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Mathematical and computational methods for Earth System Modeling

   Department of Earth Sciences

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  Prof Samar Khatiwala, Prof C Cartis  No more applications being accepted  Competition Funded PhD Project (Students Worldwide)

About the Project

Numerical models are one of the key tools for understanding the climate system and predicting its future evolution under anthropogenic forcing. However, as these models get more complex, they also become far more computationally expensive, limiting scientists’ ability to perform simulations and make more effective use of them. It also increases the need to better calibrate the models against data. To addresses these challenges, one or more projects is available to develop novel mathematical and numerical techniques, and apply them to a range of problems in ocean and climate science. The ultimate goal is efficient and scalable software implementations that can be used in state-of-the-art climate models of the kind participating in the IPCC assessments.

The student(s) will be co-supervised by Profs. Samar Khatiwala in Earth Sciences ([Email Address Removed]) and Coralia Cartis in the Mathematical Institute ([Email Address Removed]). While the specific project will depend on the interests of the student, topics include: Newton-Krylov and vector sequence acceleration methods; fast PDE solvers; derivative-free parameter optimization; surrogate modeling and low rank approximations of complex systems via linear sketching; and machine learning. Of particular interest are applications to oceanography, marine biogeochemistry, and climate modeling, for example, ocean heat and carbon uptake, the ocean biological pump, and climate sensitivity.

Students with a strong first degree in natural sciences, mathematics, computer science or other engineering fields are encouraged to apply.

Full funding is available via the Environmental Research Doctoral Training Partnership at the University of Oxford ( See and for details on how to apply. Cite Project EARTH-23-SK1 when applying.

Funding Notes

This project can be applied for via the Oxford Environmental Research Doctoral Training Partnership, which has funding. See here for how to apply:
Please only apply via Do not email us your CV.


References & Further Reading
Anderson, D. G. (1965). Iterative procedures for nonlinear integral equations. J. Assoc. Comput. Mach.,
Khatiwala, S. (2008): Fast spin up of ocean biogeochemical models using matrix-free NewtonKrylov, Ocean Modell.,
Fang, H. and Y. Saad (2009). Two classes of multisecant methods for nonlinear acceleration. Numer. Linear Algebra Appl.,
Woodruff, D. P. (2014): Sketching as a tool for numerical linear algebra,
Brezinski et al. (2018). Shanks sequence transformations and Anderson acceleration. SIAM Rev.,
Cartis, C. et al. (2019): Improving the flexibility and robustness of model-based derivative-free optimization solvers, ACM T. Math. Software,
Khatiwala et al. (2019): Air-sea disequilibrium enhances ocean carbon storage during glacial periods, Sci. Adv.,
d'Aspremont et al. (2021): Acceleration Methods,
Khatiwala, S. (2022): Fast spin-up of radiocarbon and other geochemical tracers in ocean models, J. Adv. Model. Earth Sys.,
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