Equitable canal water allocation Deliverable B.1 Report for project "Revitalising Irrigation in Pakistan" University of Canterbury, Christchurch, New Zealand in partnership with International Water Management Institute, Lahore, Pakistan 26 June 2014 EQUITABLE CANAL WATER ALLOCATION Table of contents 1 INTRODUCTION 3 2 MODEL DEVELOPMENT 3 2.1 EQUITY COSTS 2.2 ALLOCATION COSTS 2.3 ECWA MODEL 2.4 DETERMINING ALLOCATION COSTS 2.5 DETERMINING EQUITY COST 4 5 7 5 4 3 APPLICATION 9 3.1 MODEL SCENARIOS 3.2 RESULTS 9 10 4 CONCLUSIONS AND RECOMMENDATIONS 13 5 REFERENCES 13 2 Deliverable B.1 | RevIIP EQUITABLE CANAL WATER ALLOCATION 1 Introduction In the Punjab, Pakistan, irrigation water is in short supply. Some of this is entirely intentional. The warabandi system, originally designed during the British colonial times, was intended to operate as a so-called protective-irrigation system, where water is applied to as large an area as possible. This was done in order to give many farmers yield security rather than allowing optimal yields for a few. Seckler et al. (1988) state that in the same system in India a farmer can expect to irrigate one-third of their culturable command area (CCA) four times per season. This comes down to a “water duty” of 0.17 l s-1 ha-1 (1 ft3 per 416 acres). Bandaragoda (1996) suggests that for Pakistani Punjab the average water duty is 0.28 l s-1 ha-1 on 100% cropping intensity. Actual water duties range from 0.200.30 l s-1 ha-1 (Bandaragoda and Rehman, 1995). Even the most generous water duty of 0.30 l s-1 ha-1 only provides 2.6 mm of irrigation water per day in an area where the evapotranspiration during the coldest months is over 3 mm day-1 and during the hottest can reach well in excess of 9 mm day-1. On top of the intentional deficit, there is also an actual shortage of water of water. Hussain et al. (2011) estimates that for the year 2015, only 63% of the total irrigation water requirement can be met from surface water resources, assuming there are no losses at all, nor any competition from other sectors such as industry or domestic water supply. As a result, in many areas the irrigation department does not receive enough water to supply all canals under their command with sufficient water. Additionally many of the main canals in the Punjab are run-of-the-river systems. Discharges in these systems fluctuate with river level (Anwar and Haq, 2013) and very low and/or very high river levels may cause main canals to be closed all together. All these issues mean that many canals do not always run at their design discharge level. Bhutta (1990) determined that in one study area the canals run at less than 75% of their design discharge for 166 days of the year. In close to two thirds of the cases this was due to low river or main canal levels, but water diversions to other parts of the system and poor maintenance causing problems such as breaches, leakages and flooding are also at fault. Under those circumstances of varying and lower than expected discharges some decisions have to be made; what discharge should each canal receive and/or should any of the canals be closed? These decisions are made by the Irrigation Department. Current discharge amounts, canal openings and closures appear to be unorganised and somewhat haphazard. No systematic or consistent decision taking method has been discovered. As a result canal water allocation can be very inequitable with some canals receiving far more water than others (even when adjusted for area). For instance during Kharif 2011 (hot season, April-October) the 17 distributaries (sub-canals) that are supplied by Hakra Branch Canal received on average 70% of their target allocation over the season (PMIU, 2014). The distributary that received the most water got 76% of their target, whereas the canal who received the least water only got 57%. It is inequities like these that create unrest between distributaries, distrust toward the irrigation department and an unwillingness to pay for services (why pay for something you either don’t get or cannot rely on?). Equity is an important objective when it comes to the delivery of water. Each distributary should receive a similar amount of water, but similarly each distributary should have an equal share of the burden of non-delivery. Due to the chronic water shortage in the Punjab it is inevitable and unavoidable that some distributaries do not receive water. These interruptions of service should also be distributed in such a way that it is not the same canal that gets closed week after week. This paper introduces an optimisation model which provides a systematic and consistent approach to the decision making process. The model allocates the available water to the distributaries taking into account deliveries during previous weeks. By doing this it aims to reduce inequity between the distributaries. The results from the model will be compared to the schedules for several seasons as reported by the irrigation department. 2 Model development Optimisation models are built on the premise that there is a cost to be avoided i.e. minimised, or a benefit to be maximised. When considering irrigation scheduling at farm level, maximisation of the RevIIP | Deliverable B.1 3 EQUITABLE CANAL WATER ALLOCATION benefits or profits is probably the aim. At distributary level and up it often makes more sense to minimise the costs involved, since distributaries are not operated for profit (at least not in Pakistan). Operating a canal has a monetary aspect, but the direct financial costs are assumed to be similar for all distributaries and are not taken into account in this report. The indirect costs are not monetary, but related to avoiding to undesirable situations such as canals overtopping, delivering less/more than the target amount, etc. When considering these costs there are two aspects to consider, the equity costs and the allocation costs. Equity costs aim to reduce the cost of giving a particular distributary more or less water that the other distributaries. Allocation costs are meant to keep the actual delivery of water as close to the target as possible. The concepts of equity and allocation costs are explained further below. 2.1 Equity costs One of the fundamental principles of the warabandi system is equity between users (Zardari and Cordery, 2010). The system is designed such that there is a fixed amount of water available per unit area. Due to water shortages, it is not always possible to deliver the full amount. However, even if the actual amount of water supplied is less, the principle of equity between users is still valid. Inequity becomes more and more apparent as a growing season progresses. If one distributary is closed for a week, the effects are probably not too dramatic. Keeping the same distributary closed for several weeks in a row can lead to crop failure. One of the main aims of the model is to create a schedule that is equitable, not only over a season, but as much as possible also on a week to week basis. After all there is no point in closing a distributary for the first three quarters of a growing season and then trying to catch up in the last couple of weeks. By including an equity cost in the model it is possible to improve the equity in the model. Inequity between distributaries results in a higher equity cost, equity between distributaries results in lower equity costs. Minimising the model should therefore produce a more equitable opening/closing schedule. 2.2 Determining equity cost It is not enough to look at each scheduling interval individually. In a system where canal closures are a regular occurrence, real equity can only be achieved by looking over an entire growing season. Since all distributaries serve different sized command areas, equity is probably best measured though cumulative depth of delivered irrigation water. The cumulative depth can be used to determine a second penalty cost. This penalty cost, called equity cost, will ensure that those distributaries that have received less water than others will receive priority. Anwar and Haq (2013) showed how equity between distributaries can be measured using the Gini-index. The Gini-index will be used to test a number of methods for determining equity costs. The most simple way of giving priority to a particular distributary is by giving priority to those distributaries that received no water during the previous interval, or rather penalise those that did. This can be achieved through a 0/1 function: eiw 1 if irrigated during the previous interval i {1,..., N } 0 otherwise (1) where: eiw = equity cost for distributary i during interval w Another way to determine the equity cost is to look at the difference in cumulative depth between distributaries. It would seem logical to look at the deviation from the mean, but would result in negative numbers, something that should be avoided in linear programming. Therefore each equity cost is calculated based on the deviation from the maximum cumulative depth eiw ( Dmax w Diw ) f i {1,..., N } (2) where: Dmax w = maximum cumulative depth of delivered irrigation water after w intervals; Diw = cumulative depth delivered to distributary i after w intervals; and f = multiplication factor. Since 4 Deliverable B.1 | RevIIP EQUITABLE CANAL WATER ALLOCATION cumulative depth can be a small number when expressed in inches (as is the case in Pakistan), ei will also be a small number. When both allocation costs and equity costs are taken into account the equity costs may need to be multiplied by a factor f to increase the effectiveness of the equity cost. The final method described here to calculate the equity cost incorporates both giving absolute priority (through the 0/1 function) and relative priority (through the Dmax - Di function) 1 if irrigated the previous interval eiw Dmax w Di f 0 otherwise (3) 2.3 Allocation costs The damage done by over- and under-irrigation over several intervals is easy to understand. Underirrigation leads to drought stress and results in a reduction in yield. Over-irrigation leads to problems such as waterlogging and salinity issues, and also results in a reduction in yield. Both should therefore be avoided. It should be noted that in the warabandi system where protective irrigation is practised, over-irrigation can be a good thing from an agronomic perspective. In this system underirrigation is standard and over-irrigation (up to a certain point) brings the total water allocation closer to optimal. However, since there is a general water shortage it is likely that ”beneficial over-irrigation” in one part of the system results in under-irrigation in other parts. Since equity is one of the guiding principles of the warabandi system, it still should be avoided. There usually is a range over which the effect of over and under-irrigation is not too severe, and the model should aim to stay between those limits if a full allocation is not possible. Delivering water outside these ranges can lead to the problems described above and should be avoided. In fact it might be better not to deliver any water at all, rather than only a little, especially if this means another distributary can receive the full amount. This range of possibilities means that there is not one single value that determines the outcomes of the model. As a comparison, the maximum capacity of a channel is determined by a single value, go over that value and the channel will overflow its embankments, stay under the value and nothing happens. In linear programming these constraints are called “hard constraints”, they cannot be violated under any circumstances. Constraints like the allocation cost are “soft constraints”, they may be violated, but the more they are, the higher the cost. In the case of the allocation costs, while delivering 100% of the target allocation would be ideal, the actual amount can be more or less; a good example of a soft constraint. Soft constrains can be described by a piece-wise linear function. A piece-wise linear function consists of several straight line segments. Figure 1 shows an example of such a function. The points where the slope of the piece-wise linear function changes are called the breakpoints. Although a piece-wise linear function is linear in the individual segments, as a whole it is non-linear. It is still possible to use a piece-wise linear function in a linear programme through the use of special ordered sets. The concept of special ordered sets was first coined by Beale and Tomlin (1970), but the approach was already described others (e.g. Beale (1968); Beale and Small (1965); and (Land and Doig, 1960). Special ordered sets consist of a set of variables that describe the piece-wise linear function. Two markers are introduced that change position (on the break points) depending on the segment of the piece-wise linear function that is being considered. Any members of the set that do not lie between the two markers are forced to become zero. The markers now function as if they were the lower and upper bound of a normal set of variables and the linear program can now be solved. 2.4 Determining allocation costs Including allocation costs in the model will help to reduce the chances of less than an optimal allocation of water. Delivering the target amount should incur no cost, allocation between the limits should result in a small cost and delivering outside the range should incur a large cost. Minimising the model should now result in a reduction in the allocation costs. Figure 1 shows an example of the allocation costs as a function of the amount of water delivered. In this piecewise function each line RevIIP | Deliverable B.1 5 EQUITABLE CANAL WATER ALLOCATION segment represents a different scenario. The figure shows 6 segments, each corresponding to the cost of different percentage of allocated water actually delivered. 1. no or very little water supplied, 2. some, but insufficient amount of water supplied 3. sufficient water supplied, but less than optimal 4. optimal amount of water supplied 5. ample water supplied, but more than optimal 6. too much water supplied For instance, if 100% of the allocated water has been delivered, the allocation cost is 1. This is shown in Figure 1 as a point, numbered 4. Delivering exactly 100% of the target allocation is often not possible. Delivering less or more than the target amount is not necessarily detrimental. There is however a limit how much the difference can be before yield is affected. Below the lower limit the crop will suffer from drought stress, above the upper limit waterlogging will similarly result in a yield reduction. The exact limits depend on factors such as crop type, growth stage and acceptable yield loss. Figure 1 show that the lower limit has been set at 80% and the upper limit at 120% (note that these have been set arbitrarily, more research is needed to determine the appropriate limits). At those two points the allocation cost has been set 2, a higher number indicating that water deliveries between these limits are less desirable than 100% delivery, which was set at 1. The allocation cost slowly increases between 100% and the limits as shown by segments 3 and 5. In cases where not enough water can be delivered it may in fact be better to give very little or no water at all. That way more water can be supplied to another distributary, allowing that one to reach the lower limit. This can be achieved by giving the first segment a lower allocation cost than the second segment. In Figure 1 10% has been chosen as the cut off. This number was chosen to account for “leftovers”. Since it is likely that the sum of all allocations doesn’t not add up to exactly the amount of water delivered by the branch canal, there has to be a mechanism to deal with the remaining portion, or leftovers. By setting the lower limit at 10% small amounts of water can be let into a channel without incurring too large a penalty. Since there is a small penalty attached to it, the model will try to avoid creating leftovers where possible. At the upper limit of the canal capacity, segment 6 in Figure 1, the allocation cost rapidly increases as water delivery increases. At these levels the canal is at increasing risk of overtopping (some canals may in fact already have overtopped, depending on the capacity). At high rates of water application rates the high water allocation might also result in over-irrigation, waterlogging, salinity and other related problems. The limits and costs in Figure 1 are an example only. It is possible to change these so they better represent the system this function is applied to. It is possible to have a different function for each canal in the system. This makes it possible to set different levels for canals with a different capacity or other differences such as crop type. 6 Deliverable B.1 | RevIIP EQUITABLE CANAL WATER ALLOCATION Figure 1. Example of piecewise linear allocation cost function 2.5 ECWA model For the Equitable Canal Water Allocation model (ECWA), let I = {1,…,N} be a set of distributaries to be scheduled for opening or closing during a certain interval. The following parameters are known for each i ∈ I: target allocation and maximum capacity. To describe the allocation cost function, let J = {1,…,P} be a set of points that describes a piecewise linear function. The following parameters are known for each p ∈ J: “break point” and cost. Detailed descriptions of the decision variable, objective function and constraints follow below. 2.5.1 Decision variable The decision to be made by the model is: how much water should be allocated to each canal? Therefore the decision variable is Ai where Ai = allocation for distributary i. 2.5.2 Objective function The goal of the model is to reduce the costs associated with allocating water to a distributary. This can be achieved by using the following objective function N minimise c i 1 (4) i Where: ci = allocation cost of opening canal i. RevIIP | Deliverable B.1 7 EQUITABLE CANAL WATER ALLOCATION 2.5.3 Hard constraints No distributary can be allocated more water than the maximum capacity of that distributary ai Qmax i i {1,..., N } (5) where: ai = water allocation for distributary i; and Qmax i = maximum flow capacity of distributary i. The total allocation to all distributaries cannot be more than the total amount of water available N a Q i 1 (6) i where: Q = total available flow. 2.5.4 Soft constraints Each the cost of allocating water to a canal is determined by the piecewise allocation cost function which is described as follows ( y p1 - y p ) y p (x - x ) p 1 p 1 p P 1 x 1[ x p , x p 1 ) ( x) (7) where: yp = allocation cost in p; and xp = segment break p of piecewise linear cost function. The allocation for each canal is determined by the target allocation and the cost of allocating P ai y p Ai ip i {1,..., N } (8) p 1 where: Ai = target allocation for distributary i; and λip = weighted variable. The weighted variables for each distributary must add up to 1 P ip 1 i {1,..., N } (9) p 1 The allocation cost of opening each canal is determined by the weighted variables P ci x pip i {1,..., N } (10) p 1 No more than two of the weighted variable λ can be non-zero and must be adjacent. Therefore {ip } is SOS2 i N , p P (11) To include the equity cost ei in the objective function, (4) should be replaced by N minimise(ci ei ) (12) i 1 To increase the importance of the equity costs (1) or (12) can be replaced by 8 Deliverable B.1 | RevIIP EQUITABLE CANAL WATER ALLOCATION N minimise(ci ei ei ) (13) i 1 The model now consists of a decision variable, ai, objective function (4) or (12) or (13) and constraints (5)-(11) and one of (1) - (3). 3 Application The model described previously has been applied to Hakra branch canal in the Punjab, Pakistan. Hakra supplies 17 distributaries with a combined command area of around 200,000 hectares (500,000 acres). Table 1 shows the number, name, target allocation and command area for these 17 distributaries. It should be noted that distributary no.15, “Flood channel” was added long after the other distributaries. It only receives water during Kharif and even then only has junior rights. Table 1. Characteristics of distributaries supplied by Hakra branch canal (PMIU, 2014) no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Name 1L-distributary 1R-distributary 2L-distributary 2R-distributary 3L-distributary 3R-distributary 4L-distributary 4R-distributary 5R-distributary 6R-distributary 7R-distributary 8R-distributary 9-R distributary Bakhu Shah distributary Flood Channel distributary Hakra Left distributary Hakra Right distributary total Target Allocation ft3 s-1 m3 s-1 83 2 19 1 19 1 22 1 10 0 353 10 9 0 226 6 36 1 546 15 273 8 24 1 211 6 6 0 73 2 23 1 510 14 2443 69 Command Area acres hectares 17093 6918 4965 2009 4371 1769 5306 2147 1737 703 72753 29443 1685 682 43454 17586 10550 4270 101818 41206 53855 21795 6357 2573 49195 19909 1505 609 16516 6684 5976 2418 105991 42895 503127 203615 3.1 Model scenarios The irrigation department supplied data for Rabi 2010/11, Kharif 2011 and Kharif 2012 (PMIU, 2014). This data shows the allocation to each distributary for each date of the growing period. Since canal opening/closure decisions are made on a weekly basis, data was aggregated to weekly data. The weekly data for each of these three growing seasons can be found in Appendix B. The raw data can be found on the accompanying cd. Table 2 shows the different combinations of objective functions and equity cost equations that were run for each season. Table 2.Overview of model scenarios Scenario Objective function A 12 B 12 RevIIP | Deliverable B.1 Equity cost calculated from 9 10 with f = 10 9 EQUITABLE CANAL WATER ALLOCATION C D E F G H I J 10 with f = 100 11 with f = 0.1 11 with f = 10 9 10 with f = 10 10 with f = 100 11 with f = 0.1 11 with f = 10 12 12 12 13 13 13 13 13 3.2 Results All models were solved using Lingo 13.0 ®. Each run of the model takes less than one second on average. Running one entire season, or 26 weeks, for each of the different scenarios can be done in less than 4 minutes. Table 3 shows the result of one of the model runs, in this case scenario I. The first column shows the week number, with number 1 starting on October 16, 2010. Weeks 12-14 coincided with the annual closure period. During this period Hakra branch canal runs empty so that maintenance and cleaning of the canal can take place. When running the different scenarios it is best to leave these weeks out completely. This prevents a ‘normal’ closure to be scheduled both directly before the closure (in week 11) and straight afterwards (in week 15). If weeks 12-14 are left in it is possible for a distributary to not get any water for 5 weeks in a row; leaving it out decreases the chances of this happening. Ultimately whether this happens depends on the amount of water available during the weeks before and after the closure period. The second column of Table 3 shows the average discharge available during that week based on the reports from the irrigation department. The remainder of the columns shows the discharge allocated to each distributary for each week. Table 3 shows that most of the time distributaries receive their target amount; 69% of all deliveries are spot on. In 21% of scheduled deliveries a distributary gets no water at all, 7% of the time a distributary gets at least 80% of their allocation and finally 2% of the deliveries are larger than 100% (but less than the maximum capacity of the canal). In this particular schedule, it never happens that a distributary gets water, but less than 80% of their target amount. Table 3. Schedule for distributaries 1-14, 16 and 17 during Rabi 2010-2011, prepared using scenario I (in cfs) week 1 delivery 766 1 83 2 19 3 19 4 22 2 1494 0 0 0 0 3 1432 83 19 19 22 4 1401 0 19 19 5 1590 83 19 6 1850 83 19 7 1564 83 8 1771 5 10 6 0 0 353 10 7 8 9 226 0 0 9 36 10 11 0 289 0 437 13 0 14 6 0 0 211 0 16 23 17 0 0 493 0 9 226 36 471 273 24 211 6 23 22 0 353 9 181 36 0 24 199 6 23 510 19 22 10 353 0 36 546 273 24 176 6 23 0 22 10 353 9 226 36 529 24 0 6 23 510 19 19 22 0 329 9 36 0 273 24 211 6 23 510 0 19 19 22 10 0 0 226 36 546 221 24 211 6 23 408 0 0 0 9 1868 83 19 19 28 10 353 9 226 36 10 1568 83 19 19 18 0 348 9 226 36 546 11 1185 83 19 19 0 10 0 9 0 36 15 36 0 0 0 22 8 0 0 0 0 16 1486 83 19 19 0 10 0 9 226 17 1788 83 19 19 22 0 353 9 226 18 1983 83 19 19 22 10 353 0 223 36 546 19 1954 0 19 19 22 0 353 9 20 2014 83 19 19 22 21 1869 83 19 19 22 22 1926 83 19 19 22 10 12 24 0 0 311 0 0 24 211 6 23 510 0 24 211 6 23 0 273 24 173 6 23 510 0 6 0 0 36 546 273 24 211 7 23 0 36 24 211 6 23 510 0 24 211 6 23 408 0 36 455 273 24 211 0 23 510 10 353 0 226 36 437 273 24 0 6 23 483 13 353 9 226 36 552 273 24 211 6 23 9 226 36 465 273 24 211 6 23 510 0 0 0 0 0 247 0 0 0 Deliverable B.1 | RevIIP EQUITABLE CANAL WATER ALLOCATION 23 1901 0 19 0 22 10 353 9 181 36 497 24 1894 83 19 19 22 13 353 9 271 36 25 2021 83 19 19 22 0 342 9 26 1778 83 19 19 22 10 353 36 0 0 226 0 24 211 6 23 510 0 273 24 211 6 23 532 36 546 273 24 211 6 23 408 24 211 6 23 510 0 236 The cumulative supplied depth over the entire Rabi 2010-2011 for each distributary is shown in Figure 2. It can be seen that all distributaries are close together. To determine the inequity of this delivery schedule, each week the Gini-index was calculated. This is also shown in Figure 2. Initially the index starts quite high, i.e. high inequity. Since it is unavoidable that some distributaries do not get any water during that first week, it automatically means a high index. As time progresses these extremes even out and at the end of the season ends up being much lower. For scenario I during Rabi 20102011 the Gini-index is 3.3% at the end of the season, indicating low inequity. Figure 2. Cumulative supplied depth for scenario I, Rabi 2010-2011 3.3 Inequity Section 3.2 shows the results of one of the scenarios. In order to determine which combination(s) of objective function and equity cost function works best, all scenarios need to be compared. Figure 3 shows the gini-index for all scenarios plus the gini-index for the schedule as reported by the irrigation department. It shows that the initial extremes are very common, with the irrigation department’s schedule suffering from this more than the modelled scenarios. As expected the Gini-index evens out fairly soon for most scenarios, with the exception of scenarios A and F. In these two scenarios the equity cost is simply determined by giving priority to those canals that did not receive any water during the previous week. Since depth applied is not taken into account, it is perhaps not surprising that the “zigzagging” is more pronounced and that the final Gini-index is higher than for all other scenarios, including that determined by the irrigation department. There is very little difference between scenarios B-E, G-J when it comes to the Gini-index. The Gini-index for the schedule prepared by the irrigation department lays in between scenarios A & F and the remainder of the scenarios. RevIIP | Deliverable B.1 11 EQUITABLE CANAL WATER ALLOCATION Appendix D shows the Gini-index for the Kharif 2011 and Kharif 2012. Although the actual numbers are different, the trends seen in Rabi 2010-2011 are similar in both Kharif seasons, larger amount of zigzagging for scenarios A and F with a fairly high inequity compared to the other schedules, low and very similar numbers for scenarios B-E,G-J and the irrigation department’s schedule somewhere in between. If the inequity of the different scenarios is so similar, is there another way to distinguish between a good and a bad schedule? Figure 3. Gini-index for all scenarios, Rabi 2011-2012 4 Service interruption There are several issues when it comes to the delivery of water to the distributaries. First and foremost there is the reliability of the delivery. Service interruptions are a serious concern for all water users along the distributaries. The longer they last the more a crop yield is affected. As mentioned before, even though the amount of water delivered is the same, receiving water every other week for a season is far less damaging than receiving water for the first half of a season, followed by nothing for the second half. Although more research in this area is required, for the moment it is assumed that the shorter the duration of the service interruption the better. Service interruptions can be broken up into two components, the quantity that is being delivered and the frequency of that delivery. These two parameters can be easily measured and should be able to provide an insight into how well the different models described in the previous section perform. As described before, a minimum delivery of water is needed and anything less than this amount is considered wasted. For the purpose of this application of Hakra branch, deliveries of less than 80% of the target allocation fall into this category. The frequency of delivery can be measured by counting the weeks in which no water is delivered to a particular canal. Since small gaps are inevitable and unavoidable, it is proposed to only count service interruptions that last 2 weeks or longer. Table 4 shows the number of service interruptions (gap count) and duration of the longest service interruption (max gap size) for all scenarios and the schedule reported by the Irrigation Department. Even though there was very little difference between the scenarios with regards to equity, there is a significant difference when considering service interruptions. Table 4 for instance shows that for Rabi 2010-2011, the best performing scenario is scenario I. There are only 4 service interruptions that last 2 week or longer and the longest interruption lasts 3 weeks. As a comparison, the schedule reported by the Irrigation Department has a total of 42 service interruptions with a maximum length of 6 weeks. 12 Deliverable B.1 | RevIIP EQUITABLE CANAL WATER ALLOCATION The results for Kharif 2011 and Kharif 2012 show a similar pattern. The complete tables for those two seasons can be found in Appendix E. Table 4. Gap count and maximum gap size for all scenarios, Rabi 2010-2011 A B C D E F G H I Gap count 6 26 26 10 6 6 26 26 4 Max gap size 3 4 4 3 3 3 4 4 3 J IrrDept 6 42 3 6 5 Conclusions and recommendations The work done for in this study has shown that it is possible to use linear programming to determine the opening/closing schedules for a water short irrigation system. The method developed minimises inequity and limits service interruptions where possible. This has the potential to provide a much more dependable service to water users who are facing an uncertain cropping season due to water shortages. Water that is allocated in a fair and equitable way can reduce the potential for social unrest and may encourage water users to pay for the services provided. There are still some shortcomings to the models that were developed. Although there seems to be a difference between the 2 objective functions provided, three cropping seasons is not enough data to provide a definite conclusion as to which one results in a better schedule. Similarly, no sensitivity analysis was done of the multiplication factor which determines the equity cost. While it appears there are differences when using different values, it is not clear which would result in a better schedule. At the moment the model works on the principle that all water entering a branch canal must be completely allocated to the distributaries. This can result in small amounts of water being let in to a distributary. It might be possible to prevent this wastage by taking in less water, allowing the water to be reused downstream. This however is probably only ever acceptable to users within the branch canal command area if users receive some form of compensation, whether it is monetary or in the form of extra water during a subsequent interval. Canals within the same system may have different rights to water. For instance in Hakra Branch Canal the Flood Channel only has junior rights. In this study the Flood Channel was left out all together during Rabi and was assumed to have full rights during Kharif. Some adjustment to the model is necessary to fully capture the complexity of the junior rights and senior rights. For future work it would be good to use the schedules obtained with the method described in this report in a crop growth model. This will help to confirm which model gives the best results. 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Beale EML and Small RE (1965). “Mixed integer programming by a branch and bound technique”. in: Kalenich WA, ed., Proceedings of the IFIP Congress 1965, Spartan Press, Washington, 2, 450-451 Beale EML and Tomlin JA (1970). “Special facilities in a general mathematical programming system for nonconvex problems using ordered sets of variables”, in: Lawrence J, ed., Proceedings of the fifth international conference on operational research, Tavistock Publications, London, 447–454. Bhutta MN, (1990). Effect of varying discharges on the equity of water distribution in the irrigation system. Ph.D. dissertation, Centre of Excellence in Water Resources Engineering, Universwity of Engineering and Technology, Lahore, Pakistan. Hussain I, Hussain Z, Sial MH, Akram W and Farhan MF (2011). “Water balance, supply and demand and irrigation efficiency of Indus Basin”. Pakistan Economic and Social Review, 49(1), 13-38. Land AH and Doig AG (1960). “An automatic method for solving discrete programming problems”. Econometria, 28, 497-520. PMIU, 2014. Database of the Programme Monitoring and Implementation Unit for Canal Operations and Discharge Data in Irrigation Department, www.irrigation.punjab.gov.pk, accessed 2013 and 2014. Seckler D, Sampath RK, Raheja SK (1998). “An index for measuring the performance of irrigation management systems with an application”. Water Resources Bulletin, 24(4), 855-860. Zardari NU and Cordery I (2010). Éstimating the effectiveness of a rotational irrigation delivery system: a case study from Pakistan.” Irrigation and Dainage 59, 277-290. 14 Deliverable B.1 | RevIIP EQUITABLE CANAL WATER ALLOCATION Appendix A: Lingo code ECWA model RevIIP | Deliverable B.1 15 !**********************************************************************************************************; !** **; !** Equitable Canal Water Allocation model **; !** **; !** model developed by Tonny de Vries for IWMI-Pakistan **; !** **; !** RevIIP project, 2014 **; !** **; !**********************************************************************************************************; model: sets: canal: demand, allocation, cost, maxQ, PreviousAllocation, PenaltyCost; point/1..7/: costX, allocationY; link(canal, point): weight; endsets data: availability, demand, maxQ, PreviousAllocation, PenaltyCost = @OLE('C:\Users\ttd13\Documents\RevIIP\ECWA\RevIIP.ECWA.Hakra.WeeklyModel.Rabi2010_11.xl sm', 'Availability', 'Demand', 'MaxQ', PreviousAllocation, PenaltyCost); @OLE('C:\Users\ttd13\Documents\RevIIP\ECWA\RevIIP.ECWA.Hakra.WeeklyModel.Rabi2010_11.xl sm', 'allocation') = @writefor( canal(i): allocation(i)); costX = allocationY = enddata 5, 0.00, 10, 0.10, 10, 0.79, 2, 0.80, 1, 1.00, 2, 1.20, 10; 1.50; @for( canal(i): allocation(i) <= maxQ(i)); @sum(canal(i): allocation(i)) = availability; @for( canal(i): @gin(allocation(i))); @for( canal(i): cost(i) = @sum( point(p): costX(p) * weight(i,p))); @for( canal(i): allocation(i) = @sum( point(p): allocationY(p) * demand(i) * weight(i,p))); @for(canal(i): @sum( point(p): weight(i,p)) = 1); @for( link(i,p): @sos2('SOS_2' + canal(i), weight(i,p))); min = @sum( canal(i): cost(i)*penaltycost(i) +10*penaltycost(i)); end go quit !NOTE: the name and path of the document will have to be changed when run from any other location than the one mentioned above (shown above under “data”). EQUITABLE CANAL WATER ALLOCATION Appendix B: Reported schedules Hakra Branch Rabi 2010-2011 Kharif 2011 Kharif 2012 RevIIP | Deliverable B.1 17 RevIIP | Deliverable B.1 Table 5. Rabi 2010-2011, weekly discharge (cfs) for Hakra Branch Canal as reported by the Irrigation Department Distributary number 16-10-2010 23-10-2010 30-10-2010 06-11-2010 13-11-2010 20-11-2010 27-11-2010 04-12-2010 11-12-2010 18-12-2010 25-12-2010 01-01-2011 08-01-2011 15-01-2011 22-01-2011 29-01-2011 05-02-2011 12-02-2011 19-02-2011 26-02-2011 05-03-2011 12-03-2011 19-03-2011 26-03-2011 02-04-2011 09-04-2011 1 0 80 65 53 93 93 80 80 93 93 27 0 0 0 0 74 0 74 86 86 49 35 86 86 84 47 2 0 18 14 11 17 19 16 17 19 3 11 0 0 0 0 12 20 18 17 20 17 16 17 20 16 16 3 3 17 17 11 20 20 14 20 20 20 6 0 0 0 0 6 20 20 20 15 15 20 20 20 20 17 4 0 19 19 13 22 22 18 18 22 3 13 0 0 0 0 4 22 22 19 22 22 22 22 22 22 21 5 5 5 9 10 10 10 5 10 10 10 4 0 0 0 0 10 0 9 10 6 3 3 10 9 8 3 6 0 339 113 226 242 274 339 253 401 56 268 0 0 0 36 320 370 327 177 259 352 368 297 88 333 324 7 3 2 6 6 4 9 6 9 9 9 4 0 0 0 0 6 0 8 9 9 5 5 9 9 9 5 8 0 211 70 141 142 71 213 0 249 249 71 0 0 0 0 103 0 213 249 211 132 83 248 233 216 112 9 10 31 31 21 36 36 26 36 36 36 10 0 0 0 0 10 36 36 36 32 33 36 36 21 36 31 10 0 490 218 343 421 298 511 158 600 295 127 0 0 0 0 0 577 599 588 397 282 588 574 546 278 444 *Note: Distributary 15 did not receive any water during Rabi 2010-2011 and is therefore not included. 11 80 180 254 184 277 280 80 280 136 7 181 0 0 0 0 273 273 270 103 234 266 244 212 19 273 273 12 7 9 23 18 25 25 18 25 25 25 11 0 0 0 0 18 0 21 24 24 14 8 25 25 25 13 13 51 0 154 102 90 233 148 238 238 221 46 0 0 0 0 170 0 168 226 238 136 79 241 241 223 105 14 0 9 9 6 10 10 8 8 10 1 6 0 0 0 0 6 10 7 5 6 6 6 6 6 6 5 16 19 3 16 10 7 16 10 23 0 20 13 0 0 0 0 16 23 7 16 23 23 15 3 23 23 23 17 588 81 414 246 174 434 72 596 0 520 387 0 0 0 0 458 437 184 369 432 514 398 95 526 449 339 TOTAL 766 1494 1432 1401 1590 1850 1564 1771 1868 1568 1185 0 0 0 36 1486 1788 1983 1954 2014 1869 1926 1901 1894 2021 1778 13 Table 6. Kharif 2011, weekly discharge (cfs) for Hakra Branch Canal as reported by the Irrigation Department Distributary number 16-04-2011 23-04-2011 30-04-2011 07-05-2011 14-05-2011 21-05-2011 28-05-2011 04-06-2011 11-06-2011 18-06-2011 25-06-2011 02-07-2011 09-07-2011 16-07-2011 23-07-2011 30-07-2011 06-08-2011 13-08-2011 20-08-2011 27-08-2011 03-09-2011 10-09-2011 17-09-2011 24-09-2011 01-10-2011 08-10-2011 1 77 83 83 71 12 83 90 90 26 64 90 90 75 0 90 90 87 79 74 29 0 0 0 66 85 77 2 16 20 20 20 17 20 20 20 20 18 16 6 19 20 20 6 15 20 20 8 0 0 0 13 12 10 3 20 20 11 8 20 20 20 3 14 20 20 13 3 20 20 3 0 14 20 10 0 0 3 12 11 5 4 22 22 22 22 19 22 22 22 22 22 19 6 19 19 22 8 18 21 22 10 0 0 3 14 14 11 5 6 4 9 10 9 0 10 10 10 6 3 8 9 9 0 0 7 10 7 0 0 0 0 5 6 10 6 308 194 184 358 359 353 44 312 400 403 230 108 402 364 310 241 265 349 344 117 0 0 57 200 123 175 7 9 9 9 6 1 9 9 9 3 5 9 9 8 0 9 1 8 4 3 6 0 0 5 8 9 9 8 190 233 212 133 32 226 248 242 69 171 249 251 209 0 246 252 203 152 97 68 0 0 0 170 205 212 9 36 36 21 10 36 36 36 5 26 36 36 26 6 36 36 5 0 25 35 17 0 0 2 29 24 10 10 482 534 285 160 586 546 556 77 402 563 567 416 95 614 621 89 0 343 583 397 35 48 275 570 486 85 11 252 117 117 259 295 273 0 245 294 283 136 84 294 295 309 46 212 306 310 153 12 0 132 273 67 149 12 20 25 25 18 4 25 25 25 7 14 25 25 22 0 26 4 19 11 9 19 0 0 8 26 26 26 13 205 236 227 148 27 212 227 223 62 122 233 242 202 0 256 37 176 105 83 184 0 0 39 218 258 224 14 6 6 6 6 5 6 6 6 6 6 5 5 6 6 6 2 4 6 6 2 0 0 0 0 2 3 15 50 74 74 53 2 74 63 68 18 31 74 74 62 0 71 11 52 32 25 63 8 0 8 63 67 51 16 13 13 23 23 20 0 23 23 23 10 10 23 23 23 3 15 23 23 19 20 8 0 3 13 16 23 17 TOTAL 171 1883 264 1890 512 1840 521 1826 435 1879 10 1915 539 1938 534 1914 507 1909 191 1965 203 1925 526 1912 464 1918 552 1958 14 2059 209 1019 515 1604 537 2037 388 2045 134 1237 85 148 129 177 250 785 128 1808 363 1774 592 1672 Table 7. Kharif 2012, weekly discharge (cfs) for Hakra Branch Canal as reported by the Irrigation Department Distributary number 31-03-2012 07-04-2012 14-04-2012 21-04-2012 28-04-2012 05-05-2012 12-05-2012 19-05-2012 26-05-2012 02-06-2012 09-06-2012 16-06-2012 23-06-2012 30-06-2012 07-07-2012 14-07-2012 21-07-2012 28-07-2012 04-08-2012 11-08-2012 18-08-2012 25-08-2012 01-09-2012 08-09-2012 15-09-2012 22-09-2012 1 45 90 53 21 81 37 12 46 53 19 87 26 90 90 26 75 90 64 7 90 89 26 62 34 47 37 2 20 18 14 7 15 14 9 12 0 9 17 8 19 19 19 19 19 19 19 19 19 19 16 5 1 19 3 10 9 18 17 19 6 11 11 0 20 18 6 20 6 11 20 14 3 20 20 5 14 20 8 4 20 4 22 22 17 7 16 16 13 16 0 14 18 10 22 22 22 22 22 22 22 22 22 22 22 6 8 22 5 5 2 5 3 1 4 7 7 0 9 0 10 10 3 6 9 8 1 10 10 1 7 7 1 1 8 6 185 93 268 121 15 300 141 183 0 84 353 0 397 126 297 379 265 102 415 415 99 295 410 146 163 383 7 5 5 9 8 8 9 4 4 5 1 9 0 7 3 5 9 6 1 9 9 3 6 8 2 2 9 8 260 249 179 40 238 74 0 139 167 59 230 53 260 262 109 204 262 187 27 262 262 72 172 99 107 61 9 18 15 32 28 36 10 21 21 0 36 34 10 36 10 21 36 26 5 36 36 8 26 36 15 7 36 10 598 534 449 394 554 247 348 329 0 535 243 1413 91 468 650 401 177 635 647 25 519 510 421 148 454 515 11 150 90 291 179 78 214 300 209 0 234 0 292 300 86 171 302 284 43 300 300 43 214 300 141 65 291 12 13 11 25 25 4 16 25 11 0 19 0 26 11 26 26 11 7 26 22 7 26 26 17 7 13 18 13 235 258 209 135 217 74 144 148 0 168 0 235 35 178 251 102 74 258 210 34 243 254 111 59 142 171 14 8 7 5 3 5 3 2 3 0 3 5 3 6 6 6 6 6 6 6 6 6 6 5 0 0 6 15 0 0 17 32 61 53 70 63 17 43 74 18 63 23 48 81 61 0 79 86 12 59 87 43 10 85 16 23 20 9 10 16 13 13 13 0 16 0 23 3 23 23 16 23 20 3 23 23 23 23 11 9 16 17 TOTAL 311 1908 535 1958 324 1924 139 1169 347 1711 600 1690 297 1417 272 1487 157 399 79 1348 644 1732 0 2133 551 1921 564 1915 236 1927 284 1976 620 1964 485 1877 0 1832 599 1963 518 1898 271 1850 377 2094 309 1034 258 1291 183 1880 EQUITABLE CANAL WATER ALLOCATION Appendix C. Schedules for Rabbi 2010-2011 Note: schedules for Kharif 2011 and Kharif 2012 can be found on the accompanying cd 21 Deliverable B.1 | RevIIP Table 8. Scenario A, Rabi 2010-2011 week. delivery 1 766 2 1494 3 1432 4 1401 5 1590 6 1850 7 1564 8 1771 9 1868 10 1568 11 1185 15 36 16 1486 17 1788 18 1983 19 1954 20 2014 21 1869 22 1926 23 1901 24 1894 25 2021 26 1778 1 2 3 4 5 6 7 8 9 10 11 12 13 14 16 17 83 0 83 0 83 0 83 8 83 0 83 0 83 0 83 8 83 0 83 0 83 60 83 19 2 19 1 19 15 19 15 19 0 19 0 19 2 19 15 19 2 19 0 19 1 19 19 2 19 1 19 16 0 19 2 19 1 17 16 2 19 0 19 16 1 19 1 19 0 22 3 22 0 22 0 22 2 22 0 22 0 22 3 22 2 22 17 22 0 22 2 22 10 1 10 1 10 1 10 12 1 10 1 10 1 10 12 13 0 10 1 10 1 10 0 0 439 0 353 0 353 424 427 440 438 278 0 0 353 441 441 439 439 36 353 0 353 423 9 1 9 0 9 1 9 11 1 9 0 9 0 9 0 9 1 9 0 9 0 9 1 226 271 22 226 0 226 0 226 226 0 226 0 226 281 226 258 0 226 226 0 226 0 226 36 4 36 0 36 43 0 36 4 36 3 0 36 0 36 3 36 28 36 0 36 3 36 0 682 165 546 345 546 0 546 23 546 0 0 546 29 546 482 431 546 618 657 683 683 31 289 27 273 0 273 5 273 27 273 0 273 0 273 328 328 0 273 326 328 0 273 0 273 24 3 24 2 24 3 24 18 24 0 24 0 24 3 24 2 24 28 2 24 2 24 3 0 4 211 0 211 0 211 14 211 0 211 0 211 254 0 211 0 211 21 211 0 211 0 6 1 6 0 6 1 6 0 6 0 6 0 6 1 6 0 6 6 0 6 0 6 1 23 3 23 0 23 3 23 2 23 0 23 0 23 3 23 0 23 3 23 0 23 2 23 0 51 510 271 510 637 460 408 510 510 15 0 0 510 198 510 638 2 510 612 525 638 637 10 11 12 13 14 16 17 0 289 24 0 6 23 0 3 3 51 Table 9. Scenario B, Rabi 2010-2011 week delivery 1 2 3 4 5 6 7 8 9 19 19 22 10 0 9 226 36 1 766 83 2 1494 0 2 2 3 1 439 1 271 4 1 3 1432 0 19 19 22 0 353 9 200 36 0 0 24 211 6 23 510 4 1401 83 19 19 22 10 9 156 36 0 273 24 211 6 23 510 5 1590 83 19 19 22 10 345 9 0 36 0 273 24 211 6 23 510 6 1850 83 19 19 22 10 283 9 0 36 437 260 24 211 6 23 408 7 1564 83 19 19 22 10 292 0 0 36 546 273 24 211 6 23 0 8 1771 83 19 19 22 10 283 0 226 36 546 263 24 211 6 23 0 9 1868 83 19 19 22 0 0 9 226 36 546 219 24 211 6 23 425 10 1568 83 19 19 22 0 0 9 226 36 437 0 24 211 6 23 453 11 1185 0 19 0 22 0 325 9 0 36 0 0 24 211 6 23 510 0 0 0 4 682 27 15 36 0 19 1 0 0 0 0 0 0 6 16 1486 83 19 19 22 10 353 0 226 36 0 257 24 0 6 23 408 17 1788 83 19 19 22 10 353 9 226 36 0 273 24 211 0 23 480 18 1983 83 19 19 22 10 353 9 226 36 540 0 24 211 0 23 408 19 1954 83 19 19 22 0 353 9 195 36 546 0 24 211 6 23 408 20 2014 83 19 19 22 0 335 9 0 36 546 273 24 211 6 23 408 21 1869 0 19 19 0 10 294 0 0 36 546 273 24 211 6 23 408 22 1926 0 19 19 22 10 0 1 226 36 546 273 24 211 6 23 510 23 1901 83 0 0 22 10 0 9 226 36 546 273 24 211 6 23 432 24 1894 83 19 24 22 10 353 9 226 36 575 273 24 211 6 23 25 2021 83 19 19 22 0 353 9 226 36 520 273 24 0 6 23 408 26 1778 83 19 19 22 0 353 9 226 36 24 211 6 23 474 10 0 0 273 0 0 0 Table 10. Scenario C, Rabi 2010-2011 week delivery 1 2 3 4 5 6 7 8 9 19 19 22 10 0 9 226 36 10 11 12 13 14 16 17 0 289 24 0 6 23 0 3 3 51 1 766 83 2 1494 0 2 2 3 1 439 1 271 4 1 3 1432 0 19 19 22 0 353 9 200 36 0 0 24 211 6 23 510 4 1401 83 19 19 22 10 9 156 36 0 273 24 211 6 23 510 5 1590 83 19 19 22 10 345 9 0 36 0 273 24 211 6 23 510 6 1850 83 19 19 22 10 283 9 0 36 437 260 24 211 6 23 408 7 1564 83 19 19 22 10 292 0 0 36 546 273 24 211 6 23 0 8 1771 83 19 19 22 10 283 0 226 36 546 263 24 211 6 23 0 9 1868 83 19 19 22 0 0 9 226 36 546 219 24 211 6 23 425 10 1568 83 19 19 22 0 0 9 226 36 437 0 24 211 6 23 453 11 1185 0 19 0 22 9 0 36 0 0 24 211 6 23 510 15 36 0 19 1 0 0 0 0 0 0 0 0 6 16 1486 83 19 19 22 10 353 0 226 36 0 257 24 0 6 23 408 17 1788 83 19 19 22 10 353 9 226 36 0 273 24 211 0 23 480 18 1983 83 19 19 22 10 353 9 226 36 540 0 24 211 0 23 408 19 1954 83 19 19 22 0 353 9 195 36 546 0 24 211 6 23 408 20 2014 83 19 19 22 0 335 9 0 36 546 273 24 211 6 23 408 21 1869 0 19 19 0 10 294 0 0 36 546 273 24 211 6 23 408 22 1926 0 19 19 22 10 0 1 226 36 546 273 24 211 6 23 510 23 1901 83 0 0 22 10 0 9 226 36 546 273 24 211 6 23 432 24 1894 83 19 24 22 10 353 9 226 36 575 273 24 211 6 23 25 2021 83 19 19 22 0 353 9 226 36 520 273 24 0 6 23 408 26 1778 83 19 19 22 0 353 9 226 36 24 211 6 23 474 0 0 325 10 0 4 682 27 0 273 0 0 0 Table 11. Scenario D, Rabi 2010-2011 week delivery 1 2 3 4 5 6 7 8 9 10 0 9 226 36 1 439 1 271 1 766 83 19 19 22 2 1494 0 2 2 3 3 1432 83 19 19 22 10 4 1401 83 19 19 22 10 353 5 1590 83 19 19 22 0 340 6 1850 83 19 19 22 7 1564 104 19 19 22 8 1771 0 19 19 9 1868 83 19 19 10 1568 1 18 11 1185 83 19 0 10 11 12 13 14 16 0 289 24 0 6 23 0 3 4 1 3 51 24 211 6 23 510 24 211 6 23 24 0 6 23 510 4 682 9 187 36 9 36 546 40 27 0 273 0 0 9 226 36 10 341 0 36 546 0 24 211 6 23 510 10 0 9 226 36 0 273 24 211 6 23 582 22 10 353 9 220 36 546 273 24 211 6 23 22 7 353 9 36 546 0 24 211 6 23 510 19 22 10 283 0 273 24 210 6 23 408 0 0 0 0 0 0 21 0 6 0 510 0 0 0 0 9 226 36 0 273 17 0 546 0 0 0 0 15 36 0 0 17 0 10 0 9 0 0 0 0 16 1486 83 19 17 22 0 0 0 226 36 546 273 24 211 6 23 0 17 1788 83 19 19 22 10 353 9 190 36 0 273 24 211 6 23 510 18 1983 83 19 19 22 0 304 9 36 546 273 24 211 6 23 408 19 1954 83 19 19 22 10 328 0 226 36 437 0 24 211 6 23 510 20 2014 0 19 19 22 0 301 9 226 36 437 273 24 211 6 23 408 21 1869 83 19 24 22 10 353 10 265 36 0 273 24 211 6 23 510 22 1926 83 19 0 22 10 283 0 36 546 255 24 211 6 23 408 23 1901 83 19 19 22 13 423 9 226 36 0 277 24 211 6 23 510 24 1894 83 19 19 22 13 384 9 226 36 546 273 24 211 6 23 25 2021 83 19 19 22 13 0 9 226 36 547 273 24 211 6 23 510 26 1778 83 19 19 22 0 353 9 226 36 24 211 6 23 474 0 0 0 0 273 0 Table 12. Scenario E, Rabi 2010-2011 week delivery 1 2 3 4 5 6 7 8 9 83 19 19 22 10 0 9 226 36 1 439 1 271 1 766 2 1494 0 2 2 3 3 1432 83 19 19 22 10 4 1401 83 19 19 22 10 353 5 1590 0 19 19 22 0 283 6 1850 83 19 19 22 7 1564 83 19 19 22 8 1771 83 19 19 9 1868 83 19 19 10 1568 0 19 11 1185 83 15 36 0 16 1486 17 1788 18 19 0 10 11 12 13 14 16 17 0 289 24 0 6 23 0 3 3 51 4 682 4 1 24 211 6 23 510 0 24 211 6 23 0 273 24 211 6 23 484 9 187 36 9 36 546 40 27 0 273 0 9 181 36 10 341 0 36 546 0 24 211 6 23 510 13 0 9 226 36 0 273 24 211 6 23 600 22 0 353 9 181 36 546 239 24 211 6 23 22 10 353 6 36 546 0 24 211 6 23 510 19 22 0 283 19 19 22 10 19 2 0 0 83 19 19 22 10 83 19 19 22 1983 83 19 19 22 0 353 1954 83 19 19 22 10 20 2014 83 19 0 22 21 1869 99 19 19 22 22 1926 0 19 19 23 1901 83 19 19 24 1894 83 19 19 22 0 324 25 2021 70 19 19 22 10 353 26 1778 0 19 19 22 11 353 9 226 0 0 0 9 226 36 0 273 24 211 6 23 417 0 0 0 36 501 273 24 169 0 9 0 0 0 11 226 36 10 353 0 226 9 226 36 442 0 226 10 353 9 13 353 9 226 22 0 353 9 226 22 10 353 0 181 9 0 6 23 0 0 6 0 0 0 273 24 211 6 23 523 36 537 219 24 211 6 23 0 24 211 6 23 510 36 492 273 24 211 6 23 510 36 437 273 24 209 6 23 510 36 24 237 6 23 510 36 546 235 24 0 6 23 408 36 437 0 24 211 6 23 477 0 36 437 273 24 211 6 23 408 0 226 36 436 273 24 0 0 23 510 36 546 273 24 211 6 23 0 17 0 0 0 0 273 0 0 Table 13. Scenario F, Rabi 2010-2011 week delivery 1 2 3 4 5 6 7 8 9 10 0 9 226 36 1 439 1 271 1 766 83 19 19 22 2 1494 0 2 2 3 3 1432 83 19 19 22 4 1401 0 1 1 0 5 1590 83 19 19 22 6 1850 0 15 16 0 1 353 7 1564 83 19 0 22 10 424 8 1771 8 15 19 2 12 427 11 226 9 1868 83 19 2 22 1 440 1 226 10 1568 0 0 19 0 10 438 11 1185 83 19 1 22 1 278 10 0 1 353 10 0 9 22 0 226 9 0 1 226 9 9 0 0 0 226 15 36 0 0 17 0 10 0 9 16 1486 83 19 16 22 1 0 0 226 17 1788 0 2 2 3 10 353 9 281 18 1983 83 19 19 22 12 441 0 226 19 1954 8 15 0 2 13 441 9 258 20 2014 83 19 19 22 0 439 21 1869 0 2 16 17 10 439 22 1926 83 19 1 22 23 1901 0 0 19 0 24 1894 83 19 1 22 25 2021 60 1 19 2 10 353 26 1778 83 19 0 22 0 423 1 36 10 353 1 0 0 10 11 12 13 14 16 0 289 24 0 6 23 0 3 4 1 3 51 24 211 4 682 27 36 165 273 0 546 0 36 345 273 43 546 0 36 546 4 5 0 273 27 23 273 36 546 0 3 0 273 0 0 0 36 546 273 0 29 328 36 546 328 0 271 24 211 6 23 510 0 1 3 637 24 211 3 6 23 460 18 14 0 2 408 24 211 6 23 510 0 0 24 211 0 6 0 0 510 23 15 0 0 0 0 24 211 6 23 0 3 254 1 3 510 0 6 23 198 2 211 24 0 0 510 36 431 273 24 0 6 23 638 9 226 28 546 326 28 211 6 0 226 36 618 328 9 0 0 226 9 0 1 226 0 657 0 23 510 0 0 1 3 482 6 0 2 0 36 683 273 3 683 36 0 31 273 2 3 2 21 0 23 510 24 211 6 0 612 0 0 23 525 24 211 6 2 638 1 23 637 2 3 0 Table 14. Scenario G, Rabi 2010-2011 week delivery 1 2 3 4 5 6 7 8 9 19 19 22 10 0 9 226 36 10 11 12 13 14 16 17 0 289 24 0 6 23 0 3 3 51 1 766 83 2 1494 0 2 2 3 1 439 1 271 4 1 3 1432 0 19 19 22 0 353 9 200 36 0 0 24 211 6 23 510 4 1401 83 19 19 22 10 9 156 36 0 273 24 211 6 23 510 5 1590 83 19 19 22 10 345 9 0 36 0 273 24 211 6 23 510 6 1850 83 19 19 22 10 283 9 0 36 437 260 24 211 6 23 408 7 1564 83 19 19 22 10 292 0 0 36 546 273 24 211 6 23 0 8 1771 83 19 19 22 10 283 0 226 36 546 263 24 211 6 23 0 9 1868 83 19 19 22 0 0 9 226 36 546 219 24 211 6 23 425 10 1568 83 19 19 22 0 0 9 226 36 437 0 24 211 6 23 453 11 1185 0 19 0 22 9 0 36 0 0 24 211 6 23 510 15 36 0 19 1 0 0 0 0 0 0 0 0 6 16 1486 83 19 19 22 10 353 0 226 36 0 257 24 0 6 23 408 17 1788 83 19 19 22 10 353 9 226 36 0 273 24 211 0 23 480 18 1983 83 19 19 22 10 353 9 226 36 540 0 24 211 0 23 408 19 1954 83 19 19 22 0 353 9 195 36 546 0 24 211 6 23 408 20 2014 83 19 19 22 0 335 9 0 36 546 273 24 211 6 23 408 21 1869 0 19 19 0 10 294 0 0 36 546 273 24 211 6 23 408 22 1926 0 19 19 22 10 0 1 226 36 546 273 24 211 6 23 510 23 1901 83 0 0 22 10 0 9 226 36 546 273 24 211 6 23 432 24 1894 83 19 24 22 10 353 9 226 36 575 273 24 211 6 23 25 2021 83 19 19 22 0 353 9 226 36 520 273 24 0 6 23 408 26 1778 83 19 19 22 0 353 9 226 36 24 211 6 23 474 0 0 325 10 0 4 682 27 0 273 0 0 0 Table 15. Scenario H, Rabi 2010-2011 week delivery 1 2 3 4 5 6 7 8 9 19 19 22 10 0 9 226 36 10 11 12 13 14 16 17 0 289 24 0 6 23 0 3 3 51 1 766 83 2 1494 0 2 2 3 1 439 1 271 4 1 3 1432 0 19 19 22 0 353 9 200 36 0 0 24 211 6 23 510 4 1401 83 19 19 22 10 9 156 36 0 273 24 211 6 23 510 5 1590 83 19 19 22 10 345 9 0 36 0 273 24 211 6 23 510 6 1850 83 19 19 22 10 283 9 0 36 437 260 24 211 6 23 408 7 1564 83 19 19 22 10 292 0 0 36 546 273 24 211 6 23 0 8 1771 83 19 19 22 10 283 0 226 36 546 263 24 211 6 23 0 9 1868 83 19 19 22 0 0 9 226 36 546 219 24 211 6 23 425 10 1568 83 19 19 22 0 0 9 226 36 437 0 24 211 6 23 453 11 1185 0 19 0 22 0 325 9 0 36 0 0 24 211 6 23 510 15 36 0 19 1 0 0 0 0 0 0 0 0 6 16 1486 83 19 19 22 10 353 0 226 36 0 257 24 0 6 23 408 17 1788 83 19 19 22 10 353 9 226 36 0 273 24 211 0 23 480 18 1983 83 19 19 22 10 353 9 226 36 540 0 24 211 0 23 408 19 1954 83 19 19 22 0 353 9 195 36 546 0 24 211 6 23 408 20 2014 83 19 19 22 0 335 9 0 36 546 273 24 211 6 23 408 21 1869 0 19 19 0 10 294 0 0 36 546 273 24 211 6 23 408 22 1926 0 19 19 22 10 0 1 226 36 546 273 24 211 6 23 510 23 1901 83 0 0 22 10 0 9 226 36 546 273 24 211 6 23 432 24 1894 83 19 24 22 10 353 9 226 36 575 273 24 211 6 23 25 2021 83 19 19 22 0 353 9 226 36 520 273 24 0 6 23 408 26 1778 83 19 19 22 0 353 9 226 36 24 211 6 23 474 10 0 0 4 682 27 0 273 0 0 0 Table 16. Scenario I, Rabi 2010-2011 week delivery 1 2 3 4 5 6 7 8 9 83 19 19 22 10 0 9 226 36 1 766 2 1494 0 0 0 0 3 1432 83 19 19 22 4 1401 0 19 19 5 1590 83 19 19 6 1850 83 19 7 1564 83 19 8 1771 0 19 19 22 10 0 9 1868 83 19 19 28 10 353 10 1568 83 19 19 18 0 348 11 1185 83 19 19 0 10 15 36 0 0 0 22 8 16 1486 83 19 19 0 10 17 1788 83 19 19 22 18 1983 83 19 19 22 10 353 19 1954 0 19 19 22 0 353 20 2014 83 19 19 22 21 1869 83 19 19 22 22 1926 83 19 19 22 23 1901 0 19 0 22 24 1894 83 19 19 22 13 353 25 2021 83 19 19 22 0 342 26 1778 83 19 19 22 10 353 0 353 0 11 12 13 14 16 17 0 289 24 0 6 23 0 0 0 211 0 0 9 226 36 471 273 24 211 6 23 22 0 353 9 181 36 0 24 199 6 23 510 22 10 353 0 36 546 273 24 176 6 23 0 22 10 353 9 226 36 529 24 19 22 0 329 9 36 10 0 10 0 0 437 0 0 0 0 6 23 510 0 273 24 211 6 23 510 0 226 36 546 221 24 211 6 23 408 9 226 36 24 211 6 23 510 9 226 36 546 0 24 211 6 23 0 9 0 36 0 273 24 173 6 23 510 0 0 0 0 0 9 226 0 353 9 226 0 223 36 546 9 0 10 353 0 226 13 353 9 226 0 10 353 0 0 0 0 493 0 311 0 6 0 0 36 546 273 24 211 7 23 0 36 24 211 6 23 510 0 24 211 6 23 408 36 455 273 24 211 0 23 510 36 437 273 24 0 6 23 483 36 552 273 24 211 6 23 9 226 36 465 273 24 211 6 23 510 9 181 36 497 0 24 211 6 23 510 9 271 36 0 273 24 211 6 23 532 9 36 546 273 24 211 6 23 408 36 24 211 6 23 510 0 0 226 0 0 0 247 0 236 0 0 0 Table 17. Scenario J, Rabi 2010-2011 week delivery 1 2 3 4 5 6 7 8 9 83 19 19 22 10 0 9 226 36 1 439 1 271 10 11 12 13 14 16 17 0 289 24 0 6 23 0 3 3 51 1 766 2 1494 0 2 2 3 3 1432 83 19 19 22 10 4 1401 83 19 19 22 10 353 5 1590 0 19 19 22 0 283 6 1850 83 19 19 22 7 1564 83 19 19 22 8 1771 83 19 19 9 1868 83 19 19 10 1568 0 19 19 22 9 226 36 11 1185 83 19 19 22 10 0 0 0 15 36 0 19 2 0 0 0 9 0 0 16 1486 83 19 19 22 10 0 11 226 36 17 1788 83 19 19 22 10 353 0 226 18 1983 83 19 19 22 0 353 9 226 36 442 19 1954 83 19 19 22 10 0 226 20 2014 83 19 0 22 10 353 9 21 1869 99 19 19 22 13 353 9 226 22 1926 0 19 19 22 0 353 9 226 23 1901 83 19 19 22 10 353 0 181 24 1894 83 19 19 22 0 324 9 25 2021 0 19 0 0 10 283 26 1778 83 19 19 22 10 353 0 226 0 4 682 4 1 24 211 6 23 510 0 24 211 6 23 0 273 24 211 6 23 484 9 187 36 9 36 546 40 27 0 273 0 9 181 36 10 341 0 36 546 0 24 211 6 23 510 13 0 9 226 36 0 273 24 211 6 23 600 22 0 353 9 181 36 546 239 24 211 6 23 22 10 353 6 36 546 0 24 211 6 23 510 0 273 24 211 6 23 417 36 501 273 24 169 6 23 0 0 6 0 0 0 273 24 211 6 23 523 36 537 219 24 211 6 23 0 24 211 6 23 510 36 492 273 24 211 6 23 510 36 437 273 24 209 6 23 510 36 24 237 6 23 510 36 546 235 24 0 6 23 408 36 437 0 24 211 6 23 477 0 36 437 273 24 211 6 23 408 9 186 36 437 273 24 211 0 23 510 36 24 211 6 23 473 0 283 0 0 0 0 0 0 0 273 0 273 0 0 0 Appendix D. Gini-index Figure 4. Gini-index for all scenarios, Kharif 2011 Figure 5. Gini-index for all scenarios, Kharif 2012 Appendix E. Service interruptions Table 18. Service interruptions for Hakra Branch canal, Kharif 2011 A B C D E F G H I J IrrDept GapCount 4 27 27 2 6 4 27 27 2 6 60 MaxGapSize 3 4 4 2 3 3 4 4 2 3 9 Table 19. Service interruptions for Hakra Branch canal, Kharif 2012 A B C D E F G H I J IrrDept GapCount 7 26 26 6 8 7 26 26 6 8 60 MaxGapSize 4 6 6 4 5 4 6 6 4 5 8