Content uploaded by Judith Rosenow
Author content
All content in this area was uploaded by Judith Rosenow on Feb 15, 2017
Content may be subject to copyright.
108 TAC-4 Proceedings, June 22nd to 25th, 2015, Bad Kohlgrub
Angle dependent extinction of solar radiation by individual
condensation trails
J. Rosenow *, H. Fricke
Technische Universität Dresden, Institut für Luftfahrt und Logistik, Germany
Keywords: Condensation trails, solar radiative forcing, angle dependence
ABSTRACT: In this work, a continuous model is developed to estimate the solar scattering and ab-
sorption properties and their dependence on the position of the sun. The initial microphysical prop-
erties of realistic condensation trails are calculated using a flight performance model yielding pre-
cise information about altitude, true air speed, fuel flow and emission of water vapor and heat. The
evolution of the contrail microphysical properties during the diffusion regime is calculated with a
Gaussian plume model. The radiation field around the contrail is calculated with the radiative trans-
fer library libRadtran using a discrete ordinate radiative transfer solver for solar radiation. Finally,
radiative extinction due to the condensation trail is calculated utilizing a Monte Carlo simulation for
the consideration of multiple scattering. This radiative extinction model is calibrated and tested for
a wide range of realistic parameter settings. Radiative extinction strongly depends on the irradiation
angle and on the geographical orientation of the condensation trail both determining the distance
photons travel through the condensation trail. Furthermore, strong forward scattering, defined by
the particle shape and wavelength cause a reduced cooling effect at noon, when the main part of so-
lar radiation is irradiating perpendicular to the condensation trail axis. The results facilitate the pos-
sibility of improve both, the trajectory management and the network structure towards an air traffic
system with reduced environmental impact due to contrails.
1 INTRODUCTION
Long living condensation trails (short: persistent contrails) are ice crystals at flight level developed
behind an aircraft (Schumann 2005) in an ice-supersaturated environment (Schmidt 1941, Brewer
1946, Appleman 1953, Schumann 1996, and Sussmann et al. 2001). The water condenses at soot
particles, from the exhaust of the aircraft. In the Earth-atmosphere energy budget, contrails seem
like a restriction in the atmospheric energy exchange (Myhre et al. 2013, Lee et al. 2009), because
they scatter incoming shortwave solar radiation partly back to the sky and they absorb and emit out-
going longwave terrestrial radiation partly back to the Earth’s surface Myhre et al. 2013, Minnis et
al. 1999, Sausen et al. 2005 and Burkhardt et al. 2011). The impact of a single contrail on the ex-
tinction of solar radiation (solar radiative forcing ) is calculated in this study considering
the angle dependence of solar radiation due to time of day and flight path.
1.1 State of the art
The radiative forcing of contrails has been estimated several times. For example, using a global
climate model as done by Burkhardt et al. 2011. Or by observing contrails and interpreting the in-
coming and outgoing radiation with the help of satellite data as shown by Graf et al. 2012, Schu-
mann et al. 2013 and Vázques-Navarro et al. 2015. The influence of contrails on the Earth-
atmosphere energy balance has been first approximated by Hansen et al. 1997, Meerkötter et al.
1999, Myhre et al. 2001, Petty 2002, Marquart et al. 2003, Ponater et al. 2006, Solomon et al. 2007
and Corti et al. 2009 treating contrails as plane parallel layer with constant properties. However,
considering the contrail as horizontally homogenous layer, ignores the realistic three dimensional
structure of a contrail (Schulz 1997 and Gounou et al. 2007). All above publications neglect multi-
ple scattering. A detailed study of angle dependent photon transport through a three-dimensional de-
fined realistic condensation trail by Gounou et al. 2007 and Forster et al. 2011 demonstrated the im-
portance of considering large solar zenith angles. Due to an application of a Monte Carlo code for
photon transport as used by Forster et al. 2011 effects like multiple scattering are already consid-
* Corresponding author: J. Rosenow, Technische Universität Dresden, Institut für Luftfahrt und Logistik, D-01069
Dresden, Germany. Email: Judith.Rosenow@tu-dresden.de
ROSENOW and FRICKE: Angle dependent extinction of solar radiation by individual … 109
ered. However, the latest estimations of realistic contrails are still based on a radiative transport cal-
culation of the whole atmosphere with an additional contrail. They are using a coarse spatial grid
within the contrail. From a meteorological point of view, which is the estimation of the contrail in-
fluence on the energy budget, the latest results are very useful and the extinction properties of the
contrail without an atmospheric environment are not of interest. However, for an optimization of the
aircraft trajectory and flight performance with respect to minimize contrail impact on radiative forc-
ing, those calculations are insufficient. Here, photon transport through the contrail is estimated sep-
arately from the radiative transfer processes through the atmosphere. Hence, a feedback of the flight
performance on the contrail radiative forcing is possible.
2 MODEL
The influence of a condensation trail on the energy budget of the Earth-atmosphere system strongly
depends on the properties of the contrail, which are influenced by the aircraft generating the contrail
(Schumann 2000 and Jeßberger et al. 2013).
2.1 Aircraft performance model
The flight profile is generated with the help of the Enhanced Jet Performance Model (EJPM) de-
rived by Kaiser 2015 for an Airbus A320 aircraft. The EJPM optimizes fuel consumption and the
lift to drag ratio using a maximum specific range. For the current study, it provides the required
Thrust F, fuel flow , true air speed and altitude z.
2.2 Contrail life cycle model
The characteristics of the flight profile and the model atmosphere Mid-Latitude Winter by Ander-
son et al. 1986 allow the calculation of the initial dimensions and microphysical properties of the
contrail. For persistent contrail formation, the model atmosphere is manipulated by an ice-
supersaturated layer between z = 9.5 km and z = 11.5 km. Because the exhaust is captured in the
wake vortices of the aircraft, the initial characteristics of the contrail are defined at the beginning of
the dispersion regime of the wake vortices with the help of the “Probabilistic Two-Phase Wake
Vortex Decay and Transport Model” (P2P) by Holzäpfel 2003. Here, an eddy dissipation rate of
ε = 5 ∙ 10-5 m2 s-3 is assumed due to missing turbulence information. The initial contrail height is de-
fined as the distance between emission height at flight level down to the altitude the vortex fall dur-
ing the vortex regime, plus two times the vortex radius. The vortex radius r is defined as the radius,
where the tangential velocity vt (r) has reached a value of (√e)-1/2 of the tangential velocity in the
vortex core vt (rc). This fraction corresponds to the position of one standard deviation 1σ within the
Gaussian distribution function, where also a value of (√e)-1/2 times the maximum value of the func-
tion is reached.
The life cycle of the contrail is described by a Gaussian plume model as described by Schumann
et al. 1995 and applied by Rosenow et al. 2012. To overcome computational costs in the radiative
forcing calculations, an elliptical cross section is assumed. Therewith, the calculation of radiative
extinction due to the contrail is sufficient for the directions coming from one octant. Other direc-
tions of incoming photons are considered by reflecting the results of the Monte Carlo simulation in
the slice planes to the other octants. The Gaussian plume model results in a continuous calculation
of the contrail microphysics (ice particle size rp and ice water content IWC) at every position within
the contrail. Hence, for every point within the contrail and for each wavelength the solar radiative
extinction properties (scattering and absorption efficiencies Qsca , Qabs and asymmetry g parameter
for the scattering phase function) can be calculated using parameterizations from Wyser et al. 2000.
Here, non-spherical particle shapes typically found in midlatitude cirrus clouds are considered
without particle size distribution.
2.3 Radiative transfer model
Solar radiances at contrail altitude are calculated utilizing the radiative transfer model libRadtran
(Mayer et al. 2011). With libRadtran, diffuse and direct solar radiances coming from all directions
in space with a discretization of 2° are calculated at 10.5 km altitude over Berlin, Germany, on 21st
of June 2012. No clouds and a default aerosol concentration are considered. The surface library of
110 ROSENOW and FRICKE: Angle dependent extinction of solar radiation by individual …
the International Geosphere Biosphere (IGBP) from the NASA CERES/SARB Surface Properties
Project is used for surface reflectivity. The Discrete Ordinate Radiative Transfer (DISORT) solver
with 256 streams, developed by Stamnes et al. 1988 with the correlated-k scheme LOWTRAN of
Ricciazzi et al. 1998 is used to overcome computational costs due to narrow absorption bands even
in the solar spectrum. The calculations are done for 21 bands between wavelengths of λ = 275 nm
and λ = 2200 nm.
2.4 Radiative forcing model
For radiative extinction of solar radiances calculated with libRadtran, 107 photons are traced in a
Monte Carlo simulation. This simulation is necessary to consider multiple scattering events. For ra-
diative extinction Beer’s law
I = ()
is solved, where I and denote the extinguished and the original radiances [W m-2 sr-1 nm-1], re-
spectively, describes the volume extinction coefficient [m-1] and s the thickness of the extin-
guishing medium [m], or the position within. Using the geometrical cross section of a particle
[] =
(rp...particle radius [m]) and the number density of particles np [m-2] as function of
location s (Gaussian distribution), Beer’s law becomes:
I = An()
.
Considering the corresponding hemispheres of the entering and leaving photons, a calculation of the
impact of a contrail on the Earth’s energy system is possible. Therefore, three counters are generat-
ed each collecting forward scattered, backward scattered and absorbed photons. The number ratios
of photons between incoming and collected photons in each counter are weighted by the irradiated
length (here, six times the standard deviation 6σ) and the sine on the angle α between the incoming
photons and flight path as projection of the perpendicular irradiated area on the flight path (compare
Figure 1).
Figure 1: Geometry of the Monte Carlo simulation. Photons start uniformly distributed perpendicular to the
direction of arrival along line with a width of 6σh.
Hence, the intermediate results of the Monte Carlo simulation for each hemisphere are weighted
number ratios of forward scattered Sf, backward scattered Sb and absorbed Sa photons. Because they
are weighted by the irradiated width 6σ, they have the unit [m]. These weighted number ratios of
extinguished photons are multiplied with the solar radiances [W sr−1 m−2 nm−1] coming from the
particular direction and the corresponding solid angle Ω [sr]. These resulting quantities are forward
scattered Pf, backward scattered Pb and absorbed Pa powers [W m-1 nm-1] per meter contrail and per
nanometer. With these quantities, the solar radiative forcing can be calculated:
= +
ROSENOW and FRICKE: Angle dependent extinction of solar radiation by individual … 111
where the arrows are indicating the direction of irradiance. Note, for all calculations, diffuse and di-
rect solar radiation coming from all directions in space are considered.
3 CALCULATIONS
To visualize the angle dependence of solar radiative extinction due to a contrail, Figure 2 and Fig-
ure 3 show the weighted number of forward scattered Sf and backward scattered Sb photons, respec-
tively, coming from different directions above the contrail. These directions are described by their
solar zenith angle θ (as deviation from the vertical direction) and by their solar azimuthal angle φ
(as deviation from South). Here, the contrail constitutes the North- South- axis. Figure 2 and Figure
3 show two phenomena. First, the strong forward scattering defined by the high asymmetry parame-
ter g = 0.74 in the Heyney Greenstein Phase scattering function explains differences between for-
ward and backward scattering (i.e. between Figure 2 and 3) as already shown by Wyser et al. 2000.
And second, extinction depends on the travel distance through the contrail, especially through the
contrail core. Hence, the larger the angle θ (towards horizontal photon transport), the larger is the
extinction. For large solar zenith angles, the influence of the azimuthal angle φ becomes significant,
deciding on whether the contrail cross section or the longitudinal axis is irradiated.
Figure 2: Number ratios of forward Sf scattered photons to the total number of 107 photons, weighted by the
sine of the angle between incident photons and contrail axis and by the width 6σ were the photons are
starting from. The angular dependent simulation is done for a solar wavelength λ = 550 nm. The optical
properties of the contrail are described in Table 1.
Figure 3: The same as in Figure 2, except backward scattered photons Sb are considered.
The relevance of multiple scattering is shown in Figure 4. The larger the distance traveled through
the contrail, the higher the number of scattering events. In the worst case, each photon is scattered
1.6 times on average. Thus, multiple scattering cannot be neglected.
112 ROSENOW and FRICKE: Angle dependent extinction of solar radiation by individual …
Figure 4: The average number of scattering events per scattered photon Nsca for several solar zenith angles θ
and for all azimuthal angles φ. The angular dependent simulation is done for a solar wavelength λ = 550 nm
after a lifetime of 20 hours in a strong turbulent environment with ε = 10-4 m2 s-3.
The influence of the flight path on the radiative extinction is shown in Figure 5 and Figure 6,
where the backscattered powers (required for the estimation of the radiative forcing ) are
calculated for different solar zenith angles and solar azimuthal angles during the day. In Figure 5,
the contrail constitutes the North-South axis. In Figure 6, the contrail is along the East-West axis.
Hence, different combinations of zenith and azimuthal angles for direct solar radiation are expected,
resulting in different extinguished powers and radiative forcing. In Figure 5 (North-South), during
sunrise and sunset (for φ = 90 ° and φ = 270 °) the sun irradiates the contrail longitudinal axis. In
Figure 6 (East-West), during sunrise and sunset direct solar radiation irradiates the contrail cross
section while horizontal photon transport takes place. As shown in Figure 2 and Figure 3, the influ-
ence of the azimuthal angle φ increases with increasing zenith angle θ (towards a horizontal irradia-
tion). For small angles α (facing the contrail cross section) the irradiated area is minimized. Hence,
the extinguished powers are reduced but are not converging to Zero, because of the amount of dif-
fuse solar radiances coming from all directions. In general, Figure 5 and Figure 6 show that strong
forward scattering reduces the backscattered power during midday, when solar zenith angle θ is
small. The absorbed power corresponds to the available radiances, particularly the direct radia-
tion, which increases until 12 a.m.. Due to small solar absorption efficiency , , small val-
ues of absorbed power are expected.
Figure 5: Backscattered power for diurnal variations of upward () and downward () solar radiation
(λ = 550 nm) and absorbed power of downward and upward radiation () for constant contrail properties
according to Table 1. The contrail constitutes the North-South axis.
ROSENOW and FRICKE: Angle dependent extinction of solar radiation by individual … 113
Figure 6: Backscattered powers depending on diurnal variations of upward () and downward () solar
radiances (λ = 550 nm) and absorbed power of downward and upward radiation () for constant contrail
properties. The contrail constitutes the North-South axis.
3.1 Verification
To verify the radiative forcing model, a comparison with the results of other publications is done.
Mostly, the optical thickness τ is used for the description of optical contrail properties, measured
vertically through the atmosphere. In the present case of treating the contrail by a Gaussian plume
without defined boundaries, the optical thickness strongly depends on the contrail irradiated width.
The larger the irradiated width, the smaller the optical thickness, because the share of photons trav-
eling through the contrail core is reduced. This phenomenon is illustrated in Figure 7, where the op-
tical thickness is shown for a contrail with optical and microphysical properties shown as described
in Table 1.
Table 1: Contrail properties used in the Monte Carlo simulation assuming a strong turbulent environment with
=10 m2 s -3 and a contrail age of 20 hours.
Width for starting photons
6=10188
m
Horizontal standard deviation
2=3396 m
Vertical standard deviation
2=148 m
Ice particle radius
=10 m
Solar absorption efficiency
, = 0.009
Solar scattering efficiency
, = 1.96
Solar asymmetry parameter
= 0.74
Figure 7: Optical thickness τ for vertical photon transport for a contrail with the same optical and microphys-
ical properties as used in Table 1 as function of the irradiated width. Due to the definition of the contrail by a
Gaussian plume, τ decreases with increasing irradiated width without converging to a constant value.
114 ROSENOW and FRICKE: Angle dependent extinction of solar radiation by individual …
Hence, a comparison of the optical thickness is impossible unless the corresponding contrail width
is published additionally, as done by Gounou et al. 2007, Forster et al. 2011 and Vázques-Navarro
et al. 2015. This width can be interpreted as the irradiated width used in the current study. Hence,
the number ratio of extinguished to evaluated photons, which is =++ can be used
for comparison with other publications, if their optical thickness is multiplied with the contrail
width. Forster et al. 2011 published values of the optical thickness of a nonsheared contrail for sev-
eral contrail ages. These are multiplied with the corresponding contrail width and compared with
the present weighted number ratios. The results are in the same order of magnitude (compare Table
2). Differences occur due to different atmospheres, unknown turbulence and different contrail ages.
Table 2: Comparison of weighted number ratios for a wavelength of =550 nm of different ages of contrail life-
time with the product of mean optical depth and contrail width by Forster et al. 2011. The mean turbulent environment
of = 5 10 m2 s-3 is assumed.
Contrail width [m]
[m] Forster et
al. 2011
Standard devia-
tion [m]
[m] current
study
960
223.6
778.5
342.5
1680
403.2
1078.5
453.0
2880
720.0
1330.3
585.3
4320
1036.8
1539.9
677.5
6000
1020.0
1718.9
739.1
6480
528.4
1976.7
889.5
The influence of the solar zenith angle on radiative extinction can be compared with Gounou et al.
2007 as well as with Forster et al. 2011. Here, the shape of the extinction depending on solar zenith
angle should be similar to the results observed in the present study considering a single wavelength
λ = 550 nm. Figure 8 shows the typical minimum of radiative forcing at solar zenith angles around
θ ≈ 70°, although, direct and diffuse radiation are considered. A flight path along the North-South
axis is chosen, even though no differences compared to the East-West contrail are detected, proba-
bly because diffuse and direct radiances are considered.
Figure 8: Radiative forcing at λ = 550 nm as function of the solar zenith angle θ for comparison with other
works considering the optical properties of individual contrails depending on solar zenith angle. The shape of
the curve is similar to the Figures 3 and 9 of Gounou et al. 2007 [35] as well as Figures 5, 6, 10 and 11 of
Forster et al. 2011 [36].
To compare the estimated solar radiative forcing, radiative extinction is calculated for the contrail
described in Table 3 again, over Berlin on 21st of June 2012, 12 a.m. with solar zenith angle
θ = 29 ° and azimuthal angle φ = 2 ° and is integrated over 21 solar bands between wavelengths of
λ = 275 nm and λ = 2200 nm.
Table 3: Contrail properties used in the Monte Carlo simulation of the whole solar spectrum assuming a mean turbulent
environment with = 5 10 m2 s-3 and a contrail age of 20 hours.
Width for starting photons
6=9178 m
Horizontal standard deviation
2=3059 m
Vertical standard deviation
2=119 m
Ice particle radius
= 9.6 10 m
ROSENOW and FRICKE: Angle dependent extinction of solar radiation by individual … 115
The scattering and absorption efficiencies are calculated according to Key et al. 2002 using parame-
terizations from Yang. Considering both, diffuse and direct solar radiation coming from all direc-
tions in space, a radiative forcing of RF = 932.15 W m-1 per meter contrail is calculated (the RF
shown in Figure 9 is integrated). Although the estimation of the real contrail width is impossible,
the result is divided by the assumed width of the contrail core, 2 ∙ σh = 3059.8 m yielding a radiative
forcing of RF = 0.305 W m-2. The positive sign of that result seems surprisingly, however, consider-
ing a single wavelength λ = 550 nm, a negative RF occurs (compare Figure 8). Respecting the
whole solar spectrum with relevant contributions of solar radiances results in a positive RF. For
wavelengths λ > 750 nm diffuse upward radiances exceed diffuse downward radiances, probably
because atmospheric absorption and reemission is already taking place. The increased absorption
for these wavelengths in Figure 10 gives evidence for this green house effect. Hence, the amount of
downward scattered and absorbed radiation exceeds upward scattered radiances and warm the at-
mosphere (compare Figure 10).
Figure 9: Solar wavelength specific radiative forcing per meter contrail and per nanometer for a contrail de-
scribed in Table 3. For wavelengths λ > 750 nm radiative forcing is positive due to increased atmospheric ab-
sorption and reemission.
Figure 10: Wavelength specific upward scattered, downward scattered and absorbed powers per meter con-
trail and per nanometer for a contrail described in Table 3. For wavelengths λ > 750 nm downward scattered
and absorbed radiances exceed upward scattered radiances, resulting in a positive radiative forcing (compare
Figure 9).
4 DISCUSSION AND CONCLUSION
In this study, a model has been developed and tested, to calculate the angle dependence of solar ra-
diative extinction due to an aircraft induced condensation trail. Thereby, multiple scattering had
been considered and evaluated as not negligible for large solar zenith angles. The contrail is de-
scribed by a Gaussian plume, allowing the continuous calculation of extinction through the contrail.
116 ROSENOW and FRICKE: Angle dependent extinction of solar radiation by individual …
However, it does not give the exact dimensions of the contrail, complicating the determination of
the optical thickness and the radiative forcing for comparison with other publication. Whenever
possible, comparisons are done, and similar results are received. Differences in radiative extinction
due to flight path and day time are shown, yielding first hints for air traffic management, to avoid
flying during sunrise and sunset (large solar zenith angles) and when possible prefer flight paths
along North-South, instead of East-West. The results can influence an airline network structure,
when external costs are internalized. The consideration of diffuse and direct radiances, integrated
over the solar spectrum show a positive radiative forcing over Germany, even on the longest day of
the yea at noon. An advantage of the here developed approach is the combination of photon extinc-
tion calculations within the contrail (Monte Carlo simulations) with the results of the radiative
transport calculations of the atmosphere (with LibRadtran) so that changes in day time or flight di-
rection can be realized easily and without high computational costs.
REFERENCES
Appleman, H., 1953: The formation of exhaust condensation trails by jet aircraft, Bull. Amer. Meteor. Soc.
34, 14–20.
Brewer, A.W., 1946: Condensation trails. Weather 1, 34–40.
Burkhardt, U. and B. Kärcher, 2011: Global radiative forcing from contrail cirrus, Nature Climate Change 1,
54–58.
Corti, T. and T. Peter, 2009: A simple model for cloud radiative forcing, Atmospheric Chemistry and Physics
9, 5751–5758.
Forster, L., C. Emde, B. Mayer, and S. Unterstrasser, 2011: Effects of Three- Dimensional Photon Transport
on the Radiative Forcing of Realistic Contrails, American Meteorological Society, 2243–2255.
Gounou A., and R. J. Hogan, 2007:A sensitivity study of the effect of horizontal photon transport on the ra-
diative forcing of contrails, Journal of Atmospheric Sciences 64, 1706–1716.
Graf, K., U. Schumann, H. Mannstein, and B. Mayer, 2012: Aviation induced diurnal North Atlantik cirrus
cover cycle, Geophysical Research Letters 39, L16804 (2012).
Hansen, J.E., M. Sato, and R. Ruedy, 1997: Radiative forcing and climate response, J. Geophysical Research
102, 6831–6684.
Holzäpfel, F., 2003: Probabilistic Two-Phase Wake Vortex Decay and Transport Model”. Journal of Aircraft
40, 323-331.
Jeßberger, P., C. Voigt, U. Schumann, I. Sölch, H. Schlager, S. Kaufmann, A. Petzold, D. Schäuble, and F.
G. Gayet, 2013: Aircraft type influence on contrail properties, Atmospheric Chemistry and Physics 13,
11965–11984.
Kaiser, M., 2015: Optimierung von Flugtrajektorien strahlgetriebener Verkehrsflugzeuge bei konkurrieren-
den SESAR Zielfunktionen mittels Entwicklung eines hochpräzisen Flugleistungsmodells, Dissertation,
Technische Universität Dresden.
Key, J. R., P. Yang, B. A. Baum, and S. L. Nasiri, 2002: Parameterization of shortwave ice cloud optical
properties for various particle habits. J. Geophys. Res. 107, 4181.
Lee, D.S., D. W Fahey, P. M. Forster, P. J. Newton, R. C.N. Witt, L. L. Lim, B. Owen, and R. Sausen, 2009:
Aviation and global climate change in the 21st century, Atmospheric Environment 43, 3520–3537.
Marquart, S., 2003: Klimawirkung von Kondensstreifen: Untersuchungen mit einem globalen Zirkulations-
modell. Dissertation, University of Munich, Department of Physics.
Mayer, B., A. Kylling, C. Emde, U. Hamann, and R. Buras, 2011: libRadtran user’s guide. Technical report,
Technische Universität München.
Meerkötter, R., U. Schumann, P. Minnis, D. R. Doelling, T. Nakajima, and Y. Tsushima, 1999: Radiative
forcing by contrails, J. Geophysical Research 17, 1080–1094.
Minnis, P., U. Schumann, D. R. Doelling, K. M. Gierens, and D. W. Fahey, 1999: Global distribution of con-
trail radiative forcing, Geophysical Research Letters 26, 1853–1856.
Myhre G. and F. Stordal, 2001: On the tradeoff of the solar and thermal infrared impact of contrails, Geo-
physical Research Letters 28, 3119–3122.
Myhre, G., D. Shindell, F.-M. Bréon, W. Collins, J. Fuglestvedt, J. Huang, D. Koch, J.-F. Lamarque, D. Lee,
B. Mendoza, T. Nakajima, A. Robock, G. Stephens, T. Takemura, and H. Zhang, 2013: Anthropogenic
and Natural Radiative Forcing. In: Climate Change 2013: The Physical Science Basis. Contribution of
Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change,
Cambridge University Press.
ROSENOW and FRICKE: Angle dependent extinction of solar radiation by individual … 117
Ponater, M., S. Pechtl, R. Sausen, U. Schumann, and G. Hüttig, 2006: Potential of cyroplane technology to
reduce aircraft climate impact: A state-of-the-art assessment, Atmospheric Environment 40, 6928–6944.
Petty, G.W., 2002: Area-Average Solar Radiative Transfer in Three-Dimensionally Inhomogeneous Clouds:
The Independently Scattering CloudletModel”. J. Atmos. Sci. 59, 2910–2929.
Ricchiazzi, P., S. Yang, C. Gautier, and D. Sowle. ”SBDART: A research and Teaching software tool for
plane-parallel radiative transfer in the Earths atmosphere”, Bulletin of the American Meteorological Soci-
ety 79, 2101-2114.
Rosenow, J., M. Kaiser, and H. Fricke, 2012: Modeling Contrail life cycles based on highly precise flight
profile data of modern aircraft, International Conference on Research in Airport Transportation (ICRAT),
Berkley
Sausen, R., I. Isaksen, V. Grewe, D. Hauglustaine, D. S. Lee, G. Myhre, M.O. Köhler, G. Pitari, U. Schu-
mann, F. Stordal, and C. Zerefos, 2005: Aviation radiative forcing in 2000: An update on IPCC (1999).
Meteorologische Zeitschrift 14, 555–561.
Schmidt, E,. 1941: Die Entstehung von Eisnebel aus den Auspuffgasen von Flugmotoren, Schriften der
Deutschen Akademie der Luftfahrtforschung, Verlag R. Oldenburg, München/Berlin 44, 1–15.
Schultz, J., 1997: On the effect of cloud inhomogeneity on area averaged radiative properties of contrails,
Geophysical Research Letters 25, 1427–1430.
Schumann, U., 1996: On conditions for Contrail formation from aircraft exhaust, Meteorologische Zeitschrift
5, 4–23.
Schumann, U., 2000: Influence of propulsion efficiency on contrail formation, Aerospace Science and Tech-
nology 4, 391–401.
Schumann, U., 2005: Formation, properties and climatic effects of contrails. C.R. Physique 6, 549–565.
Schumann, U. and K. Graf, 2013: Aviation-induced cirrus and radiation changes at diurnal timescales, Jour-
nal of Geophysical Research 118, 1–18.
Solomon, S., D. Quin, M. Manning, M. Marquis, K. Averyt, M. M. B. Tignor, H. L. Miller Jr., and Z. Chen,
2007: Climate change 2007: The Physical Science Basis. Cambridge University Press.
Stamnes, K., S.-C. Tsay, W. Wiscombe, and K. Jayaweera, 1988: Numerically stable algorithm for discrete-
ordinate-method radiative transfer in multiple scattering and emitting layered media, Applied Optics 27,
2502–2509.
Sussmann, R. and K. M. Gierens, 2001: Differences in early contrail evolution of two-engine versus four-
engine aircraft: Lidar measurements and numerical simulations. J. Geophysical Research 106, 4899–
4911.
Vázquez-Navarro, M., H. Mannstein, and S. Kox, 2015: Contrail life cycle and properties from one year of
MSG/SEVIRI rapid-scan images. Atmos. Chem. Phys. Discuss. 15, 7019–7055.
Wyser, K., D. Mitchell P. Yang, K. N. Liou. 2000: Parameterization of the scattering and absorption proper-
ties of individual ice crystals, Journal of Geophysical Research 105, 4699–4718.
