。他们把运动方程分开。他们可以预测微尺度现象，例如龙卷风和边界层涡旋，建筑物上空的亚微尺度湍流，以及天气和全球气流。模型的水平域要么是全球性的，覆盖了整个地球; 要么是区域性的，只覆盖了地球的一部分。不同类型的模式运行是热力学，正压，流体静力学和非流体静力学。一些模型类型对大气层做出假设，从而延长了使用的时间步骤，提高了计算速度。
大气模式是围绕控制大气运动的一整套原始动力学方程建立的数学模式。它可以用湍流扩散、辐射、湿过程(云和降水)、热交换、土壤、植被、地表水、地形的运动学效应和对流等参数化来补充这些方程。大多数大气模型都是数字化的，例如。他们把运动方程分开。他们可以预测微尺度现象，例如龙卷风和边界层涡旋，建筑物上空的亚微尺度湍流，以及天气和全球气流。模型的水平域要么是全球性的，覆盖了整个地球; 要么是区域性的，只覆盖了地球的一部分。不同类型的模式运行是热力学，正压，流体静力学和非流体静力学。一些模型类型对大气层做出假设，从而延长了使用的时间步骤，提高了计算速度。
【终稿】大气模式是围绕控制大气运动的一整套原始的动力学方程所建立的数学模型。它可以通过湍流扩散、辐射、湿过程（云和降水）、热交换、土壤、植被、地表水、地形的动力学效应和对流等的参数化来补充这些方程。大多数大气模式是基于数值方法的，即将运动方程离散化。它们可以预测微尺度的现象，例如龙卷风、边界层的涡旋、流经建筑物上方的亚微尺度湍流，以及天气气流、全球气流。模式的水平区域全球性的，覆盖整个地球，也可以是区域性的（有限区域的），只覆盖部分地球。模式运行的不同类型包括热致的、正压的、流体静力学的和非流体静力学的。部分类型的模式对大气进行了一些假设，从而加长了时间步长并提高计算速度。
Forecasts are computed using mathematical equations for the physics and dynamics of the atmosphere. These equations are nonlinear and are impossible to solve exactly. Therefore, numerical methods obtain approximate solutions. Different models use different solution methods. Global models often use [[spectral method]]s for the horizontal dimensions and [[Finite difference method|finite-difference methods]] for the vertical dimension, while regional models usually use finite-difference methods in all three dimensions. For specific locations, [[model output statistics]] use climate information, output from [[numerical weather prediction]], and current [[surface weather observation]]s to develop statistical relationships which account for model bias and resolution issues.
Forecasts are computed using mathematical equations for the physics and dynamics of the atmosphere. These equations are nonlinear and are impossible to solve exactly. Therefore, numerical methods obtain approximate solutions. Different models use different solution methods. Global models often use [[spectral method]]s for the horizontal dimensions and [[Finite difference method|finite-difference methods]] for the vertical dimension, while regional models usually use finite-difference methods in all three dimensions. For specific locations, [[model output statistics]] use climate information, output from [[numerical weather prediction]], and current [[surface weather observation]]s to develop statistical relationships which account for model bias and resolution issues.
【终稿】预报是使用大气物理和动力学方程计算得来的。这些方程是非线性的，无法获得准确解。因此只能使用数值方法获得近似解。不同的模式使用不同的求解方法。全球模式通常在水平维度上采用谱方法，而在垂直维度采用有限差分法；而区域模式通常在三个维度均使用有限差分法。对于特定的位置，模式的输出统计使用气候信息、数值天气预测结果以及当前地表天气观测数据来建立统计关系，以解释模式偏差和分辨率问题。
【终稿】预报是使用大气物理和动力学方程计算得来的。这些方程是非线性的，无法获得准确解。因此只能使用数值方法获得近似解。不同的模式使用不同的求解方法。全球模式通常在水平维度上采用谱方法，而在垂直维度采用有限差分法；而区域模式通常在三个维度均使用有限差分法。对于特定的位置，模式的输出统计使用气候信息、数值天气预测结果以及当前地表天气观测数据来建立统计关系，以解释模式偏差和分辨率问题。
== Types ==
== Types 类型 ==
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.<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>
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.<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>
= = = = = 由热带模式作出的主要假设是，虽然热风的大小可能改变，但其方向不随高度而改变，因此大气的斜压性可以利用位势高度表面和它们之间的平均热风来模拟。
= = = = = 由热带模式作出的主要假设是，虽然热风的大小可能改变，但其方向不随高度而改变，因此大气的斜压性可以利用位势高度表面和它们之间的平均热风来模拟。
【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。
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 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.
'''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。
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>
[[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.
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 高度坐标随地板等高线改变。
== History ==
== 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]]
[[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}}
{{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]].<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.
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。
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。
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>
【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型的诞生。在20世纪70年代和20世纪80年代，有限区域（区域性）模型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).<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). 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.
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。
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。
==Initialization==
【终稿】由于基于大气动力学的预报模型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点（称为“location”）的模型输出统计（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}}
{{transcluded section|source=Numerical weather prediction}}
{{#section-h:Numerical weather prediction|Initialization}}
{{#section-h:Numerical weather prediction|Initialization}}
==Computation==
==Computation 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|Supercomputers are capable of running highly complex models to help scientists better understand Earth's climate.|链接=Special:FilePath/Supercomputing_the_Climate.ogv]]
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。
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。
== Parameterization ==
== Parameterization 参数化 ==
{{main|Parametrization (climate)}}
{{main|Parametrization (climate)}}
Weather and climate model gridboxes have sides of between {{convert|5|km|mi}} and {{convert|300|km|mi}}. A typical [[cumulus cloud]] has a scale of less than {{convert|1|km|mi}}, and would require a grid even finer than this to be represented physically by the equations of fluid motion. Therefore, the processes that such [[clouds]] represent are ''[[Parametrization (atmospheric modeling)|parameterized]]'', by processes of various sophistication. In the earliest models, if a column of air in a model gridbox was unstable (i.e., the bottom warmer than the top) then it would be overturned, and the air in that vertical column mixed. More sophisticated schemes add enhancements, recognizing that only some portions of the box might [[convection|convect]] and that entrainment and other processes occur. Weather models that have gridboxes with sides between {{convert|5|km|mi}} and {{convert|25|km|mi}} can explicitly represent convective clouds, although they still need to parameterize [[cloud microphysics]].<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|publisher=[[American Meteorological Society]]|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. Still, sub grid scale processes need to be taken into account. Rather than assuming that clouds form at 100% relative humidity, the [[cloud fraction]] can be related to a critical relative humidity of 70% for stratus-type clouds, and at or above 80% for cumuliform clouds,<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 |archive-url=https://web.archive.org/web/20110401013742/http://www.atmos.washington.edu/~dargan/591/diag_cloud.tech.pdf |archive-date=1 April 2011 |url-status=dead }}</ref> reflecting the sub grid scale variation that would occur in the real world.
Weather and climate model gridboxes have sides of between {{convert|5|km|mi}} and {{convert|300|km|mi}}. A typical [[cumulus cloud]] has a scale of less than {{convert|1|km|mi}}, and would require a grid even finer than this to be represented physically by the equations of fluid motion. Therefore, the processes that such [[clouds]] represent are ''[[Parametrization (atmospheric modeling)|parameterized]]'', by processes of various sophistication. In the earliest models, if a column of air in a model gridbox was unstable (i.e., the bottom warmer than the top) then it would be overturned, and the air in that vertical column mixed. More sophisticated schemes add enhancements, recognizing that only some portions of the box might [[convection|convect]] and that entrainment and other processes occur. Weather models that have gridboxes with sides between {{convert|5|km|mi}} and {{convert|25|km|mi}} can explicitly represent convective clouds, although they still need to parameterize [[cloud microphysics]].<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|publisher=[[American Meteorological Society]]|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. Still, sub grid scale processes need to be taken into account. Rather than assuming that clouds form at 100% relative humidity, the [[cloud fraction]] can be related to a critical relative humidity of 70% for stratus-type clouds, and at or above 80% for cumuliform clouds,<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 |archive-url=https://web.archive.org/web/20110401013742/http://www.atmos.washington.edu/~dargan/591/diag_cloud.tech.pdf |archive-date=1 April 2011 |url-status=dead }}</ref> reflecting the sub grid scale variation that would occur in the real world.