2.1. Case Study
2.2. System Dynamics
2.3. Proposal of the Multi-Methodological Approach SODA/SD: The Rationality
2.3.1. Step 1: Structuring the Problem
Building the Individual Cognitive Maps
Building the Congregated Cognitive Map
Construction of the Tree of Fundamental Viewpoints
2.3.2. Step 2: Application of System Dynamics for the Evaluation of Alternatives
Construction of the Causal Loop Diagram
Building the Stock and Flow Diagrams
- Population sub-model
- Water supply sub-model
- Water demand sub-model
- Water tariff sub-model
- Returned water sub-model
Model Simulation and Scenario Analysis
3.1. Stage 1: Structuring the Problem
3.1.1. Construction of Cognitive Maps
Step 1—Construction of the Individual Cognitive Maps
- “improved management of the reservoir’s hydrological balance; reuse of wastewater; stimulating water charging through efficient tariffs; control of losses and environmental education for conscious use of water”;
- “inter-basin water transfer; desalination; loss control; wastewater reuse; efficient pricing models; construction of a new dam and environmental education for conscious water use”;
- “ Expand the control of water losses; rationing water uses; raising water tariffs; conscious use of water resources; reuse of wastewater and transposition of water between river basins”;
- “improve watershed planning; greater action to control losses; develop tariffs that guide to rational water use and inter-basin water transfer”.
Step 2—Construction of the Congregated Cognitive Map
- Hierarchy of means-end concepts: Observing the congregated map, one can notice a relationship of influence between the concepts, where in the lower part of the map are located the “means” procedures, i.e., how it will achieve the objectives, and in the upper part are located the “ends” elements, which are the objectives;
- Concepts “heads” and “tails”: As can be seen, the map has only one concept “head”, represented by the number 4, located at the top of the map. This concept was proposed as a central objective that seeks to improve the water supply for the case studied. The “tails” concepts are congregated in the map and are represented by the following numbers: 13, 12, 11, 14, 7, 8, 6, 5, 10, and 9. These concepts “tails”, as described in the theoretical framework, are called means to reach the strategic and fundamental objectives of decision makers;
- Feedback loops: No feedback loop has been verified on the map;
- Clusters: The map shows the presence of three clusters, namely: efficient water pricing, demand management and supply management. The clusters are highlighted with different colours on the map (Figure 7).
3.1.2. Construction of the Tree of Fundamental Viewpoints
3.2. Stage 2: Evaluation of Alternatives
3.2.1. Model Validation
3.2.2. Model Simulation and Scenario Analysis
- Status Quo versus Scenario 1
- Scenario 2 (Impacts of Scarcity-Based tariff on water conservation)
- Scenario 3 (Impacts of leakage control on water conservation)
- Scenario 4 (Impacts of wastewater reuse on water supply)
- Scenario 5 (Impacts of inter-basin water transfer on water supply)
- Combining different scenarios
- Efficient management: In which three types of management strategies were added, SBT, the reuse of wastewater for a scenario of 100% reuse and a control of losses with an index of 25%.
- Inefficient management: No management strategy was taken into consideration.
3.3. Uncertainty Simulation by Monte Carlo Simulation
- The elaboration of system dynamics models considering the SODA method in the problem identification and structuring phase can be an alternative for the construction of these system dynamics models, which are unable to provide a broad understanding of the problem considering its controversies and multiple decisions about the water management problem.
- The use of the insights generated from the interviews with the experts (construction of the cognitive maps of the SODA method) to assist the facilitator in the preparation of the causal and stock and flow models of the system dynamics, provided a greater understanding and ease when building these models.
- Another important contribution in this study was the development and application of a water tariff structure method, called here scarcity-based tariff (SBT), which encourages the rational use of water based on its availability in the reservoir, which in turn can increase revenue in times of low water stock levels and support investment in other water management strategies.
Data Availability Statement
Conflicts of Interest
Appendix A. Individual Cognitive Maps
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|Drainage area (km2)||6727.69|
|Minimum Temperature (°C)||18–22|
|Maximum Temperature (°C)||28–31|
|Rainfall concentration period (months)||4 (February–May)|
|Scenarios||Scenario Description||Wastewater Reuse (No/Yes)||PISF|
|Population Growth (%)||Water Use|
|Loss Control (LC)|
|Parameters||Initial Value||Sensitivity Test Range|
|Loss control coefficient||0.15||[0.1, 0.3]|
|Scarcity-based tariff||1||(0, 3)|
|Rate of reuse of wastewater||0.6||[0.1, 1]|
|Population growth rate||0.01||[0.001, 0.04]|
|Domestic demand per capita||48||(40, 55)|
|Water transfer rate between basins||2||(1, 4)|
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