There is neither a universal definition of resilience nor a widely accepted water sector-specific definition of resilience. Resilience holds positive connotations, and the definition varies from sector to sector, system to system, type of disruptive event, and analysis objective (see Table 1). Water systems are comprised of both natural and engineered systems; therefore, we adopted the resilience definition for water systems proposed by NIAC ^[1]: “ability to anticipate, absorb, adapt to, and/or rapidly recover from a potentially disruptive event.” This definition emphasizes reducing the likelihood of failure and the need for fast recovery from unexpected disturbances in the operating environment.

Resilience is often related to other terminologies such as vulnerability, risk, and sustainability. Vulnerability is the pre-event characteristic of the system that creates the potential for harm to the different abilities to recover following an event. Vulnerability evaluates who or what is at risk and the degree to which human life, physical, economic, and ecosystems can be harmed.

Sustainability is considered as meeting the quality of life for present and future generations with respect to social, economic, and environmental factors. The temporal scale of sustainability is seen on a longer scale than resilience. In contrast, resilience is focused on the response of a system to any perturbations. A system cannot be sustainable if it cannot resist and recover from any shock. Therefore, a system has to be resilient to be sustainable. Sustainability and resilience refer to preserving a desirable function and services, but one is different from the other.

Risk assessment generally identifies failure or damage scenarios, likelihoods, and potential consequences. Resilience analysis seeks to explore possible threats, analyze the system's state to absorb and resist, and identify interventions to recover quickly. The main differences between the two are that risk assessment aims towards a fail-safe policy, whereas resilience analysis acknowledges a safe-fail policy. The goal of a fail-safe policy strives to assure that nothing will go wrong, whereas a safe-fail policy acknowledges that failure is inevitable. Risk analysis complements resilience analysis since we cannot deter or prevent all threats and hazards.

 2. Resilience Measures to Assess and Incorporate Resilience in the Water Systems

There are no well-accepted resilience measures (see Table 2). Earlier resilience studies in water systems considered resilience one of the performance measures of risk or sustainability ^[2][3][4][5]. Most resilience studies in water systems ignore the multifaceted interactions between human, natural, and built systems.

We considered robustness and recovery rate as two measures of resilience. Similar measures are suggested in other studies ^[6][7][8]. When the system is loaded by an external stressor, the system will attempt to withstand changes. If the system is robust enough, it will bounce back to its normal state when the stress is released from the system. The bouncing back or recovery rate will be either as per the design expectation of the engineering system or by the process of adaptation in a natural system. The robustness, in this case, measures the intrinsic nature of the resilience before any perturbation takes place in a system. If the system is further loaded, it could bounce back usually or adapt at a certain limit. The rate of recovery will depend on the system’s robustness and indirectly indicates the redundancy and resourcefulness measures considered in the disaster resiliency community. Therefore, the recovery rate measures the after-disaster response of a component or system of consideration.

We developed a resilience analysis framework to evaluate and incorporate resilience in water resources and infrastructure systems. The framework includes seven steps (Figure 2). The evaluation process starts by setting the purpose and scope of the study by analyzing the three main questions, “resilience of what”, “resilience to what”, and “resilience for whom,” to formulate the objective and scope of the resilience analysis.

The main attributes of the framework are an acknowledgment of the complexity, uncertainty, and multi-sector involvement in water systems. The framework seeks consultation with experts and stakeholders at every step of the resilience analysis to address multidisciplinary issues. The system-of-systems approach enables analysis of the performances of sub-systems and assessment of their contributions to the overall performance. Several resilience strategies in water systems are recommended in the framework, such as no regrets strategies, soft strategies, adaptability and multifunctionality strategies, safety margin strategies, and safe failure strategies (Table 4). Uncertainty analysis is required in every step of resilience analysis.

Resilient water systems can be achieved by adding flexibility, diversity, redundancy, modularity, and adaptability. Any interventions to the system would incur additional costs, trade-offs, or externalities. Therefore, feasible options are selected after a multi-criteria decision-making analysis. It is noted that the framework can be applied on any scale, which could be from a smaller watershed to river basin level to a regional scale. The temporal and spatial selection will be defined for the first time in defining the purpose and scope of the analysis.

This study proposed a framework to analyze the resilience of water systems considering their complexity, uncertainty, and multi-dimensionality. The framework can be applied to analyze and incorporate resilience by utility operators, municipalities, and water resource planning agencies responsible for planning, managing, and building water and infrastructure systems. To operationalize the framework using real case studies is beyond the scope of this paper. Our ongoing work will demonstrate a few applications in the future. We recommend interested parties test and further improve the developed framework in different case studies. In addition to this specific recommendation, we outline the following challenges in resilience analysis and recommendations for future study.

Any disastrous event will damage infrastructure systems and have a cascading impact on public life and property. Analysis approaches vary with the boundary and scope of analysis. For example, a water resilience analysis for meeting the water demand and ensuring water resource security will be different from the analysis of the resilience of communities to water-induced disaster. In this context, it is difficult to define the “resilience of what?” and the “resilience of whom?” There is not a clear boundary to stop the resilience analysis. Future studies should define the realistic objectives and boundaries of water systems resilience.

Maintaining both the functions and structures of water systems is essential to achieving resilience. Water systems are complex, dynamic, and constantly evolving due to human interventions and climate change. Natural and human systems can adapt to dynamic changes to a certain extent. In dynamic systems, both the stressors and resistance are changing. Therefore, selecting thresholds or benchmarks for each component of a system or sub-system to evaluate the resiliency goals and deciding the measures and metrics of the resilience are challenging undertakings. In addition, it is not easy to define and select a standard measure that is applicable to different environmental and economic settings. We recommend future studies evaluate threshold values and metrics for resilience analysis.

Water resources and infrastructure systems have multifaceted interactions between human, natural, and built systems. The systems are managed by multiple operators, regulators, and users. Natural and built sub-systems, such as dams, reservoirs, surface water, and groundwater, have interactions with the hydrological cycle. Climate changes can shift and alter future hydrologic events and water demand. There are challenges in measuring the scale of the system solely from the examination of parts.

Similarly, multiple sources of uncertainties in water systems exist due to imperfect knowledge of physical processes, non-linear systems, non-linear interactions between different sub-systems, and poor knowledge of system models. Feedback and nonlinearities of any complex system are generally perceived as the source of surprises. Surprises that have low frequency and high consequences are the source of unexpected functionality that unlocks a shift into a new regime. There are ongoing studies to resolve these challenges; however, the quantitative evaluation of resilience may not be possible unless we have well-established methods to analyze complexity and uncertainty.