Information about Hector, its air composition, and convective cirrus properties is available from the in situ measurements along the Geophysica flight path. The cold-point tropopause altitude was penetrated during the Geophysica ascent at 04:47 UTC (17 233 s). The tropopause was again reached at 25 296 and 26 039 s, and penetrated during final descent at about 07:25 UTC (26 700 s). The TDC cold-point temperatures at the first and last times are -87.3 and -87.1 ∘C, both at about 87 hPa pressure, 17.1 km pressure altitude, 17.4 km geometric altitude, and 375 K potential temperature. The MTP and ERA re-analysis data locate the cold-point tropopause slightly (100 to 400 m) deeper.

Figure 6 shows flight altitude, water vapor, ice particle, and nv aerosol concentration measurements during the stratospheric flight part. A similar plot with further data can be found in de Reus et al. (2009). We include earlier flight times because contrails formed in this early period. Events E1 to E6 (shaded time periods) between times 20 600 and 25 000 s (UTC times in Table 3) have been identified before by Reus et al. (2009). The six events are periods in which ice crystals were observed for at least 30 s at flight altitude. Event E6 was discussed in detail by Corti et al. (2008). The mean values of several parameters during these events were derived by de Reus et al. (2009) and are repeated in Table 3. The events occurred between 18 and 18.7 km with particle sizes between 12 and 25 µm in effective radius, reff, and 4.6 and 9.3 µm in volume mean radius, rvol. The small ratio C=rvol/reff indicates that most of the particle volume is controlled by a few large particles (Schumann et al., 2011), here measured by CIP, with maximum diameters exceeding 100 µm. The IWC reached up to about 1 mg m-3, which was assessed high compared to a climatology for low-temperature cirrus (Schiller et al., 2008). The relative humidity over ice, RHi varies between 75 and 157 % in these data. Only two of the six events (E2 and E4) exhibit ice supersaturation.

We note three additional shorter periods with ice crystals, E0, E7, and E10, also listed in Table 3. For about 15 s, around time 18 780 s, the FSSP measured ice particle concentrations up to 0.013 cm-3. This event E0 was accompanied by a significant increase in total water concentration from FISH (see Fig. 6b) though the data for t < 19 800 s did not pass outgassing quality checks (Krämer et al., 2009). We also find a slight enhancement in the depolarization signal at 532 nm wavelength of MAS, but no increase in the COPAS aerosol signals. Later, at times shortly after 21 633 and 22120 s, two short-duration ice events (E7 and E10) are found. During event E9 (22 008 s), the FSSP100 sampled only a few ice particles, but radar data (Sect. 3.2.4) indicate that this is an ice event. In addition, we see several “dry” events, without ice, with enhanced nv aerosols. For most events, at least one “large” ice particle > 25 µm was observed by CIP. CIP counted no ice particles during the ice events E0, E4, E7, E9, and E10.

In order to find indications for whether these ice or dry events could be caused by Geophysica exhaust plumes or not, we search for plume encounters, as illustrated for event E1 in Fig. 3, i.e. closest approaches of the advected plume from past flight parts with the actual flight position. Table 4 lists related analysis results with event name, day, age, and time of event, the geometric altitudes z of the Geophysica at the event, with altitude and wind changes Δz, Δu, Δv, and Δw required for perfect match, and related potential temperature changes Δθ. For event E6, we found that the measurements may have occurred in a superposition of contrails from four earlier flight segments. However, not all events are contrails. In fact, events with large negative Δθ (-16 K for event E2) would require strong descent of the air if it contains a contrail, which would likely lead to adiabatic warming and contrail evaporation (Greene, 1986; Unterstrasser and Sölch, 2010). Strong updrafts could enhance contrail ice water content. The symbols in Fig. 6a identify the times and altitudes of the events listed in Table 4, with open symbols for potential plume formation (C), and closed symbols for encounters (E).

Figure 7 shows a map with the complex Geophysica flight path. During ascent and final descent the Geophysica flew often in upper tropospheric cirrus with significant IWC > 0.01 mg m-3 (gray symbols). Stratospheric cirrus were measured while flying over the Tiwi Islands. The red symbols with event labels identify positions of computed plume and contrail encounters. Encounters of dry plumes (red outside blue flight parts) occur mainly at the periphery and to the north-east of the convective region, i.e., on the windward side in the stratosphere. This includes the events E7 and E8 with maximum nv concentrations. Event E0 without Geophysica exhaust occurred on the southern side. Event E2 coincides with the location of minimum temperature (blue star in Fig. 2a) and event E5 is close to the position of maximum temperature (red star in Fig. 2a), both occurring closely together in the cirrus flight parts over the center of the Tiwi Islands, possibly because of strong updrafts and downdrafts.

The nv aerosol peaks reach concentrations up to 1000 cm-3 in the 15 s running average measurements (up to 3300 cm-3 in the 1 s data). The magnitude of the aerosol peaks can be explained quantitatively with the nv aerosol emission index derived in the Appendix. Since NOx data are not available for this flight, we estimate plume dilution from the empirical dilution law, Eq. (4). This dilution has been derived from exhaust measurements at low to moderate turbulence and assumes penetration of the plume center. The computed concentrations are depicted by black circles in Fig. 6d. They reach the magnitude of the measured concentration peaks. Hence, it is possible that the nv aerosol peaks could be caused by Geophysica engine emissions.

For exhaust plumes at, e.g., 2000 s age, for dilution from Eq. (4), and for emission indices as given in the Appendix, we would expect peaks of 0.71, 0.65, and -0.82 nmol mol-1 for CO2, CO, and O3 (from NO titration; Zheng et al., 1994; Schulte et al., 1997), and 122 cm-3 for nv particles. Temperature may increase by 0.1 K from combustion heat. More important are temperature changes after mixing of descending wake vortices with ambient air of up to about Δθ= -5 K (see Sect. 2.3). For overshooting convection, we expect positive CO2 and CO and negative O3 mixing ratio and θ deviations correlated with positive H2O mixing ratio and aerosol concentration peaks. Hence, we expect to see the same correlations for aircraft plumes as for overshooting convection, though with smaller magnitude and with narrower plume shapes. IWC and potential temperature are not conserved during mixing with phase changes.

Scatter plots as shown in Fig. 8, but without the CO2 data, have been used before to obtain insights into the air mass composition along the flight path and their correlations to tropospheric or stratospheric origins (Chemel et al., 2009; Frey et al., 2015). The scatter plots show compact correlations of CO, O3, and H2O molar mixing ratios with potential temperature θ. CO2, and CO shows a generally decreasing trend with altitude (θ) while O3 is increasing, as expected. Still the correlation with θ appears slightly less compact for CO2 than for CO and for O3, possibly reflecting different lifetimes and different air mass origins. On average, the H2O mixing ratio was near ice saturation below 400 K and ice subsaturated above. Lifting would cause clouds to form preferentially in the more humid layer above 390 K potential temperature.

Between about 375 and 390 K, just above the tropopause, we see a vertical range of low CO2, low CO, and high O3, coinciding with low H2O and low IWC. The observed θ–CO–O3 correlations could not be explained with overshooting convection alone (Frey et al., 2015). Instead, horizontal advection of a drier and less polluted air mass from the east, with more humid air above that layer, may explain the observations. In fact, the local wind profile and 10-day trajectories (Brunner et al., 2009) show that the tropospheric and stratospheric air masses come from different directions.

The mass-specific particle concentration follows a correlation with θ very similar to that of CO. Hence, the nv aerosol and CO near the tropopause may both stem from a similar source (Allen et al., 2008; Heyes et al., 2009). However, the aerosol peaks in the range 390 < θ < 430 K, without similar peaks in CO, O3, or CO2, stand out. They cannot be explained by overshooting convection. Also, the high IWC events stay out of the correlations. The observed IWC is higher than in model simulations (Chemel et al., 2009). Similar IWC values are found near θ≈ 400 and 360 K. Latent heat release from water condensation and freezing during deep convection may cause a temperature change ΔT=LΔq/cp≈ 40 K (L = latent heat of fusion; cp = specific heat capacity at constant pressure) only when very humid boundary-layer air (with more than 1 % water vapor mass content q) gets transported without dilution from the surface up to 400 K, which is not very likely. Additional water and heat may come from lateral advection and, to minor degree, from aircraft water emissions.

Figure 8e is similar to the one shown by Corti et al. (2008), with high IWC above the tropopause. Most of the high IWC data shown in that study come from measurements during this 30 November morning flight. Based on the number of points within 10 s relative to related computed plume encounters (red symbols), contrails contribute little to the overall IWC results. However, 10 s segments may not be representative for the whole aircraft effect.

For analysis of the origin of the aerosol peaks and ice events, we refer to Fig. 9 with in situ measured signals at sufficient time resolution to identify details for the events E1 to E3, E7, and E8. Similar plots are available for the later events (Figs. S5, S6). From these figures one may try to classify the events as convective (C) or as exhaust (E) events or as a mixture of both (C+E), and we have listed our best estimates in Table 4, and these are supported by further evidence discussed below. For each event we evaluate local scatter plots, as shown for E7 in Fig. 10, and for E2 in Fig. S6. Here red points represent the data during the event duration, the blue points the neighborhood as measured shortly before and after the events, and the gray symbols show all data to characterize the variability and mean changes with altitude.

This information indicates that event E2 is likely caused by a high-reaching convective updraft, which raises air over an altitude range of 16 K in potential temperature, corresponding to about 440 m vertical ascent (see also Fig. 2b). The high CO and low O3 indicate air mass transport from slightly above the tropopause. The presence of large ice particles measured with CIP likely come from the cloud elements transported upward. The nv aerosol is slightly enhanced (about 50 cm-3) but not very high and, hence, may come from tropospheric pollution, but contributions from Geophysica exhaust cannot be excluded (C+E). CO2 is not enhanced, as one would expect for tropospheric air, but comes from the low-CO2 layer near 380 K.

The other ice events are less clear. Event E1 exhibits high total water, and many large ice particles, slightly enhanced CO2 indicating tropospheric air, but no related CO or O3 peaks. So this may be air transported horizontally from a convective tower, with mixing reducing the signatures. The mixtures may contain aircraft exhaust and contrail ice. Similar findings apply to E5, E6, and E9.

Event E7 appears to be likely a contrail. This follows from the high CO2 and high CO, significantly above instrument precisions, and slightly reduced O3, a small enhancement in gaseous H2O, a large peak in nv aerosol, and at least a few ice particle counts in spite of humidity below ice saturation. The CO peaks reach about 10 nmol mol-1 with related CO2 peak of ∼ 0.5 µmol mol-1. If these species come solely from engine exhaust, this would imply a CO emission index of 40 ± 10 g kg-1, not unrealistic compared to other measurements (Zheng et al., 1994; Fahey et al., 1995; Slemr et al., 2001). E8, E11, E12, and E13 show similar signatures, without ice, and are all potential exhaust events (E).

Evidence for the presence of cirrus clouds above Hector during the morning flight of the 30 November was provided earlier by the downward-looking lidar (MAL), mounted on the Geophysica. Figure 11 shows a plot of the MAL backscatter ratio versus time and altitude similar to the one shown by de Reus et al. (2009), and in part also by Corti et al. (2008), but including larger time and altitude ranges and higher temporal and vertical resolution. Here we have added the computed locations of potential contrail positions in the lidar curtain below the aircraft as a function of flight time and altitude. This shows that the lidar might have seen Geophysica contrails. In particular above 17.5 km altitude, between t= 20 000 and 26 000 s, at the times of the potential contrail events E1 to E13, we see several narrow clouds with low backscatter ratio at times and altitudes in approximate agreement with computed positions. Some potential plumes between 22 000 and 24 000 s above 17.5 km, related to the “dry” events in Table 4, show no corresponding backscatter cloud, possibly because of drier air with quickly sublimated contrails. The backscatter clouds are about 200 m deep; similar to a possible contrail depth. This figure shows the plume positions as computed for nominal mean wind. Variable wind and turbulence could cause slightly different plume encounter positions. If we would allow for additional vertical contrail spread by turbulence or by ice particle sedimentation, the simulated pattern might show even closer similarities to the observations.

Below 17.5 km, we see many high-backscatter clouds (backscatter ratio up to 300) at horizontal scales on the order of 200 s or 40 km and more than 1 km depth. The depolarization signals (not plotted) reach values of 30 to 70 % with the larger values for the lower and thicker clouds. These clouds are cirrus clouds, mainly in the Hector anvil. Cirrus clouds are detectable below 15 km when averaging the data over larger intervals. The lower cloud boundary or the optical thickness of the cloud below the aircraft cannot be derived from these data. MAL is a small instrument with energy per shot (3–4 µJ) and telescope aperture diameter (5 cm) limiting the signal-to-noise ratio, in particular during day time, as in this flight. The MAL lidar penetrated the cloud layer down to ground only rarely and in regions with thinner clouds near the outer edge of the anvil. Optical depth analysis was possible, however, for nighttime observations (Frey et al., 2014).

A stratospheric anvil, possibly with contrail cirrus, can be detected with DIAL (Poberaj et al., 2002; Wirth et al., 2009) and characterized in terms of occurrence, geometric scales, optical depth, and particle sizes. The lidar was mounted on board the DLR Falcon research aircraft in zenith-viewing direction during the SCOUT-O3 measurements near Darwin. Results from the same instrument during TROCCINOX are described in Kiemle et al. (2008). Water vapor profiles could be obtained during this flight only in the lower part of the cirrus clouds and underneath, because of high signal extinction within the cirrus. But, the backscatter channels at 532 and 1064 nm wavelength were most often able to record the top of the cirrus clouds, as well as layers of thin cirrus above. The backscatter ratio is the ratio of air molecule plus ice particle to solely air molecule backscatter coefficients, for an assumed lidar ratio (the ratio between extinction and backscatter coefficients) of 20 sr. The backscatter signals at 532 and 1064 nm wavelengths show similar results but the near-infrared backscatter gives the less noisy result. The Falcon and Geophysica flew simultaneously along different flight paths near Hector; the Falcon flew at altitudes below 11 km, and therefore the Falcon lidar may have observed parts of the aged Geophysica contrail.

Stratospheric cirrus up to 18.2 km altitude was observed only during the last part of the flight, 2 h after convection started, at times when also Geophysica plumes advected into the lidar beam. Figure 12 shows the observed backscatter signal for the flight period 07:35 to 07:41 UTC when the Falcon was below the southern Hector anvil. The thicker cirrus between 12 and 16 km altitude belongs to a tropospheric anvil part. The Falcon was flying in cloud-free air below this anvil. The stratospheric anvil is composed of two layers, with dimensions as listed in Table 5 (width computed for the Falcon ground velocity of 205 m s-1 in this period). The positions of computed plumes are superimposed on the 1064 nm backscatter result. We find that all prominent cirrus layers above 17.4 km, i.e. above the tropopause, occur when also contrails might be present. At least part of the observed cirrus could be contrail generated. Such stratospheric contrails would have ages of more than 1 h (up to 3 h), which is not unrealistic (Schumann and Heymsfield, 2017). During this time, the contrail advected from the Hector core by 50 to 100 km distance and might have widened through mixing and wind shear. Note that the contrail orientations are not perpendicular to the lidar picture and, hence, may appear wider than they are. In particular, the upper layer coincides with computed positions for both the lower and upper edges of the contrails (red and blue triangles). Most coincidences occur in the thicker part of the upper layer between 07:37 and 07:40 UTC but some also in the very thin branches a few minutes earlier and later. The age of the plumes is shown in the second panel of Fig. 12 and the mean ages and altitudes of the two anvils are listed in Table 5.

Figure 12 includes the color ratio. The color ratio is the ratio between the backscatter coefficients at 532 and 1064 nm wavelengths. It is close to unity in the tropospheric parts of the observed cirrus, suggesting scattering of particles that are larger than the lidar wavelengths (geometric optics regime, observable in the lower and denser parts of the cirrus). The color ratio is clearly above 1 (near 2) in the optically thinner stratospheric cirrus, suggesting smaller particles in the Rayleigh scattering regime. The color ratio is large in the gaps between the stratospheric cirrus layers likely because of very small sublimating ice particle in those gaps. The color ratio shows that the cirrus in the stratospheric anvil was composed of ice particles much smaller than in the troposphere.

Figure 12 also includes the optical depth of the cirrus layer, i.e., the vertical integral of the extinction coefficient. Note that multiple scattering by ice crystals, mainly in the forward direction, may cause the optical depth to be underestimated, by possibly 40 % for large ice particles with effective radii > 100 µm (M. Wirth, personal communication, 2016). This should be a minor issue for the thin cirrus in the stratosphere with small ice particles. The effective particle sizes for events E1 to E6 (Table 3) are below 26 µm (de Reus et al., 2009). The optical depth of the layer between 07:30 and 07:35 UTC is about 0.03 and therewith just at the edge of visibility by eye. The upper of the two cirrus layers, seen at 07:37 to 07:40 UTC in Fig. 12, has maximum optical depth of about 0.04, the one further below about 0.08.

The total extinction of the stratospheric anvils, listed in Table 5, can be related to contrail formation. The “total extinction” or “extinction area” (EA) is a term defined, e.g., in Unterstrasser and Gierens (2010), as the integral of extinction ε over the cross section area A of the cloud. Here we compute EA = ∫τdx over horizontal elements dx in flight direction with τ=∫εdz integrated over vertical elements dz within the cirrus layer. The EA values have been computed numerically from the Falcon lidar data separately for the two stratospheric anvil clouds; see Table 5. For an order of magnitude estimate, we compute the number of ice particles Nice in the anvil per cirrus length perpendicular to the lidar plane, and compare it to the number Nnv of nv exhaust particles per contrail length that might nucleate contrail ice particles. The value of Nice can be estimated for given EA and particle sizes from Nice= EA/(Qextπrarea2). This relation comes from the definition of the area radius rarea relating the mean ice particle cross section area πrarea2= Aice/Nice to the total area Aice and to the total number of ice particles per length Nice; see Eq. (7) in Schumann et al. (2011). The total area Aice is related to the mean extinction efficiency Qext by EA = Qext Aice. Assuming Qext≈ 2 and rarea≈reff≈ 15 µm, as observed for low temperature cirrus (de Reus et al., 2009; Heymsfield et al., 2014), we compute Nice= 0.45 to 1.07 × 1012 m-1. For comparison, the number Nnv of nv particles emitted per flight distance is Nnv= fmF PEInv, where PEInv is the particle number emission index (see Appendix) and f (1 to 5) the number of contrail parts crossed along the curtain. The fuel consumption per flight distance mF is about 1.2 g m-1 at cruise (∼ 846 kg h-1, Weigel et al., 2009). The particle emission index was estimated as PEInv= 2.6 × 1015 kg-1. This implies Nnv= 3 to 16  × 1012 m-1. The number of nv particles per flight distance is 3 to 35 times larger than the number of ice particles per cirrus length. Hence, the amount of exhaust particles is large enough to possibly explain the lidar-observed cirrus layers, in particular the upper one, by contrail cirrus.

The CPOL radar provides information about the Hector cloud morphology and microphysics in space and time based on radar reflectivity at 5.4 cm wavelength (May and Keenan, 2005). For monodispersed water droplets of diameter d and concentration n, the reflectivity factor is ZR=nd6. For ice particles, the ZR value is ∼ 0.2 times smaller because of lower refractive index but may be larger because of non-spherical shapes. Often one uses a logarithmic ratio Z of ZR relative to the reflectivity Z0 of a raindrop with a diameter of 1 mm in decibel (dBZ) (Hagen et al., 2012), so that ZR=Z010[(Z/dBZ)/10]. Values of Z above 40 dBZ indicate heavy precipitation. The reflectivity in cirrus anvils is often below 5 dBZ. A stratiform anvil near the tropopause and parts of the non-precipitating anvil clouds should be detectable, except for thinner cirrus layers detrained from the main convective system. The signal-to-noise ratio decreases with distance, here up to about 120 km. For weak reflectivity from large distance, the radar patterns plotted are sensitive to interpolation in the gridded data. In a few cases, the radar measured reflection from the aircraft structure (see Supplement). Contrails cannot be detected by the radar.

Figure 13 (bottom) shows the Geophysica flight path overlaid on the radar signal for the time interval including events E7 to E10. In the vertical curtain along the flight (lower panel), we see that Hector induces Z exceeding 40 dBZ in the troposphere up to about 14 km above ground. Between 14 and 18 km, Z is lower (< 15 dBZ), and a single faint cloud part (5 dBZ) is found at 20 km height, i.e., 2.6 km above the tropopause. The aircraft flew near 18 km height, above cloud parts with high reflectivity, but essentially in air masses with Z near 5 dBZ, so possibly in anvil cirrus. The data show that Hector is a mesoscale convective system with many updrafts and downdrafts (Huntrieser et al., 2009). The stronger updrafts typically have a diameter of 10 to 20 km, as visible in the horizontal cross section (upper panel).

In further such images at other times and heights (available at ftp://ftp.bom.gov.au/anon/home/cawcr/perm/; see Supplement), one finds Z values exceeding 30 dBZ above 17 km at the eastern edge of the Tiwi Islands after 04:45 UTC. Event E0 occurred in air with low Z above a strong tropospheric updraft. Event E1 occurred in a forward (upshear-tilted) anvil produced by a strongly overshooting cell (still 30 dBZ at 18 km) located to the north-west of the E1 location. The convection was most active during the times of E1 to E3. During E2 and E3 (Fig. 13, top), the Geophysica flew within about 5 km distance of a strong updraft with reflectivity reaching 30 dBZ. The updrafts were far weaker for E4 to E6. E4 and E5 occur in the remainders of clouds above dissipating convection. Event E9, for which only few ice particles were sampled in situ, is indeed an ice event close to a fresh overshooting cell near 10 dBZ. The Geophysica never passed through the center of an updraft but sampled the uppermost parts of convective clouds.

When comparing to the lidar results, it becomes obvious that clouds with high radar reflectivity occurred below 15 km altitude, not visible to MAL, as expected. The strong cloud backscatter seen in the MAL data (Fig. 11) during the dive between 25 000 and 26 200 s come from clouds below the flight level during a flight leg towards a turning point outside the Hector cloud. The optically thin anvil clouds seen by the Falcon lidar, which were observed while the Falcon flew south of strong updrafts, are not detected in the CPOL data.

The exponent of the relationship between Z and IWC, IWC ∼ ZRb, for the C-band is qualitatively similar to those for other radar wavelengths, with b in the range 0.55 to 0.65 (Liu and Illingworth, 2000; Hogan et al., 2006; Protat et al., 2016). The CPOL reflectivity for E2 is between 5 and 10 dBZ, which translates into IWC of 0.76–1.5 mg m-3 at T= -87.1 ∘C, using the Hogan et al. (2006) temperature-dependent relationship. This is in good agreement with the in situ measurements (Table 3). Relating ZR to Z as explained above, one finds that the IWC at 30 dBZ is a factor of 30 ± 10 larger than at 5 dBZ. Hence, the IWC in the overshooting clouds was more than a factor of 20 higher than measured in situ at the same heights in the neighborhood.

Satellite data provide information on Hector and its anvil. The AVHRR data have better spatial resolution than the geostationary satellite data discussed in previous SCOUT-O3 papers (Brunner et al., 2009; Chemel et al., 2009; Frey et al., 2014). NOAA-15 and NOAA-12 Hector overpasses occurred at 05:16 and 7:43 UTC. The two satellites observed Hector in its early active phase (04:47 to 07:00 UTC, 14:17–16:30 LT) and mature phase (Frey et al., 2014). The image for the first overpass is available in Fig. S8. Figure 14 shows the image for the second overpass, nearly simultaneously with the Falcon lidar observation of the southern anvil. The figure includes the flight path of the Geophysica until the satellite-overpass times. The general pattern is consistent with model studies (Frey et al., 2015), and also with the ice event locations measured in situ (see Fig. 7) and the radar data. The highest and thickest part of Hector occurs first over the eastern and later over the western parts of the Tiwi Islands. The low-temperature convective core of Hector extends over about 80 and 140 km in east–west and 50 and 60 km in north–south direction, and the BT minima are 180.1 and 184.2 K at 12 µm and 180.1 and 185.6 K at 10.8 µm, in the two images. Local overshoots are detectable as small cool spots of a few AVHRR pixels in the BT results when adapting the color scales to a narrow temperature range from 183 to 205 K. They are better seen in the radar signals, where we see cloud tops up to 20 km. The data indicate cloud-top temperatures below -93 and -89 ∘C, 6 and 2 K cooler than the cold-point tropopause. For an adiabatic lapse rate, which is close to the dry lapse rate g/cp (g= gravity) at these temperatures, the temperature differences suggest overshooting by about 620 and 200 m above the tropopause (Bedka et al., 2010), up to 18.0 and 17.6 km altitude, at these times. These altitudes are 600 to 700 m smaller than the cloud tops observed by lidar, see Figs. 11 and 12, and possibly 1000 m lower than clouds tops from radar. Hence, there were optically thin cirrus clouds, including contrails, above the optically thicker cloud parts, besides spotty convective towers. The radar signals indicate about 2 km lower cloud tops at the second overpass time compared to the first one.

We find positive BTD values outside the optically thick Hector cloud on the southern (leeward) side, likely from the anvil cirrus with small ice particles. Figure 14 includes the computed positions of the potential contrail for the time since the aircraft reached the stratosphere (cyan curve). The Geophysica is descending and returning towards Darwin after having surrounded the north-west corner of the Hector core. However, line-shaped cloud structures, possibly from Geophysica contrails in the anvil cirrus, could not be detected in the BTD signals. They may be too thin optically to be detectable this way. Also, when there are clouds below, they would overwhelm the signal, leaving the contrails undetected.

Hector is not alone. Deep convection over northern Australia has often been observed in radar data (Hassim et al., 2014), and can also be seen for this event east and south of Hector in the satellite images. An analysis of backward trajectories for the time period between start of convection (assumed at 03:00 UTC to allow for wind underestimates) and time of peak aerosol measurements (Fig. S8) shows that the convective tower east of Hector did not provide the high aerosol values that were measured with COPAS over Hector.

Interestingly, we also see a band of slightly negative BTD values along the northern edge of the Hector cloud, which is not present on the southern side. An explanation of this pattern requires a more detailed study. Such a study should include different absorption by optically thin clouds with different particle sizes (Inoue, 1985), wind-driven or convective uplift possibly causing pileus clouds (Garrett et al., 2006), presence of nitric acid, which has an 11 µm absorption band (Chepfer et al., 2007), the satellite viewing angles, and three-dimensional radiation transfer.

The MTP measures the temperature profile ahead of the aircraft from which one can derive isentropes along the flight path (Denning et al., 1989). The MTP instrument averages along line of sight segments of a few kilometer lengths. Figure 15 shows the tropopause and the isentrope altitudes, measured ±2 km above or below aircraft. The plot versus longitude identifies the flow pattern over the convective system. The mean wind comes from the east in the stratosphere. We see systematic waves on the western downwind side, supporting the reproducibility of the measurements. The variance z′ of the isentropes varies from 200 m at 370 K to 90 m at 430 K; far more than for the 16 November flight (Table 2). The variances reflect the convective activity in Hector decreasing with altitude. The isentropes are higher (by about 100 to 50 m, decreasing with height) over the center than at the boundaries of Hector. Hence, we find a systematic flow pattern with stratospheric air coming from the north-east passing over and around the convective core of the Hector cloud as if it forms an obstacle with lee waves downwind. Air from overshooting convection, after cooling by ice sublimation may contribute to this flow. Large vertical motions occur in particular near the tropopause.

First we characterize mixing. The observed width W ≈ 3 km of the contrail caused by differential lateral advection of the upper and lower edges of the wake with vertical separation D ≈ 180 m over its age ≈ 3000 s indicates a wind shear of S=W/(age D) ≈ 0.006 s-1. Wind shear might excite turbulence if the Richardson number Ri = NBV2/S2 is low (Turner, 1973). Here, strong stratification (NBV≈ 0.03 s-1), apparently larger than the shear, causes large Ri = 30, and may have prevented turbulence. The level of turbulence in the ambient air is unknown, but the MTP data indicate small variability z′ of the isentrope altitudes at horizontal scales > 10 km in this time period (see Table 2), implying small vertical gravity wave velocities w′ ≈ z′ NBV, of 6.5 and 19 cm s-1 for the upper and lower contrail altitude ranges, without mixing by breaking waves. The contrail formed downstream of a weak and dissipating Hector cloud (Brunner et al., 2009). Hence, turbulence was weak in the stratosphere in this case, and this could explain why parts of the contrail experience little dilution.

The classical (Schmidt–Appleman) thermodynamic contrail formation process is illustrated in Fig. 16, adapted from Schumann (1996) for the stratospheric conditions. The mixing line in this plot represents conditions in the plume varying from engine exit conditions (high temperature and high humidity at the right end of the mixing line) to ambient air conditions (temperature and partial water pressure at point E) with increasing dilution Ndil, if without phase change. The mixing-line gradient G=cp p EIH2O (Mair/MH2O)/[Qc(1-η)] depends on pressure p, water emission index EIH2O, molar mass ratio (Mair/MH2O)≈ 29/18, fuel combustion heat QC= 43.2 MJ kg-1, overall propulsion efficiency (η≈ 0.1 for this descending flight section), and on the specific heat capacity cp= 1004 J (kg K-1). G is smaller for the upper contrail because of lower pressure. The ambient temperature is far below the threshold temperature for liquid contrail formation, LC, with maximum liquid humidity in the plume, as listed in Table 2. There is no doubt that contrails formed during the whole Geophysica flight above about 13 km altitude, even for zero ambient humidity.

The point I2, at the lower-left end of the mixing line, close to ambient conditions E, is defined by the second intersection between the mixing line and the ice-saturation curve. I2 is reached for a dilution Ndil,I2=QC(1-η)/cpTI2-TE, where TI2, the temperature at point I2, is computed according to the given definition, and TE is the given temperature in the environment. For given G and measured RHi, we compute Ndil,I2= 1.0 × 106 for the upper and 5.2 × 106 for the lower contrail. For fully dry air (RHi =0̇), the value of Ndil,I2 is lower: 0.35 × 106 and 0.68 × 106.

For orientation, we note that the dilution of the Geophysica exhaust plume is first caused by the aircraft-induced turbulence, and reaches a value of about Ndil=ρA/mF≈ 0.5 × 106, when we assume that the exhaust from burning fuel at mass flow rate mF per flight distance (mF≈ 1 g m-1, an estimate for slow descent) gets uniformly mixed over the plume. Here, density ρ is known, and the cross section A of the young wake vortex may be estimated from A= 3 s2 (Greene, 1986; Schumann et al., 2013a), where s= 37.5 m is the wing span of the Geophysica. Hence, the contrail survives wake dilution since the dilution at the end of the wake phase is too low to dilute the humidity in the exhaust plume below ice saturation.

For known dilution Ndil,I2, one may estimate the corresponding contrail age tI2 by inverting the dilution law, Eq. (4), Ndil,I2= Ndil(tI2). Of course, the result depends on this dilution law. Moreover, the result depends strongly on the assumed ambient humidity RHi. Here, we find that the exhaust stays ice supersaturated until ages of 140 to 2400 s for RHi from 0 to 0.9, and stays longer only for nearly ice-saturated ambient conditions with RHi > 90 %; see Fig. 16.

This concept explains why the lower contrail persists until an age of about 1680 s for RHi < 87 % as measured in the lower stratospheric part of this flight. However, it does not explain nearly 1 h age for the upper contrail for the assumed dilution law. It suggests that mixing in the stratosphere is slower than suggested by Eq. (4). In fact, for a factor 0.25 reduced dilution (thin curves), the lifetime can be explained also for the upper contrail with RHi about 64 %.

Future numerical simulations of the contrail dynamics, including the ice microphysics and turbulent mixing in the aircraft wake, should overcome limitations of this thermodynamic analysis. The mixing concept assumes that the sublimation timescale tsubl≈ (4πDH2O nicer)-1 is small compared to the plume age. The tsubl depends on water vapor diffusivity DH2O in air, and on the number (nice) and size (r) of the ice particles (Korolev and Mazin, 2003). For constant pressure, the water vapor diffusivity is nearly 50 % smaller at -87 ∘C (∼ 1.5 × 10-4 m2 s-1) than at -50 ∘C (Pruppacher and Klett, 2010), but the particle concentration is high. If each nv particle nucleates an ice particle, the ice number concentration would be nice≈ρ PEInv/Ndil(t) in the plume at age t, and high because of the large particle emission index PEInv. Therefore, the timescale of sublimation stays far below the plume age, even for a radius r= 0.1 µm, a limit of visibility (see Supplement). For small ice particles, the dependency of the equilibrium vapor pressure on the ice surface tension (the “Kelvin effect”) should also be taken into account (Lewellen, 2014). It would contribute to quick sublimation of the smallest ice particles.

Figure 17 shows the change of mean temperatures in the contrail plume with time. Consistent with the Schmidt–Appleman mixing concept and dilution definition (Schumann et al., 1998), the plume temperature, the molar water vapor, and nitric acid mixing ratios, T(t)=TE+QC(1-η)/cpNdil(t),H2O(t)=H2OE+EIH2OMair/MH2O/Ndil(t),HNO3(t)=HNO3E+EIHNO3Mair/MHNO3/Ndil(t), exceed ambient conditions (E) because of the combustion emissions. We do not know the HNO3 emission index EIHNO3 for the Geophysica. Previous EIHNO3 measurements behind commercial aircraft at cruise range from 0.06 to 0.8 g kg-1 (Arnold et al., 1992; Schumann et al., 2000). For a lower bound estimate of NAT contributions, we assume EIHNO3= 0.06 g kg-1. The frost point and the NAT existence temperatures, TICE and TNAT, are calculated for given mixing ratios and ambient pressure inverting known relationships (Hanson and Mauersberger, 1988). These temperatures approach the values listed in Table 2 after infinite dilution.

The plots show the results for high (Ndil from Eq. 4) and for low (same Ndil reduced by factor 0.25) dilution. We see that the plume temperature starts high because of combustion heat. The curves show the early time period of contrail formation, when the plume temperature sinks below the dew point, after about 0.1 to 1 s plume age, and the late time period of sublimation when the plume temperature exceeds ice equilibrium temperatures at times larger than several minutes. The curves represent the results for the three plume parts as listed in Table 2: part 0: the invisible plume; part 1: the upper contrail; and part 2: the lower contrail. For part 2, we see that the plume temperature stays below the frost point, regardless of which of the dilution laws is used. For part 1, we see the plume temperature stays below the frost point only for low dilution; alternatively, the plume temperature stays below TNAT; hence, the upper contrail can be explained either by low dilution, or by formation of HNO3 hydrates, or by NAT hindering the sublimation of ice particles. For part 0, we see that the plume temperature stays above TICE and TNAT for the given age, regardless of the dilution law. Hence, the early sublimation of the contrail that formed in this flight segment, leaving behind the invisible plume, is consistent with the contrail formation concept regardless of the levels of turbulence and NAT formation.