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Computer optimisation for better water allocation
Agricultural Water Management 40 (1999) 65±70
Computer optimisation for better water allocation Robin Wardlaw1 University of Edinburgh, Dept of Civil and Environmental Engineering, The King's Buildings, Edinburgh EH9 3JN, UK
Abstract Optimisation techniques have had poor uptake at a practical level in irrigation planning and management. In this paper, an approach to real-time water allocation is presented which is relatively easy to use, and should have application beyond the purpose for which it was initially developed. # 1999 Elsevier Science B.V. All rights reserved. Keywords: Irrigation planning; Computer optimisation; Water allocation
1. Introduction and background This paper briefly describes some aspects of research being undertaken as a component of the DFID TDR project on improved irrigation system planning and management (IISPM). It is concerned specifically with the optimal allocation of scarce water resources in real time between competing users. The project has evolved from needs identified through a number of water management projects in Indonesia and, in particular, from experience of the Water Operations Centre (WOC) in south Lombok, Indonesia. A water-allocation model was developed to support the WOC in this function (MMPA, 1986, 1992; Hannan and Coals, 1995). A linear programming approach was used to solve the water-allocation problem and to maximise water supplies. Potential was identified for developing an improved generic optimisation approach which could guarantee equity and which could have a wider range of application.
1
Tel.: +44-131-650-5944; fax: +44-131-650-6781; e-mail: [email protected]
0378-3774/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 7 7 4 ( 9 8 ) 0 0 1 0 5 - X
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R. Wardlaw / Agricultural Water Management 40 (1999) 65±70
2. Research objectives The research is aimed at improving the availability of water for sustainable food production in irrigation systems with complex distribution networks, in which there is water stress and competition for scarce water resources. The research is intended to address problems of irrigation water management, and, in particular, those of ensuring optimal and equitable distribution of irrigation water to farmers in times of drought. 3. Preliminary development and evaluation of approach A number of alternative objective function formulations is possible for the waterallocation problem. The most appropriate function has been found to be of the form (Wardlaw et al., 1997b): Minimise Z
n X di ÿ xi 2 i1
di
(1)
where n is the number of irrigation schemes, di the irrigation demand for scheme i and xi the irrigation supply to scheme i. System constraints exist in the form of nodal continuity and reach capacities. A solution to the problem is achieved through quadratic programming techniques. Testing of Eq. (1) has been carried out using data for the irrigation systems of the Tukad Ayung in Bali. A simulation model was in existence for the Tukad Ayung system (Wardlaw and Wells, 1996), and provided a bench mark against which the benefits of optimisation could be assessed. The simulation model is considered to reasonably present water distribution practice in the system, much of which is by proportional division. Fig. 1 gives an indication of optimisation model performance. The optimisation model achieves equity within the system constraints, and leads to increased utilisation of the available resource. It should be noted that the system is not generally under significant stress, and that 1966 was a particularly dry year. It is not clear how well the simulation represents actual practice under extreme drought; nevertheless, it is a good evaluation tool. 4. Extension of the optimisation approach Crop-yield-based objective functions have also been developed in which the objective is to maximise the relative crop yield in all schemes in an equitable manner. These are based on the yield response to water functions of Doorenbos and Kassam (1979). It can be shown that the crop-yield-based objective function can be expressed as: Minimise Z
n X ki i1
di
di ÿ xi 2
where ki is the crop-yield response factor in scheme i.
(2)
R. Wardlaw / Agricultural Water Management 40 (1999) 65±70
67
Fig. 1. Relative irrigation deficits for 1966.
It has been demonstrated by Wardlaw and Barnes (1997a), that the Eq. (2) will produce an equitable distribution of crop yields when a system is under water stress. 5. Requirements for soil-moisture-balance modelling In much of the preliminary testing of the approach, theoretical irrigation demands have been used to drive the optimisation model. In practical real-time application, it is necessary to drive the model with estimates of actual irrigation demand. This can be achieved through incorporation of a soil-moisture-balance model in the overall optimisation approach. The functions of soil-moisture-balance modelling may be summarised as follows: calculation of field response to irrigation and rainfall, including surface runoff, groundwater recharge and baseflow, with feedback to the optimisation model determination of actual irrigation requirements calculation of actual and potential crop evapotranspiration, from which crop-yield response could be determined A soil-moisture-balance model had formed a central part of the Lower Ayung simulation model (Wardlaw and Wells, 1996). This model has formed the basis of soilmoisture-balance routines developed for the optimisation approach. 6. The integrated optimisation model IISPMOPT The soil-moisture-balance model was integrated with the optimisation model to produce the linked model called IISPMOPT. In this linked model, the soil-moisturebalance model simulates actual system response to irrigation water allocations. The soilmoisture-balance routines compute the drainage return and actual evapotranspiration in
68
R. Wardlaw / Agricultural Water Management 40 (1999) 65±70
response to a given water allocation. The integrated model can be run either with predefined irrigation demands, or in a mode in which irrigation demands are calculated, and these are then fed back to the optimisation routines for the next time step. 7. Evaluation of IISPMOPT performance The performance of IISPMOPT has been evaluated through comparison of water allocation and crop production results with those produced by the simulation model of the Tukad Ayung system. The optimisation model generally gives better and more equitable crop production than the simulation model. Three alternative optimisation approaches have also been evaluated: 1. using theoretical irrigation demands as the basis for water allocation in the optimisation mode with the equitable water allocation objective function (Opt-1 fixed demand); 2. using the calculation of actual irrigations of actual irrigation demand as the basis for water allocation in the optimisation model with the equitable water allocation based objective function (Opt-1 real time). 3. using calculations of actual irrigation demand as the basis for water allocation in the optimisation model with the yield-response-based objective function (Opt-2 real time). Fig. 2 shows annual crop losses expressed in financial terms for each of the abovementioned stages. Interestingly, the objective function based on equitable water allocation with theoretical irrigation demands provides the best overall financial operation, although not the most equitable operation. The reason for the better financial performance achieved is that the real-time estimates of irrigation demand have not yet been refined
Fig. 2. Annual crop losses (Rupiah haÿ1103) at 90% non-exceedance probability with different optimisation approaches.
R. Wardlaw / Agricultural Water Management 40 (1999) 65±70
69
sufficiently to deal with rice field activities such as weeding, which require field drainage and re-filling; these activities are scheduled in the simulation and incorporated in the theoretical demands. With improvement of the real-time forecasting component of the model, it should be possible to improve upon the performance achieved with the theoretical demands in the objective function. It should also be noted that for the Ayung system, only one rain gauge is available, and thus variations in relative irrigation demands will not occur in simulations of system operation. In a system in which rainfall variability between schemes is significant, more significant benefits would be expected from realtime calculations of irrigation demand. The performance of the crop-yield-based objective function is almost indistinguishable from that of the equitable water allocation function in real time. This result is a little surprising, but is related to the cropping patterns in the system. There are no significant differences in cropping between schemes in the Ayung system, and as a result, the equitable water-allocation function works well. In a system with wider variability in cropping between schemes, and under greater water stress, it is expected that the yieldbased function would out perform the equitable water-allocation function. In the results based on theoretical irrigation demands, it is worth noting that the schemes represented by nodes 45, 65 and 88 have lower losses than the other schemes. These schemes receive significant drainage returns from upstream. Over-irrigation of upstream schemes occurs for much of the time when theoretical irrigation demands are the basis for water allocation. As a result of delayed drainage returns, the downstream schemes may be less susceptible to water shortage. 8. Conclusions The optimisation approach developed is robust, relatively easy to apply, and has potential as a tool in decision support for real-time irrigation system operation. The approach ensures equity, and permits objectivity in a key component of system operation. Care has been taken to try and maintain simplicity and ease of use. As developed, the approach is ideal for application in the complex distribution systems found in parts of Indonesia, but is not limited to such systems. The approach could be used by scheme managers to improve the equity of their water distribution, provide targets for water allocation which can be monitored, and to enable optimal use of the available water resource. Such models will become essential as demands placed on water resources increase.
References Doorenbos, J., Kassam, A.M., 1979. Yield response to water. FAO Irrigation and Drainage Paper 33, Food and Agriculture Organisation, United Nations, Rome. Hannan, T., Coals, A.V., 1995. Real time water allocation for irrigation. J. Inst. Wat. Env. Manage. 9(1), 19±26. MMPA, 1986. West Nusa Tenggara irrigation study; south Lombok water balance. Directorate General of Water Resources Development, Jakarta.
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R. Wardlaw / Agricultural Water Management 40 (1999) 65±70
MMPA, 1992. West Nusa Tenggara agricultural development project; irrigation component for West Nusa Tenggara Province; water allocation model user manual. Directorate General of Water Resources Development, Jakarta. Wardlaw, R.B., Barnes, J.M., 1997a. Improved irrigation system planning and management: optimal allocation of irrigation water supplies. ODA TDR Research Project No 6261, Phase 2 report, University of Edinburgh, 1997. Wardlaw, R.B., Moore, D.N., Barnes, J.M., 1997b. An assessment of the potential of optimisation in real time irrigation management. Kay, M.G., Franks, T., Smith, L.E.D. (Eds.), Water: Economics, Management, Demand. E&FN Spon, London. Wardlaw, R.B., Wells, R.J., 1996. Simulating crop production and resource development impacts: the Lower Ayung Simulation Model. Proc. Instn. Civ. Engrs. Wat., Marit. and Energy 118(2).
Computer optimisation for better water allocation Robin Wardlaw1 University of Edinburgh, Dept of Civil and Environmental Engineering, The King's Buildings, Edinburgh EH9 3JN, UK
Abstract Optimisation techniques have had poor uptake at a practical level in irrigation planning and management. In this paper, an approach to real-time water allocation is presented which is relatively easy to use, and should have application beyond the purpose for which it was initially developed. # 1999 Elsevier Science B.V. All rights reserved. Keywords: Irrigation planning; Computer optimisation; Water allocation
1. Introduction and background This paper briefly describes some aspects of research being undertaken as a component of the DFID TDR project on improved irrigation system planning and management (IISPM). It is concerned specifically with the optimal allocation of scarce water resources in real time between competing users. The project has evolved from needs identified through a number of water management projects in Indonesia and, in particular, from experience of the Water Operations Centre (WOC) in south Lombok, Indonesia. A water-allocation model was developed to support the WOC in this function (MMPA, 1986, 1992; Hannan and Coals, 1995). A linear programming approach was used to solve the water-allocation problem and to maximise water supplies. Potential was identified for developing an improved generic optimisation approach which could guarantee equity and which could have a wider range of application.
1
Tel.: +44-131-650-5944; fax: +44-131-650-6781; e-mail: [email protected]
0378-3774/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 7 7 4 ( 9 8 ) 0 0 1 0 5 - X
66
R. Wardlaw / Agricultural Water Management 40 (1999) 65±70
2. Research objectives The research is aimed at improving the availability of water for sustainable food production in irrigation systems with complex distribution networks, in which there is water stress and competition for scarce water resources. The research is intended to address problems of irrigation water management, and, in particular, those of ensuring optimal and equitable distribution of irrigation water to farmers in times of drought. 3. Preliminary development and evaluation of approach A number of alternative objective function formulations is possible for the waterallocation problem. The most appropriate function has been found to be of the form (Wardlaw et al., 1997b): Minimise Z
n X di ÿ xi 2 i1
di
(1)
where n is the number of irrigation schemes, di the irrigation demand for scheme i and xi the irrigation supply to scheme i. System constraints exist in the form of nodal continuity and reach capacities. A solution to the problem is achieved through quadratic programming techniques. Testing of Eq. (1) has been carried out using data for the irrigation systems of the Tukad Ayung in Bali. A simulation model was in existence for the Tukad Ayung system (Wardlaw and Wells, 1996), and provided a bench mark against which the benefits of optimisation could be assessed. The simulation model is considered to reasonably present water distribution practice in the system, much of which is by proportional division. Fig. 1 gives an indication of optimisation model performance. The optimisation model achieves equity within the system constraints, and leads to increased utilisation of the available resource. It should be noted that the system is not generally under significant stress, and that 1966 was a particularly dry year. It is not clear how well the simulation represents actual practice under extreme drought; nevertheless, it is a good evaluation tool. 4. Extension of the optimisation approach Crop-yield-based objective functions have also been developed in which the objective is to maximise the relative crop yield in all schemes in an equitable manner. These are based on the yield response to water functions of Doorenbos and Kassam (1979). It can be shown that the crop-yield-based objective function can be expressed as: Minimise Z
n X ki i1
di
di ÿ xi 2
where ki is the crop-yield response factor in scheme i.
(2)
R. Wardlaw / Agricultural Water Management 40 (1999) 65±70
67
Fig. 1. Relative irrigation deficits for 1966.
It has been demonstrated by Wardlaw and Barnes (1997a), that the Eq. (2) will produce an equitable distribution of crop yields when a system is under water stress. 5. Requirements for soil-moisture-balance modelling In much of the preliminary testing of the approach, theoretical irrigation demands have been used to drive the optimisation model. In practical real-time application, it is necessary to drive the model with estimates of actual irrigation demand. This can be achieved through incorporation of a soil-moisture-balance model in the overall optimisation approach. The functions of soil-moisture-balance modelling may be summarised as follows: calculation of field response to irrigation and rainfall, including surface runoff, groundwater recharge and baseflow, with feedback to the optimisation model determination of actual irrigation requirements calculation of actual and potential crop evapotranspiration, from which crop-yield response could be determined A soil-moisture-balance model had formed a central part of the Lower Ayung simulation model (Wardlaw and Wells, 1996). This model has formed the basis of soilmoisture-balance routines developed for the optimisation approach. 6. The integrated optimisation model IISPMOPT The soil-moisture-balance model was integrated with the optimisation model to produce the linked model called IISPMOPT. In this linked model, the soil-moisturebalance model simulates actual system response to irrigation water allocations. The soilmoisture-balance routines compute the drainage return and actual evapotranspiration in
68
R. Wardlaw / Agricultural Water Management 40 (1999) 65±70
response to a given water allocation. The integrated model can be run either with predefined irrigation demands, or in a mode in which irrigation demands are calculated, and these are then fed back to the optimisation routines for the next time step. 7. Evaluation of IISPMOPT performance The performance of IISPMOPT has been evaluated through comparison of water allocation and crop production results with those produced by the simulation model of the Tukad Ayung system. The optimisation model generally gives better and more equitable crop production than the simulation model. Three alternative optimisation approaches have also been evaluated: 1. using theoretical irrigation demands as the basis for water allocation in the optimisation mode with the equitable water allocation objective function (Opt-1 fixed demand); 2. using the calculation of actual irrigations of actual irrigation demand as the basis for water allocation in the optimisation model with the equitable water allocation based objective function (Opt-1 real time). 3. using calculations of actual irrigation demand as the basis for water allocation in the optimisation model with the yield-response-based objective function (Opt-2 real time). Fig. 2 shows annual crop losses expressed in financial terms for each of the abovementioned stages. Interestingly, the objective function based on equitable water allocation with theoretical irrigation demands provides the best overall financial operation, although not the most equitable operation. The reason for the better financial performance achieved is that the real-time estimates of irrigation demand have not yet been refined
Fig. 2. Annual crop losses (Rupiah haÿ1103) at 90% non-exceedance probability with different optimisation approaches.
R. Wardlaw / Agricultural Water Management 40 (1999) 65±70
69
sufficiently to deal with rice field activities such as weeding, which require field drainage and re-filling; these activities are scheduled in the simulation and incorporated in the theoretical demands. With improvement of the real-time forecasting component of the model, it should be possible to improve upon the performance achieved with the theoretical demands in the objective function. It should also be noted that for the Ayung system, only one rain gauge is available, and thus variations in relative irrigation demands will not occur in simulations of system operation. In a system in which rainfall variability between schemes is significant, more significant benefits would be expected from realtime calculations of irrigation demand. The performance of the crop-yield-based objective function is almost indistinguishable from that of the equitable water allocation function in real time. This result is a little surprising, but is related to the cropping patterns in the system. There are no significant differences in cropping between schemes in the Ayung system, and as a result, the equitable water-allocation function works well. In a system with wider variability in cropping between schemes, and under greater water stress, it is expected that the yieldbased function would out perform the equitable water-allocation function. In the results based on theoretical irrigation demands, it is worth noting that the schemes represented by nodes 45, 65 and 88 have lower losses than the other schemes. These schemes receive significant drainage returns from upstream. Over-irrigation of upstream schemes occurs for much of the time when theoretical irrigation demands are the basis for water allocation. As a result of delayed drainage returns, the downstream schemes may be less susceptible to water shortage. 8. Conclusions The optimisation approach developed is robust, relatively easy to apply, and has potential as a tool in decision support for real-time irrigation system operation. The approach ensures equity, and permits objectivity in a key component of system operation. Care has been taken to try and maintain simplicity and ease of use. As developed, the approach is ideal for application in the complex distribution systems found in parts of Indonesia, but is not limited to such systems. The approach could be used by scheme managers to improve the equity of their water distribution, provide targets for water allocation which can be monitored, and to enable optimal use of the available water resource. Such models will become essential as demands placed on water resources increase.
References Doorenbos, J., Kassam, A.M., 1979. Yield response to water. FAO Irrigation and Drainage Paper 33, Food and Agriculture Organisation, United Nations, Rome. Hannan, T., Coals, A.V., 1995. Real time water allocation for irrigation. J. Inst. Wat. Env. Manage. 9(1), 19±26. MMPA, 1986. West Nusa Tenggara irrigation study; south Lombok water balance. Directorate General of Water Resources Development, Jakarta.
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R. Wardlaw / Agricultural Water Management 40 (1999) 65±70
MMPA, 1992. West Nusa Tenggara agricultural development project; irrigation component for West Nusa Tenggara Province; water allocation model user manual. Directorate General of Water Resources Development, Jakarta. Wardlaw, R.B., Barnes, J.M., 1997a. Improved irrigation system planning and management: optimal allocation of irrigation water supplies. ODA TDR Research Project No 6261, Phase 2 report, University of Edinburgh, 1997. Wardlaw, R.B., Moore, D.N., Barnes, J.M., 1997b. An assessment of the potential of optimisation in real time irrigation management. Kay, M.G., Franks, T., Smith, L.E.D. (Eds.), Water: Economics, Management, Demand. E&FN Spon, London. Wardlaw, R.B., Wells, R.J., 1996. Simulating crop production and resource development impacts: the Lower Ayung Simulation Model. Proc. Instn. Civ. Engrs. Wat., Marit. and Energy 118(2).