Themen für Masterarbeiten
The Theoretical Meteorology group offers a broad range of Bachelor and Master topics in the fields of atmospheric dynamics, its numerical analyses, and prediction at many scales. The topics are derived from the current research interests of the group, which encompass the following interrelated themes central to modern meteorology:

Waves in the atmosphere and their role in the weather and climate formation

Climate modelling and climate change

Extreme weather events

Earth’s energy cycle and energy pathways in the atmosphere

Analysis of the weather patterns

Predictability, model errors, and biases

Mathematical aspects of atmospheric dynamics
In our work, we combine statistical methods and novel diagnostics approaches. Typically, MS/Ba research is based on observation and analysis data and a hierarchy of numerical models, with complexity ranging from toy models to fullscale climate models. For mathematicallyminded students, a number of problems coalescing meteorology with geometry, analysis, and statistics is available. Below is aninexhaustive list of proposed master thesis topics. For other topics and your idea, come to discuss.
1. Interaction of inertiagravity waves and the balanced flow on the sphere
Inertiagravity waves appear at many scales in the atmosphere and ocean. In the extratropics, inertiagravity waves (IG) are important ingredient of subsynoptic dynamics and they are generated by the interaction of the flow with orography, by surface and boundary layer processes, by tropospheric moist convection and by imbalance of synoptic jets. In the tropics, the primary source of IG waves is the convective heating and tropical IG waves appear at all spatial scales. In this project, we shall employ a new numerical model to study interactions between the propagating IG waves and the background balanced flow. The model solves global nonlinear shallowwater equations on the sphere for the IG and Rossby wave amplitudes.
Supervisors: Sergyiy Vasylkevych and Nedjeljka Žagar
2. Equatorial waves and the Rossby wave source
Two wave solutions exist near the equator that are absent in the extratropical atmosphere: the Kelvin wave (KW) and mixed Rossbygravity (MRG) waves. These waves fill the frequency gap between the Rossby and inertiagravity waves that is present in the midlatitudes. Depending on their vertical scale and the zonal wavenumber, the MRG and Kelvin waves have characteristics similar to either equatorial Rossby or inertiagravity waves. Excited by latent heat release in deep tropical convection, they propagate through the equatorial waveguide, communicate effects of the heat sources far away along the equator and through their vertical energy and momentum transport they play an important role for the general circulation. In this project, we shall perform numerical simulations to quantify the contributions of these waves to the anomalous vorticity sources in the subtropics.
Supervisors: Nedjeljka Žagar and Frank Lunkeit
3. Where is the central latitude of ITCZ?
The Glossary of the American Meteorological Society defines the intertropical convergence zone (ITCZ) as “an axis, or a portion thereof, of the broad trade wind current of the Tropics. The axis is the dividing line between the southeast trades and the northeast trades and it is collocated with the ascending branch of the Hadley cell.” In research practice the ITCZ has usually been defined by the narrow belt of (proxy) observations of deep tropical convection, i.e., by the location of precipitation maxima above a certain threshold, by the surface wind convergence or by the zero crossing of the average meridional wind in the boundary layer. In this master thesis we will estimate the central latitude of ITCZ by evaluating the vertical velocity associated with the horizontal wind convergence in reanalysis data and its comparison with the precipitation maxima. Collocation properties of precipitation maxima and the latitude of strongest vertical motions will be discussed for different land and ocean regions.
Supervisor: Nedjeljka Žagar
4. Growth of forecast errors in the tropics
Many studies of the growth of errors in forecasts have focused on the quasigeostrophic dynamics and often considered the errorfree largescale initial state. In contrast, the global operational numerical weather prediction and ensemble prediction systems are characterized by significant analysis uncertainties at large scales, especially in the tropics. In fact, data suggests that the larger the scale, the greater the initial uncertainties. In this project, we shall employ a simplified numerical model to study how initial state errors in inertiagravity wave component of the tropical circulation affect the growth of forecast errors.
Supervisors: Nedjeljka Žagar and Sergiy Vasylkevych
5. Rossby wave variability
General circulation models (GCMs) simulate the spectrum of variability from weather to decadal time scales across many spatial scales. Temporal variability can be split among various time scales, variables and regions whereas details of the spatial spectrum associated with certain temporal frequency can be described as a combination of “preferred” patterns. Using the MODES (https://modes.cen.unihamburg.de) decomposition of reanalyses and climate model simulations into many scales, we shall investigate horizontal and vertical shifts in weather patterns  Rossby wave variability in midlatitudes.
Supervisor: Nedjeljka Žagar
6. Modelling the climate of Amasia
On very long time scales, continental drift effects the Earth and its climate system together with changes in the orbital parameters, etc. Recently it has been speculated that a supercontinent (Amasia) will form
over the North Pole in about 50 to 200 million years (Nature 482, 208211, 2012). This project will use a climate model of intermediate complexity (PlaSim) to analyse the climate system of this future planet
Earth. The work will focus on particular aspects depending on the
interest of the student.
Supervisor: Frank Lunkeit
7. Sensitivity of tropical wave circulation to cumulus parameterization
Atmospheric circulation, tropical waves, cumulus parameterizations
The parameterization of moist (cumulus) convection is a crucial part of climate models. Various schemes have been proposed based on assumptions made about the dominant mechanisms. The particular choice of the parameterization scheme may have a significant effect on the simulated climate, in particular on the characteristics of tropical waves. This project will use a climate model of intermediate complexity (PlaSim) in an idealized setup to compare the effect of different cumulus parameterization schemes on tropical waves. A diagnostic Tool (MODES, https://modes.cen.unihamburg.de) will be applied to decompose the circulation, and to analyse the contribution of different wave types.
Supervisors: Frank Lunkeit and Nedjeljka Žagar
8. Understanding North Atlantic midwinter suppression in stateoftheart climate simulations
We propose here a model study of the midwinter suppression in the Northern Atlantic, analysing an ensemble of CMIP model simulations over the historical period. We will first verify the existence of the relatively well understood Pacific midwinter suppression, comparing several indices of baroclinic activity in the midlatitudinal storm track belt and studying the relation with the seasonality of Arctic and subptropical tropospheric temperatures. With this knowledge, we will focus on the North Atlantic sector, to assess whether the suppression exists in models and if the mechanisms of suppression are comparable with the Northern Pacific. We will then adopt a similar analysis on the study of future climate projections, after carefully selecting the models that better sample this mode of variability.
Supervisors: Valerio Lembo and Richard Blender
9. Meridional heat transports in the midlatitudes
In a recent work it has been highlighted that the extremes in the midlatitudinal meridional heat transport result as a combination of planetary and synopticscale zonal waves. These two components are competitive, in the sense that either planetaryscale or synopticscale carry the extreme transports, but not both of them. In order to understand the relation between the two components, we will perform lagged correlations of the signals, and we will retrieve frequency spectra, in order to identify possible energy cascades from low to high wavenumbers or vice versa. Where possible, we will perform a similar wave decomposition on stateoftheart climate models, in order to investigate their statistics and compare them with observationaldependent datasets.
Supervisors: Valerio Lembo and Nedjeljka Žagar
10. The Lorenz energy cycle in climate models
The Lorenz Energy Cycle (LEC) is a classical framework for the investigation of the energy exchanges in the climate system. It describes the conversion between Available Potential Energy (APE) and Kinetic Energy (KE), emphasizing the role of the Eulerian mean circulation and eddies in a dry hydrostatic atmosphere. It is thus a potentially fundamental diagnostic of the general circulation (in the atmosphere and ocean, but we will focus on the former), encompassing a huge variety of processes occurring in the system. One of the limitations of the LEC retrieval in climate models resides in their vertical discretization. Being performed using different methods and vertical coordinates, it is not trivial how the circulation in different models, shall be compared with each other. As a result, more sophisticated, yet often less complete, diagnostics have to be developed. We will here focus on a single stateoftheart climate model, and we will investigate how different vertical discretizations affect the retrieval of LEC. Furthermore, we will compare two different techniques for LEC retrieval: one based on zonal wave decomposition through Fourier transform, the other based on gridpoint computation.
Supervisors: Valerio Lembo and Christian Franzke
11. Impact of moisture on midlatitude storms
Due to global warming, the moisture content of the atmosphere will increase. How this will affect the midlatitude circulation and storms is largely unknown. This project will use numerical models and reanalysis data to study the life cycles of midlatitude storm under global warming conditions.
Supervisor: Christian Franzke
12. Impact of global warming on North Atlantic jet stream variability
In recent years Europe has experienced extreme climate conditions (severely cold winters, flooding, heat waves, ..). This has been partially attributed to a slowdown of the atmospheric circulation. This project will explore this hypothesis using numerical model experiments and reanalysis data.
Supervisor: Christian Franzke
13. Statistical Modeling of Extremes
Extreme precipitation can lead to flooding and can have enormous impacts on societies. Climate models have still a much to coarse resolution in order to be able to simulate such extreme events. In this project we will use extreme value theory to develop statistical models for the simulation and downscaling of precipitation extremes.
Supervisor: Christian Franzke
14. How persistent are persistent extreme events?
Persistent extreme events  like heat waves, cold spells, droughts  exert a long lasting and constant stress on human health, natural ecosystems, or even on society itself. Scientific studies show that the number of excess deaths is increasing dramatically and nonlinearly during heat waves. Thus, the study of the duration of persistent events is more than relevant, especially in the context of climate change. However, the majority of mathematical and statistical methods used to analyze extreme events consider independent, identically distributed, random variables. Meaning that persistence or duration becomes a problem, and is usually eliminated. The subject of this thesis is to analyze precisely the usually ignored duration of persistent extreme events. This requires basically to count the number of consecutive values of a variable, like temperature, exceeding a certain threshold, which can be done “manually” or using standard methods of Extreme Value Theory. By increasing the threshold one can analyze the duration of more and more extreme events. The thesis is supposed to answer some of the following questions:
Do persistent extreme events have a characteristic duration, and, if yes, how does this relate to typical temporal scales measured by the autocorrelation?
Does the answer to 1) change if one preforms the study using, for example, the simplified general circulation model PUMA or using more realistic reanalysis data sets?
Does the answer to 1) change if one considers different atmospheric variables, like temperature or precipitation? That is, what is the difference between the persistence of heat waves and of long lasting precipitation events, for example?
What is the connection between temporal duration and spatial extension of persistent extreme events?
This study can be either a bachelor or a master thesis. The amount of work can be adapted accordingly.
Supervisors: Melinda Galfi
15. Bringing light into “Dunkelflaute”
A “Dunkelflaute” (dark lull) event is a persistent period of a few days or weeks during which the wind speed and solar irradiation are both very low. Whereas many people think that Dunkelflaute represents a serious threat for energy supply, especially when the energy network is relying on renewable energy resources, others claim that it does not even exist. Thus, in the context of climate change and the necessity to extend the use of renewable energies, it is extremely important to find answer to basic question related to Dunkelflaute. The interested student will use reanalysis data sets to detect and analyze Dunkeflaute events, by using also methods from the field of compound or correlated extreme events. The larger the affected spatial area, the severer are the possible economic losses. A Dunkelflaute of, say, European scale could increase the energy deficit and hinder necessary energy imports. Accordingly, the analysis should consider different spatial scales, corresponding to Northern Germany, Germany and Europe, for example. The thesis is supposed to answer some of the following questions:
 How frequent are Dunkelflaute events in reanalysis data sets?
 What kind of atmospheric conditions are characteristic during these events from a dynamical point of view?
 Can one detect a temporal change in the frequency or duration of Dunkelflaute?
 How do the properties of these events change considering different spatial scales?
This study can be either a bachelor or a master thesis. The amount of work can be adapted accordingly. It is an ideal topic in particular for students aspiring to a career in the renewable energy sector, but not exclusively.
Supervisors: Melinda Galfi and Christian Franzke