Meeting Environmental Outcomes – A Planning Framework - Water and Agriculture: Sustainability, Markets and Policies - page 202

is
an independent normally distributed random variable with mean 0 and a variance

y

where is the river flow at time t; c, and are parameters to be estimated; and

t

2.
This was used to predict future river flows, and hence dam releases required to achieve a
flood. The total predicted supplementary release P to achieve a high flow event, with a
flow rate of F megalitres per day for a duration of Dmax days, is given by:

The state transition function

The state transition function is dependent on the specification of the environmental
objective and, as a consequence, it is not possible to specify a general functional form. A
simple form is used here for illustration, where the state s is given according to how many
years have elapsed since a high flow event has occurred:

A high flow event occurs when the minimum flow rate required, F, is achieved for a
minimum of D min days.

The loss function

The strategy is determined by minimising the loss function. Again, the specification
of the loss function depends on the environmental objective. The illustrative loss function
is the sum of the average annual cost of three components:

where Q * is the volume of water on call; C is the annualised cost of a permanent
entitlement per megalitre; SV is the salvage value of water not released for environmental
purposes. Hence

is the annual opportunity cost of the water on call, and

is the opportunity cost of the released water.