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Equivalent Latitude
In differential geometry, the equivalent latitude is a Lagrangian coordinate . It is often used in atmospheric science, particularly in the study of stratospheric dynamics. Each isoline in a map of equivalent latitude follows the flow velocity and encloses the same area as the latitude line of equivalent value, hence "equivalent latitude." Equivalent latitude is calculated from potential vorticity, from passive tracer simulations and from actual measurements of atmospheric tracers such as ozone. Calculation of equivalent latitude The calculation of equivalent latitude involves creating a monotonic mapping between the values of equivalent latitude and the tracer it is based upon: higher values of the tracer map to higher values of equivalent latitude. A precise method is to assign a representative area to each of the tracer measurements, filling the entire globe. Thus, for a tracer field regularly gridded in longitude and latitude, grid points closer to the pole will take u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. A geometric structure is one which defines some notion of size, distance, shape, volume, or other rigidifying structu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrangian Coordinates
__NOTOC__ In classical field theories, the Lagrangian specification of the flow field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time. Plotting the position of an individual parcel through time gives the pathline of the parcel. This can be visualized as sitting in a boat and drifting down a river. The Eulerian specification of the flow field is a way of looking at fluid motion that focuses on specific locations in the space through which the fluid flows as time passes. This can be visualized by sitting on the bank of a river and watching the water pass the fixed location. The Lagrangian and Eulerian specifications of the flow field are sometimes loosely denoted as the Lagrangian and Eulerian frame of reference. However, in general both the Lagrangian and Eulerian specification of the flow field can be applied in any observer's frame of reference, and in any coordinate system used within the chosen fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atmospheric Science
Atmospheric science is the study of the Atmosphere of Earth, Earth's atmosphere and its various inner-working physical processes. Meteorology includes atmospheric chemistry and atmospheric physics with a major focus on weather forecasting. Climatology is the study of atmospheric changes (both long and short-term) that define average climates and their change over time, due to both natural and anthropogenic climate change, climate variability. Aeronomy is the study of the upper layers of the atmosphere, where dissociation (chemistry), dissociation and ionization are important. Atmospheric science has been extended to the field of planetary science and the study of the atmospheres of the planets and natural satellites of the Solar System. Experimental instruments used in atmospheric science include satellites, rocketsondes, radiosondes, weather balloons, radars, and lasers. The term aerology (from Ancient Greek, Greek ἀήρ, ''aēr'', "air"; and -λογία, ''-logy, -logia'') is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stratosphere
The stratosphere () is the second layer of the atmosphere of the Earth, located above the troposphere and below the mesosphere. The stratosphere is an atmospheric layer composed of stratified temperature layers, with the warm layers of air high in the sky and the cool layers of air in the low sky, close to the planetary surface of the Earth. The increase of temperature with altitude is a result of the absorption of the Sun's ultraviolet (UV) radiation by the ozone layer. The temperature inversion is in contrast to the troposphere, near the Earth's surface, where temperature decreases with altitude. Between the troposphere and stratosphere is the tropopause border that demarcates the beginning of the temperature inversion. Near the equator, the lower edge of the stratosphere is as high as , at midlatitudes around , and at the poles about . Temperatures range from an average of near the tropopause to an average of near the mesosphere. Stratospheric temperatures also vary w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flow Velocity
In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the flow velocity vector is the flow speed and is a scalar. It is also called velocity field; when evaluated along a line, it is called a velocity profile (as in, e.g., law of the wall). Definition The flow velocity ''u'' of a fluid is a vector field : \mathbf=\mathbf(\mathbf,t), which gives the velocity of an '' element of fluid'' at a position \mathbf\, and time t.\, The flow speed ''q'' is the length of the flow velocity vector :q = \, \mathbf \, and is a scalar field. Uses The flow velocity of a fluid effectively describes everything about the motion of a fluid. Many physical properties of a fluid can be expressed mathematically in terms of the flow velocity. Some common examples follow: Steady flow The flow of a fluid is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Potential Vorticity
In fluid mechanics, potential vorticity (PV) is a quantity which is proportional to the dot product of vorticity and stratification. This quantity, following a parcel of air or water, can only be changed by diabatic or frictional processes. It is a useful concept for understanding the generation of vorticity in cyclogenesis (the birth and development of a cyclone), especially along the polar front, and in analyzing flow in the ocean. Potential vorticity (PV) is seen as one of the important theoretical successes of modern meteorology. It is a simplified approach for understanding fluid motions in a rotating system such as the Earth's atmosphere and ocean. Its development traces back to the circulation theorem by Bjerknes in 1898, which is a specialized form of Kelvin's circulation theorem. Starting from Hoskins et al., 1985, PV has been more commonly used in operational weather diagnosis such as tracing dynamics of air parcels and inverting for the full flow field. Even after deta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ozone
Ozone (), or trioxygen, is an inorganic molecule with the chemical formula . It is a pale blue gas with a distinctively pungent smell. It is an allotrope of oxygen that is much less stable than the diatomic allotrope , breaking down in the lower atmosphere to (dioxygen). Ozone is formed from dioxygen by the action of ultraviolet (UV) light and electrical discharges within the Earth's atmosphere. It is present in very low concentrations throughout the latter, with its highest concentration high in the ozone layer of the stratosphere, which absorbs most of the Sun's ultraviolet (UV) radiation. Ozone's odour is reminiscent of chlorine, and detectable by many people at concentrations of as little as in air. Ozone's O3 structure was determined in 1865. The molecule was later proven to have a bent structure and to be weakly diamagnetic. In standard conditions, ozone is a pale blue gas that condenses at cryogenic temperatures to a dark blue liquid and finally a violet-black soli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonic Function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysis In calculus, a function f defined on a subset of the real numbers with real values is called ''monotonic'' if and only if it is either entirely non-increasing, or entirely non-decreasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is called ''monotonically increasing'' (also ''increasing'' or ''non-decreasing'') if for all x and y such that x \leq y one has f\!\left(x\right) \leq f\!\left(y\right), so f preserves the order (see Figure 1). Likewise, a function is called ''monotonically decreasing'' (also ''decreasing'' or ''non-increasing'') if, whenever x \leq y, then f\!\left(x\right) \geq f\!\left(y\ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sorting
Sorting refers to ordering data in an increasing or decreasing manner according to some linear relationship among the data items. # ordering: arranging items in a sequence ordered by some criterion; # categorizing: grouping items with similar properties. Ordering items is the combination of categorizing them based on equivalent order, and ordering the categories themselves. Sorting information or data In , arranging in an ordered sequence is called "sorting". Sorting is a common operation in many applications, and efficient algorithms to perform it have been developed. The most common uses of sorted sequences are: * making lookup or search efficient; * making merging of sequences efficient. * enable processing of data in a defined order. The opposite of sorting, rearranging a sequence of items in a random or meaningless order, is called shuffling. For sorting, either a weak order, "should not come after", can be specified, or a strict weak order, "should come before" (specif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Climatology
Climatology (from Greek , ''klima'', "place, zone"; and , '' -logia'') or climate science is the scientific study of Earth's climate, typically defined as weather conditions averaged over a period of at least 30 years. This modern field of study is regarded as a branch of the atmospheric sciences and a subfield of physical geography, which is one of the Earth sciences. Climatology now includes aspects of oceanography and biogeochemistry. The main methods employed by climatologists are the analysis of observations and modelling of the physical processes that determine the climate. The main topics of research are the study of climate variability, mechanisms of climate changes and modern climate change. Basic knowledge of climate can be used within shorter term weather forecasting, for instance about climatic cycles such as the El Niño–Southern Oscillation (ENSO), the Madden–Julian oscillation (MJO), the North Atlantic oscillation (NAO), the Arctic oscillation (AO), the Pac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. A geometric structure is one which defines some notion of size, distance, shape, volume, or other rigidifying structu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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