Lapse rate

The atmospheric temperature gradient, the temperature gradient in the atmosphere. Put simply described by him as the very air temperature with altitude is increasing or decreasing. Looking at the whole atmosphere, he turns to a total of three times, as shown in the adjacent diagram.

In meteorology, but it is limited to the temperature of the troposphere, and usually only the vertical component, ie the strength of the change in air temperature with increasing distance from the surface. The temperature profile of the overlying layers of the atmosphere has only a minor importance for the weather.

• The atmospheric temperature gradient in the troposphere is mostly negative, so the air temperature increases with height (up to -50 ° C in the height of the tropopause ). His regional average is -6 ° C per km. In detail, however, the extent of this temperature drop is very different and can be reversed in some areas in an increase in temperature ( temperature inversion ). The actually measurable and thus static Umgebungsgradient distinction is of two dynamic gradient moving air packages. The two dynamic gradients are responsible for the stability of the troposphere layering in its interaction with the static gradients of the air.
• The atmospheric temperature gradient of the stratosphere is only neutral ( isothermal process at about -50 ° C) and upward positive (up to about 0 ° C) equal to the stratopause.
• The atmospheric temperature gradient of the mesosphere is again negative (up to -90 ° C in the height of the mesopause ).
• The atmospheric temperature gradient of the thermosphere and the exosphere is again positive ( up to the temperatures in the universe )

The temperature gradient in the horizontal plane, ie mainly between the equator and the poles is called the meridional temperature gradient and plays an important role as a driving factor of the planetary circulation or in the energy balance of the Earth. It is out of the two positive poles to the equator, in the medium of -33 ° C ( the south pole ), or -23 ° C (north pole ) of up to 26 ° C ( the equator).

Basics

Theory

Closely connected with the change of temperature in the vertical one hand are the caused by the gravitational change in air pressure (see barometric formula ) and secondly energy transport processes on the sensible and latent heat, and ultimately a transition in thermal potential energy. It is a phenomenon that can be explained only on the basis of thermodynamics and the kinetic theory of gases. As a theoretical basis thus serve the various gas laws. For simple processes you can use the general gas equation as equation of state, but only as long as the air is a nearly ideal behavior.

The coupling between the pressure and temperature depends on the state change. An air pressure decrease corresponds to an increase in height and, conversely, a pressure increase in a decrease in height.

For a parcel of air moves vertically in the atmosphere up or down, it involves an adiabatic change of state, so it is no heat added or taken away from the outside and there is also no mixing with the surrounding air. The adiabatic temperature change such air parcels is only by pressure decrease during ascent, or conditionally pressure increase while sinking. This circulation is provided, because the radiation conditions in still a temperature atmosphere shown overlying the adiabatic limit value, the air stratification thus is unstable and results in circulation. The adiabatic assumption is a simplifying assumption, which must be provided for dynamic gradient and here due to the low mixing ability and the poor thermal conduction properties usually is valid to a good approximation. Near the ground, however, show the warming effects of charisma here so you can generally estimate no adiabatic process. There must also be dynamic processes, such as the sliding of warm air to cold air, which are also not covered by the assumption of an adiabatic process. In the stratosphere, there is no adiabatic gradient. The reason is because of the pure radiative transfer makes no temperature gradient over the adiabatic limit. Due to the absorption of the UV radiation ( heat ) the temperature gradient is even reversed. The absorption of the UV radiation does not only for heating, but also for ozone formation. Temperature gradient is less than the adiabatic limit also applies more generally to the upper atmosphere, since the radiative equilibrium generally dominates here - because the radiative equilibrium does not exceed the adiabatic limit as in the troposphere.

For comparison of temperature values ​​that were measured at different locations and heights, use is made of the potential temperature.

Illustration

To understand why the temperature changes with increasing altitude, it helps to imagine an ascending weather balloon. In this thought experiment, it is then necessary to fill the balloon with air and (somewhat less realistic ) to assume that its volume can be changed arbitrarily, so its surface is not rigid and can expand and contract freely. There is consequently a sharply defined parcel of air, isolated from its surroundings, slowly gaining height and expands adiabatically. The bottom of the air pressure acting on the balloon envelope, and presses them together to a certain volume. As altitude increases, however, the air pressure decreases and the balloon expands until its internal pressure matches that of the environment. Although the balloon neither increases nor heat was removed, the temperature of the air in the balloon has changed now. Why is that? Adiabatic means that although no heat is exchanged, the molecules but in the expansion volume work afford at the expense of their kinetic energy. Thus, the internal energy decreases in the balloon, and by the amount that had to be applied to displace the ambient air.

Consider the physical size of temperature. A possibility of the temperature measurement based on the fact that the molecules transfer their kinetic energy by impact on a meter (due to stretch, for example, the alcohol in the thermometers ). This is temperature, in addition to the individual feeling of every man this is nothing more than a macroscopic measure of the average kinetic energy of atoms and molecules that are part of the internal energy. In contrast to energy, the temperature is an intensive quantity, ie independent of the amount of substance.

With the expansion of the balloon, the kinetic energy of the molecules is reduced, we measure a lower temperature of the air in the balloon.

Looking at the other hand, an air packet in a constant height, but this is exposed to a pressure change, then this leads to a compression or expansion, and thus always at a change of temperature, either because work is rendered him or this work is done and thereby release energy.

The change of temperature and pressure can in turn have an impact on the aggregate state of the air, as these come only under certain conditions as gases before. This can be seen in the water vapor, because only he can condense to liquid water or ice to resublimation under atmospheric conditions. Since the thus released heat has an effect on the temperature, a distinction is made between dry and feuchtadiabatischen temperature gradient.

Trockenadiabatischer temperature gradient

The trockenadiabatische temperature gradient (abbreviation dalr after engl. Dry adiabatic lapse rate ) is valid for adiabatic reversible and thus isentropic conditions, without causing changes in the aggregate state. It amounts to 9.76 Kelvin or degrees Celsius per kilometer and a height is used for altitude changes of an air parcel, as long as the relative humidity remains below 100 percent, so there is no excess of the dew point and hence condensation. As a simplification, one usually estimates a gradient of one Kelvin per hundred meters. Of great importance is that, apart from small fluctuations caused by differences in air composition, this value remains constant, the decrease or increase of temperature so linear.

The derivation of the gradient based on the first law of thermodynamics ( 1.1) and the assumption of an ideal gas with a here estimated to simplify amount of mass of a mole This implies that the internal energy can be written U as a function of temperature T at constant volume V to (1.2).

(1.1)

(1.2)

Where CM, V is the molar heat capacity of air at constant volume. Then resets to the same two relations (2.1). Leaving the thermal equation of state of ideal gases in differential form feed (2.2), we obtain after rearrangement and equating the expression ( 2.3).

(2.1)

(2.2)

(2.3)

With the relation ( 3.1) one can replace the molar heat capacity at constant pressure Cm, p by the molar heat capacity at constant volume Cm, V, and using the ideal gas equation (3.2) is eliminated, the volume and gives ( 3.3).

(3.1)

(3.2)

(3.3)

Where for adiabatic processes dQ = 0, which leads to a small change to equation (3.4) and the equation is further simplified.

( 3.4)

This equation can now be equated with the barometric height formula (4.1 ), where ie is the change in height. By shortening and reshaping equation arises ( 4.2).

(4.1)

(4.2)

Solving the equation (4.2 ) to the temperature gradient dT / dh = Γ on, resulting

(4.3)

If, now, the specific heat capacity of air at constant pressure cp = 1.005 J / (g K) and the gravitational acceleration g = 9.81 m / s ² a, we obtain for the temperature gradient Γ trockenadiabatischen the value of -9.76 K / km.

With the above values ​​are those of the dry air, the right variable portion of the water vapor with some substance other values ​​is therefore usually neglected. Refers to him in the form of a specific humidity of 0.01 with a what is a fairly typical value which can be considered as average, then, a lower by 0.86 % temperature gradient. Under the condition that no condensation occurs, the influence of water vapor is therefore quite low.

A variant of the derivative is based on the adiabatic.

The logarithmic form is differentiated:

With

From the barometric formula obtained

M = 0.02896 kg / mol is the molecular weight of air = 9.806 g m -2 s the acceleration of gravity at the 45 degree of latitude, and R = 8.314 J mol -1 K- 1, the universal gas constant. The value of 1.4 for the adiabatic considered that vibrations on the air molecules are not excited to any significant degree. Thus, the temperature gradient of the Trockenadiabate

Feuchtadiabatischer temperature gradient

Although for the feuchtadiabatischen temperature gradient ( abbreviation MALR or SALR after engl. Moist or saturated adiabatic lapse rate ) are also adiabatic conditions, but explicitly for the case that a condensation of water vapor occurs. The condensation heat contained in the gaseous state ( latent heat) of 2257 kJ / kg is thus released and increases the sensible heat energy of the air. The trockenadiabatische temperature gradient is weakened by this additional energy input. How strong is this weakening of dalr depends on the temperature, because the higher it is, the greater the increase in the saturation vapor pressure curve, and thus the more water vapor condenses per Kelvin cooling, that is the more sensible heat energy per Kelvin cooling free. At high temperatures, it may therefore be less than 4 K / km, at a temperature of -40 ° C with 9 K / km but also the gradient trockenadiabatischen come pretty close. The right figure shows an idealized temperature profile is shown with a constant gradient of 6.5 ° C / km, which corresponds to the Central European average.

Umgebungsgradient

The Umgebungsgradient, usually referred to as a geometric temperature gradient represents the actual temperature profile of the atmosphere, as it can be measured by radiosondes. Through a variety of diabatic, advective and convective processes can differ significantly from the model ideas of a dry or feuchtadiabatischen gradient and also significantly scatter around its own mean. A gradient is greater than the trockenadiabatische, is referred to here as überadiabatisch and accordingly has a lower gradient than unteradiabatisch. As a symbol of the negative gradient with geometric thereby a positive numeric value is used γ.

Looking at the entire troposphere, also often prevail in different heights completely different gradients, which usually sets a characteristic of the particular weather sequence. Also, a reverse gradient in the form of an inversion is possible. The differences that result in a parcel of air is adiabatically heated or cooled via dynamic gradient, the stability stratification of the atmosphere is derived.