Presented here are thesis proposals for students, supervised by staff at the Complex Systems Modelling group.  " /> Presented here are thesis proposals for students, supervised by staff at the Complex Systems Modelling group.  " />

Master Thesis Proposals

Presented here are thesis proposals for students, supervised by staff at the Complex Systems Modelling group.  

 The scope of these proposals can be adjusted and are equally suitable for students from the 5-year integrated masters (30sp) and the 2-year master’s program in Physics (60sp) 

 

The Complex Systems Modelling group currently have the following project proposals:

 Climate

Fusion energy / plasma physics

Common introduction for fusion plasma projects

Stochastic processes / nonlinear dynamics

Climate

Atmospheric energy transport to the Arctic

Supervisor: Rune Grand Graversen (rune.graversen@uit.no)

Required courses: FYS-2018, FYS-3030

Recommended courses: FYS-2001, STA-2001, INF-1100 and MAT-3213

The sun is warming the low latitudes more than the high latitudes. For that reason energy is transport in the meridional (south-north) direction towards the poles in the atmosphere and ocean. In the midlatitudes atmospheric waves such as Rossby waves and cyclones are accomplishing this transport. A method for decomposing the Northward Atmospheric Energy Transport (ANET) into parts associated with the individual waves - such as Rossby waves and cyclones - has newly been developed (Graversen and Burtu, 2016). This method can be used for studying the importance of the different wave types on the ANET.

In this project we will study in detail situations where the different wave types – for instance Rossby waves or cyclones – are important for the ANETScientific questionsWhat is the meteorological situation in the Northern Hemisphere mid-latitude when the ANET by cyclones is strong? And what is the situation when the ANET by Rossby waves are strong? How does the ANET by Rossby waves and by cyclones impact Arctic sea ice?

Data

The ERA-Interim reanalysis data from the European Centre for Medium-range Weather Forecast(ECMWF) will be used. Based on these data a split of the meridional energy transport into wave component has been performed in advance, and the data stored at the Stallo super computer to which the student will obtain access.

Method

Situations where the ANET by a given wave type is strong will be identified, and atmospheric fields such as wind, temperature, geopotential and humidity will be studied with respect to for instance their wave structure. A Fourier decomposition is applied in order to study the wave structure. Sea-ice composites of strong and week ANET cases associated with a given wave type will be computed in order to investigate the impact on the Arctic sea ice of a given wave type.

References

Graversen R. G., and M. Burtu.: Arctic amplification enhanced by latent energy transport by atmospheric planetary waves.Q. J. R. Meteo. Soc., doi:10.1002/qj2802, accepted (2016)

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Evaluation of the potential of very high-resolution modelling in the Arctic.(60/30 ECTS points)

Supervisors:

Eirik Mikal Samuelsen (eirik.m.samuelsen@uit.no)

Rune Grand Graversen (rune.graversen@uit.no)

Required courses: FYS-2018, FYS-3030

Recommended course: STA-3300, AGF-350 (UNIS)

This master work is in cooperation with the Norwegian Meteorological Institute (MET Norway) and will be part of the Arktis 2030. Arktis 2030 is a 3-year (2018–2020) research project about Arctic weather prediction financed by the Ministry of Climate and Environment. Arktis 2030 is led by MET Norway and is building on the existing cooperation between MET Norway and CIRFA research group at IFT, UiT - The Arctic University of Norway.

Background

With the increased capability of computers in the recent years, there is a potential of running numerical weather prediction models with very high spatial resolution (dx < 1 km). However, when comparing such very high resolution models with coarser resolution models, standard ways of evaluating the models do not necessarily show increase in accuracy of the models due to increase in model resolution. Particularly since very-high resolution modelling is resource demanding, there is a need for better and more detailed evaluation in order to defend its resource demands.

For instance a small position error in the model output of the high resolution model may be “punished” twice when evaluating model results with point observations for several parameters like precipitation, wind, and temperature (double penalty). In order to get more insight of the benefits of high-resolution modelling, more detailed studies of the structures of the weather phenomena involved are needed. In addition, alternative observations relative to the conventional land-based synops stations may be applied in such studies. SAR-based satellite measured winds, radiosondes, ship observations, and aircraft observations (AIREPS) are all other possible sources of information that are normally not utilized in standard verification procedures, which may provide more insight in the potential of the high-resolution models. There is also a challenge in verifying solid precipitation during blowing conditions due to undercatchement of the snow in the rain gauges. Several correction factors may be applied to such precipitation data, but little verification of these correction methods has been done in the Arctic.

At MET Norway several experiments with the Harmonie-Arome model CY43 with 500 m horizontal resolution and 90 vertical levels without data assimilation are run for long periods in the winter 2019 and compared with Arome Arctic with 2500 m horizontal and 65 vertical levels for the same period. However, more detailed verification and evaluation are needed.

Aim of project

The aim of the project is a more detailed investigation of the results of these model runs (January 2019, and 17 to 21 February 2019). It would for instance be interesting to separate verification results based on the weather pattern, perform sensitivity studies with model setups (for instance changing maximum Richardson number) for specific days, and compare the results. Using SAR-images, radiosondes and ship observations or other alternative sources of data for verification will also be exciting. Turbulence and icing measurements (AIREPS) may also be applied in order to verify turbulence (TKE) and icing output from the models. Alternatively or additionally, comparison of different verification methods of solid precipitation against other data sources (radar, snow fall) may also be included in the project. These are some examples of the direction the project can take and will be adjusted according to the interests of the candidate.The model and observation data are all provided by MET Norway.

Tools

The project will involve analysis of data based on algorithms for retrieving weather patterns and statistical methods for comparing model and observation data, such as root-mean-square error and other metricies.

Literature

Müller, M., Batrak, Y., Kristiansen, J., Køltzow, M. A., Noer, G., & Korosov, A. (2017). Characteristics of a Convective-Scale Weather Forecasting System for the European Arctic. Monthly Weather Review, 145(12), 4771-4787.

Køltzow, M., Casati, B., Bazile, E., Haiden, T., & Valkonen, T. (2019). An NWP Model Intercomparison of Surface Weather Parameters in the European Arctic during the Year of Polar Prediction Special Observing Period Northern Hemisphere 1. Weather and Forecasting, 34(4), 959-983.

Samuelsen, E. M. 2007. A dynamical study of the storm Narve - a cold air outbreak in Finnmark - with the use of observations and numerical simulations (in Norwegian). Master thesis. University of Bergen. 

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Forecasting aircraft in-flight icing

Supervisor:

Rune Grand Graversen, rune.graversen@uit.no

Morten Andreas Ødegaard, morteno@met.no

Required courses: FYS-2018

Recommended course: FYS-2001, FYS-3030 and MAT-3213

This master work will be part of the Alertnessproject. Alertness(Advanced models and weather prediction in the Arctic) is a 4-year (2018–2021) research project about Arctic weather prediction financed by the Norwegian Research Councils program for polar research POLARPROG. Alertness is led by the Meteorological Institute of Norway (MET Norway) and is a cooperation between MET Norway, University of Bergen (UiB), Uni Research (UNI), University of Tromsø (UiT), The Royal Netherlands Meteorological Institute (KNMI), Nansen Environmental and Remote Sensing Center (NERSC) and The University Centre in Svalbard (UNIS). Alertneshome page: https://www.alertness.no

Background

Aircraft in-flight icing is a hazard to aviation. Icing happens when aircrafts is exposed to (cloud) supercooled liquid water (temperatures below 0°C). When ice accrete at aircrafts, the aircraft performances will potentially degrade and eventually become a security risk. Forecasting atmospheric icing conditions are therefore important to reduce risks in aviation. Most forecasts are based on output from Numerical Weather Prediction (NWP) models as the icing on aircrafts itself is not explicitly simulated in the NWP models. The NWP models forecast with some success the atmospheric conditions favourable for icing. Output data from the NWP models are then used in empirical relationships to forecast in-flight icing severity.

As in all weather forecasting, verification is an important part, i.e. how similar are the forecasts and the observed conditions? For aircraft in-flight icing this is challenging due to the lack of regular observations. Pilots do report when they experience icing conditions and these observations can be utilized. However, the observational data sets are very biased (e.g. no null-cases are reported, pilots avoid areas where icing is forecasted, the icing depend on aircraft etc). However, radiosonde observations (balloons) measures the vertical profile of the atmosphere, e.g. humidity, temperature, vertical and horizontal winds at a selection of (Norwegian) locations. Since several of the existing empirical relationships between atmospheric conditions and aircraft in-flight icing use parameters available from radiosonde data this is an alternative source for verification of in-flight icing.

Aim of project

The purpose of this work is to investigate radiosonde data for aircraft in-flight icing conditions. Empirical aircraft in-flight icing algorithms will be employed with input from radiosonde observations. From long radiosonde time series it is then possible to create icing climatologies. In addition, the same icing algorithms will be employed on model output from NWP models used operationally at MET Norway and the resulting icing forecasts will be evaluated.

Data

Radiosonde observations

NWP model data (arome_arctic_vc*files include vertical profiles)

Literature

Berstein B. C. Et al.: Current Icing Potential: Algorithm Description and Comparison with Aircraft Observations, J. Appl. Meteo., 44, 969-986 (2005)

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Impact of Arctic cloud cover changes – a modelling study

Supervisor: Rune Grand Graversen, rune.graversen@uit.no

Required courses: FYS-2018, FYS-3030

Recommended courses: FYS-2001, STA-2001, INF-1100 and MAT-3213

 

Background

Clouds are important for the energy balance of the Earth, they both reflect solar radiation and absorb longwave radiation whereby they contribute to both a cooling and a warming of the climate. Globally the albedo effect associated with shortwave reflections is stronger than the greenhouse effect associated with the longwave absorption, implying that overall, clouds are cooling the climate. However in the Arctic clouds are believed mostly to have a warming effect except possibly for the summer months.

Using state-of-the art climate model clouds over the Arctic will be varied, and the effect of clouds on the local Arctic climate in terms of temperature and sea ice will be studies.

Scientific questions

How sensitive is the Arctic climate to variations of clouds? Can small cloud changes cause relatively large warming and sea-ice melt in the Arctic? Do cloud changes in the Arctic impact the climate elsewhere, for instance in the Northern Hemisphere mid latitudes?ModelThe state-of-the-art climate model Community Earth System Model (CESM) from the National Center of Atmospheric Research, Boulder (NCAR), Colorado, US, will be used. The model is written in Fortran. It is installed at the Vilje super computer to which the student will obtain access.

Method

Cloud parameters that are used in the radiation code of the CESM model will be identified. Forcing experiments where the cloud parameters are perturbed will be performed. These will be compared to a control run where no perturbations were implemented. The comparison between forced and control experiments will reveal the effect on the climate of the cloud changes. The student should have some basic programing skills but do not have to have experience with climate modelling, nor specifically with the Fortran programing language.

Literature

Graversen, R. G., P. L. Lange, T. Mauritsen: Polar amplification due to the lapse-rate and surface-albedo feedback in the Community Climate System Model version 4. J. Climate,27, 4433-4450 (2014)

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Interannual variability of winter precipitation sources for western Svalbard.Project at Norwegian Polar Institute (NP)

Supervisors:

Dmitry V. Divine (NPI, UiT)

Rune Graversen (UiT)

Harald Sodemann (UiB)

Required courses: FYS-2018, FYS-3030

Recommended courses: FYS-2001, INF-1049, and MAT-3213

Background

<p">Stable water isotopes (H217O, H218O and HDO) are widely used in research on climate of the past and present including studies of the hydrological cycle on both global and regional scales. We are seeking a motivated master candidate who would be interested in employing available stable water isotope measurements and principles of Lagrangian modelling to study the intra- and inter-annual variability of atmospheric moisture transport to Svalbard.

As part of this project you will analyze the data set on the isotopic composition of stable water isotopes in fresh solid precipitation collected in Ny-Ålesund since 2011 using the Lagrangian moisture diagonstics with enabled isotopic tracers. Results of the analysis will be of benefit for a better interpretation of isotopic ice cores records from Svalbard used to establish climate variability in the region some 1000 years back in time. The project also provides an invaluable opportunity to gain familiarity with the structure and use of atmospheric reanalysis data, one of the major modern tools in modern weather and climate studies.

As this project will be implemented in cooperation with a newly funded NFR project SNOWPACE (http://www.uib.no/en/rg/meten/109877/snowpace) you will also be part of a major national initiative towards identification of the sources of the Norwegian winter season snow pack using stable water isotopes.

Scientific Questions

What are the major factors controlling the isotopic composition of stable water isotopes in winter precipitation in western Svalbard? What are the sources of moisture forming precipitation in western Svalbard during winter?

Data

1) Observations of stable water isotopes in fresh snow samples of winter (typically September-May) solid precipitation from Ny-Ålesund and other locations in western Svalbard over the period 2011-2016.

2) Real-time water vapour isotope measurements from Zeppelin station, Ny-Ålesund; data from 2015.

3) Atmospheric reanalyses data such as ECMWF ERA-Interim

4) NSIDC passive microwave daily sea ice concentrations

Tools

As a major tool for data analysis the candidate will be running the numerical implementation of Lagrangian moisture source diagnostic with an embedded module for stable water isotopes. The candidate will receive a necessary training for mastering the software and the use of atmospheric reanalysis data at the University of Bergen and hence expected to spend a period outside Tromsø. The necessary funding to cover the costs will be provided. The project will also involve analysing large datasets using Matlab, and/or Python and applying statistical techniques to datasets.

Literature

(1)Sodemann, H., V. Masson-Delmotte, C. Schwierz, B. M. Vinther, and H. Wernli (2008), Interannual variability of Greenland winter precipitation sources: 2. Effects of North Atlantic Oscillation variability on stable isotopes in precipitation, J. Geophys. Res., 113, D12111, doi:10.1029/2007JD009416.

(2)Sodemann, H., C. Schwierz, and H. Wernli (2008), Interannual variability of Greenland winter precipitation sources: Lagrangian moisture diagnostic and North Atlantic Oscillation influence, J. Geophys. Res., 113, D03107, doi:10.1029/2007JD008503.

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Model calculations of mesospheric clouds

Supervisors: Ingrid Mann and Rune Graversen

Required courses: Contact supervisor

Background

Cosmic dust and meteoroids and their fragments play an important role in the physical and chemical processes of the upper atmosphere. Cosmic dust particles that enter the atmosphere are heated, producing evaporated material that dissociates and ionizes at about 140–60 km altitude. Small meteoroids and dust particles, gaseous species that originate from the meteoroids, and small meteoritic smoke particles re-condense and are a core for ice condensation which leads to the formation of mesospheric clouds. The observed shape of the clouds indicates the transport of the particles in the atmosphere. At UiT we have observational data related to mesospheric clouds from in-situ rocket observations and from radar observations. We also collaborate with a group that carries out optical observations.

The WACCM-CARMA from the US National Center for Atmospheric Research is an atmospheric high-altitude model, Whole Atmosphere Community Climate Model (WACCM), coupled with an aerosol microphysical model (CARMA). This project aims to use output from the WACCM- CARMA model for studying the particle transport in mesospheric clouds, the shape of these clouds, and to compare with observations. Given that the model can reproduce observed aspects of the mesospheric clouds, the model can be used to investigate the physics governing these clouds. This work is linked to RCN funded projects on mesospheric dust and on Arctic climate.

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Evaluation of atmospheric reanalyses over Southern Oceanin the pre-IGY1957 period using historical ship-based weather observations.

Supervisor:

Dmitry V.Divine (NPI, UiT)

Rune Graversen (UiT)

Required courses: FYS-2018

Recommended courses: FYS-2001, STA-2001, INF-1100 FYS-3030 and MAT-3213

Background

There is a substantial gap in our knowledge of the climate in the Southern Ocean and Antarctica before the International Geophysical Year (IGY) -1957 when the first organized observational network in the region was established. Compared with a relative abundance of instrumental climate data from the Northern Hemisphere, the Antarctic region is still largely underrepresented suffering from paucity and shortness of available instrumental series. This limits the skills of climate reanalysis products and climate models for the region.Since the atmospheric reanalysis data are an essential tool for studying the ongoing changes in this regionas well as global-wise,it has further implications for understanding the signature and effects of possible future anthropogenic warming in the Antarctic region(1).

Complementary data sources such as ships’ logbooks have proven to be a successful tool in reconstructing past marine climate, providing important data, such as in the widely used International Comprehensive Ocean-Atmosphere Data Set (2) for global reanalysis for the period before the onset of the comprehensive satellite-and buoy-based ocean monitoring. Thereforeattempts to extend the contemporary instrumental data coverage both spatially and back in time using “opportunistic” ship-based weather observations have being undertaken in a number of previous studies(e.g. 3, 4).

As part of this project you will comparealready available and newly logged ship-based weather observations from the Southern Ocean for the period of ca. 1930-1960to multiple different reanalysis products, to assess their performance. The project provides an invaluable opportunity to gain familiarity with the use of reanalysis data, together with the climate andhistory of the earlier exploration of the region. You will also be part of a large multidisciplinary international initiative towards recoveryand useof historical instrumental weather observations.

Scientific Question

How well do atmospheric reanalyses perform in the Southern Ocean in the period before the IGY-1957?

Tools

The project would involve analysing large datasets using Matlab,and/or Python and applying statistical techniques to datasets, including correlation, probability density functions, and significance tests.

Data

1) Atmospheric reanalyses datarelevant for this study:

-ECMWF ERA-Interim

-JRA-55,

-NASA MERRA2

-NCAR/NCEP-CFSv2

2) Historical weatherobservations from whaling vessels (ICOADS archive, newyetunpublished data)

Literature

(1) Bromwich, D.H. et al.,(2007). A tropospheric assessment of the ERA-40, NCEP, and JRA-25global reanalyses in the polar regions, Journal of Geophysical Research, 112, D10111.

(2) Freeman, E., et al., (2016). ICOADS Release 3.0: A major update to the historical marine climate record. InternationalJournal of Climatology, 37(5), 2211–2232,doi:10.1002/joc.4775.

(3) Brohan, P., et al.,(2009): Marine Observations of Old Weather, Bull. American Meteorological Society, 90(2), 219–230,doi:10.1175/2008BAMS2522.1.

(4) Divine, D. V., and C. Dick (2006), Historical variability of sea ice edge positionin the Nordic Seas,Journal of Geophysical Research, 111, C01001

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Sea-ice cover in the Southern Hemisphere

Supervisor: Rune Grand Graversen, rune.graversen@uit.no

Required courses: FYS-2018

Recommended courses: FYS-2001, STA-2001, INF-1100, FYS-3030 and MAT-3213

Background

The sea-ice cover in the Arctic is shrinking during recent years. The Arctic ice retreat is largest during summer. On top of the over all trend, the summer sea-ice extent shows large variability from year to year. Kapsch et al., 2013, showed that the Arctic sea-ice cover by the end of the summer is strongly coupled to the atmospheric circulation over the Arctic during spring.

In the Southern Hemisphere, the summer sea-ice extent around Antarctica also shows pronouncedvariability from year to year. The reasons for this variability are not well known. The variability can be due to variations in clouds, in atmosphere transports of heat and moisture over the sea ice, andalterations of the ocean circulation, and perhaps other processes.

Scientific question

What is determining the year-to-year variability of the sea-ice cover in the Southern Hemisphere? This project aims at identifying processes important for this variability.

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The characteristics of dynamics of the upper atmosphere at high latitude

Supervisors:

Professor Chris Hall (TGO), chris.hall@uit.no

Professor Ulf-Peter Hoppe, u.p.hoppe@fys.uio.no

Required courses: Contact supervisor

Background

Climate change can be detected in the upper atmosphere as well as just in the well-known “global warming” scenario. However, in order to study this, the interactions between the different height regions in the atmosphere must be better understood. Time series from one or more atmospheric radars (either at Tromsø or on Svalbard or both) will be employed to investigate characteristics of the neutral air dynamics of between 60 and 100 km at various timescales. This region lies between the ozone layer and the aurora, and is perhaps the least understood part of our atmosphere.

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Verification study of weather forecasts over the sea ice at the Yermak Plateau

Supervisor:

Rune Grand Graversen, rune.graversen@uit.no

Marius Jonassen, marius.jonassen@UNIS.no

Morten Andreas Ødegaard, morteno@met.no

Required courses: FYS-2018

Recommended course: FYS-2001, FYS-3030 and MAT-3213

This master work will be part of the Alertnessproject. Alertness(Advanced models and weather prediction in the Arctic) is a 4-year (2018–2021) research project about Arctic weather prediction financed by the Norwegian Research Councils program for polar research POLARPROG. Alertness is led by the Meteorological Institute of Norway (MET Norway) and is a cooperation between MET Norway, University of Bergen (UiB), Uni Research (UNI), University of Tromsø (UiT), The Royal Netherlands Meteorological Institute (KNMI), Nansen Environmental and Remote Sensing Center (NERSC) and The University Centre in Svalbard (UNIS). Alertnes home page: https://www.alertness.no

Background

Numerical Weather Prediction models has a key role in weather forecasting. The models are fed by meteorological observations, make an estimate of the given state of the atmosphere at a given time and use the governing equation describing how the atmosphere develop from the initial state and into a future state. Due to the large amount of complex processes and their interactions in the atmosphere, and the limitations of computer capacity the descriptions of these processes include approximations. In addition, since observations are not continuously available in space and time and contain errors the estimated state of the atmosphere and the real atmosphere differs. The initial differences and approximations described above imply that the simulated atmosphere and the real atmosphere will diverge with time since the atmospheric system has a chaotic behaviour (i.e. to atmospheric states that are close to each other at a given time will not stay close to each other for all times). The difference between the forecasted weather and the observed weather is the forecast error.

An important part of the work of all operational forecasting centers is therefore to verify their forecasts, i.e. how similar are the forecasted and the observed weather? Knowledge about forecast errors is crucial in day-to-day forecasting (i.e. to utilize model output best you need to know the weaknesses and strengths). In addition, in the long-term model development you first need to diagnose weaknesses before they can be improved, and you need to demonstrate that a new model version improves over the old version.

The verification process compare NWP models and different types of observations (e.g. the station network operated by MET Norway, satellite measurements, etc). Typically, the density of near surface observations are much higher over land than over ocean with the implication that the model performances are better known over land than over ocean. The purpose of this work is to increase our knowledge about NWP model performances over ocean and sea ice by using observations from a AWI Polarstern expedition to the Yermak Plateau in the summer of 2017. Measurements was done on the ice, on the boat, with radiosondes and from aircrafts giving a good picture of the real atmosphere over the summer sea ice.

Aim of project

At MET Norway two NWP models (the inhouse model: AROME-ARCTIC and the IFS system from ECMWF) used for weather forecasting cover this area. Forecasts from these models will be compared with the observations to assess how well the models simulate the weather during the expedition.

Data

Observation data based on radiosonde of temperature and humidity from the Yermak Plateau will be used.

Model data:

The same variables will be obtained from two forecast models: AROME-Arctic

Literature:

Jakobsen E. et al.: Validation of atmospheric reanalyses over the central Arctic Ocean. Geophys. Res. Lett. 39, L10802, doi:10.1029/2012GL051591 (2012)

Graham R.et al.: Evaluation of six atmospheric reanalysis over the Arctic sea ice from winter to early summer, J. Clim.In press (2019)

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Fusion energy and plasma physics

Nuclear fusion is the mechanism behind the energy generation in stars, and a successful fusion power plant promises clean and sustainable energy for the foreseeable future. However, the fuel must maintain an extremely high temperature and is therefore in the plasma state. At the same time, the vessel containing the fuel should ideally be at room temperature or lower. Maintaining this division of plasma fuel and material vessel is of critical importance for a fusion power plant. 

In the highly turbulent boundary region between the plasma and the walls, coherent plasma structures called blobs or filaments move radially outward and deposit particles and heat at the walls. The highly complex and varied behavior of this turbulent fluid defies most attempts at simple and predictive description. Measurements of particle density near the walls reveal intermittent fluctuations with large amplitudes and robust shapes. These so-called filaments are elongated along the magnetic field and localized across the field lines, thus they are commonly referred to as blobs. These blobs arrive intermittently at the wall, and likely cause enhanced plasma-wall interactions compared to the expectation based on the mean plasma parameters. 

The master projects available at UiT in fusion energy focus on the behavior and prediction of the plasma fluctuations near the walls of the reactor using numerical simulations, stochastic modelling and analysis of measurement data. The ultimate goal of this research is to mitigate or limit the damage to the wall due to the fluctuations. 

 

Model comparisons for plasma turbulence data 

Supervisor: Audun Theodorsen, audun.theodorsen@uit.no
Required courses: FYS-2009, FYS-3026
Recommended courses: STA-3001

Background

(See the common Fusion energy introduction)

Previously, stochastic differential equations were proposed in order to describe these plasma fluctuations, and recently a model based on a superposition of pulses was developed at UiT. All models capture the basic statistical properties of particle density measurements near the walls of fusion reactors such as probability density functions and power spectral densities.

Research goals

The aim of this project is to find the best model among the candidates for a set of measurement data from the TCV tokamak. Statistical properties of the different stochastic models will be compared to each other and to experimental data in order to assess the best candidate. To aid in this assessment, maximum likelihood procedures or Bayesian methods may be developed.

Methods

Statistical analysis of time series data including one-time probability density functions, power spectra, conditional averaging and excess time statistics. Comparison to realizations of the stochastic model, both in detail and using Monte-Carlo studies. Maximum likelihood estimation / Bayesian methods may be included. 

References

N. H. Bian, On-off intermittent regulation of plasma turbulence, Phys. Plasmas 17, 044501 (2010), doi: 10.1063/1.3368799

A. Mekkaoui, Derivation of stochastic differential equations for scrape-off layer plasma fluctuations from experimentally measured statistics, Phys. Plasmas 20, 010701 (2013), doi: 10.1063/1.4789453

O. E. Garcia et. al., Stochastic modelling of intermittent fluctuations in the scrape-off layer: correlations, distributions, level crossings and moment estimation, Phys. Plasmas 23, 052308 (2016), doi: 10.1088/0741-3335/58/4/044006

A. Theodorsen et. al., Scrape-off layer turbulence in TCV: evidence in support of stochastic modelling, Plasma Phys. Control. Fusion 58, 044006 (2016), doi: 10.1088/0741-3335/58/4/044006

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Stochastic modelling of electric potential fluctuations

Supervisor: Audun Theodorsen, audun.theodorsen@uit.no

Required courses: FYS-3026, FYS-3035 

Recommended courses:  

Background 

(See the common Fusion energy introduction) 

A widely used model to describe the intermittent fluctuations only account well for the particle density and temperature of the plasma, and their proxies. Previous attempts at finding characteristic pulse shapes for the electric potential measurements have not yielded convincing results. As radial velocities of the pulses are commonly estimated from the electric potential difference between two vertically separated probes, this also draws blob velocity estimates into question.  

Research goals 

To understand the limitations in single-point measurements of the electric potential and construct an alternative model for the electric potential- and velocity fluctuations. 

Methods 

Simulation of seeded 2D-plasma structures using the blobmodel developed at UiT or turbulence simulations using the BOUT++ code. Statistical analysis of time series from simulation output and comparison to the statistical properties of the 2D structures. 

References

O. E. Garcia et. al., Stochastic modelling of intermittent fluctuations in the scrape-off layer: correlations, distributions, level crossings and moment estimation, Phys. Plasmas 23, 052308 (2016), doi:10.1088/0741-3335/58/4/044006

A. Theodorsen et. al., Scrape-off layer turbulence in TCV: evidence in support of stochastic modelling, Plasma Phys. Control. Fusion 58, 044006 (2016), doi:10.1088/0741-3335/58/4/044006

R. Kube et al., Comparison between Mirror Langmuir Probe and Gas Puff Imaging Measurements of Intermittent Fluctuations in the Alcator C-Mod Scrape-off Layer, J. Plasma Phys. 86 (2020), doi:10.1017/S0022377820001282.

R. Kube et al. Intermittent Electron Density and Temperature Fluctuations and Associated Fluxes in the Alcator C-Mod Scrape-off Layer, Plasma Phys. Control. Fusion 60 (2018), doi:10.1088/1361-6587/aab726.

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Stochastic processes and nonlinear dynamics

Excess statistics of intermittent signals

Supervisor: Audun Theodorsen, audun.theodorsen@uit.no

Required courses: FYS-3035

Recommended courses: STA-2001, STA-2003, FYS-2006

Background

Many physical and natural systems such as atmospheric winds, astrophysical plasmas and near-wall turbulence in magnetically confined plasmas are characterized by large-amplitude, intermittent fluctuations and display positively skewed and flattened probability densities. This rules out Gaussian statistics and transport of physical properties may be due to advection of coherent structures rather than diffusive processes. As a consequence, methods based on approximating the fluctuations as small-amplitude waves around an equilibrium or as random fluctuations around a mean value due to gradient-induced diffusion may fail or have very poor predictive powers. Using such methods may lead to misunderstanding of the physical processes and dangerous underestimation of the likelihood of large transport events.

A promising way to model such fluctuations is to use a stochastic model based on a superposition of independent pulses with random amplitudes, arriving according to a Poisson process. This so-called filtered Poisson process (FPP) is a linear model for investigating and describing the statistical properties of non-linear systems and takes large-amplitude fluctuations directly into account. The UiT Complex Systems Modelling group is using this model to describe turbulence in magnetically confined plasmas, effects of volcanoes on the climate and fluctuations in self-organized critical systems.

Scientific questions

Excess time statistics is a branch of higher-order statistics dealing with properties of a signal above a given threshold such as the rate of threshold crossings or the time spent above the threshold per crossing. The goal of this project is to find new results and to explore unanswered questions regarding the excess statistcs of the FPP, including:

  • Can we find the rate at which an FPP with Laplace distributed amplitudes crosses a threshold? Previous derivations disagree with numerical results.
  • Numerically, a special case of the FPP is seen to have exponentially distributed excess times. Can this be derived?

Methods

Mathematical derivations aided by software such as Mathematica, along with numerical realizations of the FPP for guidance and cross-validation.

References

H. Biermé and A. Desolneux, A fourier approach for the level crossings of shot noise processes with jumps, J. Appl. Prob. 49, 1 p. 100 (2012), doi: 10.1239/jap/1331216836E.

Daly and A. Porporato, Effect of different jump distribution on the dynamics of jump processes, Phys. Rev. E 81, 061133 (2010), doi: 10.1103/PhysRevE.81.061133A.

Theodorsen and O. E. Garcia, Level crossings and excess times due to a superposition of uncorrelated exponential pulses, Phys. Rev. E 97, 012110 (2018), doi: 10.1103/PhysRevE.97.012110

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Information geometry as a tool in plasma physics

Supervisor: Audun Theodorsen, audun.theodorsen@uit.no 

Required courses: FYS-3035 

Recommended courses: 

Background 

The concept of information geometry has been used in a number of studies on plasma turbulence, where it has been used to measure the time- and length scales of turbulent transport.

Originally, information geometry is a way of measuring the difference between distributions in different parameter regimes. In plasma physics, it is however used to measure flucuations in steady-state. This opens a number of unanswered questions regarding its usefullness. 

Research questions 

  • Which results already exist on information geometry for time series analysis in other domains? 
  • How does noise / periodic fluctuations affect information length? 
  • How does statistical uncertainty due to short time series affect information length? 
  • Does information length match other length or time scales in the system? 
  • Does it make sense to use information geometry to measure the transition to steady-state in a system?

Methods 

Literature survey of existing results, analysis of realizations of stochastic processes and analytical computations. 

References 

J. Anderson et. al., The Information Length Concept Applied to Plasma Turbulence, Entropy (2024), doi:10.3390/e26060494

J. Anderson et. al., Elucidating plasma dynamics in Hasegawa-Wakatani turbulence by information geometry, Phys. Plasmas (2020), doi:10.1063/1.5122865

G. Crooks, Measuring Thermodynamic Length, Phys. Rev. Lett. (2007), doi:10.1103/PhysRevLett.99.100602

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Information geometry in the Kuramoto-Sivashinsky equation

Supervisor: Audun Theodorsen, audun.theodorsen@uit.no 

Required courses: FYS-3035 

Recommended courses: 

Background 

The concept of information geometry has been used in a number of studies on plasma turbulence, where it has been used to measure the time- and length scales of turbulent transport.

Originally, information geometry is a way of measuring the difference between distributions in different parameter regimes. In plasma physics, it is however used to measure fluctuations in steady-state.  

The Kuramoto-Sivashinsky equation is a simple partial differential equation in 1+1D. It displays rich behavior with both periodic and chaotic solutions. It has chaotic attractors which are both homogeneous and non-homogeneous in space.

Research goals 

To elucidate the information geometrical difference between different parameter regimes and steady-state fluctuations for both homogeneous and non-homogeneous attractors of the Kuramoto-Sivashinsky equation. 

Methods 

Numerical simulation of the Kuramoto-Sivashinsky equation. Statistical analysis of solutions to the equation. 

References

J. Anderson et. al., The Information Length Concept Applied to Plasma Turbulence, Entropy (2024), doi:10.3390/e26060494

J. Anderson et. al., Elucidating plasma dynamics in Hasegawa-Wakatani turbulence by information geometry, Phys. Plasmas (2020), doi:10.1063/1.5122865

G. Crooks, Measuring Thermodynamic Length, Phys. Rev. Lett. (2007), doi:10.1103/PhysRevLett.99.100602

R. Wittenberg and P. Holmes, Scale and space localization in the Kuramoto-Sivashinsky equation, Chaos (1999), doi:10.1063/1.166419

D. Papageorgiou and S. Smyrlis, The route to chaos for the Kuramoto-Sivashinsky equation, Theor. Comp. Fluid. Dyn. (1991) doi:10.1007/BF00271514

J. Baez et. al., The Kuramoto–Sivashinky Equation, Not. Am. Mat. Soc. (2022), url

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