MPE CDT Student Cohort 2017

Elena Saggioro

Based at: University of Reading

Niraj Agarwal

Based at: Imperial College London

Mariana Clare

Based at: Imperial College London

George Chappelle

Based at: Imperial College London
Research project: Transit times and mean ages for non-autonomous and random compartmental systems with application to the terrestrial carbon cycle
Supervisors: Martin Rasmussen (Imperial College London, Department of Mathematics) and Valerio Lucarini (University of Reading, Department of Mathematics and Statistics)

Summary of project: Compartmental models play an important role in the modeling of many biological systems ranging from pharmacokinetics to ecology. Key values in understanding the dynamics of these systems are the transit time (the mean time a particle spends in the compartmental system), and the mean age (the mean age of particles still in the system). This project is motivated by an interest in studying the dynamics of the terrestrial carbon cycle which is typically modelled as a number of discrete pools of carbon in plant biomass, litter and soil organic matter. Many of the best studied models of the dynamics of carbon are linear, which reflects the fact that changes in carbon pools are proportional to the pool size. Perhaps the most well-known examples are studies of how terrestrial carbon dynamics respond to climate change. In these, it is often assumed that the specific rates (per unit carbon) of carbon inputs and losses from the system change over time as a function of changes in climate, such as temperature. For example, increases in temperature are normally assumed to increase the rates of soil decomposition. As a consequence, the compartmental models of interest are nonautonomous, i.e. they depend on time. Nonautonomous compartmental systems are special cases of linear nonautonomous differential equations, which, in contrast to the linear autonomous case, cannot be solved analytically in general. Yet, both the mean age of particles in the system and the transit time remain of great interest for these time-dependent systems, as both quantities can be potentially measured in the actual systems being modelled.
The first part of the project aims at extending the current results in this area to discrete time. The second part of the project aims at the analysis of transit times and mean ages of randomly perturbed nonautonomous compartmental systems. Here the transfer rates will be perturbed by bounded multiplicative noise, and an analysis of the structure and stability of the corresponding (random) mean age system will be achieved. Finally, the impact of noise on the crucial quantities will be studied theoretically and by means of a modified version of the Carnegie–Ames–Stanford approach (CASA) model, which is a nine-dimensional model for the terrestrial carbon cycle.

Stuart Patching

Based at: Imperial College London

Louis Sharrock

Based at: Imperial College London

Adriaan Hilbers

Based at: Imperial College London

Georgios Sialounas

Based at: University of Reading

Alexander Alecio

Based at: Imperial College London

Rhys Leighton Thompson

Based at: University of Reading

Manuel Santos

Based at: University of Reading

Leonardo Ripoli

Based at: University of Reading
Research project: Constructing Parameterisations for GFD systems – a comparative approach
Supervisor: Valerio Lucarini (Department of Mathematics and Statistics, University of Reading)
Co-advisor: Paul Williams (Department of Meteorology, University of Reading), Niklas Boers (Grantham Institute - Climate Change and the Environment, Imperial College London)

Description: The construction of parameterisation for multi-scale systems system is a key research area for GFD, because the dynamics of atmosphere and of the ocean covers a wide range of temporal and spatial scales of motion (Berner et al. 2017). Additionally, the variability of the geophysical fluids is characterized by a spectral continuum, so that it is not possible to define unambiguously a spectral gap separating slow from fast motions. As a result, usual mathematical methods based on homogeneization techniques cannot be readily applied to perform the operation of coarse graining. As shown in recent literature (Chekroun et al. 2015, Wouters and Lucarini 2012, 2013, Demayer and Vannitsem 2017, Vissio and Lucarini 2017), the lack of time scale separation leads unavoidably to the presence of non-markovian terms when constructing the effective equations for the slower modes of variability - which are those we want to explicitly represent - able to surrogate the effect of the faster scales - which are, instead, those we want to parameterise.
Two methods have been proposed to deal effectively and rigorously with this problem:
1) The direct derivation of effective evolution equations for the variables of interest, obtained through a perturbative expansion of the Mori-Zwanzig operator (Wouters & Lucarini 2012, 2013);
2) The reconstruction of the effective evolution equations for the variables of interest though an optimization procedure due to Kondrashov et al. (2015) and Chekroun et al. (2017).
Both methods (which we refer to as top-down and bottom-up, respectively) lead to the definition of parameterisation including a deterministic, a stochastic, and a non-markovian (memory effects) component. The two methods are conceptually analogous, but have never been compared on a specific case study of interest. The MSc project here proposed builds upon the earlier results of Vissio and Lucarini (2017) and deals with constructing and comparing the two parameterisation for the 2-level Lorenz ’96 system, which provides a classic benchmark for testing new theories in GFD. The goal will be to understand merits and limits of both parameterisations and to appreciate their differences in terms of precision, adaptivity, and flexibility.

Ben Ashby

Based at: University of Reading

Ieva Dauzickaite

Based at: University of Reading

Sebastiano Roncoroni

Based at: University of Reading

Marco Cucchi

Based at: University of Reading
Research project: Sensitivity of Extremes in Simplified Models of the Mid-latitude Atmospheric Circulation
MPE CDT Aligned student

Supervisors: Valerio Lucarini (lead supervisor) and Tobias Kuna

Project Abstract: In this project I’m going to investigate extreme events in simplified atmospheric models of the mid-latitudes using the point of view of Extreme Value Theory (EVT; Coles 2001). The idea here is to extend the work Felici et al. (2007a, 2007b), where it was first shown that EVT can be used to look at extremes generated by an atmospheric model, going beyond the diagnostic analysis, and taking advantage of the theoretical framework presented in Lucarini et al. (2016). I’m going to investigate the properties of extremes of observables where different levels of spatial and temporal coarse graining procedures are performed, so to understand the effect of averaging on our estimates of extremes. Additionally, statistics of extremes of coarse grained fields will be compared with what obtained running models with coarser resolution. Finally, I will investigate the response of the extremes to both time-independent and dependent perturbations affecting the dynamics, using response theory and pullback attractors. Throughout this work both deterministic and stochastic perturbations will be investigated, and results will be used for model error assessment and analysis of multiscale effects.
As a practical application, this work will lead to the definition of functions describing societal and economic impact of extreme climatic events, along with financial and insurance tools able to manage time-dependent risk assessment.

Jennifer Israelsson

Based at: University of Reading