The linked references indicate how poorly AR5 addresses the potential impact of contrails. Such conventional thinking assumes that in 2005 the average radiative forcing from contrails was 0.012 W/m2 (watts per square meter); however, the first linked reference finds that in 2006 it was actually 0.056 W/m2 . While the second linked reference uses the old (incorrect) estimate to calculate that by 2050 this forcing will increase seven times from 0.012 to 0.087 W/m2 for a four-fold increase in airline miles flown by 2050. If we were to apply the factor of seven times to the correct value of 0.056 we would get
0.392 W/m2 of associated positive radiative forcing by 2050.
The add to this confusion the second article indicates that aviation sulfate aerosols emitted can act as negative forcing; however, as airlines are current making great strides in reducing these emissions, it is not clear to me what the net radiative forcing from contrails and aviation aerosol emissions will be in the coming decades:
Lisa Bock &Ulrike Burkhardt (2 August 2016), "Reassessing properties and radiative forcing of contrail cirrus using a climate model", Journal of Geophysical Research Atmospheres, DOI: 10.1002/2016JD025112
http://onlinelibrary.wiley.com/doi/10.1002/2016JD025112/abstractAbstract: "Contrail cirrus is the largest known component contributing to the radiative forcing associated with aviation. Despite major advances simulating contrail cirrus, their microphysical and optical properties and the associated radiative forcing remain largely uncertain. We use a contrail cirrus parameterization in a global climate model which was extended to include a microphysical two-moment scheme. This allows a more realistic representation of microphysical processes, such as deposition and sedimentation, and therefore of the microphysical and optical properties of contrail cirrus.
The simulated contrail microphysical and optical properties agree well with in situ and satellite observations. As compared to estimates using an older version of the contrail cirrus scheme, the optical depth of contrail cirrus is significantly higher, particularly in regions with high air traffic density, due to high ice crystal number concentrations on the main flight routes. Nevertheless, the estimated radiative forcing for the year 2002 supports our earlier results. The global radiative forcing of contrail cirrus for the year 2006 is estimated to be 56mW/m2. A large uncertainty of the radiative forcing estimate appears to be connected with the, on average, very small ice crystal radii simulated in the main air traffic areas, which make the application of a radiative transfer parameterization based on geometric optics questionable."
Chen, C.-C. and Gettelman, A.: Simulated 2050 aviation radiative forcing from contrails and aerosols, Atmos. Chem. Phys., 16, 7317-7333, doi:10.5194/acp-16-7317-2016, 2016.
http://www.atmos-chem-phys.net/16/7317/2016/http://www.atmos-chem-phys.net/16/7317/2016/acp-16-7317-2016.pdfAbstract: "The radiative forcing from aviation-induced cloudiness is investigated by using the Community Atmosphere Model Version 5 (CAM5) in the present (2006) and the future (through 2050). Global flight distance is projected to increase by a factor of 4 between 2006 and 2050. However, simulated contrail cirrus radiative forcing in 2050 can reach 87 mW m−2, an increase by a factor of 7 from 2006, and thus does not scale linearly with fuel emission mass. This is due to non-uniform regional increase in air traffic and different sensitivities for contrail radiative forcing in different regions.
CAM5 simulations indicate that negative radiative forcing induced by the indirect effect of aviation sulfate aerosols on liquid clouds in 2050 can be as large as −160 mW m−2, an increase by a factor of 4 from 2006. As a result, the net 2050 radiative forcing of contrail cirrus and aviation aerosols may have a cooling effect on the planet. Aviation sulfate aerosols emitted at cruise altitude can be transported down to the lower troposphere, increasing the aerosol concentration, thus increasing the cloud drop number concentration and persistence of low-level clouds. Aviation black carbon aerosols produce a negligible net forcing globally in 2006 and 2050 in this model study.
Uncertainties in the methodology and the modeling are significant and discussed in detail. Nevertheless, the projected percentage increase in contrail radiative forcing is important for future aviation impacts. In addition, the role of aviation aerosols in the cloud nucleation processes can greatly influence on the simulated radiative forcing from aircraft-induced cloudiness and even change its sign. Future research to confirm these results is necessary."
See also:
https://en.wikipedia.org/wiki/ContrailExtract: "Contrails, by affecting the Earth's radiation balance, act as a radiative forcing. Studies have found that contrails trap outgoing longwave radiation emitted by the Earth and atmosphere (positive radiative forcing) at a greater rate than they reflect incoming solar radiation (negative radiative forcing). NASA conducted a great deal of detailed research on atmospheric and climatological effects of contrails, including effects on ozone, ice crystal formation, and particle composition, during the Atmospheric Effects of Aviation Project (AEAP). Global radiative forcing has been calculated from the reanalysis data, climatological models and radiative transfer codes. It is estimated to amount to 0.012 W/m2 (watts per square meter) for 2005, with an uncertainty range of 0.005 to 0.026 W/m2, and with a low level of scientific understanding. Therefore, the overall net effect of contrails is positive, i.e. a warming effect. However, the effect varies daily and annually, and overall the magnitude of the forcing is not well known: globally (for 1992 air traffic conditions), values range from 3.5 mW/m2 to 17 mW/m2. Other studies have determined that night flights are mostly responsible for the warming effect: while accounting for only 25% of daily air traffic, they contribute 60 to 80% of contrail radiative forcing. Similarly, winter flights account for only 22% of annual air traffic, but contribute half of the annual mean radiative forcing."