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72-542: The term troposphere derives from the Greek words tropos (rotating) and sphaira (sphere) indicating that rotational turbulence mixes the layers of air and so determines the structure and the phenomena of the troposphere. The rotational friction of the troposphere against the planetary surface affects the flow of the air, and so forms the planetary boundary layer (PBL) that varies in height from hundreds of meters up to 2 km (1.2 mi; 6,600 ft). The measures of

144-419: A meridional flow. When the zonal flow buckles, the atmosphere can flow in a more longitudinal (or meridional) direction, and thus the term " meridional flow " arises. Meridional flow patterns feature strong, amplified troughs of low pressure and ridges of high pressure, with more north–south flow in the general pattern than west-to-east flow. Sphere A sphere (from Greek σφαῖρα , sphaîra )

216-461: A right-angled triangle connects x , y and r to the origin; hence, applying the Pythagorean theorem yields: Using this substitution gives which can be evaluated to give the result An alternative formula is found using spherical coordinates , with volume element so For most practical purposes, the volume inside a sphere inscribed in a cube can be approximated as 52.4% of the volume of

288-473: A sphere is allowed to be a plane (infinite radius, center at infinity) and if both the original spheres are planes then all the spheres of the pencil are planes, otherwise there is only one plane (the radical plane) in the pencil. In their book Geometry and the Imagination , David Hilbert and Stephan Cohn-Vossen describe eleven properties of the sphere and discuss whether these properties uniquely determine

360-512: A sphere is the boundary of a (closed or open) ball. The distinction between ball and sphere has not always been maintained and especially older mathematical references talk about a sphere as a solid. The distinction between " circle " and " disk " in the plane is similar. Small spheres or balls are sometimes called spherules (e.g., in Martian spherules ). In analytic geometry , a sphere with center ( x 0 , y 0 , z 0 ) and radius r

432-413: A sphere to be a two-dimensional closed surface embedded in three-dimensional Euclidean space . They draw a distinction between a sphere and a ball , which is a three-dimensional manifold with boundary that includes the volume contained by the sphere. An open ball excludes the sphere itself, while a closed ball includes the sphere: a closed ball is the union of the open ball and the sphere, and

504-407: A unique circle in a plane. Consequently, a sphere is uniquely determined by (that is, passes through) a circle and a point not in the plane of that circle. By examining the common solutions of the equations of two spheres , it can be seen that two spheres intersect in a circle and the plane containing that circle is called the radical plane of the intersecting spheres. Although the radical plane

576-412: A valuable by-product. The sources of atmospheric water vapor are the bodies of water (oceans, seas, lakes, rivers, swamps), and vegetation on the planetary surface , which humidify the troposphere through the processes of evaporation and transpiration respectively, and which influences the occurrence of weather phenomena; the greatest proportion of water vapor is in the atmosphere nearest the surface of

648-474: A year is equal to the energy radiated (lost) into outer space. The Earth's energy balance does not equally apply to each latitude because of the varying strength of the sunlight that strikes each of the three atmospheric cells, consequent to the inclination of the axis of planet Earth within its orbit of the Sun. The resultant atmospheric circulation transports warm tropical air to the geographic poles and cold polar air to

720-529: Is a first-order discontinuity surface, in which temperature as a function of height varies continuously through the atmosphere, while the temperature gradient has a discontinuity. The troposphere is the lowest layer of the Earth's atmosphere; it starts at the planetary boundary layer , and is the layer in which most weather phenomena occur. The troposphere contains the boundary layer, and ranges in height from an average of 9 km (5.6 mi; 30,000 ft) at

792-421: Is a geometrical object that is a three-dimensional analogue to a two-dimensional circle . Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space . That given point is the center of the sphere, and r is the sphere's radius . The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians . The sphere

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864-586: Is a fundamental object in many fields of mathematics . Spheres and nearly-spherical shapes also appear in nature and industry. Bubbles such as soap bubbles take a spherical shape in equilibrium. The Earth is often approximated as a sphere in geography , and the celestial sphere is an important concept in astronomy . Manufactured items including pressure vessels and most curved mirrors and lenses are based on spheres. Spheres roll smoothly in any direction, so most balls used in sports and toys are spherical, as are ball bearings . As mentioned earlier r

936-462: Is a real plane, the circle may be imaginary (the spheres have no real point in common) or consist of a single point (the spheres are tangent at that point). The angle between two spheres at a real point of intersection is the dihedral angle determined by the tangent planes to the spheres at that point. Two spheres intersect at the same angle at all points of their circle of intersection. They intersect at right angles (are orthogonal ) if and only if

1008-418: Is also possible to define the tropopause in terms of chemical composition. For example, the lower stratosphere has much higher ozone concentrations than the upper troposphere, but much lower water vapor concentrations, so an appropriate boundary can be defined. In 1949 Alan West Brewer proposed that tropospheric air passes through the tropopause into the stratosphere near the equator, then travels through

1080-433: Is an equation of a sphere whose center is P 0 {\displaystyle P_{0}} and whose radius is ρ {\displaystyle {\sqrt {\rho }}} . If a in the above equation is zero then f ( x , y , z ) = 0 is the equation of a plane. Thus, a plane may be thought of as a sphere of infinite radius whose center is a point at infinity . A parametric equation for

1152-414: Is formed with the aid of potential vorticity , which is defined as the product of the isentropic density , i.e. the density that is measurable by using potential temperature as the vertical coordinate, and the absolute vorticity , given that this quantity attains quite different values for the troposphere and the stratosphere. Instead of using the vertical temperature gradient as the defining variable,

1224-766: Is the heat capacity ratio ( γ ≈ {\displaystyle \gamma \approx \,} 7 ⁄ 5 ) for air. The combination of the equation for the air pressure yields the dry adiabatic lapse rate : d T d z = − m g R γ − 1 γ = − 9.8 ∘ C / k m {\displaystyle {\frac {\,dT\,}{dz}}=-{\frac {\;mg\;}{R}}{\frac {\;\gamma \,-\,1\;}{\gamma }}=-9.8^{\circ }\mathrm {C/km} } . The environmental lapse rate ( d T / d z {\displaystyle dT/dz} ), at which temperature decreases with altitude, usually

1296-497: Is the locus of all points ( x , y , z ) such that Since it can be expressed as a quadratic polynomial, a sphere is a quadric surface , a type of algebraic surface . Let a, b, c, d, e be real numbers with a ≠ 0 and put Then the equation has no real points as solutions if ρ < 0 {\displaystyle \rho <0} and is called the equation of an imaginary sphere . If ρ = 0 {\displaystyle \rho =0} ,

1368-464: Is the atmospheric boundary layer between the troposphere and the stratosphere , and is located by measuring the changes in temperature relative to increased altitude in the troposphere and in the stratosphere. In the troposphere, the temperature of the air decreases at high altitude, however, in the stratosphere the air temperature initially is constant, and then increases with altitude. The increase of air temperature at stratospheric altitudes results from

1440-479: Is the numeric difference between the temperature of the planetary surface and the temperature of the tropopause divided by the altitude. Functionally, the ELR equation assumes that the planetary atmosphere is static, that there is no mixing of the layers of air, either by vertical atmospheric convection or winds that could create turbulence. The difference in temperature derives from the planetary surface absorbing most of

1512-449: Is the sphere's radius; any line from the center to a point on the sphere is also called a radius. 'Radius' is used in two senses: as a line segment and also as its length. If a radius is extended through the center to the opposite side of the sphere, it creates a diameter . Like the radius, the length of a diameter is also called the diameter, and denoted d . Diameters are the longest line segments that can be drawn between two points on

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1584-511: Is the summation of all shell volumes: In the limit as δr approaches zero this equation becomes: Substitute V : Differentiating both sides of this equation with respect to r yields A as a function of r : This is generally abbreviated as: where r is now considered to be the fixed radius of the sphere. Alternatively, the area element on the sphere is given in spherical coordinates by dA = r sin θ dθ dφ . The total area can thus be obtained by integration : The sphere has

1656-406: Is unequal to the adiabatic lapse rate ( d S / d z ≠ 0 {\displaystyle dS/dz\neq 0} ). If the upper air is warmer than predicted by the adiabatic lapse rate ( d S / d z > 0 {\displaystyle dS/dz>0} ), then a rising and expanding parcel of air will arrive at the new altitude at a lower temperature than

1728-408: The ozone layer 's absorption and retention of the ultraviolet (UV) radiation that Earth receives from the Sun. The coldest layer of the atmosphere, where the temperature lapse rate changes from a positive rate (in the troposphere) to a negative rate (in the stratosphere) locates and identifies the tropopause as an inversion layer in which limited mixing of air layers occurs between the troposphere and

1800-508: The troposphere below from the stratosphere above, and is part of the atmosphere where there occurs an abrupt change in the environmental lapse rate (ELR) of temperature, from a positive rate (of decrease) in the troposphere to a negative rate in the stratosphere. The tropopause is defined as the lowest level at which the lapse rate decreases to 2°C/km or less, provided that the average lapse-rate, between that level and all other higher levels within 2.0 km does not exceed 2°C/km. The tropopause

1872-414: The volume inside a sphere (that is, the volume of a ball , but classically referred to as the volume of a sphere) is where r is the radius and d is the diameter of the sphere. Archimedes first derived this formula by showing that the volume inside a sphere is twice the volume between the sphere and the circumscribed cylinder of that sphere (having the height and diameter equal to the diameter of

1944-399: The x -axis from x = − r to x = r , assuming the sphere of radius r is centered at the origin. At any given x , the incremental volume ( δV ) equals the product of the cross-sectional area of the disk at x and its thickness ( δx ): The total volume is the summation of all incremental volumes: In the limit as δx approaches zero, this equation becomes: At any given x ,

2016-441: The Earth heats the troposphere by means of latent heat , thermal radiation , and sensible heat . The gas layers of the troposphere are less dense at the geographic poles and denser at the equator, where the average height of the tropical troposphere is 13 km, approximately 7.0 km greater than the 6.0 km average height of the polar troposphere at the geographic poles; therefore, surplus heating and vertical expansion of

2088-433: The Earth. The temperature of the troposphere decreases at high altitude by way of the inversion layers that occur in the tropopause , which is the atmospheric boundary that demarcates the troposphere from the stratosphere . At higher altitudes, the low air-temperature consequently decreases the saturation vapor pressure , the amount of atmospheric water vapor in the upper troposphere. The maximum air pressure (weight of

2160-484: The PBL vary according to the latitude, the landform , and the time of day when the meteorological measurement is realized. Atop the troposphere is the tropopause , which is the functional atmospheric border that demarcates the troposphere from the stratosphere . As such, because the tropopause is an inversion layer in which air-temperature increases with altitude, the temperature of the tropopause remains constant. The layer has

2232-472: The above stated equations as where ρ is the density (the ratio of mass to volume). A sphere can be constructed as the surface formed by rotating a circle one half revolution about any of its diameters ; this is very similar to the traditional definition of a sphere as given in Euclid's Elements . Since a circle is a special type of ellipse , a sphere is a special type of ellipsoid of revolution . Replacing

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2304-414: The air contains water vapor , then cooling of the air can cause the water to condense, and the air no longer functions as an ideal gas. If the air is at the saturation vapor pressure , then the rate at which temperature decreases with altitude is called the saturated adiabatic lapse rate . The actual rate at which the temperature decreases with altitude is the environmental lapse rate . In the troposphere,

2376-521: The air parcel; atmospheric compression and expansion are measured as an isentropic process ( d S = 0 {\displaystyle dS=0} ) wherein there occurs no change in entropy as the air parcel rises or falls within the atmosphere. Because the heat exchanged ( d Q = 0 {\displaystyle dQ=0} ) is related to the change in entropy ( d S {\displaystyle dS} by d Q = T d S {\displaystyle dQ=TdS} )

2448-541: The atmosphere from a pressurised source combines with the carbonic acid water vapour and momentarily reduces the atmospheric pH by negligible amounts. Respiration from animals releases out of equilibrium carbonic acid and low levels of other ions. Combustion of hydrocarbons which is not a chemical reaction releases to atmosphere carbonic acid water as; saturates, condensates, vapour or gas (invisible steam). Combustion can releases particulates (carbon/soot and ash) as well as molecules forming nitrites and sulphites which will reduce

2520-405: The atmosphere lies at about 17 km over the equator. Due to the variation in starting height, the tropopause extremes are referred to as the equatorial tropopause and the polar tropopause. Given that the lapse rate is not a conservative quantity when the tropopause is considered for stratosphere-troposphere exchanges studies, there exists an alternative definition named dynamic tropopause . It

2592-413: The atmosphere) is at sea level and decreases at high altitude because the atmosphere is in hydrostatic equilibrium , wherein the air pressure is equal to the weight of the air above a given point on the planetary surface. The relation between decreased air pressure and high altitude can be equated to the density of a fluid, by way of the following hydrostatic equation: where: The planetary surface of

2664-410: The atmospheric pH of the water slightly or harmfully in highly industrialised areas where this is classed as air pollution and can create the phenomena of acid rain, a pH lower than the natural pH5.56. The negative effects of the by-products of combustion released into the atmospheric vapour can be removed by the use of scrubber towers and other physical means, the captured pollutants can be processed into

2736-551: The average environmental lapse rate is a decrease of about 6.5 °C for every 1.0 km (1,000m) of increased altitude. For dry air, an approximately ideal gas , the adiabatic equation is: p ( z ) [ T ( z ) ] − γ γ − 1 = constant {\displaystyle p(z){\Bigl [}T(z){\Bigr ]}^{-{\frac {\gamma }{\,\gamma \,-\,1\,}}}={\text{constant}}} wherein γ {\displaystyle \gamma }

2808-442: The circle with an ellipse rotated about its major axis , the shape becomes a prolate spheroid ; rotated about the minor axis, an oblate spheroid. A sphere is uniquely determined by four points that are not coplanar . More generally, a sphere is uniquely determined by four conditions such as passing through a point, being tangent to a plane, etc. This property is analogous to the property that three non-collinear points determine

2880-423: The cube, since V = ⁠ π / 6 ⁠ d , where d is the diameter of the sphere and also the length of a side of the cube and ⁠ π / 6 ⁠  ≈ 0.5236. For example, a sphere with diameter 1 m has 52.4% the volume of a cube with edge length 1   m, or about 0.524 m . The surface area of a sphere of radius r is: Archimedes first derived this formula from

2952-401: The discrepancy between the inner and outer surface area of any given shell is infinitesimal, and the elemental volume at radius r is simply the product of the surface area at radius r and the infinitesimal thickness. At any given radius r , the incremental volume ( δV ) equals the product of the surface area at radius r ( A ( r ) ) and the thickness of a shell ( δr ): The total volume

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3024-592: The dynamic tropopause surface is expressed in potential vorticity units (PVU, 1 PVU = 10  K m  kg  s ). Given that the absolute vorticity is positive in the Northern Hemisphere and negative in the Southern Hemisphere , the threshold value should be considered as positive north of the Equator and negative south of it. Theoretically, to define a global tropopause in this way,

3096-420: The effect of the expansion of dry air as it rises in the atmosphere, and the wet adiabatic lapse rate (WALR) includes the effect of the condensation-rate of water vapor upon the environmental lapse rate. A parcel of air rises and expands because of the lower atmospheric pressure at high altitudes. The expansion of the air parcel pushes outwards against the surrounding air, and transfers energy (as work ) from

3168-400: The effects of Global Warming on air circulation patterns will weaken the tropical tropopause layer cold trap. Water vapor that is able to make it through the cold trap eventually rises to the top of the stratosphere, where it undergoes photodissociation into oxygen and hydrogen or hydroxide ions and hydrogen. This hydrogen is then able to escape the atmosphere. Thus, in some sense,

3240-416: The end of the troposphere , and is approximately 17 kilometres (11 mi) above the equatorial regions, and approximately 9 kilometres (5.6 mi) above the polar regions . Rising from the planetary surface of the Earth, the tropopause is the atmospheric level where the air ceases to become cool with increased altitude and becomes dry, devoid of water vapor. The tropopause is the boundary that demarcates

3312-404: The energy from the sun, which then radiates outwards and heats the troposphere (the first layer of the atmosphere of Earth) while the radiation of surface heat to the upper atmosphere results in the cooling of that layer of the atmosphere. The ELR equation also assumes that the atmosphere is static, but heated air becomes buoyant, expands, and rises. The dry adiabatic lapse rate (DALR) accounts for

3384-436: The equation governing the air temperature as a function of altitude for a mixed atmosphere is: d S d z = 0 {\displaystyle {\frac {\,dS\,}{dz}}=0} where S is the entropy. The isentropic equation states that atmospheric entropy does not change with altitude; the adiabatic lapse rate measures the rate at which temperature decreases with altitude under such conditions. If

3456-523: The fact that the projection to the lateral surface of a circumscribed cylinder is area-preserving. Another approach to obtaining the formula comes from the fact that it equals the derivative of the formula for the volume with respect to r because the total volume inside a sphere of radius r can be thought of as the summation of the surface area of an infinite number of spherical shells of infinitesimal thickness concentrically stacked inside one another from radius 0 to radius r . At infinitesimal thickness

3528-409: The heat loss. The parcel of air loses energy as it reaches greater altitude, which is manifested as a decrease in the temperature of the air mass. Analogously, the reverse process occurs within a cold parcel of air that is being compressed and is sinking to the planetary surface. The compression and the expansion of an air parcel are reversible phenomena in which energy is not transferred into or out of

3600-714: The largest concentration of nitrogen. The Earth's planetary atmosphere contains, besides other gases, water vapour and carbon dioxide, which produce carbonic acid in rain water , which therefore has an approximate natural pH of 5.0 to 5.5 (slightly acidic). (Water other than atmospheric water vapour fallen as fresh rain, such as fresh/sweet/potable/river water, will usually be affected by the physical environment and may not be in this pH range.) Atmospheric water vapour holds suspended gasses in it (not by mass),78.08% nitrogen as N 2 , 20.95% oxygen as O 2 , 0.93% argon , trace gases, and variable amounts of condensing water (from saturated water vapor ). Any carbon dioxide released into

3672-399: The lower stratosphere and undergo a brief (hour-order or less) low-frequency vertical oscillation . Such oscillation results in a low-frequency atmospheric gravity wave capable of affecting both atmospheric and oceanic currents in the region. Most commercial aircraft are flown in the lower stratosphere, just above the tropopause, during the cruise phase of their flights; in this region,

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3744-550: The only solution of f ( x , y , z ) = 0 {\displaystyle f(x,y,z)=0} is the point P 0 = ( x 0 , y 0 , z 0 ) {\displaystyle P_{0}=(x_{0},y_{0},z_{0})} and the equation is said to be the equation of a point sphere . Finally, in the case ρ > 0 {\displaystyle \rho >0} , f ( x , y , z ) = 0 {\displaystyle f(x,y,z)=0}

3816-402: The parcel of air to the atmosphere. Transferring energy to a parcel of air by way of heat is a slow and inefficient exchange of energy with the environment, which is an adiabatic process (no energy transfer by way of heat). As the rising parcel of air loses energy while it acts upon the surrounding atmosphere, no heat energy is transferred from the atmosphere to the air parcel to compensate for

3888-410: The planetary atmosphere of the Earth. The three-cell model of the atmosphere of the Earth describes the actual flow of the atmosphere with the tropical-latitude Hadley cell , the mid-latitude Ferrel cell , and the polar cell to describe the flow of energy and the circulation of the planetary atmosphere. Balance is the fundamental principle of the model — that the solar energy absorbed by the Earth in

3960-422: The poles is called the equator . Great circles through the poles are called lines of longitude or meridians . Small circles on the sphere that are parallel to the equator are circles of latitude (or parallels ). In geometry unrelated to astronomical bodies, geocentric terminology should be used only for illustration and noted as such, unless there is no chance of misunderstanding. Mathematicians consider

4032-475: The poles, to 17 km (11 mi; 56,000 ft) at the Equator . In the absence of inversions and not considering moisture , the temperature lapse rate for this layer is 6.5 °C per kilometer, on average, according to the U.S. Standard Atmosphere . A measurement of the tropospheric and the stratospheric lapse rates helps identify the location of the tropopause, since temperature increases with height in

4104-440: The smallest surface area of all surfaces that enclose a given volume, and it encloses the largest volume among all closed surfaces with a given surface area. The sphere therefore appears in nature: for example, bubbles and small water drops are roughly spherical because the surface tension locally minimizes surface area. The surface area relative to the mass of a ball is called the specific surface area and can be expressed from

4176-458: The sphere has the same center and radius as the sphere, and divides it into two equal hemispheres . Although the figure of Earth is not perfectly spherical, terms borrowed from geography are convenient to apply to the sphere. A particular line passing through its center defines an axis (as in Earth's axis of rotation ). The sphere-axis intersection defines two antipodal poles ( north pole and south pole ). The great circle equidistant to

4248-522: The sphere with radius r > 0 {\displaystyle r>0} and center ( x 0 , y 0 , z 0 ) {\displaystyle (x_{0},y_{0},z_{0})} can be parameterized using trigonometric functions . The symbols used here are the same as those used in spherical coordinates . r is constant, while θ varies from 0 to π and φ {\displaystyle \varphi } varies from 0 to 2 π . In three dimensions,

4320-522: The sphere). This may be proved by inscribing a cone upside down into semi-sphere, noting that the area of a cross section of the cone plus the area of a cross section of the sphere is the same as the area of the cross section of the circumscribing cylinder, and applying Cavalieri's principle . This formula can also be derived using integral calculus (i.e., disk integration ) to sum the volumes of an infinite number of circular disks of infinitesimally small thickness stacked side by side and centered along

4392-408: The sphere. Several properties hold for the plane , which can be thought of as a sphere with infinite radius. These properties are: Tropopause The tropopause is the atmospheric boundary that demarcates the troposphere from the stratosphere , which are the lowest two of the five layers of the atmosphere of Earth . The tropopause is a thermodynamic gradient-stratification layer that marks

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4464-426: The sphere: their length is twice the radius, d = 2 r . Two points on the sphere connected by a diameter are antipodal points of each other. A unit sphere is a sphere with unit radius ( r = 1 ). For convenience, spheres are often taken to have their center at the origin of the coordinate system , and spheres in this article have their center at the origin unless a center is mentioned. A great circle on

4536-432: The square of the distance between their centers is equal to the sum of the squares of their radii. If f ( x , y , z ) = 0 and g ( x , y , z ) = 0 are the equations of two distinct spheres then is also the equation of a sphere for arbitrary values of the parameters s and t . The set of all spheres satisfying this equation is called a pencil of spheres determined by the original two spheres. In this definition

4608-541: The stratosphere to temperate and polar regions, where it sinks into the troposphere. This is now known as Brewer-Dobson circulation . Because gases primarily enter the stratosphere by passing through the tropopause in the tropics where the tropopause is coldest, water vapor is condensed out of the air that is entering the stratosphere. This ″tropical tropopause layer cold trap ″ theory has become widely accepted. This cold trap limits stratospheric water vapor to 3 to 4 parts per million. Researchers at Harvard have suggested that

4680-412: The stratosphere, and hence the lapse rate becomes negative. The tropopause location coincides with the lowest point at which the lapse rate is less than a prescribed threshold. Since the tropopause responds to the average temperature of the entire layer that lies underneath it, it is at its maximum levels over the Equator, and reaches minimum heights over the poles. On account of this, the coolest layer in

4752-415: The stratosphere. The general flow of the atmosphere is from west to east, which, however, can be interrupted by polar flows, either north-to-south flow or a south-to-north flow, which meteorology describes as a zonal flow and as a meridional flow. The terms are used to describe localized areas of the atmosphere at a synoptic scale ; the three-cell model more fully explains the zonal and meridional flows of

4824-451: The surrounding air. In which case, the air parcel is denser than the surrounding air, and so falls back to its original altitude as an air mass that is stable against being lifted. If the upper air is cooler than predicted by the adiabatic lapse rate, then, when the air parcel rises to a new altitude, the air mass will have a higher temperature and a lower density than the surrounding air and will continue to accelerate and rise. The tropopause

4896-508: The tropical tropopause layer cold trap is what prevents Earth from losing its water to space. James Kasting has predicted that in 1 to 2 billion years , as the Sun increases in luminosity, the temperature of the Earth will rise enough that the cold trap will no longer be effective, and so the Earth will dry out. The tropopause is not a fixed boundary. Vigorous thunderstorms , for example, particularly those of tropical origin, will overshoot into

4968-451: The tropics. The effect of the three cells is the tendency to the equilibrium of heat and moisture in the planetary atmosphere of Earth. A zonal flow regime is the meteorological term meaning that the general flow pattern is west to east along the Earth's latitude lines, with weak shortwaves embedded in the flow. The use of the word "zone" refers to the flow being along the Earth's latitudinal "zones". This pattern can buckle and thus become

5040-678: The tropopause. At the geographical poles , the Arctic and the Antarctic regions, the tropospheric temperature decreases from an average temperature of 0 °C (32 °F) at sea level to approximately −45 °C (−49 °F) at the tropopause. The temperature of the troposphere decreases with increased altitude, and the rate of decrease in air temperature is measured with the Environmental Lapse Rate ( − d T / d z {\displaystyle -dT/dz} ) which

5112-426: The troposphere occur in the tropical latitudes. At the middle latitudes, tropospheric temperatures decrease from an average temperature of 15 °C (59 °F) at sea level to approximately −55 °C (−67 °F) at the tropopause . At the equator , the tropospheric temperatures decrease from an average temperature of 20 °C (68 °F) at sea level to approximately −70 to −75 °C (−94 to −103 °F) at

5184-597: The two surfaces arising from the positive and negative thresholds need to be matched near the equator using another type of surface such as a constant potential temperature surface. Nevertheless, the dynamic tropopause is useless at equatorial latitudes because the isentropes are almost vertical. For the extratropical tropopause in the Northern Hemisphere the WMO established a value of 1.6 PVU, but greater values ranging between 2 and 3.5 PVU have been traditionally used. It

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