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    Examples of overwing condensation. (left) A Boeing 777-F1B cargo aircraft landing at Schiphol Airport, Netherlands, on 4 Jun 2012 (the photograph was taken by J. Schäfer and is used with his permission). (right) An Embraer-190 two-engine jet aircraft flying over Milan, Italy, on 25 Jun 2012, heading southwest at ~10.6-km altitude, showing both combustion and iridescent aerodynamic contrails [the photograph is from Santacroce (2012) and is used with the permission of M. Santacroce].

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    Evolution of the temperature and saturation ratio with respect to ice (Si) and water (Sw) in laminar compressible flow over an idealized Airbus A340 (root) airfoil. Values were calculated along a streamline 0.4 m (at x = 0 m) above the wing surface. Airflow velocity corresponds to jet aircraft cruise velocity (243 m s−1) at an angle of attack of 1°. Variations of the overwing temperature with angle of attack and chord length are also shown. The pressure altitude is 300 hPa and the ambient temperature and ice supersaturation are −40°C and 1, respectively. The blue region along the x axis indicates the horizontal extent of the wing, directly at the fuselage (11.70 m) and midwing (7.9 m, dotted line). Detailed model and airfoil description can be found in Gierens et al. (2009).

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    Homogeneous droplet nucleation rate as a function of temperature and saturation ratio. Expansion chamber experiments (symbols) closely match the parameterization of Wölk et al. (2002) (dashed blue lines). Figure adapted from Manka et al. (2010).

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    Calculated growth of homogeneously nucleated droplets using the Fukuta and Walter (1970) formulations for heat and vapor transport. Initial parameters are nd = 4.2 × 103 cm−3, Tinit = 20.0°C, Pinit = 722 hPa, Tmin = −39.5°C, Ptot,min = 409 hPa, and Pυ,min = 170.6 Pa (Sw,max = 8.2). Circles correspond to measured droplet radii (Fladerer and Strey 2003); the solid line is the modeled evolution of the droplet radius.

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    Modeled evolution of the LWC along two trajectories (a) 0.3 and (b) 3.0 m above an Airbus A340 airfoil due to growth of solution droplets with (blue lines) and without (orange lines) the HDN process enabled at Sw,0 = 0.9 and different ambient temperatures [T0 = −45° (solid lines), −35° (dashed), and −25°C (dotted)]. Evolution of the overwing temperature is shown in green. The wing leading edge is located at t = 0, the trailing edge at t = 0.05 s. For each T0, we calculated the airspeed (TAS = 233, 224, and 220 m s−1) and airfoil angle of attack (α = 4.0°, 5.0°, and 5.0°) using altitude-dependent approximations (see text), while the ambient pressure (P0 = 296, 371, and 460 hPa) was derived from a standard atmosphere.

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    Modeled evolution of the peak IWC over an Airbus A340 airfoil due to freezing and growth of solution droplets (black lines) and homogeneous droplet nucleation followed by homogeneous freezing (red lines) at Sw,0 = 0.9 and different ambient temperatures [T0 = −45° (solid lines), −35° (dashed), and −25°C (dotted)]. The ice saturation ratio in the trajectory with maximum total IWC is shown in green. The ambient vapor densities ρυ,0(T0) are shown in blue. The wing leading edge is located at t = 0 and the trailing edge at t = 0.05 s. Ambient pressures, flow velocities, and airfoil angles of attack are as in Fig. 5.

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    Modeled evolution of the optical depth over an Airbus A340 airfoil with the HDN process (a) enabled and (b) disabled at near water saturation (Sw,0 = 0.9) and different ambient temperatures [T0 = −45° (solid lines), −35° (dashed), and −25°C (dotted)]. Colors refer to processes of homogeneous droplet nucleation followed by homogeneous freezing (red lines) and liquid (blue lines) and homogeneously frozen solution droplets (black lines). The visibility threshold value (τυ = 0.01) is plotted in green. The wing leading edge is located at t = 0 and the trailing edge at t = 0.05 s. Ambient pressures, flow velocities, and airfoil angles of attack are as in Fig. 5.

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    Sensitivity study of the HDN–HIN processes to different initial temperatures and saturation ratios, 30 m behind the trailing edge of the wing. (a) Concentration and effective radius of homogeneously nucleated droplets. (b) Optical depth. The green contour represents the visibility threshold. Schmidt–Appleman visibility threshold for combustion contrails (high-pass turbofan jet engine, standard atmosphere) is shown in blue. Combustion and aerodynamic contrails are only persistent if S0Si,sat (dashed gray line, both panels).

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    Time evolution of the HN ice particle effective radius, mean number concentration (nm), and the particle size distribution geometric standard deviation (σg) at increments of 10 m from the wing leading edge. Trajectories are shown in gray. A 2D cross section of the wing is shown in red. The wing leading edge is located at x = 0 and the trailing edge at x = 11.7 m. Ambient temperature and water saturation ratio were −30°C and 0.9, respectively. The airfoil angle of attack was 5.0° and the true airspeed 222 m s−1 [calculated using an altitude-dependent linear approximation (see text)], while the ambient pressure was derived from a standard atmosphere.

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Microphysics of Aerodynamic Contrail Formation Processes

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  • 1 Institute for Marine and Atmospheric Research Utrecht, Utrecht University, Utrecht, Netherlands
  • 2 National Center for Atmospheric Research, Boulder, Colorado
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Abstract

Aerodynamic condensation is a result of intense adiabatic cooling in the airflow over aircraft wings and behind propeller blades. Out of cloud, condensation appears as a burstlike fog (jet aircraft during takeoff and landing, propellers) or as an iridescent trail visible from the ground behind the trailing edge of the wing (jet aircraft in subsonic cruise flight) consisting of a monodisperse population of ice particles that grow to sizes comparable to the wavelength of light in ambient humidities above ice saturation.

In this paper, the authors focus on aerodynamic contrail ice particle formation processes over jet aircraft wings. A 2D compressible flow model is used to evaluate two likely processes considered for the initial ice particle formation: homogeneous droplet nucleation (HDN) followed by homogeneous ice nucleation (HIN) and condensational growth of ambient condensation nuclei followed by their homogenous freezing. The model shows that the more numerous HDN particles outcompete frozen solution droplets for water vapor in a 0.5–1-m layer directly above the wing surface and are the only ice particles that become visible. Experimentally verified temperature and relative humidity–dependent parameterizations of rates of homogeneous droplet nucleation, growth, and freezing indicate that visible aerodynamic contrails form between T = −20° and −50°C and RH ≥ 80%. By contrast, combustion contrails require temperatures below −38°C and ice-saturated conditions to persist. Therefore, aerodynamic and combustion contrails can be observed simultaneously.

Corresponding author address: Andrew Heymsfield, NCAR, 3450 Mitchell Lane, Boulder, CO 80301. E-mail: heyms1@ucar.edu

Abstract

Aerodynamic condensation is a result of intense adiabatic cooling in the airflow over aircraft wings and behind propeller blades. Out of cloud, condensation appears as a burstlike fog (jet aircraft during takeoff and landing, propellers) or as an iridescent trail visible from the ground behind the trailing edge of the wing (jet aircraft in subsonic cruise flight) consisting of a monodisperse population of ice particles that grow to sizes comparable to the wavelength of light in ambient humidities above ice saturation.

In this paper, the authors focus on aerodynamic contrail ice particle formation processes over jet aircraft wings. A 2D compressible flow model is used to evaluate two likely processes considered for the initial ice particle formation: homogeneous droplet nucleation (HDN) followed by homogeneous ice nucleation (HIN) and condensational growth of ambient condensation nuclei followed by their homogenous freezing. The model shows that the more numerous HDN particles outcompete frozen solution droplets for water vapor in a 0.5–1-m layer directly above the wing surface and are the only ice particles that become visible. Experimentally verified temperature and relative humidity–dependent parameterizations of rates of homogeneous droplet nucleation, growth, and freezing indicate that visible aerodynamic contrails form between T = −20° and −50°C and RH ≥ 80%. By contrast, combustion contrails require temperatures below −38°C and ice-saturated conditions to persist. Therefore, aerodynamic and combustion contrails can be observed simultaneously.

Corresponding author address: Andrew Heymsfield, NCAR, 3450 Mitchell Lane, Boulder, CO 80301. E-mail: heyms1@ucar.edu

1. Introduction

Combustion condensation trails, commonly associated with “contrails,” are due to combustion of aircraft fuel and have been widely studied (e.g., the series of articles in the April 2010 issue of the Bulletin of the American Meteorological Society). These contrails generally occur at temperatures colder than −38°C (Jensen et al. 1998) resulting from the offsetting effects of vapor and heat emitted during combustion (Schmidt 1941; Schumann 1996). In contrast, aerodynamic condensation is produced by adiabatic expansion and the resulting cooling of moist air over aircraft wings. These puffs of condensation are most readily seen by a passenger on an aircraft as condensation over the wings during aircraft landing or takeoff (Fig. 1, left). Aerodynamic contrails have recently become an area of scientific interest because they can occur at much higher temperatures than combustion contrails (Gierens et al. 2009; Kärcher et al. 2009).

Fig. 1.
Fig. 1.

Examples of overwing condensation. (left) A Boeing 777-F1B cargo aircraft landing at Schiphol Airport, Netherlands, on 4 Jun 2012 (the photograph was taken by J. Schäfer and is used with his permission). (right) An Embraer-190 two-engine jet aircraft flying over Milan, Italy, on 25 Jun 2012, heading southwest at ~10.6-km altitude, showing both combustion and iridescent aerodynamic contrails [the photograph is from Santacroce (2012) and is used with the permission of M. Santacroce].

Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0362.1

The phenomenon of aerodynamic condensation can be linked to the formation of aircraft produced ice particles (APIPs), first reported by Rangno and Hobbs (1983, 1984). Cooling behind the blades of propeller aircraft can produce visible aerodynamic condensation. During research flights that measured cloud microphysical properties, Rangno and Hobbs documented the production of ice crystals from the passage of propeller aircraft through clouds at temperatures as warm as −8°C. Ice particle concentrations were more than 100 times greater than the expected concentrations of ambient ice nuclei at this temperature. Vonnegut (1986), commenting on the APIP observations, suggested that adiabatic expansion in the flow over the propeller tips was sufficient to cool the cloud droplets to the temperature for homogeneous ice nucleation (HIN), ~−39°C, if cloud temperatures were only a few degrees below −8°C, and that this could produce abundant numbers of ice crystals.

Following up on the Vonnegut suggestion, Foster and Hallett (1993) carried out laboratory measurements of HIN via rapid expansion of moist, cool air in a cloud chamber. After the injection of droplets, ice crystals were readily observed at temperatures colder than −40°C, with concentrations, although not measured, significantly greater than the concentration of condensation nuclei (CN) present in the ambient air. This is an important and relevant observation that we will address later.

Foster and Hallett (1993) found the onset conditions for ice nucleation to be consistent with HIN theory as long as the cloud droplets were exposed to the HIN onset temperature with sufficient time to freeze. Without any cloud present initially, the onset temperature dropped below −48°C, dependent on the initial chamber temperature, rather than −40°C typically associated with droplets freezing homogeneously. The homogeneous freezing temperature is warmer as the droplet volume increases (Pruppacher and Klett 1997 and references therein) and in this case the droplets were likely to be very small. Foster and Hallett interpreted the process of APIP generation to be due to homogeneous droplet nucleation (HDN) from vapor, which typically produces large numbers of submicron-size droplets—and ice crystals after HIN.

An earlier study by Maybank and Mason (1959) reported on expansions of a small volume of moist air from temperatures of −10° and −20°C to final temperatures of −45°C and colder. It was concluded that ice crystals, in concentrations ~ 106 cm−3, formed in clean air first by HDN followed by HIN. This HIN pathway occurred only when the temperature drop and thus the supersaturation was sufficient for HDN to occur. In unfiltered air, high concentrations of ice crystals (~104 cm−3) were generated at temperatures a few degrees warmer than for clean air. The warmer onset of HIN may have resulted from the presence of ice nuclei present in the unfiltered laboratory air but could also be interpreted as due to condensation on larger CN, followed by HDN, and finally by HIN.

To gain a better understanding of the APIP formation process(es), Woodley et al. (1991, 2003) studied APIP generation from the University of Wyoming King Air research aircraft in supercooled fog at temperatures between about −5° and −12°C with almost no natural ice nuclei during the Mono Lake Experiments (MOLAS). APIP generation from nine different propeller aircraft, including the King Air, was studied and interpreted. Adiabatic expansion at the propeller tips achieves a cooling of −40°C, sufficient for HIN. Woodley et al. (2003) estimated that the ice concentrations generated at the propeller tips was >105 cm−3 and suggested from laboratory experiments that the HDN process is involved in APIP generation.

Conditions conducive to APIP generation over propeller blades are analogous to those generating ice particles during the cooling of air over aircraft wings at sufficiently low temperatures. Gierens et al. (2009) quantified adiabatic cooling over a generic, idealized airfoil at an ambient temperature of −22°C for a commercial jet aircraft flying at subsonic speed and observed an overwing temperature drop exceeding 20°C. In this highly supersaturated environment, activation of ambient CN and growth of the resulting droplets could be followed by their homogeneous freezing at ambient temperatures colder than −20°C.

Using Gierens’s model, Kärcher et al. (2009) modeled the process of aerodynamic contrail formation from ambient solution droplets at temperatures from −38° to −68°C and a pressure range of 150 to 300 hPa. They initialized the particles with supercooled aqueous solutions of sulfuric acid (H2SO4) and other components that were positioned just upstream of the wing. These solution droplets then swelled by condensation in the supersaturated air in the flow over the wings, while some froze homogeneously, dependent on their size. Subsequent growth of the crystals produced was driven by the difference between ambient and ice saturation vapor pressure, which, at water saturation, increases with decreasing temperature (for temperatures of −15°C and colder). Homogeneous droplet nucleation—the generation of droplets without the need for cloud condensation nuclei—has not been considered previously in the study of aerodynamic contrails.

This study aims to identify the process(es) responsible for aerodynamic condensation and quantify the temperatures, pressures, and humidities when aerodynamic contrails form and to estimate the conditions under which these contrails occur simultaneously with combustion contrails at temperatures conducive to combustion contrail generation. We first present an overview of observations of aerodynamic condensation and laboratory experiments in section 2 and in section 3 discuss the development of a numerical model to evaluate the relative importance of the various processes that might be involved. In section 4, we conduct a sensitivity study to quantify ambient atmospheric conditions conducive of visible aerodynamic contrail formation. In section 5 we discuss the validity of our model results using recent observations. We summarize our work and draw conclusions in section 6.

2. Overview of conditions conducive of aerodynamic contrail formation

In this section, we use observations of aerodynamic condensation and laboratory studies to establish the atmospheric and overwing conditions that we think are potentially conducive of aerodynamic condensation and the subsequent generation of ice crystals.

The right panel in Fig. 1 shows an Embraer-190 two-engine jet aircraft flying over Milan, Italy, at an altitude of approximately 10.6 km. The white trails behind each engine are due to combustion, cooling, and ice growth. The iridescent trail is instead caused by overwing cooling and condensation, and the colors are due to particle sizes that are comparable to the wavelength of visible light. The color changes are due to particle growth (Sassen 1979; Kärcher et al. 2009). Using the wingspan (28.7 m) and the cruising speed (245 m s−1) to estimate the distance of the contrail behind the wing trailing edge, we show in the next section that the particles grow to visible sizes in a time of 60–80 ms, depending on their point of origin at the wing root or tip. In the extremely low temperatures reached over the wing (T ≪ −38°C), the homogeneous ice nucleation rate is sufficiently high to freeze all but the most concentrated solution droplets (Koop et al. 2000; Kärcher et al. 2009). It is therefore almost certain that the particles in aerodynamic contrails are ice and that they can occur simultaneously with combustion contrails.

Case studies can provide some insight into atmospheric conditions conducive of aerodynamic contrail formation. Published case studies by Kärcher et al. (2009) and Gierens et al. (2011) combine photos of aerodynamic contrail-generating aircraft and corresponding radiosonde measurements and indicate formation temperatures of approximately −32° and −34°C, respectively. For Fig. 1 (right), radiosonde measurements from Milano Linate Airport (LIML) recorded 4 h before the photo was taken display an ambient temperature (T0) of about −46°C and an ambient saturation ratio with respect to ice (Si,0) between 0.49 and 0.56. The humidity values are lower than required for APIPs persistence, although radiosonde measurements of relative humidity are known to have a dry bias at cold temperatures (Miloshevich et al. 2009). These observations indicate that visible condensation trails may occur over a much wider range of T0 and S0 than previously thought.

For cases where combustion and aerodynamic contrails are observed simultaneously, the combustion contrail diameter at the point where it first becomes visible behind the engine, when Scontrail > Sw,sat (Schumann 1996), can provide an alternative estimate of the saturation ratio. The initial diameter DL1 is a function of environmental parameters P0, T0, and S0 and flight parameters that govern the mixing of heat and moisture in the trail. We use the wingspan of the aircraft in Fig. 1 (28.7 m) to estimate DL1 = 3.3 ± 0.3 m. The photo in Fig. 1 is part of a series depicting cruising jet aircraft that show both contrail types, taken in the afternoon of 25 June 2012 in Milan, Italy (Santacroce 2012). For each photo the time, aircraft type, and altitude were known from flight tracker data. Estimating DL1 ± 10% for two more aircraft, and using P0 from radiosonde measurements we use Schumann’s method to constrain T0 between −45.6° (S = Sw,sat) and −53.5°C (S = Si,sat), consistent with radiosonde measurements. The radiosonde-derived temperature is at the higher end of this spectrum, and we estimate that the ambient relative humidity must have been closer to water saturation than the radiosonde measurements would suggest.

Aerodynamic contrails at cruise altitude obviously differ from instantaneously visible condensation normally seen over the wings of aircraft on takeoff or landing at temperatures ≥0°C. The left panel of Fig. 1 shows aerodynamic condensation over the wings of a Boeing 777-F1B cargo aircraft landing on Schiphol Airport, the Netherlands, on 4 June 2012. Similar to the aerodynamic contrail in the right panel, the thickness of the condensation layer is proportional to the chord length (wing depth), reaching a maximum at the wing root. Airport meteorological records for the day the picture was taken show daily mean values of T0 = 8.9°C and Sw,0 = 0.87. Thus, depending on overwing temperatures conducive of homogeneous freezing, aerodynamic condensation particles may be either liquid or ice.

The examples shown in Fig. 1 provide insight into the processes involved in aerodynamic contrail formation and their visual appearance. As air flows over the wing of the aircraft, it expands, cools, and the vapor condenses, and on the aft side of the wing, it warms, compresses, and the condensate evaporates. Because ice particles survive to much lower vapor saturation ratios than water droplets, especially at −50°C [at ice saturation (Si = 1), the saturation ratio with respect to water is about 0.6], the crystals in Fig. 1 right can survive to much lower saturation ratios in the downstream part of the flow over the wing than the water droplets in Fig. 1 (left).

Together with the ambient temperature and relative humidity, aerodynamic condensation is controlled by the amount and duration of adiabatic expansion achieved over the wing. To homogeneously freeze deliquesced CN or HDN at ambient temperatures ≥ −38°C and produce a visible trail, the overwing expansion must induce a temperature drop sufficient to cause HIN. Figure 2 shows a model simulation of the air temperature and supersaturation with respect to water and ice during the flow of air over an idealized (Joukowski) airfoil in several configurations. In this example we used an ambient temperature of −40°C and an initial saturation ratio of 0.9 with respect to water or 1.0 with respect to ice. Without condensation or freezing, the 115-hPa peak pressure deficit over the wing leads to about 30°C of cooling and a resulting water saturation ratio about 22.

Fig. 2.
Fig. 2.

Evolution of the temperature and saturation ratio with respect to ice (Si) and water (Sw) in laminar compressible flow over an idealized Airbus A340 (root) airfoil. Values were calculated along a streamline 0.4 m (at x = 0 m) above the wing surface. Airflow velocity corresponds to jet aircraft cruise velocity (243 m s−1) at an angle of attack of 1°. Variations of the overwing temperature with angle of attack and chord length are also shown. The pressure altitude is 300 hPa and the ambient temperature and ice supersaturation are −40°C and 1, respectively. The blue region along the x axis indicates the horizontal extent of the wing, directly at the fuselage (11.70 m) and midwing (7.9 m, dotted line). Detailed model and airfoil description can be found in Gierens et al. (2009).

Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0362.1

It is important to note that the pressure deficit (and therefore T and RH) and time scale of overwing flow scales with the chord length (Gierens et al. 2009) but also with the airspeed and angle of attack of the aircraft. An increased angle of attack will generate extra lift through a higher pressure difference (up to the stall angle of attack, approximately 15° for the airfoil considered here), driven by a greater expansion over the top of the wing (Fig. 2, dashed black line). Scaling the airfoil to decrease the chord length, analogous to a wing section farther from the root (Fig. 2, dotted black line), will only reduce the time scale of overwing flow. We outline our assumptions regarding the wing configuration and aircraft speed during subsonic cruise flight in the model development section.

Given the high supersaturations generated over wings, and its apparent relevance to APIPs formation over propellers, the homogeneous droplet nucleation process must be considered. The relevance of homogeneous condensation is supported by expansion chamber experiments. For example, Wölk et al. (2002) observed high rates of HDN (from 105 to 1010 cm−3 s−1) in expansion chamber experiments in clean air at a range of temperatures (from −13° to −43°C) and saturation ratios (from 6 to 22)—conditions similar to those occurring in modeled overwing flow (Fig. 2). Laboratory experiments (Table 1) indicate a strong, nonlinear dependence of the nucleation rate on the saturation ratio and of the initial cluster size on temperature. In the next section we combine Gierens’s compressible flow model from Fig. 2 with empirical characterization of the homogeneous nucleation rate based on the experiments of Table 1 in order to quantify the role of the HDN process in aerodynamic contrail formation.

Table 1.

Overview of studies determining homogeneous nucleation rate J of water and critical cluster size n* with different experimental techniques, as a function of temperature T and saturation ratio S. Critical cluster sizes are calculated from the slopes of the nucleation rate isotherms.

Table 1.

3. Model development

In this section, we develop a model that considers two pathways to aerodynamically produced condensation: 1) homogeneous droplet nucleation from the vapor phase and 2) condensation on ambient condensation nuclei. Each of these pathways can lead to ice production via HIN if the temperatures during cooling over the wings are sufficiently low. Because so little is known about heterogeneous ice nucleation under these conditions, and relatively low concentrations of ice nuclei are present compared to liquid aerosol that can homogenously freeze, this process will be ignored here.

The evolution of pressure and temperature over a commercial jet aircraft wing was simulated using a two-dimensional potential flow model developed by Gierens et al. (2009, kindly provided by K. Gierens for use in this study) for compressible flow. We used an idealized Joukowski airfoil, with parameters chosen as to match the shape of an Airbus A340 wing at the root (H = 1.6 m, L = 11.7 m), where condensation is most visible. Relevant quantities were calculated along 20 streamlines vertically spaced 0.1 m apart. The trajectory closest to the wing surface was taken above the turbulent boundary layer, which scales with chord length L and measures on the order of , with the drag factor c ≈ 0.002 (Landau and Lifshitz 1987) or about 0.16 m for L = 11.7 m.

To evaluate the different aerodynamic contrail formation processes for a wide range of atmospheric conditions, we modeled the overwing flow of a jet aircraft ascending from about 5 to 11 km (cruise altitude). Considering the importance of airspeed and angle of attack for the pressure deficit, we derived these values from the Airbus A340 flight operations manual and historical flight track data. We assumed the true airspeed increasing linearly from 218 (5.4 km) to 245 m s−1 (cruise altitude > 9.4 km). The angle of attack was taken constant at 5° during climb and 3° during cruise. The pressure deficit over the wing decreases from 210 to 170 hPa during climb, resulting from the decreasing weight of the aircraft combusting fuel and a lower climb rate aloft. As a result, the magnitude of the average temperature drop in the layer 0.16–3.0 m above the wing increases with decreasing ambient temperature: . Ambient pressures and temperatures were derived from a standard atmosphere; for example, we assume that the ambient temperature and pressure are 15°C and 1013 hPa, respectively, at ground level and −53°C and 220 hPa at cruising altitude.

a. Homogeneous condensation

Homogeneous droplet nucleation is a process whereby liquid droplets condense directly from the vapor phase, without the need for cloud condensation nuclei. Good examples are seen in everyday life, including condensation from warm water sprayed from a shower head and steam produced from a kettle boiling water (Carlon 1984). In each case, the supersaturation generated from the cooling of the heated vapor can be very large—a saturation ratio of 10 or more.

Homogeneous droplet nucleation was first quantified by Becker and Döring (1935) by calculating the free energy required to form a critical cluster of water molecules (nucleus) in unstable equilibrium with the surrounding vapor. Later corrections of the Becker–Döring classical nucleation theory by Girshick and Chiu (1990)—who included the formation-free energy of a monomer—and Wölk et al. (2002)—who devised an empirical correction based on cloud chamber experiments—have significantly improved nucleation rate predictions. We use this theoretical framework to model the HDN process, guided by the laboratory observations.

A comparison between the Wölk et al. (2002) parameterization of the nucleation rate J (cm−3 s−1) and experiments is shown in Fig. 3. The overall agreement between measurements and classical nucleation theory is good along the −53°–+47°C isotherms. Large discrepancies exist for temperatures ≤ −53°C (Mikheev et al. 2002), which may have been the result of homogeneous freezing of droplets directly after their nucleation (Wölk et al. 2013).

Fig. 3.
Fig. 3.

Homogeneous droplet nucleation rate as a function of temperature and saturation ratio. Expansion chamber experiments (symbols) closely match the parameterization of Wölk et al. (2002) (dashed blue lines). Figure adapted from Manka et al. (2010).

Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0362.1

b. Droplet growth

Growth of homogeneously nucleated droplets is determined using heat and mass flux calculations between the droplet and gas phases. We use a commonly used droplet growth model described in Heymsfield and Sabin (1989), based on Fukuta and Walter (1970) formulations for heat and vapor transport, in which curvature effects are considered. We applied a correction for the surface tension of small clusters by Merikanto et al. (2007). Values of the latent heat of evaporation–sublimation, saturation vapor pressure, and surface tension were approximated by empirical parameterizations. The interdependent quantities of vapor pressure, (droplet) temperature, and droplet radii were resolved using an ordinary differential equation solver.

The critical cluster size of newly formed droplets is given by the Gibbs–Thomson equation, which has been experimentally verified for temperatures from −70° to −15°C (Manka et al. 2010). Newly formed clusters of water proceed rapidly through different growth stages. Small droplets first enter the free molecule regime (radii ≤ 10 nm), where droplets are smaller than the mean free path of water molecules in air and the mass flux to the droplet depends on the number of collisions. Rapid growth takes place as the mass flux continuously changes to the diffusion controlled continuum regime (radii > 200 nm), where droplets grow to visible size.

Fladerer and Strey (2003) experimentally verified a commonly used droplet growth model for homogeneously nucleated droplets (Seinfeld and Pandis 1998). They measured the time evolution of homogeneously nucleated droplet size in a supersaturated environment. Their experiments show that at low temperatures (−43° to −23°C) and high saturation ratios (from 8 to 13) HDN droplets grow exponentially to visible sizes (radii ≥ 0.6 μm) in under 10 ms. In Fig. 4 we compared our small cluster growth calculations with their measurements. For mass and thermal accommodation coefficients of 0.75 and 0.96, respectively, the model shows good agreement with the data.

Fig. 4.
Fig. 4.

Calculated growth of homogeneously nucleated droplets using the Fukuta and Walter (1970) formulations for heat and vapor transport. Initial parameters are nd = 4.2 × 103 cm−3, Tinit = 20.0°C, Pinit = 722 hPa, Tmin = −39.5°C, Ptot,min = 409 hPa, and Pυ,min = 170.6 Pa (Sw,max = 8.2). Circles correspond to measured droplet radii (Fladerer and Strey 2003); the solid line is the modeled evolution of the droplet radius.

Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0362.1

c. Ambient CN initialization and growth

The initial solution droplet composition and size distribution is controlled by a prescribed CN dry mass spectrum and the ambient relative humidity, which governs deliquescence. Heymsfield (1973) measured ambient activated CN (dry) mass spectra and concentrations from an aircraft at 7–8-km altitude. Following his observations, we use lognormal mass distribution (mmin = 1 × 10−17 and mmax = 1 × 10−12 g) with an ambient CN concentration of 260 cm−3. We assume that at cruising altitude the CN are ammonium sulfate, consistent with the observations of Twomey (1971). The particle growth model described in the previous section is applied to resolve the growth and evaporation rate of the solution droplets. For liquid particles we consider both solute and curvature effects through the modified vapor diffusion and heat conduction coefficients (Fukuta and Walter 1970; Fitzgerald 1972).

d. Homogeneous freezing and ice crystal growth

Because temperatures over the wing of a cruising jet aircraft reach well below −40°C, it is likely that some deliquesced ambient CN and HN droplets can freeze homogeneously.1 However, because the droplet volumes are small and the cooling occurs over a time scale of milliseconds, it is important to quantify this process. Bartell and Chushak (2003) and Manka et al. (2012) measured the homogeneous freezing rate of small (≤6 nm) pure water droplets at temperatures relevant for APIPs formation (−80° to −55°C). The measured rates (J ≈ 1023 cm−3 s−1) can be approximated by classical nucleation theory, adapted for cubic ice (Murray et al. 2010). Homogeneous freezing of supercooled solution droplets is modeled using the empirical parameterization by Koop et al. (2000), which includes the depression of the melting point by the solutes in the drop. The formation of ice particles directly from the vapor phase or via deposition nucleation is not considered here, for reasons discussed in Kärcher et al. (2009).

Ice crystal growth rates were calculated using the droplet growth model described in section 3b without solute and curvature effects and with different parameterizations specific for the solid phase (e.g., density, equilibrium vapor pressure, and latent heat). This approach implies that we assume ice particles are initially spherical: the extremely high vapor flux driving the initial growth phase is likely to produce amorphous ice rather than fully developed crystalline structures (Kärcher et al. 2009). The habit and optical properties of aged APIPs are a subject of ongoing research. In situ measurements of ice crystal size (effective radii, reff) and habit in young combustion contrails suggest that small hexagonal plates, columns, and triangles (reff ≤ 2 µm) are abundant 1 min after formation (Goodman et al. 1998). However, ice particles aged 2–20 min are initially near spherical (Schröder et al. 2000; Gayet et al. 2012) and only grow into larger (reff ≥ 5 µm), quasi-spherical particles as the contrail transitions into cirrus (>20 min; Febvre et al. 2009). In situ observations of aged (reff ≥ 150 μm) ice crystals from aircraft-induced virga below a supercooled water cloud by a C-130 research aircraft equipped with particle imaging probes show hexagonal and columnar crystals develop at a later stage (Heymsfield et al. 2010).

4. Model results

The purpose of this study is to identify the dominant processes responsible for creating out-of-cloud overwing condensation and aerodynamic contrails; we do not consider the processes occurring within a cloud. First, we examine the relative importance of the following overwing processes for generation of the APIPs: 1) deliquescence of water vapor on CN leading to solution droplet growth, followed by homogeneous freezing and 2) homogeneous condensation followed by homogeneous freezing. Because aerodynamic contrails appear to form in relatively warm (T0 ≥ −38°C) and humid (S0Si,sat) conditions (case study; Gierens et al. 2011), both liquid droplets and ice crystals can contribute to the generation of a visible trail. We have therefore included both the liquid water content (LWC) and ice water content (IWC) at different ambient temperatures in our model.

Figure 5 shows the modeled liquid water content over an Airbus A340 wing at temperatures of −45°, −35°, and −25°C, at near water saturation (Sw,0 = 0.9) along trajectories 0.3 and 3.0 m above the wing surface. The initial decrease in solution droplet LWC is caused by evaporation in compressed and heated air at the stagnation point in front of the leading edge of the wing, followed directly by adiabatic expansion, cooling, and freezing midwing. Not all solution droplets freeze: initial evaporation increases the molality of the larger (≥1 μm) solution droplets and decreases their water activity and homogeneous freezing rate (Koop et al. 2000). Compression and evaporation prevail closer to the wing surface and at low ambient temperatures, because we assume increasing airspeed with altitude. At higher temperatures and farther from the wing surface, the homogeneous freezing rate is temperature controlled. The droplets that remain are allowed to grow in the supersaturated environment, causing an increase in the LWC, but evaporate behind the wing where S0Sw,sat.

Fig. 5.
Fig. 5.

Modeled evolution of the LWC along two trajectories (a) 0.3 and (b) 3.0 m above an Airbus A340 airfoil due to growth of solution droplets with (blue lines) and without (orange lines) the HDN process enabled at Sw,0 = 0.9 and different ambient temperatures [T0 = −45° (solid lines), −35° (dashed), and −25°C (dotted)]. Evolution of the overwing temperature is shown in green. The wing leading edge is located at t = 0, the trailing edge at t = 0.05 s. For each T0, we calculated the airspeed (TAS = 233, 224, and 220 m s−1) and airfoil angle of attack (α = 4.0°, 5.0°, and 5.0°) using altitude-dependent approximations (see text), while the ambient pressure (P0 = 296, 371, and 460 hPa) was derived from a standard atmosphere.

Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0362.1

The homogeneous formation of liquid droplets occurs over a very short time scale and is only observed in trajectories close (≤1 m) to the wing surface, where the supersaturation is sufficiently high (Tmin = −80° to −60°C, Sw,max = 18 to 61). From Fig. 3, we find that these conditions are highly conducive of HDN (J ≤ 1014 cm−3 s−1). It is important to note, however, that because S increases exponentially with decreasing T (Fig. 2), the supersaturations conducive to HDN are only present over a small fraction of the wing, where T approximates Tmin within 5°C. In the very short time frame (6 ms) within which HDN can occur, temperatures and supersaturations are relatively constant, resulting in a highly monodisperse population of particles (i.e., a particle size distribution with a geometric standard deviation σG of <1.25). Although numerous [104–106 cm−3 compared to 102–103 cm−3 for upper-tropospheric cloud condensation nuclei (CCN) (Heymsfield 1973)], these droplets freeze within 5 ms after formation (Manka et al. 2012) and the liquid phase is likely to remain subvisible over the wing (r = 0.1–1 nm; Fig. 4) during cruise flight.

Solution droplets can take up significantly more water vapor above the layer where homogeneous droplet nucleation dominates. For trajectories within the overwing HDN layer (h = 0.3 m; Fig. 5a), the solution droplet LWC increases when the HDN process is disabled (orange lines), compared to model runs where homogeneous condensation is enabled (blue lines). Much higher above the wing (h = 3.0 m; Fig. 5b), the temperature drop (green lines) is insufficient for the HDN process to occur. Here, the LWC is determined solely by growth and freezing of solution droplets, resulting in identical values for the HDN-disabled and -enabled model runs.

To explain the formation of visible aerodynamic contrails behind the wing trailing edge, we need to know the fate of ambient solution and HN droplets after freezing. Figure 6 shows the ice water content over the same idealized A340 airfoil used in Fig. 5. Upon cooling, the excess water vapor is distributed over growing HN ice particles and frozen solution droplets. As the HN ice particles are more numerous by three orders of magnitude or more (albeit smaller) than the frozen solution droplets, they form the largest contribution to the IWC despite the higher volumetric growth rate of the latter. The large number of growing particles rapidly depletes the excess water vapor to near-equilibrium values (S = Si,sat). Toward the trailing edge of the wing the air is heated adiabatically by recompression, and the particle growth rate is limited by the decreasing relative humidity. As the relatively dry air is recompressed further, a vapor deficit replaces a vapor excess (Si < 1), and sublimation lowers the IWC. During recompression the ice particles either decrease in size, or sublimate entirely, depending on their size and the vapor density. Surviving ice particles will grow until an equilibrium with the ambient water vapor is reached (Si,0 = 1) and a visible trail is formed.

Fig. 6.
Fig. 6.

Modeled evolution of the peak IWC over an Airbus A340 airfoil due to freezing and growth of solution droplets (black lines) and homogeneous droplet nucleation followed by homogeneous freezing (red lines) at Sw,0 = 0.9 and different ambient temperatures [T0 = −45° (solid lines), −35° (dashed), and −25°C (dotted)]. The ice saturation ratio in the trajectory with maximum total IWC is shown in green. The ambient vapor densities ρυ,0(T0) are shown in blue. The wing leading edge is located at t = 0 and the trailing edge at t = 0.05 s. Ambient pressures, flow velocities, and airfoil angles of attack are as in Fig. 5.

Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0362.1

The model shows a clear increase in overwing IWC and LWC with increasing ambient temperature. The limiting factor appears to be the excess water vapor; the ambient vapor density increases with temperature at constant RH. There is a minor effect of recompression on air density and the liquid and ice water content (ρa,0/ρa,min ≤ 1.2).

a. Aerodynamic contrail visibility

From Figs. 5 and 6, it appears that homogeneous droplet nucleation followed by homogeneous freezing creates large numbers of APIPs that could form a visible trail. To assess contrail visibility, the optical depth of the population of HN ice particles and frozen solution droplets can be used. First, the Mie extinction efficiency Qext is calculated from the particle radius r and refractive index n—we assume a monodisperse population of spherical particles and a scattering wavelength λ of 0.589 μm (Van de Hulst 1957):
e1
The error in Qext introduced by this approximation equals a factor of 0.9 for r ≈ 1.0 μm and a factor of 2.0 for r ≈ 0.1 μm compared to an exact Mie routine (Thomas 2012). With the ice particle number concentration ni, the optical depth τ can be calculated:
e2
For simplicity, we assume that the observer is looking at the condensation trail from directly below. We calculated the extinction along 40 stacked trajectories (streamlines) equally distributed vertically up to 5 m from the wing surface, a conservative estimate of the thickness of the condensation layer observed over the wings of landing jet aircraft (Fig. 1). The optical depth was obtained by summation through all trajectories, taking their vertical separation as Δz. We here assume a visibility threshold of τυ ≥ 0.01 for visual detection of contrails. Lidar studies by Sassen and Cho (1992) estimated the optical depth of visible cirrus at 0.03 ≤ τυ ≤ 3.0, and τυ ≈ 0.01 at low angular distances from the sun, because the scattering phase function has a strong forward peak. Kärcher et al. (2009) performed detailed radiative transfer simulations for monodisperse populations of spherical ice particles with sizes similar to the wavelength of visible light (λ = 390–700 nm) and found that iridescence is only observed within 30° angular distance from the sun, resulting in a similar threshold value (τυ = 0.01–0.03).

In Fig. 7, a time series of the aerodynamic contrail optical depth is shown for solution droplets (ice and liquid) and HN ice crystals for air temperatures between −45° and −25°C and an ambient water saturation ratio of 0.9. No visible contrails originate from growth of liquid solution or HN droplets because even at T0 = −25°C, the minimum temperature reaches well below −40°C (Fig. 5) and the homogeneous freezing rate is high enough to freeze the majority of liquid particles. When the model is run with HDN disabled (Fig. 7b), growth and freezing of solution droplets produce a visible trail (as in Kärcher et al. 2009), while liquid droplets remain invisible. Droplet salinity increase during compression and evaporation at the leading edge reduces the freezing rate and results in a lower optical depth at higher temperatures. Kärcher et al. (2009), who did not include the solute effect in their droplet freezing parameterization, reported a reverse temperature dependency.

Fig. 7.
Fig. 7.

Modeled evolution of the optical depth over an Airbus A340 airfoil with the HDN process (a) enabled and (b) disabled at near water saturation (Sw,0 = 0.9) and different ambient temperatures [T0 = −45° (solid lines), −35° (dashed), and −25°C (dotted)]. Colors refer to processes of homogeneous droplet nucleation followed by homogeneous freezing (red lines) and liquid (blue lines) and homogeneously frozen solution droplets (black lines). The visibility threshold value (τυ = 0.01) is plotted in green. The wing leading edge is located at t = 0 and the trailing edge at t = 0.05 s. Ambient pressures, flow velocities, and airfoil angles of attack are as in Fig. 5.

Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0362.1

It is apparent that growth and freezing of ambient solution droplets do not produce visible condensation. As detailed in the previous section, this is because growing HN ice particles use up most of the excess water vapor. Visible overwing condensation and aerodynamic contrails originate solely from the HDN process followed by HIN. This finding is new: to our knowledge, vapor depletion from the homogeneous nucleation process has not been considered previously in the study of aerodynamic condensation.

b. Sensitivity study

Figures 6 and 7 show a direct relationship between the IWC, the visibility of aerodynamic condensation, and ambient temperature and saturation ratio. To assess the atmospheric relevance of aerodynamic condensation we need to establish in more detail the T and S boundary conditions. Since we have shown in the previous section that solution droplet growth and freezing is unlikely to produce a visible contrail at temperatures from −50° to −20°C and Sw,0 = 0.9, we will only consider the HDN + HIN process here.

Figure 8 shows the peak concentration of HN ice particles and their effective radius (Fig. 8a) and aerodynamic contrail optical depth (Fig. 8b) 30 m behind the wing trailing edge for air temperatures between −52° and −20°C and a saturation ratio between that of ice (Si,sat) and water (Sw.sat). The distance was chosen to match the observed wing–contrail separation in Fig. 1. We applied a linear decrease of the angle of attack (6.6°–1.4°) and an increase of true airspeed (207–249 m s−1) from an altitude of 5.4 to 10.5 km—within ranges prescribed in Airbus A320 flight operation manuals—in order to enable condensation of homogeneous droplets at a constant height of 0.2 m above the wing surface at all temperatures.

Fig. 8.
Fig. 8.

Sensitivity study of the HDN–HIN processes to different initial temperatures and saturation ratios, 30 m behind the trailing edge of the wing. (a) Concentration and effective radius of homogeneously nucleated droplets. (b) Optical depth. The green contour represents the visibility threshold. Schmidt–Appleman visibility threshold for combustion contrails (high-pass turbofan jet engine, standard atmosphere) is shown in blue. Combustion and aerodynamic contrails are only persistent if S0Si,sat (dashed gray line, both panels).

Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0362.1

Figure 8a demonstrates that the HN ice particle effective radius is nearly independent of the relative humidity. The reason is that the excess vapor density—water vapor available for particle growth—is determined for the most part by the ambient vapor density, which varies an order of magnitude with ambient temperature (Fig. 6). Variations in relative humidity have a minor impact on the vapor density (factor < 1.5), as does the halving of the temperature drop by increasing T0 from −50° to −20°C (factor < 1.6). The number concentration increases with both saturation ratio and temperature, because the nucleation rate depends on the relative, rather than absolute humidity. There is a maximum number of ice particles (2 × 106 cm−3) that is not apparent in expansion chamber experiments performed under similar conditions. This is an important model result that we will address in the next section.

Aerodynamic contrails are generated within a broad range of atmospheric conditions. When water saturation is assumed in the model, visible aerodynamic contrails (Fig. 8b, green contour) are generated at T0 ≥ −49°C, but in reality water saturation is not expected at temperatures colder than −38°C. When we lower the relative humidity closer to ice saturation, a visible trail forms at about −20°C. Aerodynamic contrails are not visible at a water saturation ratio below 0.76. Comparing both panels it appears that contrail visibility is highly correlated with the number of homogeneous droplets that are generated over the wings: the higher the temperature and saturation ratio, the more HN droplets nucleate and the more visible a contrail is. This may explain the high visibility of aerodynamic condensation near the ground. The effective particle radius varies across one order of magnitude and is important only as a lower limit for the optical depth.

Because aerodynamic contrails are sometimes observed coexisting with combustion trails (Unterstrasser et al. 2012 and our Fig. 1), we can evaluate the threshold visibility temperature of the trails using the well-established Schmidt–Appleman criteria (Schmidt 1941; Appleman 1953). Visible combustion contrails can form below temperatures as high as −37°C, but the precise threshold temperature depends on the ambient vapor mixing ratio and fuel properties, such as amount of water vapor and heat produced (Schumann 1996) as well as the engine propulsion efficiency (Schumann 2000). In Fig. 8b we have added the environmental conditions for visible combustion trails for a commercial jet aircraft flying at cruise speed in a standard atmosphere (blue line) by calculating the threshold temperature corresponding to each P0Sw,0 combination and using engine parameters for a B747 burning kerosene listed in Schumann (1996). From T0 = −51° to −38°C and Sw,0 ≥ 0.8, aerodynamic and combustion contrails can be observed simultaneously.

5. Discussion

Validation of our model results remains a challenge, because observations are limited to individual cases where the contrail angular distance to the sun is less than 30° (Gierens et al. 2011) and characteristic irisation can be distinguished (Fig. 1) or where the ambient temperature is clearly too high for combustion contrails. Furthermore, determining the atmospheric conditions associated with an observation relies on accurate radiosonde measurements or reanalysis data often not resolved at high temporal (<1 h) and spatial (<1 km) resolutions associated with (aerodynamic) contrail formation and ageing (Schumann 1996). Finally, even if the aircraft type and ground speed are known, assumptions have to be made about the true airspeed (dependent on the wind speed and direction) and angle of attack. Given these uncertainties, our model adequately predicts visible aerodynamic contrail formation in the −32° to −55°C temperature range derived from the observations in Fig. 1, Kärcher et al. (2009), and Gierens et al. (2011), as well as the coexistence of aerodynamic and combustion trails.

If the radiosonde measurements associated with Fig. 1 are representative of the air mass in which the contrail formed, they suggest that aerodynamic contrails could be visible at a lower water saturation ratio than the 0.76 limit value we calculated. Possibly the moisture from the engine exhaust could contribute to additional particle growth (not modeled). Conversely, the HN ice particles generated over the wing are of minor importance as condensation nuclei in combustion contrail formation, because the number of ultrafine particles that could act as CN (Kärcher et al. 1998) in the exhaust stream 30–50 m behind the wing is much higher (n = 107 cm−3; Schröder et al. 1998; corrected for dilution using Schumann et al. 1998) than the peak number of HN ice particles (n = 106 cm−3), especially after mixing with ambient air.

An alternative model validation method is to check whether the aerodynamic contrails’ iridescent appearance can be reproduced. A detailed analysis of aerodynamic contrails’ optical properties was performed by Kärcher et al. (2009). Iridescence requires 1) a monodisperse population of 2) particles with diameters similar to the wavelength of light in 3) high enough concentrations to produce a layer with optical depth ≥ 0.01. To be consistent with the observations in Fig. 1 the required optical depth and particle size must be reached within 30 m after leaving the wing. Figure 9 shows the evolution of the ice particle effective radius behind the wing for T0 = −30°C and Sw,0 = 0.9. Between 20 and 50 m behind the leading edge of the wing, the peak effective particle radius increases from 0.5 to 0.9 μm, with a geometric standard deviation (σg) that remains well below the monodispersity threshold value of 1.25. The optical depth reaches ≥0.03 during the initial growth phase directly over the wing (Fig. 7). Fulfilling all the listed requirements, it is likely that the HDN + HIN process can produce an iridescent trail.

Fig. 9.
Fig. 9.

Time evolution of the HN ice particle effective radius, mean number concentration (nm), and the particle size distribution geometric standard deviation (σg) at increments of 10 m from the wing leading edge. Trajectories are shown in gray. A 2D cross section of the wing is shown in red. The wing leading edge is located at x = 0 and the trailing edge at x = 11.7 m. Ambient temperature and water saturation ratio were −30°C and 0.9, respectively. The airfoil angle of attack was 5.0° and the true airspeed 222 m s−1 [calculated using an altitude-dependent linear approximation (see text)], while the ambient pressure was derived from a standard atmosphere.

Citation: Journal of the Atmospheric Sciences 72, 9; 10.1175/JAS-D-14-0362.1

Conspicuously, particles in the layer directly above the wing do not grow to visible size but instead evaporate during recompression. The number of HN droplets peaks closest to the wing surface because the saturation ratio and thus the temperature drop largely determines the homogeneous nucleation rate. At a threshold temperature drop, the number of ice particles becomes so large that the maximum crystal size reached prior to recompression is limited by vapor depletion. This happens when the number of homogeneously nucleated droplets exceeds 2 × 106 cm−3. During the 40 ms of recompression, S decreases below Si,sat (Fig. 2) and survival of HN ice crystals depends on their sublimation rate, which scales inversely with particle size. Smaller particles and an extremely low vapor density ensure faster sublimation. Closest to the wing surface, ice particles are just small enough to sublimate entirely within the recompression timespan. This process explains the polydisperse particle size distribution (σg = 1.73) and peaking number concentration prior to recompression (the smallest particles have not yet evaporated) as well as the HN ice particle concentration maximum behind the wing trailing edge found in the sensitivity study (Fig. 8a).

The model predicts the formation of aerodynamic contrails at water saturation ratios of ≥0.8, well above ice saturation. It is therefore likely that aerodynamic condensation frequently occurs in, or directly above or below, supercooled water or mixed-phase clouds with temperatures between −8° and −38°C (Rangno and Hobbs 1983; Woodley et al. 1991, 2003). The ice particles produced may subsequently grow at the expense of preexisting cloud droplets through the Wegener–Bergeron–Findeisen process and precipitate from the cloud as visible streamers and—if the cloud is thin—may leave a visible hole where the liquid water droplets have either frozen and precipitated or evaporated (Heymsfield et al. 2010). Near airports, inadvertent cloud seeding can lead to local intensification of snowfall, clearly visible in radar imagery as bands of enhanced reflectivity correlating with aircraft tracks (Heymsfield et al. 2011; Lautaportti et al. 2014).

In liquid clouds—in addition to APIPs formed directly from vapor—ice particles can form through freezing of cloud droplets in the cooled air over the aircraft wing (Heymsfield et al. 2010, 2011). Using Gierens’s (2009) aerodynamic model, the maximum number of freezing cloud droplets can be estimated from the thickness of the homogeneous freezing layer above the wing, where Tmin ≤ −38°C (about 3 m at T0 = −20°C) and the number concentration of cloud droplets in an altocumulus cloud (≤120 cm−3; Fleishauer et al. 2002). Averaged over the 3-m homogeneous freezing layer, the concentration of frozen cloud droplets leaving the trailing edge is approximately three orders of magnitude smaller than the number of homogeneously condensed droplets (≤105 cm−3), under the assumed atmospheric conditions (T0 = −20°C, Sw,0 = 1), true airspeed (218 m s−1), and angle of attack (5.0°). However, homogeneous condensation may be less vigorous when the airspeed is reduced—for example, in level flight at lower altitudes near the cloud base, or during climbout.

A consequence of the high relative humidity required for visible aerodynamic contrail formation is that they remain an infrequently observed phenomenon because most aircraft cruise where the temperatures are colder than −40°C. Gierens and Dilger (2013) developed a climatology for aerodynamic contrail formation, combining global patterns of air traffic with global reanalysis data and used the less constrictive criterion of SSi,sat and an average overwing temperature of Twing ≤ −38°C for the formation conditions. They found that where the majority of commercial jet aircraft flight time is spent—at cruise altitude (150–350 hPa) outside the tropical belt (±30°)—the annual probability of ice supersaturated conditions is less than 20%. With the added elevated relative humidity constraint imposed by this study, the probability of aerodynamic contrail formation is further reduced. Combustion contrails, on the contrary, are only constrained by the ambient temperature because the engine exhaust supplies nearly all of the water vapor needed for particle growth (Schumann 1996). We underwrite the conclusion of Gierens and Dilger (2013) that the frequency of occurrence of aerodynamic contrails is unlikely to exceed that of combustion contrails.

The homogeneous droplet nucleation and freezing process may explain both aerodynamic contrails formed during cruise flight and overwing condensation visible during landing and takeoff. However, speed and other parameters differ strongly between cruise and landing or takeoff: for example, the magnitude and location of the pressure minimum over the wings changes during landing due to a steeper angle of attack, an increased wing area and drag due to flaps, and possibly turbulence. Changing the pressure distribution could influence the relative importance of liquid versus frozen HN particles in forming visible condensation. To establish the role of ambient liquid aerosol, an additional sensitivity study would be required to account for strong lower-tropospheric CN particle variations in concentration (101–105 cm−3) and size (0.01–0.1 μm) with location and altitude (Clarke and Kapustin 2010). Especially soot from aircraft exhaust near runways (n = 106 cm−3; Westerdahl et al. 2008) may act as CCN when activated (Koehler et al. 2009). Different threshold atmospheric conditions (T, S, and CN concentration) may apply for the formation of overwing condensation during landing or takeoff. Therefore, in this study we have limited our focus of APIPs visibility to aerodynamic contrails formed during out-of-cloud cruise flight.

6. Summary and conclusions

In this study we investigated in detail the formation process of aircraft produced ice particles due to the appreciable adiabatic cooling over aircraft wings during flight. We have examined the relative importance of two possible modes of aerodynamic condensation: solution droplet growth, followed by homogeneous freezing, or homogeneous condensation followed by homogeneous freezing. Toward this end, a parcel model was adapted to obtain growth rates of micron-scale solution droplets as well as nanometer-scale HDN clusters. Our key findings can be summarized as follows:

  1. Homogeneous droplet nucleation followed by homogeneous freezing is likely to explain visible aerodynamic condensation at ambient air temperatures between −20° and −50°C. Because combustion contrails form at temperatures below −38°C, there is little doubt that visible contrails are aerodynamically induced at higher temperatures.
  2. Up to 1 m above the wing surface, HN droplets are several orders of magnitude more numerous than ambient solution droplets and outcompete them for water vapor such that frozen and liquid aerosol particles remain invisible over and behind the wing.
  3. The visibility of nascent aerodynamic contrails is determined by the ambient relative humidity and number of ice particles that survive recompression at the wing trailing edge.
  4. Threshold conditions for simultaneous occurrence of aerodynamic and combustion contrails are T0 ≥ −50°C up to the warmest combustion contrail formation temperature, and Sw,0 ≥ 0.8.
  5. Commonly observed aerodynamic condensation produced by aircraft during takeoff and landing is likely due to homogeneous droplet nucleation, although depositional growth on soot with soluble components may be a key contributing process.

A detailed climatology of aerodynamic contrails based on the principles of homogeneous condensation and freezing has not yet been developed, and their global radiative forcing potential remains unknown. Because the ice particles produced are so small and have a unique growth history, the optical properties of ageing (subvisible) aerodynamic contrails may be very different from those of combustion contrails and natural cirrus. Aircraft measurements of APIP concentration, habit, and size distribution in well-definable atmospheric conditions (e.g., orographic wave clouds at temperatures > −38°C) could 1) verify model predictions, for example APIP concentrations exceeding those of ambient CN outside of jet exhaust plumes, and 2) provide insights into the micro- and macroscale development of the contrail optical properties. Such an experiment would involve laying out an aerodynamic contrail along the wind direction and sampling it perpendicular to the trail under known RH conditions and at regular time intervals.

Future work on the microphysics of overwing condensation could focus on the role of ambient aerosols at lower altitudes, where CN are more numerous, as well as on heterogeneous freezing of insoluble CN. In addition, our key finding that HN ice particles outcompete frozen solution droplets for water vapor has yet to be verified in the laboratory. Finally, more (quantitative) work is needed to better understand local meteorological effects and atmospheric relevance of APIPs near airfields, such as inadvertent local cloud seeding through the Wegener–Bergeron–Findeisen process (Heymsfield et al. 2010).

Acknowledgments

This work was carried out with support of the MMM/NCAR visitor fund and the National Science Foundation. We wish to thank Dr. Klaus Gierens for kindly providing the aerodynamic flow model and for his helpful comments on the manuscript. We thank Prof. Ulrich Schumann, Prof. Bernd Kärcher, and three anonymous reviewers for reviewing the manuscript and for their thoughtful suggestions. Thanks also go to Jeffrey Schäfer and Dr. Massimo Santacroce for allowing us to use their photographs, as well as Dr. Ben Murray for sharing his valuable insights on homogeneous nucleation.

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1

In the remainder of this paper, we will refer to homogeneously nucleated (condensed) droplets as “HN droplets” and to HN droplets that subsequently freeze homogeneously as “HN ice particles.”

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