Networks and Spatial Economics

, Volume 16, Issue 1, pp 415–446 | Cite as

Optimal 4-D Aircraft Trajectories in a Contrail-sensitive Environment

  • Bo ZouEmail author
  • Gurkaran Singh Buxi
  • Mark Hansen


Aircraft induced contrails present an important source and a growing concern for climate change in aviation. This paper develops a methodology to determine optimal flight trajectories that minimize the total flying cost in a dynamic, contrail-sensitive environment. The total flying costs consist of costs due to fuel burn, crew, passenger travel time, CO2 emission, and contrail formation. By constructing a multi-layer hexagonal grid structure to represent the airspace, we formulate the single aircraft trajectory optimization problem as a binary integer program that allows for flight altitude and heading adjustment, and contrail information update. Various cost factors are quantified, in particular the one corresponding to aviation-generated contrails, using the Global Warming Potential concept. Computational analyses show that optimal trajectories depend critically upon the time horizon choice for calculating the CO2 climate impact. Shifting flights to periods with low contrail effect is not justified, given the limited benefit but potentially large passenger schedule delay cost increase. The analyses are further extended to determining the optimal trajectories for multiple flights using a successive optimization procedure.


Contrail Flight trajectory Optimization Climate impact 



This research was sponsored by the NASA Ames Research Center through a grant to the National Center of Excellence for Aviation Operations Research (NEXTOR). The enthusiastic support from Drs. Banavar Sridhar, Tasos Nikoleris, Neil Chen, and Hok Ng, for this research is gratefully acknowledged. Gratitude extends to Abhinav Golas for his help in optimizing the code in MATLAB. An earlier version of this paper was presented at the 5th International Conference on Research in Air Transportation, in Berkeley, U.S.A. We would like to thank the two anonymous referees and Dr. Wai Yuan Szeto, the guest editor for the Special Issue, for very helpful comments and suggestions.


  1. Abramson M, Ali K (2012) Integrating the Base of Aircraft Data (BADA) in CTAS trajectory synthesizer. NASA Web. NASA-TM-2012-216051.pdf. Accessed April 28 2013
  2. Adler T, Falzarano CS, Spitz G (2005) Modeling service trade-offs in air itinerary choices. Transp Res Rec 1915:20–26CrossRefGoogle Scholar
  3. Albrecht T (2009) The influence of anticipating train driving on the dispatching process in railway conflict situations. Netw Spat Econ 9:85–101CrossRefGoogle Scholar
  4. Appleman H (1953) The formation of exhaust condensation trails by jet aircraft. Bull Am Meteorol Soc 34:14–20Google Scholar
  5. Ball M, Hoffman R, Odoni A, Rifkin R (1999) The static stochastic ground holding problem with aggregate demands. Technical research report: NEXTOR T.R. 99–1Google Scholar
  6. Barnier N, Allignol C (2009) 4D-trajectory deconfliction through departure time adjustment. ATM Seminar Web. NSTFO.pdf. Accessed April 30 2013
  7. Barnier N, Allignol C (2011) Combining flight level allocation with ground holding to optimize 4D-deconfliction. ATM Seminar Web. papers/157-Barnier-Final-Paper-4-5-11.pdf. Accessed April 30 2013
  8. Bureau of Labor Statistics (BLS) (2010) Occupational employment and wages. BLS Economics News Release Web. Accessed October 19 2011
  9. Cai X, Sha D, Wong CK (2001) Time-varying minimum cost flow problems. Eur J Oper Res 131:352–374CrossRefGoogle Scholar
  10. Campbell SE, Neogi NA, Bragg MB (2008) An optimal strategy for persistent contrail avoidance. University of Illinois Web. Accessed October 1 2012
  11. Chabini I, Abou-Zeid M (2003) The minimum cost flow problem in capacitated dynamic networks. In: Proceedings of the 82nd Annual Meeting of the Transportation Research Board. Accessed April 24 2012
  12. Chen NY, Sridhar B, Li J, Ng H (2012) Evaluation of contrail reduction strategies based on aircraft flight distances. NASA Web. publications/2012/AIAA-2012-4816.pdf. Accessed May 2 2013
  13. D’Ariano A, Pranzo M (2009) An Advanced real-time train dispatching system for minimizing the propagation of delays in a dispatching area under severe disturbances. Netw Spat Econ 9:63–84CrossRefGoogle Scholar
  14. Delta (2003) B737-800 Aircraft Operations Manual (AOM). Delta Virtual Airlines Web. Accessed March 25 2013
  15. Escuín D, Millán C, Larrodé E (2012) Modelization of time-dependent urban freight problems by using a multiple number of distribution centers. Netw Spat Econ 12:321–336CrossRefGoogle Scholar
  16. Fichter C, Marquart S, Sausen R, Lee DS (2005) The impact of cruise altitude on contrails and related radiative forcing. Meteorol Z 14:563–572CrossRefGoogle Scholar
  17. Forster P, Stuber N (2007) The impact of diurnal variations of air traffic on contrail radiative forcing. Atmos Chem Phys 7:3153–3162CrossRefGoogle Scholar
  18. Forster P, Shine K, Stuber N (2006) It is premature to include non-CO2 effects of aviation in emission trading schemes. Atmos Environ 40:1117–1121CrossRefGoogle Scholar
  19. Fuglestvedt JS, Berntsen T, Godal O, Sausen R, Shine K, Skodvin T (2003) Metrics of climate change: assessing radiative forcing and emission indices. Clim Chang 8:267–331CrossRefGoogle Scholar
  20. Fuglestvedt JS, Shine KP, Berntsen T, Cook J, Lee DS, Stenke A, Skeie RB, Velders GJM, Waitz IA (2010) Transport impacts on atmosphere and climate: metrics. Atmos Environ 44:4648–4677CrossRefGoogle Scholar
  21. George O’Neill M, Dumont JM, Hansman RJ (2012) Use of hyperspace trade analyses to evaluate environmental and performance tradeoffs for cruise and approach operations. In: Proceedings of the 12th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference and the 14th AIAA/ISSMGoogle Scholar
  22. 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. Ann Geophys 17:1218–1226CrossRefGoogle Scholar
  23. Greenstone M, Kopits E, Wolverton A (2011) Estimating the social cost of carbon for use in US federal rulemakings: a summary and interpretation. National Bureau of Economic Research Web. Accessed November 21 2011
  24. International Air Transport Association (IATA) (2011) Jet fuel price monitor. IATA Economics Web. Accessed October 7 2011
  25. International Civil Aviation Organization (ICAO) (2012) Act global. ICAO Web. Accessed 26 January 2012
  26. Li K, Gao Z, Mao B, Cao C (2011) Optimizing train network routing using deterministic search. Netw Spat Econ 11:193–205CrossRefGoogle Scholar
  27. Mannstein H, Schumann U (2005) Aircraft induced contrail cirrus over Europe. Meteorologische Z 14:549–554Google Scholar
  28. Meerkotter R, Schumann U, Doelling DR, Minnis P, Nakajima T, Tsushima Y (1999) Radiative forcing by contrails. Ann Geophys 17:1080–1094CrossRefGoogle Scholar
  29. Minnis P, Schumann U, Doelling D, Gierens K, Fahey D (1999) Global distribution of contrail radiative forcing. Geophys Res Lett 26:1853–1856CrossRefGoogle Scholar
  30. Mukherjee A, Hansen M (2007) A dynamic stochastic model for the single airport ground holding problem. Transp Sci 41:444–456CrossRefGoogle Scholar
  31. Ng H, Sridhar B, Grabbe S, Chen N (2011) Cross-polar aircraft trajectory optimization and the potential climate impact. NASA Web. Accessed May 2 2013
  32. Penner JE, Lister DH, Griggs DJ, Dokken DJ, McFarland M (ed) (1999) Aviation and the Global Atmosphere. Camb University Press, New YorkGoogle Scholar
  33. Royal Commission on Environmental Protection (RCEP) (2002) The environmental effects of civil aircraft in flight: special report. Aviation Environment Federation Web. Accessed April 27 2012
  34. Sausen R, Gierens K, Ponater M, Schumann U (1998) A diagnostic study of the global distribution of contrails part I: present day climate. Theor Appl Climat 61:127–141CrossRefGoogle Scholar
  35. Schmidt E (1941) Die entstehung von eisnebel aus den auspuffgasen von flugmotoren. Schriften der Dtsch Akad fur Luftfahrtforsch 14:1–15Google Scholar
  36. Schumann U (2005) Formation, properties and climatic effects of contrails. Comptes Rendus Phys 6:549–565CrossRefGoogle Scholar
  37. Sridhar B, Chen NY, Ng H, Linke F (2011) Design of aircraft trajectories based on trade-offs between emission sources. ATM Seminar Web. Accessed October 10 2012
  38. Sridhar B, Ng H, Chen NY (2012) Integration of linear dynamic emission and climate models with air traffic simulations. NASA Web. Accessed May 2 2013
  39. Stordal G, Myhre F (2001) On the tradeoff of the solar and thermal infrared radiative impact of contrails. Geogr Res Lett 28:3119–3122CrossRefGoogle Scholar
  40. Stuber N, Forster P, Radel G, Shine K (2006) The importance of the diurnal and annual cycle of air traffic for contrail radiative forcing. Nat 7095:864–867CrossRefGoogle Scholar
  41. U.S. Department of Transportation (DOT) (2011) The value of travel time savings: departmental guidance for conducting economic evaluations. Revision 2. DOT Web. Accessed Feb 23 2012
  42. U.S. Energy Information Administration (EIA) (2012) Voluntary reporting of greenhouse gases program (voluntary reporting of greenhouse gases program fuel carbon dioxide emission coefficients). EIA Web. Accessed Dec 17 2011
  43. Williams V, Noland RB (2005) Variability of contrail formation conditions and the implications for policies to reduce the climate impacts of aviation. Transp Res Part D 10:269–280CrossRefGoogle Scholar
  44. Williams V, Noland RB, Toumi R (2002) Reducing the climate change impacts of aviation by restricting cruise altitudes. Transp Res Part D 7:451–464CrossRefGoogle Scholar
  45. Williams V, Noland RB, Toumi R (2003) Air transport cruise altitude restrictions to minimize contrail formation. Clim Pol 3:207–219CrossRefGoogle Scholar
  46. Williams V, Noland RB, Majumdar A, Toumi R, Ochieng W, Molloy J (2007) Reducing environmental impacts of aviation with innovative air traffic management technologies. The Aeronautical J 111:741–749Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Civil and Materials EngineeringUniversity of Illinois at ChicagoChicagoUSA
  2. 2.Department of Civil and Environmental EngineeringUniversity of California at BerkeleyBerkeleyUSA

Personalised recommendations