Chambers and Quiggin (2000), the tools of duality theory are fully applicable in a
state-contingent setting. The modelling approach used here allows use of the
standard duality concepts associated with linear and nonlinear programming.
These advantages of the state-contingent approach are particularly relevant in
relation to the modelling of climate change. Climate change is expected to
produce an increase in mean temperatures and a reduction in mean precipitation
in the Murray-Darling Basin. However, as shown by Adamson, Mallawaarachchi
and Quiggin (2009) the effects of changes in mean values are modest in
comparison with those of changes in the stochastic distribution of inflows to the
system and, in particular, with increases in the frequency of drought.
Using a state-contingent production representation of uncertainty, climate
change may be represented as a change in the probability distribution of states
of nature, with hotter, drier states becoming more probable.
General specifications
The Basin is simulated at a Catchment Management Authority scale for 19
catchment regions, along with Adelaide and the Coorong. The Adelaide and
Coorong catchments allow for the representation of water quality arriving in
Adelaide and a proxy value for environmental flows represented by water
reaching the Coorong.
The model contains three states of nature, corresponding to Normal, Wet (20 per
cent above normal inflows) and Drought (40 per cent below normal inflows)
conditions. The probabilities of the the three states (Normal: 0.5, Wet: 0.3,
Drought: 0.2) and the associated inflow levels are calibrated to match the
observed historical mean and variance of inflow levels.
An activity in the model is specified by inputs and outputs in each state of
nature. A given activity may produce the same commodity in each state, or
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