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Efficient spatio-temporal modelling and interpolation of Global Sea Surface Height

   School of Mathematical Sciences

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  Dr Arthur Guillaumin  No more applications being accepted  Funded PhD Project (Students Worldwide)

About the Project

The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing in September 2022.

Big environmental data combined with modern data science offer a key opportunity to better understand our environment and address climate change. Yet environmental data poses specific challenges due to spatio-temporal dependence: 1. Modelling. Most models of spatio-temporal dependence are homogenous, which in general is not an accurate description of real-world phenomena. 2. Estimation. More complex parametric models of covariance are often not amenable to estimation via exact likelihood due to computational inefficiency and lack of robustness to model misspecification. 

In this project, you will develop new parametric covariance models and estimation methods for the analysis of Sea Surface Height (SSH). The surface height of the oceans is monitored by passing satellites on a global scale. The modelling of SSH is vital to a better understanding of the global climate and to making more accurate interpolation via kriging [1].

Firstly, your research will focus on estimating the parameters of a spatial covariance model of Sea Surface Height. You will pursue recent developments in quasi-likelihood estimation [2, 3, 4, 5, 6] for spatio-temporal data to propose a parametric estimation method that is both computationally and statistically efficient. The idea behind quasi-likelihood estimation is to maximize a computationally efficient approximation to the exact likelihood.

Secondly, you will develop more advanced parametric models of covariance that can incorporate some additional physical phenomena that drive SSH. Possible directions for this part of the project range from relaxing the assumption of spatial homogeneity [7], to modelling temporal dependence and seasonal patterns [8]. These methodological developments can also have an impact in other application areas such as econometrics.

This project will be in collaboration with C. Wortham and J. Early, NorthWest Research Associates, Seattle, USA, who have been granted funding by the NASA to develop mapping software for SSH. 

The application procedure is described on the School webpage: For further inquiries please contact [Email Address Removed]. This project is eligible for full funding through QMUL Principal's Postgraduate Research Studentships. Studentships will cover tuition fees, and a stipend at standard rates for 3-3.5 years, additional funds for conference and research visits and funding for relevant IT needs. Applicants will have to participate in a highly competitive selection process. The School of Mathematical Sciences is committed to the equality of opportunities and to advancing women’s careers. As holders of a Bronze Athena SWAN award we offer family friendly benefits and support part-time study.

Funding Notes

For September 2022 entry: Funding is available through QMUL Principal's Postgraduate Research Studentships. Studentships will cover tuition fees and a stipend at the UKRI London rate (c.£17,609 p.a. full-time, £8,804 part-time; 2022/23 rates tbc) for 3.5 years. International (including EU) applicants are eligible for UK tuition fees; however international fees are substantially higher. We are able to recruit a limited number of international (maximum 30% of intake). Due to this cap, we are unable to guarantee places to any/all international applicants.
We welcome applications for self-funded applicants year-round, for a January, April or September start.


1. Stein, M. L. (1999). Interpolation of Spatial Data: Some Theory for Kriging. 1st ed., Springer Series in Statistics, Springer.
2. Sykulski A. M., Olhede S. C., Guillaumin A. P., Lilly J. M., Early J. J (2019). The Debiased Whittle Likelihood. Biometrika 106(2), 251–266.
3. Guillaumin A. P., Sykulski A. M., Olhede S. C., Simmons F. V. (2022). The Debiased Spatial Whittle Likelihood. Journal of the Royal Statistical Society: Series B (under review).
4. Guinness J. (2018). Permutation and Grouping Methods for Sharpening Gaussian Process Approximations. Technometrics 1706, 1-15.
5. Guinness J, Fuentes M. (2017). Circulant Embedding of Approximate Covariances for Inference from Gaussian Data on Large Lattices. Journal of Computational and Graphical Statistics 26(1), 88-97.
6. Fuentes M. (2007). Approximate likelihood for large irregularly spaced spatial data. Journal of the American Statistical Association 102(477), 321-331.
7. Matsuda, Y., Yajima, Y. (2018). Locally stationary spatio-temporal processes. Japanese Journal of Statistics and Data Science 1, 41–57.
8. Napolitano A. (2016). Cyclostationarity: New trends and applications. Signal Processing 120, 385-408.

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