14
2 Terminology
Table 2.2 Aggregating flows and applying Usefulness Criterion
Symbol
Expression
Terminology
I
V1 + OS + PP
Inflow
R
V2 + RP
Return
C
ET + NR
Consumption
O
C + R
Outflow
UI
I S
Useful inflow
UR
R S
Useful return
UC
C S
Useful consumption
UO
O S
Useful Outflow
Third, for each WUS, the law of mass conservation or water balance must be
satisfied (Sutcliffe 2004). It states that total inflow into a system is equal to total
outflow plus change in storage within any given time interval, and as such multilevel
management of a WUS necessitates water balance at all levels. However, the micro
level analysis is not based on water balance because it does not consider the returns,
and as such, it is prone to errors. It is included in this book because most of the
current analyses in papers, reports and projects are done using some form of micro
level analysis. Furthermore, it should be mentioned at this point that the change in
storage is considered to be zero as will be explained fully in the Chapter on the
Theory (see Sect. 3.1). Consequently, the water balance in this book has the form of
Eq. (2.2) using the flows presented in Table 2.2:
I = O = C + R
(2.2)
A caution needs to be exercised in applying weights to the sum or difference of
the flows. Remembering that a WPI (= X) is a real flow that can be measured with
its own two weights, let us examine two distinct combination properties:
Property 1: assume that a farm (WUS) has three WPIs that obey the water balance
as follows:
X 1 = X 2 + X 3 (e.g., VA f = ET f + RF f , f for farm)
Applying the corresponding weights, say the beneficial ones, and considering
Eq. (2.1) we get:
X b1 = (X 2 + X 3 ) b → W bX1 ∗ X 1 = W bX2 ∗ X 2 + W bX3 ∗ X 3
2 Terminology
Table 2.2 Aggregating flows and applying Usefulness Criterion
Symbol
Expression
Terminology
I
V1 + OS + PP
Inflow
R
V2 + RP
Return
C
ET + NR
Consumption
O
C + R
Outflow
UI
I S
Useful inflow
UR
R S
Useful return
UC
C S
Useful consumption
UO
O S
Useful Outflow
Third, for each WUS, the law of mass conservation or water balance must be
satisfied (Sutcliffe 2004). It states that total inflow into a system is equal to total
outflow plus change in storage within any given time interval, and as such multilevel
management of a WUS necessitates water balance at all levels. However, the micro
level analysis is not based on water balance because it does not consider the returns,
and as such, it is prone to errors. It is included in this book because most of the
current analyses in papers, reports and projects are done using some form of micro
level analysis. Furthermore, it should be mentioned at this point that the change in
storage is considered to be zero as will be explained fully in the Chapter on the
Theory (see Sect. 3.1). Consequently, the water balance in this book has the form of
Eq. (2.2) using the flows presented in Table 2.2:
I = O = C + R
(2.2)
A caution needs to be exercised in applying weights to the sum or difference of
the flows. Remembering that a WPI (= X) is a real flow that can be measured with
its own two weights, let us examine two distinct combination properties:
Property 1: assume that a farm (WUS) has three WPIs that obey the water balance
as follows:
X 1 = X 2 + X 3 (e.g., VA f = ET f + RF f , f for farm)
Applying the corresponding weights, say the beneficial ones, and considering
Eq. (2.1) we get:
X b1 = (X 2 + X 3 ) b → W bX1 ∗ X 1 = W bX2 ∗ X 2 + W bX3 ∗ X 3