I've always been fascinated by what we don’t yet know about engineered or natural systems,” says Associate Professor Lucy Marshall, Deputy Director of the UNSW Water Research Centre (WRC) “particularly in water resources. Analysing our uncertainties means I get to come to work every day and learn something new.”
The central interest in all of Marshall’s research is ‘uncertainty quantification’. Much of her research is structured by a formal probabilistic approach known as Bayesian inference. “It is an elegant statistical technique that brings together two types of information; data or observations from the field and expert knowledge or ‘prior information’,” she explains. “The prior information provides a researcher with probability distributions informed by scientific or specialist knowledge, beyond what is explicitly observed. Informative priors can provide us with a lot of information, while non-informative priors have higher levels of uncertainty.”
Bayesian methods have been used across many disciplines, but it is the discipline of hydrology that has especially embraced this elegant statistical approach, fostering its expansion and development for environmental modeling. Lucy Marshall and her ARC team: Dr Hoori Ajami, Dr David Nott and Dr Yating Tang are players in a burgeoning and lively debate about modelling methodology. “The Bayesian approach,” Marshall notes, “is particularly useful as we can attribute uncertainty to field data errors, a lack of expert knowledge, or model biases.”
As a newly ARC funded Discovery Project, “Advancing uncertainty quantification in terrestrial hydrologic systems” the work is to develop Bayesian methods specifically using Approximate Bayesian Computation (ABC). The distinction between ABC and a traditional Bayesian approach is that in ABC there is no requirement to formulate a ‘likelihood’ or statistical measure of the merit of the model. Instead a series of simulations are created and then selected on how they correlate with data. “It is an easy, robust and mathematically sound way to estimate error. It is particularly suited to complex error structures.”
We can no longer study water in isolation from its environment
A/Prof Lucy Marshall
ABC is a relatively recent development in Bayesian modelling and Associate Professor Marshall is at the forefront of ABC research. Her 2012 co-authored article “Generalized likelihood uncertainty estimation (GLUE) and approximate Bayesian computation: What's the connection” was the first ABC hydrology article to be published. “These ideas have been percolating for several years, so I am very excited about this ARC project. We aim to demonstrate just how powerful ABC is, as it has, perhaps, been underestimated until now.”
A year into the three-year project and Lucy is very pleased with their progress and outputs. In 2017, using long term data sets, the team has established baseline ecohydrological models and a foundational Bayesian framework for calibrating these models. A first journal article has been published titled “A Bayesian alternative for multi-objective ecohydrological model specification”. A second is being created now, deeply influenced by the peer review process of the first article. Lucy Marshall pays homage to this process as part of any ongoing research project. “We received incredibly learned and helpful critiques, especially in the area of data quality. So, our second paper will investigate satellite data errors, including an established Bayesian approach to precipitation errors. Understanding the extension of Bayesian methods into ecohydrology has been exciting.”
In 2018, this ARC team will establish and complete an appropriate ABC framework and will use this framework “to investigate errors associated with our assumptions about model selection.” More publications will follow as Lucy and the other team members move closer to fulfilling the overall ambitions of the project. “We aim to characterise the importance of input errors in models and to more fully understand how uncertainty in rainfall and evapotranspiration is affecting the overall model. A working ABC framework will make it much easier to characterise what these data errors are.”
Developing Bayesian and Approximate Bayesian methods is not the only aspect of Lucy Marshall’s research that is innovative. Over the last decade Lucy’s interests have been shifting away from purely engineering/hydrological perspectives to the broader field of ecohydrology. This is a relatively new and expanding field that, according to UNESCO, “attempts to reverse the degradation of water resources and stop further decline in biodiversity by utilising our growing understanding of relationships between hydrological and biological processes.”
Lucy was immersed in this kind of relational thinking during her eight years spent as professor in the environmental science department at Montana State University. “There was much more emphasis on natural resources in this department and this altered and expanded my engineering focus on models as problem solving tools. I began to link my research more deeply with the actual physical systems, working more collaboratively with people in the field. In a way, my time at Montana was my second PhD.”
Yet don’t expect to see Lucy wading through rivers anytime soon. “I know where my strengths lie, and my great love, from a very early age, has always been mathematics.” Marshall believes that the creative potential of higher level mathematics is largely misunderstood, underestimated or ignored. “We need creativity in mathematics for it to be relevant in a range of fields and disciplines.” She attributes her early academic success in the USA to her awareness that mathematical research, handled with artistry, could be widely applicable. She also believes that this adaptability was consciously fostered in the broad-based training she received from CVEN.
Ecohydrology combines water and streamflow data with vegetation dynamics data
This flexibility is also reflected in the make-up of her ARC team which includes a mathematician, a statistician, an early career eco-hydrologist and an engineering hydrologist. This type of cross fertilisation not only increases the complexity of the input and the subsequent models, but allows these researchers access to knowledge bases, networks and possibilities which would have been unavailable previously.
Ecohydrology creates a natural bridge between engineering and climate change science, increasing its relevance and its capacity to heal the planet. “Ecohydrology combines, in an organic way, water and streamflow data with vegetation dynamics data. In the past the vegetation in a catchment system has often been ignored. But now we are equally concerned with issues such as leaf area indices, evapotranspiration rates, interception and soil moisture dynamics. And if we have a model that incorporates more processes, that has ecohydrological components, then it has the potential to be more robust and more accurate in the face of climatic change.”
So the ARC project “Advancing uncertainty quantification in terrestrial hydrologic systems” marries uncertainty quantification, engineering models as problem solving tools and an actual connection to the complex processes of natural ecosystems to achieve a better estimation of just how important rainfall and evapotranspiration are for any workable hydrological model.
“We can no longer study water in isolation from its environment” says Marshall. “To address climate change effectively, any model representing any water catchment system must include possibilities for massive environmental change. It is the only way a model can work now.”