Statistical Emulation for Environmental Sustainability Analysis

The potential effects of climate change on the environment and society are many. In order to effectively quantify the uncertainty associated with these effects, highly complex simulation models are run with detailed representations of ecosystem processes. These models are computationally expensive and can involve computer runs of several days for their outputs. Computationally cheaper models can be obtained from large ensembles of simulations using a statistical emulation. The purpose of this thesis is to construct cheaper computational models (emulators) from simulation outputs of Lund-Potsdam-Jena-managed Land (LPJmL) which is a dynamic global vegetation and crop model. This research work is part of a project called ERMITAGE. The project links together several key component models into a common framework to better understand how the management and interaction of land, water and the earth’s climate system could be improved. The thesis focuses specifically on emulation of major outputs from the LPJmL model; carbon fluxes (NPP, carbon loss due to heterotrophic respiration and fire carbon) and potential crop yields (cereal, rice, maize and oil crops). Future decadal changes in carbon fluxes and crop yields are modelled as linear functions of climate change and other relevant variables. The emulators are constructed using a combination of statistical techniques of stepwise least squares regression, principal component analysis, weighted least squares regression, censored regression and Gaussian process regression. Further modelling involves sensitivity analyses to identify the relative contribution of each input variable to the total output variance. This used the Sobol global sensitivity method. The data cover the period 2001-2100 and comprise climate scenarios of several GCMs and RCPs. Under cross validation the percentage of variance explained ranges from 52-96% for carbon fluxes, 60-88% for the rainfed crops and 62-93% for the irrigated crops, averaged over climate scenarios

A surrogate-based approach to modelling the impact of hydrodynamic shear stress on biofilm deformation

The aim is to investigate the feasibility of using a surrogate-based method to emulate the deformation and detachment behaviour of a biofilm in response to hydrodynamic shear stress. The influence of shear force and growth rate parameters on the patterns of growth, structure and resulting shape of microbial biofilms was examined. We develop a novel statistical modelling approach to this problem, using a combination of Bayesian Poisson regression and dynamic linear models for the emulation. We observe that the hydrodynamic shear force affects biofilm deformation in line with some literature. Sensitivity results also showed that the shear flow and yield coefficient for heterotrophic bacteria are the two principal mechanisms governing the bacteria detachment. The sensitivity of the model parameters is temporally dynamic, emphasising the significance of conducting the sensitivity analysis across multiple time points. The surrogate models are shown to perform well, and produced ~480 fold increase in computational efficiency. We conclude that a surrogate-based approach is effective, and resulting biofilm structure is determined primarily by a balance between bacteria growth and applied shear stress

Statistical emulation as a tool for analysing complex multiscale stochastic biological model outputs

The performance of credible simulations in open engineered biological frameworks is an important step for practical application of scientific knowledge to solve real-world problems and enhance our ability to make novel discoveries. Therefore, maximising our potential to explore the range of solutions at frontier level could reduce the potential risk of failure on a large scale. One primary application of this type of knowledge is in the management of wastewater treatment systems. Efficient optimisation of wastewater treatment plant focuses on aggregate outcomes of individual particle-level processes. One of the crucial aspects of engineering biology approach in wastewater treatment study is to run a high complex simulation of biological particles. This type of model can scale from one level to another and can also be used to study how to manage real systems effectively with minimal physical experimentation. To identify crucial features and model water treatment plants on a large scale, there is a need to understand the interactions of microbes at fine resolution using models that could provide the best available representation of micro scale responses. The challenge then becomes how we can transfer this small-scale information to the macroscale process in a computationally efficient and sufficiently accurate way. It has been established that the macro scale characteristics of wastewater treatment plants are the consequences of microscale features of a vast number of individual particles that produce the community of such bacterial (Ofiteru et al. 2014). Nevertheless, simulation of open biological systems is challenging because they often involve a large number of bacteria that ranges from order 1012 to 1018 individual particles and are physically complex. The models are computationally expensive and due to computing constraints, limited sets of scenarios are often possible. A simplified approach to this problem is to use a statistical approximation of the simulation ensembles derived from the complex models which will help in reducing the computational burden. Our aim is to build a cheaper surrogate of the Individual- based (IB) model simulation of biological particle. The main issue we address is to highlight the strategy for emulating high-level summaries from the IB model simulation data. Our approach is to condense the massive, long time series outputs of particles of various species by spatially aggregating to produce the most relevant outputs in the form of floc and biofilms aggregates. The data compression has the benefit of suppressing or reducing some of the nonlinear response features, simplifying the construction of the emulator. Some of the most interesting properties at the mesoscale level like the size, shape, and structure of biofilms and flocs are characterised, see Figure 1. For instance, we characterize the floc size using an equivalent diameter. This strategy enables us to treat the flocs as a ball of a sphere and or fractal depending on the shape, and we approximate the diameter of a sphere that circumscribes its boundary or outline

Bayesian emulation and calibration of an individual-based model of microbial communities

Individual-based (IB) modelling has been widely used for studying the emergence of complex interactions of bacterial biofilms and their environment. We describe the emulation and calibration of an expensive dynamic simulator of an IB model of microbial communities. We used a combination of multivariate dynamic linear models (DLM) and a Gaussian process to estimate the model parameters of our dynamic emulators. The emulators incorporate a smoothly varying and nonstationary trend that is modelled as a deterministic function of explanatory variables while the Gaussian process (GP) is allowed to capture the remaining intrinsic local variations. We applied this emulation strategy for parameter calibration of a newly developed model for simulation of microbial communities against the iDynoMiCS model. The percentage of variance explained for the four outputs biomass concentration, the total number of particles, biofilm average height and surface roughness range between 84—92% and 97–99% for univariate and multivariate emulators respectively. The simulation-based sensitivity analysis identified carbon substrate, oxygen concentration and maximum specific growth rate for heterotrophic bacteria as the most critical variables for predictions. The calibration results also indicated a general reduction of uncertainty levels in most of the parameters. The study has helped us identify the tradeoff in using different types of models for microbial simulation. The approach illustrated here provides a tractable and computationally efficient technique for calibrating the parameters of an expensive computer model