Persistent condensation trails are clouds, induced by the exhaust of an aircraft engine in a cold and ice-supersaturated environment. These artificial ice clouds can both cool and heat the atmosphere by scattering solar radiation and absorbing terrestrial radiation, respectively.
The influence of condensation trails on the Earth-atmosphere energy balance and therewith the answer to the question of the dominating process had been mostly approximated on a global scale by treating the condensation trail as plane parallel layer with constant optical properties. Individual condensation trails and the influence of the solar angle had been analyzed, always using a course spatial grid and never under consideration of the aircraft performance, generating the condensation trail. For a trajectory optimization, highly precise results of the impact of condensation trails on the radiation budget and the influence of the aircraft performance on this impact is needed, so that future air traffic may consider the main factors of flight performance on the environmental impact of condensation trails. That’s why, a model is developed in this thesis to continuously estimate the scattering and absorption properties and their dependence on the aircraft performance.:1 Introduction 3
1.1 Motivation 3
1.2 State of the art 5
1.3 Approach 6
2 Theoretical background 9
2.1 The Earth’s atmosphere 9
2.1.1 The mean vertical structure of the atmosphere 12
2.1.2 Standard atmospheres 14
2.2 Radiation 15
2.2.1 Nature of radiation 15
2.2.2 Important metrics describing radiation 17
2.2.3 Relevant spectra and principles of radiation 19
2.2.4 Solar radiation 20
2.2.5 Terrestrial radiation 21
2.2.6 Radiative transfer and extinction 22
2.2.7 Radiative transfer equation 30
2.2.8 Energy budget of the Earth-atmosphere system 32
2.3 Thermodynamics 33
2.3.1 Atmospheric stability 33
2.3.2 Turbulence 36
2.3.3 Conditions of contrail formation 41
3 Development of a radiative forcing model 45
3.1 Model atmosphere 45
3.2 Flight performance model 46
3.3 Atmospheric radiative transfer model 49
3.3.1 Two Stream Approximation 51
3.3.2 Discrete ordinate radiative transfer solver 52
3.3.3 Methods to calculate broadband radiances and irradiances 53
3.4 Contrail life cycle model 57
3.4.1 Dissipation regime 58
3.4.2 Diffusion regime 63
3.5 Contrail radiative forcing model 74
3.5.1 Consideration of multiple scattering using a Monte Carlo simulation 74
3.5.2 Geometry of the Monte Carlo simulation 75
3.5.3 Interpretation of Beer’s law 76
3.5.4 Procedure of the Monte Carlo simulation 79
3.5.5 The extinguished power per unit length contrail 87
3.5.6 Scattering and absorption efficiencies Qs, Qa and asymmetry
parameters gHG 89
3.5.7 Calibration of the Monte Carlo simulation 94
4 Calculations 99
4.1 Contrail properties 99
4.1.1 Conditions of contrail formation 100
4.1.2 Initial dimensions at the end of the dissipation regime 101
4.1.3 Microphysical properties during the diffusion regime 103
4.2 Radiative transport up to the contrail 105
4.2.1 Solar direct and diffuse radiance 106
4.2.2 Terrestrial irradiance 107
4.3 Scattering and absorption properties of radiation within the contrail 109
4.3.1 Monte Carlo simulation for solar radiation 109
4.3.2 Monte Carlo simulation for terrestrial irradiances 112
4.3.3 Relevance of multiple scattering 116
4.4 Radiative extinction 116
4.4.1 Solar zenith and azimuthal angle 118
4.4.2 Flightpath 120
4.4.3 Contrail evolution 122
4.4.4 Turbulence 126
4.4.5 Wavelength specific extinction 129
4.5 Terrestrial energy forcing of a contrail 133
4.6 Verification 135
5 Conclusion and outlook 141
5.1 Conclusion 141
5.2 Outlook 144
List of Figures 147
List of Tables 151
Abbreviations and Symbols 153
Glossary 161
Bibliography 169
Acknowledgements 183Langlebige Kondensstreifen sind Eiswolken, welche durch Kondensation von Wasserdampf an Rußpartikeln in einer eisübersättigten Atmosphäre entstehen. Der Wasserdampf entstammt einerseits aus dem Triebwerkabgas und andererseits aus der Atmosphäre. Kondensstreifen können die Atmosphäre durch Rückstreuung solarer Strahlung kühlen und durch Rückstreuung und Absorption terrestrischer Strahlung erwärmen.
Der Einfluss von Kondensstreifen auf den Wärmehaushalt der Atmosphäre und damit die Antwort auf die Frage nach dem dominierenden Effekt wurde bisher zumeist auf globaler Ebene ermittelt, wobei der Kondensstreifen als planparallele Schicht mit konstanten optischen Eigenschaften angenähert wurde. Individuelle Kondensstreifen und der Einfluss des Sonnenstandes wurden bisher nur mithilfe eines groben Rasters betrachtet und niemals unter Berücksichtigung der Flugleistung des Luftfahrzeuges, welches den Kondensstreifen generiert hat. Für eine Trajektorienoptimierung sind jedoch präzise Berechnungen des Strahlungseinflusses und eine gewissenhafte Berücksichtigung der Flugleistung notwendig. Nur so kann der zukünftige Luftverkehr die Haupteinflussfaktoren der Flugeigenschaften auf den Strahlungseinfluss der Kondensstreifen berücksichtigen. Aus diesem Grund wurde in dieser Arbeit ein Modell entwickelt, welches die Eigenschaften des Strahlungstransfers durch den Kondensstreifen kontinuierlich bestimmt und die aus der Flugleistung resultierenden Parameter berücksichtigt.:1 Introduction 3
1.1 Motivation 3
1.2 State of the art 5
1.3 Approach 6
2 Theoretical background 9
2.1 The Earth’s atmosphere 9
2.1.1 The mean vertical structure of the atmosphere 12
2.1.2 Standard atmospheres 14
2.2 Radiation 15
2.2.1 Nature of radiation 15
2.2.2 Important metrics describing radiation 17
2.2.3 Relevant spectra and principles of radiation 19
2.2.4 Solar radiation 20
2.2.5 Terrestrial radiation 21
2.2.6 Radiative transfer and extinction 22
2.2.7 Radiative transfer equation 30
2.2.8 Energy budget of the Earth-atmosphere system 32
2.3 Thermodynamics 33
2.3.1 Atmospheric stability 33
2.3.2 Turbulence 36
2.3.3 Conditions of contrail formation 41
3 Development of a radiative forcing model 45
3.1 Model atmosphere 45
3.2 Flight performance model 46
3.3 Atmospheric radiative transfer model 49
3.3.1 Two Stream Approximation 51
3.3.2 Discrete ordinate radiative transfer solver 52
3.3.3 Methods to calculate broadband radiances and irradiances 53
3.4 Contrail life cycle model 57
3.4.1 Dissipation regime 58
3.4.2 Diffusion regime 63
3.5 Contrail radiative forcing model 74
3.5.1 Consideration of multiple scattering using a Monte Carlo simulation 74
3.5.2 Geometry of the Monte Carlo simulation 75
3.5.3 Interpretation of Beer’s law 76
3.5.4 Procedure of the Monte Carlo simulation 79
3.5.5 The extinguished power per unit length contrail 87
3.5.6 Scattering and absorption efficiencies Qs, Qa and asymmetry
parameters gHG 89
3.5.7 Calibration of the Monte Carlo simulation 94
4 Calculations 99
4.1 Contrail properties 99
4.1.1 Conditions of contrail formation 100
4.1.2 Initial dimensions at the end of the dissipation regime 101
4.1.3 Microphysical properties during the diffusion regime 103
4.2 Radiative transport up to the contrail 105
4.2.1 Solar direct and diffuse radiance 106
4.2.2 Terrestrial irradiance 107
4.3 Scattering and absorption properties of radiation within the contrail 109
4.3.1 Monte Carlo simulation for solar radiation 109
4.3.2 Monte Carlo simulation for terrestrial irradiances 112
4.3.3 Relevance of multiple scattering 116
4.4 Radiative extinction 116
4.4.1 Solar zenith and azimuthal angle 118
4.4.2 Flightpath 120
4.4.3 Contrail evolution 122
4.4.4 Turbulence 126
4.4.5 Wavelength specific extinction 129
4.5 Terrestrial energy forcing of a contrail 133
4.6 Verification 135
5 Conclusion and outlook 141
5.1 Conclusion 141
5.2 Outlook 144
List of Figures 147
List of Tables 151
Abbreviations and Symbols 153
Glossary 161
Bibliography 169
Acknowledgements 18
