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Weather forecasts are based primarily on forward integrations of numerical representations of atmospheric processes. Recent progress in this area has been driven by advances in the understanding of atmospheric phenomena, improved observations of initial conditions, and more accurate numerical formulations of atmospheric prediction models. In recent decades, the quality of numerical weather prediction (NWP) has been closely linked to an exponential growth in available high-performance computing resources, yielding improved numerical representations of atmospheric processes. It is hoped that a further increase in model resolution will be beneficial, particularly in mountainous regions such as the Alps. Grid spacings on the order of magnitude of 1 km allow for the explicit resolution of moist convection and a more realistic representation of individual valleys and massifs, thereby improving the simulation of heavy orographic precipitation and natural disasters such as flash flooding, land slides, and avalanches. Although weather services are on track towards implementing operational NWP models at such high resolutions, newly resolved atmospheric phenomena are often poorly understood and traditional model formulations may not be suitable. This thesis will address these concerns by investigating both dynamical and numerical issues in high-resolution modeling of atmospheric flow past topography. In the first part, the focus is on numerical issues. It is shown that significant truncation errors may arise in high-resolution simulations of a simple mountain wave flow problem when employing NWP models with terrain-following coordinates. Using linear analytic solutions it is shown that artificial components of the numerical solutions largely stem from inconsistent treatment of metric terms. In particular, metric terms that appear in the advection and pressure-gradient operators do not always cancel when transformed back to Cartesian coordinates. Possible remedies are suggested for both split-explicit and semi-Lagrangian models and are shown to be effective with fully non-hydrostatic model simulations. In the second part of this thesis, the dynamics of shallow, embedded convection (EC) is investigated via idealized ridge flow simulations using a high-resolution NWP model. On the south side of the Alps, heavy precipitation is often associated with a southerly pre-frontal low-level flow advecting warm and moist air from the Mediterranean Sea towards the Alpine ridge. Observations using weather radar indicate that convection embedded in a broad-scale precipitation layer associated with the upslope flow may play a key role in producing heavy precipitation. Results of idealized numerical experiments indicate that stability measures of the upstream profile are useful but insufficient predictors of embedded convection. Other factors, such as the relative magnitude of the dominant timescales and the presence of perturbations in the upstream flow or in the topography, are found to have a strong impact on the development of EC. Simulations suggest that the presence of vertical wind shear favors convection in elongated roll-type circulations (banded convection) as opposed to cellular convection. Simulations show that the convective dynamics significantly increases the speed and efficiency of the orographic precipitation process. Pockets of increased cloud liquid water associated with convective updrafts facilitate the efficient collection of cloud water through coalescence with growing precipitation particles. EC leads to a spatially and temporally highly variable rainfall accumulation at the surface. This is especially true if the individual convective elements are anchored to small-scale terrain features. Regions receiving little or no rain may be within a few kilometers of regions receiving over 100 mm/h. This has implications for the predictability of orographic precipitation and hydrological modeling on the catchment scale. In summary, this study illustrates both the challenges and potential benefits of using current state-of-the-art NWP models at very high resolutions. This thesis aims to contribute to the numerical formulation of high-resolution models suitable for simulations over complex terrain, while positing that high-resolution simulations that explicitly resolve convective dynamics can help to improve our understanding of orographically influenced precipitation events. Wetterprognosen basieren zu einem großen Teil auf der numerischen L¨osung der atmosph ¨arischen Grundgleichungen. Fortschritte in der Wetterprognose wurden durch ein erweitertes physikalisches Verst¨andnis der Wetterph¨anomene erreicht, durch eine genauere Beschreibung des atmosph¨arischen Anfangszustandes sowie durch die Weiterentwicklung der numerischen Wettervorhersagemodelle erreicht. Eine Voraussetzung hierf¨ur war die starke Steigerung der Leistungsf¨ahigkeit von Supercomputern, die eine verbesserte numerische Darstellung der atmosph¨arischen Prozesse erm¨oglichte. Es besteht Grund zur Hoffnung, dass sich durch eine Erh¨ohung der r¨aumlichen Aufl¨osung auch die Vorhersagequalit¨at verbessert, insbesondere in Gebirgsregionen wie dem Alpenraum. Horizontale Modellaufl¨osungen in der Gr¨oßenordnung von 1 km erlauben die explizite Simulation von Konvektion sowie eine realistischere Darstellung einzelner T¨aler und Gebirge. Dadurch wird zum Beispiel eine bessere Simulation von Starkniederschlagsereignissen und den damit verbundenen Naturkatastrophen wie ¨Uberschwemmungen, Bergst¨urzen und Lawinen erm¨oglicht. Innerhalb der n¨achsten Jahre werden viele Wetterdienste ihre operationellen Vorhersagemodelle mit Gitterabst¨anden von 1–4 km betreiben. Dies, obwohl viele der nun aufl¨osbaren atmosph¨arischen Ph¨anomene noch ungen¨ugend verstanden sind, und obwohl die numerische Formulierung herk¨ommlicher Modelle m¨oglicherweise daf¨ur nicht geeignet ist. Die vorliegende Doktorarbeit geht diesen offenen Fragen nach, indem sie sowohl numerische Aspekte der hochaufgel¨osten Modellierung als auch die Dynamik atmosph¨arischer Gebirgs¨uberstr¨omungen untersucht. Der erste Teil dieser Arbeit widmet sich den numerischen Aspekten. Mit hochaufl ¨osenden numerischen Simulationen einer idealisierten Gebirgs¨uberstr¨omung wird gezeigt, dass numerische Wettervorhersagemodelle, die ein gel¨andefolgendes Koordinatensystem verwenden, erhebliche numerische Diskretisierungsfehler aufweisen k¨onnen. Mit Hilfe einer linearisierten analytischen L¨osung des Str¨omungsproblems wird gezeigt, dass diese Diskretisierungsfehler haupts¨achlich auf einer inkonsistenten Behandlung der metrischen Terme beruhen. Eine konsistente Behandlung verlangt die Aufhebung der linearen Anteile der metrischen Terme im Advektions- und Druckgradientenoperator, wenn die diskretisierten Gleichungen in ein kartesisches Koordinatensystem zur¨ucktransformiert werden. M¨ogliche L¨osungen f¨ur sogenannte “split-explicit” und “semi-Lagrange’sche” Modelle werden vorgestellt und ihre Effektivit ¨at anhand von nichthydrostatischen Modellsimulationen nachgewiesen. Im zweiten Teil dieser Arbeit wird auf die Dynamik von zellul¨arer Konvektion eingegangen, die in eine großskalige Gebirgs¨uberstr¨omung eingebettet ist. Starkniederschlagsereignisse auf der Alpens¨udseite gehen oft mit einer warmen und feuchten pr¨afrontalen S¨udstr¨omung einher. Wetterradar-Beobachtungen deuten darauf hin, dass in der großskaligen Str¨omung eingebettete zellul¨are Konvektion eine Schl¨usselrolle in der schnellen und effizienten Niederschlagsbildung spielt. Um dies zu untersuchen, werden idealisierte Gebirgs¨uberstr¨omungen mit einem hochaufl¨osenden Wettervorhersagemodell simuliert. Die Ergebnisse zeigen, dass Stabilit¨atsmaße der einstr ¨omenden Luftmassen zwar n¨utzlich aber nicht hinreichend sind, um das Auftreten von zellul¨arer Konvektion vorherzusagen. Andere Faktoren, wie die relative Gr¨oßenordnung der dominanten Zeitskalen, St¨orungen in der Anstr¨omung oder die Rauhigkeit in der Topographie, k¨onnen einen starken Einfluss auf die Entwicklung konvektiver Zellen aus¨uben. Die Resultate zeigen weiter, dass sich die Konvektion vorzugsweise in Form von Rollen an Stelle von einzelnen Zellen organisiert, sofern das Windprofil eine vertikale Scherung aufweist. Eine Analyse der Simulationen zeigt, dass die Konvektionsdynamik die Geschwindigkeit und Effizienz der orographischen Niederschlagsbildung wesentlich steigert. Die Konvektion f¨uhrt zu Zellen mit erh¨ohtem Wolkenwassergehalt, welche die effiziente Produktion von Niederschlag durch Koaleszenz von Niederschlagsteilchen mit Wolkentr¨opfchen erm¨oglicht. Die resultierende Niederschlagsverteilung weist eine grosse r¨aumliche und zeitliche Variabilit¨at auf. Dies ist insbesondere dann der Fall, wenn kleinskalige Unregelm¨aßigkeiten in der Topographie dazu f¨uhren, dass konvektive Zellen oder Rollen vorzugsweise an spezifischen Orten entstehen. Gebiete, die wenig oder keinen Niederschlag erhalten, liegen unter Umst¨anden nur wenige Kilometer entfernt von Gebieten mit ¨uber 100 mm/h Niederschlag. Dies hat Konsequenzen auf die Vorhersagbarkeit von orographischem Niederschlag sowie auf die hydrologische Modellierung einzelner Einzugsgebiete. Zusammenfassend werden in der vorliegenden Arbeit sowohl die Herausforderungen als auch das Potential von sehr hochaufl¨osenden Simulationen mit numerischen Wettervorhersagemodellen aufgezeigt. Dies geschieht zum einen durch einen Beitrag zur numerischen Formulierung von Wettervorhersagemodellen, die ¨uber komplexer Topographie eingesetzt werden. Zum anderen werden sehr hochaufl¨osende Modellsimulationen von zellul¨arer Konvektion dazu verwendet, das Verst¨andnis ¨uber orographisch induzierten Niederschlag zu vertiefen.

In this thesis a dynamical forecast approach is considered to evaluate the potential seasonal predictability in the European-Atlantic region with emphasis on the mean winter climate. Two state-of-the-art seasonal forecast systems are used, namely the Seasonal Forecast System 2 from the European Centre for Medium Range Weather Forecast (ECMWF) and a multi-model system developed within the joint European project DEMETER (Development of a European Multi-Model Ensemble Prediction System for Seasonal to Interannual Prediction). The predictions are verified with the ERA-40 re-analysis data. Seasonal forecasts are probabilistic in nature and hence require verification techniques based on probabilistic skill measures. Here a multi-category skill score, namely the ranked probability skill score (RPSS) is applied. The RPSS is sensitive to the shape and the shift of the predicted probability density distribution. However, the RPSS shows a negative bias for ensemble systems with small ensemble sizes. It is shown that the negative bias can be attributed to a discretization and squaring error in the quadratic norm of the RPSS. In the following two strategies are explored to tackle this flaw. First, it is shown that the RPSSl=i based on the absolute rather than the squared norm is unbiased. Nevertheless, it is not strictly proper in a statistical sense. Second, an unbiased and strictly proper skill score can be defined based on the quadratic norm, along with the reference forecast reduced to sub-samples of the same size as the forecast ensemble size. This is denoted as the de-biased ranked probability skill score (RPSSd). Based on a hypothetical set up comparable to the ECMWF hindcast system (40 members, 15 hindcast years) the RPSSd is used to show, that statistically significant skill scores can only be found for climate anomalies with a signal-to-noise ratio larger than -0.3. Furthermore, the seasonal predictability is evaluated using a forecast approach (FA) based on 2m mean temperature predictions on grid-point scale for the years 1987-2001. The ECMWF Seasonal Forecast System 2 provides a marked improvement in skill relative to climatological forecasts over the North-Atlantic Ocean with maximum values of up to 30 %. Over Europe no significantly positive skill scores are found. The DEMETER multi-model has higher forecast skills than individual models. Moreover, the potential predictability is investigated applying a perfect model approach (PMA). Such approach assumes that the climate system is fully represented by the model physics. The potential winter predictability over the European continent amounts to approximately -10%. The 3r part of the thesis examines the potential seasonal predictability is examined via the leading mode of the European winter climate variability, namely the North Atlantic Oscillation (NAO). The PMA shows that the mean winter NAO and the NAO temperature related impact is potentially predictable for lead time 1 month, but with a gain in skill of only -8 % compared to climatology. Using the FA, the results are quite different. For the period 1959-2001, the NAO skill score is not statistically significant, while the skill score is surprisingly large (16 % to 27 % relative to the observed climatology) for the period 1987-2001. For this period a weak relation between the strength of the NAO amplitude and the skill score of the NAO is found. This contrasts with ENSO variability where the amplitude dependent forecast skill is strong. Finally, the seasonal forecasts are examined from the end user's perspective. A so-called "Klimagram" is introduced to assess seasonal climate forecasts for particular cities or regions. A first analysis reveals that the forecast skills can be improved in a relative sense, looking at spatial and temporal averaged quantities. Overall, this study suggests a positive potential seasonal predictability in the European-Atlantic domain in winter. However, the potential benefit is rather small and constitutes a fraction only, compared to currently possible results in the tropics.

Over the last decade, flooding events on the southern side of the European Alps have claimed over 100 lives and property damage has amounted to more than 30 billion Swiss Francs. Accordingly, policy-makers and the public are strongly interested in precise and early forecasts in order to improve the options for control actions which are needed for warning and for damage prevention and minimization. Commonly used methods of runoff and flood prediction based on observed data are strongly limited with respect to their capabilities of providing the necessary lead time for small to medium scale alpine river catchments. Hence, there is a great need for advanced forecast methods. The aim of this thesis is to investigate the current potential of such an advanced approach for a medium scale mountain watershed. For this purpose, series of high-resolution numerical weather predictions are used to drive a detailed catchment model. Target areas of the investigations are the river catchments of Ticino, Verzasca and Maggia. The catchments cover a total area of 2627 km2 and drain directly from the north into the Lago Maggiore.Due to its particular location in the European Alps, these pre-alpine to high-alpine catchments are relatively frequently affected by heavy precipitation and corresponding flooding events. The first part of the thesis presents the hydrological Water Flow and Balance Simulation Model WaSiM-ETH.The theoretical basics of this highly detailed catchment model are described as well as the possible model applications and the potential for future model Upgrades. In the second part of the thesis, spatially distributed simulations investigate the hydrological water balance of the Ticino-Verzasca-Maggia watershed. In these simulations,the physically based WaSiM-ETH catchment model is driven by meteorological data from surface Station networks. The simulations are performed in hourly time Steps using a spatial grid resolution of 500 m x 500 m. The calibration and Validation of WaSiM-ETH are carried out using measured runoff data for the periods 1993-1996 and 1997-2000, respectively. The impact of reservoir management and artificial runoff redistributions on the natural catchment water balance is considered. Using the calibrated model WaSiM-ETH,seven relevant flooding events leading to considerable damages in the period between 1993 and 2000 are thoroughly analysed in the third part of the thesis. The model experiments are focused on runoff simulations using different meteorological model inputs. On the one hand, WaSiM-ETH is driven by meteorological data of either surface Station networks or weather radar. On the other hand, the Simulation results of five high-resolution numerical weather prediction models (3-14 km mesh) are used as model input into WaSiM-ETH in order to reproduce the selected flood events. The experimental design of this model coupling is described.Particular attention is paid to the "scale problem", i.e. the disaggregation of the coarser grid data of the weather models (e.g. 10 km mesh) to the finer grid of the hydrological model (0.5 km mesh). Although the results of the flood forecasting experiments (leading times up to 36 hours) are of varying accuracy, they clearly suggest that coupled atmospheric-hydrological modelling has a great potential. Nevertheless, there are also some obvious problems and limitations concerning this technique which are particularly evident in sensitivity studies. The latter make clear that relatively small inaccuracies in precipitation forecasting often grow into considerable errors in flood forecasting. The contribution of hydrological models to the process of verification and evaluation of high resolution atmospheric simulations is discussed in the last part of the thesis. This is done by concatenating daily forecasts of the former operational weather prediction model of Switzerland to a 3.5-year forecast sequence (1996-1999) which is subsequently provided as meteorological input for the hydrological WaSiM-ETH model. The results of these coupled model runs are compared to measured runoff data and to simulated catchment water balances which are based on computations with the Swiss weather model itself and on observation-driven WaSiM-ETH model runs. In addition, high-resolution weather predictions of another model are used for modelling the river runoff by means of coupled simulations for a 2.5-monthsequence (MAP-SOP 1999). The Simulation results agree in general with the observed and simulated runoff sequences. Nevertheless,they also make clear the need to adjust the precipitation forecasts with respect to their bias before using them for hydrological flood forecasting., Zürcher Klima-Schriften, 82, ISBN:3-906-148-30-0