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( = 14). A penalty of $30 million is imposed if a high flow event lasting ten days is
not achieved in the fifth and any subsequent states. The penalty is assumed to decline at a
constant rate to zero as the event reaches the 14 day target. The penalty used here is
arbitrary, but is ultimately related to the level of reliability achieved under the release
strategy. A clear alternative is to specify the level of reliability as a constraint. However,
this does add to the technical difficulty of solving the optimisation problem.
The water entitlement Q* for environmental release is determined endogenously
given the annual cost C of holding that entitlement; assumed to be $70 per megalitre a
year, a value close to the annualised cost of purchasing a permanent high security
entitlement in the Murrumbidgee River at a discount rate of five per cent. The salvage
value or opportunity cost of the water actually released is $50 per megalitre, a value close
to the average traded price in the physical allocation or temporary water market.
The problem as formulated is not well suited to traditional optimisation methods as
the loss function is discontinuous and the state transition equation is subject to jumps. A
modified genetic algorithm was used to estimate the values of , , , and Q* that
minimised the loss function (Goldberg 1988). The algorithm was implemented in Visual
Basic and is available from the authors on request. Convergence of the algorithm to an
optimal solution was tested by perturbing the estimated parameters.
The hydrological link between supplementary dam releases and flow rates at Wagga
Wagga was based on a simple routing model without flow attenuation or upstream
overbank losses. Attenuation does generate significant variability in flows that are not
accounted for in the evaluation of the criteria for a successful high flow event. The
optimal release strategy was subsequently evaluated in the Murrumbidgee IQQM model
to gain a more accurate assessment of the impact of the release rules on flow regimes.
The solution
The optimal release strategy is shown in Figure F. The volume of water on call is
slightly above 140 gigalitres, which is substantial. This, however, reflects the relatively
stringent criteria for a successful high flow event, and penalty for failure. The volume of
water actually released is substantially smaller, averaging about 25 gigalitres a year. In
years when a release is made, the average volume of the release is 75 gigalitres.
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