Directory UMM :Data Elmu:jurnal:A:Agricultural Water Management:Vol43.Issue3.Apr2000:

Agricultural Water Management 43 (2000) 327±343

A new planning model for canal scheduling
of rotational irrigation
C. Santhia,*, N.V. Pundarikanthanb
a

Blackland Research Center, 808 E. Blackland Road, Temple, TX 76 502, USA
b
Center for Water Resources, Anna University, Chennai 600 025, India
Accepted 20 June 1999

Abstract
Water distribution systems often have multi-objectives such as equity, adequacy and timeliness.
The canal systems distributing the water have different design capacities, command areas and
lengths requiring different duration of operation. Irrigation scheduling under these conditions
especially for rotational water distribution becomes a complex process. Optimisation techniques
have limitations in the above situations either because of their pre-de®ned mathematical structure or
because of the computational requirements to represent the reality. Hence, this study purports to
develop a new multi-criteria approach for scheduling the rotational distribution system on a weight
basis. Application of this model is demonstrated with an example of an irrigation system in India

where rotational distribution is practised at distributary canal level. The results indicate that the
performance of the water distribution system is better with the present model compared to the
conventional scheduling procedure used. The concept can be extended to any level of rotational
distribution, starting from main canal down to farm outlets. # 2000 Elsevier Science B.V. All rights
reserved.
Keywords: Irrigation scheduling; Rotational water distribution; Water duty; Multi-objective; Adequacy; Equity;
Timeliness and Operational convenience

1. Introduction
The growing demand for water has ushered in the need for efficient utilisation of water
in the irrigation sector with different methods of management. All these methods aim at
meeting the crop demand with the available water to get maximum production.
*

Corresponding author. Tel.: ‡1-254-770-6609; fax: ‡1-254-770-6690.
E-mail address: csanthi@brcserv0.brc.tamus.edu (C. Santhi).
0378-3774/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 3 7 7 4 ( 9 9 ) 0 0 0 6 5 - 7

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C. Santhi, N.V. Pundarikanthan / Agricultural Water Management 43 (2000) 327±343

Scheduling of water delivery is one among them and it is a core activity that has more
influence on the performance of the system compared to other irrigation activities
(Chambers, 1988). Scheduling of an irrigation water distribution system should be based
on the objectives or targets of the irrigation system that can be measured with
performance indicators. Levine (1982), Lenton (1984), Sampath (1988), Bos and
Nugteren (1990), Molden and Gates (1990), Garces (2000), and many others have
presented the concepts and definitions of performance indicators that describe the quality
of irrigation service provided by the managers of the water delivery system. It is also
realised that there are complexities in identifying the objectives, defining them and
assessing them at different levels of an irrigation system by different interest groups with
differing perspectives. The complexities are well described in the literature (Chambers,
1988; Smith, 1990). Limited attempts are made to develop scheduling models with the
perspective of achieving the objectives of system's goals. This paper describes a new
scheduling model that can consider workload (operational convenience), equity, adequacy
and timeliness criteria of an irrigation system.

2. Review of water distribution scheduling procedures

A variety of canal water distribution procedures are in vogue today. The Warabandhi
system in the States of Haryana and Uttar Pradesh in India aims at sharing the available
water equitably among the users (supply based where the users adjust their crop water
demand according to the supply). The Shejpali system adopted in the State of
Maharashtra aims at meeting the demand adequately (demand based where the irrigation
manager will take care of supplying the requirement of each user). Most of the irrigation
systems in southern part of India aim at both of these objectives, namely, equity and
adequacy. These operational objectives may be conflicting with or contributing to each
other in different magnitudes depending upon the water availability (Abernethy, 1986).
These canal systems were designed as continuous water supply systems. The increase in
cropping area and changes in cropping pattern in course of time increased the demand in
these systems. So, the main canal capacity is inadequate to run all the distributary canals
simultaneously. Rotational water distribution has been introduced in some of the systems
to manage the shortage of water.
In most of the irrigation systems, the system manager who prepares the irrigation
schedule relies mainly on his experience or rules of thumb. He distributes the water to the
canals according to the water duty specified. Water duty is the number of acres of land
irrigated per cubic feet per second (cusec) of water in a crop season. Water duty does not
vary with time. It gives an approximate estimation of water required for a crop over a
gross period like a season. Typically, duties of 60 acres/cusec and 120 acres/cusec are

adopted for a wet crop like rice and dry crop like groundnut, respectively. It is only an
approximate procedure for allocating water. It does not account for the losses occurring
along the lengths of the canals. So, this often results in a plan that is far from the optimal
solution in terms of application of water. In addition, scheduling of rotational irrigation is
more complex compared to continuous irrigation as it requires additional managerial
inputs in terms of number of gate operations, monitoring points and travel distance of

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329

gate operator. It is also a time-consuming process, if the canals are large in number and
vary in design discharge, length and command area. The manager requires special skill to
lay down priorities for allocating the water with a defined set of objectives, develop and
implement an irrigation schedule under these complex situations.
A number of models have been developed for irrigation scheduling with optimisation
and simulation techniques. Rajput and Michael (1989) developed a procedure for
operation of canals using water balance equation for the estimation of daily soil moisture
status taking a hypothetical case of four branch canal system. This model can be applied
to real field situations only if the number of branch canals in the network is in multiples

of four. Vedula et al. (1993) have developed an irrigation scheduling model for optimal
allocation of water during different periods of the season for a single crop using dynamic
programming. The model takes into account the soil moisture contribution for estimating
the irrigation requirement. Yuanhua and Hongyuan (1994) have developed a model for
canal scheduling with rotational water distribution by computing the initial soil moisture
daily through water balance equation and forecasting the weather data and subsequently
the irrigation date and depth. Most of these models have difficulties in field applications
for the following reasons: (a) the assumptions made and or the pre-defined mathematical
structure involved in developing the optimization problem do not match with the real
conditions of the field, and (b) the field measurement data required for these models
such as the soil moisture status or plant stress are generally not collected and used in
most of the irrigation systems in many countries. Similar observations are reported by
Hill and Allen (1996) while developing an irrigation scheduling calendar in Pakistan.
Furthermore, the models developed by Vedula et al. (1993) and Yuanhua and Hongyuan
(1994) do not provide a plan/procedure for canal operation. Zhi et al. (1995) have
proposed a 0±1 linear programming model for outlet scheduling. However, application of
this model is limited to irrigation systems where the distribution outlets along the canal
(be it main, lateral, tertiary) have the same discharge capacity and such systems are
hypothetical.
Formulating an optimisation model for gate operation scheduling involves 0±1 integer

variables and tracking of the previous states of the gate. For most of the practical
problems, the number of integer variables become very large as the number of gates
increases. Thus, the problem becomes quite complex to be solved with personal
computers. This difficulty forces the researchers to approximate the problem to handle
hypothetical problems.
Many of these optimisation models as well exclude the ``soft or managerial tasks'' such
as minimisation of the gate operations, monitoring points and travel distance of the gate
operator. It is necessary to consider such managerial tasks while scheduling the rotational
water distribution for effective management.
The objective of this paper is to formulate a multi-criteria mathematical model for
irrigation canal scheduling with rotational distribution which includes the objectives of
achieving minimisation of gate operations, equity, adequacy and timeliness. Application
of the model is demonstrated with an irrigation system in India, having the above
complexities. The multi-objectives of water distribution are expressed in terms of
measurable criteria and on a weight basis and they in turn form the basis for design of the
scheduling model.

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C. Santhi, N.V. Pundarikanthan / Agricultural Water Management 43 (2000) 327±343

3. Model development
This model is developed based on multi-criteria approach. The various criteria considered
in the model for rotational water distribution are equity, adequacy, timeliness and locational
or convenience of operation. They are represented in terms of weights. Weights get assigned
to each distributary canal based on each of these criteria. The weights assigned are less than
1.00 and they are either constant or dynamic with respect to the time of operation. Since these
criteria are independent of each other, the final weight is obtained on a multiplicative basis
(by multiplying the individual weights) for each distributary canal. The distributary canals
are ranked for operation based on the final weight. The weights of the locational, equity,
adequacy and timeliness criteria are computed as follows (Santhi, 2000):
3.1. Locational criteria
It is desirable to group the distributary canals based on location such that the workload
or travel distance of the gate operator and the losses in conveyance are minimised in the
case of rotational distribution. This locational weight is represented as follows:
The distributaries are grouped and attempt is made to open any one group of distributary
canals during a particular turn (t) such that the travel time (workload) of the gate operator is
minimised. Turn is defined as a duration for which a group is supplied water. Rotation is a
duration comprising of a few turns such that in each rotation, all the groups get one turn of
irrigation. For example, the canals in an irrigation system can be grouped into two groups and

in a rotation of a fortnight duration, the first group can be issued water in the first turn (i.e.,
first week) and the second group can be issued water in the second turn (i.e., second week).
For the sake of understanding, a week is taken as a turn. However, it can be of any time interval
depending on the rotational practice in the system. Suppose, if there are `g' groups, then if a
particular group is favoured for release in the first week, next time it will be favoured after `g'
weeks as each group requires a week. The number of groups of distributary canals can be
decided depending on the water demand of the command area, capacities of the main canals
and distributary canals. Grouping of the canals should be done in such a way that each group
is almost similar in size in terms of command area and water requirements. The number of
groups can be decided as follows:
Pn
distributary capacityk
:
g  kˆ1
main canal capacity
For practical application, this is one of the most important criteria to be considered
while scheduling the canals. The weight for this criterion is defined as follows:
W1kt
W1kt
W1kt

W1kt

ˆ 0:9
ˆ 0:1
ˆ 0:9
ˆ 0:1
..
.

for
for
for
for

k 2 Group
k2
= Group
k 2 Group
k2
= Group

1
1
2
2
..
.

of
of
of
of

dist:
dist:
dist:
dist:

canals;
canals;

canals;
canals;

W1kt ˆ 0:9 for k 2 Group g of dist: canals;
W1kt ˆ 0:1 for k 2
= Group g of dist: canals;

t ˆ 1; …g ‡ 1†; …2g ‡ 1†; . . . ; …m ÿ g ‡ 1†
t ˆ 1; …g ‡ 1†; …2g ‡ 1†; . . . ; …m ÿ g ‡ 1†
t ˆ 2; …g ‡ 2†; …2g ‡ 2†; . . . ; …m ÿ g ‡ 2†
t ˆ 2; …g ‡ 2†; …2g ‡ 2†; . . . ; …m ÿ g ‡ 2†
..
.
t ˆ g; 2g; 3g; . . . ; m
t ˆ g; 2g; 3g; . . . ; m
(1)

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331

where, W1kt is the weight for the distributary canal `k' for the turn `t', `n' the number of
distributary canals, `g' the number of groupings of canals for turns in a rotation and `m'
the number of turns in a crop season.
3.2. Adequacy criteria
Adequacy relates to the desire to deliver targeted amounts of water needed for crop
irrigation to delivery points in the system (Molden and Gates, 1990). This can be
represented as
!
1X 1X
PA ;
(2)
PIA ˆ
T T R R
where PIA is the adequacy performance indicator, T represents time and R represents
region, PAˆQD/QR if QDQR else PAˆ1, QDˆactual amount delivered by the system and
QRˆamount of water required for consumptive use. In this study, a weight for adequacy is
formulated based on the concept of Eq. (2).
In the present model, based on the concept of Eq. (2), the weights are assigned to each
canal in proportion to its required duration of operation over the crop duration. The
duration of operation of each canal is computed as follows: the crop water requirement is
computed using the modified Penmen method (Doorenbos and Pruitt, 1977). Average
weather parameters (computed from data pertaining to 15 years) are used in crop water
estimation. The effective rainfall estimated from the actual rainfall is used to find out the
water requirement in the field. Irrigation water requirement at each outlet (minor canal
head) is computed from the actual water requirement, application and distribution
efficiencies and the area under each outlet. Irrigation demand at the head of the
distributary canal is computed by lumping the irrigation requirements of the outlets under
that canal head and applying conveyance losses. Canals losses were measured at different
locations along the main and distributary canals at different times through flow
measurements and ponding method. The canal losses for different reaches are assumed to
be constant during the season. When crops are irrigated, the weather conditions have less
influence on seepage losses from canals. The antecedent moisture has major influence on
canal losses. However, the antecedent moisture remains fairly constant when water flows
in the canals during the irrigation season. Hence, the seasonal variation is not considered
in computing the canal losses.
Number of days of operation of each distributary canal is computed dividing the
demand by its discharge capacity. This weight takes care of the adequacy (satisfying the
crop demand). Thus, this weight for each of the distributary canal remains constant
throughout the crop season.
W2k ˆ

dk
D

for k ˆ 1; 2; 3; . . . ; n;

(3)

where W2k stands for the weight of the distributary k, dk for the duration of operation
required (in days) to meet the demand of the distributary canal k at full supply discharge
and D for the crop duration (in days). For example, if a distributary canal requires 100

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C. Santhi, N.V. Pundarikanthan / Agricultural Water Management 43 (2000) 327±343

units of water for a crop season, and the sluice capacity is 2 units/day, then the
distributary canal has to be run for 50 days. If the crop duration is 150 days, then this
weight is assumed as 50/150ˆ0.333. Formulating a weight for adequacy in Eq. (3) in this
manner can be justi®ed intuitively.
3.3. Equity criteria
Equity is one of the main objectives of the rotational water distribution in many cases.
It can be defined as the spatial uniformity of the ratio of the delivered amounts of water to
the targeted amounts (Molden and Gates, 1990). They have defined a performance
indicator for equity as follows:
 
1X
QD
CVR
;
(4)
PIE ˆ
QR
T T

where PIE is the performance indicator for equity, T represents time, CVR the spatial
coef®cient of variation over the region R for the ratio (QD/QR), QD the actual amount of
water delivered by the system and QR the amount of water required for consumptive use.
Based on Eq. (4), a weight is formulated to achieve equity. It is to be noted that to
estimate this indicator, the water delivered to the distributary canals needs to be known.
As the present model is a planning model, it can only recommend the amount of water to
be delivered and this needs to be used in the estimation of equity. Further, the present
model attempts to give a water release calendar at the main canal head and so the losses
in the canals needs to be accounted for. Thus, the fairest way to achieve equity is to
allocate the water in proportion to the irrigable area under the canals with proper
accounting of conveyance losses. Conveyance loss, being an in¯uential factor of equity,
has to be incorporated in the equity calculations.
A
W3k ˆ Pn k

kˆ1

where

Ak ˆ

Ak

for k ˆ 1; 2; 3; . . . ; n;

Ak
…1 ÿ lossk †length…k†

for k ˆ 1; 2; 3; . . . ; n;

(5)

(6)

W3k is the weight representing the equity criteria indirectly, Ak the virtual area of the
distributary canal k, Ak is the area of the distributary canal k, lossk is the percentage of
loss per kilometre (expressed as a fraction) of the distributary canal k and length (k)
stands for the length of the distributary k. It assumes that the loss increases with the
length of the canals (Hiemcke, 2000).
3.4. Timeliness criteria
Timeliness means correspondence of water deliveries to crop needs throughout the
season (Rao, 1994). It is expressed in the model such that the requirement of each canal
of each rotation (r) is satisfied within that rotation.

C. Santhi, N.V. Pundarikanthan / Agricultural Water Management 43 (2000) 327±343

W4kri ˆ

333



P
Rkr ÿ iÿ1
jˆ1 Xkrj

; k ˆ 1; 2; 3; . . . ; n;
Rkr
r ˆ 1; 2; 3; . . . …no: of rotations in a season†;
i ˆ 1; 2; 3; . . . …no: of days in a rotation†;

(7)

where W4kri is the timeliness weight of the distributary canal `k' for the day `i' in the
rotation `r', Rkr is the demand of the distributary canal `k' for the rotation `r' and
iÿ1
X

Xkrj

jˆ1

the net release to the distributary canal `k' till the previous day (iÿ1) in the rotation `r'.
In this case, weights get assigned to each canal every day, based on the releases
of water made in the canals till the previous day in a rotation against the total
requirements over a rotation. The dynamic nature of this weight will give more
priority for the less considered distributary canal (which has not received water or
received less water) for operation in a sequential manner in the subsequent days in that
rotation `r'.
As all these weights are independent of each other but at the same time they have joint
or combined effects on the overall water delivery performance. Hence, the combined
weight has been calculated by multiplying the individual weights and it is used as a single
parameter to be optimised. Thus, the final weight of each of the distributary canal is
computed as
Wkti ˆ W1kt W2k W3k W4kri ;

(8)

where, Wkri is the ®nal weight of the distributary canal `k' for the day `i' in the rotation
`r'. The distributary canals are ranked for operation according to the ®nal weight
computed on each day. On each day, the distributary canals are selected for operation
according to the ranks as long as the sum of their demand at the head of the main canal is
less than the main canal capacity. This procedure is repeated for the entire crop season to
get the schedule for operation of the distributary canals. Fig. 1 gives the computational
sequence of the above procedure for scheduling.
The following assumptions and constraints are made in the formulation of this
mathematical model for scheduling:
1. The gate operation is considered either `full open' or `full close' for ease of operation
and management.
2. Distributary canal runs for a day, even if the demand is satis®ed before the end of the
day.
3. On any day, the total releases to be made in the distributary canals cannot exceed the
discharge capacity of the main canal.
4. Distributary canal runs at the design discharge capacity and main canal close to its
design capacity.

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C. Santhi, N.V. Pundarikanthan / Agricultural Water Management 43 (2000) 327±343

Fig. 1. Computational procedure for the scheduling model.

4. Application
Application of the above model is demonstrated with the left bank main canal (LBMC)
of the Sathanur Irrigation Project in the State of Tamil Nadu in India. The canals in this
system are designed on duty basis for wet crops and irrigated dry crops and not on `crop
water requirement' basis. Also, the canal sluices are designed with different discharge
capacities that are not in proportion with the command area or water requirement. This is
due to the reason that some standard sizes of sluices are made and used. In developing
countries like India, it is nothing uncommon. Hence, the actual water demand, the
duration and time of operation of each canal outlet vary, making it necessary to prepare a
gate operation schedule in advance, before each season. At present, the water manager

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335

(Executive Engineer) prepares an irrigation plan and follows it during the season. The
irrigation plan is worked manually based on experience, gross estimates of crop demand
on water duty basis in each crop season, and the water availability in the Sathanur
reservoir. The scheduling and operation of this irrigation system mainly aims at equity.
However, when the water availability is very low, achieving the equity over the entire
command area will seriously affect the supply-demand ratio and thus the crop production.
So, the water manager advises the farmers to curtail their sowing area. This irrigation
system is a typical system having all the complexities discussed above and thus the
advantages of the multi-criteria scheduling model over the conventional (manual)
scheduling are demonstrated and discussed for this system.
LBMC of this system has 41 distributary canals (n ˆ 41) including a few direct outlets,
providing irrigation over a direct command of 8313 ha. Table 1 gives the details of the
distributary canals. Water is distributed in rotation among the distributary canals with
each rotation being of 15 days. Irrigation is given for 3±4 months in a year, usually,
between January and April. The present discussion deals with a condition of allocating of
61.0 million cubic metre to the LBMC, covering seven rotations of water delivery for
groundnut, (irrigated dry crop) which is the normal situation in the command. This
quantity is enough to meet the demand of the entire command. Performance of the water
distribution effected from the model is compared with that of manual scheduling
procedure used in the crop season in 1996.
Crop water requirement and effective rainfall were computed based on average
weather conditions over 15 years. The average (daily) weather conditions were used as
there was not much variation in weather parameters like sunshine, temperature from year
to year in the command area of the irrigation system. The long term average weather
conditions would be representative for a planning model. The crop season in this
Sathanur irrigation system falls after the post-monsoon (rainfall) season. Hence, there is
no significant rainfall during the crop season. However, the actual rainfall can also be
used to estimate the effective rainfall and the irrigation requirement during the
implementation, if required. Irrigation requirement is used along with other efficiencies
to compute the demand as explained in the model development. As explained earlier, the
weight for the locational criteria representing the grouping of the canals is computed as
given below:
1. Locational criteria: In this case, canals are put into two groups (gˆ2) as per the
existing practice. The ®rst 29 distributary canals are grouped to get more weights and
the rest of the 12 canals in another group to get lesser weights in the odd weeks (turns)
and vice-versa during the even weeks (turns) of each rotation (i.e., seven rotations with
14 turns and so one turn for each group). This kind of grouping has been done based
on the command area, location and lengths of the distributary canals of this system so
as to reduce the travel distance of the ®eld staff. Then, Eq. (1) for this case can be
written as,
W1kt
W1kt
W1kt
W1kt

ˆ 0:9
ˆ 0:1
ˆ 0:1
ˆ 0:9

for
for
for
for

k ˆ 1; 2; 3; . . . ; 29 and t ˆ 1; 3; 5; . . . ; 13;
k ˆ 30; 31; . . . ; 41 and t ˆ 1; 3; 5; . . . ; 13;
k ˆ 1; 2; 3; . . . ; 29 and t ˆ 2; 4; 6; . . . ; 14;
k ˆ 30; 31; . . . ; 41 and t ˆ 2; 4; 6; . . . ; 14:

(9)

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C. Santhi, N.V. Pundarikanthan / Agricultural Water Management 43 (2000) 327±343

Table 1
Details of the distributary canals in the LBMCa
DY. No.

Name of the DY.

Chainage (km)

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41

DI 1R
DI 1L
DI 2R
DI 3R
DI 5R
DI 6R
DI 7R
DI 8R
DY 1R
DY 2R
DY 3R
DI 9R
DI 10R
DI 11R
DI 12R
DI 13R
DY 4R
DY 5R
DI 15R
DI 16R
DI 17R
DY 6R
DY 7R
DI 18R
DI 19R
DI 20R
DY 8R
DY 9R
DI 21R
DY 10R
DY 11R A
DY 11R B
DY 11R C
DY 12R
DI 22R
DY 13R
DI 23R
DI 24R
DI 25R
DY 14R
DY 15R

2.96
2.96
3.30
4.30
5.00
5.20
6.20
6.40
7.80
8.40
9.90
11.10
11.60
12.30
12.50
13.40
15.20
15.20
16.64
17.73
20.04
21.13
21.98
22.58
23.18
23.60
24.75
25.75
26.67
26.98
27.36
27.36
27.80
29.34
30.30
31.36
31.48
32.28
33.70
33.75
35.20

a

Direct area (ha)
2.93
2.14
5.70
23.80
25.70
20.79
9.25
42.86
86.35
248.87
100.32
24.24
9.81
3.93
12.10
27.25
1000.00
721.00
84.71
60.54
19.58
262.89
53.31
10.45
9.00
11.47
71.24
316.00
12.77
1945.44
1000.00
618.76
171.52
156.46
28.57
156.29
47.64
6.67
39.39
69.39
794.18

Discharge (m3/s)
0.014
0.014
0.014
0.024
0.026
0.021
0.014
0.045
0.099
0.286
0.115
0.024
0.014
0.014
0.014
0.027
1.979
1.979
0.089
0.064
0.020
0.302
0.061
0.014
0.014
0.014
0.082
0.363
0.014
2.088
1.862
1.862
0.197
0.180
0.030
0.180
0.050
0.014
0.041
0.080
0.913

DI Ð direct irrigated outlets; DY Ð distributary canal.

2. Adequacy criteria: As explained in Eq. (3), for this system, the duration of operation
of each distributary canal (dk) is calculated in days based on the demand at the head of
the distributary canal and the discharge capacity of the canals. The crop duration of
groundnut (D) is taken as 105 days.

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337

3. Equity criteria: Equity criteria for this canal system is computed as per Eq. (5). The
equity consideration is taken care of by making an account for the conveyance losses
occurring along the length of canals. In this case, based on the measurements made,
losses in the canals are taken as 2% per kilometre (expressed in fraction with reference
to the downstream demand for the unlined canals (distributary canals) and 1% for
lined canals (main canal).
4. Timeliness criteria: The crop water demand in each rotation is met within that rotation
by a way of giving priorities for operation of the canals according to the releases made
till the previous day in that rotation in each canal.
W4kri ˆ

…Rkr ÿ

Piÿ1
jˆ1

Xkrj †

for distributary k ˆ 1; 2; 3; . . . ; 41;
Rkr
rotations r ˆ 1; 2; 3; . . . ; 7; and days in a rotation i ˆ 1; 2; 3; . . . ; 15:

(10)

5. The distributary canals are ranked for operation according to the ®nal weight
computed on each day. Then, the distributary canals are selected for operation
according to the ranks such that the sum of the demand of the distributary canals
(computed at the head of the main canal) is less than the capacity of the main canal on
any day. This procedure is repeated for the entire season.
Fig. 2 shows the days of operation of the distributary canals in one of the rotations
(third rotation) in the season for illustration. It could be seen that the distributary canals of
this system are grouped into two and their operational days fall within their respective
turns for operation. So, the gate operator can operate a few canals at a time and thereby
his travel distance for gate operation is reduced. The number of gate operations is also
reduced by running the distributary canals either with full supply discharges or full close.
Fig. 3 shows the adequacy of water distribution in the distributary canals indicated by
the ratio of supply to demand as per the present model and manual scheduling. It could be
noticed that the releases of water were more than the requirements in many of the
distributary canals in the manual scheduling. Releases made in some of the direct outlets
and distributary canals deviate more from the demand in the case of conventional manual
scheduling. This indicates the inefficiency in water utilisation. The reason for this can be
attributed to the duty-based operation, that is a very approximate way of estimating the
irrigation requirement.
The depth of supply made per hectare (ha) in different distributaries indicates the level
of equity in water distribution. On an average, the distributary canals receive 0.54 m
depth of water per ha at the field outlets as per the model and 0.65 m/ha as per the manual
procedure (Fig. 4). However, the equity (uniformity) in water distribution among the
distributary canals is high in the case of present model compared to the manual
scheduling. Modified inter-quartile ratios, another measure of equity (Abernethy, 1986),
computed for these cases are 1.19 (model) and 1.76 (manual). This indicates that inequity
in water distribution can be reduced from 76% in the conventional scheduling to 19% in
the present model. The reason for inequity could be that the canal losses are accounted on
a gross basis while estimating the demand in the conventional scheduling and not
accounted for the actual length of the canals.

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Fig. 2. Days of operation of the distributary canals of the LBMC in third rotation.

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Fig. 3. Ratio of supply to demand in the distributary canals of the LBMC.

Fig. 4. Depth of water supplied per hectare in the distributary canals of the LBMC.

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Fig. 5. Timeliness in water distribution in the distributary 6R of the LBMC.

The comparison for timeliness in water distribution between the present model and
conventional manual procedure is shown for the distributary canal, 6R, for illustration
(Fig. 5). It is evident from this figure that the timing of water deliveries does not match
with the crop needs in the case of the conventional manual procedure whereas the present
model could meet the crop needs. It could be observed that the releases are more than the
demand in the beginning of the season and less than the demand at the end of the season
(critical period), which might considerably affect the crop production in the case of
conventional scheduling.
This model is developed considering the locational, equity, adequacy and timeliness
criteria in the irrigation scheduling. However, it is not necessary to use all of them in all
the systems. Depending on the system's objective, it is also possible to consider only a
few of them and use the same model with some modifications. For example, Fig. 6 shows
the depth of water supplied per hectare in the distributary canals under adequacy,
locational and timeliness criteria combination (denoted as `productivity option') and also
under equity, locational and timeliness criteria combination (denoted as `equity option')
for a condition of allocating of 40.0 million m3 of water from the reservoir for irrigation
in a season. This represents the condition of water shortage in a season and at least
61.0 m3 of water is required to meet the demand in the entire command. The productivity
option tries to achieve full crop production in a group of distributaries by meeting the full
crop water requirement and no production in rest of the distributaries without release of
water. On the other hand, the equity option aims to share the available water to all
distributaries and achieves a certain level of production. It is also possible for the manger
to make a decision among these options in advance, when the water availability is very
less. For example, let us assume that water available for irrigation is only in the order of
25±30% of the total demand. In this situation, on an average, depth of 0.18 m/ha could be
supplied. But, it may not be wise to go for equity option as the crop production will be
reduced more than 40% in all the canals if the depth of supply is less than the minimum

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341

Fig. 6. Depth of water supplied per hectare under productivity and equity options in the LBMC under short
supply condition.

permissible level of 0.20 m for groundnut in this command area. So, the manager can
decide to go for productivity option by giving water to a few canals. This kind of
approach is useful for decision making when there is shortage of water in a season.

5. Conclusions
An improved multi-criteria scheduling procedure for rotational water distribution is
presented in this paper. This model has incorporated the manpower management aspect
along with other irrigation performance indicators. This model is computationally
intensive so that it cannot be worked manually but a simple Personal Computer is
sufficient.
The various criteria involved in rotational water distribution are represented by weights
to design or plan the water delivery schedule in this study. The weights discussed here are
not exhaustive as this study focuses only on water delivery component of an irrigation
system. For the case study, the concern is mainly on the weights discussed here. However,
other suitable weights can also be framed according to the requirement elsewhere in a
system. Economic criterion or social criterion may be considered explicitly. The
relationship between yield or any economic indicator and each of the weights considered
are not known directly or requires many assumptions for defining the relationships, given
different levels, inputs and complexities associated within an irrigation system as
explained in the introduction (Smith, 1990). Hence, trade-off among the weights has not
been analysed in this study.

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The developed model is demonstrated with Sathanur irrigation system in India. It is
observed from the case study that the water distribution pattern obtained from the present
model is more effective in fulfilling the multiple objectives. It is also observed that the
present model is more efficient in meeting the crop needs compared to the duty based
conventional scheduling. The performance of the water delivery among the canals can be
improved to the range of supply to demand ratio of 0.95±1.05, from the present range of
supply to demand ratio of 0.85±5.90. The crop water requirement based water delivery
schedule has advantages over the conventional scheduling. They are: (a) it helps to meet
the crop needs as well as to achieve the equity by distributing the water proportionately
among the canals, and (b) it is also possible to include more than one crop in the
scheduling model, if needed. In a few pockets of the command area of Sathanur, farmers
grow crops other than the notional or authorised and tend to use more water. In the
manual procedure, this is not considered as incorporating them in calculation procedure
makes it difficult. It can be easily accommodated in the model if proper database on area
and locations is available. The present model can also be used to get different scheduling
scenarios (water distribution pattern) by varying the number of rotations, duration of each
rotation and percentage of discharge through the distributary canals. This model will be
useful for planning and operating rotational water distribution system having multiple
objectives. The potential of the model can be well observed when the distribution canals
are larger in number and vary in discharge capacity.

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