Atmospheric model
In
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 methods for the horizontal dimensions and 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 observations to develop statistical relationships which account for model bias and resolution issues.
Types
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 baroclinicity in the atmosphere can be simulated using the 500 mb (15 inHg) and 1,000 mb (30 inHg) geopotential height surfaces and the average thermal wind between them.[1][2]
Barotropic models assume the atmosphere is nearly
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.[6]
History
The
Because the output of forecast models based on
Initialization
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.[23] 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,[24] or every six hours in SYNOP reports.[25] 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.[26] The data are then used in the model as the starting point for a forecast.[27]
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.[28] Information from weather satellites is used where traditional data sources are not available. Commerce provides pilot reports along aircraft routes[29] and ship reports along shipping routes.[30] Research projects use reconnaissance aircraft to fly in and around weather systems of interest, such as tropical cyclones.[31][32] 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.[33] Sea ice began to be initialized in forecast models in 1971.[34] 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.[35]
Computation
A model is a computer program that produces
The equations used are nonlinear partial differential equations which are impossible to solve exactly through analytical methods,[43] with the exception of a few idealized cases.[44] 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.[43] The visual output produced by a model solution is known as a prognostic chart, or prog.[45]
Parameterization
Weather and climate model gridboxes have sides of between 5 kilometres (3.1 mi) and 300 kilometres (190 mi). A typical
The amount of solar radiation reaching ground level in rugged terrain, or due to variable cloudiness, is parameterized as this process occurs on the molecular scale.[48] Also, the grid size of the models is large when compared to the actual size and roughness of clouds and topography. Sun angle as well as the impact of multiple cloud layers is taken into account.[49] Soil type, vegetation type, and soil moisture all determine how much radiation goes into warming and how much moisture is drawn up into the adjacent atmosphere. Thus, they are important to parameterize.[50]
Domains
The horizontal domain of a model is either global, covering the entire Earth, or regional, covering only part of the Earth. Regional models also are known as limited-area models, or LAMs. Regional models use finer grid spacing to resolve explicitly smaller-scale meteorological phenomena, since their smaller domain decreases computational demands. Regional models use a compatible global model for initial conditions of the edge of their domain. Uncertainty and errors within LAMs are introduced by the global model used for the boundary conditions of the edge of the regional model, as well as within the creation of the boundary conditions for the LAMs itself.[51]
The vertical coordinate is handled in various ways. Some models, such as Richardson's 1922 model, use geometric height () as the vertical coordinate. Later models substituted the geometric coordinate with a pressure coordinate system, in which the
Global versions
Some of the better known global numerical models are:
- GFS NOAA
- NOGAPS – developed by the US Navyto compare with the GFS
- GEM Global Environmental Multiscale Model – developed by the Meteorological Service of Canada (MSC)
- IFS developed by the European Centre for Medium-Range Weather Forecasts
- UM Unified Model developed by the UK Met Office
- ICON developed by the German Weather Service, DWD, jointly with the Max-Planck-Institute (MPI) for Meteorology, Hamburg, NWP Global model of DWD
- ARPEGE developed by the French Weather Service, Météo-France
- IGCM Intermediate General Circulation Model[40]
Regional versions
Some of the better known regional numerical models are:
- WRF The Weather Research and Forecasting modelwas developed cooperatively by NCEP, NCAR, and the meteorological research community. WRF has several configurations, including:
- WRF-NMM The WRF Nonhydrostatic Mesoscale Model is the primary short-term weather forecast model for the U.S., replacing the Eta model.
- WRF-ARW Advanced Research WRF developed primarily at the U.S. National Center for Atmospheric Research (NCAR)
- HARMONIE-Climate (HCLIM) is a limited area climate model based on the HARMONIE model developed by a large consortium of European weather forecastign and research institutes . It is a model system that like WRF can be run in many configurations, including at high resolution with the non-hydrostatic Arome physics or at lower resolutions with hydrostatic physics based on the ALADIN physical schemes. It has mostly been used in Europe and the Arctic for climate studies including 3km downscaling over Scandinavia and in studies looking at extreme weather events.
- RACMO was developed at the Netherlands Meteorological Institute, KNMI and is based on the dynamics of the HIRLAM model with physical schemes from the IFS
- RACMO2.3p2 is a polar version of the model used in many studies to provide surface mass balance of the polar ice sheets that was developed at the University of Utrecht
- MAR (Modele Atmospherique Regionale) is a regional climate model developed at the University of Grenoble in France and the University of Liege in Belgium.
- HIRHAM5 is a regional climate model developed at the Danish Meteorological Institute and the Alfred Wegener Institute in Potsdam. It is also based on the HIRLAM dynamics with physical schemes based on those in the ECHAM model. Like the RACMO model HIRHAM has been used widely in many different parts of the world under the CORDEX scheme to provide regional climate prjections. It also has a polar mode that has been used for polar ice sheet studies in Greenland and Antarctica
- NAM The term North American Mesoscale model refers to whatever regional model NCEP operates over the North American domain. NCEP began using this designation system in January 2005. Between January 2005 and May 2006 the Eta model used this designation. Beginning in May 2006, NCEP began to use the WRF-NMM as the operational NAM.
- RAMS the Regional Atmospheric Modeling System developed at Colorado State University for numerical simulations of atmospheric meteorology and other environmental phenomena on scales from meters to hundreds of kilometers – now supported in the public domain
- MM5 The Fifth Generation Penn State/NCAR Mesoscale Model
- ARPS the Advanced Region Prediction System developed at the University of Oklahoma is a comprehensive multi-scale nonhydrostatic simulation and prediction system that can be used for regional-scale weather prediction up to the tornado-scale simulation and prediction. Advanced radar data assimilation for thunderstorm prediction is a key part of the system..
- HIRLAM High Resolution Limited Area Model, is developed by the European NWP research consortia[55] co-funded by 10 European weather services. The meso-scale HIRLAM model is known as HARMONIE and developed in collaboration with Meteo France and ALADIN consortia.
- GEM-LAM Global Environmental Multiscale Limited Area Model, the high resolution 2.5 km (1.6 mi) GEM by the Meteorological Service of Canada (MSC)
- ALADIN The high-resolution limited-area hydrostatic and non-hydrostatic model developed and operated by several European and North African countries under the leadership of Météo-France[40]
- COSMO The COSMO Model, formerly known as LM, aLMo or LAMI, is a limited-area non-hydrostatic model developed within the framework of the Consortium for Small-Scale Modelling (Germany, Switzerland, Italy, Greece, Poland, Romania, and Russia).[56]
- Meso-NH The Meso-NH Model[57] is a limited-area non-hydrostatic model developed jointly by the Centre National de Recherches Météorologiques and the Laboratoire d'Aérologie (France, Toulouse) since 1998.[58] Its application is from mesoscale to centimetric scales weather simulations.
Model output statistics
Because forecast models based upon the equations for atmospheric dynamics do not perfectly determine weather conditions near the ground, statistical corrections were developed to attempt to resolve this problem. Statistical models were created based upon the three-dimensional fields produced by numerical weather models, surface observations, and the climatological conditions for specific locations. These statistical models are collectively referred to as model output statistics (MOS),[59] and were developed by the National Weather Service for their suite of weather forecasting models.[16] The United States Air Force developed its own set of MOS based upon their dynamical weather model by 1983.[17]
Model output statistics differ from the perfect prog technique, which assumes that the output of numerical weather prediction guidance is perfect.[60] MOS can correct for local effects that cannot be resolved by the model due to insufficient grid resolution, as well as model biases. Forecast parameters within MOS include maximum and minimum temperatures, percentage chance of rain within a several hour period, precipitation amount expected, chance that the precipitation will be frozen in nature, chance for thunderstorms, cloudiness, and surface winds.[61]
Applications
Climate modeling
In 1956, Norman Phillips developed a mathematical model that realistically depicted monthly and seasonal patterns in the troposphere. This was the first successful climate model.[12][13] Several groups then began working to create general circulation models.[62] The first general circulation climate model combined oceanic and atmospheric processes and was developed in the late 1960s at the Geophysical Fluid Dynamics Laboratory, a component of the U.S. National Oceanic and Atmospheric Administration.[63]
By 1975, Manabe and Wetherald had developed a three-dimensional
By the early 1980s, the U.S.
Limited area modeling
The Movable Fine-Mesh model, which began operating in 1978, was the first
See also
- Atmospheric reanalysis
- Climate model
- Numerical weather prediction
- Upper-atmospheric models
- Static atmospheric model
- Chemistry transport model
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Further reading
- Roulstone, Ian; Norbury, John (2013). Invisible in the Storm: the role of mathematics in understanding weather. Princeton: Princeton University Press. ISBN 978-0-691-15272-1.