A bi-objective model for water allocation and scheme water scheduling

Barnard, Johannes Jacobus (2019-04)

Thesis (MEng)--Stellenbosch University, 2019.

Thesis

ENGLISH ABSTRACT: "Water is life" | this common expression is often referred to as a cliche, but Earth's inhabitants can truly bear witness to the accuracy of this statement. As a result of global warming, the El Nin~o phenomenon, a growing population and expanding economies, water has globally become a cherished commodity. In the Western Cape, South Africa, a devastating drought experienced over the two-year period 2017/2018 has propelled the innovation of more e ective and e cient water management strategies to the forefront, especially in the farming sector, where farmers are currently compelled to produce agricultural crops with less water. An irrigation and scheme water supply schedule may, for example, be employed with the aim of proposing how crops should be irrigated during their various growth stages, if natural water supply is insufficient, and how additional scheme water supply should be scheduled to enhance efficient water use. An open-air irrigation reservoir typically serves as a water storage facility for the purpose of irrigating agricultural crops. Evaporation (the process of transforming water vapour into the atmosphere) from such a reservoir water surface may, however, result in a reduced reservoir capacity of up to 20%. In this thesis, two novel mathematical models are proposed which form the basis of a decision support system for farmers aimed at providing bene cial agricultural crop irrigation strategies. The first is a single-objective optimisation model which proposes an irrigation schedule in conjunction with a scheme water supply schedule in which the goal is to maximise the total profit obtainable from crop yield. This maximisation process is subject to a user-specified reservoir water capacity that should be left over in an open-air reservoir at the end of a speci ed scheduling horizon. If possible, additional water resources may be obtained from scheme water supply in order to aid with the irrigation of crops. These additional water resources, however, usually come at a cost, which is also included in the total profit calculation. The second model is a bi-objective optimisation model which aims to maximise the total profit from crop yield while simultaneously maximising the reservoir water contents at the end of the last scheduling period. When plotted in objective space, the solutions to the model form a Pareto front that is presented as the basis of decision support to the decision maker (farmer), providing him with an overview of numerous implementable irrigation and scheme water supply schedules for a variety of end-period reservoir water levels. Both the single-objective and bi-objective optimisation models are validated in three ways, namely by face validation, by random benchmark validation and by consulting an expert in the field of crop irrigation and farming. Embedded in the decision support system, these models enable the decision maker to develop a course of action in terms of crop irrigation for a tailored farming scenario.

AFRKIKAANSE OPSOMMING: "Water is lewe" | daar word dikwels na hierdie algemene uitdrukking as 'n cliche verwys, maar die Aarde se populasie kan werklik van die waarheid van hierdie stelling getuig. As gevolg van aardverwarming, die El Nino-fenomeen, 'n toenemende bevolking en groeiende ekonomiese, het water wêreldwyd 'n gekoesterde hulpbron geword. In die Wes-Kaap, Suid-Afrika het 'n ernstige droogte oor die tweejaar-periode 2017/2018 dringende innovasie van doeltreffender waterbestuurstrategiee genoop, veral in die boerderysektor, waar boere tans verplig is om landbougewasse met minder water te kweek. 'n Besproeiings- en skemavoorsieningskedule kan byvoorbeeld aangewend word om te bepaal hoe gewasse tydens hul verskillende groeistadia besproei moet word indien natuurlike water beskikbaarheid onvoldoende is, en hoe addisionele skemavoorsiening geskeduleer behoort te word om doeltreffende watergebruik te verhoog. 'n Opelugbesproeiingsreservoir dien gewoonlik as 'n waterbergingsfasiliteit vir die besproeiing van landbougewasse. Verdamping (die omskakelingsproses van waterdamp na die atmosfeer) vanaf silo 'n reservoirwateroppervlak kan egter na 'n verminderde reservoir-kapasiteit van tot 20% lei. Twee nuwe wiskundige modelle word in hierdie tesis voorgestel wat as basis vir 'n besluitsteunstelsel vir boere kan dien en wat daarop gemik is om voordelige besproeiingstrategiee vir landbougewasse te verskaf. Die eerste is 'n enkeldoelige optimeringsmodel wat 'n waterbesproeiingskedule tesame met 'n skema-watervoorsieningskedule voorstel, met die doel om die totale wins wat uit gewasopbrengs verkry kan word, te maksimeer. Hierdie maksimeringsproses is onderworpe aan 'n gebruikersgespesifieerde reservoir-waterkapasiteit wat aan die einde van 'n gespesifiseerde skeduleringshorison in 'n opelugreservoir moet oorbly. Indien moontlik, kan bykomende waterhulpbronne uit skemavoorsiening vir die besproeiing van gewasse gebruik word. Hierdie addisionele waterhulpbronne is egter gewoonlik teen 'n koste beskikbaar, wat ook in die totale winsberekening ingesluit word. Die tweede model is 'n twee-doelige optimeringsmodel wat daarop gemik is om die totale wins wat uit gewasopbrengs verkry kan word, te maksimeer, en terselfdertyd die waterinhoud van die reservoir aan die einde van die laaste skeduleringsperiode te maksimeer. Wanneer die oplossings van hierdie model in die doelfunksieruimte uitgestip word, word 'n Pareto-front verkry wat as die basis vir besluitsteun aan die besluitnemer (boer) voorgelê kan word, en aan hom 'n oorsig bied oor die verskeidenheid van implementeerbare besproeiings- en skemavoorsieningskedules vir verskeie oorblywende reservoir-watervlakke aan die einde van die laaste skeduleringsperiode. Beide die enkel-doelige en die twee-doelige optimeringsmodelle word op drie maniere gevalideer, naamlik deur sigvalidering, deur lukrake toetsvalidering en deur 'n deskundige op die gebied van gewasbesproeiing en boerdery te raadpleeg. Hierdie modelle word in die besluitsteunstelsel geinkorporeer en stel die besluitnemer sodoende in staat om 'n plan van aksie in terme van gewasbesproeiing vir 'n gespesifieerde boerdery-scenario te ontwikkel.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/105766
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