Surface-Atmosphere Interactions of Heterogeneous Surfaces on Multiple Scales by Means of Large-Eddy Simulations and Analytical A

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Surface-Atmosphere Interactions of Heterogeneous Surfaces on Multiple Scales by Means of Large-Eddy Simulations and Analytical A Surface–atmosphere interactions of heterogeneous surfaces on multiple scales by means of large-eddy simulations and analytical approaches Zur Erlangung des akademischen Grades eines DOKTORS DER NATURWISSENSCHAFTEN von der Fakultät für Bauingenieur-, Geo- und Umweltwissenschaften des Karlsruher Instituts für Technologie (KIT) genehmigte DISSERTATION von M.Sc. Konstantin Kröniger aus Unterammergau Tag der mündlichen Prüfung: 26.11.2018 Referent: Matthias Mauder Korreferent: Olivier Eiff Korreferent: Björn Maronga Karlsruhe (2018) Abstract The effect of surface heterogeneities on surface–atmosphere exchange is of signif- icant importance not only for atmospheric measurements but also for numerical weather or climate simulations, as these heterogeneities interact with the atmo- spheric turbulence on many different scales. While the number of numerical in- vestigations on atmospheric flow above heterogeneous surfaces is continuously in- creasing, only a small amount of analytical theories exist, which is due to the non- linearity of the governing equations. In the current thesis, surface–atmosphere interactions of heterogeneous surfaces were studied on several scales by means of analytical and numerical approaches, where large-eddy simulations (LES) were em- ployed for the latter. At first, the micro-γ-scale heterogeneity of leading canopy edges was investigated by constructing an analytical solution to the governing equations of two-dimensional edge flow in neutral atmospheric stratification. To determine the missing model parameters (integration constants) and to test the model against LES, several simulations of varying canopy length scales were performed. The canopy- edge-flow model was further compared to the analytical model of Belcher et al. [J. Fluid. Mech., 44:479-504, 2003]. This comparison showed that the Belcher et al. (2003) model is mainly applicable to shallow canopies, while the newly developed model featured the best results for canopies that were dense enough to ensure a full adjustment of the atmospheric flow. Besides investigating the interactions of micro- γ-scale heterogeneities, a distinct meso-γ-scale heterogeneity, namely the isolated semi-arid forest Yatir, was analyzed by detailed LES. These simulations were used to determine occurrence, location and strength of secondary circulations, as these flow features could be of major importance for the surface–atmosphere exchange of the semi-arid ecosystem. The numerical exploration revealed the formation of secondary circulations in all three cases of varying atmospheric stability (weakly- convective, mildly-convective, and strongly-convective scenarios). While the occur- ring circulations featured a horizontal extent that was too small to couple the full for- est to the surrounding shrubland, investigations on the aerodynamic resistance to heat transfer showed that the secondary circulations affect the surface–atmosphere exchange by enhancing exchange in regions of updraft and reducing exchange in regions of downdraft. As the aforementioned mechanisms are directly related to surface heterogeneities, homogeneous parametrizations of surface–atmosphere ex- change are insufficient to capture those. However, parametrizing surface hetero- geneities is important for the application of meso-scale models to simulate atmo- spheric flow, as the grid resolution of these models is too coarse to resolve many important heterogeneity scales. To account for those scales, an aerodynamic resis- tance parametrization for heterogeneous surfaces was constructed from analytical investigations, which is the third part of this thesis. The analytical derivation is based on linking the covariance function of the actual heterogeneous scenario to a corresponding homogeneous covariance function in spectral space. From assum- ing the shape of the turbulent spectra for the homogeneous case and by neglecting advection and dispersive fluxes, correction factors to the bulk aerodynamic resis- tance were extracted. Comparison of this novel covariance-function approach with the conventional bulk and tile approaches for three scenarios of idealized surface heterogneities revealed that the covariance-function approach features the smallest deviation from the LES reference, which illustrates the advantage of using this novel parametrization within the framework of meso-scale models. ii Zusammenfassung Der Einfluss von Oberflächenheterogenität auf die Wechselwirkungen zwischen Ober- fläche und Atmosphäre ist nicht nur für Messungen des turbulenten Austausches, sondern auch für Wetter- und Klimasimulationen von signifikanter Bedeutung, da Oberflächenheterogenitäten mit der atmosphärischen Turbulenz auf verschiedenen Skalen wechselwirken. Während die Anzahl an numerischen Studien zu atmosphä- rischen Flüssen über heterogenen Oberflächen stetig zunimmt, existiert nur eine geringe Zahl an analytischen Theorien, was durch die nichtlineare Natur der zu- grundeliegenden Gleichungen begründet ist. In dieser Dissertation wurden Wech- selwirkungen von heterogenen Oberflächen mit der Atmosphäre unter Zuhilfenah- me von analytischen und numerischen Methoden auf verschiedenen Skalen unter- sucht, wobei „large-eddy” Simulationen (LES) für den numerischen Teil Verwendung fanden. Die erste Untersuchung bezog sich auf die mikro-γ skalige Heterogenität von windzugewandten Vegetationskanten, die in einer analytische Lösung für den mittleren atmosphärischen Fluss durch eine solche Kante in neutraler Schichtung resultierte. Um die fehlenden Modellparameter (Integrationskonstanten) zu bestim- men, und um das Modell gegen LES zu testen, wurden mehrere Simulationen mit variierten Vegetationslängenskalen durchgeführt. Des Weiteren wurde das neu ent- wickelte Modell mit dem analytischen Modell von Belcher et al. [J. Fluid. Mech., 44:479-504, 2003] verglichen. Dieser Vergleich zeigte, dass das Modell von Belcher et al. (2003) hauptsächlich für Vegetation von geringer Dichte angewandt werden kann, während das neu entwickelte Modell die besten Ergebnisse für Vegetation er- zielte, die dicht genug war um eine vollständige Anpassung des atmosphärischen Flusses zu bewirken. Neben atmosphärischen Wechselwirkungen von mikro-γ ska- ligen Heterogenitäten, wurde mit dem semiariden Yatirwald auch eine ausgeprägte meso-γ skalige Heterogenität unter Zuhilfenahme von detaillierten LES untersucht. Diese Simulationen fanden bei der Bestimmung von Auftreten, Position und Stärke von Sekundärzirkulationen Verwendung, welche eine entscheidende Rolle für den atmosphärischen Austausch des semiariden Ökosystems spielen könnten. Die nu- merische Studie resultierte in einem Auftreten von Sekundärzirkulationen in allen drei Fällen von unterschiedlicher atmosphärischer Stabilität (schwach konvektiver, leicht konvektiver und stark konvektiver Fall). Obwohl die horizontale Ausdehnung der Zirkulationen zu klein war um den ganzen Wald mit dem umgebenden Busch- land zu koppeln, zeigten Untersuchungen des aerodynamischen Widerstandes für Wärmeaustausch, dass die Sekundärzirkulationen die atmosphärischen Wechsel- wirkungen in Regionen mit Aufwind verstärkten und in Regionen mit Abwind ab- schwächten. Da die zuvor genannten Mechanismen direkt mit der Heterogenität der Oberfläche verknüpft sind, können sie nicht durch homogenen Parametrisierungen beschrieben werden. Dennoch ist die Parametrisierung von heterogenen Oberflä- chen für atmosphärische Simulationen unter Verwendung von mesoskaligen Mo- dellen wichtig, da die Rasterung dieser Modelle zu grob ist um viele wichtige Skalen der Oberflächenheterogenität aufzulösen. Um auch diese Skalen zu berücksichti- gen, wurde eine Parametrisierung des aerodynamischen Widerstandes für hetero- gene Oberflächen entwickelt, was den dritten Teil dieser Dissertation darstellt. Die analytische Herleitung der Parametrisierung basiert auf der Verknüpfung der Kova- rianzfunktion des eigentlichen, heterogenen, Szenarios mit der Kovarianzfunktion eines zugehörigen, homogenen, Szenarios im Spektralraum. Unter Annahmen über die Form der Turbulenzspektren des homogenen Szenarios, und unter Vernach- lässigung von Advektion und dispersiven Flüssen, wurden Korrekturfaktoren für den aerodynamischen Bulkwiderstand bestimmt. Des weiteren zeigte ein Vergleich des Kovarianzfunktionsansatzes mit den konventionellen „bulk” und „tile” Metho- den für drei Szenarien von idealisierten Oberflächenheterogenitäten, dass der Ko- varianzfunktionsansatz die kleinsten Abweichungen von der LES Referenz besitzt. Dieses Ergebnis demonstriert den Vorteil einer Verwendung der neuen Methode in mesoskaligen Modellen. iv Contents Abstract i Zusammenfassung iii Acknowledgements vii List of manuscripts ix List of symbols xi 1 Introduction 1 1.1 Application of flow dynamics to atmospheric conditions . .2 1.1.1 Governing equations . .3 1.1.2 Covariance functions and turbulence spectra . .5 1.1.3 Kolmogorov theory . .6 1.1.4 Similarity theory . .7 1.2 Numerical approaches for modeling atmospheric flow . 10 1.3 Canopy–atmosphere interactions . 12 1.3.1 Modified governing equations . 12 1.3.2 Horizontally-homogeneous canopies . 13 1.4 Effect of surface heterogeneities on the atmospheric flow . 14 1.4.1 Canopy edge flow . 15 1.4.2 Secondary circulations . 16 2 Analytical models 19 2.1 Effect of leading edges on the mean flow within a homogeneous canopy 19 2.2 Aerodynamic resistance parametrization for heterogeneous surfaces . 21 3 Numerical experiments 23 3.1 Large-eddy simulations of flow across leading canopy edges . 23 3.2 Large-eddy simulations of the Yatir forest . 24 3.3 Large-eddy simulations
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