How Different Are They?

Numerical simulations of homogeneously nucleated natural cirrus and contrail-cirrus. Part 1: How different are they?

Simon Unterstrasser1∗, Klaus Gierens1, Ingo Sölch1 and Martin Lainer1,2

1Deutsches Zentrum für Luft- und Raumfahrt (DLR) – Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany 2now at: Institute of Applied Physics, University of Bern, Bern, Switzerland

(Manuscript received January 15, 2016; in revised form May 11, 2016; accepted June 17, 2016)

Abstract The evolution of contrail-cirrus and natural cirrus formed by homogeneous nucleation is studied over up to ten hours by means of a Large-Eddy Simulation (LES) model equipped with a Lagrangian ice microphysics module. This is the first time that both cloud types are investigated in a single study. Characteristics of their life cycles depend strongly on the synoptic scenario. Weak, but enduring updraughts allow for the longest life times of contrail-cirrus. For cirrus clouds, the updraught speed during their formation is most crucial. Once contrails lose their linear shape they are hardly distinguishable from natural cirrus which makes it difficult to evaluate the extent and effect of the anthropogenic cloud modification. Despite their different formation mechanisms (contrails are generated locally and have initially much higher ice crystal number concentrations than natural cirrus) we could not single out microphysical criteria that could help to distinguish in general between both cloud types in observations. Keywords: Large eddy simulation, Lagrangian ice microphysics, Natural cirrus, contrail cirrus, aviation

1 Introduction bias because their detection efficiency increases with the optical thickness of the observed contrail or cir- The most important contribution of aviation to anthro- rus (Kärcher et al., 2009). Satellite missions like the A- pogenic climate change is due to formation of con- train carry nowadays combinations of active and pas- trails that may persist for hours in the atmosphere sive instruments and a synergistic use of these mea- under favourable conditions. Growing in lateral ex- surements allows retrieving more quantities than before. tent they sometimes cover the local sky. This result However, the question arises whether there are micro- has been obtained mostly from climate models that physical and radiative properties that can be exploited have been retrofitted with modules to describe contrails to distinguish between contrail-cirrus and natural cir- (e.g. Ponater et al., 2002; Burkhardt and Kärcher, rus over their whole lifetime. To answer such questions, 2009). Alternatively, a combined model-observational cloud resolving modelling can help, and additionally, the approach was employed (Schumann and Graf, 2013). results of those models can guide measurements in air- It would be desirable to corroborate the results of borne campaigns in order to corroborate or disprove the such climate simulations with observations, but airborne model predictions. measurement campaigns are not able to provide a global This paper is intended to make such numerical com- perspective and are often biased to the thickest and parisons between contrail-cirrus and cirrus clouds. We easiest-to-observe contrails. Nevertheless, aircraft mea- are guided by a number of relevant questions: surement campaigns with the German research aircraft • What are the essential differences between contrail- HALO (High Altitude LOng range) like ML-Cirrus, cirrus and cirrus? which took place in spring 2014, can supply a wealth of • Which differences survive up to the end of their data due to their rich instrumentation (ACP/AMT Spe- lifetime (or at least up to the end of a simulation)? cial Issue, 2016). This can help to gain a deeper pro- • Which processes and properties of the ambient atmo- cess understanding and to indirectly improve climate es- sphere are relevant for the emergence of these differ- timates. ences? Measurements from satellites give a global (or at • Is it possible to exploit these differences for a dis- least hemispheric) view (Iwabuchi et al., 2012), but tinction of both cloud types in remote sensing, in-situ have difficulties to distinguish between contrail-cirrus applications or a synergistic use of various measure- (old contrails which have lost their initial linear shape) ment techniques? and natural cirrus. They suffer from a similar selection There is a vast literature on both cirrus cloud and con- ∗Corresponding author: Simon Unterstrasser, DLR Oberpfaffenhofen, 82234 trail simulations, but for a rigorous comparison simula- Wessling, Germany, e-mail: [email protected] tions of these clouds in the same atmospheric situation

© 2016 The authors DOI 10.1127/metz/2016/0777 Gebrüder Borntraeger Science Publishers, Stuttgart, www.borntraeger-cramer.com 2 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus Meteorol. Z., PrePub Article, 2016 or even together in a single simulation are necessary. To simplify the description of our simulation results However, the latter introduces complications by the in- we refer to cirrus if we speak of a naturally formed teraction between contrail and cirrus and should be only cirrus. The term “contrail” refers both to linear contrails the second step after separate simulations of contrails and aged contrails where the term contrail-cirrus would and cirrus for the same atmospheric background. First, be more appropriate. Conveniently, this circumvents the the basic differences resulting from the essentially dif- need to distinguish between contrail and contrail-cirrus. ferent formation pathways of contrails and cirrus clouds The neutral term ice cloud is used, if the cloud type is have to be understood in such situations. Even without unspecified. the complex interaction between cirrus and embedded Section 2 presents the methodology and introduces contrails too many parameters like meteorological con- the employed model and the design of the numerical set- ditions or aircraft properties influence the contrail evolu- up. Section 3 juxtaposes the evolution of contrail and tion, that it is well conceivable that a distinct difference of cirrus and highlights the most prominent differences. found in one situation will not be found or will be in- The results are discussed in Section 4 and conclusions significant in another one. are drawn in Section 5. Contrail evolution depends sensitively on meteorological parameters like temperature, humidity, vertical 2 Methods wind shear, but also on atmospheric stability, depth of the supersaturated layer in which they are formed, radi- In this section, the employed model with its numerical ation scenario (i.e. position of the sun, ambient cloudi- set-up is introduced and properties that will be used in ness), and of course on aircraft properties (fuel flow the later analysis are defined. rate, wing span, weight, speed) (Jensen et al., 1998; Un- terstrasser and Gierens, 2010a; Unterstrasser and 2.1 Model description Gierens, 2010b; Lewellen et al., 2014; Lewellen, The numerical simulations have been carried out with 2014; Unterstrasser and Görsch, 2014). For cir- the non-hydrostatic anelastic model EULAG (Smo- rus clouds these are vertical wind speed, depth of the larkiewicz and Margolin, 1997) which employs the supersaturated layer, temperature, pressure, concentra- positive definite advection scheme MPDATA (Smo- tion of heterogeneous ice nuclei, stability, radiation sce- larkiewicz and Margolin, 1998) in its Eulerian oper- nario, etc. (e.g. Dobbie and Jonas, 2001; Liu et al., ation mode. A microphysical module using Lagrangian 2003; Spichtinger and Gierens, 2009b; Spichtinger tracking of ice crystals (Sölch and Kärcher, 2010)is and Gierens, 2009a; Jensen et al., 2011; Sölch and fully coupled to EULAG and forms the version EULAG- Kärcher, 2011). Moreover, contrails usually appear in LCM. With this model version the simulation of both clusters instead of single isolated objects, at least in natural cirrus and contrails is possible. Recent examples regions of intense air traffic, and there is competition are studies of a mid-latitude cirrus cloud system with for the available water vapour (Gierens, 1998; Unter- special focus on aggregation (Sölch and Kärcher, strasser and Sölch, 2013). Moreover, cirrus clouds are 2011) and the contrail evolution during the vortex phase often found close to contrails and their formation may (Unterstrasser, 2014; Unterstrasser and Görsch, be suppressed by contrails, diminishing the cirrus cloud 2014). coverage (Burkhardt and Kärcher, 2011). Thus, con- The microphysical module LCM uses an explicit rep- trail evolution does also depend on whether there are resentation of size-resolved non-equilibrium aerosol and other contrails or cirrus clouds nearby and how close ice microphysics. Ice crystals are represented in the they are. model by Lagrangian simulation particles (SIPs). Ev- It would be counterproductive to vary all these pa- ery SIP represents a large number of ice crystals with rameters in one study because that would render the pa- identical properties, and the actual number of SIPs as per unreadable. Instead we have concentrated on a few well as the number of ice crystals a SIP represents vary important parameters, mainly wind shear (important for dynamically during a run of the model. In particular, the lateral growth of contrails) and vertical wind speed a SIP splitting technique (Unterstrasser and Sölch, (important for the number of ice crystals nucleated in a 2014) is applied to ensure sufficiently high SIP concen- homogeneous cirrus nucleation event and the amount of trations in the diluting contrails. In its complete form available water vapour). This means, that the list of rel- the LCM comprises non-equilibrium growth of liquid evant questions will not be completely answered in this supercooled aerosol particles, their homogeneous freez- paper, and only first results can be provided. Proceed- ing, heterogeneous nucleation of ice nuclei in the de- ing on this way will eventually provide insight, being position or immersion mode, growth of ice crystals by helpful in several directions. On the one hand, reliable deposition of water vapour, their gravitational sedimen- recipes for observation and measuring strategies may be tation, aggregation between ice crystals due to differ- identified that are able to distinguish contrail-cirrus from ential sedimentation, turbulent dispersion of ice crys- natural cirrus on a global scale. On the other hand, the tals, latent heat release, and radiative impact on parti- findings can help to advance contrail parametrisations in cle growth. Nucleation of ice is sub-cycled and the nu- global scale models (Burkhardt and Kärcher, 2009; cleation time step is usually smaller than the dynami- Rap et al., 2010; Schumann, 2012). cal time step. Not all of above mentioned processes are Meteorol. Z., PrePub Article, 2016 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus 3

Figure 1: Left: Vertical profile of relative humidity RHi in the beginning (solid) and after an adiabatic temperature decrease by 2 K (dashed) and 4 K (dotted), respectively. The thickness of the ice supersaturated layer increases from 1200 m to 1380 m or 1550 m. The flight altitude of the contrail-producing aircraft is at zCA = 2000 m. The temperature at cruise altitude TCA = T(zCA) = 217 K. Right: Snapshot of the extinction coefficient χ of an exemplary contrail-cirrus after 3 h. The overlaid grid illustrates the divisions used in Figure 11. switched on in the present simulations in order to reduce and Görsch, 2014). A 2D model, the domain of which the complexity of the situations. For the sake of sim- is perpendicular to flight direction and represents some plicity, heterogeneous nucleation, aggregation and ra- portion of the UT/LS (upper tropospheric/lower strato- diation are deactivated, although they can strongly al- spheric) region, is used. In the vertical direction (coordi- ter the evolution of natural and contrail-cirrus (e.g. Liu nate z), the domain dimension is 3 km. In the horizontal et al., 2003; Spichtinger and Gierens, 2009a; Unter- direction (coordinate x), the domain dimension can be strasser and Gierens, 2010b; Sölch and Kärcher, as large as 80 km. In the (vertical) middle of the domain 2011; Lewellen, 2014). an ice-supersaturated layer of 1 km thickness and initial Several types of crystal habits are included via habit- relative humidity (with respect to ice) of 120 % is pre- dependent mass-size and mass-area relationships which scribed (see Figure 1 left). Figure 1 right depicts a typi- enter the expressions for microphysical and radiative cal aged contrail that is tilted due to vertical wind shear quantities (capacitance, fall speed, extinction cross- and that has developed a fall streak penetrating into the section). A priori, a specific habit type has to be selected subsaturated layer beneath. as the model is not yet capable of predicting the habit The total simulation time ranges between 6 h and evolution. In this study, hexagonal columns are cho- 10 h. The dynamical time step is 2 s or 1.25 s depending sen for both the contrail and cirrus simulations. Possi- on vertical wind shear. The nucleation time step ranges ble differences in the habit characteristics between con- from 0.1 s to 0.5 s depending on the updraught speed trails and cirrus are not considered in the simulation and wsyn. analysis. Synoptic scale updraughts with various intensities −1 −1 The information contained in the SIPs is mapped on ranging from wsyn = 1cms to 20 cm s are pre- the Eulerian grid, which is used for all non-ice variables. scribed. The final adiabatic cooling is either 2 K or 4 K Then, e.g., the ice water content at each grid point is and corresponds to an uplift of roughly 200 m or 400 m, computed by summing up the ice mass represented by respectively. This implies shorter updraught periods for each SIP belonging to this grid box and dividing this larger wsyn. In further scenarios, no updraught or a weak −1 sum by the grid box volume. downdraught with wsyn = −1cms is prescribed. Ta- The subgrid turbulence model uses the TKE-ap- ble 1 summarises the updraught velocities and periods proach. Synoptic scale updraught motion is prescribed of the various scenarios. The temporal evolution of the via an external forcing term in the temperature equation ∗ = background relative humidity RHi (t)atz 2000 m is in order to accommodate for the adiabatic temperature shown in Figure 2. change. Details of the implementation can be found in The various updraught scenarios are associated with Unterstrasser and Gierens (2010b). different synoptic situations. Slow updraught is found in prefrontal zones, a region where large decks of 2.2 Simulation set-up contrail-cirrus have been observed (Haywood et al., 2009; Laken et al., 2012). Stronger updraught occurs The simulation set-up for the present study follows due to gravity waves. Note that the strong updraught that of the recent simulations of contrail-cirrus with scenario used in this study does not correspond to a full EULAG-LCM (Unterstrasser, 2014; Unterstrasser wave cycle as the downdraught phase is neglected. 4 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus Meteorol. Z., PrePub Article, 2016

Figure 3: ∗ Temporal evolution of the root mean square of the turbu- Figure 2: Temporal evolution of relative humidity RH (t)atz = 0.5 i lent velocity ﬂuctuations given byu ˆ = u2 + w2 .Thesumis 2000 m for various w (as indicated in the legend or given in i i i syn taken over all grid boxes. The solid curve depicts the default case, Table 1). The ﬁnal adiabatic cooling is 2 K (dotted) or 4 K (solid). the dotted one the case with stronger turbulence.

Table 1: Characteristics of the various updraught scenarios: updraught speed wsyn, approx. time of cirrus formation tnuc. The length • simulation of a contrail interacting with natural cirrus of the updraught period tupdr is given in the third/fifth column and the (referred to as INTERACTION simulation) final hypothetical relative humidity RHi, f is given in the fourth/sixth = column (“1” or “2” stands for the 4 K and 2 K-case, respectively). At t 0, all CONTRAIL and INTERACTION simu- The rightmost column indicates the colours used in several plots lations are initialised with the same 5 minute old contrail throughout the paper. that is about 500 m deep and 200 m broad and contains 12 about N0 = 1.7·10 ice crystals per meter of flight path. wsyn tnuc tupdr1 RHi, f 1 tupdr2 RHi, f 2 colour This corresponds to a an ice crystal ‘emission’ index of in cm/s in s in s in % in s in % 2.8 · 1014(kg fuel)−1 and roughly half of the ice crys- −1 – 10000 107 magenta tals surviving the vortex phase (Unterstrasser, 2014). 0 – – 120 black Data of a 3D vortex phase simulation with EULAG- 1 – 20000 150 red LCM (Unterstrasser, 2014) are incorporated into the 2 10200 20000 190 10000 150 blue present simulation domain (see Figure 15 in the latter 5 4000 8000 190 4000 150 green reference for an illustration). For this, the 3D-fields (e.g. 10 2000 4000 190 – – grey perturbations of water vapour concentration q and po- 20 1000 2000 190 1000 150 brown v tential temperature θ) are averaged along flight direction, interpolated on the coarser grid and embedded into the The atmosphere is assumed to be stably stratified enlarged 2D model domain. SIPs with similar positions − − (neglecting the coordinate y along flight direction) and with a Brunt-Väisälä frequency N = 10 2 s 1, a typ- BV ice crystal sizes are merged in order to reduce their over- ical value for the upper troposphere. Background tur- all number. bulent velocity fields were produced by a-priori simu- 6 lations and have a root mean square (rms) valueu ˆ = Around 10 SIPs represent the contrail-cirrus, which was shown to be sufficient for most analyses of such 2 + 2 0.5 ≈ −1 i ui wi 0.1ms . The temporal evolution simulations (Unterstrasser and Sölch, 2014). Produc- ofu ˆ is displayed in Figure 3. Although the rms-value ing robust probability density functions (as shown in is supposed to decay slowly over time, as no “forced Figure 8) requires higher SIP numbers and thus a SIP turbulence”-mechanism is included, in the displayed splitting technique is applied in selected simulations caseu ˆ even increases after 3 hours, probably due to la- (see Section 3.1 and 4.1 in Unterstrasser and Sölch, tent heating effects. 2014). Homogeneous nucleation is initiated preferentially at The cruise altitude of the contrail generating aircraft the top of the supersaturated layer where the nucleation is zCA = 2000 m (above the bottom of the domain). The threshold humidity of RHcrit ≈ 155 % is surpassed first temperature at cruise altitude is TCA = 217 K, a typical (see Figure 2). Cirrus formation starts at different points value of the extra-tropical upper troposphere. The only in times tnuc in the various scenarios (see Table 1). difference between the CONTRAIL simulation and the Three kinds of simulations are performed: INTERACTION simulation is that homogeneous nucleation is switched off or on. For the CIRRUS cases, the • simulation of a contrail only (referred to as CON- simulation domain is initially void of ice crystals and the TRAIL simulation) domain width is reduced to 10 km to reduce computing • simulation of natural cirrus only (referred to as CIR- costs. Up to 5 · 106 SIPs are generated to resolve the RUS simulation) highly non-linear ice nucleation process. The stochastic Meteorol. Z., PrePub Article, 2016 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus 5

Table 2: Differences between natural cirrus clouds and contrails (incl. contrail cirrus).

Cirrus formed by homogeneous nucleation Contrail Formation needs considerable supersaturation is possible even in completely dry air, persistence requires at least ice saturation Ice crystal number 3/2 proportional to wsyn depends on aircraft and depends on temperature meteorological properties Ostwald ripening rarely occurs Ostwald ripening occurs Ice crystal size ice crystal size mode ice crystal size mode growing with time, 10 µm hardly growing with time, ≈ 10 µm close to monomodal size distribution two modes possible (core and fall streak) In-cloud relative humidity frequently RHi 100% RHi ≈ 100% in the core frequently RHi 100% in the fall streaks Lifetime longer for higher updraught speed longer for longer updraught duration

nucleation implementation and a SIP merging technique The mean optical thickness τm is the average of τ as described in Unterstrasser and Sölch (2014) are over all contrail columns with τ ≥ τc = 0.005. employed. The mean ice crystal concentration nmean is the aver- For the sake of completeness, INTERACTION sim- age of n over all contrail parts with n ≥ 102 m−3. ulations have been introduced here, even though their Following Yang et al. (2000, their Eq. 13), the effec- presentation and discussion is deferred to PART2 (Un- tive ice crystal diameter of the total cloud is given by terstrasser et al., 2016). 3 i Vi Deff = , (2.2) 2.3 Deﬁnitions 2 i Ai

Let us first introduce several quantities. Some of them where i runs over all SIPs of the domain. Vi is the total are motivated by analysing the contrail evolution. Never- volume of all ice crystals in SIP i and Ai is the total theless, most definitions are also meaningful for a cirrus projected area of the hexagonal crystals in SIP i. cloud. The ice crystal size distributions are given in terms The total extinction E of a contrail is the horizontal of L,whereL is the maximum size of ice crystals. − −τ(x) integral of the extinction 1 e ,whereτ(x)isthe The computation of L and A is based on mass- optical thickness along the vertical direction. i size and mass-area relations of Mitchell (1996) for hexagonal columns. E = (1 − e−τ) dx ≈ τ dx = τ˜ × B˜ (2.1) τ(x)isgivenby χdz,whereχ is the extinction coef- 3 Comparison of contrail with cirrus ficient. Total extinction measures the disturbance of the evolution shortwave radiative flux. For small τ-values the approximation holds and E can be interpreted as product of As we are seeking differences between contrails and characteristic optical thicknessτ ˜ and width B˜ and com- cirrus clouds, we start with their essentially different prises information about microphysical and geometric formation mechanisms (see Table 2) and consider the properties. Details can be found in Unterstrasser and question how initially different properties are transferred Gierens (2010a, see their Eq. 12). This quantity can- to later stages of the evolution. not be directly translated into a (solar) radiative forcing. If the environment is cold enough (Schumann, This requires further knowledge on the incident radia- 1996), contrail formation occurs in a confined area be- tion fluxes which depend inter alia on solar zenith an- hind an aircraft and the ice crystals get redistributed gle, surface albedo or the presence of underlying water by the trailing wake vortices during the first few min- clouds (Forster et al., 2012). utes. The number of ice crystals produced in the cooling The definition of a width BOD of a contrail considers exhaust plume and surviving the vortex phase depends its visibility by a human observer. It takes into account on fuel, combustion, aircraft and meteorological pa- all contrail columns with τ larger than 0.02, which is rameters (e.g. Kärcher and Yu, 2009; Unterstrasser roughly the visibility threshold. and Görsch, 2014; Unterstrasser, 2016). The present 6 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus Meteorol. Z., PrePub Article, 2016 simulations start with about 20 cm−3 on average and locally up to 200 cm−3 ice crystals in the 5 minute old contrail. Cirrus crystals form whenever and wherever the relative humidity surpasses a certain threshold, well above the saturation level (depending on the temperature or ice forming properties of the background ice nuclei) and their number depends strongly on the vertical wind speed, if we focus on homogeneous nucleation only. This leads to two characteristic differences, in terms of geometry and microphysics: 1. Young contrails are small scale clouds that spread and get diluted over time, whereas the cirrus spatial scales are determined by the humidity field. 2. The ice crystal number concentrations rarely exceed 10 cm−3 in cirrus (Krämer et al., 2009) while it typically ranges from 104 cm−3 to 105 cm−3 in freshly generated contrails (Schröder et al., 2000). The strong dilution during the jet and vortex phase (Schumann et al., 1998; Unterstrasser et al., 2014) and crystal loss during the latter of the two phases (Sussmann and Gierens, 1999) reduce contrail crystal concentrations substantially. In contrast to the crystal concentration the ice mass concentration is for both, the contrail and cirrus, rather determined by the ambient conditions (absolute humidity and vapour mass in excess of ice saturation). The differences resulting from ice mass concentrations are thus expected to be less important. In the following, results of the simulations of cirrus and contrails are presented and it is investigated whether significant differences between both cloud types remain for a while. We begin with juxtaposing the evolution of cirrus and contrails for various “synoptic” scenarios (speed and duration of updraught, wind shear); Subsec- tions 3.1 and 3.2 focus on basic properties of and funda- mental differences between cirrus and contrails, respectively. In Subsection 3.3, a refined comparison between both cloud types follows.

3.1 Cirrus Figure 4: Simulations of cirrus are carried out up to 10 h, with Temporal evolution of several cirrus properties for various synoptic scenarios (colour coding for w see Table 1 or legend in w = 2cms−1,5cms−1,10cms−1 and 20 cm s−1.The syn syn bottom panel): total extinction E, effective diameter Deff as well as initial relative humidity in the moist layer is 120 % the mean ice crystal number concentration and the total ice crystal and the uplift is stopped once the layer is adiabatically number (from top to bottom). The low shear cases are denoted with cooled by 4 K. As a consequence of the ﬁxed total solid lines, the high shear cases with dotted lines. Colour coding for adiabatic cooling, the amount of excess vapour (the wsyn,seeTable1. The ﬁnal adiabatic cooling ΔTcool is 4 K in any vapour that is available for deposition on ice crystals) case. is eventually equal in all simulations. Figure 4 compiles various cirrus properties: total extinction, effective diameter as well as the total number the updraught speed wsyn. More ice crystals nucleate for and mean concentration of ice crystals. The faster the higher wsyn. air layer rises, the earlier RHi crosses the nucleation This N-variation has major implications. The crys- threshold and cirrus ice crystals form. Most notably is tals are smaller for higher wsyn and the effective diam- the strong dependence of total ice crystal number N on eters reach maximum values between 30 µm and 70 µm Meteorol. Z., PrePub Article, 2016 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus 7

3.2 Contrail In this section the contrail evolution up to 6 hours in the absence of cirrus formation is discussed. For this, homogeneous nucleation is switched off. Uplift scenarios as in the CIRRUS simulations (with adiabatic cooling of 4 K) and additional cases with wsyn = 1, 0, and 1cms−1 are considered. The ambient relative humidity of the latter cases evolves as shown by the red, black, and magenta curves in Figure 2. Note that in the case −1 wsyn = −1cms the downdraught is stopped before the moist layer gets subsaturated. Figure 6 displays the evolution of characteristic contrail properties, viz. total extinction, mean optical thick- Figure 5: Relationship between updraught speed wsyn and maxi- ness, mean number concentration and geometric width, N ∗ mum normalised total ice crystal number max of a cirrus cloud. over simulation time. It shows results of simulations N ∗ = max (N)/N where N is an arbitrarily chosen scaling max t scal scal with low (left) and high (right) wind shear s. The evolu- factor. The two types of symbols show the low and high wind shear 1.5 tion of crystal number and effective diameter, which do cases. The dashed line shows the analytic approximation ∝ wsyn following Kärcher and Lohmann (2002). not depend strongly on s, are displayed in Figure 7 for the low wind shear cases only. In the downdraught scenario (magenta lines) the contrail evolves differently from all other cases and this ex- ceptional case is discussed first. A much stronger loss of ice crystals and a lower total extinction compared to −1 the wsyn ≥ 0cms -cases can be observed. The contrail (see second row of Figure 4). This implies a higher to- soon becomes faint. The optical thickness takes values tal extinction for the same ice mass and a longer life around the visibility threshold and the contrail width time as sedimentation fluxes are smaller. After ten hours starts to decrease after two hours as an increasing por- −1 only the cirrus at wsyn = 20 cm s , although emerging tion of the contrail becomes sub-visual or vanishes com- as the first one, has a non-negligible total extinction (see pletely. It is noteworthy that a contrail can survive for first row of Figure 4) because it consists of the smallest quite a while (not just minutes) in (slowly) subsiding ar- 1.5 eas, albeit as a faint specimen. crystals. Figure 5 shows a Nmax ∼ wsyn relationship (where the maximum of N is taken over time). This is The remainder of this section focuses on the climati- ≥ −1 in accord with earlier analytical estimates by Kärcher cally more relevant cases with wsyn 0cms (Duda and Lohmann (2002) who related ice crystal concentra- et al., 2009). Generally, the contrails are initially narrow and spread over time. The contrail width B in- tions n to wsyn. The excellent agreement between both OD approaches is somewhat surprising as the simulation creases with time, roughly in a linear fashion. Depend- takes into account several process not accounted for in ing strongly on vertical wind shear s, BOD attains values −1 −1 the analytical approach. For instance, 1.) the total crys- of 20 km for s = 0.002 s and 60 km for s = 0.006 s . tal number N is used here instead of some typical crystal This is in line with width values for contrails up to one concentration and 2.) the effect of sedimentation is con- hour age retrieved by scanning lidar (Freudenthaler sidered. Moreover, turbulent motions enhance ice crystal et al., 1995). formation due to the non-linear character of nucleation. There are three sources of excess water vapour that In particular for small wsyn, this effect can be strong as deposits on contrail ice crystals: the turbulent fluctuations represent the major contribu- 1. entrainment of fresh supersaturated air through the tion to the actual updraught speeds. A sensitivity study contrail borders, mainly in horizontal direction with stronger turbulence (û = 0.32 m s−1) pronounces the enhancement and shows a weaker dependence of 2. the decrease of the saturation pressure due to adia- Nmax on wsyn. The exponent of the fit function is then batic cooling in the contrail’s interior, and around 1.2 (not shown). 3. the moist layer below for ice crystals falling into it. A fairly weak impact of vertical wind shear s on cirrus properties is found. Slightly fewer ice crystals The relevance of the entrainment mechanism in- form for higher vertical wind shear (see bottom row of creases with wind shear, that of the cooling mechanism Figure 4). A similar tendency was found in Spichtinger with uplift speed and that of the sedimentation mecha- and Gierens (2009b). Note, however, that in our set-up nism with the thickness of the ice supersaturated layer. the moist layer and with it the cirrus extends horizontally Inside the contrail, high ice crystal number concentra- throughout the whole domain. The effect of shear may tions imply a short deposition time scale. The available be larger in situations with a less uniform or laterally water vapour gets quickly converted into ice and relative confined moist layer. humidity is close to saturation. 8 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus Meteorol. Z., PrePub Article, 2016

Figure 6: Temporal evolution of several contrail properties for various synoptic scenarios (colour coding for wsyn see Table 1 or legend in bottom right panel): total extinction E, mean optical thickness τm, mean number concentration and width BOD (from top to bottom). The left panel shows the low shear case (s = 0.002 s−1), the right one the high shear case (s = 0.006 s−1). Solid lines: standard scenarios; dotted lines: shorter updraught period (resulting ΔTcool is 2 K). The vertical bars in the top panels indicate the times the updraughts comes to a halt.

Let us ﬁrst consider the low wind shear cases (left soon sedimentation leads to a substantial loss of ice mass column of Figure 6). Over the ﬁrst two to three hours and after six hours the total extinction is well below its the ice mass (not shown) and total extinction grow with peak value. Contrails seem to be most long-living in an time. The growth rate increases with wsyn.Atsomere- environment with slow, but steady updraught (blue and versal point in time, total extinction starts to decrease as red solid lines). In these cases, the total extinction grows sedimentation losses are no longer balanced by deposi- over the whole simulation period of six hours. tional growth. In the simulations, this occurs after the Mean optical thickness values, τm, decrease from updraught comes to a halt. If the updraught is strong, about 1 in the beginning to < 0.2 after an hour, as the but short, ice crystals quickly grow in the beginning. But contrails get tilted. Subsequently, τm may increase for a Meteorol. Z., PrePub Article, 2016 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus 9

Figure 7: Analogous to Figure 6, but only simulations with low wind shear are shown, as the high wind shear results are similar. The displayed quantities are effective diameter Deff and total ice crystal number for various updraught speeds wsyn (colour coding see Table 1 or legend in right panel). while, however starts to drop again, once the updraught 50 µm to 60 µm. Interestingly, the final value is fairly motion stops. The vertical bars in Figure 6 mark the end insensitive to the uplift speed. The observed pattern is of the updraught in the various cases and clearly show similar to the one in a preceding study on contrail- the coincidence with the onset of the τm-decrease. Con- cirrus produced by different aircraft (Unterstrasser trails facing a slow, but steady updraught are eventually and Görsch, 2014). A more detailed discussion of the optically thickest. This may explain the formation of spatially-resolved effective diameters is deferred to Sec- very long living contrails as observed by Minnis et al. tion 3.3.1. The mean ice crystal number concentrations (1998), Duda et al. (2004), Haywood et al. (2009) and (see right panel) drop strongly over time due to dilu- Laken et al. (2012). tion and the formation of a fallstreak both increasing the The number of ice crystals is steadily decreasing contrail area. Compared to this aging effect, the shear- in all contrails. Notably, ice crystals are lost by two induced differences in nmean appear to be of secondary different effects. The obvious one is that ice crystals fall importance. −1 into the dry layer below and sublimate there. However, In the cases with wsyn ≥ 2cms and ΔTcool = 4K ice crystals are also lost inside the originally moist layer (as used for the CIRRUS simulations), RHi increases to once relative humidity approaches 100 %. The latter 190 % outside of the contrail and suppression of homo- is enhanced by Ostwald ripening, which is a spectral geneous nucleation is actually not realistic. As the con- broadening of the ice crystal size distribution due to trail growth by entrainment may thus be overestimated, the Kelvin effect (Lewellen, 2012). Lewellen et al. simulations with ΔTcool = 2KandRHi, f inal ≈ 150 % are (2014) coined the term “in-situ loss” for this effect. The added. In these scenarios it is more plausible that cirrus relative importance of the two mechanisms depends on formation has not yet started (dotted lines in Figs. 2, 6 the environmental conditions and a closer inspection is and 7). All statements made above remain valid for the deferred to Section 3.3.4. In combination, there is a non- 2 K cases. linear and non-monotonic relation between wsyn and the ice crystal number at the end of the simulations. 3.3 Detailed Comparison In a high-wind-shear environment, the contrail evolution is in many aspects similar to the low-wind-shear case. Thus it suffices to point out the apparent differ- 3.3.1 Crystal sizes and number concentrations ences: 1.) Optical thickness has moderately lower values. Generally, τm seems to depend more sensitively on Figure 8 shows histograms (PDFs) of ice crystal concen- = wsyn. 2.) Total extinction attains larger values, as the con- trations n for three cloud ages (t 0.5 h, 2 h and 4.5 h). trails become broader and cover a larger area. 3.) Total Contrail PDFs are shown for low and high vertical wind extinction increases over a longer period. The entrain- shear, cirrus PDFs for low and high updraught speed, ment of fresh supersaturated air is stronger and sedimen- as these parameters presumably have the largest impact tation losses are balanced over a longer period. on n. The evolution of total ice crystal number and effec- The cirrus PDFs have one pronounced peak depend- −3 −3 −1 tive diameter of the ice crystals are similar for both ing wsyn; at around 0.1 cm –1 cm for 20 cm s and − − − values of wind shear. Thus, Figure 7 shows only the 0.001 cm 3–0.01 cm 3 for 2 cm s 1. Over time a tail low-wind-shear results. The effective diameters increase with smaller concentration values emerges. The simu- within the first two hours (see left panel). After this ini- lated concentrations cover a large range (< 10−5–1 cm−3) tial growth period they remain nearly constant at about similar to what large observational data sets reveal 10 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus Meteorol. Z., PrePub Article, 2016

In contrast to the cirrus PDFs, the contrail PDFs have two distinct peaks after half an hour. Concentrations of 10 cm−3–100 cm−3 are found in the contrail core (right peak). Such concentrations have been often measured in contrail cores of this age (Heymsfield et al., 1998; Poellot et al., 1999; Schröder et al., 2000; Febvre et al., 2009). The left peak at around 0.01 cm−3–0.1 cm−3 represents the developing fall streak and compares well to measurements of the contrail periphery in Heyms- field et al. (1998). After 2 hours the fall streak of the contrail becomes mature and the most likely concentrations shift to 0.001 cm−3–0.01 cm−3 (comparable to the values in a ‘low updraught’ cirrus). The right peak representing the contrail core becomes less pronounced over time. On the one hand, the maximum concentrations drop due to dilution. High shear accelerates this process. On the other hand, the relative frequency drops. This is simply due to the fact, that the fall streak covers a larger and larger area and the relative fraction of the contrail core area decreases. The concentrations in the contrail core are similar to those in a high updraught cirrus. These results indicate that aged contrails may be identified as such only if the updraught speed is low and the contrail core is sampled. As in-situ measurements are the preferred observation method to determine number concentrations, questions arise, how likely the core of a contrail is hit and sampled. Compared to the PDFs of number concentrations, PDFs of ice mass concentrations or intermediate mo- ments (i.e. total length or total surface area) show smaller differences between cirrus and contrails (not shown) as ice mass is more strongly influenced by ambient humidity conditions. Consider now Figs. 9 and 10 for the analysis of ice crystal size distributions (SD). Here, the size L refers to the maximum dimension of an ice crystal in any direction. Driven by the high number concentrations, any initial supersaturation in a contrail core is quickly reduced and the ice crystals grow to approximately 10 µm size (as confirmed by several measurements: Heymsfield et al., 1998; Poellot et al., 1999). They cease growing in the Figure 8: Relative occurrence frequency of ice crystal number concentrations in 30 min, 2 h and 4.5 h old cirrus or contrails. Con- same moment when the uplift stops. Thus, in a contrail trail at weak and high wind shear (black: s = 0.002 s−1; green: core there are small ice crystals at an approximately ice s = 0.006 s−1); cirrus at low and high updraught speed (blue: saturated state, which favours the occurrence of Ostwald −1 −1 wsyn = 2cms ;brown:wsyn = 20 cm s ). Note that here the in- ripening, an effect that manifests itself in the SDs as a dicated times refer to the age of the cloud, not to the simulated time sublimation tail (see Figure 9 bottom). In contrast, there as, e.g., in Figure 10. On top of each panel, the extent of the sampling is less competition for excess vapour in a cirrus and area for each specific cloud is documented. individual cirrus crystals can grow over a much longer period, even beyond the point the uplift stops. They attain much larger sizes than contrail crystals (except for contrail fall streaks). The predominance of large crystals (Krämer et al., 2009; Luebke et al., 2013). The maxi- excludes Ostwald ripening in cirrus clouds in most cases mum observed values are larger than our simulated ones. (see Figure 10). Those may have been measured when the real updraught The contrail fall streaks consist of the largest ice speeds exceeded our maximum value of 20 cm s−1 or crystals with maximum sizes of about 300 µm (Figure 9 when the measured cirrus was “polluted” by contrails top). Note that simulations with ΔTcool = 2K aredis- (as already pointed out by Ström and Ohlsson, 1998). played, as ΔTcool = 4 K-simulations may overestimate Meteorol. Z., PrePub Article, 2016 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus 11

Figure 9: Contrail ice crystal size distributions for various contrail ages (see label on top) and updraught speeds wsyn (colour coding see Table 1 or legend in bottom right panel). The top row shows the SD on linear scale, the bottom row on a log scale. The vertical wind shear −1 is s = 0.002 s . The updraught period is chosen such that ΔTcool is at most 2 K.

Figure 10: Cirrus ice crystal size distributions for various times (see label on top) and updraught speeds wsyn (colour coding see Table 1 or legend in right panel). The vertical wind shear is s = 0.002 s−1. 12 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus Meteorol. Z., PrePub Article, 2016

Figure 11: Spatial dependence of size distributions in a 3 h old contrail. The contrail is separated into four 500 m thick layers (left) or four 3.8 km broad columns (right). The sub-domains and the colour coding are depicted in Figure 1 right. The black curves show the size −1 −1 distribution of the total contrail as already shown in Figure 9. Depicted is the case with wsyn = 5cms and s = 0.002 s .

the entrainment and crystal growth at the contrail bor- Measuring high concentrations of small ( 10 µm) ders. Such large contrail crystals were also observed crystals may thus be a robust indication for a contrail during the SUCCESS measurement campaign (Lawson and can be exploited in the analysis of in-situ data. How- et al., 1998). ever, at lower ﬂight altitudes with higher temperatures Occasionally, a second mode at about 100 µm ap- and/or for reduced soot emissions the mean sizes of the pears in the SDs. The mechanism behind this may be small particle mode can be higher (Unterstrasser and best explained by an inspection of height-resolved SDs Gierens, 2010a; Unterstrasser and Gierens, 2010b; depicted in Figure 11 left. This second mode is an ac- Lewellen, 2014). In a sensitivity study, which we call cumulation mode produced from two effects, namely “factor 10”-experiment, the initial ice crystal number is the growth of ice crystals falling from the contrail core reduced by a factor of 10, but still most crystals are through the supersaturated layer (reaching maximum smaller than 20 µm (not shown). Experience from pre- sizes larger than the second mode) and the sublimation vious simulations tells that the effect of a temperature below the supersaturated layer. That is, the second mode variation (covering the most common ﬂight altitudes) appears because it is populated from both sides, from is lower than that seen in the “factor 10”-experiment. smaller growing crystals in the moist layer (blue to green However, for temperatures around 230 K (just below the curve) and from larger sublimating crystals in the dry threshold for contrail formation), much fewer ice crys- layer underneath (green to red curve). Moreover, Fig- tals nucleate initially (Kärcher et al., 1998)andthe ure 11 left shows that crystal sizes below 10 µm only modal sizes may exceed the 20 µm-limit. appear in the top 500 m of a contrail (brown curve). As discussed above, the heterogeneity of contrails in In the simulated cirrus SDs, no second mode is vertical direction (discussed in terms of SDs, see Fig- evident. Furthermore, the maximum crystal sizes are ure 11 left) is linked to the effect of sedimentation. Yet, smaller than those of the contrails. But this result can- contrails are also heterogeneous in horizontal (i.e. trans- not be generalised, as the maximum sizes in contrails verse) direction (Figure 11 right) due to their localised can be smaller, when the formation of the fall streak is formation and subsequent spreading, even for homoge- inhibited (due to a reduced depth of the moist layer or a neous background conditions as prescribed in the simu- cirrus forming below the contrail, Unterstrasser et al., lations. In particular, high concentrations of small crys- 2016). Moreover with aggregation switched off, the for- tals are only found in columns where the contrail core mation of very large crystals (exceeding mm size) and is located. This generally demonstrates that in-situ mea- of a second mode in cirrus size distributions (Mitchell surements with an incomplete sampling of the contrail et al., 1996; Ivanova et al., 2001; Sölch and Kärcher, system must be interpreted with care. 2010) may be suppressed in our simulations. The effect The effective diameter Deff can be derived from of aggregation in contrail-cirrus has not been studied so satellite measurements (Nakajima and King, 1990; far and is a topic of future research. The modal sizes Bugliaro et al., 2011). The retrieved values may be of cirrus ice crystals depend, as expected, on wsyn and representative of the cloud top only though (Platnick, range from 40 µm to more than 100 µm. In any case, the 2000). It turned out that in the presented simulations sizes are larger than those found in a contrail core. the maximum effective diameters in cirrus depend on Meteorol. Z., PrePub Article, 2016 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus 13

−1 Figure 12: Spatial dependence of effective diameters Deff in contrails (left and middle) and cirrus (right) for wsyn = 2cms (blue) and 20 cm s−1 (brown). The domain is separated into four 10 km broad columns (left) or four 500 m thick layers (middle and right). The line styles of the sub-domains are solid, dotted, dashed, dash-dotted from left to right or from top to bottom, respectively. updraught speeds (maximum values of 30 µm–70 µm) (McFarquhar and Heymsﬁeld, 1998; Mitchell, whereas in contrails Deff reaches values of 50 µm–60 µm 2002). This neglects Qext-variations in the Mie-regime irrespective of wsyn. These are Deff-values averaged over (van de Hulst, 1981) which could be of relevance for the whole cloud, which is rather coarse, as a contrail the smallest ice crystals in a contrail (Schumann et al., or cirrus usually covers several pixels of a satellite im- 2011; Baum et al., 2005). age. Therefore, it is useful to evaluate Deff for distinct segments of the cirrus and contrails (Figure 12) simi- 3.3.2 In-cloud relative humidity lar to the SDs in Figure 11. Again, there is a strong dependence on horizontal contrail location (left panel), In this section, RHi inside the clouds is evaluated, i.e. all while the cirrus is fairly homogeneous in horizontal grid boxes with n > 0 are considered in the following. D direction (not shown). The contrail eff-values depend Figure 13 shows PDFs of in-cloud RHi for cirrus (bot- also strongly on altitude and are fairly insensitive to up- tom) and contrail (top) for three different cloud ages. In draught speed. In the contrail top, Deff is around 20 µm the latter case, the scenarios with ΔTcool = 2K,which and in the fall streaks around 50 µm–80 µm. Cirrus ice corresponds to a maximum background RH∗ of around crystal nucleation occurs throughout a deep supersat- i 155 %, are evaluated. In 1 hour old contrails, RHi is in urated layer and Deff-values increase slightly with de- most parts close to saturation consistent with analytic creasing altitude. Unlike contrails, cirrus effective diam- estimates and in-situ measurements (Kaufmann et al., eters depend strongly on updraught speed. In the subli- 2014). Nevertheless, there are also high supersaturation ∗ mation layer (dash-dotted curves), Deff decreases. Com- values reaching RHi . These occur in the entrainment mon to all simulations is the pattern of an initial growth area and in the fall streaks. After 4 hours, the high su- period followed by a period of quasi-constant values, as persaturation in these areas is reduced to well below the already seen for the Deff averaged over the whole cloud. background humidity. After 8 hours, virtually all val- In the model, the contrail effective diameters are ues between 80 % and 150 % occur; values < 100 % ap- within the range of cirrus effective diameters. Thus, the pear in the lowermost dry layer. The PDFs of the various simulations imply that Deff-measurements alone are in wsyn-cases are qualitatively similar. general not sufﬁcient to distinguish between cirrus and The bottom row shows the corresponding data for contrails. If strong updraughts can be ruled out, small cirrus. For a strong, but short updraught (brown curve) Deff-values hint at the presence of contrails. However, RHi is close to saturation for all displayed times (30 min, we want to mention two caveats of this conclusion. 1 h and 2 h). For smaller wsyn, supersaturation is main- −1 Satellite retrievals usually employ an inversion tech- tained over a longer period. For wsyn = 2cms ,values nique that degrades for small crystal sizes and optical around 110 % are most likely after two hours. In a few thickness. Hence, the determination of Deff in particular spots, RHi is close to the nucleation threshold and nu- in contrail cores is associated with larger errors. cleation is still on-going. In the model, Deff is given by Eq. 2.2. Interpreting Many cirrus observations and simulations support the Deff as a radiative property of an ice cloud, one implic- existence of in-cloud supersaturation (Ovarlez et al., itly assumes a constant extinction cross-section Qext = 2 2002; Haag et al., 2003; Gao et al., 2004; Spichtinger 14 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus Meteorol. Z., PrePub Article, 2016

Figure 13: Relative occurrence frequency of in-cloud relative humidity for various cloud ages (see label in each panel) and updraught speeds wsyn (colour coding see Table 1 or legend in top right panel). Note that here the indicated times refer to the age of the cloud, not −1 to the simulated time as, e.g., in Figure 10. In the top row contrail cases with low shear s = 0.002 s and ﬁnal cooling ΔTcool = 2K are shown; in the bottom row cirrus cases. Only grid boxes with non-zero ice crystal number concentration are considered. The black vertical line highlights RHi = 100 %. et al., 2004; Krämer et al., 2009; Diao et al., 2014), Figure 14 shows the contrail total extinction for two −1 which may be even more frequent in clouds formed scenarios (wsyn = 1 and 20 cm s ) and the cirrus total −1 by heterogeneous nucleation (Gierens, 2003; Kärcher extinction for one scenario (wsyn = 2cms ). In gen- et al., 2006), which is not treated in our study. eral, the contrail evolution seems to be more strongly affected by the turbulence realisation, whereas the cir- 3.3.3 Turbulence rus evolution depends more sensitively on the turbulence intensity. Next, the impact of the turbulence realisation and in- Apparently, the cirrus formation starts earlier in the tensity on the contrail and cirrus evolution is studied. strong turbulence case. Stronger vertical motions induce Simulations with a higher turbulence intensity use a larger RHi-deviations from the mean state and nucle- background turbulent velocity ﬁeld U with a higher ation is triggered about one hour earlier compared to the rms valueu ˆ = 0.32 m s−1 instead of the default value default case. 0.1 m s−1 (see Figure 3). Moreover, for each selected Moreover, more ice crystals form, raising the total scenario four simulations with different turbulence real- extinction. Note that this turbulence enhancement of ice isations of U are performed. Technically this is done by crystal generation is strongest in the depicted slow uplift an horizontal shift of the initial contrail position within case. Its relative importance decreases with increasing the simulation domain. For the cirrus simulations, which wsyn (not shown). The cirrus evolution depends only run on a 10 km domain, four different slices are ex- weakly on the turbulence realisation (at least for the tracted from U of the a-priori simulation, which uses weakly turbulent default case examined here). a 40 km domain. The global statistical properties of U Contrail evolution is also affected by a variation of are unchanged for the different realisations of U. the turbulence intensity, however to a smaller extent Meteorol. Z., PrePub Article, 2016 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus 15

direction may average out some differences and reduce the spread of the model results. Lewellen et al. (2014) ﬁnds that full 3D simulations show a smaller spread than quasi-3D simulations where the downstream extent of the model domain was reduced.

3.3.4 Crystal loss As already noted, ice crystals in contrails are lost by two different mechanisms. Figure 15 details the fractions of ice crystals that are lost by sedimentation (green) or in-situ (blue). In the ‘no updraught’ case (panel 1a) a large fraction of ice crystals is lost, mainly in-situ. Sedimentation plays a minor role (for the number, not Figure 14: Temporal evolution of total extinction E for two selected for the mass budget). contrail scenarios (brown and red) with ΔTcool = 4K and s = 0.002 s−1. One scenario is displayed for the cirrus simulations (blue; Even in slowly ascending air masses, in-situ loss the values are scaled with a factor of 0.5 to fit into the plot). occurs. After around two hours, ice crystals are not lost Colour coding for wsyn given in Table 1 or in the legend. For each in-situ any longer and sedimentation takes over. In the scenario, four simulations with different turbulence realisations are strong updraught case (panel 1c), in-situ loss is small displayed. Additionally, simulations with stronger turbulence are in the beginning and sedimentation loss sets in quickly. shown (thicker lines with plus signs). Dehydration in combination with an interrupted ascent favours the shrinking of crystals in the aged contrail, which then sublimate in-situ. With higher wind shear than the cirrus evolution. Clearly, stronger turbulence (panel 2a), contrails spread faster and crystals grow leads to a quicker contrail diffusion which leads to a larger. Thus there is stronger sedimentation, which is faster increase of total extinction during the first few approximately balanced by less in-situ loss. hours. However, turbulence induced contrail diffusion Figure 16 details the importance of the Kelvin ef- is just one of several processes contributing to contrail fect on the extent of in-situ loss and the implications on spreading and the situation becomes more intricate after contrail total extinction and effective diameter. In our around 3 hours. By then, wind shear has tilted the con- model, a Kelvin correction factor ω = exp(ak/r)en- trail core and has stretched it laterally. Ice crystals per- ters the ice mass growth equation and accounts for the petually fall out of the core into supersaturated air and increase of saturation vapour pressure over the curved form a strong fall streak as depicted in Figure 1.This surface of small ice crystals. r is the radius of the ice combined shear/sedimentation effect becomes more im- crystals, which are assumed to be spherical here. ak is portant with time and the contrail spreading becomes a parameter that depends inter alia on the surface ten- less dependent on contrail diffusion and turbulence in- sion σ for a water vapour-ice interface (see Eq. 5 in tensity. Lewellen, 2012, for a definition). So far, ak was around Testing various turbulence realisations, one might ex- 2.3 · 10−9 m in all simulations. Small ice crystals are pect that young and localised contrails are most suscep- not perfect spheres with uniform curvature which is one tible to changes in the exact flow pattern and that differ- source of uncertainty in the current implementation of ences in the contrail properties are the largest in the be- the Kelvin correction. The shape assumption is less crit- ginning. This is clearly not the case. Rather, the contrail ical for large crystals, as ω anyway tends to 1 for large r evolution becomes more chaotic after around 2–3 hours and the correction term vanishes. To account for the un- such that the output of individual simulation runs have certainty, simulations with doubled and halved ak (blue to be interpreted implicitly acknowledging that it rep- and green curves, respectively) and omitted Kelvin cor- resents a single sample from an ensemble of possible rection (red curves) are performed. As in the top row of developments under otherwise equal conditions. In par- Figure 15, scenarios with various wsyn are analysed. The −1 ticular for wsyn = 20 cm s (brown curves), phases of black curves depict the simulations with the default ak- increasing and decreasing total extinction alternate in an value and are equal to those already shown in Figure 15. unpredictable fashion. A closer inspection of the sim- The smaller ak is chosen, the fewer ice crystals are lost. ulations reveals that at later times portions of ice crys- Even in the case with the Kelvin effect omitted, ice crystals fall out from the core randomly and it is not pre- tals can be lost in-situ loss, as seen in the top right and dictable when and where this leads to the formation of left panel, where the red dashed lines are below 1. This new strong bands within the fall streak. This late-time demonstrates that Ostwald ripening enhances sublima- randomness may be even larger in heterogeneous condi- tion, but is not the only cause as turbulence-induced fluc- tions with more patchy fields of relative humidity. tuations around ice saturation similarly lead to a broad- Due to our 2D-approach, our simulations may over- ening of the size distribution (Kärcher et al., 2014) estimate the importance of the turbulence realisation, and to loss of ice crystals. In the scenario with wsyn = though. Simulating more than just one slice along flight 2cms−1 (middle panel), where the uplift prevails over 16 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus Meteorol. Z., PrePub Article, 2016

Figure 15: Ice crystal number loss in contrails and cirrus. The red area shows the fraction of existing ice crystals, the green area the fraction lost due to sedimentation and the blue area the fraction lost in-situ (see also labels in bottom left panel). The numbers are normalised by the initial number (contrail cases) or the total number of generated ice crystals (cirrus cases). Panels 1a–1c show contrail cases with low shear and various wsyn, panel 1d a high wind shear contrail case. Panels 2a and 2b same conditions as 1a and 1b, but with switched off Kelvin effect. Panels 2c and 2d show cirrus cases with weak and strong updraught. the total simulated period and water vapour becomes 3.3.5 Lifetimes and radiative effects constantly available, ice crystals are lost in-situ only if the Kelvin effect is included. The different formation mechanisms lead to contrasting The Kelvin effect more or less introduces a cut-off contrail vs. cirrus lifetimes as well. For a cirrus there is filter in the sense that ICs with sizes below a certain the following causal chain: strong uplift → many small threshold are eventually driven to sublimate. Changing ice crystals → slow growth → slow sedimentation → or switching off the Kelvin correction in the model af- long lifetime, and vice versa. In contrast, the corre- fects only the left tail of the ice crystal size distribu- sponding causal chain for contrails is: strong uplift → tion, whereas the evolution of the larger ice crystals strong crystal growth → strong sedimentation → short remains unaffected. Consequently, sedimentation losses lifetime, and vice versa for slow but positive uplift. are unaffected by such a variation, i.e. the differences be- The deposition time scale in a contrail core is very tween the dashed and dotted lines are the same in each small (minutes or shorter, see Khvorostyanov and panel. Moreover, total extinction and effective diameter Sassen, 1998, Table 1), thus the crystals cease to grow are barely affected. The contribution of the smallest ice as soon as an uplifting motion stops or even reverses. crystals is anyway small, such that it makes no differ- The duration of the uplift has thus a stronger influence ence whether or not they are lost in-situ. Hence, it can on the lifetime of a contrail than its strength. A contrail be concluded that the uncertainties in the Kelvin effect with weak but steady uplift lives longer than its counter- implementation have a negligible effect on most contrail part in a strong but short updraught. properties. Neglecting this effect, as usually done in bulk In a cirrus there can be much larger deposition time microphysical approaches, which cannot explicitly sim- scales such that further growth of ice crystals is to some ulate the spectral broadening, seems acceptable. degree decoupled from the vertical motion; the duration Unlike to contrails, in-situ loss does not happen in of an uplift thus affects cirrus properties less strongly the cirrus simulations as the ice crystals are too large than the updraught speed. to be affected by the Kelvin effect. Hence, only sedi- The definition of a width is less meaningful for a mentation effectively reduces the crystal number (panel cirrus than for a contrail, where the width is the hori- 2b and 2c in Figure 15). In the slow updraught case zontal extent perpendicular to the flight direction. Wind (panel 2b), there is permanent ice crystal production shear (normal to the flight direction) changes the width over the whole simulation period. Nevertheless, ice crys- of these clouds, but in relative terms this effect is much tal number drops, once production is outweighed by sed- stronger for a narrow object like a contrail than for an al- imentation losses. ready wide object like a cirrus. This implies that total ex- Meteorol. Z., PrePub Article, 2016 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus 17

Figure 16: Importance of the Kelvin effect on the contrail evolution. Normalised ice crystal number, total extinction and effective diameter are depicted for various implementations of the Kelvin effect (colours; Kelvin effect switched off (red), ak/2 (green), default ak (black) and ak ∗ 2 (blue)) and updraught scenarios (panels). In the top panel, the depicted quantities are similar to Figure 15; the dotted line shows the ice crystal number, the difference between the dashed and dotted line represents the fraction of ice crystals lost by sedimentation, and the difference between the dashed line and 1.0 shows the fraction of ice crystals lost in-situ. tinction of a contrail is sensitive to wind shear while the pends on the flight altitude relative to the bottom of the total extinction of a cirrus is less so and depends more moist layer; a contrail embedded in a cirrus cloud can strongly on the horizontal extent of supersaturated layer. have an IWP much smaller than that of the cirrus. This In our simulations, the cirrus total extinction scales with effect on the optical thickness is partly compensated (or horizontal domain size. The optical thickness is propor- over-compensated) by the small effective size of the ice tional to ice water path IWP. The cirrus will always fill crystals in the contrail core. The optical thickness of the moist layer and thus its IWP is close to the maxi- both contrails and cirrus clouds increase with the up- mum possible. For a contrail, its geometrical depth de- draught speed, but that of cirrus clouds is more sensi- 18 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus Meteorol. Z., PrePub Article, 2016 tive to the vertical motion (more crystals and more ex- can be identified as an anthropogenic cloud because it cess moisture) than that of contrails (merely more excess has, even after hours, a much higher concentration of ice moisture). crystals than natural cirrus formed in-situ if updraught −1 speeds wsyn 10 cm s can be ruled out during formation of the latter. Heterogeneous nucleation, which 4 Discussion is neglected in our simulations, would make this dis- tinction even clearer since it leads to cirrus with lower 4.1 Model aspects ice crystal concentrations than homogeneous nucleation. Our previous work (Unterstrasser and Gierens, Typically, a contrail core is also characterised by small 2010a; Unterstrasser and Gierens, 2010b) that fo- crystals (mostly L < 20 µm), much smaller than typical cused on contrail-to-cirrus transition relied on a two crystals in natural cirrus. Thus, a contrail core can be moment bulk scheme. We investigated the importance identified as such in in-situ measurements on the basis of temperature, relative humidity, vertical wind shear of small crystals with very large concentration. Contrail and several other parameters in scenarios with time- fall streaks cannot be distinguished from natural cirrus constant background RHi. Comparing LCM simulations in this way, as they consist of much fewer and larger −1 crystals similar to what can be found in cirrus. with wsyn = 0cms with our previous BULK simulations, it is found that integrated contrail properties Besides such microphysically based approaches, like total extinction, ice crystal number and mass agree other methods like 1.) chemical identification, 2.) ice qualitatively well (Lainer, 2012). In-situ loss cannot be crystal residue analysis and 3.) trajectory computations simulated with the BULK model, as only size-resolved may be helpful. microphysics allows the explicit simulation of the Ost- Aircraft emit chemical species that can be regarded wald ripening. Nevertheless, the total ice crystal num- as a passive tracer. Peaks in time series of such in- ber evolution is similar, as in the BULK model a nu- situ measured species can be attributed to aircraft ex- merical artefact (Gierens and Bretl, 2009), which we haust plumes. However, ice crystals do sediment in con- called turbulent sublimation, leads to crystal loss of trast to gaseous exhaust species. Hence, the assumption about the same magnitude. Several other aspects are that the contrail and exhaust plume are collocated is more plausibly treated in the LCM approach than in only valid for younger contrails. Using LES simulations, Eulerian approaches, e.g. sedimentation (Wacker and Lewellen et al. (2014, their Figure 4) contrast the dis- Seifert, 2001; Milbrandt and McTaggart-Cowan, persion of a contrail and an exhaust plume of a passive 2010). The low numerical diffusion in LCM leads to tracer. Their findings imply that mainly the cores of aged less smooth ice microphysical fields that have more fine- contrails can be identified with this approach, while their scale structures than the BULK results (cf. e.g. Figure 1 fall streaks are likely to be missed. with Figure 1 of Unterstrasser and Gierens, 2010a). So far, analysing ice crystal residues (IR) by mass Both aspects (spectral resolution + Lagrangian advec- spectrometry aimed at investigating the chemical com- tion) give a sound basis to carry out in-depth microphys- position of aerosols involved in the formation process of ical analysis (e.g. PDFs of number concentrations, evo- natural cirrus clouds (Pratt et al., 2009; Cziczo et al., lution of size distributions). 2013). This powerful analysis technique may further be Some models for contrail-cirrus include mechanisms used to detect contrails as elemental carbon (EC) has to sustain turbulence in order to keep its strength at the a prominent signature in the mass spectrum. Assuming initial level. In our simulations, no “forced turbulence”- that nucleation on soot, which consists mainly of EC, ex- mechanism is taken into account. Rather, the contrail clusively occurs in the cooling aircraft exhaust jets and spreading is mainly due to vertical wind shear and sed- rarely under natural atmospheric conditions, observed imentation. The contrail gets tilted and stretched in the EC IRs give evidence of anthropogenic cloud forma- lateral direction and ice crystals then fall into crystal- tion. In-flight operation of mass spectrometers features free areas below. The level of ambient turbulence is less a high temporal resolution of 5 to 100 Hz. Nevertheless, important for this effect as discussed in Section 3.3.3 the actual number of detected IRs is often low (a few ten and thus a forcing mechanism does not seem to be of to hundred IRs for a whole flight leg), as the detection primary significance. Similarly, Lewellen et al. (2014) efficiency, in particular of soot, is low (Brands et al., found that “including turbulence regeneration is less im- 2011). Hence, the spatial sampling of IRs is too coarse portantif...meanwindsheardrivemoresignificantlev- to routinely identify contrails. Moreover, the lower de- els of turbulent diffusion” (their Section 2.d). tection limit is 150 nm for IR size, which may not be low enough to safely detect aircraft soot, whose size 4.2 Contrail identification is roughly 50 nm (Kinsey et al., 2010; Stettler et al., 2013). Returning thematically to the important question Air parcel trajectories can be computed by using whether microphysical criteria can be found that help NWP model output and flight track data. Considering to distinguish contrail-cirrus from natural cirrus in ob- contrail formation criteria, forward calculations starting servations, the idealised simulations reveals that this is from the aircraft position can help to locate the advected only possible under certain conditions. A contrail core contrails (Duda et al., 2004; Schumann, 2012; Schu- Meteorol. Z., PrePub Article, 2016 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus 19 mann et al., 2013), whereas backward calculations start- (Kärcher et al., 2015; Lewellen et al., 2014; Unter- ing from a given contrail position can help to match strasser, 2014; Unterstrasser, 2016),howeveritis the contrail to a specific flight (implicitly also deter- unaffected by wsyn. In strong but short updraughts, ice mining the contrails’ age). Schumann (2012) goes be- crystal growth is fast and sedimentation-induced contrail yond a simple trajectory program, as it includes simpli- demise sets in quickly. The largest contrail lifetimes oc- fied contrail microphysics, which approximates the ef- cur in slow but enduring updraughts where water vapour fect of sedimentation and the contrail life cycle. Despite becomes continuously available. This may explain the this advanced treatment, it is hardly possible to match formation of very long living contrails as observed by the advected flight tracks (forward trajectories over a Minnis et al. (1998) and Laken et al. (2012). few hours) to specific peaks, e.g. in the lidar backscatter The ice crystal number concentrations n in young ratio of the observed ice cloud or in-situ sampled trac- contrails and in the contrail core of aged contrails are ers. This is due to the fact that the modelled wind fields higher than in most cirrus clouds. In contrail fall streaks, are too coarse to compute trajectories with sufficient ac- concentrations are substantially smaller than in the core curacy (Schumann et al., 2013). A rather small error and are similar or smaller than in cirrus. The average n of 2 m s−1 in the horizontal wind results in an offset of over the complete contrail drops strongly due to contrail 40 km in the horizontal position for a 6 hour old con- dilution and later becomes similar to the values found in trail. As contrails are rather narrow objects, it turns out cirrus. that the offset between the real and the computed po- Ice crystals of a cirrus are lost due to sedimentation, sition is larger than the object’s dimension itself. Cur- i.e. the ice crystals fall into the subsaturated layer below rently, pure trajectory analyses are not powerful enough and sublimate there. In contrails, the fraction of ice crys- to unambiguously match possible contrail observations tal lost by sedimentation is usually smaller than in cirrus. to specific flights, but they can add a piece of evidence. A second type of loss can occur in contrails. Consistent The above presented methods rely on different tech- with Lewellen (2012) and Lewellen et al. (2014),in- niques and data sources, which complement each other. situ loss of ice crystals due to spectral ripening occurs, Hence, a synergistic use of several such methods (as ex- even in slowly ascending air masses. We have not fo- emplified in Schumann et al., 2013) may give a strong cused on subsidence (wsyn < 0), which also causes ice indication that an observed ice cloud is at least affected crystal loss. by aviation. Nevertheless, distinguishing contrails from The contrail size distribution (SD) has two distinct cirrus on a local scale, where both cloud types can be peaks, one peak around L = 20 µm, and a second one strongly intermixed, remains a challenge. at L > 100 µm which depends on the depth of the −1 moist layer. In scenarios with wsyn 2cms , spectral ripening occurs and the left tail of the SD reaches down 5 Conclusions to sizes L < 1 µm. In our set-up the cirrus SDs are narrower than the contrail SDs. However, this result may The Lagrangian ice microphysical module LCM to- not be generalised, as we neglected aggregation and gether with the flow solver EULAG has been used to more heterogeneous background conditions may also perform separate simulations of both contrails and cir- produce broader SDs. rus (formed by homogeneous nucleation) in the same If one can rule out high updraught speeds, observing idealised environment. For this, scenarios with constant many small ice crystals indicates the presence of con- updraught speed (i.e. cooling rates) over a certain time trails. period were used. We fixed the overall adiabatic cooling In PART 2 (Unterstrasser et al., 2016), simula- to 4 K implying that the amount of condensible water tions of contrails becoming embedded in cirrus are dis- vapour is eventually the same in each scenario. This is a cussed and it is analysed how strongly contrail and cirrus standard approach in cirrus and contrail modelling and co-exist and impact each other and whether it is mean- revealed considerable differences between contrails and ingful trying to draw a strict separation line between cirrus, in terms of their life cycle, size distribution and contrails and cirrus. importance of ambient parameters. The cirrus characteristics are strongly controlled by the updraught speed wsyn. The number of ice crystals in the simulated cir- Acknowledgements 1.5 rus is proportional to wsyn confirming analytical estimates, which used simplifying assumptions (Kärcher The first author S. Unterstrasser is partly funded by and Lohmann, 2002). The exponent decreases to 1.2, the DFG (German Science Foundation, contract number when stronger turbulent motion is added to the mean UN286/1-2). Computational resources were made avail- ascent. The cirrus lifetime is larger for stronger up- able by the German Climate Computing Center (DKRZ) draughts, as ice crystals and sedimentation losses are through support from the German Federal Ministry of smaller. Education and Research (BMBF). The work contributes Contrail formation and the number of ice crys- to the DLR project WeCare. We thank J. Schneider tals generated in a contrail and surviving the vortex for discussions on the ice crystal residue technique and phase depends on atmospheric and aircraft parameters U. Schumann for comments on the manuscript. 20 S. Unterstrasser et al.: Comparison of natural and contrail-cirrus Meteorol. Z., PrePub Article, 2016

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