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53-527: The TCCON is designed to investigate several things, including the flow (or flux ) of carbon between the atmosphere, land, and ocean (the so-called carbon budget or carbon cycle ). This is achieved by measuring the atmospheric mass of carbon (the airborne fraction ). The TCCON measurements have improved the scientific community's understanding of the carbon cycle , and urban greenhouse gas emissions . The TCCON supports several satellite instruments by providing an independent measurement to compare (or validate)

106-474: A r g m a x n ^ n ^ p d q d t ( A , p , n ^ ) . {\displaystyle \mathbf {I} (A,\mathbf {p} )={\underset {\mathbf {\hat {n}} }{\operatorname {arg\,max} }}\mathbf {\hat {n}} _{\mathbf {p} }{\frac {\mathrm {d} q}{\mathrm {d} t}}(A,\mathbf {p} ,\mathbf {\hat {n}} ).} In this case, there

159-423: A (single) scalar: j = I A , {\displaystyle j={\frac {I}{A}},} where I = lim Δ t → 0 Δ q Δ t = d q d t . {\displaystyle I=\lim _{\Delta t\to 0}{\frac {\Delta q}{\Delta t}}={\frac {\mathrm {d} q}{\mathrm {d} t}}.} In this case

212-402: A closed surface, in other words the net outflux from a 3D region, is found by adding the local net outflow from each point in the region (which is expressed by the divergence ). If the surface is not closed, it has an oriented curve as boundary. Stokes' theorem states that the flux of the curl of a vector field is the line integral of the vector field over this boundary. This path integral

265-467: A flux according to the electromagnetism definition, the corresponding flux density , if that term is used, refers to its derivative along the surface that was integrated. By the Fundamental theorem of calculus , the corresponding flux density is a flux according to the transport definition. Given a current such as electric current—charge per time, current density would also be a flux according to

318-494: A magnetic field opposite to the change. This is the basis for inductors and many electric generators . Using this definition, the flux of the Poynting vector S over a specified surface is the rate at which electromagnetic energy flows through that surface, defined like before: The flux of the Poynting vector through a surface is the electromagnetic power , or energy per unit time , passing through that surface. This

371-596: A meeting is held in a location that rotates between North America, the Western Pacific, and Europe hosted by a participating institution. In 2015 the meeting was held at the University of Toronto . The main instrument at each TCCON site is a Bruker IFS 125HR (HR for high resolution, ~0.02 cm) or occasionally 120HR Fourier transform spectrometer . Sunlight is directed into the spectrometer by solar tracking mirrors and other optics. The spectrometers measure

424-532: A positive point charge can be visualized as a dot radiating electric field lines (sometimes also called "lines of force"). Conceptually, electric flux can be thought of as "the number of field lines" passing through a given area. Mathematically, electric flux is the integral of the normal component of the electric field over a given area. Hence, units of electric flux are, in the MKS system , newtons per coulomb times meters squared, or N m /C. (Electric flux density

477-419: A slab, and then more generally in terms of temperature gradients or differentials of temperature, across other geometries. One could argue, based on the work of James Clerk Maxwell , that the transport definition precedes the definition of flux used in electromagnetism . The specific quote from Maxwell is: In the case of fluxes, we have to take the integral, over a surface, of the flux through every element of

530-404: Is j  cos  θ , while the component of flux passing tangential to the area is j  sin  θ , but there is no flux actually passing through the area in the tangential direction. The only component of flux passing normal to the area is the cosine component. For vector flux, the surface integral of j over a surface S , gives the proper flowing per unit of time through

583-435: Is the integral over a surface; it makes no sense to integrate a second-definition flux for one would be integrating over a surface twice. Thus, Maxwell's quote only makes sense if "flux" is being used according to the transport definition (and furthermore is a vector field rather than single vector). This is ironic because Maxwell was one of the major developers of what we now call "electric flux" and "magnetic flux" according to

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636-458: Is "to flow". As fluxion , this term was introduced into differential calculus by Isaac Newton . The concept of heat flux was a key contribution of Joseph Fourier , in the analysis of heat transfer phenomena. His seminal treatise Théorie analytique de la chaleur ( The Analytical Theory of Heat ), defines fluxion as a central quantity and proceeds to derive the now well-known expressions of flux in terms of temperature differences across

689-462: Is a concept in applied mathematics and vector calculus which has many applications to physics . For transport phenomena , flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface. The word flux comes from Latin : fluxus means "flow", and fluere

742-417: Is also called circulation , especially in fluid dynamics. Thus the curl is the circulation density. We can apply the flux and these theorems to many disciplines in which we see currents, forces, etc., applied through areas. An electric "charge," such as a single proton in space, has a magnitude defined in coulombs. Such a charge has an electric field surrounding it. In pictorial form, the electric field from

795-514: Is commonly used in analysis of electromagnetic radiation , but has application to other electromagnetic systems as well. Confusingly, the Poynting vector is sometimes called the power flux , which is an example of the first usage of flux, above. It has units of watts per square metre (W/m ). National Institute for Environmental Studies The National Institute for Environmental Studies ( NIES :国立環境研究所, Kokuritsu-Kankyō kenkyūsho)

848-408: Is drawn by curves (field lines) following the "flow"; the magnitude of the vector field is then the line density, and the flux through a surface is the number of lines. Lines originate from areas of positive divergence (sources) and end at areas of negative divergence (sinks). See also the image at right: the number of red arrows passing through a unit area is the flux density, the curve encircling

901-613: Is heavy cloud cover). Current TCCON sites are located in the United States , China , Canada , Germany , Poland , France , Japan , Australia , New Zealand , South Korea , Réunion , and Ascension Island . A former site was in Brazil . Sites can change when an instrument needs to be moved to a new location. TCCON members collaborate from a variety of different institutions. In North America some of these include Caltech , JPL , Los Alamos National Laboratory , NASA Ames , and

954-408: Is maximized across the disk that is perpendicular to it. The unit vector thus uniquely maximizes the function when it points in the "true direction" of the flow. (Strictly speaking, this is an abuse of notation because the "arg max" cannot directly compare vectors; we take the vector with the biggest norm instead.) These direct definitions, especially the last, are rather unwieldy. For example,

1007-399: Is no fixed surface we are measuring over. q is a function of a point, an area, and a direction (given by a unit vector n ^ {\displaystyle \mathbf {\hat {n}} } ), and measures the flow through the disk of area A perpendicular to that unit vector. I is defined picking the unit vector that maximizes the flow around the point, because the true flow

1060-469: Is sometimes referred to as the probability current or current density, or probability flux density. As a mathematical concept, flux is represented by the surface integral of a vector field , where F is a vector field , and d A is the vector area of the surface A , directed as the surface normal . For the second, n is the outward pointed unit normal vector to the surface. The surface has to be orientable , i.e. two sides can be distinguished:

1113-604: Is the concentration ( mol /m ) of component A. This flux has units of mol·m ·s , and fits Maxwell's original definition of flux. For dilute gases, kinetic molecular theory relates the diffusion coefficient D to the particle density n = N / V , the molecular mass m , the collision cross section σ {\displaystyle \sigma } , and the absolute temperature T by D = 2 3 n σ k T π m {\displaystyle D={\frac {2}{3n\sigma }}{\sqrt {\frac {kT}{\pi m}}}} where

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1166-407: Is the vector area  – combination A = A n ^ {\displaystyle \mathbf {A} =A\mathbf {\hat {n}} } of the magnitude of the area A through which the property passes and a unit vector n ^ {\displaystyle \mathbf {\hat {n}} } normal to the area. Unlike in the second set of equations,

1219-509: Is the electric flux per unit area, and is a measure of strength of the normal component of the electric field averaged over the area of integration. Its units are N/C, the same as the electric field in MKS units.) Two forms of electric flux are used, one for the E -field: and one for the D -field (called the electric displacement ): This quantity arises in Gauss's law – which states that

1272-530: Is zero. As mentioned above, chemical molar flux of a component A in an isothermal , isobaric system is defined in Fick's law of diffusion as: J A = − D A B ∇ c A {\displaystyle \mathbf {J} _{A}=-D_{AB}\nabla c_{A}} where the nabla symbol ∇ denotes the gradient operator, D AB is the diffusion coefficient (m ·s ) of component A diffusing through component B, c A

1325-529: The D -field flux equals the charge Q A within it. Here the expression "flux of" indicates a mathematical operation and, as can be seen, the result is not necessarily a "flow", since nothing actually flows along electric field lines. The magnetic flux density ( magnetic field ) having the unit Wb/m ( Tesla ) is denoted by B , and magnetic flux is defined analogously: with the same notation above. The quantity arises in Faraday's law of induction , where

1378-562: The University of Toronto . In Europe some of these include Karlsruhe Institute of Technology , Max Planck Institute for Biogeochemistry , University of Bremen , Agencia Estatal de Meteorología , Royal Belgian Institute for Space Aeronomy , Finnish Meteorological Institute , and Pierre and Marie Curie University . In the western Pacific some of these include University of Wollongong , National Institute of Water and Atmospheric Research , National Institute for Environmental Studies , JAXA , and National Institute of Meteorological Research of

1431-578: The Republic of Korea. New sites are admitted into the network when site investigators demonstrate required hardware, and data processing ability. Uniformity is maintained across the network by using the same FTS model and the same retrieval software. GGG is the software of the TCCON. It includes the I2S (interferogram to spectrum) FFT , and GFIT spectral fitting subroutines. GFIT is also the fitting algorithm that

1484-400: The absorption of direct sunlight by atmospheric trace gases primarily in the near infrared region. This remote sensing technique produces a precise and accurate measurement of the total column abundance of the trace gas . The main limitation to this technique is that measurements can not be recorded when it is not sunny (i.e. there are no measurements available at nighttime or when there

1537-424: The area at an angle θ to the area normal n ^ {\displaystyle \mathbf {\hat {n}} } , then the dot product j ⋅ n ^ = j cos ⁡ θ . {\displaystyle \mathbf {j} \cdot \mathbf {\hat {n}} =j\cos \theta .} That is, the component of flux passing through the surface (i.e. normal to it)

1590-499: The area of that cross section, or the amount of sunlight energy that lands on a patch of ground each second divided by the area of the patch, are kinds of flux. Here are 3 definitions in increasing order of complexity. Each is a special case of the following. In all cases the frequent symbol j , (or J ) is used for flux, q for the physical quantity that flows, t for time, and A for area. These identifiers will be written in bold when and only when they are vectors. First, flux as

1643-406: The arg max construction is artificial from the perspective of empirical measurements, when with a weathervane or similar one can easily deduce the direction of flux at a point. Rather than defining the vector flux directly, it is often more intuitive to state some properties about it. Furthermore, from these properties the flux can uniquely be determined anyway. If the flux j passes through

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1696-445: The curve ∂ A {\displaystyle \partial A} , with the sign determined by the integration direction. The time-rate of change of the magnetic flux through a loop of wire is minus the electromotive force created in that wire. The direction is such that if current is allowed to pass through the wire, the electromotive force will cause a current which "opposes" the change in magnetic field by itself producing

1749-595: The data license is followed. Data have been used for a variety of analyses. Some of these include The satellite missions supported by the TCCON include the Greenhouse Gases Observing Satellite (GOSAT) , SCIAMACHY , and the Orbiting Carbon Observatory-2 (OCO-2) . Flux Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux

1802-401: The electromagnetism definition. Their names in accordance with the quote (and transport definition) would be "surface integral of electric flux" and "surface integral of magnetic flux", in which case "electric flux" would instead be defined as "electric field" and "magnetic flux" defined as "magnetic field". This implies that Maxwell conceived of these fields as flows/fluxes of some sort. Given

1855-511: The entire column of atmosphere above a site (PBL and free troposphere are simultaneously measured) the measurements are an improvement over the traditional in situ near surface measurements in this regard. TCCON has improved the CO 2 mass gradient measurements between the northern and southern hemispheres. The first annual TCCON meeting was in San Francisco, California in 2005. Every year

1908-457: The field, the flux for the sides is zero and there is an equal and opposite flux at both ends of the tube. This is a consequence of Gauss's Law applied to an inverse square field. The flux for any cross-sectional surface of the tube will be the same. The total flux for any surface surrounding a charge q is q / ε 0 . In free space the electric displacement is given by the constitutive relation D = ε 0 E , so for any bounding surface

1961-442: The flux of the electric field E out of a closed surface is proportional to the electric charge Q A enclosed in the surface (independent of how that charge is distributed), the integral form is: where ε 0 is the permittivity of free space . If one considers the flux of the electric field vector, E , for a tube near a point charge in the field of the charge but not containing it with sides formed by lines tangent to

2014-405: The magnetic flux is time-dependent either because the boundary is time-dependent or magnetic field is time-dependent. In integral form: where d ℓ is an infinitesimal vector line element of the closed curve ∂ A {\displaystyle \partial A} , with magnitude equal to the length of the infinitesimal line element, and direction given by the tangent to

2067-412: The most common forms of flux from the transport phenomena literature are defined as follows: These fluxes are vectors at each point in space, and have a definite magnitude and direction. Also, one can take the divergence of any of these fluxes to determine the accumulation rate of the quantity in a control volume around a given point in space. For incompressible flow , the divergence of the volume flux

2120-727: The probability of finding a particle in a differential volume element d r is d P = | ψ | 2 d 3 r . {\displaystyle dP=|\psi |^{2}\,d^{3}\mathbf {r} .} Then the number of particles passing perpendicularly through unit area of a cross-section per unit time is the probability flux; J = i ℏ 2 m ( ψ ∇ ψ ∗ − ψ ∗ ∇ ψ ) . {\displaystyle \mathbf {J} ={\frac {i\hbar }{2m}}\left(\psi \nabla \psi ^{*}-\psi ^{*}\nabla \psi \right).} This

2173-408: The red arrows denotes the boundary of the surface, and the orientation of the arrows with respect to the surface denotes the sign of the inner product of the vector field with the surface normals. If the surface encloses a 3D region, usually the surface is oriented such that the influx is counted positive; the opposite is the outflux . The divergence theorem states that the net outflux through

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2226-570: The satellite measurements of the atmosphere over the TCCON site locations. The TCCON provides the primary measurement validation dataset for the Orbiting Carbon Observatory (OCO-2) mission, and has been used to validate other space-based measurements of carbon dioxide . The TCCON was established partly because of modeling errors between mixing efficiency between the PBL and the free troposphere . Because TCCON measurements are of

2279-627: The second factor is the mean free path and the square root (with the Boltzmann constant k ) is the mean velocity of the particles. In turbulent flows, the transport by eddy motion can be expressed as a grossly increased diffusion coefficient. In quantum mechanics , particles of mass m in the quantum state ψ ( r , t ) have a probability density defined as ρ = ψ ∗ ψ = | ψ | 2 . {\displaystyle \rho =\psi ^{*}\psi =|\psi |^{2}.} So

2332-407: The surface does not fold back onto itself. Also, the surface has to be actually oriented, i.e. we use a convention as to flowing which way is counted positive; flowing backward is then counted negative. The surface normal is usually directed by the right-hand rule . Conversely, one can consider the flux the more fundamental quantity and call the vector field the flux density. Often a vector field

2385-497: The surface here need not be flat. Finally, we can integrate again over the time duration t 1 to t 2 , getting the total amount of the property flowing through the surface in that time ( t 2  −  t 1 ): q = ∫ t 1 t 2 ∬ S j ⋅ d A d t . {\displaystyle q=\int _{t_{1}}^{t_{2}}\iint _{S}\mathbf {j} \cdot d\mathbf {A} \,dt.} Eight of

2438-763: The surface in which flux is being measured is fixed and has area A . The surface is assumed to be flat, and the flow is assumed to be everywhere constant with respect to position and perpendicular to the surface. Second, flux as a scalar field defined along a surface, i.e. a function of points on the surface: j ( p ) = ∂ I ∂ A ( p ) , {\displaystyle j(\mathbf {p} )={\frac {\partial I}{\partial A}}(\mathbf {p} ),} I ( A , p ) = d q d t ( A , p ) . {\displaystyle I(A,\mathbf {p} )={\frac {\mathrm {d} q}{\mathrm {d} t}}(A,\mathbf {p} ).} As before,

2491-675: The surface is assumed to be flat, and the flow is assumed to be everywhere perpendicular to it. However the flow need not be constant. q is now a function of p , a point on the surface, and A , an area. Rather than measure the total flow through the surface, q measures the flow through the disk with area A centered at p along the surface. Finally, flux as a vector field : j ( p ) = ∂ I ∂ A ( p ) , {\displaystyle \mathbf {j} (\mathbf {p} )={\frac {\partial \mathbf {I} }{\partial A}}(\mathbf {p} ),} I ( A , p ) =

2544-400: The surface. The result of this operation is called the surface integral of the flux. It represents the quantity which passes through the surface. According to the transport definition, flux may be a single vector, or it may be a vector field / function of position. In the latter case flux can readily be integrated over a surface. By contrast, according to the electromagnetism definition, flux

2597-429: The surface: d q d t = ∬ S j ⋅ n ^ d A = ∬ S j ⋅ d A , {\displaystyle {\frac {\mathrm {d} q}{\mathrm {d} t}}=\iint _{S}\mathbf {j} \cdot \mathbf {\hat {n}} \,dA=\iint _{S}\mathbf {j} \cdot d\mathbf {A} ,} where A (and its infinitesimal)

2650-407: The term corresponds to. In transport phenomena ( heat transfer , mass transfer and fluid dynamics ), flux is defined as the rate of flow of a property per unit area, which has the dimensions [quantity]·[time] ·[area] . The area is of the surface the property is flowing "through" or "across". For example, the amount of water that flows through a cross section of a river each second divided by

2703-428: The transport definition—charge per time per area. Due to the conflicting definitions of flux , and the interchangeability of flux , flow , and current in nontechnical English, all of the terms used in this paragraph are sometimes used interchangeably and ambiguously. Concrete fluxes in the rest of this article will be used in accordance to their broad acceptance in the literature, regardless of which definition of flux

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2756-947: Was established in 1974 as a focal point for environmental research in Japan. In 2001 it became an Independent Administrative Institution . NIES is organised into eight centers, each of which is subdivided into a further number of sections responsible for different specializations within the broader field to which they belong. The eight centers are responsible for research in eight different fields, with programs dedicated to these research areas. July 1971 Environment Agency established November 1971 NIES Founding Committee established March 1974 National Institute for Environmental Studies established April 1985 Emperor Showa visits NIES July 1990 Restructuring of NIES to include global environmental research October 1990 Center for Global Environmental Research established January 2001 Environment Agency becomes Ministry of

2809-577: Was used for ATMOS which flew on the Space Shuttle , and is used for spectral fitting of spectra obtained by a balloon borne spectrometer. Data from each site is processed by the investigators that head that particular site. Atmospheric abundances of gases are uploaded and saved in uniform formats and data are hosted at Caltech with the Caltech Library and are available from http://tccondata.org . Data are made publicly available provided

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