Persistent Contrails and Contrail Cirrus. Part I: Large-Eddy Simulations from Inception to Demise

DECEMBER 2014 L E W E L L E N E T A L . 4399

D. C. LEWELLEN,O.MEZA,* AND W. W. HUEBSCH West Virginia University, Morgantown, West Virginia

(Manuscript received 2 October 2013, in ﬁnal form 10 March 2014)

ABSTRACT

Large-eddy simulations with size-resolved microphysics are used to model persistent aircraft contrails and contrail-induced cirrus from a few wing spans behind the aircraft until their demise after many hours. Schemes for dynamic local ice binning and updating coupled radiation dynamically as needed in individual columns were developed for numerical efficiency, along with a scheme for maintaining realistic ambient turbulence over long times. These capabilities are used to study some of the critical dynamics involved in contrail evolution and to explore the simulation features required for adequate treatment of different components. A ‘‘quasi 3D’’ approach is identified as a useful approximation of the full dynamics, reducing the computation to allow a larger parameter space to be studied. Ice crystal number loss involving competition between different crystal sizes is found to be significant for both young contrails and aging contrail cirrus. As a consequence, the sensitivity to the initial number of ice crystals in the contrail above a threshold is found to decrease significantly over time, and uncertainties in the ice deposition coefficient and Kelvin effect for ice crystals assume an increased importance. Atmospheric turbulence is found to strongly influence contrail properties and lifetime in some regimes. Water from fuel consumption is found to significantly reduce aircraft-wake-induced ice crystal loss in colder contrails. Ice crystal shape effects, coupled radiation, and precipitation dynamics are also considered. An extensive set of simulations exploring a large parameter space with this model are analyzed in a companion paper.

1. Introduction evaluating global impact of contrails (Ponater et al. 2002; Rap et al. 2010; Frömming et al. 2011; Chen and It is not uncommon for portions of the upper tropo- Gettelman 2013), contrails remain the most uncertain sphere to be apparently cloud free (or containing only component of aviation impact on climate (Lee et al. thin cirrus) yet highly supersaturated with respect to ice 2010). (e.g., Gierens et al. 2012). For such conditions ice clouds Contrail evolution is a complex process dependent on seeded by the passage of aircraft (contrails) can persist many properties of the aircraft and of the ambient at- and grow into significant cloud cover that at late times mosphere. Exploring these sensitivities involves dy- could easily be mistaken for natural cirrus (Minnis et al. namics on length scales ranging from nanometers for the 1998). Given the projected increases in air traffic in the ice microphysics to kilometers for the late-time atmo- coming decades and potential impact of increased cloud spheric dispersion. This makes numerical simulation of cover on climate, understanding the formation, prop- contrails challenging. A large number of simulations are erties, and effects of persistent contrails is of clear im- required to fully represent the phenomena given the size portance (Penner et al. 1999). Despite recent progress in of the parameter space, but with an a priori unknown level of complexity required to make these representa- tions suitably faithful. * Current affiliation: Inter American University of Puerto Rico, Bayamon, Puerto Rico. Persistent contrail evolution involves the growth of ice within an expanding wake-plume volume in an ice- supersaturated environment. In the young contrail the Corresponding author address: David C. Lewellen, Department of Mechanical and Aerospace Engineering, P.O. Box 6106, West volume expansion is driven by aircraft-induced dynam- Virginia University, Morgantown, WV 26506-6106. ics: engine jets, trailing vortex interactions, and residual E-mail: [email protected] Brunt–Väisälä oscillations set up by the wake-vortex

DOI: 10.1175/JAS-D-13-0316.1

Ó 2014 American Meteorological Society 4400 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 71 descent. Effects with longer time scales take over later crystal loss involving competition between different on: atmospheric dispersion, ice sedimentation, and crystal sizes in the ice spectrum. An analytic treatment buoyant forcing due to radiative or latent heating. Pre- of this effect along with a more general analysis of dif- vious simulation studies (e.g., Gierens 1996; Chlond ferent regimes of ice-size spectra development has been 1998; Gierens and Jensen 1998; Jensen et al. 1998; presented in Lewellen (2012). Khvorostyanov and Sassen 1998; Sussmann and Gierens The model and simulation procedures are described in 1999; Lewellen and Lewellen 2001a; Chen and Lin 2001; section 2, with further details given in the appendix. Paoli et al. 2004; Paugam et al. 2010; Wong and Miake- Sample simulation results are given in section 3. Some Lye 2010; Naiman et al. 2011; Unterstrasser and Sölch key physical results are discussed at more length in 2010) have generally been limited to specific age regimes section 4, followed by concluding remarks in section 5. of contrail evolution, typically with greatly simplified ice microphysics and/or fluid dynamics and sampling only small regions of the relevant parameter space. 2. Contrail model In a more extensive study (Unterstrasser et al. 2008; a. Fluid mechanics and earlier model Unterstrasser and Gierens 2010a,b) contrails have been simulated from ;20 s to several hours over a wider The starting point for the present work was the large- sampling of parameter space, though with bulk ice mi- eddy-simulation (LES) model used for studies of wake crophysics and 2D, prescribed (rather than simulated) dynamics, wake-plume chemistry, and contrails de- wake dynamics, and ambient atmosphere. In another scribed in Lewellen and Lewellen (1996, 2001a,b); only approach, Schumann (2012) describes a contrail-cirrus a brief summary is given here. A 3D finite-difference prediction model (CoCIP), designed to model the full implementation of the incompressible Navier–Stokes contrail life cycle but at a dramatically simplified level to equations is employed, second-order accurate in space allow the modeling of large populations of contrails. and time, with a direct solver for the pressure and Here we describe a more comprehensive approach, a variable time step. The piecewise parabolic method simulating contrails starting at 1-s age from realistic (PPM) is used for advection of the liquid-ice potential aircraft conditions and following the evolution with 3D temperature Qli, total water mixing ratio qt, ice number fluid mechanics, size-resolved (‘‘binned’’) microphysics, densities, and passive species concentrations. The sub- and coupled radiation through the wake and ambient- grid model uses a quasi-equilibrium second-order tur- turbulence-dominated regimes out to the demise of the bulence closure scheme with a prognostic equation for resulting contrail cirrus many hours later. Novel strate- the subgrid turbulence kinetic energy (TKE) and di- gies are used to improve numerical efficiency. These agnostic equation for the subgrid turbulence length scale capabilities are used to explore some of the critical dy- L. The physical damping of turbulence by stable tem- namics involved in contrail evolution and to assess what perature or rotation gradients is included by appropriate is required for adequate simulation of different facets— reductions in L. The latter helps prevent unphysically for example, whether detailed initial conditions, 3D fluid large subgrid diffusion in vortex cores if they are only mechanics, binned microphysics, and/or realistic ambi- modestly resolved and was developed and used exten- ent atmospheric motions are required to reproduce sively for tornado simulations (Lewellen et al. 2000; contrail-averaged quantities. A ‘‘quasi 3D’’ simulation Lewellen and Lewellen 2007). mode is established as a useful approximation, which The aircraft wake–contrail is initialized as an in- makes practical the coverage of large regions of pa- stantaneous line source in the downstream (y) direction. rameter space with the simulations. There are competing needs of relatively large domains This paper describes the model and highlights some in the cross-stream (x) and vertical (z) directions to general features of the simulation results that have not handle sheared and precipitating contrails and fine grid appeared elsewhere. A companion paper (Lewellen 2014, resolution to treat both the wake-vortex cores and spe- hereafter Part II) analyzes a large set of full-lifetime cies dispersal from the exhaust jets. To meet these effi- simulations for a single aircraft including significant ciently we employ 1) stretched grids in x and z to shear and coupled radiation, emphasizing late-time concentrate fine grid spacing where it is needed, 2) ver- and lifetime-integrated behavior. An extensive para- tical and cross-stream grid tracking to keep the falling metric study focused on young contrail behavior will be vortices or drifting contrail within the fine grid region, presented elsewhere, including different aircraft and and 3) different grids and domains for different stages physically based parameterization of the results. A sig- of the evolution as the needs change. The x and y nificant and surprising result from the present work is boundary conditions are chosen periodic. The Boussinesq the importance in both young and old contrails of ice approximation and periodic boundary conditions DECEMBER 2014 L E W E L L E N E T A L . 4401 in z are used for early simulation segments on smaller domains (with imposed shifts to account for mean temperature or velocity gradients); the anelastic approximation and a closed domain in z are used for later segments on deep domains.

The main limitations of the contrail studies of Lewellen FIG. 1. Dynamic local binning schematic. A global space of ng ice and Lewellen (2001a) were the use of simple bulk ice mass bins defined with fixed mass ratio between neighboring bins 5 R microphysics and omission of coupled radiation or any (mj11/mj m) such that the full range of ice crystal mass expected during a contrail’s evolution is encompassed. In the simulation, means of maintaining ambient atmospheric turbulence. only a subset of this bin space with nl , ng bins is employed with the We describe the model improvements to surmount choice, specified by the starting index within the global space, al- these limitations below, with further details given in the lowed to vary with space and time [is 5 is(x, t)] so as to best rep- appendix. resent the local evolving ice-size spectrum. The overall CPU and memory needs are effectively reduced by the ratio nl/ng with no loss b. Ice microphysics with dynamic local binning in simulation accuracy. Binned microphysics schemes are more numerically costly than their bulk counterparts. For a given appli- analogous to (1) is for the time evolution of the average cation, however, there is often no definitive way to test mass in the local spectrum, m, ak is set to 1, and Cfy is the adequacy of a bulk scheme other than to compare its replaced by a parameterization of the form amb chosen to results with those of a size-resolved scheme. This moti- try to incorporate some of the spectral and shape effects. vated the development of the numerically more efficient In contrail evolution the range of crystal sizes that is bin-resolved scheme described here. The main LES significantly populated varies greatly with location and code handles the advection, diffusion, and sedimenta- time (e.g., a spectrum of small crystals in the cores of tion of ice species. For ice crystal diffusional growth and young contrails versus a spectrum of larger crystals in sublimation we adapted subroutines from the National precipitation streamers). The number of ice bins re- Aeronautics and Space Administration (NASA) Ames quired locally is typically a modest fraction of the global Community Aerosol and Radiation Model for Atmo- requirements for the full contrail evolution. Accordingly spheres (CARMA; e.g., Jensen et al. 1994; Ackerman a dynamic local ice binning, as shown in Fig. 1, was et al. 1995). For later reference, the basic equation em- employed to reduce the computational costs. For each ployed for the growth of a crystal of mass m is (see, e.g., grid cell only the local ice spectrum and thermodynamic Pruppacher and Klett 1997) variables are passed to the CARMA routines at each time step to update the ice spectrum. In each grid cell the a /d local bin space is dynamically shifted up or down within dm 4pCf (1 1 dS 2 e k ) 5 " y i # , (1) the global space during the simulation as needed for best dt 2 R T Ls 1 y following the evolving crystal spectra. Details of the 2 KRyT ei(T)D* implementation are given in the appendix. By default we assume spherical ice crystals, but some where dSi is the supersaturation, ei is the vapor pressure effects of crystal shapes have been explored as will be with respect to ice, Ls is the latent heat of sublimation, Ry discussed later. Pressure perturbations due to fluid mo- and D* are the gas constant and diffusivity for water va- tions are accounted for in computing local saturation por (the latter modified by kinetic theory effects for small conditions. These have a small effect within the trailing crystals), K is the thermal diffusivity, and fy is a ventilation vortex cores but are negligible elsewhere. Buoyancy due coefficient (51 for small spheres). The C and d are the to latent heat release is included; fragmentation and crystal capacitance and characteristic length, both taken aggregation of ice crystals are not (as the latter is equal to the radius r for spherical crystals, and ak 5 2si–y/ expected to be very small at contrail temperatures; see, (riRyT) is taken in analogy with the Kelvin equation for e.g., Connolly et al. 2012). We have developed a new and droplets but using the surface tension for an ice–water numerically efficient scheme for including spectrally vapor interface si–y, and ice density ri. The growth rate resolved homogeneous freezing nucleation but defer its varies for different sized crystals, via the C factor and description elsewhere; this process is not generally en- Kelvin term, and the size spectrum naturally develops countered during contrail evolution unless a persistent over time, in contrast with a bulk model where the de- updraft is imposed, and so is not included in the simu- velopment of only one or more moments of the spectrum lations considered here. The crystals in this work are are followed. For example, in the simple bulk model used treated as pure ice; that is, the aerosol core options in in Lewellen and Lewellen (2001a), the expression CARMA are not utilized here. 4402 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 71 c. Coupled radiation do not. The generation, maintenance, and properties of turbulence in the upper troposphere and lower strato- Radiation processes can play an important role in ice- sphere are complex and not well understood (see, e.g., cloud evolution (e.g., Dobbie and Jonas 2001). The ef- Quante and Starr 2002). Accurately simulating the in- fects of radiative heating or cooling of the contrail have teraction of gravity waves producing intermittent patches been included in the LES by adapting the two-stream of turbulence with LES would require both very large radiation routine from CARMA, which is spectrally domains (for the spectrum of traveling waves) and rela- resolved, using 26 solar and 18 infrared wavelength bins. tively fine grids (for resolving turbulence generation in The work of Gounou and Hogan (2007) comparing breaking waves); however, for useful sensitivity studies a fully 3D radiative transfer model or the independent we assume that it is sufficient to simulate quasi-steady column approximation (ICA) applied to idealized con- ambient turbulence with realistic, statistically re- trails suggests that the ICA is not an unreasonable producible behavior across the range of conditions likely choice for contrail modeling, where the concern is the to be encountered at cruise flight level, regardless of how effect of radiation on the contrail dynamics itself the motions are initially generated or maintained. (though for computing the radiative forcing of the con- Unstratified homogeneous isotropic turbulence is trail on Earth, the uncertainty is likely greater; Forster completely categorized statistically given the turbulent et al. 2012). Taking advantage of the ICA, we choose dissipation rate. This is not true for the stratified case the frequency for updating the radiative heating rates where the mix of waves and turbulence, along with the in each vertical column independently, dynamically energy transfer rate, can differ significantly on different adjusting each as is needed during the evolution. In scales and in time. Moreover, in this case there can be implementing this scheme, the modification of crystal- significant energy loss through wave transport out of the vapor exchange rates due to direct radiative heating of domain or temperature mixing within. The parameter crystals are not included (since the microphysics updates space is multidimensional, including at least stratifica- occur more frequently); however, these contributions tion, mean shear, gravity wave spectrum, turbulence are minor corrections for crystal sizes of a few tens of strength on different length scales, and level of in- microns or less (Gierens 1994) and so should not sig- termittency. To provide representative solutions we nificantly impact the contrail dynamics. Further details perform a separate LES of decaying turbulence to pro- are discussed in the appendix. Given that the contrail is duce velocity perturbation fields that are then added generally optically thin, localized spatially, and that the periodically to the contrail LES. Varying the amplitude radiative heating rates typically change more slowly of the initial temperature perturbations T , the age of than other dynamics in the simulation, this scheme amp the added field f , and time between additions t dramatically reduces the CPU requirements without age add along with the mean shear and stratification allow dif- compromising the accuracy of the computation. In- ferent quasi-steady turbulence states to be achieved. clusion of both coupled longwave and shortwave radi- The fields produced have a realistic patchy character as ation now generally increases the simulation time over expected since in between regenerative additions they the same case with no radiation by 20% at most, com- represent LES Navier–Stokes solutions for the desired pared with an overall order of magnitude increase if the stratification and shear. This is in contrast to the scheme radiation update is computed everywhere at each time employed in Paugam et al. (2010), where velocities from step. a simulation with an unstable Richardson number are imposed on the desired stable conditions. Further details d. Late-time turbulence maintenance and sample results are given in the appendix. Including Our treatment of ambient turbulence for young con- turbulence regeneration is less important if either cou- trails was discussed in Lewellen and Lewellen (1996) and pled radiation or mean wind shear drive more significant Lewellen et al. (1998). Beyond a few Brunt–Väisälä pe- levels of turbulent diffusion in and around the contrail. riods aircraft wake-induced dynamics die away leaving e. Quasi-3D simulation ambient turbulence, wind shear, and large-scale uplift/ subsidence as primary drivers of contrail evolution. The For exploring some sensitivities, a full 3D LES should most relevant conditions are stably stratified with a mix- not be required. A caricature of the most important fluid ture of low-amplitude gravity waves and turbulence since motions—the strong downward motion of the wake aircraft avoid regions of strong turbulence for safety. The vortices and the expansion of the plume through mixing turbulence levels are expected to be lower than generally with the ambient environment—should suffice. For this found in natural cirrus since the latter usually requires an purpose we conduct some simulations with only a mini- active source of uplift for its nucleation whereas contrails mal number of downstream grid points (typically six DECEMBER 2014 L E W E L L E N E T A L . 4403 independent points plus two additional for imposing TABLE 1. Grid and ice binning parameters for 3D simulations. periodic boundary conditions). On larger scales the Time Domain Fine grid spacing simulation is effectively 2D, but 3D eddies are crudely Grid period (x 3 y 3 z km3) (Dx 3Dy 3Dz m3) resolved in a narrow spatial range of scales determined 1 0–2 s 0.84 3 0.052 3 1 0.4 3 0.4 3 0.4 by the downstream resolution (and hence the choice 2 2–90 s 0.84 3 0.26 3 1 0.6 3 2. 30.6 of downstream domain size). This 3D eddy scale was 3 90–300 s 0.84 3 0.26 3 1 1.25 3 1.6 3 1.25 roughly chosen in the range expected to be most 4 5–15 min 1.52 3 1.04 3 1.6 5 3 4.8 3 5. important—on the order of a fraction of the vortex spacing 5 15–90 min 6 3 2.08 3 4163 16 3 16 3 3 3 3 for the wake-dominated contrail and of the contrail 6 1.5–12 h 12 4.16 42528 25 Ice bins 48 global, 20 local depth (before precipitation) for older contrails—with 50-nm–2.6-mm radius; mass ratio 2 the results proving to be rather insensitive to the precise choice. The dramatic reduction in memory and CPU time requirements of this quasi-3D approximation contrail formation (see, e.g., Schumann 1996) are con- (Q3D) allows a much larger parameter space to be ex- sidered. It is expected that essentially all of the contrail plored as well as the ability to test bin or grid resolutions ice crystals are produced during the initial rapid mixing that might be prohibitive in 3D. Because of the small and cooling of the exhaust jets. Accordingly, the total downstream extent, there is a larger spread in results crystal number is set consistent with the fuel flow rate between different turbulent realizations than arises with and an assumed ice crystal number emission index full 3D simulations (cf. Fig. 9), so averaging over a small EIiceno. This quantity is effectively an aircraft variable in ensemble of Q3D simulations is sometimes desirable; our treatment. We consider variations in the simulations this is not an issue for studying sensitivities that do not around a nominal value of 1015 particles per kilogram strongly affect the fluid dynamics (e.g., changing ice of fuel, consistent with in situ aerosol measurements microphysics). (Schröder et al. 2000; Anderson et al. 1998) and jet- As will be shown below, the Q3D approximation plume ice nucleation modeling (Kärcher and Yu 2009). proves to be a much better physical approximation to Delayed nucleation tied to the contrail is expected to be the full dynamics than one would expect a priori. It is of secondary importance at most. In the wake-dominated sometimes true that only a limited subset of degrees of regime vertical displacements are almost entirely down- freedom need be included to represent the physics that ward (relative to the ambient atmosphere at rest). At determines some averaged quantities. A discussion of late times radiative heating of the contrail can produce why that might be the case here is given in section 4a. sustained updrafts, but supersaturations are depleted by The success of such a reduced treatment is not entirely the existing contrail itself, limiting the possibilities for unexpected—we have seen similar in reproducing some new ice nucleation [a result supported by the simulation mean aspects of atmospheric boundary layer behavior tests of Unterstrasser and Gierens (2010b)]. Further using LES with greatly restricted degrees of freedom details on simulation initialization and some sensitivity (e.g., Lewellen and Lewellen 1998)—but ultimately the tests are given in the appendix. utility in any given case can be confirmed only by comparison with fully 3D simulations. 3. Contrail evolution from seconds to hours f. Initialization and modeling choices Contrails exhibit a wide range of behavior, as even The initialization, modeling, and grid choices are casual observation of the sky under different conditions partly aircraft specific. Those used here for a B-767 with will attest. The primary sets of 3D simulations considered 2 wingspan of 47.25 m, flight speed 237 m s 1 at altitude of here are summarized in Table 2. Temperature T and rel- 2 21 10.7 km, total circulation in the wake of 391 m s , fuel ative humidity with respect to ice (RHi)arethetwomost 2 2 flow 5.78 kg km 1, specific combustion heat 43 MJ kg 1, important ambient variables governing contrail evolu- and assumed propulsion efficiency of 30% are given for tion. Persistent contrails are found within sizable ranges illustration. Table 1 lists the domains and grid resolu- of both (Iwabuchi et al. 2012). To best illustrate different tions used for different time periods. The simulations dynamical elements that arise in different regimes we are initialized from 2D Boeing wake rollup calculations highlight in particular ‘‘warm’’ cases with T 5 225 K (Czech et al. 2005) in two steps: an initial high-resolution (toward the upper end of the observed range) and ‘‘cold’’ short-domain run without ice for the early turbulent cases with T 5 205 K (toward the low end of the observed spread of the exhaust jet followed by the introduction of range) along with a more typical temperature for cruise ice crystals distributed spatially like an exhaust tracer altitude of 218 K. Note that for fixed RHi warm and cold species. Only cases satisfying the Appelman criterion for also correspond respectively to ‘‘relatively moist’’ versus 4404 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 71

TABLE 2. Ambient conditions at flight level for principal 3D unchanged by these ambiguities. It is approximately simulations. Three further variations of the simulations with as- twice the total extinction E defined in Unterstrasser and terisks were performed with coupled longwave radiation, varying Gierens (2010a,b). For a given orientation and width the upwelling blackbody radiation temperature for each case Tsfc 5 258, 278, and 298 K. The low and moderate ambient-turbulence definition one can recover a mean optical depth from S levels are quantified in Fig. A1. Unless noted otherwise, we assume in the limit of approximating the extinction efficiency as 5 15 21 an air pressure of 238.5 hPa, EIiceno 10 kg , potential tem- independent of crystal size, Q ’ 2; for example, 2 ext perature gradient of 2.5 K km 1, and no mean uplift, subsidence, or ð ð wind shear (though the ambient-turbulence fields do introduce 1 Dy such motions locally). To illustrate precipitation dynamics, we 5 t D dy dx t consider deep supersaturated layers with initial profiles with con- W y 0 ð ð ð stant RHi above flight level down to 1 km below, linearly dropping Dy 1 j to RH 5 50% at 1.5 km below flight level and below. 5 dy dx dz å pr 2N Q ’ S W i D j j ext /2 (2) W y 0 j Simulation RHi (%) T (K) Turbulence S30T225m 130 225 Moderate for optical depth t on a vertical path, contrail width W,

S30T225l 130 225 Low and crystal number densities Nj for crystal radius rj.We S10T225m* 110 225 Moderate consider only properties of the contrail itself; to de- S30T218m 130 218 Moderate S10T218m* 110 218 Moderate termine the radiative impact of the contrail on Earth’s S30T205m 130 205 Moderate surface, one would need to fold in information about the S10T205m 110 205 Moderate incoming radiation and environments above and below S10T205l 110 205 Low the contrail as well. Figures 4–6 illustrate some of the contrail spatial evolution. The main events of the wake-dominated re- ‘‘relatively dry.’’ Both higher (130%) and lower (110%) gime (cf. Fig. 5)—exhaust entrainment–detrainment values of RHi within the observed range were considered. into the trailing vortex system, vortex fall, linking, ring In the naming convention used for the simulations the dynamics and decay, and Brunt–Väisälä oscillation of first number indicates RHi, the second number indicates the wake–—affect the contrail appearance in the same T, T and the trailing letter indicates the ambient-turbulence ways as was described when simulating with bulk mi- level. In some cases multiple turbulent realizations of crophysics (Lewellen and Lewellen 2001a) or, for many a given simulation were performed by choosing different facets, just a passive exhaust tracer (Lewellen and random number seeds governing the perturbations for Lewellen 1996). We emphasize here structure evolution wake and ambient-turbulence initializations; this can at later times and changes that depend on spectrally give some indication of the statistical uncertainty in the resolved microphysics. results. The qualitative behavior from these sample ca- For much of the evolution most of the contrail volume ses is representative of that we have seen in much larger is driven close to ice saturation because crystal number sets of simulations (e.g., in Part II). densities are typically large in young contrails and time For each simulation the results constitute a five- scales long in older contrails. As a consequence, for dimensional space: time-evolving ice-size spectra in conditions with constant ambient RH , saturation mix- three spatial dimensions. To assess the effects of dif- i ing ratio q , and air density r, M(t) scales essentially with ferent physical parameters or modeling choices it is s the growth of the plume cross-sectional area, A(t): convenient to distill this to a few simple metrics. For this purpose we choose the time-evolving total (i.e., in- ’ 2 M(t) (RHi 1)qsrA(t). (3) tegrated over the x and z directions, averaged over y) ice crystal number N(t), mass M(t), and surface area S(t) per At very low temperatures the water from the aircraft meter of flight path (Figs. 2 and 3) and the contrail- exhausts becomes competitive in the young contrail and averaged ice crystal size spectrum at selected times. In should be added to (3). Until precipitation becomes the absence of crystal growth/sublimation, pure fluid important, the atmospheric pressure p enters the dy- dynamic motions would leave these measures invariant. namics significantly only through qs and r but drops out It is natural to characterize the radiative effects of cloud in the combination in (3); the insensitivity to p that this layers in terms of an optical depth, but this is an am- predicts for young contrail dynamics was confirmed in biguous measure for contrails given their limited hori- simulation tests. zontal extent and nonuniform cross section. The The value of M(t) increases with plume growth dom- quantity S(t) provides an approximate measure of op- inantly driven by exhaust jet mixing (until ;10 s de- tical depth integrated for the contrail as a whole, pending on aircraft), vortex fall (;300 s depending on DECEMBER 2014 L E W E L L E N E T A L . 4405

FIG. 3. Time histories of total (a) ice crystal number and (b) ice surface area per meter of ﬂight path from cases S10T225m with varying coupled radiation: none (dashed line), coupled longwave

with Tsfc 5 258, 278, 298 K (thin to thick solid lines, respectively).

regions below. Often a rough equilibrium is established between new ice growth on the contrail edges (driven by turbulent mixing) and precipitative ice loss within the FIG. 2. Time histories of total (a) ice crystal number, (b) ice mass, older parts in the center. The precipitation growth of and (c) ice surface area per meter of ﬂight path from sample 3D the contrail occurs much sooner in the warm cases than simulations. Line colors indicate different combinations of RH i the cold. Consideration of a large set of simulations (Part and T, and dashed lines indicate different ambient-turbulence levels as follows: S30T225m (black solid lines, three different tur- II) shows that the time scale for this initial growth of the bulent realizations included), S30T225l (black dashed), S10T225m contrail precipitation plume downward is essentially that (green), S30T205m (blue), S10T205m (red solid), and S30T205l required for a single crystal growing in the given ambient (red dashed). conditions to fall through the supersaturated-layer depth,

depending strongly on T and RHi but much less on aircraft and stratification), Brunt–Väisälä oscillation EIiceno, turbulence level, shear, or coupled radiation. At (;20 min depending on stratification), ambient turbu- late-enough times (not reached in all of the simulations), lence, and mean wind shear (which is not included in the the entire remaining plume precipitates downward and simulations here but considered at length in Part II). N(t)andS(t) drop off rapidly (cf. Figs. 3 and 6). Eventually crystals around the plume edges become Ambient-turbulence levels or coupled radiation can large enough that sedimentation velocities exceed tur- affect the contrail evolution significantly over time bulent mixing velocities and precipitation becomes the scales longer than ;30 min (Figs. 2 and 3). Increased dominant means of bringing ice crystals into contact turbulence increases plume dispersion and with it M(t) with supersaturated air. The resultant growth in ice and S(t). In the absence of precipitation the growth seen crystals and increase in fall velocities provides a positive in the simulations is roughly a power law, M(t) ; t0.8 or t1 feedback—essentially a ‘‘precipitation instability.’’ A for the ‘‘low’’ and ‘‘moderate’’ turbulence, respectively. rapid increase in vertical extent of the contrail ensues This is consistent with the rough ;t0.8 dilution rate for [(e.g., from ;(40 to 90) min in Figs. 4 and 6] until the full exhaust species out to a few hours found from in situ depth of the supersaturated layer is reached. Eventually measurements by Schumann et al. (1998). Including the total ice mass falls as ice is lost to subsaturated coupled radiation can either increase or decrease the 4406 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 71

FIG. 4. Mean vertical profiles (z 5 0, indicating flight level) of (a) engine tracer concentration, (b) ice crystal number, (c) ice mass, and (d) ice surface area, per meter of flight path from simulation S10T225m. Times shown are 10, 90, 300, 900, and 1800 s; and 1, 1.5, 3, 6, 9, and 12 h (colors progressing through the spectrum from red to blue). ice crystal number, ice surface area, and contrail lifetime and Lewellen 1996). In the simulations there is a natural (e.g., Fig. 3), depending on the regime. Different regimes clumping that occurs so that the dominant wavelength of coupled radiation behavior are explored in Part II. tends to increase in time. If conditions are such as to Early in the evolution the wavelength of the most foster more rapid precipitation, these structures will be prominent downstream periodicity in the ice distribu- directly reflected in the precipitation patterns as well. tion (e.g., Fig. 5) is set by the Crow instability (Lewellen Since the lowest precipitation streamers originate from

FIG. 5. Drift plot of cross-stream-integrated ice surface area showing young contrail development for cases (top) S10T205m and 2 (bottom) S10T218m. The horizontal axis sweeps over both time and downstream distance (drift velocity 5 12 m s 1) to illustrate both temporal and spatial evolution. The plot format as described in Lewellen et al. (1998) is motivated by scanning lidar measurements. DECEMBER 2014 L E W E L L E N E T A L . 4407

FIG. 6. Drift plot of (top) vertically integrated and (bottom) cross-stream-integrated ice surface area showing long-time contrail development for case S10T225m with coupled longwave radiation with Tsfc 5 298 K. The drift format is as in Fig. 5, but over much longer 2 times with a slower drift velocity (2 m s 1).

the younger contrail at flight level, and subsequent sedimentation and evaporative loss of ice. The spatial streamers precipitate from two sides of the parent pop- distribution of crystal number is also seen to be far less ulation, there is a natural tendency for the precipitation uniform during the contrail evolution than that of the ice streamers to exhibit a shorter periodicity than the ice mass, with the uniformity of the ice surface area distri- mass distribution at flight level for the mature contrail. bution lying in between. In particular the number den- This has been reported in some contrail observations sities in the precipitation streamers are typically orders with large ice mass (Atlas et al. 2006). Over time am- of magnitude less than those near flight level for most bient turbulence, waves, and shear can destroy all rem- of the evolution. In the contrail-averaged size spectra nants of the periodic structure inherited from the young (Fig. 7) the precipitation plume contribution adds only contrail. a small shoulder to the number distributions; nonethe- In the absence of ice nucleation, N(t) monotonically less this sometimes dominates the ice mass (cf. Fig. 7c). decreases. The most dramatic losses are tied to adiabatic The ice crystal size spectrum shifts to larger sizes in heating in the falling trailing vortex system producing time as crystals are lost. There is often a long period in subsaturated conditions (Lewellen and Lewellen 2001a; which the spectral shape (displayed logarithmically) is Sussmann and Gierens 1999), but there are also signifi- nearly constant, just changing in magnitude and mean cant number losses during this period and throughout crystal size (cf. Fig. 7a); the dynamics responsible are the later evolution (discussed more below) that do not discussed more below. The local spectra differ signifi- depend on the local qt falling below the ice saturation cantly in different spatial regions: around the original mixing ratio qs as well as losses at later times through flight level small crystals and high number densities precipitation. Initially the spatial evolution of ice crystal dominate, at the plume edges larger crystals arise, and in number parallels that of a passive exhaust tracer (e.g., the precipitation plume the crystal size progressively Fig. 4)—driven by advection and diffusion. The differ- increases, and number densities decrease, with distance ences in these distributions grow in time because of from flight level. These differences between core and 4408 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 71

FIG. 7. Evolving spectra of ice crystal numbers vs crystal radius FIG. 8. Sample results from Q3D simulations for RHi 5 130%, from (a) S10T205l and (b) S30T225m. (c) Spectra of total ice mass for T 5 218 K, and low ambient turbulence with precipitation present S30T225m. The times and line colors are as in Fig. 4. (solid lines) or turned off (dashed lines), and Kelvin effect in the microphysics present (thin red lines) or turned off (thick black lines). (a) Ice crystal number, (b) ice mass, and (c) ice-size distri- precipitation regions are well known already from in situ bution at contrail age 5 h. measurements (e.g., Heymsfield et al. 1998; Lawson et al. 1998; Atlas et al. 2006) and 2D simulations (Jensen et al. 1998; Unterstrasser and Gierens 2010b); the latter precipitation is allowed. The crystal size spectra are have demonstrated as well that the vapor pressure is paired depending on the former effect for smaller size driven near ice saturation in the contrail core as is found crystals but on the latter for larger. Of the two effects here. The evolution of the spectral widths in Fig. 7 are in precipitation dominates the influence on the large at least rough agreement with the measurements within crystal spectra and M(t) evolution, while the Kelvin contrails at different times of Schröder et al. (2000), effect strongly influences the small crystal spectrum and though differences in (and incomplete knowledge of) N(t) evolution. The surprising importance of the Kelvin the ambient conditions in the measurements precludes effect even at late times is discussed below. a more quantitative comparison. Idealized simulations with some physics turned off help to isolate the different physical mechanisms influ- 4. Further discussion encing each contrail metric. Figure 8 provides an ex- a. Quasi-3D simulation ample. Among the four simulations only two distinct behaviors of N(t) arise, depending on whether the Kelvin Contrails exhibit significant 3D structures at different term in the microphysics is included or not, and only two ages that are readily apparent in the simulations (e.g., behaviors of M(t), depending on whether or not Figs. 5 and 6). Turbulence in the exhaust jets leads to DECEMBER 2014 L E W E L L E N E T A L . 4409 small-scale downstream clumping, the Crow instability produces characteristic periodic downstream puffs with spacing of a few wingspans, these in turn influence subsequent patterns of precipitation streamers, and ambient wind shear and wave fields modulate different patterns in older contrails and contrail cirrus. Which if any of these 3D dynamics significantly affect contrail- averaged metrics? Figure 9 compares the cold and warm B-767 simulations from an ensemble of turbulent realizations of Q3D simulations for the same conditions. The agreement is quite respectable and is representative of results we have found when comparing Q3D simulation with 3D across the range of conditions we have considered. In contrast, a 2D simulation run within the LES (not shown) compares poorly. The Q3D simulations differ from the 2D in effectively allowing one scale of 3D motions to be crudely resolved, chosen on the order of a fraction of the vortex spacing for the wake- dominated contrail and of the contrail depth (before precipitation) for older contrails. The Q3D simulation excludes 3D eddies on larger scales. The wake dynamics and exhaust dispersion for the first tens of seconds do not critically involve such modes, nor does aging contrail FIG. 9. Comparison for cases S10T205l and S30T225m of 3D (dashed lines, three different turbulent realizations for S30T225m case) cirrus (where shear typically dominates the large-scale and quasi-3D (solid lines, four different turbulent realizations for each dispersion). The 3D component omitted from Q3D case) simulation results. Time histories of total (a) ice crystal number simulations that plausibly is of greatest quantitative and (b) ice mass. importance is the wake-vortex dynamics at intermediate times. The depth reached by the wake-vortex system (the subgrid model being designed for 3D rather than affects the fraction of ice crystals surviving the wake 2D applications). This leads to a slowly decreasing regime and the later contrail spread (because sub- spacing of the vortex pair, a downward acceleration, and sequent vertical growth is inhibited by stratification). A a greatly overestimated total vertical extent. The Q3D priori the Crow instability dynamics would seem criti- simulations develop some resolved smaller-scale mixing cally involved in setting the average depth, but the leading to an essentially similar trajectory of descent of success of the Q3D approximation over a large param- the vortex system as that found in the 3D simulations. eter space suggests otherwise. The results are consistent b. Ice crystal number loss with the average vertical extent being determined by the balance between the downward wake momentum and Figure 8 shows that there are crystal losses dependent the positive buoyancy acquired in falling through the on the Kelvin effect that persist even to ages of several ambient stratification, together with smaller-scale en- hours. This component, which we dub ‘‘in situ loss,’’ can trainment (detrainment) into (out of) the vortex system. occur even without conditions becoming subsaturated Both Q3D and 3D simulations represent these elements and can be the dominant loss mechanism at late times in approximately the same way. Fully 3D simulations until precipitation into subsaturated layers wins out. permit reconnection and reorientation of vortex seg- Figure 10 shows that in situ loss is critical in the wake- ments, which affect the contrail appearance greatly (e.g., dominated regime as well. Crystal-loss fractions are

Fig. 5) but its average properties to a much lesser extent. significant even for large RHi and greatly exceed the Mixing scales smaller than the vortex spacing are im- losses found with the Kelvin effect turned off or with the portant, however. Different 2D treatments of the de- bulk microphysics of Lewellen and Lewellen (2001a). scent of a wake-vortex in a stably stratified atmosphere This irreversible loss leads to significant differences in can give widely varying predictions for the evolution contrail properties that persist in time. [see, e.g., Table 1 of Widnall (1975)] depending largely The in situ loss rates and the shape of the ice crystal on the entrainment–detrainment assumptions made. In spectrum that results are derived analytically from the our 2D simulations (not presented here) the mixing into governing equations for diffusional growth of spheri- and out of the falling vortex system is underestimated cal crystals in Lewellen (2012);herewelimitourselves 4410 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 71

known as Ostwald ripening [as pointed out to us by J. Ross (2009), personal communication] or ‘‘spectral ripening,’’ which has also been considered for liquid water clouds (Çelik and Marwitz 1999; Wood et al. 2002). This effect is amplified in contrail evolution by long integration times allowing a small effect to accu- mulate and low turbulence and vertical velocities pre- venting other dynamics from taking over (in contrast to most natural-cirrus evolution). It is the combination of the growth in mean crystal size and the spectral broadening due to the moisture scavenging that permits the nearly constant spectral shape (displayed logarithmically) noted earlier in Fig. 7a to arise. The mean in situ loss rate is unmodified by modest vertical oscillations but can be eliminated by suffi- FIG. 10. Total ice crystal number evolution in young contrails ciently large plume mixing or ascent or low-enough simulated with bulk microphysics (long dashed lines), binned mi- number concentrations (Lewellen 2012). While the in crophysics (solid lines), or binned without the Kelvin effect (short situ loss rates can be quantitatively examined in the 5 dashed lines). Results from Q3D simulations with ambient T simulations, the rates for actual contrails are more 218 K and RHi 5 110% (thin lines) or 130% (heavy lines). The number losses around 100 s are forced by wake-vortex descent and uncertain. The Kelvin effect is quantitatively more those around 700 s are forced by descent in a Brunt–Väisälä oscil- poorly understood for ice crystals than for water drops lation of the wake plume. and, as noted below, uncertainties in the ice deposition coefficient factor in as well. While a shift in the critical vapor saturation level is certainly present for small to summarizing the basic physical mechanism. For crystals, and the basic effect of large crystals growing at small spherical crystals, surface energy (Kelvin) effects the expense of smaller ones is likely robust, there may shift the critical vapor supersaturation level that sepa- be significant quantitative changes owing to crystal rates sublimation from growth away from zero to growth and shape effects. There are also smaller re- a value depending on crystal radius, 1 2 eak/r [cf. (1)]. sidual crystal losses that can remain even in the absence 23 Given that ak ; 2 3 10 mmismuchlessthanthemean of the Kelvin effect (barely evident in Fig. 8) depending crystal sizes encountered in the contrail, the magnitude on the combined effects of gravity wave magnitude and of the Kelvin-dependent effect seen in the figures is at parcel mixing. first surprising. Its origin is in the local competition c. Sensitivity to EI between different sized crystals together with dynamics iceno forcing the system close to saturation. In the young The changes in crystal-loss mechanisms seen with descending contrail adiabatic heating forces the water spectrally resolved microphysics alter the sensitiv- vapor mixing ratio qy below qs but the high number ities to EIiceno. Figure 11 shows sample Q3D results densities ensure that conditions never get far from varying EIiceno. Because of the in situ crystal losses the equilibrium (the simulations rarely show vapor satu- fraction of the total crystals lost in the wake- ration levels in these regions below 97% and generally dominated regime rises with EIiceno faster than the above 99%). Even the small differences due to the expectations from bulk treatments (e.g., Lewellen and Kelvin effect for modest crystal sizes are relevant in Lewellen 2001a; Unterstrasser et al. 2008). Moreover, comparison to the small levels of subsaturation main- this sensitivity remains for older contrails, contrary to tained in most regions experiencing crystal loss. This the expectations based on bulk treatments that the broadens the size spectrum leading to more rapid fraction of crystals lost would be approximately in- crystal loss. dependent of EIiceno (e.g., Unterstrasser and Gierens At late times conditions are naturally driven toward 2010a). One consequence is that the sensitivity to 14 21 equilibrium (qy / qs) so they appear slightly super- EIiceno .;10 kg diminishes significantly over saturated to the larger crystals but, because of the time; in Fig. 11 an initial factor of 1000 difference in Kelvin effect, slightly subsaturated to the smallest. crystal number is reduced to ;3withinafewhours. Large crystals scavenge moisture from small ones This insensitivity is one sided, however: for small- leading to a slow but persistent crystal loss. This rep- enough EIiceno the crystal number densities are re- resents an example of the more general phenomenon duced sufficiently so that in situ losses are absent over DECEMBER 2014 L E W E L L E N E T A L . 4411

to the order of magnitude consistent with in situ measurements anyway by the crystal losses during the wake-dominated regime. The quantity M(t), governed dominantly by plume volume and ambient conditions, is

relatively insensitive to EIiceno unless it drops below 2 about 1014 kg 1 (Fig. 11b); the time scale for reaching the equilibrium state in (3) exceeds plume expansion time scales if ice number densities are small enough. d. Sensitivity to water from fuel consumption The ice crystal number losses in the young contrail are greatly reduced at colder temperatures (e.g., Figs. 2 and 5). Reduced crystal loss for dryer conditions and thus smaller crystals seems counter intuitive, but it proves to be an effect of water from fuel combustion. The water

from the engines raises qt/qs locally in the contrail (particularly in those regions with highest crystal num-

ber densities) to a much greater extent the smaller qs, and hence the smaller T. For example in S10T205 the

engine water raises qt/qs in the young (;30 s) contrail core from the ambient 110% to over 200% while in S30T225 the corresponding increase is only from 130% to ;138%—explaining the enhanced crystal survival in

the former case despite the decreased ambient RHi.As discussed more in Part II, this is one factor in raising the potential signiﬁcance of cold contrails despite their relatively low ice water content. That very low temperature conditions lead to greatly reduced ice number losses was noted in Unterstrasser et al. (2008) but attributed to changes in growth–sublimation rates with temperature.

FIG. 11. Effects of varying EIiceno on total (a) ice crystal number, e. Further microphysics uncertainties (b) ice mass, and (c) ice surface area, for Q3D simulations with 5 5 RHi 110%, T 218 K, and low ambient turbulence [dashed 1) ICE CRYSTAL SHAPE EFFECTS patterns from top to bottom in (a) indicate 1017,1016,1015,1014, 13 12 11 11 10 ,10 , and 10 per kilogram of fuel]. The two EIiceno 5 10 per For the present simulations we have assumed spherical kilogram of fuel cases shown differ by the choice of initial radius of ice crystals for simplicity. In situ sampling of contrails the ice crystals (0.2 mm for double crosses and 8.0 mm for double suggest that the shapes of small (;20-mm diameter or asterisks). less) crystals that are found in young contrails or contrail cores are quasi spherical (e.g., Gayet et al. 1998; Schröder the time scales available. The dramatic changes in et al. 2000; Febvre et al. 2009) while the shapes of the contrail evolution suggested in Fig. 11 from reductions larger ones found in the contrail periphery or in pre- in EIiceno below this threshold are considered more in cipitation streamers are more complex (e.g., bullet ro- Part II. It is interesting that the EIiceno suggested by settes, extended columns, or irregular) (e.g., Lawson et al. both jet-plume ice nucleation modeling for current 1998; Heymsfield et al. 1998; Gayet et al. 1998). Iwabuchi aircraft [the soot-dominated regime of Kärcher and et al. (2012) found results consistent with this picture Yu (2009)] and in situ aerosol measurements (Schröder from a large survey of the optical properties of persistent et al. 2000; Anderson et al. 1998)isofthesameorderof contrails. Crystal shapes can affect growth rates, sedi- 2 magnitude (;1015 kg 1)asthelowerrangeoverwhich mentation velocities, and optical properties. To assess in situ losses are found to be large in the wake- their potential importance for contrail evolution Meza dominated regime here. Even if the mechanisms lim- (2010) added to the current LES model the option of iting the crystal numbers in the initialization stage using nonspherical shapes: hexagonal columns, plates, considered by Kärcher and Yu (2009) were absent, the bullet rosettes, or a mass-dependent combination of ice crystal numbers in contrails would tend to be forced shapes (near spherical for small sizes, hexagonal columns 4412 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 71 of varying aspect ratio for midrange, and bullet rosettes a given crystal mass that results amplifies the Kelvin- for the largest). The shape effects were incorporated dependent in situ crystal loss, thereby reducing N(t) through modifications of C, fy,andd in the ice growth significantly relative to the result for spheres. [(1)] and of sedimentation velocity as a function of crystal 2) ICE DEPOSITION COEFFICIENT mass; the effects on coupled radiation were only partially included. The precise implementation and comparison of The ice deposition (or accommodation) coefficient bi results for different shapes are given in Meza (2010), but is poorly determined experimentally, with results in the we summarize the main findings here. literature ranging over more than two orders of magni- For realistic shape assumptions and in the absence tude (e.g., Pruppacher and Klett 1997, their Table 5.5). of coupled radiation none of the differences in N(t)and The default choices made by different cirrus modelers M(t) for different conditions due to shape effects were covers nearly as large a range and have a significant found to be large in comparison to the Q3D realization impact on the crystal number densities produced via spread. Some more significant differences were found in homogeneous nucleation in natural-cirrus simulations

S(t) but were consistent with being primarily geometrical (Lin et al. 2002). The quantity bi appears in the ice rather than dynamical, representing the change in surface growth [(1)] effectively through modifying the water va- area for fixed number density and mass given by shape por diffusion coefficient D (Pruppacher and Klett 1997): change alone. This suggests that while it may be important 1/2 to consider shape differences when assessing the radiative 5 1 ’ D 2p D* D/(1 lb/r) with lb . (4) impact of a contrail, it might be sufficient to perform bi RyT simulations with spherical crystals to determine N(t)and

M(t) and then assess shape effects on the radiative impact There is negligible effect as bi approaches 1 or as crystals afterward. The exception would be cases where the radi- grow large compared to the mean free path of water ative heating–cooling of the contrail itself strongly couples vapor (a fraction of a micron for contrail conditions). As into its dynamics, together with a heating–cooling rate already noted, contrail dynamics are such that ‘‘small that is strongly shape dependent. Preliminary sets of crystal’’ effects can have an extended range of influence. simulations with coupled radiation in Meza (2010) did not Figure 12 shows results from simulations varying bi away identify any dramatic crystal shape-dependent effects, but from the CARMA assumed value of 0.93. There is in- more complete treatment of the radiation for nonspherical creasing sensitivity seen in crystal losses as bi drops shapes is required before drawing final conclusions. below 0.1 and profound differences in M(t)aswellas The relative insensitivity of the contrail evolution to N(t) when the values become small enough. The sensi- crystal shape that was found is perhaps not unexpected: tivity is dominantly through the effect of bi on in situ small ice crystals in the contrail do not differ much from crystal loss (Lewellen 2012), although significant sensi- spheres, while large crystals have significant fall veloci- tivity remains even with Kelvin effects excluded since ties shortening lifetimes and so limiting their contribu- bi 1 reduces overall ice growth rates. Recent labo- tion to contrail-integrated metrics.1 For any compact ratory measurements designed specifically for cirrus shape, such as a hexagonal column with aspect ratio conditions (Skrotzki et al. 2013) recommend the value of around one, the shape-dependent factors that might bi 5 0.7 and may, if confirmed, significantly reduce this directly affect contrail evolution (e.g., the capacitance uncertainty, though it remains unexplained why some factor or sedimentation velocity) do not vary much from measurements give much lower values and remains the spherical results (even though the optical properties a possibility that bi may vary with crystal size, habit, might be quite distinguishable). Further, within the supersaturation, and/or temperature. contrail core, the growth of ice mass is generally governed by mixing rates of ambient air into the contrail or 5. Concluding remarks vertical displacement of it, rather than growth rates for individual crystals that can be affected by shape. Meza In this work, contrails have been simulated from a few (2010) found large differences in contrail evolution due wing spans behind the aircraft through the wake-vortex to shape only when the smallest crystals were assumed evolution, transition to contrail cirrus, and eventual (unphysically) to be bullet rosettes: the reduced d for demise through precipitation of the constituent ice crystals into subsaturated air. The use of dynamic local ice binning, column by column dynamic updating of 1 Further discussion on the potential effects of nonspherical radiative heating, a scheme for providing resolved am- crystal shapes integrated over the contrail’s lifetime are given in bient atmospheric turbulence, and the surprising success Part II. of a quasi-3D simulation mode make practical the DECEMBER 2014 L E W E L L E N E T A L . 4413

turbulence level as if it were universal, particularly in the absence of other turbulence production (e.g., from mean shear or coupled radiation). More importantly, the inclusion of binned microphysics significantly increases rates of ice crystal number loss in both young and old contrails because of local competition between large and small crystals for available moisture and how this is modified by the Kelvin effect. This adds to previous contrail work suggesting the need for improved microphysics (Huebsch and Lewellen 2006; Unterstrasser and Sölch 2010). It might be possible to approximately incorporate these effects through suitable modifications of 2D fluid dynamics and bulk microphysics models a pos- teriori, but they will not naturally be present. For lower ambient temperatures the water from the

aircraft engines becomes important in boosting qt/qs in the young contrail and thereby signiﬁcantly reducing crystal number losses in the wake-dominated regime. The fractional rate of ice crystal number loss is also strongly dependent on the crystal number densities themselves (in contrast to simple expectations from bulk models). As a consequence, the sensitivity to changes in effective ice crystal number emission index are dra- 14 21 matically reduced over time for EIiceno .;10 kg . Given the sensitivity of the simulations to the Kelvin

effect and the ice deposition coefficient bi through their impact on crystal-loss rates, improving the observational constraints on these would be useful. Quantitative differences aside, most of our conclusions on contrails of more than a few minutes’ age are consistent with other studies (e.g., Jensen et al. 1998; FIG. 12. Effects of varying ice deposition coefficient: bi 5 1 (solid line), 0.5 (short dashed), 0.3 (long dashed), 0.1 (long–short dashed), Lewellen and Lewellen 2001a; Unterstrasser and Gierens 0.01 (starred–dashed). Results from Q3D simulations with RHi 5 2010a,b), including the critical importance of ambient 110%, T 5 218 K, and low ambient turbulence. RHi, the primary role of temperature in determining crystal size, the very small fraction of crystal number but significant fraction of ice mass found in precipitation exploration of a large parameter space of detailed con- streamers and their efficiency in removing moisture trail simulations out to many hours of simulated time. from large volumes, and the critical importance of While the simulations are more numerically costly than coupled radiation in some regimes but not others. Sed- the approach of Unterstrasser and Gierens (2010a,b), imentation plays a critical role in the vertical spread of they have the advantage of permitting a direct assess- the contrail and its ultimate lifetime. The time scale for ment of the effects on contrail dynamics of explicit the initial onset of significant precipitation growth is binned ice microphysics, 3D fluid dynamics, realistic dominantly governed by RHi and T. The contrail/ resolved aircraft wake dynamics, and resolved ambient contrail-cirrus lifetime is generally shortened by fac- atmospheric turbulence/waves. tors leading to larger crystal sizes, including higher RHi Some of these effects prove more critical than others. or T, lower ice numbers, increased turbulent mixing with While 3D dynamics can dramatically affect contrail supersaturated air, and increased wake-induced or in appearance, comparing 3D and Q3D results suggests situ crystal loss. An assessment of the effects of different that including a very limited range of scales of 3D tur- physical variations on overall contrail significance bulence may be sufficient for mean contrail properties. therefore requires covering a sizable parameter space Inclusion of resolved ambient turbulence/waves dem- with simulations over the full lifetime. The model de- onstrates their importance to older contrail extent and scribed here is efficient enough for such studies, taken lifetime; it is not appropriate to consider only a single up in a companion paper (Part II). 4414 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 71

The simulations here show a clear potential for long- spatial point x is checked to see whether the spectrum lived, large-volume contrails. Even if the ice cloud in most would be better represented in local bin space if is(x, t) of this volume is not optically apparent it could still have were shifted up or down by 1. The spectrum is then significant radiative impact. At the same time the aging ‘‘folded back’’ from the expanded bin space into the contrail can sometimes transform a very large volume appropriately shifted local space. The crystals outside that was highly supersaturated into one that is near zero the new local space are simply added to the nearest size supersaturation, extending from just above flight level bin that is included. Both total ice number and qt are down through the depth of the supersaturated layer in the conserved in the folding process; ice mass is not. Ideally vertical and over several kilometers in the horizontal the number of local bins should be chosen large enough even in the absence of strong mean wind shear. This so that the number of crystals folded back is always could possibly provide subsequent aircraft with a corridor negligible. The latter is monitored by the code so that in which to fly without producing significant contrails a simulation may be terminated if an increase in number themselves. While this would be a drifting corridor, of local bins is required. The simple shifting criterion of conditions for which it might be toughest to track (e.g., minimizing the number of crystals at the local bin ends is large cross-stream shear) would tend to give wider targets found to work well. When crystals evaporate out of the of subsaturated horizontal extent. By removing the su- smallest global bin they are removed completely from persaturation in this region the corridor could also lead to the simulation. Physically crystals evaporating out of the a reduction in natural cirrus. Because of the extensive smallest local (but not global) bin should sometimes be interaction of a single contrail over its lifetime with both removed as well, in regimes where large crystals are the horizontal (particularly with wind shear) and the growing at the expense of small ones so that down- vertical extent of the ice-supersaturated region, these shifting of the local space is not appropriate. This is di- effects may need to be accounted for explicitly in regional agnosed by crystals piling up in the lowest local bin after and global simulations of contrail effects. Because of the the spectrum is folded back; accordingly, crystals evap- potential depletion of ice supersaturation, this may be orating out of the lowest local bin are removed if its bin particularly important in regions of heavy air traffic or for population exceeds that of the next larger bin. future projections of increases in air traffic. Based on several tests we choose for the simulations

here Rm 5 2, ng 5 48, nl 5 20, and smallest global bin Acknowledgments. This research has been supported corresponding to crystal radius of 50 nm. The local by the Boeing Company. We thank Steve Baughcum binning scheme was critically tested by running it and Mikhail Danilin for important contributions concurrently with a conventional global binning within throughout the course of this work, Eric Jensen and the same simulation for different contrail conditions. Andy Ackerman for providing access to CARMA, Contrail simulations were also performed varying the Michael Czech and Jeffrey Crouch for providing 2D ice bin resolution. In addition, in Lewellen (2012) dif- wake results for initialization, and Tim Rahmes and ferent ice binning choices in parcel model tests were John Ross for useful input and discussions. We thank compared against exact analytic solutions of ice spec- three anonymous reviewers for comments leading to trum development for numerically challenging regimes improvements in the presentation of this work. with in situ crystal loss. The tests suggest that for contrail simulation a bin mass ratio of 3.0 is probably marginally adequate, while a ratio of 2.0 generally re- APPENDIX produces results of a much finer binning well (though somewhat overestimating in situ crystal loss; Lewellen Additional Model and Simulation Details 2012). Parcel model tests showed that, for a bin mass ratio of 2.0, even as few as 10 local bins faithfully represents the a. Ice microphysics evolution in different growth regimes. Within contrail At each time step in each grid cell where the ice simulations the concurrent local–global tests showed al- numbers are not numerically insignificant, the local ice most indistinguishable results (much less than typical spectrum (cf. Fig. 1) is passed to the CARMA routine Q3D realization differences) using 15 local bins. An ad- for updating the diffusional growth, performed in a bin vantage of the dynamic local binning is that the largest space extended from the local space by one bin on either and smallest crystal sizes represented in the global space end. Advection and diffusion updates in each spatial may be selected conservatively without significant in- direction are conducted on the subspace of the global creases in numerical cost. Sensitivity tests showed no bin space that is populated along the given spatial line. apparent change in results when the choice of 50-nm At the end of each time step the ice spectrum at each minimum radius was shifted up or down by a few bins. DECEMBER 2014 L E W E L L E N E T A L . 4415

Early in the contrail dynamics the restriction on the coordinates) are added, with the pressure and tempera- time step set by the wake fluid mechanics is generally ture interpolated between the surface values and those at more stringent than that set by the ice physics. At late the bottom of the LES domain, and a constant relative times the microphysics is substepped on a shorter in- humidity with respect to water assumed (taken as 30% terval than the fluid mechanics if necessary (an existing for the simulations here). A constant CO2 concentration feature of CARMA). When populations of crystals with of 350 ppmv is assumed throughout the column and the large fall velocities become significant, the LES time ozone mixing ratio taken from the U.S. standard atmo- step is reduced if necessary so that the fall velocity sat- sphere midlatitude profile; no other trace gasses are in- isfies the Courant condition. If the population is physi- cluded in the radiation computations. When incoming cally insignificant, then its fall velocity is simply reduced solar radiation is included (as for some runs in Part II), to maintain stability with the current time step. latitude, date, surface albedo, and either time-varying or constant solar zenith angle can be specified. b. Coupled radiation with dynamically adjusted independent column updates c. Late-time turbulence maintenance For each grid column in the domain, vertical profiles For each of the domains in Table 1 except grid 1 of T, qy, and ice particle concentrations are passed to the (where ambient atmospheric turbulence plays no sig- CARMA radiative transfer routine to compute a radia- nificant role) a preliminary LES to produce ambient- tive heating rate for each point in the column. The turbulence fields was performed with periodic boundary contributions from all columns are stored and used to conditions, uniform grid spacing in each direction and update local conditions at each time step. For a single the desired ambient stratification, mean shear, and do- column denote the vertical heating rate profile HR(z, t) main size. These were initialized with temperature and time between updates dtR. Then dTE [ dtR 3 perturbations 12Tamp with 1 and 2 randomly chosen in maxz[HR(z, t 1 dtR) 2 HR(z, t)] provides an estimate of each grid cell and distributed uniformly between 21 and the maximum error in temperature due to the delay in 1. Fields from these decaying turbulence simulations updating the heating rates. Since the coupled radiation were taken at a chosen age fage and these added to the mainly affects the contrail dynamics through buoyancy- contrail LES every tadd seconds to maintain some am- induced changes in parcel heights, a natural temperature bient turbulence in the main simulations over long difference scale to consider in the simulation is dT0 [ times. Before adding the aged turbulence fields to the gDz, where g is the potential temperature gradient and contrail LES the horizontal mean averages were re- Dz is the finest vertical grid spacing. After each update if moved and the domain shifted by a random amount in dTE . fRdT0 then dtR is halved; if dTE , fRdT0/3 then it is x, y, and z so that the sequential additions were effec- doubled. The tolerance fR is an input for the scheme. The tively independent of each other even though for each dtR’s are allowed to vary for each column independently, domain only a single field from the corresponding de- with the exception of requiring that the values for caying turbulence LES was utilized. The accompanying neighboring columns differ by no more than a factor of 2. subgrid TKE field was also added but the temperature This avoids potential problems associated with horizontal perturbations were not, since this would interact un- advection of sharp-edged clouds. In addition to these physically with the ice dynamics. The initially imposed updates, the heating rates in all columns are computed for mean vertical shear in the contrail LES persists on its the first time step and for each LES output cycle (typically own over the course of a simulation (without any every 300 s at late times). A value of fR 5 0.01 has been nudging or imposed pressure gradients required) since chosen for the simulations here. A set of contrail test only perturbations away from the horizontal average are cases showed that changing to fR 5 0.001 or 0.1 produced added, periodic horizontal boundary conditions are little or no differences in mean contrail development. used, and the shear and stratification levels are chosen Other components of the radiation scheme are taken such that the mean shear does not directly drive a shear essentially as is from CARMA. For our sensitivity studies instability. here and in Part II we take the upwelling blackbody ra- After repeated field additions the turbulence statistics diation temperature Tsfc as our primary variable. Condi- of the simulation, averaged over periods long compared tions above the LES domain are specified via a blackbody to tadd, become quasi steady. The state is determined by temperature of downwelling infrared radiation at domain the choice of stratification, shear, Tamp, fage, and tadd as top and an assumed integrated water column above the well as the domain size and grid resolution. The turbu- domain (taken as 130 K and 0, respectively, for the sim- lence and gravity wave amplitudes can be increased by ulations here and in Part II). Between the LES domain increasing Tamp and/or decreasing tadd; the relative im- and the surface, 10 evenly spaced layers (in pressure portance of gravity waves compared to turbulence is 4416 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 71 increased by increasing fage and/or tadd; and the level of intermittency increases with increased tadd. The numerical overhead of this scheme is minimal. Given the use of different domains and grids for different simulation segments, a practical consideration is the extent to which the character of the fields can be matched across different domains or grids. This was found empirically to be achieved approximately if the same Tamp, fage, and tadd are chosen and in addition the same resolution is used for the preliminary dying turbulence simulation in each case; Fig. A1 provides an example from the current simulations. For the simulations of Table 2 we chose fage and tadd both equal to 10 min (roughly the Brunt–Väisälä period for the given stratification) and chose Tamp 5 0.2 K and 2 K for the low and moderate turbulence cases, respectively. The horizontal and vertical resolutions for the decaying turbulence simulations were chosen to be 50 and 33 m, respectively. The mean dissipation levels produced (Fig. A1) fall within the broad range observed in the upper troposphere or lower stratosphere [e.g., as given in 2 23 Table 17.3 of Quante and Starr (2002)]. FIG. A1. (a) Mean dissipation rate (m s ) and (b) vertical 2 velocity variance (m2 s 2) vs time for sample simulated ambient- d. Simulation initialization turbulence fields such as those employed in the contrail simulations. Thick solid lines are from low-turbulence simulation on 12 3 The 2D Boeing results are utilized five spans behind 3 3 ; 4 4km domain; other lines from medium-turbulence simulation the aircraft ( 1-s age) and include velocities, down- on 12 3 4 3 4km3 domain (solid line), 0.84 3 0.26 3 1km3 domain stream vorticity, a passive exhaust tracer, and a modeled (long dashed), and 12 3 0.32 3 4km3 Q3D domain (short dashed). turbulent eddy viscosity. From the latter a turbulent The small-scale dissipation rate and vertical velocity variance are kinetic energy is estimated, a fraction of which is used to chosen to roughly quantify the ambient-turbulence state, as the initialize the subgrid TKE field for the LES and a small most important impact on contrails is through mixing rates and vertical motions. fraction is used for resolved velocity perturbations. The velocity field from the 2D calculation is combined with these random perturbations (and a mean ambient shear microphysics simulation with sufficient spatial resolu- profile if desired) to form the LES velocity field. The tion to maintain the initial tight vortex cores throughout spreading exhaust jets rapidly develop their own re- the vortex-dominated stages of the LES. Our previous solved turbulence and the LES subgrid TKE adjusts on studies initialized with more diffuse cores (Lewellen and a fast time scale as well so that the simulation results are Lewellen 1996, 2001a) suggest that this is not required in not very sensitive to the magnitudes of perturbations or order to simulate the dispersion of the exhaust species subgrid TKE chosen. The velocity field is extended from and basic vortex dynamics well. Accordingly, we run the the smaller domain of the 2D simulation by integrating 2-s simulation on grid 1 with the subgrid rotational the vorticity field using Biot–Savart’s law. The passive damping turned off to modestly diffuse the vortex cores tracer from the 2D model is used directly to initialize so that they can be well resolved on grid 2. a passive tracer in the LES and is scaled (given a fuel Results from the initial LES are used to initialize the flow rate, propulsion efficiency, and specific combustion main contrail simulation on grid 2 with ice introduced. heat) and added to a desired ambient gradient to form Periodic copies were used to extend from the smaller to the LES potential temperature field. larger downstream domain and an ambient-turbulence The fine resolution in grid 1 of Table 1 is required to field of desired character added as discussed earlier. The resolve the small vortex cores provided by the 2D initialization times represent a compromise. The LES Boeing simulation as well as being beneficial in rapidly must be initialized late enough that the approximations of developing realistic jet turbulence. Comparison be- takingthewaketobeuniformdownstream,andthehot tween the 0.4-m-resolution LES and a 0.25-m-resolution exhaust jets to be incompressible, are reasonable. It must test run out to 15 s supported the adequacy of the coarser be early enough to generate the large concentration resolution. It is numerically costly to run the full binned fluctuations in the exhaust jets that are a product of 3D DECEMBER 2014 L E W E L L E N E T A L . 4417 turbulence in the early stages. This prompted the ;1-s the new grid. The fields are sufficiently well resolved that initialization age and high-resolution LES. Ice initializa- any nonconservation of species that this interpolation tion is delayed in part to ensure that the exhaust jets have could in principle produce are in practice confirmed to cooled so as to become supersaturated with respect to ice. be negligible. The new downstream domain is always A much longer delay is undesirable because it would slow chosen to be an integer multiple of the old one, with the the initial development of the Crow instability, which fields periodically continued into the expanded domain. necessitates the longer downstream domain. A fresh ambient-turbulence field generated for the new Ice is introduced in a single size bin (generally 0.2-mm expanded domain is added at the start to break the radius). Simulation tests showed results to be insensitive symmetry between the periodic copies of the contrail to the initial ice spectral distribution: in the young wake downstream and to provide local variations in the new plume the number densities are sufficiently high that the regions added in the cross-stream directions. Given the crystals rapidly (in ;1 s) adjust their mean size to presence of the contrail, the domain expansion in the achieve local equilibrium conditions regardless of their cross-stream directions is not done as a periodic copy starting point, and the mixing in the exhaust jets is rapid and so is not required to be an integer multiple of the enough that it quickly governs the shape of the local size old domain. Because the cross-stream boundaries spectrum, washing out the memory of the initial bin are always located far from the expanding contrail and distributions. Figure 11 provides an example showing the fresh turbulence addition dominates the decayed that even if the initial crystal numbers are much less and turbulence remaining on the old grid, any discon- the initial bin size significantly raised, the effects wash tinuities in the ambient velocity fields produced by this out after the wake-dominated regime. procedure have negligible effect on the subsequent For simplicity the ice has been introduced spatially contrail evolution. following a passive exhaust tracer. Given the complex- Given the vertical grid tracking utilized in the code, ities of ice nucleation in the turbulent cooling jets this it is necessary throughout the simulation segments and need not be the case physically. Simulations with the ice regridding steps to keep track of where the original number density initially distributed spatially as some flight altitude lies within the grid at each time. Hy- power of the local tracer concentration C with the total drostatic balance within the domain is then assumed to numbers held constant, were compared to test the sen- obtain the mean pressure at each level in the grid from sitivity. Varying over the range from C1/3 to C3, the re- the pressure assumed at flight level. This same capa- sulting changes in contrail properties still proved small. bility is employed if a uniform uplift or subsidence is to This is consistent with changes in results due to engine be included in the simulation (as is done for some cases placement, which, while more significant, are generally in Part II). not dramatic. Note that in these sensitivity tests only persistent contrails were considered; significant changes REFERENCES to the evolution of short-lived contrails in subsaturated conditions have not been ruled out. Ackerman, A. S., O. B. Toon, and P. V. 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