Lapse Rates

Lapse rates are progression at which air temperature changes with increasing / decreasing height in the atmosphere.  The rate is considered positive when temperature decreases with elevation, zero when temperature is constant with elevation, and negative when temperature is increasing with elevation.  While there are two different class of lapse rates, normal and adiabatic. The difference between normal and adiabatic lapse rates determine the vertical stability, or instability, of the atmosphere. That is, an air parcel’s tendency to embrace or prohibit vertical motion.

Environmental Lapse Rate—non-rising air that is affected by radiation, convection, and/or condensation. It averages about 6.5°C/km.

Dry Adiabatic Lapse Rate—rate of cooling with increasing altitude. It is constant at about 10°C/km.

Moist Adiabatic Lapse Rate—air, saturated with water vapor, is not constant but is determined by the combined effects of expansion cooling and latent heating (LH) because saturated air cools slower than dry due to the heating produced by condensing water vapor. Is always less than the dry adiabatic lapse rate.

Due to the fact that density differences are affected by the differences between the adiabatic lapse rates and the environmental lapse rate, one may notice that absolute instability occurs when the environmental lapse rate (Г_E) exceeds the dry adiabatic lapse rate (Г_D) [i.e. Г_E > Г_D]. Whereas, absolute stability occurs when the environmental lapse rate (Г_E) is less than the wet adiabatic lapse rate (Г_W) [i.e. Г_E < Г_W]. However, when the environmental lapse rate (Г_E) falls between the wet adiabatic lapse rate (Г_W) and the dry adiabatic lapse rate (Г_D) [i.e. Г_W < Г_E < Г_D] the atmosphere is considered conditionally unstable, as you can see from the picture below.

Lines on the Skew-T

Hypothetical Lapse Rates on a Skew-T Diagram

Thermodynamic Diagrams (Skew-T Log-P)

The vertical measurements, or soundings, are taken when a weather balloons released with a rawinsonde—a light-weight instrument equipped with a radio transmitter that sends measured data back to a receiver on the earth. Whereas a radiosonde, often used synonymously, consists of the measuring devices rather than the rawindsonde, which refers to the addition of radio tracking capabilities to determine wind speeds and directions as well. Rawinsonde observations, or raobs, are taken twice daily at 00:00 and 12:00 UTC (Universal Time Clock) or equivalently, GMT (Greenwich Mean Time), 365 days per year. (For an excellent description of rawinsondes, see http://www.aos.wisc.edu/~hopkins/wx-inst/wxi-raob.htm).

Thermodynamic diagrams allow for analysis of temperature, moisture, pressure and wind in the atmosphere. By plotting the soundings of temperature and dew point, one can investigate how adiabatic processes determine instability and may be used to help predict severe weather—certain profiles indicate certain weather to be expected. The psuedo-adiabatic diagram at first looks very confusing. However, once we take apart the diagram and look at each line individually, we will determine the purpose of each line. When you get past the part of searching for the right line, the information is easily attainable.

Find Temperature (T)—lifted dry adiabatically—by starting at the initial point (given temperature and pressure) and travel upwards parallel to the nearest dry adiabat. When lifting the parcel wet adiabatically it is important to stay equidistant between two wet adiabats since the wet adiabats diverge with decreasing pressure. Do not go parallel to just one!

Find Mixing Ratio (w) by locating the value of the constant mixing ratio, w, line at the given pressure and dew point. Interpolate—approximate between the known values by the fractional distance between each one—if necessary.

Find Saturation Mixing Ratio (w_s) by locating the value of the constant mixing ratio, w, line at the given pressure and temperature. Interpolate—approximate between the known values by the fractional distance between each one—if necessary.

Thickness of a Layer (ΔZ) is the vertical distance between two levels of constant pressure. In usage, it is the vertical distance between to isobaric surfaces. Since warm air is less dense than cold air (at the same atmospheric pressure), to travel through a layer of air that is warmer it will require a greater vertical distance to drop a given amount of pressure.

Find Lifting Condensation Level (LCL)—the level at which air, dynamically lifted, reaches saturation—by locating the intersection of the constant mixing ratio, w, line through the dry adiabat line.

Find Equivalent Potential Temperature (θ_e) by lifting a parcel dry adiabatically until it reaches the lifting condensation level (LCL) then lift it wet adiabatically until all the vapor is condensed out. The wet adiabat will be parallel to the dry adiabat, since all vapor is removed causing no latent heat to be released. When this occurs, follow a dry adiabat back to 1000 mb.

Find Convection Condensation Level (CCL)—the height at which a parcel of air, if heated sufficiently from below, will rise adiabatically until condensation begins—by locating the intersection of the constant mixing ratio (w) line through the surface dew-point temperature, T_D (with the observed temperature sounding—as measured by a radiosonde). In the most common case this is the height of the base of cumulus clouds (which are produced by thermally-induced turbulent eddies—i.e. convection solely from surface heating).

Find Convective Temperature (T_c)—the surface temperature that must be reached to start the formation of convective clouds by solar heating of the surface layer—by locating the convection condensation level (CCL) and following it dry adiabat down to the surface pressure isobar.

Find the Level of Free Convection (LFC)—the level at which a lifted parcel of air becomes unstable (when the temperature of the parcel becomes warmer than the environmental temperature; T_parcel > T_environment)—by lifting the parcel dry adiabatically until you reach the LCL (lifting condensation level) then lifting it wet adiabatically thereafter. The LFC is the beginning of CAPE (convective available potential energy) / PBE (positive buoyant energy).

Find Equilibrium Level (EL)—the point of intersection where the temperature of the parcel becomes colder than the environmental temperature (T_parcel < T_environment = stable air). The EL indicates the end of CAPE (convective available potential energy).

 Find Potential Temperature (θ)—from the temperature, follow the dry adiabat to 1000 hPa. The isotherm value at this point is the potential temperature (the dry adiabat is an isotherm of constant potential temperature).

Find Equivalent Potential Temperature (θ_e)—from the LCL, follow a saturation adiabat up to a pressure where the saturation adiabat parallels the dry adiabat. Follow the dry adiabat down to 1000 hPa, the temperature at this level is the equivalent potential temperature.

Find Equivalent Temperature (T_e)— from the LCL, follow a saturation adiabat up to a pressure where the saturation adiabat parallels the dry adiabat. Follow the dry adiabat down to 1000 hPa, then follow a dry adiabat back up to the original pressure. The isotherm at this point is the equivalent temperature.

Find Wet-Bulb Temperature (T_w)—from the LCL, proceed down a saturation adiabat to the original pressure level. The isotherm at this point is the wet-bulb temperature.

Find Wet-Bulb Potential Temperature (θ_w)—at a given pressure level, find the LCL (for that level), then proceed down a saturation adiabat to 1000 hPa. The temperature at this point is the wet-bulb potential temperature.

Convective Available Potential Energy (CAPE)—the region where the air will experience positive buoyant energy (PBE), which indicates instability.

Convective Inhibition (CIN)—the region where the air experiences negative buoyant energy (NBE), which indicates stability (resisting vertical movements).

Parcel Stops when NBE (above the EL) is equal to the PBE (between the LFC and EL).

Atmospheric Stability and Instability

            Instability is a race to get cold between the parcel and the environment, and we want to environment to win. We could help the environment win by making the environment cool more slowly and / or make the parcel cool at a slower rate. The parcel method, for example, talks about the parcel being a hypothetical box that does not allow any transfer of heat in or out but, allows only adiabatic temperature changes.

The stability of the parcel is dependent on the parcel’s motion after a forced displacement. As the parcel undergoes adiabatic change, its temperature is compared to the surrounding environment to relate differences in density. If the parcel returns to its original position it is considered stable, whereas if the parcel continues moving away from its original position it is considered unstable. Moreover, if a parcel is displaced but remains at its new position it is considered neutral.

            Due to the fact that density differences are affected by the differences between the adiabatic lapse rates and the environmental lapse rate, one may notice that absolute instability occurs when the environmental lapse rate (Г_E) exceeds the dry adiabatic lapse rate (Г_D) [i.e. Г_E > Г_D]. Whereas, absolute stability occurs when the environmental lapse rate (Г_E) is less than the wet adiabatic lapse rate (Г_W) [i.e. Г_E < Г_W]. However when the environmental lapse rate (Г_E) falls between the wet adiabatic lapse rate (Г_W) and the dry adiabatic lapse rate (Г_D) [i.e. Г_W < Г_E < Г_D] the atmosphere is considered conditionally unstable, as you can see from the picture below.

            On the other hand, especially with regard to the potential for severe storm development, another type of stability becomes important: potential instability. While, static stability (discussed above) considers what happens to a small parcel (box) of air when lifted or lowered while the surrounding air is kept in place, potential instability contemplates what happens when an entire layers of air are displaced upward [i.e. a mass of warm air displaced upward by the movement of a cold front].

Focus on the Environment and Social Impacts: Owens Lake Dust Storms

Understanding Weather and Climate (7th Edition) (MasteringMeteorology Series) by Edward Aguado, James E. Burt

Adiabats & Potential Temperature

Dry Adiabat = 333

·         Potential Temperature – A measure of heat. It is the temperature air would be if brought dry adiabatically to 1000 mb.

·         How much warmer will the potential temperature increase?

o   Has hidden heat, Lift up, pressure decreases, starts expanding, starts making hidden heat into real heat, which is determined by how much latent heat is left in the parcel

o   Wet adiabatic line will be parallel to the dry adiabatic line

§  Vapor starts condensing which makes latent heat turn into real heat

·         Latent heat becoming real is what is increasing the potential temperature -  delta = measure of real heat