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Exner Function
The Exner function is an important parameter in atmospheric modeling. The Exner function can be viewed as non-dimensionalized pressure and can be defined as: : \Pi = \left( \frac \right)^ = \frac where p_0 is a standard reference surface pressure, usually taken as 1000 hPa; R_d is the gas constant for dry air; c_p is the heat capacity of dry air at constant pressure; T is the absolute temperature; and \theta is the potential temperature. References *Pielke, Roger A. ''Mesoscale Meteorological Modeling.'' Orlando: Academic Press, Inc., 1984. *U.S. Department of Commerce, National Oceanic and Atmospheric Administration, National Weather Service. ''National Weather Service Handbook No. 1 - Facsimile Products.'' Washington, DC: Department of Commerce, 1979. See also *Barometric formula *Climate model *Euler equations *Fluid dynamics *General circulation model *Numerical weather prediction *Primitive equations The primitive equations are a set of nonlinear partial differential ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atmospheric Model
An atmospheric model is a mathematical model constructed around the full set of primitive dynamical equations which govern atmospheric motions. It can supplement these equations with parameterizations for turbulent diffusion, radiation, moist processes ( clouds and precipitation), heat exchange, soil, vegetation, surface water, the kinematic effects of terrain, and convection. Most atmospheric models are numerical, i.e. they discretize equations of motion. They can predict microscale phenomena such as tornadoes and boundary layer eddies, sub-microscale turbulent flow over buildings, as well as synoptic and global flows. The horizontal domain of a model is either ''global'', covering the entire Earth, or ''regional'' (''limited-area''), covering only part of the Earth. The different types of models run are thermotropic, barotropic, hydrostatic, and nonhydrostatic. Some of the model types make assumptions about the atmosphere which lengthens the time steps used and increases ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gas Constant
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per amount of substance, i.e. the pressure–volume product, rather than energy per temperature increment per ''particle''. The constant is also a combination of the constants from Boyle's law, Charles's law, Avogadro's law, and Gay-Lussac's law. It is a physical constant that is featured in many fundamental equations in the physical sciences, such as the ideal gas law, the Arrhenius equation, and the Nernst equation. The gas constant is the constant of proportionality that relates the energy scale in physics to the temperature scale and the scale used for amount of substance. Thus, the value of the gas constant ultimately derives from historical decisions and accidents in the setting of units of energy, temperature and amount of substa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heat Capacity
Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity is an extensive property. The corresponding intensive property is the specific heat capacity, found by dividing the heat capacity of an object by its mass. Dividing the heat capacity by the amount of substance in moles yields its molar heat capacity. The volumetric heat capacity measures the heat capacity per volume. In architecture and civil engineering, the heat capacity of a building is often referred to as its thermal mass. Definition Basic definition The heat capacity of an object, denoted by C, is the limit : C = \lim_\frac, where \Delta Q is the amount of heat that must be added to the object (of mass ''M'') in order to raise its temperature by \Delta T. The value of this parameter usually varies considerably depending on the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absolute Temperature
Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics. Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic work and heat transfer as defined in thermodynamics, but the kelvin was redefined by international agreement in 2019 in terms of phenomena that are now understood as manifestations of the kinetic energy of free motion of microscopic particles such as atoms, molecules, and electrons. From the thermodynamic viewpoint, for historical reasons, because of how it is defined and measured, this microscopic kinetic definition is regarded as an "empirical" temperature. It was adopted because in practice it can generally be measured more precisely than can Kelvin's thermodynamic temperature. A thermodynamic temperature reading of zero is of particular importance for the third law of thermodynamics. By convention, it is reported on the ''Kelvin scale'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Potential Temperature
The potential temperature of a parcel of fluid at pressure P is the temperature that the parcel would attain if adiabatically brought to a standard reference pressure P_, usually . The potential temperature is denoted \theta and, for a gas well-approximated as ideal, is given by : \theta = T \left(\frac\right)^, where T is the current absolute temperature (in K) of the parcel, R is the gas constant of air, and c_p is the specific heat capacity at a constant pressure. R/c_p = 0.286 for air (meteorology). The reference point for potential temperature in the ocean is usually at the ocean's surface which has a water pressure of 0 dbar. The potential temperature in the ocean doesn't account for the varying heat capacities of seawater, therefore it is not a conservative measure of heat content. Graphical representation of potential temperature will always be less than the actual temperature line in a temperature vs depth graph. Contexts The concept of potential temperature applies ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barometric Formula
The barometric formula, sometimes called the ''exponential atmosphere'' or ''isothermal atmosphere'', is a formula used to model how the pressure (or density) of the air changes with altitude. The pressure drops approximately by 11.3 pascals per meter in first 1000 meters above sea level. Pressure equations There are two different equations for computing pressure at various height regimes below 86 km (or 278,400 feet). The first equation is used when the value of standard temperature lapse rate is not equal to zero: P = P_b \left frac\right The second equation is used when standard temperature lapse rate equals zero: P = P_b \exp \left frac\right/math> where: *P_b = reference pressure ( Pa) *T_b = reference temperature ( K) *L_b = temperature lapse rate (K/m) in ISA *h = height at which pressure is calculated (m) *h_b = height of reference level ''b'' (meters; e.g., ''hb'' = 11 000 m) *R^* = universal gas constant: 8.3144598 J/(mol·K) *g_0 = gravitational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Climate Model
Numerical climate models use quantitative methods to simulate the interactions of the important drivers of climate, including atmosphere, oceans, land surface and ice. They are used for a variety of purposes from study of the dynamics of the climate system to projections of future climate. Climate models may also be qualitative (i.e. not numerical) models and also narratives, largely descriptive, of possible futures. Quantitative climate models take account of incoming energy from the sun as short wave electromagnetic radiation, chiefly visible and short-wave (near) infrared, as well as outgoing long wave (far) infrared electromagnetic. An imbalance results in a change in temperature. Quantitative models vary in complexity. For example, a simple radiant heat transfer model treats the earth as a single point and averages outgoing energy. This can be expanded vertically (radiative-convective models) and/or horizontally. Coupled atmosphere–ocean–sea ice global climate models ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler Equations
200px, Leonhard Euler (1707–1783) In mathematics and physics, many topics are named in honor of Swiss mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. Many of these items named after Euler include their own unique function, equation, formula, identity, number (single or sequence), or other mathematical entity. Many of these entities have been given simple and ambiguous names such as Euler's function, Euler's equation, and Euler's formula. Euler's work touched upon so many fields that he is often the earliest written reference on a given matter. In an effort to avoid naming everything after Euler, some discoveries and theorems are attributed to the first person to have proved them ''after'' Euler. Conjectures *Euler's conjecture (Waring's problem) *Euler's sum of powers conjecture * Euler's Graeco-Latin square conjecture Equations Usually, ''Euler's equation'' refers to one of (or a set of) differential equations (DEs). It is cus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Circulation Model
A general circulation model (GCM) is a type of climate model. It employs a mathematical model of the general circulation of a planetary atmosphere or ocean. It uses the Navier–Stokes equations on a rotating sphere with thermodynamic terms for various energy sources (radiation, latent heat). These equations are the basis for computer programs used to simulate the Earth's atmosphere or oceans. Atmospheric and oceanic GCMs (AGCM and OGCM) are key components along with sea ice and land-surface components. GCMs and global climate models are used for weather forecasting, understanding the climate, and forecasting climate change. Versions designed for decade to century time scale climate applications were originally created by Syukuro Manabe and Kirk Bryan at the Geophysical Fluid Dynamics Laboratory (GFDL) in Princeton, New Jersey. These models are based on the integration of a variety of fluid dynamical, chemical and sometimes biological equations. Terminology The acronym ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Weather Prediction
Numerical weather prediction (NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in the 1950s that numerical weather predictions produced realistic results. A number of global and regional forecast models are run in different countries worldwide, using current weather observations relayed from radiosondes, weather satellites and other observing systems as inputs. Mathematical models based on the same physical principles can be used to generate either short-term weather forecasts or longer-term climate predictions; the latter are widely applied for understanding and projecting climate change. The improvements made to regional models have allowed for significant improvements in tropical cyclone track and air quality forecasts; however, atmospheric models perform poorly at handling processes that occur in a relatively const ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Primitive Equations
The primitive equations are a set of nonlinear partial differential equations that are used to approximate global atmospheric flow and are used in most atmospheric models. They consist of three main sets of balance equations: # A ''continuity equation'': Representing the conservation of mass. # ''Conservation of momentum'': Consisting of a form of the Navier–Stokes equations that describe hydrodynamical flow on the surface of a sphere under the assumption that vertical motion is much smaller than horizontal motion (hydrostasis) and that the fluid layer depth is small compared to the radius of the sphere # A '' thermal energy equation'': Relating the overall temperature of the system to heat sources and sinks The primitive equations may be linearized to yield Laplace's tidal equations, an eigenvalue problem from which the analytical solution to the latitudinal structure of the flow may be determined. In general, nearly all forms of the primitive equations relate the five var ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
