Agriculture Reference
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the reservoir. These plants release water only when the other uses are
satisfied in each period. Once all the other users have received the amount
of water established in their water right (hereafter referred to as
'allotment') it is possible to accumulate water in the reservoirs in prevision
for possible drought periods and until their storage capacity is reached.
All the agents are organised spatially around two systems
(upstream and downstream) regulated by two reservoirs that, logically, are
interdependent. A scheme established in this way describes a large number
of situations that could be represented as particular cases of it. The
interdependencies translate into two aspects: first, the agents located
downstream are, to some extent, subsidiaries of their homologues and of
the upstream priority uses; secondly, the reservoirs are managed in a co-
ordinated manner in order to meet the needs of the totality of the users.
For practical purposes, we assume that the city and environmental
requirements are given and, whenever possible, coincide with the
allotment. By contrast, we assume that both farmers and hydropower have
a profit function that depends on the volume of water used. This means that
the requirement of the cities and the minimum flow act as mere
restrictions, whilst the water used by farmers and hydropower are our main
variables.
2.2 Variables
The allotment (maximum quantity established in the water right) and
effective applied water levels are represented by and respectively,
with
k = 1, 2, 3, 4
types of use;
j =1,2
systems and
t = 1, 2
sub-periods of
the water year mentioned above. We denote by the minimum levels of
the reservoirs dedicated to guaranteeing drinking water.
Two important state variables of the model are and
represents the volume of water supply per period in each system and
corresponds to the initial reserves plus the quantity of water it
receives, either in the form of the natural upstream inflows of the river
or from the earlier return flows
2
with being the rate of
return flows of use
k
in system
j-1
and in period
t.
Thus, there are two flow
variables (C,
U
) and three state variables
As regards the variable (reservoir reserves of system
j
at period
t
), this takes values between 0 and the maximum capacity of the reservoir
Furthermore, and in function of whatever is the amount of the
upstream flows and the intensity of the uses, it will take values above or
below the security reserve Thus, if the available water is insufficient
even for urban uses, the reserve will be null until these are satisfied and,
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