# Sequential Bayesian inference for spatio-temporal probabilistic models of changes in global vegetation and ocean properties using Earth Observation data.

### This Project has been filled

The Earth’s vegetation is changing as a result of both human activity and climate change. Large scale shifts in vegetation will fundamentally alter terrestrial ecosystems, with a range of potential consequences – from impacts on biodiversity to altered carbon and hydrological cycling. In northern high latitudes plants are growing more as the climate warms, resulting in a “greening” of the land surface. Within the next 50 years the tundra biome is expected to become climatically suitable for trees, the boreal treeline is already shifting northwards and woody shrub abundance in tundra is increasing. These changes will have a profound impact on ecosystem function and climate feedbacks; while CO2 uptake from the atmosphere through photosynthesis is likely to increase, taller denser plant canopies will decrease the reflectivity of the land surface, resulting in greater warming. To understand the implications of changing vegetation distributions, it is vital we can model important biophysical parameters from space over time.

**A map of Leaf Area Index (LAI) produced by remote sensing. Leaf area varies greatly with seasons and between years, and differentiating long-term trends from short-term fluctuations and sensor calibration issues is difficult**

Similarly, ocean currents also vary on both short and long time scales, with attributing differences to longer-term trends, for example climate change, being difficult. It is known that the oceans play a central role in climate change, and are changing rapidly as they absorb large amounts of heat from the atmosphere, but it is often unclear how exactly that is playing out in current conditions.

These spatio-temporal problems can be described through statistical models that relate the sequential observed data to a dynamical hidden process through some unobserved static parameters. In the Bayesian framework, the probabilistic estimation of the unknowns is represented by the posterior distribution of these parameters. Learning those distributions is crucial not only for prediction/forecasting purposes but also for uncertainty quantification. Unfortunately, in most realistic models for earth observation problems, the posteriors of both static and dynamic parameters are intractable and must be approximated. Importance Sampling (IS)-based algorithms are Monte Carlo methods that have shown a satisfactory performance in many problems of Bayesian inference, both for inferring static parameters and the hidden states [1]. Particle filters (also called sequential Monte Carlo methods) are the de facto IS-based computational tools in this context. See [2] and [3] for two tutorials in adaptive IS and particle filtering, respectively.

In this project, we focus in developing inferential tools for probabilistic spatio-temporal models with applications in earth observation problems. We consider the challenging problem of estimating biophysical parameters from remote sensing (satellite) observations acquired across time. Just as an example, let us focus in the aforementioned problem where the estimation of the evolving Leaf Area Index (LAI) is key for forecasting the change of Earth’s vegetation. It is important to track evolution of LAI through time in every spatial position on Earth because LAI plays an important role in vegetation processes such as photosynthesis and transpiration, and is connected to meteorological/climate and ecological land processes [4, 5]. We also consider oceanography applications by considering complex dynamical models that require sophisticated inferential tools for learning the probabilistic estimates of the evolving states and also the unknown parameters of the model. We will propose novel computational methods in order to overcome current limitations of more traditional IS-based techniques in such a challenging context, including adaptive IS methods for learning static parameters in high dimensional spaces [6] and extensions of [7] to observational spaces with big amount of data. Many applications in earth observation can be benefited from the development of these methodologies. See [5] and [8] for the application of recent IS methodological advances in remote sensing problems.

During this thesis, on top of the collaborations with the institutions within the CDT (University of Edinburgh’s School of Mathematics and GeoSciences, the National Oceaonography Centre, and Space Intelligence Ltd), we will collaborate with one world-leading group in geoscience and remote sensing data at the University of Valencia (Spain), led by Prof. Gustau Camps-Valls [link]. The student will be based in the Univeristy of Edinburgh’s School of Mathematics, but travel to visit supervisors at the other locations.

References

[1] C. P. Robert and G. Casella, Monte Carlo Statistical Methods. Springer, 2004.

[2] M. F. Bugallo, V. Elvira, L. Martino, D. Luengo, J. Miguez, and P. M. Djuric, “Adaptive importance sampling: the

past, the present, and the future,” IEEE Signal Processing Magazine, vol. 34, no. 4, pp. 60–79, 2017.

[3] A. Doucet and A. M. Johansen, “A tutorial on particle filtering and smoothing: Fifteen years later,” Handbook of

nonlinear filtering, vol. 12, no. 656-704, p. 3, 2009.

[4] J. M. Chen and T. A. Black, “Defining leaf area index for non-flat leaves,” Plant, Cell & Environment, vol. 15, no. 4,

pp. 421–429, 1992.

[5] L. Martino, V. Elvira, and G. Camps-Valls, “Group importance sampling for particle filtering and mcmc,” Digital

Signal Processing, vol. 82, pp. 133–151, 2018.

[6] L. Martino, V. Elvira, D. Luengo, and J. Corander, “Layered adaptive importance sampling,” Stat. Comput., vol. 27,

no. 3, pp. 599–623, May 2017.

[7] V. Elvira, J. Miguez, and P. M. Djuric, “Adapting the Number of Particles in Sequential Monte Carlo Methods

Through an Online Scheme for Convergence Assessment,” IEEE Trans. Sig. Proc., vol. 65, no. 7, pp. 1781–1794,

2017.

[8] L. Martino, V. Elvira, and G. Camps-Valls, “The recycling gibbs sampler for efficient learning,” Digital Signal

Processing, vol. 74, pp. 1–13, 2018.