Taylor’s law in satellite time series of vegetation productivity

Background: Taylor’s law is considered a semi-natural-law and originally comes from ecology. It describes how the variance of a quantity grows with its mean, following variance = a · mean^b. It was first found for insect and animal counts, but it also shows up in many other data. The exponent b tells us something about stability. If b is below 2, places with high values fluctuate less, relative to their mean, than places with low values. With Landsat data back to 1985, this can be tested for vegetation at every pixel.

Short description: The thesis tests Taylor’s law with long satellite time series of vegetation, for example from Landsat. For each pixel, a robust yearly vegetation measure is derived, and its mean and variance over the years are calculated. The relationship between mean and variance across all pixels then gives the exponent b. Comparing b between land cover types, regions or elevation zones shows where vegetation is more or less stable. Part of the work is to check how far the results depend on the choice of vegetation index and on the number of available observations.

Taylor’s law from satellite time series (schematic). Each Landsat pixel becomes one point, and the slope b shows how variability scales with productivity.

Suggested reading

Taylor, L. R. (1961). Aggregation, variance and the mean. Nature, 189, 732–735. https://www.nature.com/articles/189732a0

Badgley, G., Field, C. B., & Berry, J. A. (2017). Canopy near-infrared reflectance and terrestrial photosynthesis. Science Advances.

Vadrevu, K. (2026): Power law scaling reveals systemic divergence in fire risk across South and Southeast Asian countries. Environmental Research Letters. 10.1088/1748-9326/ae962a

Start: Anytime

Prerequisites/qualification

·        Remote Sensing & GIS

·        Basic programming skills

·        Good basic statistics (regression, power laws)

·        Interest in ecology

Storing Sentinel-2 time series in neural networks: Implicit neural representations

Background: Satellite data are usually stored as a grid with one value per pixel. Implicit neural representations (INRs) instead treat the data as a function of location and time and train a neural network to learn it. You give the network a location and a date, and it returns the values for that place and time. This can save a lot of storage, but the network only stores an approximation. Its quality is usually judged by a single number, the average reconstruction error. What this number hides, which information is lost and where, is largely unknown.

Source: https://gkvoelkl.github.io/python-streamlit-neural-earth-field/en/01-geodaten-als-funktion.html

Short description: The thesis trains an INR on a Sentinel-2 time series of a chosen region and compares the reconstruction with the original data, pixel by pixel and date by date. The aim is to find out what gets lost. Possible candidates are sudden changes (e.g., a meadow mown on a specific date that shows a sharp drop in NDVI), small objects such as single buildings or ponds or extreme values such as the peak of the growing season. The result is a clear picture of which information an INR keeps and which it does not.

Suggested reading

Sitzmann, V., Martel, J., Bergman, A., Lindell, D., & Wetzstein, G. (2020). Implicit neural representations with periodic activation functions. Advances in Neural Information Processing Systems, 33, 7462–7473.

Madadikhaljan, M., Prexl, J., Wittmann, I., Albrecht, C. M., & Schmitt, M. (2026). Location Is All You Need: Continuous spatiotemporal neural representations of Earth observation data. arXiv:2604.07092.

https://gkvoelkl.github.io/python-streamlit-neural-earth-field/en/01-geodaten-als-funktion.html

Start: Anytime

Prerequisites/qualification: This topic is technically demanding and suits students who enjoy coding and have trained neural networks before.

·        Remote Sensing

·        Very good Python skills and experience with PyTorch

·        Experience training neural networks

Observation density and apparent greening trends in pretrained EO embeddings of alpine ecosystems

Background: Pretrained embeddings such as TESSERA or AlphaEarth Foundations summarise a year of satellite observations in one vector per pixel. Yet the number of clear observations behind each embedding varies between places and years. Bayle et al. (2024) showed that Landsat-based greening trends in the Alps were overestimated because the number of summer observations increased over time. Whether embeddings show the same artefact has not been tested, and in embeddings it could easily go unnoticed.

Short description: The thesis transfers the idea of Bayle et al. to embeddings of alpine vegetation from 2017 onwards. Greening trends are calculated from NDVI and from embeddings for the same pixels, for example along a “greenness axis” in embedding space. A locally runnable model such as TESSERA is then fed with time series that have the same number of observations each year. If trends shrink, part of the greening comes from the data rather than the vegetation. Bare rock serves as a control.

 

Processing chain from satellite remote sensing measuring of Earth's surface reflectance to pixelwise greening trends. What happens if we reconstruct this approach with embeddings? Figure source: Bayle, A. (2026)

Suggested reading:

Bayle, A., Gascoin, S., Berner, L. T., & Choler, P. (2024). Landsat-based greening trends in alpine ecosystems are inflated by multidecadal increases in summer observations. Ecography, 2024(12), e07394. https://doi.org/10.1111/ecog.07394

Bayle, A. (2026): Satellite Remote Sensing of Alpine Vegetation Dynamics: Challenges and Perspectives. Global Change Biology, https://doi.org/10.1111/gcb.70968

Feng, Z., Atzberger, C., Jaffer, S., Knezevic, J., Sormunen, S., Young, R., et al. (2025). TESSERA: Temporal Embeddings of Surface Spectra for Earth Representation and Analysis. arXiv:2506.20380. https://doi.org/10.48550/arXiv.2506.20380

Start: Anytime

Prerequisites/qualification

• Remote Sensing & GIS
• Good Python skills
• Good basic statistics (e.g., trend analysis)

Measuring ecosystem recovery with spectral indices, fractional cover and semantic categories

Background: After a disturbance such as a landslide, a fire, an avalanche or a wind-throw, satellite data are often used to track how quickly vegetation returns. A common measure is vegetation cover, but it can be described in very different ways. A spectral index such as NDVI gives a unitless value, spectral unmixing gives the share of vegetation in each pixel, and semantic approaches assign a knowledge-based vegetation category. These approaches exist side by side but are rarely compared. Depending on which one is used, the same surface may appear recovered after three years or only after ten.

Schematic figure of ecosystem recovery, here with tree cover as a proxy. How do recovery intervals differ for spectral indices, fractional cover and a semantic approach? Figure source: Mandl et al., 2024

Short description: The thesis tracks recovery on disturbed areas in a region of choice with Sentinel-2 or Landsat time series. Vegetation cover is described in three ways, as NDVI, as vegetation fraction from unmixing, and as the corresponding semantic vegetation category. For each area, recovery is measured as the time until vegetation reaches its pre-disturbance level or a fixed threshold. Very high resolution imagery from different years serves as reference. The result shows how strongly recovery estimates depend on the chosen measure and where the approaches disagree, for example with sparse, dry or patchy vegetation.

Suggested reading

Mandl, L., Viana-Soto, A., Stritih, A., Seidl, R., & Senf, C. (2024). Spectral-unmixing based forest recovery indicators for predicting long-term recovery success. Remote Sensing of Environment. https://doi.org/10.1016/j.rse.2024.114194

Okujeni, A., van der Linden, S., Tits, L., Somers, B., & Hostert, P. (2013). Support vector regression and synthetically mixed training data for quantifying urban land cover. Remote Sensing of Environment, 137, 184–197. https://doi.org/10.1016/j.rse.2013.06.007

Sudmanns, M., Augustin, H., van der Meer, L., Baraldi, A., & Tiede, D. (2021). The Austrian semantic EO data cube infrastructure. Remote Sensing, 13(23), 4807. https://doi.org/10.3390/rs13234807

Start: Anytime

Prerequisites/qualification: 

·        Remote Sensing & GIS

·        Basic programming

·        Interest in ecosystem dynamics

Three-dimensional surface information in pretrained EO embeddings

Suggested by: Lisa Mandl

Background: Embeddings are derived from images taken from above, but these images contain indirect information about height, such as shadows, texture or radar backscatter from building walls. It is unclear whether embeddings keep this information or mainly encode the land cover type that usually goes with a certain height. AlphaEarth Foundations combines many data sources, including spaceborne lidar, and uses spatial context. TESSERA works pixel by pixel on Sentinel-1 and Sentinel-2 time series.

Short description: The thesis tests how much height information AlphaEarth Foundations and TESSERA embeddings contain, using airborne laser scanning (ALS) data (where available) as reference. Simple models are trained on the embeddings to predict object heights, with classical Sentinel-1 and Sentinel-2 features as a baseline. The key question is whether embeddings capture height differences within a class (e.g., low vs. high buildings) or only between classes. Study area and objects (e.g. buildings, vegetation) are flexible.

Building height map, here for Berlin. How much of height information is stored in geospatial embeddings? Data source: https://zenodo.org/records/4066295#.X4QRNmgzYmI

Suggested reading

Brown, C. F., Kazmierski, M. R., Pasquarella, V. J., Rucklidge, W. J., Samsikova, M., Zhang, C., et al. (2025). AlphaEarth Foundations: An embedding field model for accurate and efficient global mapping from sparse label data. arXiv:2507.22291.

Feng, Z., Atzberger, C., Jaffer, S., Knezevic, J., Sormunen, S., Young, R., et al. (2025). TESSERA: Temporal Embeddings of Surface Spectra for Earth Representation and Analysis. arXiv:2506.20380. https://doi.org/10.48550/arXiv.2507.22291

Frantz, D., Schug, F., Okujeni, A., Navacchi, C., Wagner, W., van der Linden, S., & Hostert, P. (2021). National-scale mapping of building height using Sentinel-1 and Sentinel-2 time series. Remote Sensing of Environment, 252, 112128. https://doi.org/10.1016/j.rse.2020.112128

Start: As soon as possible

Prerequisites/qualification

• Remote Sensing
• Good Python skills + basic machine learning
• Interest in the topic 

Virtual pasture ABM

suggested by: Gudrun Wallentin

Background 

This research accompanies the revitalisation of a traditional alpine cattle pasture “Vierkaseralm” on Untersberg near Salzburg City. The study area was abandoned by the last farmer in 1958, since then shrubs (mainly Pinus mugo) have encroached the former grasslands. In summer 2021 the pasture was revived, the cattle got GPS devices and the area was scanned with a UAV. The data that have been collected since then provide a unique opportunity for scientific monitoring of pasture revitalisation.

Short description

This thesis aims to use agent-based simulation modelling to gain a better understanding of the cattle-grassland interaction dynamics following an alpine pasture revitalisation project. The available reference model will be modified, calibrated and validated with the cattles' GPS data and other available datasets in a pattern-oriented modelling approach, also using data-driven optimisation paradigms. Based on this reference model, the thesis will use scenario-based reserach to simulate alternative agro-ecological management strategies and / or test assumptions on cattle behaviour and vegetation dynamics. 

 

Suggested reading

Wallentin (2026) "Spatial Simulation" eBook

Start

anytime

Prerequsites/qualification
Interest in the topic. On-site involvement in the revitalisation activities is possible and highly welcome.

Utilizing Tracking Data to Create Defensive Performance Indicators for Football Players

Suggested by: Philip Schnittkamp, https://www.plaier.com/

Supervisor: Christian Neuwirth 

Short description: Football (or otherwise known as soccer) is one of the most complex sports to analyze with data. The low-scoring nature of the sport, as well as the fact that 22 players are active on a huge pitch at the same time, are just some of the reasons for the huge complexity of modeling team and player strengths. While the analysis of so-called event data has taken huge strides over the last years and is arguably especially helpful when analyzing the individual performance of attacking players, the rise of tracking data allows for much more complex spatio-temporal analysis on both the collective (team) and individual (player) level. Since then, public research has often concentrated on analyzing offensive patterns such as attacking pitch control, passing decision optimization, or off-ball runs to create space. Although there have also been major advances in analyzing defensive patterns like pressing efficacy or defensive compactness, there are still enough areas on the defensive side that remain un- or at least underexplored, especially on the individual player level.

The main idea of this master thesis is to further develop upon existing ideas and models to measure defensive player performance based on tracking data, specifically in terms of optimal defensive positioning to suppress the opposition’s threat. The utilization of several different statistical methods is conceivable to achieve this goal: already existing pitch control frameworks, neural nets, agent-based modelling approaches, etc. While the ultimate goal is to create a defensive performance measure on the individual player level, this is inevitably connected to the team level: Any good individual performance measure should, in the best case, lead to team success in the end to demonstrate its validity.

The following research questions should guide the analysis:

• Which players (and teams) are effective in hindering their opponents from spatio-temporally controlling the most dangerous areas of the pitch?
• What are the optimal defensive positions each player can take on to suppress the opposition’s threat based on their teammates’ and opponents’ positioning at any given time?
• Which players (and teams) are effective in taking on (close to) optimal positions on the defensive side? Which players (and teams) are effective in lowering opponent threat in comparison to expectation based on the opponent’s usual performances?
• Can a team’s defending style influence these results? And does it make sense to quantify this based on different areas of the pitch and/or different phases of defending?
• Are some players better at positioning themselves optimally in different areas of the pitch and/or different phases of defending?
• Are teams that are more effective in terms of defensive positioning better at hindering opponents from scoring goals? Are they more successful overall?

Start/finish: Anytime.

Prerequisites/qualifications: Experience with coding in Python (preferrable) or R is required. Personal interest and at least basic knowledge in football would be highly beneficial.

Suggested reading:

• Spearman, W. (2016, February). Quantifying pitch control. In OptaPro Analytics Forum [Internet]. https://doi.org/10.13140/RG.2.2.22551.93603.
• Fernández, Javier & Bornn, Luke. (2018). Wide Open Spaces: A statistical technique for measuring space creation in professional soccer.
• Higgins, Lewis & Galla, Tobias & Prestidge, Brian & Wyatt, Terry. (2023). Measuring the pitch control of professional football players using spatiotemporal tracking data. Journal of Physics: Complexity. 4. https://doi.org/10.1088/2632-072X/acb67d.
• Spearman, W. (2018, February). Beyond expected goals. In Proceedings of the 12th MIT sloan sports analytics conference (pp. 1-17).
• Peters, Andrew & Parmar, Nimai & Davies, Michael & James, Nic. (2026). Applying an Expected Pass Turnovers model to inform pressing strategies in professional football. International Journal of Performance Analysis in Sport. 1-16. https://doi.org/10.1080/24748668.2026.2671547.
• Forcher, L., Beckmann, T., Wohak, O., Romeike, C., Graf, F., & Altmann, S. (2024). Prediction of defensive success in elite soccer using machine learning - Tactical analysis of defensive play using tracking data and explainable AI. Science and Medicine in Football, 8(4), 317–332. https://doi.org/10.1080/24733938.2023.2239766
• Forcher, L., Forcher, L., Altmann, S., Jekauc, D., & Kempe, M. (2024). Is a compact organization important for defensive success in elite soccer? – Analysis based on player tracking data. International Journal of Sports Science & Coaching, 19(2), 757-768.
• Forcher, L., Altmann, S., Forcher, L., Jekauc, D., & Kempe, M. (2022). The use of player tracking data to analyze defensive play in professional soccer - A scoping review. International Journal of Sports Science & Coaching, 17(6), 1567-1592.

 

Next-Generation EO Archive Storage: Evaluating Zarr and Icechunk for Temporal Access Efficiency and Data Maintainability in Sen2Cube.at

 Suggested by: Luke McQuade, Martin Sudmanns

Short description

Assess Zarr + Icechunk as a future storage option for Sen2Cube

Cloud-optimized GeoTiff (COG) is now an established format for archived EO data, offering reduced data transfer costs when afforded by the user requirements, e.g., area of interest (spatial subsetting) and spatial resolution (overviews/pyramids). However, there are downsides to this format. Typically, COGs are stored as a collection of files - one for each acquisition - and for time series analyses, this means having to open several files, and make several network requests, for even tiny AoIs.

Zarr is a recent alternative, offering chunking across the time dimension as well (and others). Could this be an improvement over COG for Sen2Cube?

Even though data are treated as historical as soon as they enter an archive, occasionally defects are encountered and have to be rectified, or enhancements (to metadata especially) must be made. Icechunk offers a solution for making such changes without having to reprocess lots of data. Could this be used, in conjunction with Zarr, to improve the updateability of Sen2Cube?

Start

As soon as possible

Prerequisites/qualification

• Remote Sensing & GIS
• Programming (e.g., Python)
• Interest in the topic 

Semantic vs. Index-Based Bare Soil Mapping from Sentinel-2 Time Series: A Comparative Analysis Using Sen2Cube.at

 Suggested by: Dirk Tiede, Martin Sudmanns

Bare soil mosaic calculation based on semantic categorie in a semantic EO data cube

Short description

Mapping of bare soil exposure across agricultural landscapes is essential for monitoring soil erosion risk, estimating carbon stocks, and evaluating the effectiveness of soil conservation practices such as cover cropping. Reliable and temporally dense bare soil information furthermore provides the foundation for downstream tasks like soil organic carbon modelling and cropland management assessment at regional to national scales.

This thesis topic proposes to investigate whether semantic, knowledge-driven classification within the Sen2Cube.at Earth observation data cube framework can produce comparable bare soil composites from Sentinel-2 time series in contrast to conventional index- and threshold-based approaches. Rather than relying on normalised spectral indices such as NDVI or NBR2 - which lose absolute reflectance intensity, are influenced by clouds and may misclassify sparsely vegetated or mixed pixels as bare soil - the semantic approach encodes expert knowledge about surface conditions directly into the classification logic, potentially leveraging the full spectral profile of each observation. The resulting bare soil composites will be compared against established index-threshold products, such e.g. as the soil spectral suite developed at DLR, using both quantitative accuracy assessment against reference data and a qualitative analysis of how each method handles spectrally ambiguous surfaces. The comparison will specifically examine whether it produces more temporally consistent composites under varying conditions and different time periods.

Suggested reading

Sudmanns, M., Augustin, H., van der Meer, L., Baraldi, A., & Tiede, D. (2021). The Austrian semantic EO data cube infrastructure. Remote Sensing, 13(23), 4807. https://www.mdpi.com/2072-4292/13/23/4807

Heiden, U., d’Angelo, P., Schwind, P., Karlshöfer, P., Müller, R., Zepp, S., Wiesmeier, M., & Reinartz, P. (2022). Soil Reflectance Composites—Improved Thresholding and Performance Evaluation. Remote Sensing, 14(18), 4526. DOI: 10.1016/j.rse.2017.11.004

Start

As soon as possible

Prerequisites/qualification

• Remote Sensing & GIS
• Basic Scripting/Programming (e.g., Python)
• Interest in the topic 

Spatial Performance Indicators for Parcel Pickup Stations

Suggested by: Martin Loidl

Short description: Parcel delivery systems increasingly rely on decentralised pickup stations whose performance and sustainability depend strongly on their spatial setting. Identifying suitable locations requires a detailed understanding of the spatial context and accessibility of potential locations.
This master thesis focuses on developing a spatial, data-driven approach to analyse and evaluate locations for parcel pickup stations. It includes compiling a comprehensive geodata inventory and applying accessibility modelling to assess site quality for walking, cycling, public transport, and motorised modes. Visual and analytic methods will be used to identify relationships between spatial structure, usage patterns, and CO2-reduction potential. The thesis may also involve developing or adapting automated GIS workflows for location scoring, or analysing the effect of different location types (e.g., residential areas, retail clusters, transportation hubs) on expected user behaviour.

By Matti Blume - Own work, CC BY-SA 4.0
https://commons.wikimedia.org/w/index.php?curid=69491925

Research for this master thesis should address one or more of the following questions (but is not limited to):

• Which spatial, infrastructural, and demographic characteristics define high-quality locations for parcel pickup stations?
• How can multimodal accessibility be modelled to support objective and comparable assessment of potential locations?
• How do different location types influence usage patterns and the potential reduction of motorised delivery trips?

References, suggested reading:

• PRANDTSTETTER, M., SERAGIOTTO, C., BRAITH, J., EITLER, S., ENNSER, B., HAUGER, G., HOHENECKER, N., SCHODL, R. & STEINBAUER, M. 2021. On the Impact of Open Parcel Lockers on Traffic. Sustainability, 13, 755. doi:10.3390/su13020755 
• NIEMEIJER, R. & BUIJS, P. 2023. A greener last mile: Analyzing the carbon emission impact of pickup points in last-mile parcel delivery. Renewable and Sustainable Energy Reviews, 186, 113630. doi:10.1016/j.rser.2023.113630 
• VAN DER MEER, L., WERNER, C. & LOIDL, M. 2024. Assessment of bicycle accessibility to mobility hubs under different criteria for cycling network quality. AGILE GIScience Ser., 5, 48. doi: 10.5194/agile-giss-5-48-2024
• OZYAVAS, P., BUIJS, P., URSAVAS, E. & TEUNTER, R. 2025. Designing a sustainable delivery network with parcel locker systems as collection and transfer points. Omega, 131, 103199. doi:10.1016/j.omega.2024.103199

Start/finish: anytime

Prerequisites/qualifications: Interest in spatial analysis, mobility behaviour, and data-driven urban logistics. Experience with GIS and data management is required; scripting skills (Python, R) are beneficial for automated workflows.