System Dynamics Optimisation Approach to Irrigation Demand Management

Transcription

1 Bureau of Meteorology From the SeletedWorks of Amgad Elmahdi 2005 System Dynamis Optimisation Approah to Irrigation Demand Management Amgad ELMAHDI Hetor Malano Teri Ethells Shahbaz khan Available at:

2 System Dynamis Optimisation Approah to Irrigation Demand Management 15 Elmahdi,A., 25 H. Malano, 3 T. Ethells and 45 S. Khan 1,2,3 Dept Civil & Env Engineering, The University of Melbourne, 4 CSIRO Land and Water & Charles Sturt University, 5 Cooperative Researh Centre for Irrigation Futures A.Elmahdi@ivenv.unimelb.edu.au Keywords: Dynami modelling; Optimisation; Agriultural management; Water management, Crop alloation. EXTENDED ABSTRACT Signifiant problems of water shortage and deteriorating water quality are ontributing to a growing water risis in many ountries. This situation requires reative solutions to ahieve sustainable resoure management. In the Murrumbidgee river basin, irrigation extration and land learing have had major impats on the river environment (DLWC 1995). Irrigation demand has hanged the natural flow regime of the river whih has indued signifiant environmental hanges. Inreased demands for water have led to redued river flows and a reversal of the seasonal flow patterns. Finding ways to meet irrigation demands and also ahieve positive environmental and eonomi outomes requires the aid of modelling tools to analyse the impat of alternative poliy senarios. These senarios seek to assess the impat of options for the alloation of limited water resoures between agriultural prodution and the environment. omparison shows that VENSIM optimizer does ahieve the same results. This paper onludes that system dynami optimisation approah is a useful tool for irrigation ompanies and athment managers to evaluate alternative river system management senarios. In partiular, NSOM has the apability to ompare the simulation and optimisation dynami results synhronized in time for eah variable involved in the model. In general based on a preliminary analysis, it is shown that seleting the appropriate rop mix ould have positive impats and benefits for irrigation deliveries and environmental flow. Further researh is required to test, alibrate the NSOM model with atual data and study multiobjetives optimisation. This paper presents a novel approah for optimizing these objetives by ombining system dynamis and onstrained linear objetive optimisation approahes. The network simulation optimisation model NSOM has been oupled with a linear programming mathematial algorithm that inludes the system onstraints. The model uses an eonomi rationale (i.e. a farmer s eonomi deision to maximise the gross margin per Megalitre) that involves assessing alternative ropping mixes and seleting the rop mix that maximises the net return and minimises water used. The optimisation results from this model have been ompared with results from a ommerial linear programming solver to verify the apabilities of VENSIM optimizer. The 196

3 1. INTRODUCTION Integrated water management in irrigated agriultural areas is the best strategy to improve rop yields and optimise the use of the available water resoures. The main limiting fators for inreased agriultural prodution are the availability of suitable land and water. In addition, a redution in water availability, onfliting water uses and other water-related environmental problems are rapidly inreasing in many parts of the world inluding Australia. Aording to Grigg (1996), the real risis in water management is a reeping risis -whih needs a sustainable response at present. Inreasingly, researhers and poliy makers are advoating sustainable development as the best approah to today s and future water problems (Louks, 2000). Water sarity or dereasing water alloations in developed ountries ould drive and enourage deision makers to look for improved management through hanges in ropping pattern systems. The agriulture setor in Australia onsumes about 75% of total available water resoures. Crop water requirements depend on many fators suh as temperature, humidity, rainfall and evaporation. Typially, ropping patterns and ropping deisions are affeted by several fators suh as limati foreasted growing ondition and water alloation. Taking into onsideration this approah, the ropping pattern of the different ultivated rops under a given alloation is a variable that an be used to improve the produtivity of onsumed water. The overall goal of the urrent study is to re-alloate rops in suh a manner that the optimal pattern is ahieved by minimising the water defiit (differene between available water and total water requirement) in an agriulture area while maximising the eonomi return. The urrent study is arried out on a regional sale at an irrigation area level. The model hanges the ropping mix and determines the optimal rop mix that will maximise the net return and gross margin per Megalitre and minimise water use. The optimal rop mix is determined through testing one ase where eah rop area has been allowed to vary within the set boundary values. The study has been performed using the system dynamis programming tool VENSIM with an optimiser algorithm. The network simulation optimisation model NSOM was developed to determine the amount of irrigation water demand for eah ase senario. Development of mathematial models to generate optimal irrigation poliies has been performed by researhers sine Most of the optimisation models have adopted linear programming (LP), Quadrati programming (QP) and dynami programming (DP) approahes. 2. SYSTEM DYNAMICS Irrigation water demand management is a diffiult variable to impat due to the pressure of unontrolled variables suh as limati onditions. Diffiulties inrease further when eonomi and environmental perspetives are integrated with realities of biophysial proesses. The dynami harater of ontributing variables and how they affet water use in the future is not aptured through traditional modelling approahes. Although the appliation of optimisation tehniques has been a major field of researh in water resoures planning for many years, their suessful adaptation to pratial water alloation problems has not been validated in pratie, partly due to the fat that most appliations have dealt with oversimplified systems (Yeh 1985; Simonovi and Fahmy, 1999). Therefore, there is a need to explore new tools to represent the omplex relationships found in irrigation systems. One promising option is system dynamis (SD), a feedbak-based, objet-oriented approah. Although not a novel approah, system dynamis offers a new way of modelling the future dynamis of omplex systems. Aording to Simonovi and Fahmy (1999), system dynamis is based on a theory of system struture and a set of tools for representing omplex systems and analysing their dynami behaviour. The most important feature of system dynamis is that it helps to eluidate the endogenous struture of the system under onsideration, and demonstrate how different elements of the system atually relate to one another. This then failitates experimentation as relations within the system are hanged to reflet different deisions. What makes using system dynamis different from other approahes used for studying omplex systems (suh as optimisation) is the use of feedbak loops. The SD tool used in this study to model irrigation demand has four basi building bloks; stok, flow, onnetor and onverter. Stoks (levels) are used to represent anything that aumulates; an example would be water stored in storage or dams. Flows (rates) represent ativities that fill and drain stoks; an example inludes releases or inflows. Connetors (arrows) are used to establish the relationship among variables in the 197

4 model, the diretion of the arrow indiates the dependeny relationships. They arry information from one element to another element in the model. Converters transform input into output. Stoks and flows help desribe how a system is onneted by feedbak loops whih reate the nonlinearity found so frequently in modern day problems. Figure 1 desribes the ausal loop diagram with some positive () feedbak and negative (-) relationships. Computer software is used to simulate a system dynamis model of the problem being studied. Running "what if" simulations to test ertain poliies on suh a model an greatly aid understanding of how the system hanges over time. inflow river flow dam - downstream releases storage level flooding CONCEPTUAL MODEL A Network Simulation Optimization Model (NSOM) (Elmahdi et al. 2004) has been developed to test the feasibility and issues in applying system dynamis to the problem of effetively balaning water alloation needs. The purpose of the model is to analyse the historial water alloation for an irrigation area within the onstraints of environmental flow rules based on eonomi rationale (Figure 2 and Table 1). The model uses VENSIM as a software development tool to onfigure the water balane network model. The outputs of NSM model are total ost, total yields, total return, irrigation demand, gross margin, losses, surfae water used, ground water pumping. Fundamentally, a water balane must be determined whih an best math the demand and environmental flows within system onstraints. upstream flooding storage Area Figure 1. Causal loop diagram Moreover, the inherent flexibility and transpareny is partiularly helpful for the development of simulation models for omplex water systems with subjetive variables and parameters (Simonovi 2000). Compared with the onventional simulation suh as hydrologial modelling or optimisation models, the system dynamis approah an better represent how different hanges in basi elements affet the dynamis of the system in the future. It is therefore partiularly useful for representing various what if senarios within omplex systems, partiularly when there are strong influenes from environmental or eonomi elements. Reent appliations of the SD approah in the field of water resoures have been few but inlude work on river-basin planning (Palmer et al. 1999), an assessment of water resoures long-term water resoure planning and poliy analysis (Simonovi and Fahmy 1999), reservoir operation (Ahmed and Simonovi, 2000), and analysis of water alloation within the onstraints of environmental flow rules based on eonomi rationale (Elmahdi et al 2004). Figure 2. NSM model omponents The purpose of VENSIM is to provide a programming environment for model development and help solve problems that would be hard to address mathematially without the aid of simulation. Moreover, the VENSIM environment effetively insulates the user from both the underlying mathematis and the details of the language speifiation. Furthermore, the VENSIM modelling language is a rih and readable way of representing dynami systems. In the Murrumbidgee irrigation distrits, the last deade has brought major water poliy initiatives. Furthermore, the ombination of signifiant dry periods along with the introdution of CAP, Water Sharing Plans and resulting environmental flow rules, has led to the alloations announed at the start of the season being redued and never reahing 100% of entitlement. This situation has driven a signifiant effort to study and overome the onsequenes of redued water availability within the ontext of farmer s eonomi needs. Thus, the main objetive of this researh is to garner insights about how best to optimize the 198

5 irrigation system within the onstraints of the system (both physial and institutional) based on an eonomi rationale by developing and applying NSOM. Table 1. NSOM model parameters, foring funtion, proess and states. per ha for rop ( fertilizers, herbiides, sowing, et) ($/ha) and MWN minimises water need. The first item of the first objetive funtion gives the total inome, the seond item gives the irrigation ost from surfae water, the third item gives the ground water pumping ost to math the demand and the fourth item gives the total variable ost suh as fertilizers and pestiides ost. The first item in the seond objetive funtion gives the total irrigation needed and the seond item gives the total ground pumping. The final ratio objetive funtion MR maximises the ratio of maximum net return over minimum water needed (Equation 3): 4. NSOM MODEL FORMULATION AND APPLICATION The objetive funtion of the NSOM model is formulated to maximise the net return and minimise the amount of irrigation water used. This is ahieved by maximising one funtion formulated as a ratio of net return (Equation 1) over water use (Equation 2). As the objetive funtion and the onstraints are of the linear form, a linear programming funtion an be used. The linear programming tehnique is utilized to determine the optimal alloation of the ropping area taking into onsideration the speified onstraints. The NSOM has been applied to the Coleambally irrigation area (CIA) in NSW. CIA region is haraterised with its limate and onsequently its rop onsumptive use. 4.1 Objetive Funtion MNB = ( {IN m m Y (,m) GWP * P * A (,m) * A * IC} * PC A * VC IN, m) A( MWN = ) (, m) m ) (1) GWP ( (2) where MNB is maximum net benefit, Y is yield for rop (tonnes/ha), P is rop prie ($/tonnes), A is the rop area for rop (ha), IN (,m) is the irrigation water need for rop in month m (Ml/ha), IC is irrigation or water ost ($/ML), GWP (,m) is supplementary ground water pumping for rop in month m (ML/ha), PC is ground water pumping ost ($/ML), VC is variable ost MR = MNB / MWN (3) The objetive funtion is subjet to the following physial and environmental onstraints (Equations 4-8): 4.2 Area Availability to Total Area A( ) TA (4) () The sum of all rop area is equal or less the total farm area, where TA is the total area. 4.3 Water Demand to Water Availability IN,m) * A( WA ) (,m) ( (5) Total irrigation water needed in the irrigation area should not exeed total water available for the irrigation area. 4.4 Pumping Target for Eah Month GWP (,m) Pump(m) (7) (,m) Total pumping from irrigation area in any month should not exeed the allowable pumping, used to meet water requirement (to avoid GW mining and pollution of aquifers). 4.5 Environmental Flow Target EFm TEF m (8) 199

6 The environmental flow in eah month should equal or exeed the target flow is where EF is environmental flow in month m at the end of the system. In pratie, this is equal to 300 ML/ day when the alloation exeeds 80% and 200 ML/day when the alloation less than 80% and TEF is target environmental flow in month m. Of ourse, to meet the end of system target, it is important to aount for all abstrations whih is outside the sope of this study. Deision variables are the amount of land at irrigation area for growing rop (ha), denoted as A. The assumption is same irrigation effiieny and soil type. It is important to adjust rop patterns on an eonomi basis and optimum uses of resoures. To demonstrate the potential of this approah, the NSOM model has been applied to CIA for one year with a low alloation and for 10 seleted rops. It is important to note that this example has not yet been alibrated for the CIA irrigation area. Further researh is needed to validate the model and test the sensitivity parameters, in partiular, losses. 5. PRELIMINARY MODEL RESULTS The purpose of NSOM is to demonstrate the apability of system dynamis to simulate and optimize a omplex system suh as irrigation system. It is the first attempt to build a linear onstraint optimisation ase through system dynamis. A key assumption within the urrent version of NSOM is that the irrigation area has the same effiieny aross the spatial dimension. Additionally, the model doesn t aount for soil suitability or swithing osts to move between different rops (in pratie the infrastruture osts of shifting ould be high and this will need to be onsidered as part of future researh). The model has been used to determine the optimal water use and the rop pattern of the different rops. The base ase rop pattern of one year has been ompared with the optimal rop pattern. The total ultivated area is kept without hange. The areas of the different rops have been allowed to hange so that the optimal rop area of these rops is determined. One ase has been studied where the area of eah rop was allowed to hange within a ertain limit where both the minimum and maximum allowed total rop area is hanged from the base ase rop area ultivated in that year. This limit is 50% - 150%. The optimal ropping mix of the rop areas and amount of irrigation water is determined. Table 2 shows the base ase rop pattern in year 2003 while Figure 3 shows the base ase rop onsumptive use in CIA. Assuming the water effiieny is the same in the CIA area. The NSOM model is solved to determine the optimal alloation of the 10 rops (Figures 4-8). Table 2. The atual rop pattern Crops Base ase Area ha Rie Wheat Oats 1255 Barley 3138 Maize 3138 Canola Soybean 4393 Win pasture Luerne Vines Total ML July Monthly water onsumption August Sep Ot Nov De Jan Feb Marh April May June Months Monthly water onsumption Figure 3. Monthly rop water onsumption It is lear from Figures 4 and 5 that the total water use and the distribution of all the rops have been hanged from the atual ase. The ultivated area of these rops with high onsumptive use has been dereased while those with low onsumptive use have been inreased. 200

7 Rie Atual and optimal area sim_result 50%-150% 600,000 Objetive 120 wheat Vines soybean atual area optimal area 500,000 rops Oats Maize Luerene 400,000 Canola Barley 300,000 Winter pasture area (ha) 200,000 Objetive Funtion Figure 4. Atual (base ase) and optimum ropping area Figure 6 shows the monthly variation in irrigation water need, it is very lear the demand urve has been hanged from the atual ase partiularly during the summer season. sim_result 50%-150% total Biophysial 120 Figure 7. Atual (base ase) and optimum net profit The total irrigation water used has been dereased by 23%, whih ould be used to help improve the seasonality of flows and the river health in terms of environmental flows. This paper represents the first attempt to build the optimization ase approah using system dynamis. Therefore, the same ase has been built in other linear programming ommerial software, to test the sensitivity and apability of system dynami total Biophysial demand Figure 5. Atual (base ase) and optimum total water use Figure 8 shows the optimum rop area estimated by system dynami ompared with other LP programming. The advantage of system dynami is dealing with omplex system and this tool has the apability to ompare the simulation and optimisation dynami results synhronized in time for eah variable involved in the model. ML Irrigation demand for Atual and optimum ropping system Atual demand Optimum demand July August Sep Ot Nov De Jan Feb Marh April May June Months Rie Winter pasture wheat Vines Soybean Oats Maize What is Best WB optimization result GIPLAS optimization result Luerene Vensim optimization result Canola Initial Area Barley Figure 6. Atual and optimum monthly rop onsumption in ML Figure 8. Atual and optimum area with different LP programming The main objetive of this study is to maximize the net profit and minimize the irrigation water used through the optimal rop mix area. Figure 7 shows the net profit inreased from the base ase. 201

8 6. CONCLUSIONS AND RECOMMENDATIONS A system dynami optimisation (linear) programming model has been developed to determine the optimal water use and rop pattern of an agriultural area against two objetives: to maximize the net profit and minimize the amount of the irrigation water used. To demonstrate proof of onept, a preliminary NSOM model has been applied to the Coleambally Irrigation Area onsidering that the same effiieny without alibration. The optimal rop area has been determined for one year. One ase has been studied where the rop area has been allowed to hange within a ertain limit. The preliminary analysis results show that a onsiderable amount of water volume an be saved and reused. The volume savings ould be used to improve the seasonality of flows (by hanging the demand urve as shown in figure 6) and in onsequene improve the river health. The water volume saved is estimated to be about 23% when the rop areas are allowed to hange between 0.5 and 1.5 times the atual ultivated rop area. This study provides insight as to how best to manage the agriultural area in CIA when there is a shortage of the irrigation water. Moreover, this paper onludes that a system dynami approah has the potential to help stakeholders optimize the system, by evaluating and analysing key deision variables. It is reommended that further researh be onduted to validate the model and investigate the eonomi and environmental impliation of applying this model. Beder, Sharon (1996). The nature of Sustainable development. 2 nd ed., Sribe. Newham,VIC. Grigg, N.S Water resoures management: Planning, regulations and ases. New York, New York, USA: MGraw-Hill. Louks, D.P Sustainable Water Resoures management. Water international 25(1):3-11 Palmer, R. N., Mohammadi, A., Hahn, M. A., Kessler, D., Dvorak, J. V. and Parkinson, D.: 1999, Computer Assisted Deision Support System for High Level Infrastruture Master Planning: Case of the City of Portland Supply and Transmission Model (STM), palmer/papers/imp-asce.pdf. Simonovi, S. P.: 2000, Tools for water management: one view of the future, Water International 25(1), Simonovi, S. P. and Fahmy, H.: 1999, A new modelling approah for water resoures poliy analysis, Water Resoure. Res. 35(1), Yeh, W.W., 1985, Reservoir management and operation models: a state of the art review, Water Resoure. Res. 21 (12) ACKNOWLEDGMENTS The NSOM model system has been developed with the assistane of a grant from CRC Irrigation future (CRC-IF) and the University of Melbourne Sholarship offie. 8. REFERENCES Ahmed, S. and Simonovi, S.P. 2000, system dynamis modelling of reservoir operations for flood management, j.comp.engrg. ASCE 14 (3), Amgad Elmahdi, Hetor Malano and Shahbaz khan 2004, A system dynami approah and irrigation demand management Modelling, Environmental Engineering Researh Event 2004 onferene 6-9 Deember Published by University of Wollongong Press ISBN: X. ( 202