An approach to measuring resilience to manage water supply systems

Water supply systems are exposed to events that affect the normal service provision. Water companies should follow their own policy rules to manage and overcome these types of threats. In this article, resilience is identified as the capacities of the system to delimit the impacts of hazardous event, which may be characterized by its severity and duration. The effects of disruptive events to the water service delivery are classified into water scarcity, discontinuity of water supply, discontinuity of hydraulic conditions and discontinuity of drinking water quality. The loss of service level is established by failure thresholds named as a standard level, a normative level, an accepted level and a critical level. These thresholds allow formulating management actions at different stages to reach the standard level of service that identifies when the systems returns to normal conditions. The global model defined by the loss of service and time is used to measure resilience by means of a resilience factor. It depends on each type of defined threat and considers the mentioned failure thresholds. The methodology is applied to a complex real-life system, managed by Canal de Isabel II Gestion (Spain) for different study cases: a drought, pipe breaks and events that affect the water quality conditions. Real data allow contrasting the protocols of management established by the water company. The methodology helps water utilities update their protocols for a certain hazard and provide useful information to plan their investments in order to improve the system resilience.


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The concept of resilience is being used in a great range of discipline areas, such as sociology, presented for water supply systems as the response capacity of a system in the face of a disruptive 43 event.
44 Some index has been presented in order to establish a measure of Resilience. The Argonne 45 National Laboratory Resilience Index uses a great number of variables to measure the resilience of 46 drinking water system [5]. This index considers preparedness, mitigation measures, response 47 capabilities and recovery mechanisms. Todoni [6] explains that, in water supply systems, failures or 48 modified and increased demand conditions increase the internal energy dissipation, and if a surplus 49 of energy is not available, there is a failure in the delivery. The author defines resilience as the 50 capability of the designed system to react and overcome stress conditions, as well as describes that 51 an increase in resilience mean a decrease of the internal energy dissipation. The resilience index of 52 Todoni compares the amount of power dissipated in the network to satisfy the total demand and the 53 maximum power that would be dissipated internally to satisfy constrains of demand and head. This  67 Francis and Bekera [14] propose a metric to quantify resilience that incorporates resilience capacities 68 (absorptive and adaptive capacity and recoverability). The Department of Homeland Security:

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Science and Technology Directorate [15] presents a resilience model ("bathtub" shape) to describe 70 the behaviour of the system after being impacted. The total area within the resilience profile is used 71 to compare the resilience levels, measured in performance-time units. They also include four profile 72 types to classify the systems from high to low resilient. It should be noted that the calculation of an 73 area in a resilience model allow comparing different systems and reaching to the conclusion that a 74 system is resilient. Diverse interpretations of resilience lead to the need of a standard and 75 measurable definition. In addition, system managers want to establish performance standards and 76 resilience standards of the system.

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In the article, a resilience model for water supply systems is proposed and a metric named as specific consequences. In this article, resilience is presented as the capacities of the system to guarantee that the consequences of a hazardous event are limited. In general, end users are satisfied 96 if the water is continuously supplied, under satisfactory pressure conditions, with good quality and 97 enough quantity. As a result, the following types of consequences due to disruptive events are 98 considered, as they affect water service provision in water supply systems: A) water scarcity, (B) or in conjunction. In the type of threat A, a drought should be analysed as an episode. In the type of 102 threat B, pipe breaks may be studied as a simple disruptive event or a set of them (sum of pipe 103 breaks over a year). In this article, each threat is independently considered. In addition, episodes Protocols, resources and technologies used in water supply systems help to define and satisfy 106 different levels of service, both under normal conditions and after a hazardous event. Protocols 107 mean the detailed sequence of actions or processes followed by the company to cope with the 108 normal operation of the system. Protocols influence the response capability of the system. Water  procedure to calculate the resilience factor for a type of threat (for example, type A), based on Figure   127 1, is the following: factor. F is the service function; s F , the standard level; n F , the normative level and a F , the 135 accepted level of service. The subscript A is referred to the type of threat A. This formulation is 136 applicable to other cases. It is possible that a threat remains in the first level of severity. In this case, 137 the normative resilience is the unique resilience factor that has to be calculated. It should be noted in   should be considered in order to aggregate the resilience factors. More research is needed in order to 159 define quantitatively these specific weights. If four types of threats (A to D) occurred at the same 160 time in the system, the resilience factor of the system would be: The global resilience factor, f R , should integrate similar levels of severity in order to 163 represent the society´s perception of failures. Thus, different weights should be used for each type of 164 threat. Water utilities may use the resilience factor in order to know how they are prepared for 165 certain hazardous events. When a water company contrast its system resilience (established by its

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The other case studies are pipe breaks and water quality failures. In the case of pipe breaks, the ( ) The normative resilience factor is represented in Figure 2

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The water supply over the disruption period has been compared to the water supply under 220 normal conditions in order to contrast the management protocols of contingencies. In that way, it is 221 possible to know if the water supply reached the established terms. Figure 2 shows the water supply

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It may be observed that the voluntary reduction of water is higher than the one expected by the 243 protocols, which is represented with the resilience factor. Thus, it may be conclude that protocols in 244 case of contingencies are effective. In Figure 3, it is also represented the date of July 2005, because the 245 water company launched a campaign called "The challenge of water" addressed to end users to save were accustomed to use less water than they used to.

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If the water reserves overcome the second level of severity, the protocols of the company 250 establish a water supply reduction of 26.0% over 24 months. In the same way, if the third level of 251 severity is reached, water supply should be decreased in 51.4% over 12 months. The time since the 252 drought is declared until the accepted and critical levels are reached has to be considered in order to 253 calculate resilience. In the study case, the drought was always in the first level of severity, so no 254 additional actions had to be taken.

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In the case of pipe breaks that cause water supply discontinuity or water quality failures that 256 produces water drinking discontinuity, the resilience factor is measured by means of the number of

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The system resilience factor should be calculated in future analysis with all types of threats that 269 generate disturbance in the system at the same time. It

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critical level. When these thresholds are exceeded, the system is in the level of severity 1, 2, 3 and 3, 292 respectively. A resilience model that allows calculating a resilience factor is proposed. It measures 293 the loss of service function from the standard level and also considers the disruption period.

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The methodology was applied to the complex real-life water supply system of the Autonomous

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Region of Madrid (Spain), managed by the water company Canal Isabel II Gestión. For the study 296 case of a drought of first level of severity, the failure thresholds are exposed. Results show that the 297 normative resilience factor is year • % 4 . 9 . The effectiveness of protocols is contrasted with real 298 data of water supply over the disruption period. It has been demonstrated that the voluntary water 299 supply was even greater than the required by the protocols. Therefore, protocols in case of first level 300 of severity were adequate that type of threat. It has been verified that the end users were accustomed 301 to use less water than they usually need, once the drought had finished. Furthermore, the resilience 302 factor for different pipe breaks and water quality failures are presented. More research is needed to 303 establish failure thresholds for these types of events and define the specific weights to aggregate the 304 resiliencies factors. The methodology allows measuring resilience of the systems, assessing 305 protocols, technologies and resources used in the company, as well as planning in order to improve 306 the system resilience.