Summary

We will develop novel methods for probabilistic modeling and prediction in applications of Earth observation and ecology. For instance, we will estimate biophysical parameters and atmospheric parameters from remote sensing and time-series observations.

Project background

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 that we can model important biophysical parameters from space over time. Moreover, interactions between land and atmosphere also affect the weather. Thus, understanding and modeling these interactions through statistical models is of utmost importance for weather forecasting.

We focus in developing inferential tools for probabilistic spatio-temporal models with applications in Earth observation problems. We consider the challenging problem of estimating model parameters (e.g., biophysical parameters) from remote sensing (satellite) observations acquired across time. Just as an example, let us focus on 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 will propose novel computational methods to overcome current limitations of more traditional IS-based techniques in such a challenging context, e.g., IS methods for learning static parameters in high dimensional spaces [6] and extensions [7] to observational spaces with a big amount of data. Many applications in earth observation can benefit from these methodologies. See [5] and [8] for the application of recent IS methodological advances in remote sensing problems.

Research questions

In this project, we  focus on generic methodological questions for modeling and prediction of spatio-temporal processes in Earth applications. In particular:

• We aim at modeling effectively (realistic enough) processes such as vegetation evolution or climate change, and associated efficient predictions (computationally feasible).
• We also put a focus on rare-events estimation, i.e., the prediction of extreme events that can have a high socio-economic impact (e.g., extreme temperatures, droughts, deforestation, etc. ).
• We aim at designing novel grounded methods in statistical machine learning, computational statistics, and statistical signal processing, able to deal with large amount of data, provide uncertainty quantification metrics, and work in high-dimensional models (which are required for these ambitious applications).

Methodology

Spatio-temporal processes in Earth observation, ecology, and environmental sciences can be well described through statistical models that relate the sequential observed data to a dynamical hidden process through some unobserved static model parameters. These parameters are often interpretable and are essential for prediction purposes, also providing domain experts with further understanding. 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. 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.

The tentative timeline is as follows:

• 1st year: We will get used to common statistical models used across several biophysical and atmospheric application domains (e.g., frequentist approaches, such as GAMs and GLMs, and Bayesian approaches such as hierarchical models). We will identify limitations (e.g., not accounting  for spatial or dynamical interactions).
• 2nd: We will develop more ambitious models (richer, higher-dimensional, with uncertainty quantification, etc.), which will require novel computational methods to perform estimation. We will consider tailoring methods in machine learning and computational statistics, and/or developing new ones. While working in the applications mentioned in the proposal, we will put more emphasis in toy scenarios, low-dimensional models, and examples where we can get better insights so the designed models/methods are robust and explainable.
• 3rd: We will put a stronger focus on the applications discussed in this proposal. We will work jointly with experts in Geosciences, understanding the needs of such applications, and refining the methods to provide high-performance, interpretable solutions with uncertainty quantification.

Training

A comprehensive training programme will be provided comprising both specialist scientific training and generic transferable and professional skills.

Requirements

Essential:

– A Bachelor’s degree in Engineering, Statistics, Mathematics, Computer Science, Physics or similar.

– Programming ability in high-level scientific development language, e.g., MATLAB, Python, R.

– Some training in Bayesian modeling and Monte Carlo methods.

– High motivation, curiosity, and proactivity.

Desirable:

– Mathematical maturity with emphasis on estimation and inference.

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.