The Dry Adiabatic Lapse Rate

The adiabatic lapse rate for a dry atmosphere, which may contain water vapor but which has no liquid moisture present in the form of fog, droplets, or 

FIGURE 4-5 Illustration of the adiabatic lapse rate. As this air parcel is raised in altitude by 1000 m, the air pressure decreases and the parcel expands and cools by 9.8°C (5.4°F for an altitude increase of 1000 ft). Assuming no heat is lost or gained by the parcel (i.e., the process is adiabatic), its temperature will increase to its original value on being lowered to its original height. 

In Section 4.1.1, Eqs. [4-1] and [4-2] were used to estimate the relationship between air pressure and altitude, assuming temperature to be constant with height. When combined with a third equation, Eqs. [4-1] and [4-2] also can be used to calculate the dry adiabatic lapse rate. The third equation, presented as the following Eq. [4-7], is based on an adiabatic process for air that rises and expands due to a decrease in pressure. By definition for an adiabatic process, heat flow into the rising air is assumed to be zero. Therefore, conser- 

Equation [4-2], which is derived from the ideal gas law, can be rearranged 

The quantity (CT MW) is the heat capacity expressed in units of energy per mole per degree, and equals 5/2 R for diatomic gases. Thus, 

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Fig. 19-4. Vertical expansion of continuous plumes related to vertical temperature structure, The dashed lines correspond to the dry adiabatic lapse rate for reference.

Using the dry adiabatic lapse rate, by how much would you expect the temperature to change from the earth s surface to an altitude of 1000 feet, which, as seen in Fig. 2.19, sometimes corresponds to the bottom of the inversion layer in the Los Angeles area ... 

At the dry adiabatic lapse rate (9.8°C decrease in temperature per kilometer increase in altitude), a rising parcel of dry air that does not exchange heat with the environment will cool by expansion due to the decrease in air pressure and will achieve the same temperature as the surrounding air—a case of neutral stability. That is, air movement is then neither favored nor retarded by buoyancy. Observed lapse rates are usually -5 to -7°C km-1, reflecting heat exchange with the environment and the possibility of heat release due to water condensation at higher altitudes. 

FIGURE 4-7 The skew T-log P diagram, or adiabatic chart. On this chart all lines of temperature versus altitude for dry conditions (i.e., no condensation of water vapor) are nearly straight lines with a slope corresponding to the dry adiabatic lapse rate of 9.8°C/1000 m (5.4°F/1000 ft). These are called dry adiabats and slope upward to the left. Wet adiabats have a variable slope and appear as curved lines. Horizontal lines denote altitude lines of constant temperature slope upward to the right. 

FIGURE 4-10 Emission of pollutants from a smokestack, a typical continuous source, under a variety of meteorological conditions. The dry adiabatic lapse rate is represented as a dashed line and the actual measured lapse rate as a solid line in the left panels. Vertical mixing is strongest when the adiabatic lapse rate is less than the actual measured lapse rate and the atmosphere is unstable (top). Weak lapse is a term used to express the existence of a stable atmosphere, which results in less vigorous vertical mixing. An inversion, in the third panel from the top and in part of the last three panels, results in a very stable atmospheric layer in which relatively little vertical mixing occurs (Boubel et al, 1994). 

The regions of the atmosphere are defined by the vertical temperature profile. At the bottom is the troposphere where temperature decreases with height from the surface (which is warmed by the sun). The rate of change of temperature (the lapse rate) depends on the amount of moisture in the air since the latent heats of condensation and evaporation affect the heat of a rising or descending air parcel. For dry air the dry adiabatic lapse rate is — 9.8 K km but a more typical value of the environmental lapse rate (for air containing some water vapor) is — 6.5 K km The troposphere extends up to about 10 km, though this varies with... 

The decrease of temperature with increasing altitude is called the lapse rate. Combining the hydrostatic equation and the expression for potential temperature, we can evaluate the dry adiabatic lapse rate (Td), i.e., the temperature decrease which would be associated with a vertical adiabatic displacement. Logarithmic differentiation of equation (3.9)... 

If potential temperature varies with height, then the actual lapse rate (F = — W H differ from the dry adiabatic lapse rate. This difference... 

FIGURE 16.2 Temperature profiles for (a) an unstable atmosphere and (b) a stable atmosphere. The dry adiabatic lapse rate is also shown. 

If the environmental lapse rate lies between the dry and moist values, then the stability of the atmosphere depends on whether the rising air is saturated. When an air parcel is not saturated, then the dry adiabatic lapse rate is the relevant reference state and the atmosphere is stable. For a saturated air parcel inside a cloud, the moist adiabatic rate is the applicable criterion for comparison and the atmosphere is unstable. Therefore a cloudy atmosphere is inherently less stable than the corresponding dry atmosphere with the same lapse rate. 

Thus a cloudy atmosphere is inherently less stable than a dry atmosphere, and a stable situation with reference to the dry adiabatic lapse rate may actually be unstable for upward displacements of a saturated air parcel. 

The rapidity with which temperature decreases with altitude. The normal lapse rate is defined to be 3.6 degrees F per 1000 feet change in altitude. The dry adiabatic lapse rate is about 5.5 degrees F per 1000 feet, and the wet adiabatic lapse rate varies between 2 and 5 degrees F per 1000 feet, latent heat... 

C per 100 m this is called the dry adiabatic lapse rate (DALR), or dTldz. As soon as the air parcel is saturated by water vapor, it partly condenses and is then heated by the released heat. Then, the wet adiabatic temperature gradient (lapse rate) is observed, which lies between 0.4 °C at large temperatures and 1 °C for low temperatures. During adiabatic changes, the potential tew/jeramrc remains constant,... 

The dry adiabatic lapse rate is a fixed rate, entirely independent of ambient air temperature. A parcel of dry air moving upward in the atmosphere, then, will always cool at the rate of 9.8°C/1000 m, regardless of its initial temperature or the temperature of the surroimding air. When the ambient lapse rate exceeds the adiabatic lapse rate, the ambient rate is said to be superadiabatic, and the atmosphere is highly unstable. When the two lapse rates are exactly equal, the atmosphere is said to be neutral. When the ambient lapse rate is less than the dry adiabatic lapse rate, the ambient lapse rate is termed sub-adiabatic, and the atmosphere is stable. 

A rising parcel of dry air containing water vapor will continue to cool at the dry adiabatic lapse rate until it reaches its condensations temperature, or dew point. At this point, the pressure of the water vapor equals the saturation vapor pressure of the air, and some of the water vapor begins to condense. Condensation releases latent heat in the parcel, and thus the cooling rate of the parcel slows. This new rate is called the wet adiabatic lapse rate. Unlike the dry adiabatic lapse rate, the wet adiabatic lapse rate is not constant but depends on temperature and pressure. In the middle troposphere, however, it is assumed to be approximately -6 to -7°C/1000 m. 

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