Saturated adiabatic lapse rate

If an ascending air parcel reaches saturation, the addition of latent heat from condensing moisture will partially overcome the cooling due to expansion. Therefore, the saturated adiabatic lapse rate (of cooling) is smaller than y. ... 

Dry air rising in the atmosphere has to expand as the pressure in the atmosphere decreases. This pV work decreases the temperature in a regular way, known as the adiabatic lapse rate, Td, which for the Earth is of order 9.8 Kkm-1. As the temperature decreases, condensable vapours begin to form and the work required for the expansion is used up in the latent heat of condensation of the vapour. In this case, the lapse rate for a condensable vapour, the saturated adiabatic lapse rate, is different. At a specific altitude the environmental lapse rate for a given parcel of air with a given humidity reaches a temperature that is the same as the saturated adiabatic lapse rate, when water condenses and clouds form Clouds in turn affect the albedo and the effective temperature of the planet. Convection of hot, wet (containing condensable vapour) air produces weather and precipitation. This initiates the water cycle in the atmosphere. Similar calculations may be performed for all gases, and cloud layers may be predicted in all atmospheres. 

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). 

Moist Adiabatic Lapse Rate Calculation Calculate the moist adiabatic lapse rate at 0°C and 1 atm. An expression for the water vapor saturation vapor pressure as a function of temperature is given in Table 17.2. 

Our previous discussion focused on a rising air parcel. The same conclusions are applicable to a sinking air parcel. If A > T, then the atmosphere enhances its motion, whereas if A < T, the atmosphere suppresses it. Finally, if the air parcel is saturated with water vapor, one would need to use the moist adiabatic lapse rate Ts instead of T in the discussion above. 

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. 

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,... 

If a parcel of air being lifted dry adiabatically achieves a relative humidity of 100% (i.e., becomes saturated), water vapor condenses to form a cloud, and latent heat of condensation is released. (This discussion does not consider the latent heat that can be released when ice is present.) Thus, the parcel now cools at a rate less than dry adiabatic, the rate depending on whether all or part of the condensate stays within the parcel. If all of it remains, the first law of thermodynamics can again be used to derive the moist adiabatic lapse rate. The resulting lapse rate is not constant as is the diy adiabatic lapse rate, bnt is dependent on pressnre and temperature. For 1000 kPa and 20°C, this lapse rate is 4°C km , while at the same pressnre and a temperatnre of 0°C, it increases to 6°C km. At temperatnres below abont —30°C, the moist adiabatic lapse rate approximates the diy adiabatic rate. 

The parametrization of cumulus cloud rainfall utilizes some form of one-dimensional cloud model. These are called cumulus cloud parametrization schemes. Then-complexity ranges from instantaneous readjustments of the temperature and moisture profile to the moist adiabatic lapse rates when the relative humidity exceeds saturation, to representations of a set of one-dimensional cumulus clouds with a spectra of radii. These parametrizations typically focus on deep cumulus clouds, which produce the majority of rainfall and diabatic heating associated with the phase changes of water. Cumulus cloud parametrizations remain one of the major uncertainties in mesoscale models since they usually have a number of tunable coefficients, which are used to obtain the best agreement with observations. Also, since mesoscale-model resolution is close to the scale of thunderstorms, care must be taken so that the cumulus parametrization and the resolved moist thermodynamics in the model do not double count this component of the and Sq.. 

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. 

Since dwx,s/dz, the rate of change of the saturation water vapor mass fraction, will be negative during condensation of water, < r = g/cp. Therefore the rate of cooling of saturated air is less than for dry air. For example, for 1000 mbar and 0°C a lapse rate of 5.8°C km is calculated, or about 60% of the dry adiabatic rate. 

Numerous in-cloud measxnements, along with theoretical and laboratory studies, have indicated that entrainment takes place that is, air in the environment surroimding a parcel of air is mixed into the parcel and becomes part of the rising current. A rising parcel of cloudy air into which dry air is entrained cools at a faster rate than moist adiabatic, because heat is required (1) to evaporate sufficient condensate, increasing the mixing ratio of the air to saturation, and (2) to warm the air from its original temperature to the parcel temperature. The lapse rate in an entrained parcel of air falls somewhere between the moist and dry adiabatic rates. 

It is possible for an environmental lapse rate to be both stable and unstable, depending on whether or not the air parcel is saturated. Profile CC is said to be conditionally unstable because it is stable for dry adiabatic processes but unstable for moist adiabatic processes. 

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