Contrail - Wikiparency

# Contrail > [[PORTAL_Aviation|Aviation]] · [[PORTAL_Avionics|Avionics]] spine.  ## Microsims — three.js ### Contrail (three.js) <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Contrail.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Contrail — three.js microsim"></iframe> </div> **Open it full-screen:** [Contrail.html](https://wikitube-3d-microsims.netlify.app/Contrail.html) · library `threejs` · route `microsim/threejs/` ### Related microsims Live sims on neighbouring articles: - [[Turbojet]] - [[Environmental_impact_of_aviation]] - [[Cirrus_cloud]] - [[Sustainable_aviation_fuels]] - [[Tropopause]] - [[Fuel_economy_in_aircraft]] *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4).*  ## Overview A contrail is a cloud made by an aircraft, and the most important thing about it is that it is a **threshold phenomenon**. Two aircraft of the same type, at the same flight level, four minutes apart, can leave completely different skies behind them: one a clean blue wake, the other a white line that widens for the next three hours. Nothing about the engines changed. What changed was the air. Two independent questions decide what happens, and conflating them is the commonest error in popular accounts. The first question is **formation**. Hot, wet exhaust leaves the engine at something like 600 K and mixes with ambient air at 220 K. Because heat and water are both conserved during that mixing, every intermediate state of the plume lies on a *straight line* in the plane of temperature against water vapour partial pressure. If that line rises above the saturation vapour pressure curve **over liquid water**, the plume passes briefly through a water-supersaturated state, droplets condense on the soot particles the engine has just emitted, and those droplets freeze within a fraction of a second. A visible trail appears. If the line stays below the liquid curve, nothing forms at all — not a faint contrail, nothing. This is the **Schmidt–Appleman criterion**, set out by Ernst Schmidt in 1941 and independently by Herbert Appleman in 1953, and put on its modern quantitative footing by Ulrich Schumann in 1996. It is a yes/no test, which is why contrail behaviour looks so discontinuous from the ground. The second question is **persistence**. Ice, once it exists, no longer cares about liquid saturation; it cares about saturation over ice. If the ambient air is subsaturated with respect to ice, the crystals sublimate and the trail is a short stub trailing a few aircraft lengths behind the wing. If the ambient air is **ice-supersaturated**, the crystals keep growing on the ambient vapour, wind shear stretches the plume sideways, and the contrail becomes indistinguishable from natural cirrus within an hour. Ice-supersaturated regions (ISSRs) are invisible, common — of order 10–20% of the upper troposphere by volume at mid-latitudes — typically only a few hundred metres deep but a hundred kilometres or more across, and they have ragged three-dimensional edges. That geometry is why this simulation is built in three dimensions rather than as a cross-section: the aircraft flies bodily into and out of a humid body of air, and you watch the trail change state as it crosses the boundary. ## The physics ### The mixing line Consider a parcel of exhaust that has been diluted with a mass *m* of ambient air per kilogram of fuel burned. Two things have been added to that air. **Water.** Combustion converts every hydrogen atom in the fuel into water. If the fuel's hydrogen mass fraction is *X*H, then burning 1 kg of it releases *X*H kg of hydrogen, and each kilogram of hydrogen becomes 18.015/2.016 = 8.937 kg of water. So the water emission index is fixed by stoichiometry alone: > **EIH₂O = 8.937 · *X*H** For Jet A-1, *X*H ≈ 0.138 and EIH₂O ≈ 1.23 kg per kg of fuel. For hydrogen, *X*H = 1 and EIH₂O = 8.94. **Heat.** Burning that kilogram releases *Q*, the net (lower) heating value — about 43.2 MJ/kg for Jet A-1. But not all of it ends up in the plume. A fraction *η*, the **overall propulsion efficiency**, leaves the aircraft as useful propulsive work rather than as thermal energy in the exhaust. Only *Q*(1 − *η*) heats the plume. The temperature excess and the vapour-pressure excess of the diluted parcel are therefore > Δ*T* = *Q*(1 − *η*) / (*c*p · *m*) and > Δ*e* = (EIH₂O / *m*) · *p* / *ε* where *c*p = 1004 J kg⁻¹ K⁻¹ is the isobaric specific heat of air, *p* is the ambient pressure, and *ε* = *M*water/*M*air = 0.6222 converts a mixing ratio into a partial pressure. Dividing one by the other, **the dilution *m* cancels**: > **G = Δ*e*/Δ*T* = EIH₂O · *c*p · *p* / ( *ε* · *Q* · (1 − *η*) )** [Pa K⁻¹] That cancellation is the whole reason the criterion is tractable. Because the slope does not depend on how far the plume has mixed, *all* states of the plume lie on one straight line through the ambient point — the **mixing line**. At 250 hPa with Jet A-1 and *η* = 0.30, G ≈ 1.64 Pa K⁻¹. ### The threshold temperature The critical case is the mixing line that is exactly **tangent** to the liquid saturation curve. Tangency means the curve's own slope equals G, which defines a unique temperature *T*LM — the threshold temperature when the ambient air is already saturated with respect to water. Schumann's widely used approximation is > *T*LM = −46.46 + 9.43 ln(G − 0.053) + 0.720 [ln(G − 0.053)]² (°C, G in Pa K⁻¹) The simulation does not use that fit; it solves *d e*sat,liq/*dT* = G directly by bisection, using the Sonntag (1994) saturation formulations. The two agree to within 0.05 K across 0.1 < G < 5 Pa K⁻¹, which is a useful mutual check on both. Real air at cruise is not water-saturated, so the operative threshold is lower. With ambient relative humidity *U* over **water**, the ambient point is (*T*, *U·e*sat,liq(*T*)) and the marginal mixing line is the one that still just reaches the tangency point. That gives the threshold temperature *T*LC as the solution of > *U · e*sat,liq(*T*LC) + G · (*T*LM − *T*LC) = *e*sat,liq(*T*LM) **A contrail forms if and only if *T*ambient < *T*LC.** At 250 hPa with *η* = 0.30 and water-saturated air, that threshold sits near 231 K (−42 °C); in dry air it falls by several kelvin more. ### Why the water curve, when the product is ice? At 220 K, ice is enormously more stable than supercooled water, and the air is often already supersaturated with respect to ice. Yet the criterion is written against the *liquid* curve. The reason is nucleation kinetics, not thermodynamics. Soot particles are poor deposition nuclei: growing ice directly from vapour on dry soot requires ice supersaturations far larger than a plume reaches. What soot *is* good at, once the plume becomes water-supersaturated, is acting as a cloud condensation nucleus. Liquid droplets activate on it in the Köhler sense, and a supercooled droplet at 220 K freezes homogeneously in well under a second. The liquid phase is a short-lived but obligatory intermediate, and that is why the water curve is the gate. ### The counterintuitive efficiency term The (1 − *η*) in the denominator is worth dwelling on. A more efficient engine converts more of the fuel's chemical energy into thrust and therefore dumps *less* heat into its plume — but it emits exactly the same water, because EIH₂O is pure stoichiometry. The plume is wetter per degree of warming, the mixing line is steeper, and the threshold temperature rises. **More efficient engines make contrails at warmer temperatures, and therefore more often.** In the simulation, holding everything else fixed at 250 hPa, raising *η* from 0.20 to 0.40 lifts the water-saturated threshold from about 229.9 K to 232.9 K — a 3 K shift, which at a typical 0.65 K per 100 m lapse rate is nearly half a kilometre of flight level. Engine efficiency has improved steadily since the 1950s, so the contrail-favourable fraction of the atmosphere has grown even as fuel burn per seat-kilometre has fallen. The same arithmetic explains why liquid hydrogen is such a dramatic case: EIH₂O = 8.94 against 1.23, and *Q* = 120 MJ/kg against 43.2, giving G ≈ 4.3 Pa K⁻¹ at 250 hPa and a threshold near 242 K. A hydrogen aircraft would make contrails almost everywhere it is cold enough for cirrus to exist at all. ### Persistence, spreading, and soot Formation is necessary but not sufficient for a contrail that matters. Persistence requires RHice > 100%. Note that the two humidities are not independent: the same vapour pressure gives RHice = RHwater · *e*sat,liq/*e*sat,ice, and that ratio is 1/0.593 at 220 K. Air at 150% over ice is only 89% over water — comfortably subsaturated by the liquid measure, which is precisely why ISSRs are invisible and why the formation and persistence tests are genuinely different tests. A persistent contrail then evolves like a very thin cirrus cloud. Vertical mixing in stably stratified air is weak, so the plume stays a few tens of metres deep; the width comes almost entirely from **vertical wind shear** acting across that depth, which stretches the plume horizontally at roughly *s·H·t*. With shear *s* ≈ 0.006–0.02 s⁻¹ and depth *H* ≈ 100–200 m, a contrail reaches kilometres in width within an hour. Crystals also sediment at a few centimetres per second, so an ageing contrail sags and develops fallstreaks. The number of ice crystals is set by the number of soot particles, of order 10¹⁵ per kilogram of fuel for a modern combustor at cruise. This is where sustainable aviation fuels enter. Aromatics are the soot precursors, so paraffinic SAF blends cut non-volatile particulate number sharply; the ECLIF/ND-MAX flight campaigns measured roughly 50–70% fewer soot particles behind a SAF blend than behind conventional Jet A-1, with a broadly comparable reduction in ice crystal number. Crucially, that does **not** cut contrail optical depth by the same factor. For a fixed mass of condensed ice, *N* times as many crystals are each *N*−1/3 smaller in radius, so total cross-section — and hence extinction — scales only as *N*1/3. Cutting soot number by 60% reduces optical thickness by roughly a quarter, not by 60%. The simulation implements exactly this scaling, which is why the SAF toggle visibly thins the trail without abolishing it. ### Radiative forcing: what is and is not settled Contrail cirrus traps outgoing longwave radiation and reflects incoming sunlight. In the global mean the longwave term wins and the net effect is warming, with a strong diurnal asymmetry: night flights get no offsetting shortwave cooling at all, and a small minority of flights — of order a few per cent — produce most of the forcing, because they are the ones that happen to cross large ISSRs. The magnitude, however, is genuinely uncertain and should not be quoted as a single settled number. The most widely cited assessment, Lee et al. (2021), gives a best estimate of about 57 mW m⁻² of effective radiative forcing from contrail cirrus for 2018, with a 5–95% confidence interval spanning roughly 17–98 mW m⁻² — and explicitly assigns it **low confidence**. On that accounting contrail cirrus is the largest single aviation forcing term, larger than aviation's accumulated CO₂, but the error bar is nearly a factor of six wide and it is asymmetric. Several distinct sources of uncertainty are still live: how many ice crystals actually survive the wake-vortex phase; how contrail cirrus interacts with and partly displaces natural cirrus; how much water vapour contrails redistribute downward by sedimentation; and how well the "effective" forcing captures the rapid cloud adjustments that follow. Work published since 2021 has pushed estimates both up and down, and the operational question — whether rerouting a small number of flights around ISSRs actually reduces warming, given the CO₂ cost of the detour — is being actively tested in flight trials whose early results are encouraging but not yet conclusive. Treating contrail forcing as large but poorly constrained is the honest position. ## Controls -> what each maps to | Control | Symbol | Range and units | What it does in the model | |---|---|---|---| | Cruise altitude | *z* | 8.0–13.5 km | Sets ambient pressure *p* and baseline temperature from the ICAO standard atmosphere. *p* enters G linearly; *T* enters the criterion directly. Climbing usually helps formation (colder) but can leave the moist layer, killing persistence | | Temperature offset | Δ*T* | −12 to +12 K from ISA | Added to the standard-atmosphere temperature at all altitudes. Represents a warm or cold air mass. Horizontally uniform by design, so that along-track changes in trail state are attributable to humidity alone | | Peak RH over ice | RHi | 40–160 % | Scales the peak of the humidity field in the core of the main moist layer. Sets RH over water through *e*sat,ice/*e*sat,liq, hence *T*LC; and independently decides persistence through the 100% line | | Engine efficiency | *η* | 0.15–0.50 (dimensionless) | Appears as (1 − *η*) in the denominator of G. Higher *η* means less waste heat per unit water, a steeper mixing line, and a **warmer** threshold — more contrails | | Fuel hydrogen content | *X*H | 12.5–16.0 mass % | Fixes EIH₂O = 8.937·*X*H exactly, and sets the net heating value through an empirical linear fit to alkane heating values. Also modulates soot number, since aromatics are the precursors | | Low-aromatic SAF | — | on / off | Multiplies soot emission index by 0.40. Changes ice crystal number, and therefore optical thickness as *N*1/3. Does **not** move the formation threshold appreciably | | Liquid hydrogen | — | on / off | Overrides the fuel to *X*H = 100%, EIH₂O = 8.94, *Q* = 120 MJ/kg, zero soot but non-zero ambient nuclei. G roughly triples | | Pause / Reset | — | buttons (space, R) | Freeze the flight; restore all defaults and re-fly the domain | Live readouts: ambient temperature (K and °C), RH over ice and over water, the Schmidt–Appleman threshold *T*LC, whether the criterion is met and by how many kelvin, the predicted trail state (none / short-lived / persistent and spreading), predicted lifetime, and — in the expandable panel — ambient pressure, G, *T*LM, the ambient and saturation vapour pressures, EIH₂O, *Q*, soot emission index, ice crystals per metre of flight, and the real (unexaggerated) depth and width of the oldest plume in the domain. ## Learning objective **Explain why a contrail is a threshold phenomenon rather than a gradual one, by deriving the mixing-line slope G and showing that it is independent of dilution; and then separate that formation test from the completely independent persistence test, using the fact that saturation over ice and saturation over water differ by a factor of about 0.6 at cruise temperature. Use the model to predict, and then verify, that raising engine efficiency makes contrails *more* likely, and that reducing soot thins a contrail only as the cube root of the particle number.** ## Limits and connections This model is deliberately clean, and it is worth being explicit about what has been left out. **The wake-vortex phase is not simulated.** For the first one to two minutes the plume is wrapped into the aircraft's trailing vortex pair, which descends 100–200 m and warms adiabatically. A substantial fraction of the newly formed crystals — sometimes more than half, and very sensitively dependent on ambient supersaturation and aircraft weight — sublimates before the vortices break up. The simulation starts its puffs after that phase, which means it overstates the survival of marginal contrails. **The humidity field is idealised.** It is a smooth analytic construction: two moist layers, two along-track patches with soft, meandering edges. Real ISSR boundaries are fractal and the humidity distribution inside them is not smooth. Temperature is horizontally uniform, which is a modelling choice made so that along-track changes in trail state can be attributed unambiguously to humidity. Real ISSRs are usually associated with dynamical features that change temperature too. **Plume growth is parametrised, not resolved.** Eddy diffusivities, the shear rate and the crystal fall speed are fixed constants chosen from the observed ranges, not computed. There is no radiative feedback — real contrail cirrus heats itself and drives weak circulations that affect its own spreading — and no interaction with pre-existing natural cirrus, which matters because contrails partly compete for the same vapour. **Nucleation is assumed not to be particle-limited.** At very low soot numbers the assumption that every available particle activates a droplet begins to fail, and the effective threshold shifts slightly; this is exactly the regime that hydrogen combustion and very clean SAF would enter, so the model's hydrogen case should be read as indicative rather than predictive. **Drawn scales are exaggerated and labelled.** The domain is 250 km by 70 km by 9 km; the vertical axis is stretched eight times, the trail cross-section is drawn three and a half times oversize, and the aircraft glyph is around 180 times oversize. All the numbers in the readouts are the real physical ones. The exaggerations are constants, so the *ratio* between a fresh contrail and a twenty-minute-old one — which is the quantity the simulation is about — is untouched. Connections worth following: the efficiency term *η* is the same overall propulsion efficiency that governs [[Fuel_economy_in_aircraft]] and is set by the thermodynamics in [[Turbojet]]; the moist layers live just below the [[Tropopause]], which is why cruise altitude selection matters so much; a persistent contrail is physically a [[Cirrus_cloud]] with an artificial origin; the soot pathway is the subject of [[Sustainable_aviation_fuels]]; and the forcing question sits inside [[Environmental_impact_of_aviation]]. ## References Appleman, H. (1953). The formation of exhaust condensation trails by jet aircraft. *Bulletin of the American Meteorological Society*, 34(1), 14–20. Bier, A., & Burkhardt, U. (2019). Variability in contrail ice nucleation and its dependence on soot number emissions. *Journal of Geophysical Research: Atmospheres*, 124(6), 3384–3400. Burkhardt, U., & Kärcher, B. (2011). Global radiative forcing from contrail cirrus. *Nature Climate Change*, 1(1), 54–58. Gettelman, A., Chen, C.-C., & Bardeen, C. G. (2021). The climate impact of COVID-19-induced contrail changes. *Atmospheric Chemistry and Physics*, 21(12), 9405–9416. Gierens, K., Schumann, U., Helten, M., Smit, H., & Marenco, A. (1999). A distribution law for relative humidity in the upper troposphere and lower stratosphere derived from three years of MOZAIC measurements. *Annales Geophysicae*, 17(9), 1218–1226. International Civil Aviation Organization (1993). *Manual of the ICAO Standard Atmosphere, extended to 80 kilometres*, 3rd ed. Doc 7488/3. ICAO, Montreal. Jensen, E. J., Ackerman, A. S., Stevens, D. E., Toon, O. B., & Minnis, P. (1998). Spreading and growth of contrails in a sheared environment. *Journal of Geophysical Research: Atmospheres*, 103(D24), 31557–31567. Kärcher, B. (2018). Formation and radiative forcing of contrail cirrus. *Nature Communications*, 9, 1824. Kärcher, B., & Yu, F. (2009). Role of aircraft soot emissions in contrail formation. *Geophysical Research Letters*, 36(1), L01804. Lee, D. S., Fahey, D. W., Skowron, A., Allen, M. R., Burkhardt, U., Chen, Q., Doherty, S. J., Freeman, S., Forster, P. M., Fuglestvedt, J., Gettelman, A., De León, R. R., Lim, L. L., Lund, M. T., Millar, R. J., Owen, B., Penner, J. E., Pitari, G., Prather, M. J., Sausen, R., & Wilcox, L. J. (2021). The contribution of global aviation to anthropogenic climate forcing for 2000 to 2018. *Atmospheric Environment*, 244, 117834. https://doi.org/10.1016/j.atmosenv.2020.117834 Murphy, D. M., & Koop, T. (2005). Review of the vapour pressures of ice and supercooled water for atmospheric applications. *Quarterly Journal of the Royal Meteorological Society*, 131(608), 1539–1565. Schmidt, E. (1941). Die Entstehung von Eisnebel aus den Auspuffgasen von Flugmotoren. *Schriften der Deutschen Akademie der Luftfahrtforschung*, 44, 1–15. Schumann, U. (1996). On conditions for contrail formation from aircraft exhausts. *Meteorologische Zeitschrift*, 5(1), 4–23. Schumann, U. (2012). A contrail cirrus prediction model. *Geoscientific Model Development*, 5(3), 543–580. https://doi.org/10.5194/gmd-5-543-2012 Schumann, U., Penner, J. E., Chen, Y., Zhou, C., & Graf, K. (2015). Dehydration effects from contrails in a coupled contrail–climate model. *Atmospheric Chemistry and Physics*, 15(19), 11179–11199. Sonntag, D. (1994). Advancements in the field of hygrometry. *Meteorologische Zeitschrift*, 3(2), 51–66. Spichtinger, P., Gierens, K., & Read, W. (2003). The global distribution of ice-supersaturated regions as seen by the Microwave Limb Sounder. *Quarterly Journal of the Royal Meteorological Society*, 129(595), 3391–3410. Teoh, R., Schumann, U., Majumdar, A., & Stettler, M. E. J. (2020). Mitigating the climate forcing of aircraft contrails by small-scale diversions and technology adoption. *Environmental Science & Technology*, 54(5), 2941–2950. Unterstrasser, S., & Gierens, K. (2010). Numerical simulations of contrail-to-cirrus transition — Part 1: An extensive parametric study. *Atmospheric Chemistry and Physics*, 10(4), 2017–2036. Voigt, C., Kleine, J., Sauer, D., Moore, R. H., Bräuer, T., Le Clercq, P., Kaufmann, S., Scheibe, M., Jurkat-Witschas, T., Aigner, M., Bauder, U., Boose, Y., Borrmann, S., Crosbie, E., Diskin, G. S., DiGangi, J., Hahn, V., Heckl, C., Huber, F., … Anderson, B. E. (2021). Cleaner burning aviation fuels can reduce contrail cloudiness. *Communications Earth & Environment*, 2, 114. **On the spine:** [[Aircraft]] · [[Aircraft_flight_dynamics]] · [[Fixed-wing_aircraft]] · [[Helicopter]] · [[Turbojet]] · [[Jet_engine]] · [[Sonic_boom]] · [[Contrail]] · [[Air_traffic_control]] · [[Avionics]] · [[Aviation]].  **Part of the [[Aviation]] hub** — main article for section A26, *Contrails*. Related sections: Environmental impact of aviation · Turbofan.  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Contrail) : [Wikitube](https://en.wikitube.io/wiki/Contrail) --- *PORTAL_Aviation three.js batch · 2026-08-05 · sim staged in `_3d_deploy_stage/`.*