Optical Properties of Condensation Trails

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

Data-driven airport management enabled by operational milestones derived from ADS-B messages

Standardized, collaborative decision-making processes have already been implemented at some network-relevant airports, and these can be further enhanced through data-driven approaches (e.g., data analytics, predictions). New cost-effective implementations will also enable the appropriate integration of small and medium-sized airports into the aviation network. The required data can increasingly be gathered and processed by the airports themselves. For example, Automatic Dependent Surveillance-Broadcast (ADS-B) messages are sent by arriving and departing aircraft and enable a data-driven analysis of aircraft movements, taking into account local constraints (e.g., weather or capacity). Analytical and model-based approaches that leverage these data also offer deeper insights into the complex and interdependent airport operations. This includes systematic monitoring of relevant operational milestones as well as a corresponding predictive analysis to estimate future system states. In fact, local ADS-B receivers can be purchased, installed, and maintained at low cost, providing both very good coverage of the airport apron operations (runway, taxi system, parking positions) and communication of current airport performance to the network management. To prevent every small and medium-sized airport from having to develop its own monitoring system, we present a basic concept with our approach. We demonstrate that appropriate processing of ADS-B messages leads to improved situational awareness. Our concept is aligned with the operational milestones of Eurocontrol’s Airport Collaborative Decision Making (A-CDM) framework. Therefore, we analyze the A-CDM airport London–Gatwick Airport as it allows us to validate our concept against the data from the A-CDM implementation at a later stage. Finally, with our research, we also make a decisive contribution to the open-data and scientific community

Fundamental framework to plan 4D robust descent trajectories for uncertainties in weather prediction

Aircraft trajectory planning is affected by various uncertainties. Among them, those in weather prediction have a large impact on the aircraft dynamics. Trajectory planning that assumes a deterministic weather scenario can cause significant performance degradation and constraint violation if the actual weather conditions are significantly different from the assumed ones. The present study proposes a fundamental framework to plan four-dimensional optimal descent trajectories that are robust against uncertainties in weather-prediction data. To model the nature of the uncertainties, we utilize the Global Ensemble Forecast System, which provides a set of weather scenarios, also referred to as members. A robust trajectory planning problem is constructed based on the robust optimal control theory, which simultaneously considers a set of trajectories for each of the weather scenarios while minimizing the expected value of the overall operational costs. We validate the proposed planning algorithm with a numerical simulation, assuming an arrival route to Leipzig/Halle Airport in Germany. Comparison between the robust and the inappropriately-controlled trajectories shows the proposed robust planning strategy can prevent deteriorated costs and infeasible trajectories that violate operational constraints. The simulation results also confirm that the planning can deal with a wide range of cost-index and required-time-of-arrival settings, which help the operators to determine the best values for these parameters. The framework we propose is in a generic form, and therefore it can be applied to a wide range of scenario settings

Interdependent Uncertainty Handling in Trajectory Prediction

The concept of 4D trajectory management relies on the prediction of aircraft trajectories in time and space. Due to changes in atmospheric conditions and complexity of the air traffic itself, the reliable prediction of system states is an ongoing challenge. The emerging uncertainties have to be modeled properly and considered in decision support tools for efficient air traffic flow management. Therefore, the subjacent causes for uncertainties, their effects on the aircraft trajectory and their dependencies to each other must be understood in detail. Besides the atmospheric conditions as the main external cause, the aircraft itself induces uncertainties to its trajectory. In this study, a cause-and-effect model is introduced, which deals with multiple interdependent uncertainties with different stochastic behavior and their impact on trajectory prediction. The approach is applied to typical uncertainties in trajectory prediction, such as the actual take-off mass, non-constant true air speeds, and uncertain weather conditions. The continuous climb profiles of those disturbed trajectories are successfully predicted. In general, our approach is applicable to all sources of quantifiable interdependent uncertainties. Therewith, ground-based trajectory prediction can be improved and a successful implementation of trajectory-based operations in the European air traffic system can be advanced. Document type: Articl

GWAS meta-analysis of over 29,000 people with epilepsy identifies 26 risk loci and subtype-specific genetic architecture

Epilepsy is a highly heritable disorder affecting over 50 million people worldwide, of which about one-third are resistant to current treatments. Here we report a multi-ancestry genome-wide association study including 29,944 cases, stratified into three broad categories and seven subtypes of epilepsy, and 52,538 controls. We identify 26 genome-wide significant loci, 19 of which are specific to genetic generalized epilepsy (GGE). We implicate 29 likely causal genes underlying these 26 loci. SNP-based heritability analyses show that common variants explain between 39.6% and 90% of genetic risk for GGE and its subtypes. Subtype analysis revealed markedly different genetic architectures between focal and generalized epilepsies. Gene-set analyses of GGE signals implicate synaptic processes in both excitatory and inhibitory neurons in the brain. Prioritized candidate genes overlap with monogenic epilepsy genes and with targets of current antiseizure medications. Finally, we leverage our results to identify alternate drugs with predicted efficacy if repurposed for epilepsy treatment

Advanced Flight Planning and the Benefit of In-Flight Aircraft Trajectory Optimization

The implementation of Trajectory-Based Operations, invented by the Single European Sky Air Traffic Management Research program SESAR, enables airlines to fly along optimized waypoint-less trajectories and accordingly to significantly increase the sustainability of the air transport system in a business with increasing environmental awareness. However, unsteady weather conditions and uncertain weather forecasts might induce the necessity to re-optimize the trajectory during the flight. By considering a re-optimization of the trajectory during the flight they further support air traffic control towards achieving precise air traffic flow management and, in consequence, an increase in airspace and airport capacity. However, the re-optimization leads to an increase in the operator and controller’s task loads which must be balanced with the benefit of the re-optimization. From this follows that operators need a decision support under which circumstances and how often a trajectory re-optimization should be carried out. Local numerical weather service providers issue hourly weather forecasts for the coming hour. Such weather data sets covering three months were used to re-optimize a daily A320 flight from Seattle to New York every hour and to calculate the effects of this re-optimization on fuel consumption and deviation from the filed path. Therefore, a simulation-based trajectory optimization tool was used. Fuel savings between 0.5% and 7% per flight were achieved despite minor differences in wind speed between two consecutive weather forecasts in the order of 0.5 m s−1. The calculated lateral deviations from the filed path within 1 nautical mile were always very small. Thus, the method could be easily implemented in current flight operations. The developed performance indicators could help operators to evaluate the re-optimization and to initiate its activation as a new flight plan accordingly

Optical Properties of Condensation Trails

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

Optical Properties of Condensation Trails

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