Adaptive optimal sustainability framework in urban water supply system under different runoff scenarios

6 Recent droughts have caused a crisis in the water supply procedure, because as available water resources 7 become more limited, the imbalance between the growing water demand and water supply in different 8 sectors leads to unsustainability in the system. Thus, this study proposes a dynamic model to optimize water 9 supply system under different scenarios aimed at improving sustainability of system. In fact, due to the 10 negative impacts of the water crisis, the sustainability of the dynamic water supply system is evaluated and 11 optimized according to the performance indicators of the system. Also, to investigate the proposed model, 12 a real case study of the Sistan basin in Iran over ten years period is conducted. Based on the model, different 13 management insights along with the scenario analysis are considered in order to assess the sustainability of 14 system in more detail. According to the final output, the highest level of sustainability is related to the 15 domestic sector because it has higher reliability and less vulnerability than other sectors.


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Due to rapid population growth and climate change, meeting water demand in a regional water supply 19 system has become a major challenge for decision makers (Xiong et al. 2020;Brown et al. 2015). However, 20 the lack of available water resources, along with the lack of proper water supply management, increasingly 21 threatens the sustainability of the urban water supply system, and the environment (Rathnayaka et al. 2016). 22 Indeed, the sustainability of the water supply system depends on improving efficiency of adaptation 23 measures on both supply and demand sides, so that on the demand side, demand management to delay the 24 need for new resources, and on the supply side, rising the efficiency of optimal use of water resources 25 should be considered (Waite 2010). By definition, sustainability of water supply system is formulated as 26 the geometric mean of performance indices: reliability, resilience, and vulnerability; and it reflects the 27 integrated behavior of the system by considering the possible consequences of the imbalance between water 28 demand and water supply (Sandoval-Solis et al. 2011; Srdjevic and Srdjevic 2017). Indeed, the mentioned 29 indices are considered as the main indicators for analyzing the performance of water supply system in the 30 long-run (Gu et al. 2017; Hashimoto et al. 1982), which in sustainable management of large-scale water 31 programming model regarding the security of water resources to manage sustainability of regional water 48 system. 49 Although research on sustainability of water supply system has been well highlighted in the literature, 50 recently, the sustainability of the water supply system seems to be addressed as one of the major concerns 51 when it comes to multi-sectoral sustainability. To this end, this paper develops a dynamic optimal 52 framework to improve sustainability of water supply system considering various performance indicators 53 including resilience, reliability, and vulnerability. However, given that the process of water supply to the 54 sub-areas causing shrinkage of water resources in the basin area, thus, in order to have a long-term vision 55 of the water supply process and to verify that the system is sustainable, in practice, it is vital to propose an 56 optimal framework to improve the sustainability of system. In general, the sustainability measure evaluates 57 water management policies according to the system performance indices intending to investigate the 58 integrated behavior of the system, taking into account possible adverse consequences such as imbalance 59 between supply and demand (Loucks 1997; Sandoval-Solis et al. 2011). However, according to the above 60 descriptions, the main contributions of this study are listed below: 61 1) A dynamic optimization framework has been proposed to cope with drought in the long-term water 62 supply process and to evaluate the system sustainability measure in different sectors. 2) Due to the uncertainty in the supply process, different scenarios of water demand and water supply 64 are applied as a management perspective for reviewing and analyzing periodic decisions. 65 The remainder of this paper is organized as follows. Section 2 develops the framework of this study and 67 case study. Section 3 expands dynamic optimization model. Section 4 proposes study area and data 68 collection. Section 5 includes results and analysis. Section 6 gives concluding remarks. 69 70 2. Framework of indices impacting on sustainability of system during water 71 supply process 72 In general, the sustainability of a water supply system is a reflection of an adaptive operational approach in 73 which the decision maker adjusts system performance based on the amount of available water resources in 74 a given period (Ajami et al. 2008). Indeed, the optimal performance of system in the long run, regarding 75 limited resources, reflects the improvement of system sustainability, so that a performing system is also 76 considered as a sustainable system (Fechete and Nedelcu 2019). Thus, the sustainability of the water supply 77 system is the integration of performance indicators (as shown in Fig.1) that are adaptive features of the 78 system for the use of available water resources and, in fact summarizes the alternative performance of the To this end, the definition provided for the sustainability measure of the water supply system is as follow 86 Where, j t S is defined as value of the sustainability, j t  is reliability index, j t  refers to resilience indicator, By definition, reliability of system is the probability that satisfactory state of system will remain unchanged 94 for a certain time. Thus, water supply system reliability is measured by whether the system meets a Where, j t  treats as a binary variable (0 and 1), so that if the requested demand is supplied in period t, then

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Resilience refers to the probability that a system will improve from a failure state to an UN failure state. 103 Therefore, the resilience of the water supply system for sector is referred to as the probability that the Where j t  is defined as the transition between failure and UN failure modes in the given period whose 108 value is 1 or 0: 109 if y failure and y UN failure It needs to mention that j t y is referred to a given time series of a parameter of interest. In addition, the definition of water shortage in period is as follows: 122 However, the rate of water shortage in sector depends on the gap between the amount of water demand 124 j t D and water supply j t x in period .

Dynamic optimization model 126
Based on the applied long-term evaluation framework, a dynamic model is proposed to optimize the 127 sustainability of the water supply system in a given period. 128

Constraints are listed as below: 130
The volume of water in the reservoir based on the volume of water availability related to the prior period 131 and the rate of runoff is defined as below: 132 Where, 1 t l  is the volume of available water in the reservoir in period − 1, t I is the rate of runoff during 134 the period , and l is referred to the maximum capacity of the reservoir.

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Besides, the amount of water allocated to different sectors must be less than the amount of water in the 136 reservoir: 137 In addition, the volume of water transferred to sub-areas must be less than the amount of available water in 139 the reservoirs: 140 However, the global dynamic model of this study to reduce the impacts of drought on the water supply 142 system and maximizing the level of sustainability in the optimal system is as follow: 143

Case study and data collection 145
The Sistan Basin (30°-31.5° N to 61°-66° E), also known as Hamoon watershed, is located in Sistan and 146 Baluchestan province of Iran near the border of Iran-Afghanistan. In recent years, due to the arid climatic 147 conditions of the region and the reduction of the average annual rainfall (60 mm, which occurs mainly in winter) on the one hand, and operating of successive dams on the Helmand River as the main source of 149 water supply in this basin, on the other hand, the drought situation has become extremely acute (He at al. water supply different sectors, so this study considered the Sistan basin as a the study area (Fig.2).

Adopted optimal water supply to sub-sectors
172 Table 3 are listed the optimal outputs related to water allocation between sectors of the two sub-areas. 173 According to the output, the amount of water allocated to the agricultural sector in Zabol is more than other 174 sectors since the demand for water in this sector has been higher. For the city of Zahedan, the largest volume 175 of water has been allocated to the industrial sector, so that between 2015 and 2017, the volume of water 176 allocated to this sector was higher than 40.00 * 10 6 3 . Also, the volume of water allocated to the domestic 177 sector of Zahedan in the whole period is almost four times that of Zabol city, so that the most water allocated 178 to this sector is related to the year 2015 with a value equal to 30.19 * 10 6 3 . 179 By analysis of system sustainability (as shown in Table 4), the domestic sector has acquired the highest 180 value for both sub-areas (0.491, 0.389) since the status of this sector in all three factors of reliability, 181 resilience (resilience factor has not changed because the status of the system did not alter from failure to 182 UN failure), and vulnerability is better than other two sectors.

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In addition, Figure 3 shows an analysis maintaining the deviation between the total volume of water 192 supplied to each sub-areas and total water demand. Based on the final output, the maximum gap between 193 water demand and water supply for Zahedan city was experienced in 2008 and 2010 with water supply rate 194 of 70.30 * 10 6 3 and 81.48 * 10 6 3 and water demand equal to 76.95 * 10 6 3 and 88.32 * 10 6 3 , 195 respectively, while this rate for Zabol city is related to 2009 and 2013 with a value equal to 63.25 * 10 6 3 196 and 72.66 * 10 6 3 for the supply side and 69.98 * 10 6 3 and 78.10 * 10 6 3 for the demand side. 197 Although the optimal process of water supply has reduced the deviation between water demand and water 198 supply, due to increasing demand for water regarding population growth and also reducing runoff rates in 199 the Sistan basin, the unsustainability of the water supply system is still prominent. to analyze the sustainability of water supply system. Indeed, according to historical runoff data, 207 the two new scenarios, streamflow rate 90% and 70% of current runoff rate, are considered to 208 provide an optimal solution and to assess sustainability measure.

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By comparing the outputs listed in Table 5 with Table 3, the deviation between water demand and water 213 supply for the domestic sector under the following scenarios is slightly different, while this value for the 214 other two sectors, as the largest water recipient sectors, has further deviated. 215 In addition, according to the analysis of sustainability measure indicated in Figure 5, in the first scenario Sistan basin will experience rainfall reduction and temperature rising, which means that the situation of 229 water resources will be more limited. On the other hand, the increase in demand for water due to population 230 growth causes the expansion to deviate between the demand for water and water supply. However, 231 adaptation measures for water supply focus on proposing water distribution policies and strategies between 232

S U S T A I N A B I L I T Y V A L U E
practical managerial insights compatible with the current situation, such as the development of leverage 234 policies such as tariffs for water, the use of advanced technologies to reduce demand for water, such as the 235 development of drip irrigation systems, treatment and reuse of wastewater, can be alternatively effective 236 for conserving water resources. Thus, this study applies the demand shrinkage scenarios ( at 10% and 20% 237 less than the actual demand) proposed by He et al. (2021) to evaluate the sustainability of the water supply 238 system. 239 According to the output listed in Table 6, the reliability and resilience of all three agricultural, industrial, 240 and domestic sectors show an improvement compared to Table 4, but the value of the vulnerability factor 241 for all three sectors has not changed much. In general, with the improvement of these factors, the 242 sustainability of the system has become more optimal than before. 243 244

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In general, due to climate change, the water crisis problem is becoming more acute, which can be minimized 249 with proper planning. While the multi-sectoral users in sub-areas request different volumes of water by 250 different priorities, the development of new adaptive measures to prioritize water supply between key 251 sectors can increase system sustainability. Besides, in areas such as Sistan, which is highly dependent on 252 the volume of runoff, proposing managerial insights is very effective in reserving available waters. In this 253 regard, the rate of water consumption depends on the rate of population (Of Sciences 1999), so that 254 increasing population and the need for food, would increase consumption of fresh water. Therefore, 255 strategic simulation of population distribution patterns in order to analyze water demand, development of 256 more efficient irrigation systems, and alteration of crop patterns, etc. can help to better manage the limited 257 water resources. However, according to the above description, the superiority of the proposed model is as 258 follows: 259 1) The proposed framework in this study is a practical mechanism to optimize the water supply system 260 environment, which provides a long-term perspective to the basin authorities and facilitates the 262 planning of limited water resources in order to maximize the sustainability of system. 263 2) To minimize the impacts of runoff uncertainty on the optimal water supply process, the 264 development of appropriate adaptive measures to maintain the deviation between water supply and 265 water demand is effective. To this end, a sole focus on water resources management does not lead 266 to adaptation, and the development of new policies such as demand shrinkage scenarios can lead 267 to increased long-term system sustainability. 268

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Since the sustainability of the water supply system depends on the status of regional water resources, this 270 study proposed an optimal framework for the sustainability of water supply system between three sectors 271 in an uncertain environment. In fact, an assessment index was applied for the sustainable development of 272 the system, to analyze shortage in the regional water supply system based on the performance indicators. 273 Also, a case study from Iran was proposed to examine the developed model. However, this study lists the 274 following recommendations based on the outputs: 1) Based on the degree of drought, decision makers can 275 first distinguish the more sensitive sectors according to the objective function and then allocate water to 276 each of these sectors according to their priority for system sustainability. 2) Sustainable water conservation 277 and mitigation of drought impacts require the development of innovations that are compatible with the 278 severity of the water crisis in the sectors that receive the most water. 3) Given that the uncertainty of climate 279 change has not been proposed in this study, projecting the climate change patterns to examine the scale and 280 amount of runoff and then planning for optimal water allocation in the basin area can lead to the 281 development of strategic management of system sustainability. 4) Finally, the expansion of long-term 282 policies with a focus on increasing system reliability and resilience versus reducing system vulnerability 283