Zusammenfassung ................................................. 1
Abstract ........................................................ 3
1 Introduction ................................................. 5
1.1 Thesis goals and outline ................................ 7
2 Background ................................................... 9
2.1 Thunderstorm structures ................................. 9
2.1.1 Deep moist convection ............................ 9
2.1.2 Organization of convection ...................... 10
2.2 Charging mechanisms of thunderclouds ................... 12
2.3 Lightning .............................................. 14
2.3.1 Lightning detection with LINET .................. 14
2.3.2 Lightning initiation and lightning types ........ 15
2.3.3 Definition of a "flash" ......................... 17
2.4 The flash rate ......................................... 18
2.4.1 General considerations .......................... 18
2.4.2 Application to a two-plate capacitor ............ 20
2.4.3 Assumptions and their limitations ............... 22
2.4.4 Interpretation of the flash-rate equation ....... 24
2.5 Single-parameter approaches ............................ 26
2.5.1 Popular single-parameter approaches and their
limitations ..................................... 26
2.5.2 Flash rate and generator power .................. 30
2.5.3 The Grewe et al. (GR0l) parameterization ........ 32
3 The New Lightning-Frequency Parameterization ................ 37
3.1 Parameterizations ...................................... 37
3.1.1 Area of the capacitor plates .................... 38
3.1.2 The lightning efficiency, γ ..................... 39
3.1.3 Lightning charge and generator-current
density ......................................... 39
3.2 Definition of a cell in the PR92, YMUK09, and GR0l
approaches ............................................. 44
4 Implementation .............................................. 49
4.1 Description of the algorithm ........................... 49
4.2 Implementation of the algorithm ........................ 52
4.2.1 Source-code organization ........................ 52
4.2.2 The module src_lightning.f90 .................... 53
4.2.3 Input and output ................................ 57
4.3 COSMO-DE-specific additions ............................ 58
4.4 Other parameterizations ................................ 59
5 Tests of the New Lightning Parameterization ................. 61
5.1 Individual observed cumulonimbus clouds ................ 6l
5.2 Environmental parameters ............................... 74
6 Application ................................................. 77
6.l Application to individual simulated cumulonimbus
clouds ................................................. 77
6.l.l 22 August 2008 .................................. 79
6.l.2 2 April 2008 .................................... 79
6.1.3 5 July 2009 ..................................... 80
6.1.4 1 March 2008 .................................... 81
6.l.5 26 May 2009 ..................................... 82
6.2 Observed and simulated lightning over southern
Germany ................................................ 83
6.2.1 22 August 2008 .................................. 83
6.2.2 5 July 2009 ..................................... 89
7 Discussion ................................................. 103
7.1 Lightning data ........................................ 103
7.2 The D10 approach ...................................... 104
7.3 The PR92, YMUK09, and GR0l approaches ................. 107
7.4 D10 application: individual cells in COSMO-DE ......... 110
7.5 COSMO-DE implementation - entire domain ............... 111
7.6 Sounding-derived parameters ........................... 115
8 Conclusions and Outlook .................................... 117
8.1 Future work ........................................... 120
A Mathematical Details ....................................... 121
A.l The electrostatic field in a two-plate capacitor ...... 121
A.2 The rate of change of the electrostatic, field in
a two-plate capacitor ................................. 126
A.3 The charging current .................................. 120
A.4 The generator power ................................... 128
В The COSMO-DE Model ......................................... 131
С List of Abbreviations and Symbols .......................... 133
Bibliography .................................................. 139
Acknowledgments ............................................... 147
Curriculum Vitae .............................................. 149
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