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Q-Vectors
Q-vectors are used in atmospheric dynamics to understand physical processes such as vertical motion and frontogenesis. Q-vectors are not physical quantities that can be measured in the atmosphere but are derived from the quasi-geostrophic equations and can be used in the previous diagnostic situations. On meteorological charts, Q-vectors point toward upward motion and away from downward motion. Q-vectors are an alternative to the omega equation for diagnosing vertical motion in the quasi-geostrophic equations. Derivation First derived in 1978, Q-vector derivation can be simplified for the midlatitudes, using the midlatitude β-plane quasi-geostrophic prediction equations: # \frac - f_v_a - \beta y v_g = 0 (x component of quasi-geostrophic momentum equation) # \frac + f_u_a + \beta y u_g = 0 (y component of quasi-geostrophic momentum equation) # \frac - \frac \omega = \frac (quasi-geostrophic thermodynamic equation) And the thermal wind equations: f_ \frac = \frac \frac (x ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasi-geostrophic Equations
While geostrophic motion refers to the wind that would result from an exact balance between the Coriolis force and horizontal pressure-gradient forces, quasi-geostrophic (QG) motion refers to flows where the Coriolis force and pressure gradient forces are ''almost'' in balance, but with inertia also having an effect. Origin Atmospheric and oceanographic flows take place over horizontal length scales which are very large compared to their vertical length scale, and so they can be described using the shallow water equations. The Rossby number is a dimensionless number which characterises the strength of inertia compared to the strength of the Coriolis force. The quasi-geostrophic equations are approximations to the shallow water equations in the limit of small Rossby number, so that inertial forces are an order of magnitude smaller than the Coriolis and pressure forces. If the Rossby number is equal to zero then we recover geostrophic flow. The quasi-geostrophic equations were fir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frontogenesis
Frontogenesis is a meteorological process of tightening of horizontal temperature gradients to produce fronts. In the end, two types of fronts form: cold fronts and warm fronts. A cold front is a narrow line where temperature decreases rapidly. A warm front is a narrow line of warmer temperatures and essentially where much of the precipitation occurs. Frontogenesis occurs as a result of a developing baroclinic wave. According to Hoskins & Bretherton (1972, p. 11), there are eight mechanisms that influence temperature gradients: horizontal deformation, horizontal shearing, vertical deformation, differential vertical motion, latent heat release, surface friction, turbulence and mixing, and radiation. Semigeostrophic frontogenesis theory focuses on the role of horizontal deformation and shear. Kinematics Horizontal deformation in mid-latitude cyclones concentrates temperature gradients—cold air from the poles and warm air from the equator. Horizontal shear has two effects on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Omega Equation
The omega equation is a culminating result in synoptic-scale meteorology. It is an elliptic partial differential equation, named because its left-hand side produces an estimate of vertical velocity, customarily expressed by symbol \omega, in a pressure coordinate measuring height the atmosphere. Mathematically, \omega = \frac, where represents a material derivative. The underlying concept is more general, however, and can also be applied to the Boussinesq fluid equation system where vertical velocity is w = \frac in altitude coordinate ''z''. Concept and summary Vertical wind is crucial to weather and storms of all types. Even slow, broad updrafts can create convective instability or bring air to its lifted condensation level creating stratiform cloud decks. Unfortunately, predicting vertical motion directly is difficult. For synoptic scales in Earth's broad and shallow troposphere, the vertical component of Newton's law of motion is sacrificed in meteorology's primitive equ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermal Wind
The thermal wind is the vector difference between the geostrophic wind at upper altitudes minus that at lower altitudes in the atmosphere. It is the hypothetical vertical wind shear that would exist if the winds obey geostrophic balance in the horizontal, while pressure obeys hydrostatic balance in the vertical. The combination of these two force balances is called ''thermal wind balance'', a term generalizable also to more complicated horizontal flow balances such as gradient wind balance''.'' Since the geostrophic wind at a given pressure level flows along geopotential height contours on a map, and the geopotential thickness of a pressure layer is proportional to virtual temperature, it follows that the thermal wind flows along thickness or temperature contours. For instance, the thermal wind associated with pole-to-equator temperature gradients is the primary physical explanation for the jet stream in the upper half of the troposphere, which is the atmospheric layer extendin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coriolis Parameter
The Coriolis frequency ''ƒ'', also called the Coriolis parameter or Coriolis coefficient, is equal to twice the rotation rate ''Ω'' of the Earth multiplied by the sine of the latitude \varphi. :f = 2 \Omega \sin \varphi.\, The rotation rate of the Earth (''Ω'' = 7.2921 × 10−5 rad/s) can be calculated as 2''π'' / ''T'' radians per second, where ''T'' is the rotation period of the Earth which is one ''sidereal'' day (23 h 56 min 4.1 s). In the midlatitudes, the typical value for f is about 10−4 rad/s. Inertial oscillations on the surface of the earth have this frequency. These oscillations are the result of the Coriolis effect. Explanation Consider a body (for example a fixed volume of atmosphere) moving along at a given latitude \varphi at velocity v in the earth's rotating reference frame. In the local reference frame of the body, the vertical direction is parallel to the radial vector point ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal 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 substance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Specific Heat
In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat that must be added to one unit of mass of the substance in order to cause an increase of one unit in temperature. The SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg−1⋅K−1. For example, the heat required to raise the temperature of of water by is , so the specific heat capacity of water is . Specific heat capacity often varies with temperature, and is different for each state of matter. Liquid water has one of the highest specific heat capacities among common substances, about at 20 °C; but that of ice, just below 0 °C, is only . The specific heat capacities of iron, granite, and hydrogen gas are about 449 J⋅kg−1⋅K−1, 790 J⋅kg−1⋅K−1, and 14300 J⋅kg−1⋅K−1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geostrophic
A geostrophic current is an oceanic current in which the pressure gradient force is balanced by the Coriolis effect. The direction of geostrophic flow is parallel to the isobars, with the high pressure to the right of the flow in the Northern Hemisphere, and the high pressure to the left in the Southern Hemisphere. This concept is familiar from weather maps, whose isobars show the direction of geostrophic winds. Geostrophic flow may be either barotropic or baroclinic. A geostrophic current may also be thought of as a rotating shallow water wave with a frequency of zero. The principle of ''geostrophy'' or ''geostrophic balance'' is useful to oceanographers because it allows them to infer ocean currents from measurements of the sea surface height (by combined satellite altimetry and gravimetry) or from vertical profiles of seawater density taken by ships or autonomous buoys. The major currents of the world's oceans, such as the Gulf Stream, the Kuroshio Current, the Agulhas Curr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ageostrophic
Ageostrophy or (ageostrophic flow) is the difference between the ''actual'' wind or current and the geostrophic wind or geostrophic current. Since geostrophy is an exact balance between the Coriolis force and the pressure gradient force, ageostrophic flow reflects an imbalance, and thus is often implicated in disturbances, vertical motions (important for weather), and rapid changes with time. Ageostrophic flow reflects the existence of all the other terms in the momentum equation neglected in that idealization, including friction and material acceleration Dv/Dt, which includes the centrifugal force in curved flow. See also *geostrophic A geostrophic current is an oceanic current in which the pressure gradient force is balanced by the Coriolis effect. The direction of geostrophic flow is parallel to the isobars, with the high pressure to the right of the flow in the Northern ... * geostrophic wind References External linksMeteo 422 – Lecture 17 – The Omega Equation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Series
A Fourier series () is a summation of harmonically related sinusoidal functions, also known as components or harmonics. The result of the summation is a periodic function whose functional form is determined by the choices of cycle length (or ''period''), the number of components, and their amplitudes and phase parameters. With appropriate choices, one cycle (or ''period'') of the summation can be made to approximate an arbitrary function in that interval (or the entire function if it too is periodic). The number of components is theoretically infinite, in which case the other parameters can be chosen to cause the series to converge to almost any ''well behaved'' periodic function (see Pathological and Dirichlet–Jordan test). The components of a particular function are determined by ''analysis'' techniques described in this article. Sometimes the components are known first, and the unknown function is ''synthesized'' by a Fourier series. Such is the case of a discrete-ti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geopotential Height
Geopotential height or geopotential altitude is a vertical coordinate referenced to Earth's mean sea level, an adjustment to geometric height (altitude above mean sea level) that accounts for the variation of gravity with latitude and altitude. Thus, it can be considered a "gravity-adjusted height". It is the altitude all aircraft's pressure altitude, barometric altimeters are calibrated to. Definition At an elevation of h, the geopotential is defined as: :\Phi(h) = \int_0^h g(\phi,z)\,dz\, , where g(\phi,z) is the acceleration due to gravity, \phi is latitude, and z is the geometric elevation. Thus geopotential is the gravitational energy, gravitational potential energy per unit mass at that elevation. The geopotential height is: :(h) = \frac\, , which normalizes the geopotential to g_0 = 9.80665 m/s2, the standard gravity at mean sea level. Usage Geophysics, Geophysical sciences such as meteorology often prefer to express the horizontal Pressure-gradient force, pressure gradie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meteorological Concepts
Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not begin until the 18th century. The 19th century saw modest progress in the field after weather observation networks were formed across broad regions. Prior attempts at prediction of weather depended on historical data. It was not until after the elucidation of the laws of physics, and more particularly in the latter half of the 20th century the development of the computer (allowing for the automated solution of a great many modelling equations) that significant breakthroughs in weather forecasting were achieved. An important branch of weather forecasting is marine weather forecasting as it relates to maritime and coastal safety, in which weather effects also include atmospheric interactions with large bodies of water. Meteorological pheno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
