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Virtual Temperature
In atmospheric thermodynamics, the virtual temperature (T_v) of a moist air parcel is the temperature at which a theoretical dry air parcel would have a total pressure and density equal to the moist parcel of air. The virtual temperature of unsaturated moist air is always greater than the absolute air temperature, however, as the existence of suspended cloud droplets reduces the virtual temperature. Introduction Description In atmospheric thermodynamic processes, it is often useful to assume air parcels behave approximately adiabatically, and approximately ideally. The specific gas constant for the standardized mass of one kilogram of a particular gas is variable, and described mathematically as :R_x = \frac, where R^* is the molar gas constant, and M_x is the apparent molar mass of gas x in kilograms per mole. The apparent molar mass of a theoretical moist parcel in Earth's atmosphere can be defined in components of water vapor and dry air as :M_\text = \frac M_v + \frac M_d, ...
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Atmospheric Thermodynamics
Atmospheric thermodynamics is the study of heat-to-work transformations (and their reverse) that take place in the earth's atmosphere and manifest as weather or climate. Atmospheric thermodynamics use the laws of classical thermodynamics, to describe and explain such phenomena as the properties of moist air, the formation of clouds, atmospheric convection, boundary layer meteorology, and vertical instabilities in the atmosphere. Atmospheric thermodynamic diagrams are used as tools in the forecasting of storm development. Atmospheric thermodynamics forms a basis for cloud microphysics and convection parameterizations used in numerical weather models and is used in many climate considerations, including convective-equilibrium climate models. Overview The atmosphere is an example of a non-equilibrium system. Atmospheric thermodynamics describes the effect of buoyant forces that cause the rise of less dense (warmer) air, the descent of more dense air, and the transformation of water ...
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Dalton's Law
Dalton's law (also called Dalton's law of partial pressures) states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases. This empirical law was observed by John Dalton in 1801 and published in 1802.J. Dalton (1802)"Essay IV. On the expansion of elastic fluids by heat,"''Memoirs of the Literary and Philosophical Society of Manchester'', vol. 5, pt. 2, pages 595–602; see page 600. Dalton's law is related to the ideal gas laws. Formula Mathematically, the pressure of a mixture of non-reactive gases can be defined as the summation: p_\text = \sum_^n p_i = p_1+p_2+p_3+\cdots+p_n where ''p''1, ''p''2, ..., ''pn'' represent the partial pressures of each component. p_ = p_\text x_i where ''xi'' is the mole fraction of the ''i''th component in the total mixture of ''n'' components . Volume-based concentration The relationship below provides a way to determine the volume-based concentration of any ...
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Maximum Potential Intensity
The maximum potential intensity of a tropical cyclone is the theoretical limit of the strength of a tropical cyclone. Maximum potential intensity Due to surface friction, the inflow only partially conserves angular momentum. Thus, the sea surface lower boundary acts as both a source (evaporation) and sink (friction) of energy for the system. This fact leads to the existence of a theoretical upper bound on the strongest wind speed that a tropical cyclone can attain. Because evaporation increases linearly with wind speed (just as climbing out of a pool feels much colder on a windy day), there is a positive feedback on energy input into the system known as the Wind-Induced Surface Heat Exchange (WISHE) feedback. This feedback is offset when frictional dissipation, which increases with the cube of the wind speed, becomes sufficiently large. This upper bound is called the "maximum potential intensity", v_p, and is given by :v_p^2 = \frac\frac\Delta k where T_s is the temperature of th ...
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Skew-T Log-P Diagram
A skew-T log-P diagram is one of four thermodynamic diagrams commonly used in weather analysis and forecasting. In 1947, N. Herlofson proposed a modification to the emagram that allows straight, horizontal isobars and provides for a large angle between isotherms and dry adiabats, similar to that in the tephigram. It was thus more suitable for some of the newer analysis techniques being invented by the United States Air Force. Such a diagram has pressure plotted on the vertical axis, with a logarithmic scale (thus the "log-P" part of the name), and the temperature plotted skewed, with isothermal lines at 45° to the plot (thus the "skew-T" part of the name). Plotting a hypothetical set of measurements with constant temperature for all altitudes would result in a line angled 45° to the right. In practice, since temperature usually drops with altitude, the graphs are usually mostly vertical (see examples linked to below). The major use for skew-T log-P diagrams is the plotting o ...
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Convective Available Potential Energy
In meteorology, convective available potential energy (commonly abbreviated as CAPE), is the integrated amount of work that the upward (positive) buoyancy force would perform on a given mass of air (called an air parcel) if it rose vertically through the entire atmosphere. Positive CAPE will cause the air parcel to rise, while negative CAPE will cause the air parcel to sink. Nonzero CAPE is an indicator of atmospheric instability in any given atmospheric sounding, a necessary condition for the development of cumulus and cumulonimbus clouds with attendant severe weather hazards. Mechanics CAPE exists within the conditionally unstable layer of the troposphere, the free convective layer (FCL), where an ascending air parcel is warmer than the ambient air. CAPE is measured in joules per kilogram of air (J/kg). Any value greater than 0 J/kg indicates instability and an increasing possibility of thunderstorms and hail. Generic CAPE is calculated by integrating vertically the loc ...
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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 ...
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United States Air Force
The United States Air Force (USAF) is the air service branch of the United States Armed Forces, and is one of the eight uniformed services of the United States. Originally created on 1 August 1907, as a part of the United States Army Signal Corps, the USAF was established as a separate branch of the United States Armed Forces in 1947 with the enactment of the National Security Act of 1947. It is the second youngest branch of the United States Armed Forces and the fourth in order of precedence. The United States Air Force articulates its core missions as air supremacy, global integrated intelligence, surveillance and reconnaissance, rapid global mobility, global strike, and command and control. The United States Air Force is a military service branch organized within the Department of the Air Force, one of the three military departments of the Department of Defense. The Air Force through the Department of the Air Force is headed by the civilian Secretary of the Air Force ...
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Celsius
The degree Celsius is the unit of temperature on the Celsius scale (originally known as the centigrade scale outside Sweden), one of two temperature scales used in the International System of Units (SI), the other being the Kelvin scale. The degree Celsius (symbol: °C) can refer to a specific temperature on the Celsius scale or a unit to indicate a difference or range between two temperatures. It is named after the Swedish astronomer Anders Celsius (1701–1744), who developed a similar temperature scale in 1742. Before being renamed in 1948 to honour Anders Celsius, the unit was called ''centigrade'', from the Latin ''centum'', which means 100, and ''gradus'', which means steps. Most major countries use this scale; the other major scale, Fahrenheit, is still used in the United States, some island territories, and Liberia. The Kelvin scale is of use in the sciences, with representing absolute zero. Since 1743 the Celsius scale has been based on 0 °C for the freezing ...
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Mixing Ratio
In chemistry and physics, the dimensionless mixing ratio is the abundance of one component of a mixture relative to that of all other components. The term can refer either to mole ratio (see concentration) or mass ratio (see stoichiometry). In atmospheric chemistry and meteorology Mole ratio In atmospheric chemistry, mixing ratio usually refers to the mole ratio ''ri'', which is defined as the amount of a constituent ''ni'' divided by the total amount of all ''other'' constituents in a mixture: :r_i = \frac The mole ratio is also called amount ratio. If ''ni'' is much smaller than ''n''tot (which is the case for atmospheric trace constituents), the mole ratio is almost identical to the mole fraction. Mass ratio In meteorology, mixing ratio usually refers to the mass ratio of water \zeta, which is defined as the mass of water m_\mathrm divided by the mass of dry air (m_\mathrm-m_\mathrm) in a given air parcel: :\zeta = \frac The unit is typically given in \mathrm\,\mathrm^. The ...
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Kelvin
The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and physicist William Thomson, 1st Baron Kelvin (1824–1907). The Kelvin scale is an absolute thermodynamic temperature scale, meaning it uses absolute zero as its null (zero) point. Historically, the Kelvin scale was developed by shifting the starting point of the much-older Celsius scale down from the melting point of water to absolute zero, and its increments still closely approximate the historic definition of a degree Celsius, but since 2019 the scale has been defined by fixing the Boltzmann constant to be exactly . Hence, one kelvin is equal to a change in the thermodynamic temperature that results in a change of thermal energy by . The temperature in degree Celsius is now defined as the temperature in kelvins minus 273.15, meaning t ...
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Unitless
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1), ISBN 978-92-822-2272-0. which is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Dimensionless quantities are distinct from quantities that have associated dimensions, such as time (measured in seconds). Dimensionless units are dimensionless values that serve as units of measurement for expressing other quantities, such as radians (rad) or steradians (sr) for plane angles and solid angles, respectively. For example, optical extent is defined as having units of metres multiplied by steradians. History Quantities having dimension one, ''dimensionless quantities'', regularly occur in sciences, and are formally treated within the field o ...
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Scalar (mathematics)
A scalar is an element of a field which is used to define a ''vector space''. In linear algebra, real numbers or generally elements of a field are called scalars and relate to vectors in an associated vector space through the operation of scalar multiplication (defined in the vector space), in which a vector can be multiplied by a scalar in the defined way to produce another vector. Generally speaking, a vector space may be defined by using any field instead of real numbers (such as complex numbers). Then scalars of that vector space will be elements of the associated field (such as complex numbers). A scalar product operation – not to be confused with scalar multiplication – may be defined on a vector space, allowing two vectors to be multiplied in the defined way to produce a scalar. A vector space equipped with a scalar product is called an inner product space. A quantity described by multiple scalars, such as having both direction and magnitude, is called a '' ...
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