Introduction

         The picture shown in Figure 1 is a picture of three contrails in different stages of life taken on February 17, 1999 at 5:30 CST. The youngest one lies on the right side while the older more diffuse ones resides to the left. This paper will attempt to explain the causes and conditions necessary for contrail formation. Also, I will explain the evolution of contrails from their formation to their demise. Finally, I will discuss why certain contrails last for hours as those in the photograph did and others last for only minutes.

Contrial Formation

         A contrail is a cloud formed from the mixture of warm, unsaturated jet exhaust and cold ambient air (Schrader 1997). The warm engine exhaust contains significant amounts of water, unburned fuel and other particulates. As a parcel of exhaust goes down stream from the engine proper, it becomes more and more diluted with the surrounding air. The relative humidity of that parcel rises as the it cools and its saturation vapor pressure drops. When the mixture reaches saturation with respect to water, water droplets form around already abundant condensation nuclei. These water droplets freeze into ice crystals less than one micrometer within a few seconds (Coleman 1996). Contrails have never been observed as remaining in water droplet form for any period of time although at least one study, Pilie and Jiusto 1958, claimed otherwise. Direct nucleation of ice crystals in contrails does  occur, but the amount of ice crystals produced in this fashion alone is not enough to produce a visible contrail (Jenson et al. 1998). Thus, a parcel within the exhaust trail should become saturated with respect to water and supersaturated with respect to ice causing water droplets to form which freeze which produce the contrails one sees (Jenson et al. 1998).

         Contrail formation typically occurs in the upper Troposphere between nine and twelve kilometers is height with temperatures ranging between -35ƒC and -55ƒC (Jensen e. al. 1998, Schrader 1997). Most contrails last on the order of seconds to a few minutes and only a small minority will last for hours as in the contrails photographed (Jensen et. al. 1998). A newly formed contrail will be approximately one kilometer wide and one-half a kilometer tall. As a contrail evolves, it grows greatly in the horizontal plane sometimes extending over 20 kilometers in width (Spinhirne et al. 1998). Examples of this horizontal evolution is shown in the photograph. Contrails can also be 100ís of kilometers long given the right atmospheric conditions and a plane on a steady course.

Critical Temperature

      Contrails can form when the ambient temperature fall below the critical temperature (Tc) at the level an airplane is flying (Coleman 1996, Schrader 1997). The critical temperature is the temperature below which contrails can form and is a function of the ambient relative humidity (or mixing ratio), pressure, ambient temperature, exhaust parcel temperature, and the contrail factor. (Coleman 1996). There are in fact two distinct types of critical temperature, Tlc which is the critical temperature assuming liquid saturation and Tic which assumes saturation with respect to ice (Jenson et. al. 1998). By definition, Tlc will be a lower temperature than Tic since ice saturation occurs at a warmer temperature than that of water saturation. In all contrail cases studied under the SUCCESS project using a DC 8 to create contrails, Tlc was higher that the ambient temperature (Toon and Miake-Lye 1998). Visible contrails were not observed when the ambient temperature was between Tlc  and Tic or when the ambient temperature was only greater that Tic (Jenson et. al. 1998). This implies that water saturation in the exhaust parcel is necessary for contrail formation and also supports the theory that water drops form initially and freeze almost instantainialously. One possible explanation for the process by which this occurs is that water droplets and other particulate in the exhaust parcel can make up for a lack of water vapor in the ambient air. Some of it may evaporate during the initial entrainment process bringing the mixture up to saturation with respect to water and allowing more condensation to form.  Contrails that lasted for more than a few minutes during this study all occurred when the ambient air was significantly supersaturated with respect to ice. If this were not the case the exhaust parcel would remain saturated for only a few seconds and most of the ice crystals formed would sublimate with in a minute (Jenson et al. 1998).
 
        The Norman 00Z sounding, Figure 2, taken approximately 30 minutes after the photograph of the contrails was taken shows a plentiful amount of moisture between 380 and 225 millibars. This is the level at which the observed contrails most likely occurred since I believe the aircraft is believed to be a commercial aircraft with high bypass engines. This layer of the atmosphere according to the sounding was very supersaturated with respect to ice and possibly saturated with respect to water given humidity errors of a radiosond at higher levels. The closer to ambient saturation with respect to water the higher the possibility for contrail formation due to injection of heterogeneous condensation nuclei and contrail persistence due to ample moisture supply. See the Appendix for Tlc calculations based on the radiosond data.
 

Affects of Different Engines on Contrails

         The onset of contrail formation also depends on the type of engine and fuel that engine is burning. There are three types of aircraft engines that can produce contrails. First are non bypass or propeller engines that have no ìjet exhaustî as the engine is an internal combustion type. The second are a low-bypass engines which are first and second generation jet engines. Examples include the J57 found on all B-52s up to the G model and JT3D found on numerous commercial jet transports built into the early 70ís. Finally there are the high bypass engines such as the CFM-68 that are found on all modern commercial and military transport aircraft. Each type of engine has a different contrail factor (Cf) which is 1000*((mw*Cp)/E where mw is the mass of water vapor in the aircraft exhaust, Cp is the specific heat of air at a constant pressure, and E is the total energy released by the engine (Coleman 1996). The contrail factor is lowest with non bypass engines and highest with high bypass engines. Also, the higher the contrail factor, (amount of bypass), the higher the
critical temperature and thus the lower the level at which a contrail may form as more energy and water vapor are available to produce them since the exhaust from higher bypass engines is warmer that that of low bypass engines (Coleman 1996). Please refer to the tables in the appendix from Schrader that detail the effects the contrail factor has on the critical temperature and the level of formation.  Engine settings also play a role in the formation of contrails. The higher the trust setting the more water vapor released and the more likely hood of contrail formation. Finally, the type of fuel burned affects contrail formation as different fuels release different amount of water vapor and other substances into the atmosphere.
 Long lasting contrails like the ones observed usually occur in parts of the sky that have preexisting patches of cirrus clouds. Since the cirrus clouds are formed of ice crystals like the contrails, cirrus clouds in a region of the sky suggests supersaturation with respect to ice and sufficient heterogeneous nuclei for ice crystals to form (Jenson et al. 1998). The GOES-8 satellite photographs, Figure 3 and Figure 4, taken at approximately at the same time as the contrails were present shows significant cirrus clouds around the Norman area providing a condition necessary for contrail persistence.
 

Contrial Persistance

         If contrails persist for hours, they modify from their original form. As a parcel of jet exhaust becomes more distant from the parent engine, the turbulence caused by the engine wake will cause the contrail to spread slowly in the vertical and horizontal directions.The horizontal breadth of the contrail will over take its vertical height as the pressure, temperature, and moisture changes in the vertical are much greater than in the horizontal preventing contrail spreading further than
about one kilometer either side of the original contrail (Spinhirne et. al. 1998). However, a spreading contrail does not necessarily mean more ice crystal formation. Experiments during the SUCCESS project showed that the total number of ice crystals does not change over time, but rather a decrease in the particle number density occurs producing the optical effect of a contrail becoming translucent and finally invisible (Spinhirne et al. 1998).  Note how the translucentance varies in the contrail photograph. Eventually the exhaust parcel will become completely entrained with its surroundings and no longer be recognizable. At this stage, the contrail will be so optically thin as to be invisible, though it is detectable in the infrared using using a lidar instrument (Jenson et al. 1998)

Conclusions

         Horizontal winds in the upper level of the Troposphere will advect the contrail in the direction of the prevailing wind. The process of  horizontal advection will aid in the horizontal spreading of the contrail since the advection causes more mixing with the surrounding air. Also possible in rare cases of strong sinking motion is a contrail that appears to have rain coming from it. In reality, the contrailís ice crystals are being forced down (and possibly melting) and then are evaporating/sublimating after they are advected a few hundred meters down fro their original position.
 The contrails observed on February 17, 1999 were most likely cause by commercial jet traffic using high bypass engines. This suggests that the contrails where relatively low and warm which is consistent with my observation of them. Critical temperature calculations were carried out in the Appendix on the atmospheric layer most likely to contain the contrail (225-380 millibars). However, critical temperatures above the 300 millibar layer are greater than the ambient temperature; thus, the contrail could not have formed above the 300 millibar layer. The critical temperature calculations do suggest the contrail occurred in the layer between 300 millibars and 380 millibars which is again consistent with my observations. Also, it is very possible that all three contrails formed in the same location, but advected over after a period of time giving the effect of the contrails forming side-by-side. If this occurred, it would further support my supposition that the airplanes causing them were commercial and flying in a air corridor. What ever the cause they were long lasting contrails that persisted in recognizable form until darkness set in that day. Given the 00Z sounding and satellite data, the conditions for this persistence seem to fit with currently understood contrail theory.
 

References

Coleman, Rich F., 1996: A New Formulation for the Critical Temperature for    Contrail Formation. Journal of Applied Meteorology, 35, 2270-2282.

Jensen Eric J., et al., 1998: Environmental Conditions Required for Contrail    Formation and Persistence. Journal of Geophysical Research, 103, 3929-3936.

Schrader, Mark L., 1997: Calculations of Aircraft Contrail Formation Critical    Temperatures. Journal of Applied Meteorology, 36, 1725-1729.

Spinhirne James D., et al., 1998: Evolution of the Morphology and Microphysics of   Contrail Cirrus from Remote Sensing. Geophysical Research Letters, 25,
 1153-1156.

Toon Owen B. and Richard C. Miake-Lye, 1998: Subsonic Aircraft: Contrail and   Cloud Effects Special Study.Geophysical Research Letters, 25, 1109-1112.