A new planning model for canal scheduling
of rotational irrigation
C. Santhi
a,*, N.V. Pundarikanthan
baBlackland Research Center, 808 E. Blackland Road, Temple, TX 76 502, USA bCenter 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: [email protected] (C. Santhi).
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.
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.
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:
g
Pn
k1distributary capacityk
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:
where,W1ktis 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
where PIA is the adequacy performance indicator, T represents time and R represents region,PAQD/QRifQDQRelsePA1,QDactual amount delivered by the system and QRamount 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
dk
D fork1;2;3;. . .;n; (3)
whereW2k stands for the weight of the distributaryk, dk for the duration of operation required (in days) to meet the demand of the distributary canalkat full supply discharge andDfor the crop duration (in days). For example, if a distributary canal requires 100
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 50/1500.333. 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:
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),QDthe actual amount of water delivered by the system andQRthe 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.
W3k
W3kis the weight representing the equity criteria indirectly,Ak the virtual area of the
distributary canalk,Akis the area of the distributary canalk, losskis 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
W4kri
whereW4kri is the timeliness weight of the distributary canal `k' for the day `i' in the rotation `r',Rkris the demand of the distributary canal `k' for the rotation `r' and
X
iÿ1
j1
Xkrj
the net release to the distributary canal `k' till the previous day (iÿ1) in the rota-tion `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
WktiW1ktW2kW3kW4kri; (8)
where,Wkriis 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.
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
(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 (n41) 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 (g2) 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,
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.
Table 1
Details of the distributary canals in the LBMCa
DY. No. Name of the DY. Chainage (km) Direct area (ha) Discharge (m3/s)
1 DI 1R 2.96 2.93 0.014
31 DY 11R A 27.36 1000.00 1.862
32 DY 11R B 27.36 618.76 1.862
33 DY 11R C 27.80 171.52 0.197
34 DY 12R 29.34 156.46 0.180
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
RkrÿPijÿ11Xkrj
Rkr
for distributary k1;2;3;. . .;41;
rotations r1;2;3;. . .;7; and days in a rotation i1;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.
Fig.
2.
Da
ys
of
operati
on
of
the
distrib
utary
cana
ls
of
the
LB
MC
in
third
ro
Fig. 3. Ratio of supply to demand in the distributary canals 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 m3of water from the reservoir for irrigation in a season. This represents the condition of water shortage in a season and at least 61.0 m3of 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
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.
Fig. 6. Depth of water supplied per hectare under productivity and equity options in the LBMC under short supply condition.
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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