ScienceWise - Summer 2010

Thirst for Data

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How Mathematical Modellers are Helping Improve the World’s Water Distribution

We’re all aware of the increasing pressures on the world’s water resources and the need to manage these as effectively as possible. But whilst heated arguments rage between various users and interest groups, the immense complexity of water catchments and river systems make it very hard to know what effect changes in various allocations will have on the system as a whole. This is where decision makers are increasingly turning to mathematical modellers like Dr Barry Croke of the Australian National University.


Dr Croke’s research is conducted jointly in the Mathematical Sciences Institute and the Fenner School of Environment and Society. He says, “Modellers can contribute in many ways to improve our decision making in society. Decisions about environmental issues are almost always trade-offs among possible outcomes, for example how to share water between cities and the rural sector, or among different industrial uses and the environmental health of a waterway. But what water managers and policy makers would really like to know is what outcomes will occur under different scenarios of water usage.”


This is where good mathematical modelling can really play a vital role. It becomes possible to play out various policies in a virtual environment over time scales that simply wouldn’t be practical to test on a trial and error basis. It also enables scientists to explore the interaction between things we have some control over, like water allocation policies and those that are less predictable such as possible future climate regimes.


But how do you go about creating such models? In an ideal world, modellers would have access to all the data on key variables over a very long period of time. But one of the really critical issues in managing environmental issues at present is the speed at which things are changing, and the lack of reliable information. Many key drivers and internal states are not directly observable using current technology, and there is considerable uncertainty in the available data.
Dr Croke explains, “The task for the modeller is to develop techniques for handling these limitations that enable useful predictions to be made. In order to achieve this goal, models need to represent the important processes involved in a way that minimises as much as possible the uncertainty in the predictions.”


Generally speaking, mathematical models tend to be either deterministic or stochastic. A deterministic model will produce the same outcome for the same input values (both data and parameter values) and these are generally used where the inputs are known. Stochastic models can accept a distribution of input values and produce a distribution of results. Dr Croke is working on the development of deterministic models that are able to handle input values with large errors and minimise the effect of those errors as they propagate through the model.


When we’re modelling a real system such as the flow of a river, we can use knowledge about the underlying physical processes to reduce errors.” Dr Croke explains, “For example, in observing stream discharge, we measure the water level in the stream. This is converted into a flow rate by use of a rating curve - an experimentally derived relationship between water level and discharge. Uncertainty in the rating curve results in uncertainty in the discharge that is related to that of neighbouring values.”


By incorporating these ideas into the model it’s often possible to reduce the error range of a particular value because the physics dictates that it must be either higher or lower than the preceding value depending on the relative water levels. This enables Dr Croke’s models to reduce the uncertainty by as much as a factor of three.


Integrated modelling is a demanding activity that is continually exposed to widespread scrutiny by other scientists and land users. “However”, Dr Croke says, “The rewards are there. You have the opportunity to work with a lot of enthusiastic, like-minded people who are striving to improve natural resource management outcomes. Managers and authorities can adopt your models. You see improvements to the way resources are managed.”


Barry has recently travelled to India to model the response of shallow groundwater resources to heavy water usage and the way in which this has and will impact different socioeconomic groups. One of these projects is based in the Purulia district of West Bengal and looks at the impacts of water development on a village, addressing issues such as gender, land ownership and location within a catchment. These projects are collaborative efforts involving a number of research institutions in India and Australia, as well as NGOs, and are co-funded by the Australian Centre for International Agricultural Research and the Indian Government.

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