Dry adiabats

Fig. 8. Characteristic plume patterns where (--) represents dry-adiabatic lapse rate and (—), air (a) fanning (b) fumigation (c) lofting and (d) looping.

However, away from the surface, processes frequently are adiabatic. For example, if a volume (parcel) of air is forced upward over a ridge, the upward-moving air will encounter decreased atmospheric pressure and will expand and cool. If the air is not saturated with water vapor, the process is called dry adiabatic. Since no heat is added or subtracted. Ah in Eq. (17-13) can be set equal to zero, and introducing the hydrostatic equation... 

Thus air cools as it rises and warms as it descends. Since we have assumed an adiabatic process, -ATIAz defines the dry adiabatic process lapse rate, a constant equal to 0.0098 K/m, is nearly 1 K/lOO m or 5.4°F/1000 ft. 

Comparing the temperature of this parcel to that of the surrounding environment (Fig. 17-6), it is seen that in rising from 100 to 300 m, the parcel undergoes the temperature change of the dry adiabatic process lapse rate. The dashed line is a dry adiabatic line or dry adiabat. Suppose that... 

If the temperature structure, instead of being that of Fig. 17-6, differs primarily in the lower layers, it resembles Fig. 17-7, where a temperature inversion (an increase rather than a decrease of temperature with height) exists. In the forced ascent of the air parcel up the slope, dry adiabatic cooling produces parcel temperatures that are everywhere cooler than the environment acceration is downward, resisting displacement and the atmosphere is stable. 

A useful concept in determining stability in the atmosphere is potential temperature. This is a means of identifying the dry adiabat to which a particular atmospheric combination of temperature and pressure is related. The potential temperature 0 is found from... 

There is usually some descent (subsidence) of air above surface high-pressure systems. This air warms dry adiabatically as it descends, decreasing the relative humidity and dissipating any clouds in the layer. A subsidence inversion forms as a result of this sinking. Since the descending air compresses as it encounters the increased pressures lower in the atmo-... 

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.

Environmental lapse rate (ELR) Dry adiabatic lapse rate (DALR)... 

Combining Eqs. (D) and (M), one obtains the temperature-altitude profile, or lapse rate, for a dry adiabatic gas ... 

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 ... 

Figure 2. Schematic vertical profiles (a) h (dashed) and h (solid) and (b) q (dashed) and q (solid), (c) The temperature profile, corresponding to cpT = h — gZ — Lyq, illustrates die constant lapse rate within the boundary layer and the reduced lapse rate above the boundary layer. The boundary level (1 km) is indicated by die horizontal dashed line in each panel. These profiles illustrate typical climatic values that are determined by moist convective adjustment in the free atmosphere and dry adiabatic convection in the boundary layer. [Used by permission of Geological Society of America, from Forest et al. (1999), Geol. Soc. Am. Bull., Vol. Ill, Fig. 2, p. 500.]...

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. 

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-... 

It is important not to confuse this dry adiabatic lapse rate with the rate of change in temperature with height in a Standard Atmosphere. The latter represents average conditions in Earth s atmosphere, where heating, mixing, and wet adiabatic processes also are occurring. 

Wet adiabatic lapse rates can be determined from Fig. 4-7, which is a skew T-log P diagram (or adiabatic chart). On this chart, dry adiabats are lines having a nearly constant slope of 9.8°C/1000 m (5.4°F/1000 ft). The wet adiabats are curved and have slopes that not only vary with the temperature at which the adiabat originates but also change along the length of the adiabats. Note that the wet adiabats tend to approach the slope of the dry adiabats at low temperatures, where the absolute amount of moisture in saturated air is small (see Table 4-3). 

Frequently, both kinds of adiabats must be employed to follow the behavior of a parcel of air. A parcel of dry air may rise by its own buoyancy, or may be pushed up by orographic lifting, which occurs when winds meet mountains and are deflected upward. The temperature of the air parcel follows the dry adiabat until water vapor condensation is incipient with further cooling, condensation can occur. If it is assumed that supercooling (a nonequilibrium situation in which air cools below the dew point without condensation) does not occur, the parcel of air then moves upward following the corresponding wet adiabat. Conditional stability refers to conditions under which dry,... 

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. 

Use Fig. 4-7, beginning at 25°C and 1000 m, and follow the slope of the dry adiabats until the air parcel reaches 21°C, which occurs at an altitude of approximately 1500 m. (Strictly, it must cool a bit more, because the expansion of the rising air causes the partial pressure of water to decrease somewhat.) Thereafter, the air follows a wet adiabat at 3500 m (2000 m above the cloud base) the temperature is approximately 12°C. The average wet adiabatic lapse rate in the bottom 2000 m of cloud is therefore 9°C/2000 m, or 4.5°C/1000 m. 

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). 

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