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

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).

Evaporation and Condensation

Figure 5–2b shows what happens when we remove the covering on the liquid water surface. Without the covering, some of the molecules at the surface can escape into the overlying volume as water vapor. The process whereby molecules break free of the liquid volume is known as evaporation. The opposite process is condensation, wherein water vapor molecules randomly collide with the water surface and bond with adjacent molecules. At the beginning of our hypothetical experiment, no condensation could occur because no water vapor was present. As evaporation begins, however, water vapor starts to accumulate above the surface of the liquid.

At the early stages of evaporation, the low water vapor content prevents much condensation from occurring, and the rate of evaporation exceeds that of condensation. This leads to an increase in the amount of water vapor present. With increasing water vapor content, however, the condensation rate likewise increases. Eventually, the amount of water vapor above the surface is enough for the rates of condensation and evaporation to become equal, as shown in Figure 5–2c. A constant amount of water vapor now exists in the volume above the water surface due to offsetting gains and losses by evaporation and condensation. The resulting equilibrium state is called saturation. When this equilibrium exists in the atmosphere, the air is said to be saturated.

The state of saturation described here can occur whether or not air (or other gases, for that matter) exists in the container. In other words, the water vapor is not “held” by the air (although this erroneous statement is frequently made). Water vapor is a gas, just like the other components of the air. Thus, it does not need to be “held” by air any more than the oxygen, nitrogen, argon, and other gases of the atmosphere need to be held by water vapor! When the air is saturated, there is simple an equilibrium between evaporation and condensation; the dry air plays no role in achieving this state. It is also important to realize that the exchange of water vapor and liquid described here applies as well to the change of phase between water vapor and ice. The change of phase directly from ice to water vapor, without passing into the liquid phase, is called sublimation. The reverse process (from water vapor to ice) is called deposition (Figure 5–3).

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

Some Meteorological Symbols

Static Stability

If the environment is cooling slower than the wet adiabatic lapse rate is	Stable
If the parcel is cooling faster than the dry adiabatic lapse rate	Unstable
̶        Depends on if the parcel is cooling at the wet adiabatic lapse rate or the dry adiabatic lapse rate ̶         When ΓE falls between ΓW and ΓD.	Conditionally unstable
Depends on water vapor capacity	Saturation

 

̶        Race to get cold (lapse rate): Instability is in a race (atmosphere) between the environment and the parcel, we want the environment to win (by being colder) at a rate of 10 at the PBL (planetary boundary layer)

̶        PBL (Planetary Boundary Layer): The part of the atmosphere that cools at a rate of 10/km

“Since the density differences are affected by the differences between the adiabatic lapse rates and the environmental lapse rate, one may denote absolute instability occurring when the environmental lapse rate, ΓE , exceeds the dry adiabatic lapse rate, ΓD; absolute stability occurring when ΓE is less than the wet adiabatic lapse rate, ΓW ; and conditional instability when ΓE falls between ΓW and Γ . The atmosphere may be considered potentially unstable, (or synonymously convectively unstable) when referring to the atmosphere's potential for releasing instability, even when the atmosphere appears to be stable. A layer may be strongly stable (that is, it has a negative D lapse rate) and yet still considered to be potentially unstable. This is favored when the bottom of a specific layer is warm and moist while the top of the layer is substantially drier.”

Dynamically lifting a layer of the atmosphere

̶        Lapse rate decreases as it goes up

̶        Bottom layer saturates more quickly than the top

“The original layer is considered convectively unstable if at the point of total saturation, the layer has a lapse rate greater than the ΓW. This criterion can be represented by determining the change of the equivalent potential temperature with height. If dθe/ dZ<0, the atmosphere is considered convectively unstable.”

“If θ_e at the bottom is greater than θ_e at the top, as it is in this case, then the layer’s lapse rate is greater than the local wet adiabatic lapse rate and the layer is convectively unstable.”

̶        Turbulent Eddies mixes the atmosphere in the PBL (or CBL)

o   Mechanically induced T.E.

§ 
Result of roughness and wild speed

o   Thermally induced T.E

̶        Redistributes heat and water vapor (w)

̶       
Constant: Heat, w, potential temperature,

Sun give off radiation à ground absorbs radiation à warms up the ground à ground warms up the air à upward flux of sensible heat

Flux: flow through an area

Sensible heat: The heat through touch

Three ways to transfer heat

o   Convection

o   Conduction

o   Radiation

How does the density change with height?

̶        Decrease with height because pressure is decreasing with height because there is less weight of the air above you

̶        dp / dz > 0

̶        Heating the air makes it less dense and needs to cool at 34C /km

As I go down into the molecular boundary layer the decrease in density due to an increase in temperature has to more than compensate for the increase in density due to an increase in pressure.

What 2 things influence density?

̶        Temperature

̶        Pressure

OLR (Outgoing Long-wave Radiation): making the ground cold à air in contact with ground gets cold à atmosphere more dense à doesn’t want to overturn àT.E. makes it overturn anyway (calm night will be the coldest) àcauses frost because the temperature closer to the ground is colder

LLNJ (Low Level Nocturnal Jet)

CCL - Convective condensation level; the lowest level at which condensation will occur as a result of convection due to surface heating.

The CCL, or Convection Condensation Level, is the height to which a parcel of air, if heated sufficiently from below, will rise adiabatically until condensation begins. In the most common case, this is the height of the base of cumulus clouds which are produced by thermally-induced turbulent eddies (convection solely from surface heating).

The CAP will break when the PBE between the LFC and EL is greater than the NBE/CIN above the EL and the next LFC.

T and T_D affect θe.

The higher the θe the more likely I am to get thunderstorms.

The Anvil forms at the EL and the overshooting top is when the parcel bounces around the EL.

To break a CAP

̶        Increase temperature

̶        Increase Dewpoint

̶        Convective battering

                                                         

What is the effect of the air coming down into the boundary layer?

̶        The air is colder but as I bring it down it gets warmer

Convective battery

Mon Test: Part 2 of lab, soundings,

Tues: Multiple choice and short answer

Labeling the Graph

LIFTED INDEX LI = T₅₀₀ - Tp₅₀₀

If ( - ) then it is unstable

θ on the dry adiabat = constant

θ on the wet adiabat = increasing

θe = total heat, never changes

PBL (Planetary Boundary Layer): The part of the atmosphere that cools at a rate of 10/km

NBE/CIN/CAP