A multiobjective ant colony optimization approach for scheduling environmental flow management alternatives with application to the River Murray, Australia

Authors


Abstract

[1] In regulated river systems, such as the River Murray in Australia, the efficient use of water to preserve and restore biota in the river, wetlands, and floodplains is of concern for water managers. Available management options include the timing of river flow releases and operation of wetland flow control structures. However, the optimal scheduling of these environmental flow management alternatives is a difficult task, since there are generally multiple wetlands and floodplains with a range of species, as well as a large number of management options that need to be considered. Consequently, this problem is a multiobjective optimization problem aimed at maximizing ecological benefit while minimizing water allocations within the infrastructure constraints of the system under consideration. This paper presents a multiobjective optimization framework, which is based on a multiobjective ant colony optimization approach, for developing optimal trade-offs between water allocation and ecological benefit. The framework is applied to a reach of the River Murray in South Australia. Two studies are formulated to assess the impact of (i) upstream system flow constraints and (ii) additional regulators on this trade-off. The results indicate that unless the system flow constraints are relaxed, there is limited additional ecological benefit as allocation increases. Furthermore the use of regulators can increase ecological benefits while using less water. The results illustrate the utility of the framework since the impact of flow control infrastructure on the trade-offs between water allocation and ecological benefit can be investigated, thereby providing valuable insight to managers.

1. Introduction

[2] River basin development, including land conversion, overallocation of water and the construction of barriers (e.g., dams) has altered many rivers and their adjacent wetlands and floodplains worldwide [Kingsford, 2000; Millennium Ecosystem Assessment, 2005]. To preserve and restore these systems, much focus has been given to environmental flow management [Arthington and Pusey, 2003; Arthington et al., 2010; Kingsford and Auld, 2005; Tharme, 2003], which aims to follow the “natural flow paradigm” developed by Poff et al. [1997] and “mimic components of natural flow variability,” in terms of flow frequency, duration, timing, rate of change, and magnitude [Arthington et al., 2006]. These flow components are integral to maintaining and preserving biota within river-floodplain system [Junk et al., 1989].

[3] The management and delivery of environmental flows (in terms of the five important flow components) is not an easy task, since (i) there are generally large numbers of wetlands and floodplains containing a variety of flora and fauna with different flow requirements that need to be taken into account, for instance, lignum shrubland (Muehlenbeckia florulenta) prefer an inundation duration of 1–6 months while great crested grebes prefer 2–5 months [Rogers and Ralph, 2011]; (ii) there is generally limited water available for environmental purposes, given that there are a number of users (e.g., irrigation, domestic, and industrial supply) all vying for the same water resource [Wallace et al., 2003]; and (iii) there might be flow restrictions as a result of constraints in the system (e.g., upstream flows are limited to particular values in particular months) [Murray-Darling Basin Authority (MDBA), 2011b]. Therefore, in order to use environmental water effectively and efficiently so as to maximize the ecological integrity of rivers, wetlands, and floodplains, a number of environmental flow management alternatives (EFMAs) can be utilized, including upstream flow releases or the operation of gates and pumps to regulate water entering and leaving wetlands. Since decisions in relation to EFMAs (e.g., reservoir flow releases or gate operations) are made at discrete time steps over a specific planning horizon (e.g., a number of years) and at numerous locations (e.g., different wetlands), the search space for this scheduling problem generally becomes very large, especially when extended spatial and temporal scales are considered [Szemis et al., 2012]. Due to this complexity, there is potential benefit in employing optimization approaches to schedule EFMAs to maximize ecological integrity, given a particular environmental flow allocation.

[4] Optimization studies in this area have mainly focused on the development of optimal reservoir/weir operating rule parameters or monthly reservoir releases, while attempting to maintain an appropriate balance between the environment and other potential water users (e.g., irrigators), rather than how to schedule a given environmental water allocation in order to maximize ecological outcomes [e.g., Chang et al., 2010; Chaves et al., 2003; Higgins et al., 2011; Homa et al., 2005; Shiau and Wu, 2004, 2007; Suen and Eheart, 2006; Tilmant et al., 2010; Yang, 2011; Yin et al., 2010, 2011]. Consequently, ecological objectives have been generally treated in a rather simplistic fashion. In order to overcome this shortcoming, Szemis et al.[2012] introduced an optimization framework for the development of environmental flow management schedules for maximizing the ecological response of rivers, wetlands, and floodplains that incorporates different EFMAs (i.e., wetland gate operations, reservoir releases), flow components (i.e., flood timing, flood duration, dry period, depth), and water allocation constraints. The framework is also able to cater for the relative importance of different ecological assets, species, and processes. However, the approach has only been tested on a hypothetical case study thus far. In addition, the optimization framework is single objective, whereas in practice, there is significant interest in the optimal trade-offs between the amount of water allocated to the environment and the corresponding optimal ecological responses of affected wetlands and floodplains or particular species.

[5] In order to address the shortcomings in existing literature identified above, the objectives of this paper are (i) to extend the single-objective optimization approach developed by Szemis et al.[2012] to include multiple objectives and compare the performance of three multiobjective algorithms in order to determine which is most suitable for the EFMA optimization problem, so that the optimal trade-offs between ecological response and environmental flow allocations can be obtained and (ii) to apply the approach to a real case study in the South Australian reaches of the River Murray. This case study is well suited to testing the multiobjective EFMA approach, as flow in the River Murray is overallocated and a number of options are being considered for increasing the ecological health of the many wetlands and floodplains in the region. These include different environmental flow allocations and infrastructure options for maximizing the benefit of these allocations. One of these infrastructure options is the utilization of wetland regulators to enable direct control over the flow regime in the wetlands (e.g., introducing a drying phase to wetlands that are permanently inundated) and to reduce evaporation losses [Higgins et al., 2011]. However, where these regulators should be located and how they should be operated, as well as their effect on the optimal trade-offs between the amount of water allocated to the environment and the corresponding optimal ecological response, is unknown. The second infrastructure option considered is the potential increase in the maximum rate of upstream environmental flow releases, thereby enabling the magnitude of flow events, and hence levels of inundation, to be increased. However, the impact of these system constraints on the optimal trade-offs between environmental flow allocations and ecological response is currently unknown.

[6] The remainder of this paper is organized as follows. The case study area, problem formulation, and multiobjective optimization approach used to develop the environmental flow management schedules, including the comparative study of three multiobjective algorithms, are described in sections 2 and 3. The analyses conducted are described in section 4, while the results, discussion, and limitations are discussed in section 5. Finally, the conclusions of the study are given in section 6.

2. Case Study: River Murray in South Australia

[7] The South Australian reaches of the River Murray are part of the Murray-Darling river system, which is located in south eastern Australia and spans a number of Australian States, including Victoria, New South Wales, Queensland, and South Australia (see Figure 1) [Reid and Brooks, 2000]. Since the 1920s, the South Australian reaches of the River Murray have become significantly regulated with the construction of six locks along the river channel and a number of upstream structures in New South Wales and Victoria [George et al., 2005]. An annual water entitlement of 1850 GL has been allocated to South Australia by the Murray-Darling Basin Authority (MBDA). This is predominantly for main channel flows, irrigation, and water supply for Adelaide, the capital of South Australia, which has a population of 1.21 million [Australian Bureau of Statistics, 2012], with only 38.7 GL of this entitlement being used for wetlands, and recreational and environmental use [South Australian Murray-Darling Basin Natural Resources Management Board, 2009].

Figure 1.

Map of case study area adapted from Murray-Darling Basin Authority website (http://www.mdba.gov.au/river-data/spatial-data-services/spatial-information).

[8] The increase in river regulation and overallocation of water (due to an expansion of irrigation), and the effect of drought over a long period of time, have reduced the flow variability within the river system and highly stressed and altered the biota in the river and adjacent wetlands and floodplains [Overton et al., 2010]. In response, the Commonwealth Government of Australia approved a basin wide plan developed by the MDBA that determined the water allocation for each user and intends to increase the annual environmental water for the entire basin by 3200 GL/yr, taking it to a total volume of 4023 GL/yr [MDBA, 2012d]. In addition, the MBDA modeled and recommended the relaxation of system constraints, such as increasing the maximum flow releases from Hume Dam (an upstream dam) from 25,000 to 40,000 ML/day in order to allow higher flows to reach the South Australian River Murray and inundate mid-elevation to high-elevation floodplains [MDBA, 2012b]. However, many scientists recommend that further investigations should be conducted to assess the impact of an increase in the environmental water allocation to 4000 GL/yr, ensuring that high-elevation floodplains are inundated periodically [Government of South Australia (GSA), 2012].

[9] The case study area under investigation is a reach of the River Murray between Locks 1 and 2 shown in Figure 1. This reach spans 89.0 km [Overton et al., 2006] and accommodates eight wetlands and a large number of high lying floodplains along the river channel. Due to the construction of the locks, the wetlands closer to Lock 1 have become permanently inundated (i.e., continual connection to the river) and experience no drying, which has reduced the ecological health of the biota, such as Lignum (Muehlenbeckia florulenta), which dies when inundated for a prolonged period of time [Kingsford, 2000; Smith and Smith, 1990; Walker and Thoms, 1993]. In contrast, wetlands closer to Lock 2 are temporary and rarely inundated due to upstream system constraints. Each wetland and surrounding floodplain houses a variety of flora and fauna, ranging from high-lying river red gums (Eucalyptus camaldulensis) to water birds and fish (e.g., ibis and carp gudgeon) [Turner, 2007].

[10] As discussed in section 1, the use of wetland regulators has been suggested in the case study area. Currently, there are two wetlands with gates [Schultz, 2007; Turner, 2007], with a proposal to add flow regulation systems to a further three [Ecological Associates (EA), 2007; Overton et al., 2010]. In addition to the manipulation of regulators, ecological response can also be influenced by upstream flow releases from the South Australian border. As stated in section 1, the objectives of this paper are to investigate the effect system constraints and regulator locations and settings have on the optimal trade-off between environmental flow allocations and different aspects of ecological integrity within the case study area. The methodology for achieving this is given in section 3.

3. Methodology

[11] In order to investigate the optimal trade-offs between environmental flow allocations and ecological response(s) for the case study area under a range of scenarios, optimal EFMA schedules (i.e., flow releases and regulator settings) have to be identified over the selected planning horizon. This is achieved by modifying the optimization framework presented by Szemis et al. [2012] to incorporate a multiobjective optimization approach. The steps in the framework are shown in Figure 2 and include problem formulation, which includes the identification of the river reaches, wetlands, and floodplains to be managed, as well as the indicator(s) for measuring ecological response, and potential management alternatives and associated suboptions (section 3.1). The objective function and constraints are then identified (section 3.2), after which a trial schedule of flow releases and regulator settings can be developed over the adopted planning horizon, and assessed by calculating the objective functions using a hydrological model (section 3.3).

Figure 2.

Steps in optimization framework.

[12] This process of developing and evaluating management schedules is repeated multiple times and guided by a multiobjective optimization algorithm in order to develop the final Pareto front, which contains EFMAs that represent the optimal trade-offs between the total environmental flow allocation and the corresponding ecological response(s). Based on the rationale presented in Szemis et al. [2012], Ant Colony Optimization (ACO) is used as the optimization algorithm, since (i) it can solve complex nonlinear problems, in contrast to traditional optimization methods, such as linear programming, which can only solve linear problems [Taha, 1997], and dynamic programming, which suffers from the “curse of dimensionality” [Madej et al., 2006], and (ii) unlike other metaheuristics, such as Genetic Algorithms [Goldberg, 1989], it can accommodate the sequential nature and the conditional dependencies of the EFMA scheduling problem by using a decision tree graph to represent the problem [Szemis et al., 2012] and is capable of adjusting constraints dynamically during the optimization process in order to reduce the size of the search space [Afshar, 2010; Foong et al., 2007, 2008; Szemis et al., 2012]. In order to ensure that the most appropriate multiobjective ACO algorithm is selected, a comparison between three multiobjective ACO algorithms is conducted, as discussed in section 3.5.

3.1. Problem Formulation

3.1.1. Identification of Assets and Ecological Indicators

[13] The first step of the Problem Formulation stage involves the identification of the ecological assets to be managed, Hi, where i ranges from 1 to q. In this case study, the management of eight wetland areas is considered (i.e., q = 8) (Step 1, Table 1), which include the wetlands themselves, the high-lying floodplain areas surrounding the wetlands, and the adjacent main river channel. Baseline surveys and wetland management plans have been used to delineate areas of vegetation within the wetland and floodplain areas, as well as to identify the location of certain fish and waterbirds [EA, 2007; Marsland and Nicol, 2008; Schultz, 2007; Sinclair Knight Merz (SKM), 2004; Smith and Fleer, 2006; Turner, 2007; Waanders, 2007; Watkins et al., 2007].

Table 1. Details of Problem Formulation for Case Study
Problem Formulation StepsSpecification
1Managed Ecological Assets Hi, i =1 to qq = 8
2Ecological Indicator Ei,r r = 1 to s(i)Murray Flow Assessment Tool (MFAT) [Young et al., 2003]
Total number of species = 211
3Planning Horizon Yv, v = 1 to KYK = 5 years
Time Interval t, t = 1 to TMonthly, T = 60 months
4Management Alternatives Ma, a = 1 to hh = 6 (1 reach and 5 asset scale)
5Management Alternative Suboption Ma,m and/or Ma,dReach—magnitude and duration, Asset—duration

[14] The Murray Flow Assessment Tool (MFAT) developed by Young et al. [2003] is used as the ecological indicator (Ei,r, where r is the number of species per wetland or floodplain) in order to quantify the ecological response of each species (i.e., vegetation, waterbird, and fish) within the river, and adjacent wetlands and floodplains (Step 2, Table 1). MFAT is a habitat simulation model that was developed specifically for the River Murray and can be used to determine the impact of different flow scenarios on the ecological response of biota in terms of two ecological processes, that is, recruitment (e.g., promoting seed germination) and maintenance (e.g., preserving adult habitat) [Young et al., 2003]. This is achieved by using a number of response curves that are based on the five flow components discussed previously (i.e., frequency, duration, timing, rate of change, and magnitude) and include factors such as depth, dry period, flood timing, rate of depth change, inundation area, and flow magnitude. The response curves used for the case study area are those given in Cooperative Research Centre for Freshwater Ecology (CRCFW) [2003] and Overton et al [2010], and include species such as river red gum (Eucalyptus camaldulensis), black box woodland (Eucalyptus largiflorens), ribbon weed herbland (Vallisneria americana), main channel specialists (e.g., Murray cod), and colonial nesting waterbirds. It should be noted that as part of the MFAT score calculation, weights need to be placed on the recruitment and maintenance processes, which are chosen based on literature or expert opinion. A total of 211 species have been defined for the case study area and the proportions of each species type per wetland are given in Table 2. As can be seen, approximately 60% of the species are floodplain flora, followed by waterbirds, fish, and a small proportion of wetland flora.

Table 2. Species Composition in Case Study Area
AssetWetland NameSpecies Composition (% per asset)Regulator
Floodplain FloraWetland FloraWaterbirdFish
1Markaranka50.00.042.08.0 
2Cadell73.00.018.018.0 
3Morgan50.011.025.014.0Current
4Brenda Park53.00.029.018.0Current
5Murbko Flat64.013.017.06.0Proposed
6Murbko South85.04.00.011.0 
7Murbpook52.07.030.011.0Proposed
8Sinclair61.022.00.017.0Proposed

3.1.2. Selection of Planning Horizon and Time Interval

[15] The third step of the problem formulation includes the selection of the planning horizon, Yv (v = 1, K years) and time interval, t, where t ranges from 1 to the final interval, T (Table 1). A planning horizon of five years has been selected, as environmental water management plans in the study area are generally developed over five years [EA, 2007; Schultz, 2007], while a monthly time step has been chosen, since wetland gate operations are set on a month-by-month basis [Schultz, 2007; Turner, 2007]. This means that the final interval, T, equals 60.

3.1.3. Determination of Management Alternatives and Suboptions

[16] The identification of the management alternatives Ma, (where a ranges from 1 to h) and suboptions constitute the final two steps of the problem formulation process. The environmental flow release at the South Australian border has been selected as the sole reach scale management alternative, while the asset scale management alternatives include the operations of gates at selected wetlands. Currently, flow at two wetlands (i.e., Morgan and Brenda Park, see Figure 1) can be regulated, with another three being proposed, as shown in Table 2. Consequently, there are six management alternatives (i.e., h = 6) that can be considered in the development of environmental flow management schedules (Table 1). Next, the suboptions for each of the management alternatives, Ma, are defined. Duration, Ma,d, and magnitude, Ma,m, suboptions have been selected as the only reach-scale management suboptions, while duration suboptions have been selected for all asset-scale management alternatives (see Table 1). The number of possible duration suboptions (Ma,d) available at each monthly time step ranges from 1 to p, with p varying from 12 for July to 1 for June the following year. On the other hand, the number of magnitude suboptions ranges from 1 to n, with the selection of the maximum number of magnitude suboptions (n) dependent on the case study area and system constraints. This is discussed detail in the next section.

3.2. Identification of Objective Functions and Constraints

[17] Once the problem has been formulated, the objective functions and constraints need to be defined (Figure 1). As discussed previously, the two broad objectives that need to be considered in the problem being addressed are the maximization of ecological response and the minimization of environmental water allocation. However, as ecological response is comprised of a number of different components (e.g., different types of ecological assets such as wetlands, and floodplains, different species, different ecological processes), the objective of optimizing ecological response can be represented by one or more objective functions, corresponding to different levels of aggregation of these components. In order to account for this, the single ecological response objective introduced by Szemis et al. [2012] has been modified to enable consideration of multiple ecological objectives. To develop the multiecological response objective, the number of assets, species, and years considered in the case study area need to be defined as sets. Consequently, the number of assets ranging from 1 to q is defined in set H, while the number of species per ith asset (e.g., wetland) is identified as the Ri set, with each ith asset housing s(i) species. Finally, the total year set, V, ranging from 1 to a maximum year of YK is also defined, with the sets shown below.

display math
display math
display math

[18] Once the asset, species and year sets have been defined, the ecological components that are of interest (e.g., specific area of wetlands or vegetation species) as part of the gth ecological response objective, where g ranges from 1 to fg are defined in the form of g subsets, which also range from 1 to fg. When fg = 1, a single-objective function is used, in which the ecological responses of all components are aggregated, when fg = 2, two ecological objective functions are used in which different subsets of ecological components are considered and so on. The subsets are given below.

display math
display math
display math

where Hg is the gth subset of H and contains ecological components related to the assets and enables examination of the ecological response of wetlands and floodplains at different locations, while Ri,g is the gth subset of Ri and contains information about which species (e.g., fish) are included in the gth ecological response objective. Last, Vg is the gth subset of V, which defines the years considered and allows for the investigation of ecological responses at a specific year or over a number of years.

[19] Once the fg subsets are defined, each of the g ecological response objectives can be determined using equation (1). It should be noted that each objective function includes weights in order to account for the relative importance of various aspects of the problem, such as favoring certain species or wetlands.

display math(1)

where Ei,v,r is the MFAT value for asset i, for indicator type r in the vth yearly time interval for each of the g objective functions corresponding to g separate ecological components. In equation (1), each of the g objective function values is obtained by summing (i) values of each ecological indicator used in the particular objective function over the wetland areas (including the floodplain areas surrounding the wetlands and the adjacent river reach) defined in subset Ig, (ii) values of the species indicators identified in Ri,g to be aggregated in the gth objective function, and (iii) ecological indicator values used in the particular objective function over the years defined in subset Vg, over which the schedule of EFMAs has been developed (i.e., the planning horizon, which is five years in this instance), with the total number of years considered in the gth ecological response function defined as YK,g. Weights, w1i, w2r, and w3v place emphasis on the ith wetlands, floodplains, or river reaches, rth ecological indicator and YKth year, respectively, and are defined by the user before commencement of the optimization process. Consequently, each objective function is sufficiently flexible to cater for particular aspects of the problem (e.g., favoring sensitive or endangered species).

[20] Another component of the extension from the single to the multiobjective optimization framework presented in this paper is the addition of an environmental water allocation objective, FW, which accounts for the total amount of environmental water that is allocated over the five year planning horizon and is given below:

display math(2)

where At is the environmental water allocation in month t, which is calculated using the reach-scale management alternative magnitude suboptions selected at each tth time step.

[21] In addition, constraints are defined on the magnitude and duration of the suboptions for a particular management alternative, Ma, as given in equations (3) and (4):

display math(3)
display math(4)

where the magnitude suboptions (Ma,m) are constrained by minimum and maximum values of Ma,m_min and Ma,m_max, respectively, and the duration suboptions (Ma,d) are constrained by minimum and maximum values of Ma,d_min and Ma,d_max, respectively, for each management alternative. Each management alternative must therefore be assessed individually in order to determine appropriate values for the above constraints. The specification of Ma,m_min, Ma,m_max, Ma,d_min, and Ma,d_max is user-defined, based on the requirements of the case study area under consideration (e.g., Ma,m_max could be selected based on a maximum achievable flow in the case study area).

[22] A further constraint relates to the maximum allowable monthly flow at the South Australian border, which permits the assessment of the impact of system flow constraints, and is given as follows:

display math(5)

[23] The monthly flow has been defined as Qt, while Qtmax is the maximum flow at the South Australian border each tth month. The selection of Qtmax is user-defined and is generally based on system constraints within the case study area.

3.3. Development of Management Schedules

[24] After the objectives and constraints have been defined, management schedules are developed (as shown in Figure 2), which is done by selecting values for each of the suboptions. Based on the framework developed by Szemis et al. [2012], the management alternatives and suboptions are represented in the form of a decision tree graph, which is able take into account the sequential nature and temporal dependencies associated with the EFMA scheduling problem (e.g., the fact that the values of decision variables selected at one time period, such as the duration of a particular flow release, have an effect on the options that are available at subsequent time periods). Using this graph, a management schedule is developed by selecting one of the available alternatives at each of the nodes. Determination of the management schedules that provide the best possible trade-offs between the competing objectives of minimizing the environmental water allocation and maximizing the ecological response(s) is achieved over a number of iterations with the aid of the multiobjective ant colony optimization algorithm, details of which are given in section 3.5.

[25] An example decision tree graph that incorporates magnitude and duration suboptions, as well as the conditional dependencies associated with the duration suboptions via dynamic constraints, is given in Figure 3. The example considers four magnitude options (i.e., 0, 200, 400, and 800 gigalitres (GL)) and three duration suboptions and is constructed over three time steps.

Figure 3.

Example of an EFMA schedule graph for environmental flow releases (in Gigalitres (GL)) incorporating dynamic constraints.

[26] If the maximum duration has been selected at the first time step, then no other decision paths need to be made available at subsequent time steps (decision points), as shown by the bottom path in Figure 3. In this way, the decision tree is adjusted based on the selection made at the first decision point, thereby reducing the size of the search space and increasing the likelihood that global or near globally optimal solutions are identified. On the other hand, if a duration option of one is chosen at the first time step (top path), then the potential duration suboptions are considered again at the following time step. However, the number of available options decreases from three to two, as there are only two more time steps remaining. If the number of available duration suboptions is not adjusted dynamically then three duration options would be considered after each magnitude suboption, which results in a significantly larger search space. Therefore, this form of dynamically constraining the decision tree graph ensures that feasible EFMA schedules are developed, as well as ensuring that the optimization algorithm is able to find optimal solutions more efficiently and cater for the conditional dependencies associated with the EFMA problem [Szemis et al., 2012].

3.4. Calculation of Objective Function

[27] In order to evaluate the objective functions defined in section 3.2 for the selected management schedules, a hydrological simulation model is developed for the river reach under investigation. This is achieved with the aid of backwater curves (T. Bjornsson, personal communication, 2010) that relate river height to river flows at the South Australia border (e.g., 5000 ML/day, 10,000ML/day). This allows a relationship between flow and river height along the length of the main channel to be developed, such that for a certain flow release at the South Australian border, the corresponding river height at the eight wetland locations can be determined. In addition to this, fill values (i.e., the river level at which the wetland or floodplain is flooded) at the eight wetland locations, as well as area versus average depth curves for each of the specified areas of floodplain and wetland flora and fauna, have been determined using ArcGIS and a range of data sources, including a Digital Elevation Model (DEM) obtained from the Department of Environmental, Water and Natural Resources baseline surveys [Marsland and Nicol, 2008; SKM, 2004; Smith and Fleer, 2006; Waanders, 2007] and wetland management plans [EA, 2007; Schultz, 2007; Turner, 2007]. Once the flow versus river height relationships have been developed and the fill values obtained, the hydrological models can be developed using the equations employed in Szemis et al. [2012], as detailed below.

[28] To ensure that the model adequately simulates the hydrology, whereby wetlands fill quickly once the river level breaches the fill value and when gates are opened, equation (6) is used, while equation (7) is utilized to simulate the slow draining of a wetland when the gates are closed, or when the river level drops below the fill value. Equation (6) represents the water balance for a wetland as follows:

display math(6)

where It are the inflows, Ot are the outflows, and St are the storages at time t. The outflows Ot are the sum of the flows out of the wetland (Ow) and evaporation (Et), while the inflows are the sum of rainfall (Rt) and flows into the wetland. A simple relationship of 0.7× (pan evaporation) is used to determine the evaporation from wetlands, in meters/month, with average monthly evaporation sourced from the Australian Bureau of Meteorology website (http://www.bom.gov.au/climate/data/). The value of 0.7 is chosen as it is a common value used to determine evaporation within the Murray-Darling Basin [Gippel, 2006].

[29] To simulate gate operation, logical (If-Then) statements are used to adjust the appropriate components of the water balance equations. If a gate is closed, the inflow at that time step is set to zero (i.e., It = 0.0) and if there is water in the wetland at that time, wetland storage at subsequent time steps is only affected by rainfall and evaporation for the duration of the gate closure, as follows:

display math(7)

[30] If there is water remaining in the wetland at the time step the gate is opened, water is allowed to flow out of the wetland until the fill value is reached, after which water remains in the wetland and only is affected by evaporation and rainfall (i.e., equation (7)). It should be noted that average monthly rainfall data in the case study area have been used. These were obtained from the Australian Bureau of Meteorology website (http://www.bom.gov.au/climate/data/).

[31] Once the river level is above the fill value or maximum gate height (i.e., the maximum river level at which the gate can operate), the floodplain hydrological model is used. This model utilizes equation (6), whereby floodplain hydrology is only dependent on the river level (i.e., if the river level is above the fill value, the floodplain is inundated and the area of flooding is dependent on the height of the river. For example, as the river level increases, so does the area and depth of inundation). It should be noted that the mass balance constraints associated with the problem are also satisfied within each hydrological model.

[32] A number of assumptions have also been made for both models, including (i) water seepage is negligible since it is small compared to the evaporation loss and (ii) the rate of river level rise and fall occurs over each month. Additionally, the storage capacity of the wetlands has been examined and it has been determined that this is very small compared with the magnitude of the streamflows, and thus has a negligible effect on downstream flows.

3.5. Multiobjective Optimization

[33] As mentioned in section 3, a multiobjective ACO algorithm is used to iteratively determine management schedules that improve all objective functions with the aim of finding schedules that represent globally optimal or near globally optimal trade-offs between all objectives (i.e., schedules that are on the Pareto front—see Figure 2). The traditional multiobjective ACO procedure for determining optimal or near optimal trade-offs is shown in Figure 4, where a trial EFMA schedule is initialized, after which the optimization process takes place. This firstly involves the construction of a trial schedule for each b ants during each iteration. Ants achieve this by traveling to each time step and selecting magnitude and duration suboptions until they reach the final time step, T. The selection of these suboptions is done probabilistically based on the j pheromone matrices (τj) associated with each suboption, with the number of pheromone matrices used dependent on the multiobjective ACO algorithm used, as discussed below. As part of the optimization process, the j pheromone matrices are manipulated to increase pheromone levels for suboptions that have contributed to good overall solutions, so that they are more likely to be selected in subsequent iterations. Additionally, pheromone evaporation is applied to suboptions of schedules that do not perform well, which in turn deters the algorithm from choosing these paths again.

Figure 4.

Traditional Ant Colony Optimization procedure.

[34] Once an iteration has been completed by an ant, the resulting schedule is evaluated using fitness functions, which are the objective functions (i.e., equations (1) and (2)) transformed in order to efficiently guide the search of the algorithms. Further details regarding the fitness functions are given in section 3.5.4. The calculation of the fitness functions is achieved with the aid of the hydrological model of the case study area (see section 3.4). This model is also used to assess whether there are any constraint violations (see section 3.5.4). The process of selecting an EFMA schedule and evaluating it against the fitness functions is repeated for each ant. The pheromone levels are then updated and this process continues until the maximum iteration, w, is reached. It should be noted, that once the final iteration is complete, the convergence of the Pareto front is checked using the hypervolume, which measures the volume of area dominated by the approximated Pareto front set [Zitzler and Thiele, 1999]. This has been selected to indicate the point at which there is no further reduction in the volume of the Pareto front, thereby suggesting convergence has been reached.

[35] As part of this study, the performance of three multiobjective ACO algorithms that utilize the traditional ACO procedure (shown in Figure 4) has been compared to determine the most suitable algorithm for the case study area. The algorithms considered include the Pareto Ant Colony Optimization Algorithm (PACOA) [Doerner et al., 2004], COMPETants [Doerner et al., 2003], and m-ACO variant 3 (m-ACO3) [Alaya et al., 2007]. These algorithms have been selected because they use different pheromone updating approaches in determining the optimal or near optimal trade-off. PACOA uses multiple pheromone matrices, as well as the best and second best solution during the pheromone update process, COMPETants uses multiple colonies and pheromone matrices, while m-ACO3 employs a single pheromone matrix and updates the pheromone level using the nondominated solutions determined after each iteration. It should be noted that other ACO algorithms, such as the population-based ACO [Guntsch and Middendorf, 2003], have not been considered in this comparison, as they do not follow the traditional ACO process shown in Figure 2. A description of the three algorithms used, and the pheromone update process utilized in each, is presented in the following sections.

3.5.1. Pareto Ant Colony Optimization (PACOA)

[36] The PACOA developed by Doerner et al. [2004] utilizes Ant Colony Systems [Dorigo and Gambardella, 1997] as the underlying ACO algorithm, however, unlike Ant Colony Systems, it uses both the first and second best solutions during the global pheromone update [García-Martínez et al., 2007]. In addition, the algorithm employs multiple pheromone matrices, one for each objective considered. The pheromone update process is given by the following equation:

display math(8)

where the pheromone level on all suboptions is reduced at a rate that is controlled by the pheromone evaporation factor (ρ), while an increase in pheromone levels for each jth fitness function (Δτj) is based on whether that particular suboption is part of the best or second best solution. The b trial schedules generated by the b ants then undergo a nondominated sorting process in order to determine the schedules that are on the Pareto front for that particular iteration and are subsequently stored in an offline storage matrix. Readers are referred to Doerner et al. [2004] for a detailed description and the equations used in the PACOA.

3.5.2. COMPETants

[37] The COMPETants algorithm proposed by Doerner et al. [2003] utilizes multiple colonies and pheromone matrices to determine the optimal or near-optimal Pareto front. Each colony focuses on one objective and constructs solutions independently from each other, with the exception of a group of ants, called spies, that use a weighted sum approach that aggregates the pheromone matrices for each objective.

[38] As was done by López-Ibáñez and Stützle [2012], the COMPETants algorithm is formulated using a single-colony algorithm in which the ants are divided into subgroups that either focus on a given objective or act as spies. The pheromone levels for each subgroup are then updated using equation (8), with the level of pheromone increase for each jth objective, inline image, given in equation (9) as follows:

display math(9)

[39] The update process is independent for each subgroup, such that ants from each subgroup update their own pheromone matrix using the best solution.

[40] As was done by López-Ibáñez and Stützle [2012], the COMPETants algorithm employed in this study equally portioned the number of ants used between the j objectives and spy subgroups. For further information regarding the COMPETants algorithm, readers are referred to Doerner et al. [2003] and López-Ibáñez and Stützle [2012].

3.5.3. m-ACO variant 3 (m-ACO3)

[41] The ACO variant suggested by Alaya et al. [2007] proposes the use of a single pheromone matrix, which is updated using the nondominated solution determined in the current iteration set. The pheromone values, inline image, are updated using equation (8) (with j = 1.0) and the increase in pheromone level inline image during the pheromone update process is based on whether a suboption is in the nondominated solution set for the current iterations, P, which is shown in equation (10).

display math(10)

[42] This is different to the two previous algorithms, which use the best solutions to update pheromone levels after each iteration.

3.5.4. Fitness Functions

[43] Before the performance of the multiobjective ACO algorithms can be compared, the objectives defined in equations (1) and (2) need to be transformed to fitness functions (i.e., equations 11 and 12) in order to effectively guide the search of the algorithms, as the algorithms (i) attempt to minimize all objectives, whereas the aim of this study involves the minimization of the environmental water allocation objective and the maximization of the fg ecological response objectives (i.e., MFAT score) and (ii) like other evolutionary algorithms, are unable to explicitly take into account the constraints that are not directly related to the decision variables, necessitating the inclusion of penalties in the fitness functions. Therefore, the following fitness function/s (YE,fg) have been developed, such that FE,fg would be maximized:

display math(11)

[44] As can be seen, a penalty of 1000 is used if the system flow constraints at the South Australia border are violated for the fg ecological response objectives considered. This value was found to produce good results as part of preliminary trials.

[45] The fitness function corresponding to the objective of minimizing the total environmental water allocation (FW, equation (2)), YW, is shown below.

display math(12)

[46] In order to take into account the system flow constraints, the fitness function above also includes a penalty to deter the algorithms from selecting infeasible solutions and instead encourage the determination of optimal schedules within the given constraints. The optimal form of the penalty was determined as part of preliminary trials and has been selected since it is able to severely penalize solutions that include flows that significantly exceed system constraints, while marginally penalizing solutions that include only slight violations of system constraints. This deters the algorithm from developing infeasible solutions, while simultaneously encouraging the search for good solutions and quicker convergence.

3.5.5. Comparison of Performance of Multiobjective Optimization Algorithms

[47] Before the performance of the multiobjective ACO algorithms can be compared, a comprehensive sensitivity analysis is required to determine the optimal values of the parameters that control the searching behavior of each algorithm. The range of values tested, as well as the final values selected, are given in Tables 3 and 4. As can be seen in Table 4, two different sets of optimal parameter sets are selected, depending on the size of the search space, as dictated by the number of management alternatives (h) considered within the EFMA schedule development. It should be noted that each sensitivity run was repeated ten times (i.e., with 10 random starting positions in decision space) so as to minimize the impact of the starting position on the results obtained.

Table 3. Range of ACO Parameters Investigated for Each Algorithm
ACO ParameterRange of Values Tested
Number of ants (ant)30, 300, 510, 1200
Initial pheromone inline image1.0, 10.0
Evaporation rate (ρ)0.02, 0.1, 0.5, 0.9, 0.98
Evaluations102,000, 240,000
Table 4. Adopted ACO Parameters for Each Algorithm
PACOA ParameterAdopted Value(s)
h <4h = 6
PACOACOMPETantsm-ACO3PACOACOMPETantsm-ACO3
Number of ants (ant)300510305101200300
Initial pheromone inline image1.01.01.01.01.01.0
Evaporation rate (ρ)0.10.10.10.10.10.5
Evaluations102,000240,000

[48] Finally, to ensure that the Pareto fronts generated by each algorithm have converged when the optimal ACO parameters in Table 4 are used, the hypervolume of the Pareto front, as described in section 3.5, has been assessed. The hypervolume convergence for each algorithm when the number of management alternatives is less than 4 is given in Figure 5. As can be seen, all algorithms have converged, with the PACOA converging to a hypervolume of approximately 3.0 × 105 at 160 iterations, COMPETants converging to a hypervolume of approximately 2.9 × 105 at 140 iterations, and m-ACO3 converging to a hypervolume of 2.7 × 105 at 700 iterations. This indicates that the number of evaluations selected is sufficiently large for each of the algorithms to converge to a given Pareto front. It should be noted that hypervolume convergence has also been assessed for the case of six management alternatives, with the results obtained similar to those shown in Figure 5.

Figure 5.

Hypervolume convergence for each multiobjective ACO algorithm when h < 4.

[49] In order to assess the quality of the Pareto fronts obtained, the empirical attainment function (EAF) developed by da Fonseca et al. [2001] is used. This is because it enables Pareto fronts obtained by two algorithms to be compared, which is not the case for other measures, such as the chi-square-like deviation developed by Srinivas and Deb [1994] [López-Ibáñez and Stützle, 2012]. Use of the EAF involves determining the probability that each point in the objective space is attained by an algorithm in a single run [López-Ibáñez and Stützle, 2012]. To assess two Pareto fronts, the difference in EAFs of each point in the objective space is determined. In this study, a graphical technique [López-Ibánez et al., 2006, 2010; López-Ibáñez and Stützle, 2012] is utilized in order to achieve this, with plots generated using the eaf R package, which is available at http://cran.r-project.org/package=eaf.

[50] In order to compare the performance of the three multiobjective algorithms, one of the studies (i.e., Investigation 3) described in section 4 is used, which considers two objectives (i.e., total ecological response and environmental water allocation), three management alternatives (h) (i.e., flow releases and the operation of two wetland regulators) and an upstream flow constraint of 1800 GL/month. The number of flow magnitude suboptions (n) equals 28, while the number of duration suboptions equals 12 at the beginning of the year, but changes depending on selections made during the investigation. Further details, such as the asset (H), species (Ri), and year (V) sets for this investigation are given in section 4.1 and Tables 5 and 6. The graphs comparing the Pareto fronts developed by PACOA, COMPETants, and m-ACO3 for Investigation 3 in terms of EAF difference are given in Figure 6. As can be seen, PACOA performs better than both COMPETants and m-ACO3 (top and middle plots). This is shown by the black region in the PACOA graphs (i.e., left graphs), indicating that the PACOA algorithm attained the points in the objective space at least 80% more frequently than COMPETants and m-ACO3, whereas the regions of white in the m-ACO3 and COMPETants plots (i.e., right graphs) suggest that the same probability of attaining these points is achieved by all algorithms. On the other hand, the graph that compares the performance of COMPETants and m-ACO3 (bottom plot) indicates that COMPETants performs better for solutions that minimize environmental water allocation, as indicated by the black region in the top left corner (see left graph), while m-ACO3 finds solutions that maximize the MFAT score and, in turn, the ecological response of the wetlands and floodplains in the case study area.

Table 5. Details of Investigations for Trade-Offs Between Environmental Allocation and Total Ecological Response
InvestigationUpstream System Flow Constraint, Qtmax (GL/month)Magnitude Suboptions (n)Ecological Response Objectives (fg)Management Alternatives (h)Regulators
1120020132
2165026132
3180028132
4240037132
5300045132
Table 6. Details of Number of Species Per Asset and Number of Years Considered in Total Ecological Response Objective (g = 1) for Investigations 1–5 and 7–10
Asset Set iHNumber of Species (s(i)) in Ri,1 (g = 1)Number of Years (YK,1)
1265
2155
3285
4175
5535
6275
7275
8185
Figure 6.

Comparison of performance of PACOA, COMPETants, and m-ACO3 using EAF differences plots.

[51] The results of the comparison study indicate that the PACOA performs best, given that it is able to develop Pareto fronts with solutions that favor the objectives investigated (i.e., water allocation and ecological response), as indicated by the spread of the black region in the upper EAF difference plots in Figure 6. It should be noted that additional analyses have been conducted for the case where the number of management alternatives, h, equaled 6, with results obtained following a similar trend as those shown in Figure 6. Based on these findings, the PACOA is used for the analysis for the case study area, with details of the analysis conducted and results given in sections 4 and 5, respectively.

4. Analyses Conducted

[52] In order to meet the objectives stated in section 1, two studies have been formulated. The first of these (section 4.1) focuses on the impact of upstream flow constraints on the optimal trade-offs between environmental flow and ecological response. Two analyses have been conducted as part of this study. The first examines the trade-offs between environmental flow and the total ecological response of the case study area for a range of upstream system constraints, while the second investigates the trade-offs between environmental flow, the wetland ecological response, and the floodplain ecological response. The second study (section 4.2) examines the impact of the number of regulators on the optimal trade-offs between environmental water allocation and resulting ecological score in the case study area. Details of the two studies and corresponding investigations are given in Tables 5-7 and are discussed in detail in the following subsections. It should be noted that minimum monthly flows within the river channel have been set to South Australian entitlement flows [MDBA, 2012a], while weights for recruitment and maintenance within MFAT have been set to 0.5 each, with the exception of the weight for the wetland flora species, which has been set to 0.25 for recruitment, and 0.75 for maintenance [CRCFW, 2003]. An equal preference has been given to all species and assets, and each optimization run has been repeated 10 times with different starting positions in the solution space.

Table 7. Details of Investigations Conducted as Part of Examining the Trade-offs Between Environmental Flow, Wetland Ecological Response, and Floodplain Ecological Response
InvestigationUpstream System Flow Constraint, Qtmax (GL/month)Magnitude Suboptions (n)Ecological Response Objectives (fg)Management Alternatives (h)Regulators
6180028232

4.1. Impact of Upstream Flow Constraints

4.1.1. Trade-Offs Between Environmental Flow Allocation and Total Ecological Response

[53] As discussed in section 2, the Murray-Darling Basin (MDB) is a highly regulated system with many users, resulting in a number of system constraints. Five investigations (i.e., Investigations 1–5 in Table 5) have been conducted in order to assess the effect different upstream flow constraints, including maximum upstream releases of 1200, 1650, 1800, 2400, and 3000 GL/month, have on the optimal trade-off between total environmental flow allocation and total ecological response. These constraints have been selected based on the current situation in the MDB, where flows less than or equal to 1200 GL/month (or 40,000 ML/day) at the South Australian border can be achieved relatively easily, whereas flows of 1200–2400 GL/month (or 40,000 and 80,000 ML/day) are much more difficult to achieve due to upstream system constraints [Heneker and Higham, 2012], while flows equal to or greater than 3000 GL/month (or 100,000 ML/day) are not deliverable unless these constraints are relaxed by altering existing upstream flood mitigation constraints at times when there are large inflow events at a number of upstream tributaries [MDBA, 2011a, 2012c].

[54] It should be noted that for each investigation, the number of flow magnitude suboptions (n) differs, as shown in Table 5, while the duration suboptions for each investigation begin with 12 months at the beginning of each year, but are then dynamically changed depending on prior selections made during a particular iteration. As part of these investigations, only one ecological response objective is considered (i.e., g = 1), that is, the total ecological response of the case study area, with the number of assets (i.e., i) in the H set equal to 8, while the number of species considered in each Ri set (s(i)) and the number of years (YK) are shown in Table 6. In addition, only the two existing regulators at Morgan and Brenda Park wetlands are taken into account resulting in three EFMAs (i.e., h = 3), including upstream flow releases and the operation of these two regulators. Consequently, the total search space consists of 10135 discrete combinations of decision variable values.

4.1.2. Trade-Off Between Environmental Flow Allocation, Wetland Ecological Response, and Floodplain Ecological Response

[55] The final investigation (i.e., Investigation 6) as part of this study examines the trade-off between three objectives, that is, the environmental water allocation, the ecological response of the wetlands, and the ecological response of the floodplains for a given upstream flow constraint. This investigation has been conducted because wetlands and floodplains lie on different regions of the flood gradient, each with different flow requirements [Rogers, 2011], and the trade-off between these three aspects is currently unknown. Details of the investigation are given in Table 7, with the upstream system flow constraint set to 1800 GL/month and the number of magnitude options (n) set to 28. The number of ecological objectives, fg, equals two, with one ecological response objective focusing on the wetlands (i.e., g = 1), and the other on the floodplains (i.e., g = 2). In order to account for the two ecological response objectives, fg subsets needed to be defined, with details of each asset subset (Hg), number of species subset in each asset (Ri,g) and the number of years subset V (i.e., YK) given in Table 8. As in Investigations 1–5, two regulators at Brenda and Morgan are in operation resulting in a total of three EFMAs (i.e., flow releases and two regulators), with a total search space of 10122 discrete combinations of decision variables.

Table 8. Details of Number of Species Per Asset and Number of Years Considered in Wetland Ecological Response (g = 1) and Floodplain Ecological Response (g = 2) Objectives for Investigation 6
Asset Set iHNumber of Species (s(i)) in Ri,1 (g = 1)Number of Species (s(i)) in Ri,2 (g = 2)Number of Years for g = 1 and g = 2 (YK,g)
113135
21105
314145
4895
519345
64235
713145
87115

4.2. Impact of Additional Regulators

[56] In recent years, it has been suggested that the flow regime within a wetland should be controlled in order to maximize ecological health, while maintaining the same level of water use and reducing evaporation loss [Overton et al., 2010]. As mentioned previously, two of the wetlands in the case study area currently have regulators, with an additional three wetlands proposed to have such control structures (see Table 2). However, the impact of these control structures on the optimal trade-off between environmental flow allocation and ecological response has not been assessed in previous studies. Consequently, an additional four studies have been formulated, the results of which can be compared with results obtained in Investigations 1 and 3. Thus, the effect of zero and five regulators is examined under the current system constraint of 1200 GL/month in Investigations 7 and 8, respectively, and under an increased system constraint of 1800 GL/month in Investigations 9 and 10, respectively. The number of management alternatives for each Investigation ranges from 1 to 6, depending on the number of regulators considered (Tables 5 and 9), resulting in a search space ranging from 1087 to 10177discrete combinations of decision variable values. It should be noted that the total ecological response objective (i.e., g = 1) of the case study area is considered in Investigations 7–10 and thus uses the same asset (H), species (Ri), and year (V) sets as defined in Investigations 1–5, which are given in Table 6.

Table 9. Details of Investigations Conducted as Part of the Assessment of the Impact of Additional Regulators
InvestigationUpstream System Flow Constraint, Qtmax (GL/month)Magnitude Suboptions (n)Ecological Response Objectives (fg)Management Alternatives (h)Regulators
7120020 10
8 65
9180028110
10 65

5. Results and Discussion

[57] The results obtained are in the form of optimal trade-offs between the total amount of water available for environmental purposes and ecological response. In order to assess the impact of different upstream flow constraints, and numbers of regulators on the optimal trade-off between environmental flows and ecological response, as per the stated objectives of the paper, the discussion of the results focuses on the following issues:

[58] 1. The impact of different upstream flow constraints and numbers of regulators on various aspects of the optimal trade-off curve between environmental flow and ecological response, such as changes in the rate of increase in ecological response relative to the rate of increase in environmental flow, changes in the presence and location of “break points,” at which a change in the relative rate of change in one objective occurs to that of the other, and changes in the best possible ecological response (sections 5.1.1 and 5.2.1).

[59] 2. The impact of different upstream flow constraints and numbers of regulators on the effectiveness of a number of proposed environmental flow allocations (sections 5.1.2 and 5.2.2). These include the current (2012) allocation of 2105 GL/yr (i.e., 10,525 GL over 5 years) (Allocation 1), the allocation of 4023 GL/yr (i.e., 20,115 GL over 5 years) that the MDBA is trying to achieve by 2019 [MDBA, 2012d] (Allocation 2), and the allocation of 4823 GL/yr (or 24,115 GL over 5 years) [GSA, 2012] (Allocation 3), which has been suggested by independent scientists, such that required salt export from the Lower Murray Region and adequate water for significant floodplains along the South Australian River Murray can be met [Bloss et al., 2012; Higham, 2012].

5.1. Impact of Upstream Flow Constraints

5.1.1. Impact on Optimal Trade-Off Curve

5.1.1.1. Trade-Offs Between Environmental Flow Allocation and Total Ecological Response

[60] The optimal trade-offs between environmental water allocation and corresponding MFAT score obtained as part of each investigation described in section 4.1 are shown in Figure 7. It can be seen that there is little improvement in MFAT score with increased environmental water allocation at the current upstream flow constraint of 1200 GL/month. In contrast, as the upstream flow constraint is relaxed to between 1650 GL/month and 3000 GL/month (Investigations 2–5), there is an almost linear increase in MFAT score with an increase in environmental flow allocation up to a certain point, at which there is a very small increase in MFAT score with increased flow allocation. This point is termed a breakpoint and identifies a solution at which there is a significant change in the ecological benefit obtained per unit allocation of environmental water, as mentioned previously. The locations of the breakpoints are shown in Figure 7, with BP1 through to BP5 referring to the breakpoints for Investigations 1–5, respectively.

Figure 7.

Optimal trade-offs between environmental water allocation (GL/5 yr) and MFAT score for Investigations 1–5.

[61] The breakpoint values for each of the five investigations are given in Table 10. As can be seen, for Investigation 1, the breakpoint occurs at an MFAT score of 0.15 and an allocation of 5324 GL/5 yr. After this point, there is very little additional benefit in allocating more water, since the rate of MFAT score increase per 1000 GL is only 0.003, whereas the same value is 0.022 before the breakpoint. The breakpoints for the remaining four investigations are much more distinct (Figure 7 and Table 10). For Investigations 2–5, the increase in MFAT score/1000 GL of additional upstream release before the break point is approximately the same at around 0.03 (ranging from 0.028 for Investigation 5 to 0.035 for Investigation 3) and reduces significantly to less than 0.004 after the break point (ranging from 0.002 for Investigation 3 to 0.003 for Investigation 4). However, the flow allocation, and hence MFAT score, at which the breakpoints occur increases significantly from Investigation 2 to Investigation 5, indicating the increased benefits of additional environmental flow allocations as the upstream system constraints related to the maximum flow release are relaxed.

Table 10. MFAT Score and Allocation at the Breakpoint for Each Investigation, as Well as the Rate at Which the MFAT Score Increases Per 1000 GL Environmental Allocation Before and After the Breakpoints
InvestigationMFAT ScoreAllocation (GL/5 yr)Change in MFAT Score/1000 GL in Region Before BreakpointChange in MFAT Score/1000 GL in Region After Breakpoint
10.1553240.0220.002
20.2573500.0340.003
30.2880550.0350.002
40.3311,0550.0300.002
50.3813,2000.0280.002

[62] The increased benefit of additional environmental flow allocations as upstream system constraints are relaxed can also be seen from the maximum MFAT scores that can be achieved, and the corresponding flow allocations (Table 11). The maximum MFAT score that can be achieved with the current system constraint (Investigation 1) is 0.17, which is much lower than those obtained as part of the other Investigations, which ranged from 0.27 for Investigation 2 (i.e., 1650 GL/month upstream flow release constraint) to 0.41 for Investigation 5 (i.e., 3000 GL/month upstream flow release constraint).

Table 11. Maximum MFAT Scores and Corresponding Allocations (GL/5 yr) for Each Investigation
InvestigationMFAT ScoreAllocation (GL/5 yr)
10.1712,000
20.2714,400
30.3122,125
40.3626,000
50.4129,500
Table 12. Maximum MFAT Scores for Each Allocation and Investigation
InvestigationAllocation
123
10.160.170.17
20.260.270.27
30.290.310.31
40.330.360.37
50.340.400.40

[63] The reason for the increase in MFAT scores with increasing system constraints is a corresponding increase in the maximum water level that can be achieved. For example, with the current system constraint (Investigation 1), some of the temporary wetlands, such as Cadell, and the higher elevated floodplains containing river red gums (Eucalyptus camaldulensis) and black box woodland (Eucalyptus largiflorens), which account for the majority of the species in the case study area (see Table 2), cannot be inundated. This, and the effect of drought, have resulted in the deterioration of many of the high lying floodplain species in the South Australian River Murray [GSA, 2012; Overton et al., 2010]. In addition, current system constraints prevent the inundation of 50% or more of the floodplain area, which is a requirement for achieving higher MFAT scores for the floodplain species [Young et al., 2003]. As discussed above and illustrated in Figure 7, at the current system constraint, MFAT scores are virtually independent of any additional environmental flow allocation, as the occurrence of the larger flow events needed to inundate key ecological assets is prevented.

[64] As the upstream flow constraints are relaxed to 1650 and 1800 GL/month, there are significant benefits associated with increased environmental flow allocations (Figure 7), as greater areas of the wetlands and floodplains can be inundated and two of the temporary wetlands (Cadell and Markaranka) can be filled, almost doubling the corresponding MFAT scores to 0.27 and 0.31, respectively (Table 11). This enables some of the important flora species to be restored or maintained. This trend continues as the constraints are relaxed further to 2400 and 3000 GL/month, with increased environmental flow allocations resulting in maximum MFAT scores of 0.36 and 0.41, respectively (Table 11).

[65] As can be seen in Figure 7, there are a number of step changes in the trade-off curves for Investigations 2–5, with points along the step changes for Investigations 2 (i.e., Points A–F) and 5 (i.e., Points 1–6) labeled and shown in Figure 8. For Investigations 2 and 5, each step change is the result of an additional major flow release (where a major flow release is defined as the largest flow release relative to other monthly flow releases) over the five year planning horizon. For example, for Investigation 2, the region between points A and B included one major flow release, while the regions between points C and D and points E and F, included two and three major flow releases, respectively. Similarly, for Investigation 5, the regions between points 1 and 2 and points 5 and 6 included one and three major flow releases, respectively. For regions of the trade-off curves that included a particular number of major releases (e.g., regions A–B, E–F, 1–2, and 3–4, Figure 8), MFAT scores increased with little additional environmental water allocation as a result of the inundation of the temporary wetlands, Cadell and Markaranka. For example, flows greater than 1500 GL/month are required to inundate Cadell, which can only be achieved when the environmental allocation is greater than 1375 GL. Once this allocation is obtained for the planning horizon, Cadell's MFAT score can increase from 0.04 to 0.14, resulting in a significant increase in MFAT score with minimum additional environmental water (i.e., regions A–B).

Figure 8.

Optimal trade-offs between environmental water allocation (GL/5 yr) and MFAT score for Investigations 2 (i.e., 1650 GL/month) and 5 (i.e., 3000 GL/month).

[66] Overall, the results highlight the need to assess the impact of a range of upstream system flow constraints on the ecological integrity of the case study area. The limited ecological benefit of increasing environmental flow allocations at the current system constraints and the step changes in the trade-off curves, provide valuable insight to water managers and ensures that optimal EFMA schedules can be developed that use the available water in the most efficient manner, while also maintaining the integrity of the biota.

5.1.1.2. Trade-Off Between Environmental Flow Allocation, Wetland Ecological Response, and Floodplain Ecological Response

[67] The optimal tradeoffs between environmental water allocation, the ecological response of the wetlands and the ecological response of the floodplains in terms of the MFAT score that have been developed as part of Investigation 6 can be seen in Figure 9, where two slices of the three objective trade-off are shown. It can be seen in the top graph that the wetland MFAT score ranges from 0.20 to 0.45 as the environmental water allocation increases from 0 to 50,000 GL/5 yr. Additionally, there is an increase of 0.10 in the MFAT score as the allocation increases from 0 to 10,000 GL/5 yr mark. However, after this point, an additional allocation of 30,000 GL/5 yr is required to achieve the same increase of 0.10 in the wetland MFAT score. This suggests that after the 10,000 GL/5 yr environmental water allocation point, the ecological benefit for the wetlands as more water is added into the case study area is minor.

Figure 9.

Optimal trade-off between environmental water allocation (EWA (100 GL/5 yr)) and wetland and floodplain MFAT score for Investigation 6.

Figure 10.

Optimal trade-offs between environmental flow allocation and MFAT score for Investigations 1, 3, and 7–10.

[68] It can also be seen in the top graph that there is very little spread in the points along the wetland MFAT score axis, indicating that the same wetland MFAT score can be achieved at a given environmental allocation, irrespective of the timing, magnitude, and duration of the management alternatives selected as part of the development of an EFMA schedule. In contrast, when comparing the trade-off between floodplain MFAT score and environmental water allocation in the bottom graph in Figure 9, it can be seen that the spread of points along the floodplain MFAT axis becomes greater at higher allocations. This suggests that at higher allocations, the scheduling of management alternatives (e.g., magnitude, duration) can have a major impact on the overall floodplain MFAT score, with differences in floodplain MFAT scores of 0.1 being obtained for a given allocation and wetland MFAT score. In addition, it can be seen that once the environmental water allocation of 40,000 GL/5 yr has been exceeded, the floodplain MFAT score begins to decrease to 0.10, suggesting that too much environmental water has been released, thereby prolonging inundation of these areas and reducing the overall ecological integrity of the floodplains. Finally, it can be seen that the overall floodplain MFAT score achieved is much less than that achieved for the wetlands. This is because of the system constraint (i.e., 1800 GL/month) considered in this investigation, which is not high enough to result in inundation of larger portions of the floodplains at higher elevations.

[69] Overall, this study highlights the valuable insights that can be obtained when assessing the trade-offs between different components of ecological response (in this case the wetlands and floodplains) and environmental water allocation. In particular, the sensitivity of the floodplain MFAT scores at higher allocations can provide further information to water managers, specifically in the selection of the best EFMA schedule at higher allocations, which will ensure not only the best wetland ecological outcome, but also that for the floodplains.

5.1.2. Impact on Effectiveness of Various Environmental Flow Allocations

[70] The MFAT scores at the three suggested environmental flow allocations considered for each investigation are shown in Figure 7 and Table 12. It can be seen that for Investigation 1, an MFAT score of approximately 0.17 is achieved at each allocation, indicating that at the current system constraint of maximum upstream releases of 1200 GL/month, the allocation of environmental water above the current allocation in the MDB does not increase the overall ecological benefit within the case study area. As discussed in section 5.1.1, this is because the maximum possible flows are not sufficient to inundate the temporary wetlands and achieve the 50% floodplain area inundation needed in the MFAT calculation [Young et al., 2003]. Similarly, there is very little change in MFAT scores for the different flow allocations for Investigations 2 and 3, with increases ranging from 0.01 to 0.02 when moving from Allocation 1 to Allocation 2, and no further increase in the scores when moving to Allocation 3. On the other hand, there is a slight increase in MFAT scores when moving from flow Allocations 1 to 3 for Investigations 4 and 5, with a maximum increase in MFAT score of 0.04 for Investigation 4 and a maximum increase of 0.06 for Investigation 5, suggesting that there is only a slight ecological benefit associated with increased environmental water allocations if the upstream flow release constraint is increased to 2400 GL/month or greater.

[71] Overall, the results suggest that there is limited ecological benefit beyond Allocation 1 (i.e., the current environmental allocation), while the upstream flow constraint has a significant impact. As discussed above, this is because the major factor affecting the ecological health of the case study area is whether the high lying wetlands and floodplains can be inundated or not. This requires the occurrence of high-magnitude flows, which simply cannot be achieved unless the upstream flow constraints are relaxed. However, this results in flooding of upstream agricultural and recreational (e.g., holiday houses) areas located adjacent to the Murray River, which can result in other problems, such as the loss of crops and profits. On the other hand, unless the system constraints are relaxed, the required ecological benefits within the case study area can only be achieved if natural major flooding occurs.

5.2. Impact of Additional Regulators

5.2.1. Impact on Optimal Trade-Off Curve

[72] The optimal trade-offs between environmental water allocation and MFAT score developed as part of the investigations discussed in section 4.2 are shown in Figure 10. As can be seen, the general shape of the trade-off curves is not affected by the number of regulators (i.e., zero, two, or five) for both upstream system flow constraints considered (i.e., 1200 and 1800 GL/month). However, there was a distinct advantage in the addition of more regulators, as indicated by a shift in the trade-off curves to the right with an increase in the number of regulators for both of the upstream system constraints.

[73] The maximum MFAT scores and associated environmental flow allocations for each investigation are given in Table 13. For Investigations 7 and 9, where no regulators are present, an environmental allocation greater than 29,000 GL/5 yr is required to achieve MFAT scores of 0.18 and 0.30, respectively. Once two regulators are in operation within the case study area (i.e., Investigations 1 and 3), a water saving of 20,000 GL/5 yr is achieved in order to obtain MFAT scores that are similar to those obtained in the corresponding investigations that considered no regulators. As the number of regulators in operation increases to five in Investigations 7 and 9, there is little difference in the scores and allocations obtained compared with those obtained in the investigations where two regulators are used (i.e., Investigations 1 and 3).

Table 13. Maximum MFAT Scores and Associated Allocations Achieved for Each Regulator in Operation
RegulatorsSystem Constraint (GL/month)InvestigationMFAT ScoreAllocation (GL/5 yr)
0120070.1832,478
180090.3029,100
2120010.1712,000
180030.3122,125
5120080.1817,750
1800100.3415,225

[74] Overall, the use of two regulators for both system constraints considered does not alter the maximum MFAT score, but results in a substantial reduction in the environmental water allocation required to achieve this score. This suggests that the regulators are best used as water saving measures and would benefit areas where limited water is available as a result of drought or when multiple users are present, as is the case in the South Australian reaches of the River Murray.

5.2.2. Impact on Effectiveness of Various Environmental Flow Allocations

[75] The MFAT scores at the three suggested environmental flow allocations for each investigation are shown in Figure 10, Tables 14 and 15. It can be seen in Table 14 that at the current environmental allocation (i.e., Allocation 1), for the upstream system flow constraint of 1200 GL/month, the MFAT score increases marginally by 0.01 as the number of regulators increases from two to five. Once the allocation increases to the volume proposed by the MDBA (i.e. Allocation 2), the MFAT score gradually increases from 0.16 to 0.18 as more regulators are considered, while at Allocation 3 (i.e., the allocations proposed by environmental scientists), a 0.01 improvement in MFAT score is obtained when five regulators are taken into account. This indicates that at lower allocations, a marginal ecological benefit is achieved with the operation of two regulators, however, once the allocation increases to Allocation 3, a small improvement in MFAT score is only obtained when five regulators are in operation.

Table 14. MFAT Scores Achieved for Each Allocation and Investigation for the 1200 GL/Month System Constraint
RegulatorsInvestigationAllocations
123
070.150.160.17
210.160.170.18
580.170.180.18
Table 15. MFAT Scores Achieved for Each Allocation and Investigation for the 1800 GL/Month System Constraint
RegulatorsInvestigationAllocations
123
090.260.290.31
230.290.310.33
5100.300.340.34

[76] The MFAT scores achieved for a system constraint of 1800 GL/month are given in Table 15 for each of the three environmental water allocations considered. It can be seen that at Allocation 1, there is a marginal increase in MFAT score of 0.03 when two regulators are considered, while the addition of three regulators increases the MFAT score by 0.01. On the other hand, for Allocations 2 and 3, a score of approximately 0.29 is achieved when no regulators are in operation, which increases to 0.31 and 0.34 as the number of regulators increases from two to five, respectively. This suggests that a positive impact can only be achieved at larger allocations when 5 regulators are considered, compared with the use of two regulators, which improved the score for all allocations.

[77] In summary, this study showed the improvement in MFAT scores achieved as additional regulators are introduced in the case study area for different environmental flow allocations. It showed that if five regulators are in operation, an improvement in MFAT score can only be achieved at higher allocations, while the use of two regulators can marginally improve the ecological health at lower allocations.

5.3. Limitations

[78] While the results obtained provide valuable insight into the management of environmental water in order to maximize ecological response, there are some limitations with the findings as a result of the uncertainties associated with the ecological scores calculated using the Murray Flow Assessment Tool (MFAT). The MFAT model uses preference curves to develop a relationship between flow and ecological response for species types, however, knowledge of these ecological relationships is imperfect, thereby introducing uncertainty into the model and the final results [Fu and Merritt, 2012]. To overcome this shortcoming, a sensitivity analysis, as conducted by Norton and Andrews [2006] and Fu and Merritt [2012] on the preference curves and/or aggregation approach, could be performed. Such an analysis would examine the robustness and variance of the likely ecological response that could be obtained for a given EFMA schedule. This would provide detailed information to water managers and further understanding of the likely ecological benefit that could be achieved for a particular EFMA schedule. However, such an analysis is beyond the scope of this study. Finally, it should be noted that the results and conclusions obtained from this analysis are only applicable to the case study area.

6. Summary and Conclusion

[79] In this paper, the optimization framework developed by Szemis et al. [2012] is extended to incorporate multiple objectives and applied to a real case study in the South Australian River Murray. The aim is to assess the trade-offs between environmental flow allocations and ecological benefits based on the impact of (a) upstream system flow constraints and (b) the number of regulators used to control the flow at wetlands. In order to achieve this, the performances of three multiobjective ACO algorithms (i.e., COMPETants [Doerner et al., 2003], m-ACO3 [Alaya et al., 2007], and PACOA [Doerner et al., 2004]) are compared, with the PACO algorithm found to perform best (see section 3.5.5). The PACOA is coupled with a hydrological model consisting of eight wetlands, five of which can be regulated. Each wetland is composed of a variety of flora and fauna species, obtained using DEM and baseline survey data of the case study area. The management options considered as part of the development of EFMA schedules include the scheduling of environmental flow allocations and regulator operations. The ecological benefit of each EFMA schedule developed is assessed using the Murray Flow Assessment Tool developed by Young et al. [2003], while a hydrological model is used to determine the total environmental water allocation.

[80] Two studies are undertaken to achieve the objectives of the paper. In the first study, the impact of upstream system flow constraints on the optimal trade-off between environmental water allocation and ecological benefit is assessed, while in the second study, the effect of additional regulators on these trade-offs is investigated. The shape of the trade-off curve, the effectiveness of three different environmental water allocations and the impact of flow releases and gate operations on EFMA schedule development are analyzed for each study.

[81] The results of the first study indicate that increased environmental water allocations only have a positive ecological impact if the current upstream flow constraints are relaxed, which enables large areas of floodplain flora to be inundated. In addition, results from assessing the trade-offs between environmental flow allocation, floodplain ecological response, and wetland ecological response indicate that floodplain scores are more sensitive at higher allocations compared with the wetland ecological response. The results of the second study indicate that the addition of regulators only marginally improves the ecological response in the case study area, but that this can be achieved with significantly smaller volumes of water. In addition, the results obtained indicate that at lower system constraints (e.g., 1200–1800 GL/month), the allocations recommended by the MDBA and environmental scientists may be too large for the case study area, as only a marginal ecological benefit is achieved for Allocations 1–3. However, once the system constraints are relaxed, there is a significant improvement in the MFAT scores as environmental allocations increase from those recommend by the MDBA to those proposed by the environmental scientists.

[82] Overall, the studies provide valuable insight into the EFMA scheduling problem, particularly the ecological benefit gained from an increase in environmental allocation for a range of upstream system flow constraints and numbers of regulators. The approach presented in this study enables water managers to make informed decisions regarding the management of environmental releases, regulator operation, and investment in additional infrastructure, particularly when there is limited water available, as is the case for the South Australian River Murray.

Acknowledgments

[83] This work is supported by the University of Adelaide and the eWater CRC. The Digital Elevation Model (DEM), as well as regulator and baseline survey data, have been provided by the South Australian Department of Environment, Water and Natural Resources. The authors would also like to thank Tumi Bjornsson and Richard Thompson from the South Australian Department of Environment, Water and Natural Resources for their advice throughout the study, as well as the anonymous reviewers, who have provided valuable comments that have led to significant improvements in the quality of this paper.

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