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).

Thermal Wind

            Thermal Wind is the vertical shear of the geostrophic wind cause by a horizontal temperature gradient—it “blows” parallel to the thickness contours, leaving low thickness to the left. The Thermal Wind Equation states that the vertically averaged shear of the geostrophic wind (within the layer between any two pressure surfaces) is related to the horizontal gradient of thickness of the layer, in the same manner in which geostrophic wind is related to geopotential height.

Expressed as a linear relationship between vertical wind shear of the geostrophic wind and the horizontal temperature gradient,

            In a barotropic atmosphere—where density is only a function of pressure—the slope of the isobaric surfaces are independent of temperature thus, the geostrophic wind doesn’t increase with height. In other words, there is a complete absence of the horizontal temperature (thickness) gradients such that on constant pressure surfaces. However, the slope of the isobaric surfaces and the speed of the geostrophic wind may vary from level to level due to those thickness variations.

            In an Equivalent Barotropic Atmosphere, isobars and isotherms, on a horizontal surface map, have the same shape.

            In a Baroclinic Atmosphere—where density is a function of both pressure and temperature—the height and thickness contours intersect such that the geostrophic wind exhibits a component normal to the isotherms (or thickness contours). In other words, the horizontal temperature gradients cause the thickness of the layers between isobaric surfaces to increase with higher temperatures. When multiple layers are stacked on each other the geostrophic wind and the slope of the isobaric surfaces increase with height.

Virtual Temperature

     A fictitious temperature that dry air would need to attain in order to have the same density as the moist air at the same pressure is considered virtual temperature. The fact that moist air is less dense than dry air was first clearly stated by Sir Isaac Newton in his “Opticks.” However, the basis for this relationship was not generally understood until the latter half of the 18^th century.

At any rate, due to that fact, and at the same temperature and pressure, the virtual temperature is always greater than the actual temperature. The use of virtual temp allows us to use the gas constant for dry air, R_d, saving us from constantly having to calculate gas constants for moist air—the value of which would vary with water vapor content.

            However, virtual temperature correction is usually neglected except in certain calculations relating to the boundary layer. Nonetheless, in moving from a given pressure surface to another pressure surface located above or below it, the geopotential height (used as the vertical coordinate in most atmospheric applications in which energy plays a role—i.e. large scale motions) is related geometrically to the thickness of the intervening layer which, in turn, is directly proportional to the mean virtual temperature of the layer. The mean virtual temperature is used for determining the thickness of a layer between two pressure surfaces (p₁ and p₂).

where e is vapor pressure, p is pressure, and ε is approximately equal to 0.622.