Potential temperature, atmospheric

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... 

If the potential temperature decreases with height, the atmosphere is unstable- If the potential temperature increases with height, the atmosphere is stable. The average lapse rate of the atmosphere is about 6.5°C/km that is, the potential temperature increases with height and the average state of the atmosphere is stable. 

Describe in the first column of the table what specific materials and quantities could be combined, how they could be combined, and for how long. Use the second column to indicate whether or not ambient, unconfined conditions apply (ambient temperature, atmospheric pressure, noninerted and nonenriched atmosphere with 21% oxygen, and no enclosure or confinement). Assume published compatibility data will be valid only if ambient, unconfined conditions apply, unless the data indicate otherwise. Use the third column to indicate that, for this scenario under these conditions, a chemical reaction will occur that has the potential for any of your predetermined undesired consequences. Document any comments and the source of your information in the last column. 

The outgrowth of C. botulinum requires a suitable medium, temperature, atmosphere, pH, Eh potential, and water activity. Toxin is usually only produced in optimal or close-to-optimal conditions. Nutrient demands of C. botulinum are complex, and include amino acids, B vitamins, and minerals. In broth, non-proteolytic strains of type B and F grow and produce toxin at 4°C, but in crab meat the outgrowth and toxin production occurs solely at 26°C (Alberto et al., 2003). 

Empirical equations have been formulated to enable calculation of the Bimsen solubility coefficient for any given temperature and salinity at = 1 atm. These empirical equations are presented in the online appendix on the companion website for the most common gases foimd in seawater but being empirical, they are still subject to refinement. The equilibrium gas concentrations computed from the Bimsen solubility coefficient should be thought of as the gas concentration that a water mass would attain if it were allowed to equilibrate with the atmosphere at its in situ salinity and potential temperature. 

In addition, surface temperatures shall be limited to prevent any ignition of the potentially explosive atmosphere. All components (including the wiring)... 

Jackett, D. R., McDougall, T. J., Feistel, R., Wright, D. G., Griffies, S. M., 2006. Algorithms for density, potential temperature, conservative temperature, and the freezing temperamre of seawater. Journal of Atmospheric and Oceanic Technology, 23, 1709-1728. 

The stability of the atmosphere can be related directly to the net gradient of the virtual potential temperature in the vertical direction as follows ... 

Neutral atmosphere An atmosphere in which the potential temperature is constant with respect to height. Buoyant motion in a neutral atmosphere is negligible, but vertical mixing is not suppressed. Mixing will occur throughout the full depth of a neutral layer. 

Temperature inversion In a temperature inversion, the potential temperature of the atmosphere increases with increasing height, creating a stable atmosphere in which vertical motion is suppressed. 

Because, in a stably stratified atmosphere, the potential temperature increases monotonically with height, it is often used as the vertical coordinate in atmospheric problems. Such a system is called the isentropic coordinate system because a constant 0 surface corresponds to a surface of constant entropy S (0) = cp In 0 + constant. In this framework, the vertical velocity... 

Let us assume that an air parcel somewhere in the atmosphere has a temperature T and pressure p and is initially in equilibrium (same Tand p) with the surrounding atmosphere. If this air parcel is moved dry adiabatically to the surface with a pressure of po = 1000 mbar, it will attain a temperature 9 called the potential temperature. The potential temperature can be calculated from (16.5) integrating from initial conditions (T,p) to the final state (0,po) to find that... 

For p = po the potential temperature is equal to the surface temperature To. and the potential temperature profile of the atmosphere starts at the surface temperature. The potential temperature is used in meteorology to compare the temperature of air parcels under identical conditions. As we will see subsequently, it is also useful in the stability analysis of the atmosphere. 

If the adiabatic dry air parcel is always in equilibrium with the atmosphere during its motion from the original position to the surface, the atmosphere by definition is neutral and its temperature profile satisfies (16.8). No matter where the air parcel starts in this atmosphere, it will always attain the same temperature when brought to the surface at pressure po- In other words, the potential temperature of the air parcel will not change during its motion and will always be equal to 0. The equilibrium of the air parcel with the surrounding environment means that the neutral atmosphere (or a neutral atmospheric layer) has the same potential temperature at all heights z and therefore dQ/dz = 0. Plots of altitude versus potential temperature for a neutral (adiabatic) atmosphere are vertical lines at 0 = 7b. 

For a neutral atmosphere 0 = const = 7o and also T = 7o — Fz. Combining these two results and solving for the potential temperature, we find that... 

Although p0 and Tq in (16.39) refer to the constant surface values, equations of precisely the same form can be derived in which p0 and 7o are replaced by pe and Te, the reference profiles. The equations written in this form will be useful later when we consider the dynamics of potential temperature in the atmosphere. 

Case 1. If m(0 > 0, then qz > 0 and Rf < 0. For this case, positive values of n tend to be associated with positive values of 0 and vice versa. This case corresponds to an unstable atmosphere (decreasing potential temperature with height). If an air parcel moves upward because of a positive fluctuation in its velocity u v it rises to a region of lower potential temperature. However, the air parcel temperature changes adiabatically during this small rapid fluctuation, and its potential temperature remains constant. As a result, the air parcel potential temperature will exceed the potential temperature of its surroundings and will cause a positive potential temperature fluctuation 0 in its new position. 

The temperature 9 defined by (14.12) is called the potential temperature. We introduce the potential temperature because an actual atmosphere is seldom adiabatic and we want to relate the actual temperature profile to the adiabatic lapse rate. Adiabatic temperature profiles based on potential temperature are vertical on a plot of c versus 0, thereby facilitating such comparisons. 

---