# Risk and Uncertainty Quantification in Environmental Modelling

Supervisor: Professor Jerzy Filar

Mathematical models of environmental problems often demand understanding of complex dynamics and interactions between many physical and biological variables on the one hand, and human inputs on the other. Uncertainties accompanying such models stem from multiple sources. Sometimes they manifest themselves as cascading errors and at other times they involve the risk of key variables crossing undesirable thresholds. In both cases they undermine confidence in either the model or, worse still, the underlying science.

The accompanying mathematical problems can be studied using a wide range of approaches including (but not limited to) perturbation theory, stochastic processes, partially observable Markov decision processes, statistical methods, dynamical systems and simulation. They can also be applied in several important contexts including (but not limited to) conservation of natural resources, optimizing harvests of fish subject to sustainability constraints or generating warning signals for species whose abundance drops to low levels. One particularly challenging problem is that of designing controls that minimize the probability of a catastrophe, consistently over time, while achieving satisfactory and sustainable resource consumption. A related problem, also stemming from fishery science applications, is that of devising a “balanced harvest” strategy that ultimately restores the proportions of age cohorts of the harvested species to those that are natural for that species.

There are several PhD, Masters’ or Honours’ research projects that can be designed on this general theme and tailored to the particular student’s background and interests. For some projects co-supervision with scientists from the Queensland Department of Agriculture and Fisheries, or CSIRO may be required.

## Project members

Supervisor: Professor Jerzy Filar