DISS. ETH NO. 18492Modeling of orographic cirrus cloudsA dissertation submitted to theETH ZURICHfor the degree ofDoctor of Sciencespresented byHANNA JOOSDipl. Met., Hamburg University, Germanyborn 11 December 1979citizen of Germanyaccepted on the recommendation ofProf. Dr. U. Lohmann, examinerDr. P. Spichtinger, co-examinerDr. M. Giorgetta, co-examiner2009iiContentsAbstract vZusammenfassung vii1 Introduction 11.1 Cirrus clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Orographic gravity waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Orographic cirrus clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Overview over this dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Orographic cirrus in the future climate 72.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3 Model verication: Simulation of the INCA-case . . . . . . . . . . . . . . . . . . . . . 92.4 Idealized Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.5 Simulations with IPCC initial proles . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.5.1 Model setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.5.2 South America: linear ow regime . . . . . . . . . . . . . . . . . . . . . . . . . 182.5.3 South America: hydraulic jump . . . . . . . . . . . . . . . . . . . . . . . . . . 222.5.4 North America: linear ow regime . . . . . . . . . . . . . . . . . . . . . . . . . 222.5.5 North America: hydraulic jump . . . . . . . . . . . . . . . . . . . . . . . . . . 252.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Orographic cirrus in the global climate model ECHAM5 313.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2 Parameterization of cirrus clouds: homogeneous freezing . . . . . . . . . . . . . . . . . 333.3 Calculation of the vertical velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.3.1 Linear theory for gravity waves . . . . . . . . . . . . . . . . . . . . . . . . . . 353.3.2 Orography in ECHAM5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.4.1 Global simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.4.2 Comparison with measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 403.5 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 Inuence of a future climate on the microphysical and optical properties of orographiccirrus clouds in ECHAM5 474.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.2 Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.2.1 Moist Brunt-V ais ala frequency in the calculation of the vertical velocity . . . . . 504.2.2 Parameterization of an orographic cirrus cloud cover . . . . . . . . . . . . . . . 514.2.3 Reduction of the vertical velocity . . . . . . . . . . . . . . . . . . . . . . . . . 534.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.3.1 The current climate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.3.2 A future climate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65iii5 Summary and Outlook 695.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.1.1 Cloud resolving simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.1.2 Global simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.2.1 Calculation of the vertical wave phase . . . . . . . . . . . . . . . . . . . . . . . 715.2.2 Coupling of gravity waves and liquid/ mixed-phase clouds . . . . . . . . . . . . 715.2.3 Parameterization of gravity waves from additional sources . . . . . . . . . . . . 725.2.4 Cirrus cloud cover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72A The subgrid-scale orography in ECHAM5 75List of Symbols and Abbreviations 81List of Figures 85List of Tables 89Bibliography 91ivAbstractCirrus clouds play a crucial role in modulating the earth radiation budget. They cover approximately 30%of the Earth and consist purely of ice crystals. On the one hand, ice crystals scatter the incoming solarradiation back to space leading to a cooling (albedo effect of clouds). On the other hand, they effectivelytrap the outgoing long wave radiation leading to a warming (greenhouse effect of clouds). Which effectdominates depends on the clouds macrophysical and microphysical properties like vertical extension ofthe cloud, optical thickness, ice crystal shape, ice water content and ice crystal number concentration.For optically thick clouds, the scattering of incoming solar radiation dominates the trapping of long waveradiation leading to a cooling, whereas for optically thin clouds the opposite effect dominates. Until nowit is believed that, on a global scale, cirrus clouds warm the present climate. However, an estimate ofthe net radiative effect of cirrus clouds based on general circulation models (GCM) is difcult becauseGCMs simulate a fourfold difference in high cloud amount. This is caused by the fact that complexinteractions of dynamical and thermodynamical processes that lead to cirrus formation, are not properlytaken into account. Furthermore it has been shown that there is a lack of cirrus clouds over mountainousregions in GCMs as the dynamical processes leading to the formation of orographic cirrus clouds are nottaken into account. The aim of this work is therefore to improve the understanding of orographic cirrusclouds, their microphysical and optical properties and their representation in global circulation modelsin the present-day and future climate.A cloud resolving model is used in order to determine the key parameters inuencing the microphysicaland optical properties of orographic cirrus clouds in the present and future climate. First, the capabilityof the model in realistically simulating orographic cirrus has been shown by comparing the simulatedresults to aircraft measurements of an orographic cirrus taken during the INCA-campaign. In order toinvestigate the inuence of a warmer climate on the microphysical and optical properties, the model hasbeen initialized with vertical temperature, moisture and wind proles taken from an IPCC A1B scenariorun representative for the present climate and for the period 2090-2099. Two regions representativefor North and South America for the corresponding summer and winter months have been investigated.Furthermore the behavior of orographic clouds in a linear and non-linear ow regime are shown. Theadditional moisture in a warmer climate leads to a slight dampening of the propagation of gravity wavesand the associated vertical velocities. Together with the higher temperatures, fewer ice crystals nucleatehomogeneously. Assuming that the relative humidity does not change in a warmer climate, the specichumidity in the model is increased, leading to an increased ice water content of the clouds. The net effectof an increased ice water content and a decreased ice crystal number concentration is an enhanced opticaldepth. This behavior is a robust feature in our simulations that appears in the summer and winter months,North and South America and in the linear and non-linear ow regime.In a next step, a parameterization of orographic cirrus clouds has been developed and implemented in theECHAM5 GCM. With this new parameterization changes in orographic cirrus clouds in a future climatehave been estimated.To improve the simulation of orographically excited cirrus in ECHAM5, a coupling of gravity wavedynamics and cloud microphysics has been implemented. The maximum vertical velocity induced bygravity waves is calculated and used directly in the calculation of the ice crystal number concentration.As the ice crystal number concentration strongly depends on the vertical velocity, the addition of a gravitywave induced vertical velocity leads to higher ice crystal number concentrations in the upper troposphere.A comparison of the new parameterization with measurements shows a better agreement. However, thesimulated vertical velocities and ice crystal number concentrations are slightly overestimated.To investigate orographic cirrus clouds in a warmer climate, a newer model version of the ECHAM5model has been used, in which the effective radius of ice crystals depends on the ice crystal numbervconcentration. Furthermore a reduced vertical velocity for the freezing parameterization based on boxmodel simulations has been calculated, as the comparison of the simulated and measured values showsan overestimation of the simulated vertical velocity and ice crystal number concentration. The box modelresults were further used to develop a parameterization of an orographic cirrus cloud cover dependent onthe horizontal wave length of the gravity waves. The inuence of additional moisture on the propagationof gravity waves is investigated by using the dry and moist Brunt-V ais ala frequency, respectively, in thecalculation of the gravity wave induced vertical velocity in two different simulations.With these new parameterizations implemented, simulations of the present and future climate are per-formed. From the present to the future climate the vertical velocity increases, as a smaller Brunt-V ais alafrequency in the future climate leads to less ow blocking and higher effective mountain heights overmost mountain ranges. The opposite effect can be seen over dry regions. The ice crystal number concen-tration decreases in the future climate despite the increased vertical velocities. Higher temperatures leadto a faster growth of ice crystals and the supersaturation is depleted faster such that no new crystals cannucleate. The ice water content increases as more water vapor is available in a warmer climate. The neteffect of a decreased ice crystal number concentration and an increased ice water content is an increasedoptical depth in a future climate. This result agrees very well with the cloud resolving simulations. Theeffect of orographic cirrus clouds on the radiation budget is given by an increased short- and long wavecloud forcing whereas the latter dominates.The results of the cloud resolving as well as the global simulations point into the direction that an in-creased optical depth of orographic cirrus clouds might be expected in a future climate. Furthermorethe microphysical properties of cirrus clouds in ECHAM5 could be improved as compared to satellitemeasurements by taking more realistic dynamical processes for cirrus formation into account. This re-sult emphasizes the important role of subgrid-scale dynamical processes for the correct representation ofcirrus clouds in GCMs.viZusammenfassungZirruswolken haben einen grossen Einuss auf das Strahlungsbudget der Erde. Sie bedecken etwa 30%der Erde und bestehen ausschliesslich aus Eiskristallen. Einerseits streuen die Eiskristalle die einfallendeSonnenstrahlung zur uck ins All, was zu einer Abk uhlung f uhrt und mit dem Albedo-Effekt der Wolkenbezeichnet wird. Andererseits k onnen sie durch Absorption und R uckstrahlung der von der Erde emit-tierten langwelligen Strahlung erw armend wirken (Treibhauseffekt der Wolken). Welcher dieser beidenEffekte dominiert, h angt von den makro- und mikrophysikalischen Eigenschaften der Wolke ab. Dazugeh oren beispielsweise die vertikale Ausdehnung der Wolke, die optische Dicke, die Form der Kristalle,der Eiswassergehalt oder die Eiskristallanzahl. Bei optisch dicken Zirren uberwiegt der Albedo-Effektder Wolken, w ahrend bei optisch d unnen Wolken der Treibhauseffekt dominiert. Auf einer globalenSkala uberwiegt bei Zirren vermutlich der Treibhauseffekt. Solche Absch atzungen basierend auf Ergeb-nissen der Globalen Zirkulationsmodelle (GCM) sind jedoch schwierig, da diese bis heute nicht in derLage sind, den Bedeckungsgrad der Zirren und deren mikrophysikalische und optische Eigenschaftenrichtig zu berechnen. Zus atzlich konnte gezeigt werden, dass GCMs uber Gebirgen keine ausreichendeZirrusbew olkung simulieren, da die dynamischen Prozesse, die zur Bildung von orographischen Zirrenf uhren, in den GCMs nicht enthalten sind. Deshalb ist das Ziel dieser Arbeit, unser Verst andnis vonorographischen Zirren, ihrer mikrophysikalischen und optischen Eigenschaften sowie deren Simulationin GCMs zu verbessern und den Einuss eines w armeren Klimas auf diese abzusch atzen.Um die wichtigsten Parameter, die die mikrophysikalischen und optischen Eigenschaften von orographi-schen Zirren im heutigen sowie im zuk unftigen Klima bestimmen, zu untersuchen, wurden Simulatio-nen mit einem wolkenau osenden Modell durchgef uhrt. Die F ahigkeit des Modells realistische oro-graphische Zirren zu simulieren wurde getestet, indem die simulierten Ergebnisse mit Messungen einerorographischen Zirruswolke verglichen wurden, die im Rahmen der INCA-Kampagne durchgef uhrt wur-den. Um den Einuss eines w armeren Klimas auf die mikrophysikalischen und optischen Eigenschaftenzu untersuchen, wurde das Modell mit vertikalen Temperatur-, Feuchte- und Windprolen aus einemIPCC A1B Szenariolauf initialisiert, die repr asentativ f ur das heutige sowie das zuk unftige Klima (2090-2099) sind. Die Simulationen wurden f ur zwei Regionen, die Nord- und S udamerika representieren,sowie f ur die jeweiligen Sommer- und Wintermonate durchgef uhrt. Zus atzlich wurden alle Simula-tionen f ur ein lineares und ein nicht lineares Str omungsregime durchgef uhrt. Die zus atzliche Feuchtein einem w armeren Klima f uhrt zu einer schwachen D ampfung der Schwerewellen und den mit ihnenverbundenen Vertikalgeschwindigkeiten. Zusammen mit einer Zunahme der Temperatur, bilden sichweniger Eiskristalle durch homogenes Gefrieren. Unter der Annahme, dass die relative Feuchte in einemzuk unftigen Klima konstant bleibt, nimmt die spezische Feucht im Modell zu, was zu einer Zunahmedes Eiswassergehaltes der Wolken f uhrt. Die Abnahme der Eiskristalle f uhrt in Kombination mit derZunahme des Eiswassergehaltes zu einer h oheren optischen Dicke. Dieses Ergebniss zeigt sich in allenhier durchgef uhrten Simulationen.In einem n achsten Schritt wurde eine Parametrisierung f ur orographische Zirren entwickelt und in dasECHAM5 GCM implementiert. Mit Hilfe dieser neuen Parametrisierung ist es m oglich, den Einusseines w armeren Klimas auf orographische Zirren auf einer globalen Skala abzusch atzen.Um die Simulation von orographischen Zirren in ECHAM5 zu verbessern, wurde die Dynamik derSchwerewellen mit der Wolkenmikrophysik gekoppelt. Dazu wurde die maximale Vertikalgeschwindig-keit die in einer orographischen Schwerewelle auftritt berechnet, und direkt in der Berechnung derEiskristall anzahl verwendet. Da die Eiskristallanzahl stark von der Vertikalgeschwindigkeit abh angt,f uhrt dies zu einer betr achtlichen Zunahme der Eiskristallanzahl in der oberen Troposph are. Der Ver-gleich dieser neuen Parameterisierung mit Messungen zeigt eine bessere Ubereinstimmung. Allerdingssind sowohl die Vertikalgeschwindigkeiten als auch die Eiskristallanzahl leicht ubersch atzt.viiUm den Einuss eines zuk unftigen Klimas auf orographische Zirren zu untersuchen, wurde eine neuereModellversion von ECHAM5 verwendet, in der die Berechnung des Effektivradius der Eiskristallevon der Eiskristallanzahl abh angt. Zus atzlich wurde basierend auf Boxmodellsimulationen eine re-duzierte Vertikalgeschwindigkeit berechnet, die in die Berechnung des homogenen Gefrierens eingeht,da der Vergleich von simulierten und gemessenen Werte eine leichte Ubersch atzung der simuliertenWerte gezeigt hat. Die Simulationen des Boxmodells wurden weiterhin f ur die Entwicklung einer ein-fachen Parametrisierung f ur den Bedeckungsgrad f ur orographische Zirren verwendet. Dieser h angtvon der horizontalen Wellenl ange der Schwerewelle ab. Der Einuss einer h oheren Feuchte in einemzuk unftigen Klima wird untersucht, indem zwei unterschiedliche Simulationen durchgef uhrt werden,wobei in einer die trockene und in der anderen die feuchte Brunt-V ais ala Frequenz in der Berechnungder schwerewelleninduzierten Vertikalgeschwindigkeit verwendet wird.Mit diesen neuen Parametrisierungen wurden Simulationen des heutigen und zuk unftigen Klimas ba-sierend auf dem IPCC A1B Szenario, durchgef uhrt. Die Vertikalgeschwindigkeit nimmt uber den mei-sten Gebirgen im zuk unftigen Klima zu. Verursacht wird dies durch eine Abnahme der Brunt-V ais alaFrequenz in einem zuk unftigen Klima, was zu einer Verminderung des ow-blocking und somit zueiner erh ohten effektiven Bergh ohe f uhrt. Der gegenteilige Effekt zeigt sich uber den sehr trockenen Re-gionen der Erde. Trotz der meist h oheren Vertikalgeschwindigkeit in Zukunft, nimmt die Eiskristallan-zahl ab, da h ohere Temperaturen zu einemschnelleren Wachstumder Kristalle f uhren. Die Ubers attigungwird schneller abgebaut, so dass keine neuen Kristalle mehr gebildet werden k onnen. Der Eiswasserge-halt nimmt in einemzuk unftigen Klima zu, da mehr Wasserdampf vorhanden ist. Die Kombination dieserbeiden Effekt f uhrt zu einer Zunahme der optischen Dicke. Der Einuss von orographischen Zirren aufden Strahlungshaushalt besteht in einem erh ohten kurzwelligen und langwelligen cloud forcing, wobeidas langwellige clolud forcing dominiert.Die Ergebnisse der wolkenau osenden sowie der globalen Simulationen deuten auf eine Zunahme deroptischen Dicke in einem zuk unftigen Klima hin. Ausserdem konnte die Simulation der mikrophysikali-schen Eigenschaften von Zirren in ECHAM5 allein durch die Berechnung realistischerer dynamischerProzesse sowie deren Kopplung an die Eismikrophysik, verbessert werden.viiiChapter 1Introduction1.1 Cirrus cloudsCirrus clouds play an important role in the climate system. They consist purely of ice crystals and coverapproximately 30 % of the Earth (Wylie and Menzel, 1999). As ice crystals interact with the short-waveand long-wave radiation, cirrus clouds have a great potential to modulate the Earths radiative budget.They can either warm or cool the Earth-Atmosphere system depending on their microphysical and opti-cal properties. On the one hand, ice crystals scatter the short-wave radiation back to space and thus leadto a cooling (albedo effect of clouds). On the other hand, the long-wave radiation can be trapped effec-tively which leads to a warming (greenhouse effect of clouds). For optically thin cirrus, the absorptionof infrared radiation and re-emission at lower temperatures dominates the scattering of incoming solarradiation, leading to a warming. For a high optical depth the scattering of incoming solar radiation dom-inates, leading to a cooling. Which effect is more pronounced thus depends on macrophysical propertiessuch as the optical thickness of the cloud, which in turn depends on the microphysical properties likeice crystal number concentration, ice water content, crystal size and shape (Wendisch et al., 2007). Asthese properties are mainly determined by the interaction of dynamical and thermodynamical processes,it is very difcult to estimate the overall effect of cirrus clouds on the radiative budget. Until now it isbelieved that cirrus clouds lead to a net global warming (Chen et al., 2000). However, Zhang et al. (2005)showed that different models simulate a fourfold difference in high cloud amount. This uncertainty arisesfrom the complex interaction of dynamical and thermodynamical processes which are not implementedin the models or not resolved by the coarse model grid. The poor representation of cirrus thus exhibitsa signicant source of uncertainty in predicting future climate. Thus, one basic requirement for an im-proved prediction of climate change is the correct representation of cirrus clouds in general circulationmodels (GCM).For the formation of cirrus clouds, high supersaturations with respect to ice are needed, hence cirrusformation is associated with (cloud free) ice supersaturated regions (ISSR). This is obvious when com-paring the spatial distributions of ISSRs and cirrus clouds (Spichtinger et al., 2003b). The supersaturationneeded for cirrus formation depends on the freezing process. Cirrus can form via heterogeneous or ho-mogeneous freezing. Heterogeneous freezing is initiated by solid aerosols, the so-called ice nuclei (IN).The properties of these ice nuclei determine the critical supersaturation required for the initiation of thefreezing process. Homogeneous freezing denotes the freezing of supercooled solution droplets. Thefreezing of droplets of a certain size is initiated when the supersaturation exceeds a critical threshold.Koop et al. (2000) showed, that the threshold only depends on temperature and is mostly independentof the nature of the solute. In general, the supersaturation threshold is lower for heterogeneous freezing(DeMott et al., 2003). However, the lack of efcient ice nuclei in the upper troposphere, the frequentmeasurement of high ice crystal number concentrations and high relative humidities and the prevalenceof mesoscale temperature uctuations strongly suggests that the homogeneous freezing is the most im-portant freezing mechanism (Sassen and Dodd, 1989; DeMott et al., 2003; Haag et al., 2003). Thepresence of IN can modify the microphysical properties of cirrus especially at low cooling rates and foroptically thin clouds (K aercher, 2002; Spichtinger and Gierens, 2009b).ISSRs form due to different cooling mechanisms, including synoptic-scale vertical motion, turbulence,convection or gravity waves, leading to an increase in relative humidity beyond ice saturation or due tomoisture advection. Aircrafts measure a typical horizontal extent of ISSRs of 150 km (sometimesa few 1000 km) in the mid-latitudes, however, very large extended ISSRs up to 4000 km were rarely12 Chapter 1. Introductionobserved (Gierens and Spichtinger, 2000). Typical vertical extents are 500 m at mid and high latitudeswhereas the variability in layer thickness is large (Spichtinger et al., 2003a). The ice supersaturatedregions dene the overall thermodynamical conditions necessary for cirrus cloud formation. The micro-physical properties, on the other hand, are determined by the mesoscale variability in cooling rates at thepoint of freezing (Haag and K archer, 2004; Hoyle et al., 2005).Various studies show, that the observed microphysical properties can only be calculated correctly by tak-ing mesoscale vertical velocity/temperature uctuations into account. Sources for these mesoscale veloc-ity/temperature uctuations are mesoscale gravity waves arising from different sources like convection,geostrophic adjustment, baroclinic instability and stratied ow over mountains (Fritts and Alexander,2003). The mesoscale velocity uctuations exhibit one key factor determining the ice crystal numberconcentration in a homogeneous freezing event. They induce adiabatic cooling and the relative humiditywith respect to ice (RHi) increases. If the critical threshold for homogeneous freezing is exceeded, crys-tals start to form. The higher the vertical velocity and the associated cooling rate, the more crystals canform because of the steep increase in the nucleation rate (Koop et al., 2000). Thus the calculation of arealistic vertical velocity is crucial to simulate realistic microphysical properties.This has also been shown by Lin et al. (1998) who investigated the broadness of the crystal spectrawhich develops if an air parcel follows sine waves with different amplitudes. The observed broad crystaldistribution could be reproduced by varying the initial position of the air parcel in the wave trajectorywhereas the maximum ice crystal number concentration is determined by the amplitude of the wave. Noadditional processes are needed to explain the observed properties. Hoyle et al. (2005) also investigatedthe origin of high ice crystal number concentrations in cirrus clouds and found that the observed high icecrystal number densities are obtained only when small-scale temperature/vertical velocity uctuationsare taken into account. K archer and Str om (2003) investigated the role of dynamical variability andaerosols for cirrus cloud formation based on the INCA (Interhemispheric differences in Cirrus propertiesfrom Anthropogenic emissions) measurements (Gayet et al., 2004). They could show, that variability inmesoscale vertical velocities combined with pure homogeneous freezing is responsible for most of theobserved variance in the ice crystal number concentration. However, it is possible that the presence ofIN inuences the properties of optically thin or even subvisible cirrus with low ice crystal number con-centration formed in weak updrafts (Gierens, 2003; Spichtinger and Gierens, 2009b). With increasingupdrafts this inuence is diminished as the amount of IN is limited and the evolving ice crystal numberconcentration exceeds the available IN. All these studies emphasize the importance of mesoscale dynam-ical features in determining microphysical and optical properties of cirrus clouds.Recent studies indicate that the ice crystal number concentration plays an important role for the tran-sition from a warming of cirrus clouds to a cooling (Fusina et al., 2007). In order to account for theinuence of ice crystal number concentration on the radiative properties of cirrus clouds and to predictthe global net effect of cirrus clouds on the radiative budget and changes in a future climate it is neces-sary to include the effect of mesoscale dynamics on cirrus cloud properties in global circulation models.As orographic gravity waves are one important and widespread source for mesoscale uctuations thisdissertation attempts to improve the understanding of orographic cirrus clouds and their representationin global climate models also with regard to the future climate.1.2 Orographic gravity wavesOrographic gravity waves lead to the formation of orographic clouds. They can form only when theatmosphere is stably stratied and when air is forced to ow over mountains. A uid parcel which isdisplaced vertically will then undergo buoyancy oscillations. In a uid that has no upper boundary, likethe atmosphere, gravity waves may propagate vertically and horizontally. As the density of the atmo-sphere decreases exponentially with height, the amplitude of a gravity wave that propagates high intothe atmosphere, grows with height. The associated vertical displacement of air induces adiabatic coolingand provides regions for cloud formation throughout the whole troposphere.Gravity waves are able to transport momentum from the Earths surface to regions in the atmosphere1.3. Orographic cirrus clouds 3where they dissipate. The magnitude of the momentum ux may be large enough to strongly inuencethe large-scale mean ow (McFarlane, 1987). Large mountains or weak winds can additionally leadto non-linear effects like ow blocking. This means that only part of the ow is able to ow over themountain, whereas the ow in the low levels is blocked. This effect also leads to a transfer of momentumbetween the atmosphere and the surface of the Earth. The inuence of mountains on the atmospherehas been recognized and investigated intensely during the last century. There are several publicationsdescribing the linear theory of mountain waves (see e.g. (Queney et al., 1960; Smith, 1979). The devel-opment of nonlinear mountain wave regimes are described in e.g. Smith (1989); Wurtele et al. (1996).Due to the processes described above, the representation of orographic gravity waves in numericalweather prediction and climate models is very important. McFarlane (1987) and Palmer et al. (1986)showed that the inadequate representation of the unresolved orography and the missing inuence of ver-tically propagating gravity waves on the large-scale ow lead to deciencies in the simulated large scalecirculation especially in the northern hemispheric winter. When the effect of subgrid-scale orographyon the momentum transport was parameterized, the systematic westerly bias could be reduced. In thescheme described in Palmer et al. (1986) the orography is isotropic and it is assumed that most of themomentum is transported by long, hydrostatic waves. However, this scheme was not able to predict thedrag exerted by low-level wave breaking (Gregory et al., 1998). It therefore was developed further basedon the work of Baines and Palmer (1990) and Lott and Miller (1997). It includes an anisotropic subgrid-scale orography and takes into account the drag due to ow blocking and low-level wave breaking. Thisscheme is implemented in the ECHAM5 GCM used in this dissertation. The subgrid-scale orography,which provides the basis for orographic gravity waves and is used in this parameterization, is describedin more detail in appendix A.1.3 Orographic cirrus cloudsThe vertically propagating gravity waves induce vertical displacement of air in the whole troposphere.Adiabatic cooling is induced in the rising air parcel and the relative humidity with respect to ice (RHi)within the parcel starts to increase. If the critical threshold for freezing is exceeded, ice crystals start tonucleate. The supersaturation is then depleted by growing ice crystals. Depending on the path of theair parcel, further freezing events are possible if the RHi gets again high enough. In the downdraft ofthe gravity wave, ice crystals start to evaporate. As ice crystals can survive in subsaturated air, they canbe advected downstream over several hundreds of kilometers. Thus, orographically induced ice crystalsare a plausible formation mechanism of large-scale cirrus clouds downstream of big mountain ranges(Dean et al., 2007). On the other hand, if RHi is not high enough and/or the ice crystals are small, theycan completely evaporate leading to a cloud with the typical lenticularis shape. Figure 1.1 shows twoexamples of orographic clouds. In the left panel, ice crystals form in the updraft of a gravity wave. Theice crystals survive the downdraft region and are advected over 200 km. In contrary, in the right panel,a lenticularis cloud can be seen where the ice crystals evaporate in the downdraft of the wave.In general, the vertical velocities and cooling rates induced by orographic gravity waves are very highsuch that it is assumed that homogeneous freezing is the dominant freezing mechanism for orographiccirrus clouds at temperatures below the homogeneous freezing threshold (K archer and Str om, 2003). Allsimulations presented in this work therefore only consider homogeneous freezing.Measurements in an orographic cirrus cloud at very cold temperatures (T 0.03 are considered. The positionof the mountain peak is indicated by the triangle.nucleation (see K archer and Lohmann (2002b); Spichtinger and Gierens (2009a)). The mean ICNC forthe warm case is 0.12109m2which represents a reduction of 59%, whereas for the cold case there is anincrease of 303% to 1.17109m2. In the warm case there is no second maximum in the IWP. Due to thewarmer temperatures there are less crystals which grow more rapidly and start to sediment. Thereforethe horizontal extent of the cloud is reduced compared to the reference case but the mean optical depthis higher. In the cold case the crystals are advected over about 80 km without a drastic fallout and startto grow in the second small updraft region. The resulting optical depth for T=230 K amounts to 0.88 andfor T=210K to 0.54. This corresponds to a decrease/increase of 13%/42% for the cold and warm case,respectively. Thus, in the warm case the increase of IWP dominates the decrease in ICNC and the mean is highest although the cloud is not as large in its horizontal extent. For the cold case the decrease in IWPdominates the strong increase in ICNC and the optical depth decreases compared to the reference case.Thus temperature changes inside the ISSR change the optical depth of the cloud by changing the IWPand ICNC. This example points out that changes in IWP strongly dominate the behavior of and cannotbe compensated by changes in ICNC. Only for the highest temperature (T=230 K) does sedimentationbecome important. The increased sedimentation leads to a reduction of the horizontal extent of the cloudand the IWP and could therefore also lead to a decrease of .When the initial supersaturation is increased to 130%, more water vapor is available and the IWP is higherthan in the reference case. In the warmest case (T=230 K) the crystals start to sediment. However, therestill remain some ice crystals in this case (Rhi = 130%, T=230 K) and the mean decreases comparedto the case where T=220 K and is even lower than for the cold case. This is caused by the fact that is still higher than 0.03 and is therefore taken into account for the calculation of the mean value of .In contrast, in the case where Rhi= 120% the crystals sediment completely leading to a higher meanvalue of but a smaller horizontal extent. Thus if the increase in temperature is strong enough and theinitial ice supersaturation is high, the increase in due to more IWP is not necessarily the dominanteffect anymore as the cloud ice is reduced due to sedimentation and the optical depth is reduced. As atemperature increase of 10 K inside the ISSR may not be realistic for a future climate, we can concludethat the increase in IWP at warmer temperatures and constant relative humidity and the resulting increase16 Chapter 2. Orographic cirrus in the future climateFigure 2.7: ICNC, IWP and optical depth after t = 5 h for (left) RHi=120% and three different positionsof ISSR, (middle) comparison of a decrease in temperature due to a change of the height of the ISSR (blueline) and shift of the initial temperature prole (red line) to T=210 K at RHi=120% and (right) same asin the middle panel but for a temperature increase to T=230 K at RHi=120%. Note that the vertical axisdiffers in each column. The position of the mountain peak is indicated by the triangle.in optical depth is the dominant process. However, it has to be considered that the opposing effect of areduced optical depth due to sedimentation is also possible. If the supersaturation is reduced to 110%,a slightly different picture shows up. As the initial RHi is relatively low, the difference in IWP betweenthe different temperatures is not as much pronounced as for high RHi. Therefore the reduction in ICNCdue to warmer temperatures is not completely compensated by the increase in IWP and the resulting for the warm case is slightly lower than for T=220 K but still higher than for the cold case.Change of height of the ISSRIn a changing climate an increase in moisture is expected. This increase inuences the propagation ofgravity waves in the atmosphere and leads to an increase of the vertical wavelength of the waves, whichmeans that the ISSR shifts to a different position in the wave. Therefore, we investigated the changesof the formation of orographic cirrus due to a change of the height of the ISSR which corresponds to adifferent position in the wave phase compared to the reference case. The different heights of the ISSR canbe seen in g.2.5. The height of the ISSR is chosen in a way that the temperatures inside the low/highISSR amount to 230/210 K for a better comparison to the other cases discussed in sec. 2.4.1. In thecase of the high and low ISSR the maximum vertical velocities are lower than in the reference case anddecrease from 0.8 ms1to 0.6 ms1. Furthermore, for the low case, the air rst has to pass a region ofstrong downdraft before it reaches the updraft region where a cloud can form. Fig. 2.7 shows the resultsfor the three different heights of the ISSR. The left panel shows the results when the ISSR is shifted toa higher/lower position so that the temperature inside the lower/higher ISSR amounts to 210 K/230 K,respectively. The initial supersaturation is 120%. Due to the decrease in temperature at constant RHi theIWP decreases strongly for the high ISSR. However, no cloud forms when the ISSR is at its low position.Although the vertical velocity in the high and low case are nearly the same, the net lifting of the air in thelow case is much less. Therefore the critical supersaturation for the homogeneous freezing is not reached2.5. Simulations with IPCC initial proles 17and no cloud forms. For the high case the initiation of the freezing event is shifted 10 km upstreamdue to the backward shift of the waves crest with height. The ICNC shows a strong increase for the highcase as the temperature inside the ISSR is T=210 K. We again observe that the decrease in IWP due tothe colder temperature is the dominant effect and the resulting optical depth is decreased. The middlepanel shows the results for the simulations where the temperature inside the ISSR has been changed toT=210 K once due to a change in the initial temperature proles (red lines) and once due to the shiftof the ISSR to a higher position (blue lines). Thus, a comparison of the changes due to a temperaturechange only and due to a combined change of temperature and vertical velocity is possible. In both casesthe IWP decreases strongly due to the lower temperature, but for T=210 K the IWP is nearly the same, asthe IWP is mainly determined by the RHi, but the position of the cloud is shifted upstream for the highposition of the ISSR. For the increase of ICNC a difference between both simulations can be seen. Here,the change in the dynamics as well as the change in temperature affects the ice crystal formation. Thedecrease in temperature leads to an increase in ICNC in both cases. This increases is more pronouncedin the case where the initial temperature prole is shifted as then the ISSR remains in the region with thehighest vertical velocities. When the ISSR is shifted to a higher position, the maximum vertical velocitydecreases and hence the ICNC. The resulting optical depth is therefore lowered even more for the highISSR as the dynamical changes suppress the strong increase in ICNC. The right panel shows the sameas the middle panel but for an increase in temperature due to a lowering of the ISSRs position and ashift in the initial temperature prole. It can be seen that in this case the shift of the initial temperatureprole leads to an enhanced IWP and optical depth, whereas in the case of the low ISSR the change in thedynamics completely suppresses the formation of a cloud. When the initial supersaturation is enhancedto RHi=130%, a cloud forms even in the low ISSR (not shown here). However, the resulting IWP islower compared to the case where the ISSR is in the reference height although the temperature is muchhigher and much more water vapor is available. Therefore a strong reduction of the can also be seenhere as the dynamical changes dominate the increase in temperature.We carried out the same simulations for a non-linear ow regime by increasing the mountain height h0to 850 m which leads to h = 0.94. For this regime we found the same features for the development of theorographic cirrus clouds as in the linear ow regime (not shown).2.5 Simulations with IPCC initial prolesIn order to investigate the formation of orographic cirrus clouds in a changing climate, simulations withinitial proles for the equivalent potential temperature, wind speed, pressure and specic humidity fromthe IPCC fourth assessment report have been carried out (Meehl et al., 2007). We used the results fromthe ECHAM simulation obtained for the A1B emission scenario and investigated the effect of a warmerclimate on the formation of orographic cirrus in a linear and non-linear ow regime for two regionsrepresentative for the Northern and Southern Hemisphere. All simulations have been performed for theparticular winter and summer months.2.5.1 Model setupFor simulating orographic cirrus clouds we use a 2d domain (x-z-plane) with a horizontal extension of320 km and a vertical extension of 20 km with a bell shaped mountain in the middle of the domain. Twodifferent ow regimes have been investigated. The change from the linear to the non-linear ow regimewas performed by increasing the mountain height from 600 m in the linear to 1850 m in the non-linearcase. The horizontal and vertical resolutions are dx = 250 m and dz = 50 m for the linear ow regimeand dx = 1000 m for the non-linear regime. The simulations for the linear ow regime have been carriedout for 6 hours. For the non-linear case the simulations are extended to 10 h because it takes much longeruntil a stable ow is reached.The model is initialized with the ambient equivalent potential temperature, pressure and wind proles18 Chapter 2. Orographic cirrus in the future climatee(z), p(z) and u(z) taken from the IPCC simulations. Two regions representative for the Northern andSouthern Hemisphere have been selected in order to investigate the effect of a warming climate. In theSouthern Hemisphere mean proles averaged over a region from 60W to 80W and from 40S to 55Srepresentative for the tip of South America have been taken. For North America a region from 115W -130W and 45N - 60N has been selected. For both cases the proles for the particular winter and sum-mer month (December, January, February and June, July, August) are taken. Additionally, only valuesover land are used for the calculation of the mean vertical proles. In order to represent the conditionsof the beginning and the end of the 21 century, a ten year mean for the years 2001-2010 and 2090-2099has been calculated. Figure 2.8 shows the initial proles for the Southern and Northern Hemisphere forthe winter and summer months. In order to account for the inuence of moisture on the static stabilityand hence the propagation of gravity waves, the simulations are performed with the equivalent potentialtemperature e instead of the potential temperature . The equivalent potential temperature is calculatedase = exp

LvqcpT

T + Lvcpq

p0p

Rdcp(2.4)where T is the temperature of air, p is the pressure, p0 is a reference pressure, Rd = 287 Jkg1K1is thespecic gas constant of air, cp = 1004 Jkg1K1is the specic heat of dry air at constant pressure, Lv isthe latent heat of evaporation which has been set to 2500 kJkg1and q is the water vapor mixing ratio.In order to simulate the formation of orographic cirrus a supersaturated layer is implemented. The initialsupersaturation is RHi=130%. For every hemisphere simulations with the initial proles of e(z), u(z) forthe beginning (A1B0) and the end of the century (A1B9) have been carried out. Furthermore, we assumethat the relative humidity with respect to water stays constant in a changing climate. This assumptionis based on model simulations that produce increases in water vapor concentrations which are similarto those which are predicted if a constant relative humidity is assumed (Held and Soden, 2000). Theassumption of a constant relative humidity with respect to water leads to a decrease in relative humiditywith respect to ice. However, for the temperature increase we consider here, this decrease is very small.Therefore we can also assume the relative humidity with respect to ice to stay constant.2.5.2 South America: linear ow regimeFigure 2.9 shows the resulting ow regime for the simulation initialized with the IPCC proles for SouthAmerica after t = 5 h with the initial proles for 2001-2010 (A1B0) and 2090-2099 (A1B9). In all cases agravity wave develops which propagates through the whole troposphere. In winter time, the atmosphereis much more stably stratied than in summer and the vertical velocities occuring in the wave lie between-1.5 ms1and 1.3 ms1. The simulation A1B9 shows higher velocities, however, the vertical velocitiesinside the supersaturated layer are only slightly higher in the simulation A1B9. The increase in windspeed in a future climate as well as the increase in moisture have an inuence on the ow regime. Theincrease in moisture in a future climate inuences the stability of the atmosphere. It leads to a less stableprole and thus to smaller amplitudes and vertical velocities (Jiang, 2003; Durran and Klemp, 1983)if the increase in moisture is most pronounced near the surface. However, as can be seen in Fig. 2.8(upper panels) the moist Brunt-V ais ala frequency nearly stays the same and the inuence of a change inmoisture is very weak. The increase in horizontal wind speed leads to an increase of the amplitudes. Inthe resulting ow the effects of increased moisture and horizontal wind speed nearly compensate eachother and the amplitudes and vertical velocities remain nearly the same for both simulations. As thevertical wavelengths also depends on the stability and hence the moisture, a weak increase in the verticalwavelength can be seen for the run A1B9. The ISSR therefore lies in a slightly different phase of thewave.During the summer months the atmosphere is less stable and the developing gravity wave is weaker thanin the winter case. The maximum/minimum vertical velocities therefore only reach +0.6 ms1and -0.5ms1in the A1B0 and A1B9 scenario. However, the gravity wave for A1B9 is slightly weaker then for2.5. Simulations with IPCC initial proles 19Figure 2.8: Ten year mean of the initial proles of temperature T, difference of potential temperature and equivalent potential temperature e between A1B9 and A1B0, moist Brunt-V ais ala frequency N,wind speed u and specic humidity q for 2001-2010 (black) and 2090-2099 (blue) for the SouthernHemisphere winter and summer month (upper two panels) and Northern Hemisphere winter and summermonths (lower two panels).A1B0 as the vertical prole for A1B9 is less stable in the lowest levels and the horizontal wind speed issmaller (see Fig. 2.8, second row).In order to investigate the changes in cirrus cloud properties in a changing climate, again the verticallyintegrated ice crystal number concentration (ICNC), the ice water path (IWP) and the optical depth arecalculated. Figure 2.10 shows the results for the two simulations after 5 hours for summer and winter.An orographic cirrus cloud develops above the mountain top in both seasons. As the downdrafts of thegravity waves are not very strong, the crystals survive this downdraft and are advected more than 150 km20 Chapter 2. Orographic cirrus in the future climateFigure 2.9: Flow regime for South America after t = 5 h for the initial proles of A1B0 (left) and A1B9(right) and for winter (JJA, upper panels) and summer (DJF, lower panels). Grey lines denote the linesof constant potential temperature, colors indicate the vertical velocity in m s1. The black box shows theinitial position of the supersaturated layer.downstream. There are several effects inuencing the optical depth of the developing cirrus cloud. Firstof all, the assumption of a constant relative humidity in a changing climate with higher temperaturesleads to a strong increase in IWP. In the winter case (left panel), the mean IWP averaged over the wholecloud increases from 10.1 gm2in the A1B0 simulation to 13.4 gm2. ICNC is inuenced by the verti-cal velocities and the temperature in their formation region. As in the winter case the vertical velocity isnearly the same in the ISSR for both simulations, the strong reduction of ICNC in the A1B9 simulationis caused by the much warmer temperatures in the A1B9 case. The temperature in the middle of theISSR in 8000 m height increases from T=223.6 K for the A1B0 simulation to T=227.1 K for the A1B9case. This strong increase speeds up the growth rates of the ice crystals. Therefore the supersaturation isdepleted faster and no new crystals can be formed. Additionally they grow large enough to sediment outand thus represent a sink for the water vapor. However in this case no reduction of the horizontal extentof the cloud can be seen as the differences in temperatures are much weaker here than in the idealizedsimulations. The resulting optical depth shows an increase for the A1B9 case. Thus, the increase in IWPdominates over the reduction of the ICNC and the resulting cloud is optically thicker in the A1B9 case.This behavior shows that the thermodynamical changes are more important than the dynamical changesfor this particular case.In order to estimate the effect of the uncertainty in the predicted warming on the formation of orographiccirrus and to evaluate if changes due to the uncertainty in the predicted warming are bigger than thechanges from current to future climate, additional simulations have been performed. From the regionalclimate projections from the IPCC (Christensen et al., 2007) the minimum and maximum warming for2.5. Simulations with IPCC initial proles 21Figure 2.10: Optical depth, ICNC and IWP for the Southern Hemisphere for winter (left) and summer(right). Black lines show the results for the initial proles for A1B0, blue lines show the results ob-tained for A1B9, dark blue lines show the results for the A1Bmax simulation and red lines for the A1Bminsimulation.the region of South America for summer (DJF) and winter (JJA) has been taken. For winter (JJA) thepredicted increase in surface temperature over land varies between 1.7 K and 3.6 K. The initial proleused in the simulation before is based on the ECHAM A1B simulation and shows an increase in surfacetemperature of 2.1 K for the Southern Hemisphere. Therefore two additional simulation have been per-formed where we added/subtracted +1.5/-0.4 K to the temperature prole T(z)A1B9 in order to obtain theextreme values of the predicted temperature change.For simplicity it is assumed that the stability remainsthe same as in A1B9 but only the temperature changes. This assumption is justied as the dynamicalchanges are negligible here.Figure 2.10 (left panels) shows the results for the minimum and maximum predicted temperature changefor the Southern Hemisphere winter months (JJA). A strong increase in IWP from the beginning to theend of the century for all simulations can be seen as the temperature increases. The higher temperaturesalso lead to a strong reduction of the ICNC for all simulations as the ice crystals grow faster, the super-saturation is depleted faster and no new crystals can nucleate. The decreases are most pronounced forthe A1Bmax simulation where the highest temperatures are reached. The resulting optical depth is muchhigher for all simulations at the end of the century. However, the mean optical depth is largest for theA1Bmin simulation. This is caused by a strong increase in IWP but a small decrease in ICNC.In the summer case (DJF) a slightly different picture emerges. The IWP increases as again more watervapor is available. However, ICNCalso increases very strongly although the temperature is much warmerin the A1B9 case. This can be explained here as follows: The critical supersaturation for the initiation ofthe homogeneous freezing process decreases with increasing temperature. Therefore, in the upper partof the ISSR the critical supersaturation is only exceeded in the warmer A1B9 case and crystals start toform. In the colder A1B0 case where the critical supersaturation is higher, the relative humidity withrespect to ice stays below the critical value and no crystals can form. This increase in IWP combinedwith an increase in ICNC leads to a strong increase in optical depth from 0.08 to 0.87 in the A1B9 case.Compared to the winter months, the optical depth is lower in summer. The IWP is similar for both cases22 Chapter 2. Orographic cirrus in the future climateas it is mainly determined by the initial supersaturation. However, the ICNC is an order of magnitudelower than winter. This is caused by much lower vertical velocities combined with higher temperaturesduring the summer months.For the summer months we also investigated the effects of the uncertainty in the predicted warming onthe properties of orographic cirrus. Here, the predicted warming lies between 1.5 K and 4.3 K. TheECHAM A1B simulation predicts a surface warming of 2.0 K. Therefore we added/subtracted +2.3/-0.5K to the original temperature prole of the summer months. Again, for all A1B9 simulations the opticaldepth is much higher. The highest optical depth is reached for the A1Bmax case where the increase intemperature and hence IWP is strongest. As mentioned earlier, ICNC increases, as due to the warmertemperatures the critical supersaturation is exceeded. The ICNC for A1Bmin is higher than for A1B9 asthe temperature is slightly lower which leads to more ice crystals. The highest ICNC is reached in theA1Bmax case where the critical value of the supersaturation is exceeded in a larger region than in thecolder cases of A1Bmin and A1B9.In general, we can state that for all cases the increase in IWP and hence the optical depth from the cur-rent to the future climate is the dominant effect. The changes in the results due to the uncertainties in thepredicted warming are much less than the changes from A1B0 to A1B9. Therefore it could be possiblethat there is a trend towards optically thicker orographic cirrus clouds in a warmer climate.2.5.3 South America: hydraulic jumpTo investigate the effects of a warmer climate in a different ow regime, additional simulations with anincreased mountain height have been performed. The increase in mountain height leads to higher Froudenumbers and the ow becomes non-linear. Figure 2.11 shows the resulting ow regime after t = 10hfor the beginning and the end of this century for the winter and summer months. Due to the changesin moisture one could expect a shift to a more linear regime as the onset of gravity wave breaking isdelayed (Jiang, 2003). However, since in our case the changes in moisture are weak this effect cannot beseen here. The resulting ow regimes are very similar, only a slight increase in the vertical wavelengthfrom A1B0 to A1B9 can be seen for the winter month which is caused by the increase in moisture. Theresulting optical depth of the cirrus clouds for the four simulations is shown in gure 2.12. As the owneeds a spinup time of 5 h in winter and 4 h in summer until it becomes stable, we show the timedevelopment of the optical depth for both seasons. We evaluate the results after t = 5h for JJA and after t= 4h for DJF when the ow becomes stable. As can be seen very clearly, the resulting optical depth aftert = 5h and t = 4h, respectively, is higher for the A1B9 simulation. Thus, the same features as in the linearcase show up. The changes in the ow regimes for the current and future climate are relatively weak, butdue to the higher temperatures in a future climate we obtain less ice crystals but more ice water contentand thus a higher optical depth in both seasons as shown in gure 2.13. As in the linear ow regime thethermodynamical changes dominate the dynamical changes for this South American case. In contrastto the linear ow regime, here the optical depth is higher in summer. The changes in the ow regimebetween summer and winter are not as much pronounced here. The IWP increases and ICNC decreasesfrom winter to summer as the temperatures are higher. As in the simulations before the increase in IWPis the dominant process, the optical depth increases from winter to summer.2.5.4 North America: linear ow regimeFigure 2.14 shows the resulting ow regime for the simulations initialized with the IPCC proles forNorth America after t=5h for the winter month DJF. The vertical proles averaged over JJA for thisregion show an unstable region in the lower levels. Therefore, no gravity waves develop and it is notpossible to investigate the effect of a changing climate on the formation of orographic cirrus cloudsbased on the ECHAM IPCC simulations. We therefore also looked at the results for spring (March,April May) and autumn (September, October, November). For these seasons the same features as forthe winter months that are described in this section are seen, and are therefore not shown here. Again a2.5. Simulations with IPCC initial proles 23Figure 2.11: Flow regime for South America after t = 10 h for the initial proles of A1B0 (left) andA1B9 (right) for winter (JJA, upper panels) and summer (DJF, lower panels). Grey lines denote the linesof potential temperature, colors indicate the vertical velocity in m s1. The black box shows the initialposition of the supersaturated layer.gravity wave develops, which propagates through the whole troposphere. In the northern hemisphere thedifference in temperature and moisture is more pronounced than in the southern hemisphere. Thereforethe inuence of the additional moisture is stronger. The static stability decreases, as can be seen in themoist Brunt-V ais ala frequency in Fig. 2.8 (third row) and thus the amplitude and vertical velocity. Themaximum vertical velocity in the A1B0 simulation amounts to 1.5 ms1, in the A1B9 simulation to 1.3ms1. However, the vertical velocities inside the ISSR are only slightly higher. The increase of the verti-cal wavelength is also much more pronounced than in the southern hemispheric case and the ISSR shiftsin a different wave phase. Figure 2.15 shows the results of IWP, ICNC and optical depth for the NorthernHemisphere. The orographic cloud again develops above the mountain top and has a horizontal extentof more than 150 km. In this case it can be seen that the ISSR shifts in a different position in the wavephase as in the A1B9 simulation a leeward shift of the formation region of the cloud can be seen. Again,the dominant process is the strong increase in IWP from 6.7 gm2to 9.4 gm2under the assumptionof a constant relative humidity in a warmer climate. The reduction in ICNC is more pronounced than inthe southern hemispheric case. First, there is a slight decrease in the vertical velocities occuring insidethe ISSR and second, the warmer temperatures in a changing climate lead to a faster growth rate. Asthe temperature in a height of 8000 m increases from 219 K to 222 K the crystals grow faster and lesscrystals can be formed. The difference in the growth rates is more pronounced in this cold temperaturerange than in the warmer southern hemispheric case and the reduction of the ICNC is more pronounced.However, the strong increase in IWP still dominates the reduction in ICNC and the resulting opticaldepth of the cloud is higher in the A1B9 simulation.24 Chapter 2. Orographic cirrus in the future climateFigure 2.12: Time development of the optical depth for the A1B0 (left) and A1B9 (right) simulations forsouthern hemispheric winter (JJA, upper panels) and summer (DJF, lower panels). The triangle denotesthe top of the mountain, and the black line shows the point in time when the ow becomes stable. Thesmall panels show the time average from 5-10 h and 4-10 h, respectively.In order to estimate the uncertainties in the predicted warming we again made some additional simula-tions where we used the maximumand minimumtemperature changes predicted for the years 2090-2099.As the ECHAM A1B run predicts an increase of surface temperature of +4.5 K we added/subtracted+1.3/-2.9 K from the ECHAM temperature prole T(z)A1B9, based on the regional climate projections(Christensen et al., 2007). Again, the stability stays the same. The results of this simulations can be seenin g. 2.15. Due to the increase in vertical wavelength the air rst undergoes a stronger downdraft in theA1B9 simulation before it is lifted. Thus, the net lifting is smaller in A1B9 compared to A1B0 and theformation of the cloud is shifted downwind. The temperatures inside the ISSR amount to TA1B0=219.5K, TA1B9=222.9 K, TA1Bmin=221.1 K and TA1Bmax=225.4 K. The increase in temperature inside the ISSRfrom A1B0 to A1Bmin is not much pronounced and the increase in IWP from 6.7 g m2to 7.2 g m2is rather weak. Therefore, the resulting optical depth for the A1Bmin simulation is only slightly higherthan in A1B0. When the temperature is increased further, IWP increases strongly and ICNC decreases.For these cases, the increase in IWP again strongly dominates over the decrease in ICNC and the result-ing cloud is optically thicker in a future climate. These simulations combine the two effects of warmer2.5. Simulations with IPCC initial proles 25Figure 2.13: ICNC and IWP for the simulations A1B0 and A1B9 averaged over t = 5-10 h for JJA and t= 4-10 h for DJF for South America. The triangle denotes the tip of the mountain.Figure 2.14: Flow regime for North America after t = 5 h for the initial proles of A1B0 (left) and A1B9(right). Grey lines denote the lines of constant potential temperature, colors indicate the vertical velocityin m s1. The black box shows the initial position of the supersaturated layer.temperatures and a shift in the wave phase, also described in the idealized simulations. A warmer temper-ature does not necessarily lead to more ice water content. It also depends strongly on the position of theISSR in the wave phase. Additionally, the reduction of the ICNC can be very strong in cases where thevertical velocities in the ISSR decrease. Therefore, the resulting optical depth is not necessarily higherif dynamics dominate over the thermodynamical features.2.5.5 North America: hydraulic jumpFor the North American case we also changed the ow regime by increasing the height of the mountainfrom 600 m to 1850 m in order to obtain a non-linear ow regime. The resulting ow is shown in gure2.16. In this case the changes in the ow regime are more pronounced than in the South American26 Chapter 2. Orographic cirrus in the future climateFigure 2.15: Optical depth, ICNC and IWP for the Northern Hemisphere. Black lines show the resultsfor the initial proles for A1B0, blue lines for A1B9, dark blue lines show the results for the A1Bmaxsimulation and red lines for the A1Bmin simulation.case. After a spinup time of 3h a reasonably stable ow regime develops. The decrease in stability leadsto a slight increase in vertical wavelength and to a weak damping of the maximum vertical velocity.The time evolution of the ow (not shown here) shows an increased vertical velocity in the rst updraftregion from A1B0 to A1B9 and a decrease in vertical velocity in the second updraft region inside theISSR. This feature is caused by the increase in vertical wavelength. In order to assess the changes inthe optical properties of the cloud, we again show the time development of the optical depth in gure2.17. The resulting optical depth does not show a strong increase as in the South American case. Thisbehavior can be explained with the simulated mean ICNC and IWP shown in Figure 2.18. The IWPincreases from A1B0 to A1B9 in the rst updraft region, however, in the second updraft region, the IWPdecreases. ICNC increases from A1B0 to A1B9 for the rst updraft region, although there is a strongincrease in temperature which would lead to a decrease in ICNC. However, the dynamical changes arestrong enough to overcompensate this effect and the higher vertical velocity in the rst updraft regionleads to an increase in ICNC. In the second updraft region, we have a decrease in vertical velocity fromA1B0 to A1B9 followed by a strong reduction in ICNC and IWP. Therefore, the resulting optical depth isincreased in the rst updraft region and decreased in the second updraft region. Here, dynamics stronglyinuence the microphysical properties of the cloud and nearly offset the thermodynamical changes. Theoptical depth averaged over the whole cloud from 3-10 h increases 15% from 0.57 for A1B0 to 0.66for A1B9.In table 2.1 the results of the IWP, ICNC and optical depth for all simulations initialized with the IPCCproles are summarized. As can be seen from this table, all simulations show an enhanced optical depthof the clouds in a future climate. The increase in IWP dominates in all cases over the decrease in ICNC.2.6. Summary and Conclusions 27Figure 2.16: Flow regime for North America after t = 10 h for the initial proles of A1B0 (left) andA1B9 (right). Grey lines denote the lines of potential temperature, colors indicate the vertical velocity inm s1. The black box shows the initial position of the supersaturated layer.Figure 2.17: Time development of the optical depth for the A1B0 (left) and A1B9 (right) simulations.The triangle denotes the top of the mountain, and the black line shows the point in time when the owbecomes reasonably stable. The upper panel shows the time averaged optical depth from 3-10 h. In theupper right panel we also show the time averaged optical depth for the A1B0 simulation for a bettercomparison.Thus, the dynamical changes are less important than the thermodynamical changes. This effect is morepronounced for the non-linear ow regimes where a strong increase of 17.2%, 15.6% and 15.7% issimulated.2.6 Summary and ConclusionsThe anelastic non-hydrostatic model EULAG has been used to investigate the formation of orographiccirrus clouds in a changing climate. Therefore, different simulations with a detailed cloud microphysicshave been carried out. To show the models capability to represent orographic cirrus clouds and to pro-duce realistic results, the INCA case was simulated and compared to measurements. Second, some keyparameters which determine the microphysical properties of the developing cloud, like the initial relative28 Chapter 2. Orographic cirrus in the future climateFigure 2.18: ICNC and IWP for the simulations A1B0 and A1B9 averaged over t=3-10 h for NorthAmerica. The triangle denotes the tip of the mountain.humidity, the temperature inside the ISSR and the shift of the position of the ISSR in the vertical wavephase have been investigated with idealized simulations and thirdly, idealized simulations initialized withthe IPCC A1B proles for the beginning and end of the century calculated with the ECHAM model havebeen carried out.The comparison with the INCA measurements shows a very good agreement. Although the simulation isonly 2-dimensional the simulated and measured distributions of vertical velocity, ice water content andice crystal number concentration agree very well.The idealized simulations show that one important factor which determines the optical depth is the tem-perature inside the ISSR which determines how much water vapor is available for the formation of icewhen a constant relative humidity is assumed. The strong increase in IWP with increasing temperaturedominates the reduction of ICNC and the mean optical depth increases. However, in the idealized sim-ulations the increase in temperature is very strong (10K) such that the crystals grow very large and startto sediment. This can lead to a decrease of the horizontal extent of the cloud and/or a decrease of themean optical depth due to the loss of cloud ice by sedimentation. Additionally, the position of the ISSRin the vertical wave phase has a strong inuence on the microphysical properties. It could be shown thatwhen the ISSR is shifted to a lower position where the vertical velocities are smaller, the resulting IWPand optical depth is much smaller than for the reference case although the initial RHi is the same andmuch more water vapor is available at the warmer temperatures in the lower layer. The layer which isshifted to a higher position and thus lower temperatures shows a strong increase in ICNC. The opticaldepth for the highest layer is therefore higher than for the lowest layer although the IWP is much less.If the temperature inside the ISSR is increased due to a shift of the initial temperature prole or due to achange of the height of the ISSR, the resulting IWP and optical depth for the temperature shift are muchhigher than for the change of the height as the ISSR lies in a different phase of the wave. In general,when the temperature increases at a constant relative humidity, the following increase in IWP and opticaldepth is the dominant process. The decrease of ICNC which would lead to a decrease in optical depthcannot compensate the effect of an increased IWP.For the simulations with the IPCC proles it seems that under the assumption of a constant relativehumidity in a changing climate (Held and Soden, 2000), the increase in IWP due to the increase in hu-midity and temperature is the dominant effect. All simulations for the linear as well as the non-linearow regime for both seasons show the same behavior with an increase in optical depth for the end of thecentury. However, in the North American case the optical depth increases very slightly for the A1Bmin2.6. Summary and Conclusions 29Table 2.1: ICNC, IWP and optical depth averaged over the whole cloud ( > 0.03) for all simulationsinitialized with the IPCC proles. Values in brackets denote the percental change compared to theassociated A1B0 run.South America ICNC [109m3] IWP [gm2] optical depthA1B0 - linear, winter 1.25 10.1 1.84A1B9 - linear, winter 0.87 (-30.4%) 13.5 (+33.6%) 1.93 (+4.9%)A1Bmin - linear, winter 0.92 (-26.4%) 13.1 (+29.7%) 1.94 (+5.4%)A1Bmax - linear, winter 0.71 (-43.2%) 15.1 (+49.5%) 1.92 (+4.3%)A1B0 - non-linear, winter 5.2 16.1 4.29A1B9 - non-linear, winter 4.5 (-13.5%) 22.8 (+41.6%) 5.03 (+17.2%)A1B0 - linear, summer 0.01 1.7 0.08A1B9 - linear, summer 0.09 (+800%) 13.7 (+705%) 0.84 (+950%)A1Bmin - linear, summer 0.12 (+1100%) 15.3 (+800%) 0.97 (+1112%)A1Bmax - linear, summer 0.12 (+1100%) 17.1 (+905%) 0.98 (+1125%)A1B0 - non-linear, summer 4.5 31.1 6.08A1B9 - non-linear, summer 3.5 (-22.2%) 44.2 (+42.1%) 7.03 (+15.6%)North America ICNC [109m3] IWP [gm2] optical depthA1B0 - linear, winter 1.5 6.7 1.53A1B9 - linear, winter 1.0 (-33.3%) 9.4 (+40.2%) 1.66 (+8.4%)A1Bmin - linear, winter 1.4 (-6.6%) 7.2 (+7.4%) 1.57 (+2.6%)A1Bmax - linear, winter 0.9 (-40.0%) 10.6 (+58.2%) 1.71 (+11.7%)A1B0 - non-linear, winter 0.28 5.2 0.57A1B9 - non-linear, winter 0.20 (-28.5%) 6.6 (+26.9%) 0.66 (+15.7%)simulation as the increase in moisture and the following change in the ow regime is much more pro-nounced and the effect of an increased IWP at constant RHi is not dominant anymore. However, if thetemperature increase from A1B0 to A1B9 is large enough the increase in IWP dominates again and theoptical depth increases from A1B0 to A1B9. All simulations point into the direction that the increasein IWP is the most dominant effect and that the change in the ow regime and vertical velocities playa secondary role here. All these effects and their inuence on the microphysical and optical propertiesare summarized in g. 2.19. The predicted increase in temperature in the IPCC simulations are smallenough that the reduction of the horizontal extent or lifetime of the cloud due to sedimenting ice crystalsdoes not occur in our simulations. Nevertheless it cannot be ruled out completely.These simulations only represent rst ideas about the behavior of orographic cirrus in a changing climate.In order to make more quantitative conclusions additional simulations are necessary. Nevertheless, wecould show that we can expect an inuence of the changing climate on the microphysical and opticalproperties of orographic cirrus clouds. As the cirrus cloud cover over continents which are formed due toorographic forcing is quite substantial (Dean et al., 2005), a strong inuence on the radiative budget canbe expected. In order to make reliable predictions of the change in cirrus cloud cover and microphysicalproperties the change in atmospheric stability caused by an increased moisture and its inuence on theow regime as well as the change of the temperature and water vapor in the upper troposphere have tobe considered.30 Chapter 2. Orographic cirrus in the future climate Vertical velocity Temperature (RH=const.) ICNC ICNC IWC optical depth optical depth optical depth +++Figure 2.19: Schematic of possible dynamical and thermodynamical changes in orographic cirrusclouds in the future climate and the following changes in microphysical and optical properties. Thedominant effect is highlighted in red.AcknowledgmentsWe thank the European Centre for Medium-Range Weather Forecasts (ECMWF) for computing timeand Andreas Minikin (DLR) and Jean-Francois Gayet (LMP) for providing the INCA data. This workcontributes to the TH-project Orographic cirrus clouds in the climate model ECHAM5 (grant: TH-1806-1) supported by ETH Research Fonds. This work was partly supported by the European Commissionwithin the framework of the Marie Curie Fellowship Impact of mesoscale dynamics and aerosols on thelife cycle of cirrus clouds (IMDALCC).Chapter 3Orographic cirrus in the global climate model ECHAM5A comparison of satellite data with simulations from global circulation models showsthat there is a lack of cirrus cloud amount in large-scale models above and in the lee ofmountains. The formation of orographic cirrus clouds due to gravity waves is usually notparameterized in large-scale models. To improve the simulation of such orographically ex-cited cirrus clouds a coupling of the gravity wave dynamics and the cloud microphysics hasbeen implemented in the climate model ECHAM5. As homogeneous freezing of solutiondroplets strongly depends on the vertical velocity, an increased vertical velocity due to grav-ity wave activity in the upper troposphere leads to the formation of cirrus clouds with higherice crystal number densities. A comparison of the new parameterization with measurementsshows a better agreement with observations.H.Joos, P. Spichtinger, U. Lohmann, J.-F. Gayet and A. Minikin, 2008. Orographic cirrus in the global climate modelECHAM5. J. Geophys. Res., 113, D18205, doi:10.1029/2007JD0096053132 Chapter 3. Orographic cirrus in ECHAM53.1 IntroductionCirrus clouds play an important role in the climate system. They cover approx. 30% of the earth andcan inuence the radiative budget of the earth in two different ways. Ice crystals scatter part of theincoming solar radiation back to space. This leads to a cooling of the underlying atmosphere (albedoeffect of clouds). On the other hand, ice crystals reduce the outgoing long wave radiation and can leadto a warming (greenhouse effect of clouds). Which process is dominant depends on the properties of thecirrus cloud like ice crystal number density, thickness of the cloud and ice water content. In general it isthought that optically thin cirrus have a warming effect and optically thick cirrus a cooling effect. Thus,a net global warming of the Earth-atmosphere system due to cirrus clouds is possible (Chen et al., 2000).However, an estimate of the global inuence of cirrus clouds on the radiative budget is very complex asthe formation processes and the life cycle of cirrus clouds are not very well known (Spichtinger et al.,2005a,b) and especially the transition from the cooling to the warming regime is not yet completely un-derstood. Recent studies indicate that the ice crystal number density plays a crucial role for the transitionfrom warming to cooling due to cirrus clouds (Fusina et al., 2007).Ice crystals form either due to homogeneous freezing of supercooled solution droplets or due to hetero-geneous nucleation. Thereby homogeneous freezing of droplets of a certain size starts when the relativehumidity with respect to ice exceeds a threshold which depends only on the temperature (Koop et al.,2000). The heterogeneous freezing is initiated by aerosol particles, the so-called ice nuclei. The super-saturation with respect to ice, which is required for heterogeneous freezing depends on the properties ofthe ice nuclei. In general, the supersaturation threshold for heterogeneous nucleation is lower than forhomogeneous freezing (DeMott et al., 2003).An important factor for triggering the formation of ice is the vertical velocity. It induces adiabatic cool-ing and thus an increase of the relative humidity with respect to ice. Mesoscale velocity uctuations inthe range of 10-50 cm/s amplify homogeneous nucleation (Haag and K archer, 2004; Hoyle et al., 2005).For example, if the vertical velocity increases from 10 to 100 cm/s, the number of newly frozen par-ticles rises more than one order of magnitude (K archer and Lohmann, 2002b). Amongst others, thesemesoscale uctuations in the vertical velocity can be induced by gravity waves. One important source ofgravity waves are mountains producing orographic waves. There are lots of mountainous regions in theworld, where an inuence of the gravity waves on the formation of clouds has to be considered (K archerand Str om, 2003). An additional process which contributes to the vertical velocity induced by gravitywaves is turbulence created by gravity wave breaking. This process is not yet included in the proposedparameterization. Dean et al. (2005) analyzed satellite data from the ISCCP project and compared themwith the results of the 19-level HadAM3 version of the United Kingdom Met Ofce Unied Model. Theyshowed that the model does not simulate sufcient high cloud cover over land especially in the regionsof the mountains. Therefore they proposed a parameterization of orographic clouds described in Deanet al. (2007).In this parameterization Dean et al. (2007) calculate temperature perturbations due to subgrid-scale oro-graphic gravity waves which can lead to the formation of ice. However, only the ice water content canbe inuenced with this parameterization. In order to improve the simulation of cirrus clouds and theirinuence on the radiative budget, it is necessary to include the vertical velocity induced by gravity wavesin the calculation of ice crystal formation.The comparison of the cirrus cloud cover simulated with the ECHAM5 global climate Model (GCM)used in this study (Lohmann et al., 2007) with observations from the International Satellite Cloud Cli-matology Project (ISCCP) (Rossow and Schiffer, 1999) also shows a lack of cirrus cloud cover overcontinents and in the mountainous regions, as shown in gure 3.1. The grey shaded regions in the rightpanel show where the gravity wave scheme can be activated. There are some regions where one wouldexpect a more pronounced lack of cirrus cloud amount like the tip of south America. However, in theISCCP dataset only clouds with an optical depth > 0.1 are detected. This leads to an underestimationof thin cirrus. Additionally, thin cirrus overlying thicker low-level clouds could be assigned to a wrongcloud class and thus additionally lead to an underestimation of cirrus (Dean et al., 2005). The cloud3.2. Parameterization of cirrus clouds: homogeneous freezing 33Figure 3.1: Annual mean ISCCP Cirrus cloud amount (percentage of a grid box covered with cirrus)for the years 1983-2005 (left) and the difference between a three year ECHAM5 simulation and ISCCP.Cirrus clouds are dened as clouds above 440 hPa and an optical depth t). The thresholds depend on themodel resolution. The higher the resolution, the lower the thresholds. For the resolution of T63 usedin this study the thresholds are: ht = 300m and t = 75m. The areas where this conditions are fullledand which represent potential formation regions of gravity waves are shown in gure 3.1 (grey shadedregions). However, gravity waves do not develop necessarily at every time step. It also depends on theangle between the orography and the low level wind if gravity waves are excited or not.The wavelength of the excited wave L if air ows over this mountain depends on the angle between theincident ow and the normal ridge direction. Additionally, ow blocking is considered, which leads to areduction of the excited wavelength and the height of the mountain as seen by the ow. Flow blockingoccurs, when the non-dimensional mountain height Hn = NHU exceeds 0.5. Figure 3.3 shows a schematicof the orography in ECHAM5. The left panel shows two different mountains with different geographicalorientations and anisotropy. The length l(z) that is seen by the incident ow and which corresponds tothe half wavelength of the gravity wave depends on the wind direction and is shown here with blackarrows. The right panel shows a cross section of the mountain. If there is ow blocking, the height ofthe mountain hm which excites gravity waves is reduced to Ze f f and the length l(z) seen by the ow andthus the wavelength L is reduced as well. To calculate the reduced wavelength in a blocked-ow regimeand the reduced effective mountain height Ze f f the height of the blocked ow Zb has to be calculated. Itis dened as the lowest level between Zmax and Zmin that satises the conditionZ ZmaxZbNU dz Hnc = 0.5 (3.20)where Hnc is a critical non-dimensional mountain height which is set to 0.5. Thus, Ze f f can be calcu-lated asZe f f = min(HncUN, ZmaxZmin). (3.21)Hence, if there is no ow blocking, Ze f f takes its maximal value and is reduced when ow blockingoccurs. For a more detailed description see Lott and Miller (1997).The length that is seen by the incident ow at a given altitude z < Zb can be written asl(z) 2 max(acos, bsin)

Zbzz +

1/2(3.22)where l(z) corresponds to the half wavelength L. As we are interested in the smallest possible l(z),here z denotes the level just below the level which describes the blocking height Zb. If there is no owblocking the last term in brackets in eq.(3.22) is set to one and l(z) only depends on the angle betweenthe incident ow and the SSO. The wavenumber k used in the calculation of the gravity wave inducedvertical velocity is given by k = 2/(2 l(z)).3.4. Results 39 Zeffhalf wavelength (L/2) blocking height ZbzL/2k=2/LxUnormal ridge direction L/2yUFigure 3.3: Schematic picture of the subgrid-scale orography in ECHAM5. Mountains are describedas ellipses which have different orientations in the coordinate system depending on the orientation ofthe mountains in nature (left panel). The excited wavelength L differs depending on the orientation ofthe mountain and the wind direction (black arrows). Right panel: Cross section through a mountain. Ifthere is ow blocking, the height of the mountain hm seen by the ow is reduced to Ze f f and the excitedwavelength also decreases.3.4 ResultsIn order to investigate the inuence of gravity waves on the formation of cirrus clouds simulations withthe ECHAM5 GCM (Roeckner et al., 2003) were carried out. We used a horizontal resolution of T63(1.875 x 1.875) and 31 vertical levels using a timestep of 12 minutes. The simulations were run forthree years after a spin-up time of three months. Climatological sea surface temperature and sea-iceextent with a reference period from January 1979 - February 1996 were used. One reference run (REF)was performed, where the previous vertical velocity described by eq. (3.3) is used. In a second simulation(GWD) the original vertical velocity is replaced by the vertical velocity that contains a contribution fromthe gravity waves and is described by eq. (3.18).Additionally, a nudged simulation was performed in order to compare the simulation to observations fromthe INCA (Interhemispheric differences in cirrus properties from anthropogenic emissions) campaign(Gayet et al., 2004), which took place during March/April 2000 at Punta Arenas, Chile. Nudging isa special assimilation technique where the dynamical model variables are relaxed to observations ormeteorological analysis (Davies, 1976). The advantage of a nudged simulation is that the dynamics inthe model can be pushed towards observations so that a comparison of certain episodes or measurementcampaigns is possible (Kuo and Guo, 1989). For this study the reanalysis data from the ERA40 project(Uppala et al., 2005) at ECMWF (European Centre for Medium-Range Weather Forecasts) were used asobservations. In the model, the relaxation timescales for the divergence is 48 hours, for the vorticity sixhours and for the temperature and surface pressure 24 hours (Jeuken et al., 1996).3.4.1 Global simulationAs already mentioned in Fig. 3.2 the probability of occurrence for vertical velocities in the range 10-200cm/s is too small in the simulations considered. Despite the additional term that contains a contributionfrom the TKE, vertical velocities in the above mentioned range are generated with a too low frequency.Figure 3.4 shows the probability of occurrence of the vertical velocity induced by gravity waves (wgw),the large-scale vertical velocity (wl), the vertical velocity used in the reference run (wl+t) and the newtotal vertical velocity (wges) for the upper troposphere from 160-285 hPa. By employing the gravity wavedynamics a contribution to the vertical velocity develops mainly in the range from 20-200 cm/s. This is40 Chapter 3. Orographic cirrus in ECHAM5Figure 3.4: Histogram of vertical velocities [m/s] (left panel) and ice crystal number concentration[cm3] (right panel) averaged over the whole globe and the upper troposphere from 165-285 hPa. wlarge(red) denotes the synoptic scale vertical velocities, wgw (turquoise) the vertical velocity induced by grav-ity waves, w (blue) the synoptic scale part plus a contribution from the TKE and wges (light green) thenew total vertical velocity.exactly the range where the probability of occurrence was too low. Adding a vertical velocity induced bygravity waves thus leads to a more realistic distribution of the vertical velocities in the upper troposphere.The changes in the vertical velocity also inuence the probability of occurrence of the ice crystal numberconcentration (ICNC). The ICNCvalues shown here are only sampled over the cloudy part of the grid boxwhenever clouds occur. As the cloud fraction is not inuenced by the new parameterization, the changein ICNC in the two different