Synopsis: Develop a spline approximation framework for spatio-temporal environmental monitoring at global scales.
Level: Bachelor/Master (including Master Thesis).
Description: One aid towards addressing the current environmental crisis consists in building a “digital twin” of the Earth. The latter would take the form of an exhaustive computer simulation relying on past and current data from global Earth observatory networks, so as to assess the planet’s current and future health. This digital twin would serve as a central authority on environmental matters, allowing scientists and policy-makers to propose quantitative and efficient environmental policies supported by scientific evidence. It would also empower citizens around the world by openly distributing maps and other augmented data products providing easily interpretable and data-driven answers to rising public concerns about environmental and health issues.
To ingest instrumental data of various types as well as potentially non uniform precisions or spatiotemporal coverages, the Earth digital twin will need to resort to novel data enrichment and homogenization techniques. Such techniques include for example the spherical spline approximation framework provided in , which demonstrates how physical phenomena of interest in environmental sciences can be efficiently approximated at any location on the Earth using only finitely many discrete and potentially corrupted measurements (such as regional averages or spatial samples at specific locations). This approximation framework is however currently limited to instantaneous measurements, and is not well-suited for dynamic spherical fields with strong temporal variations.
The goal of this project is hence to extend the spline approximation framework of  to spatio-temporal spherical fields. The novel approximation framework will be tested on live in-situ surface temperature measurements from more than 20,000 weather stations, ship- and buoy-based observations of sea surface temperatures, and temperature measurements from Antarctic research stations.
 Matthieu Simeoni, Functional Inverse Problems on Spheres: Theory, Algorithms and Applications, PhD Thesis, Swiss Federal Institute of Technology Lausanne (EPFL), under the supervision of Profs. M. Vetterli, V. Panaretos and P. Hurley, 2019.
Deliverables: A spatio-temporal spline approximation framework for time-varying spherical fields, a Python 3 implementation of the framework for the specific case of temperature anomalies, an interactive web map of global temperature anomalies (similar to this map) with higher spatio-temporal resolution than NASA’s map released on January 15, 2020.
Prerequisites: Good knowledge of Python 3 (and more specifically numerical computing packages such as Numpy). Strong mathematical skills and a taste for abstraction and rigorous mathematics. Some previous knowledge of functional analysis, approximation theory, inverse problems or sparse recovery is a plus.
Type of Work: ~50% theory, ~50% programming. Can be adapted depending on the student’s profile/skills.