First‐order reliability method for estimating reliability, vulnerability, and resilience

Abstract

Abstract. Reliability, vulnerability, and resilience provide measures of the frequency, magnitude, and duration of the failure of water resources systems, respectively. Traditionally, these measures have been estimated using simulation. However, this can be computationally intensive, particularly when complex system-response models are used, when many estimates of the performance measures are required, and when persistence among the data needs to be taken into account. In this paper, an efficient method for estimating reliability, vulnerability, and resilience, which i s based on the First-Order Reliability Method (FORM), is developed and demonstrated for the case study of managing water quality in the Willamette River, Oregon. Reliability, vulnerability, and resilience are determined for different dissolved oxygen (DO) standards. DO is simulated using a QUAL2EU water quality response model that has recently been developed for the Oregon Department of Environmental Quality (ODEQ) as part of the Willamette River Basin Water Quality Study (WRBWQS). The results obtained indicate that FORM can be used to efficiently estimate reliability, vulnerability, and resilience. IntroductionThe risk-based performance measures reliability, vulnerability, and resilience were first introduced to the water resources community by Heshimoto et el. computational inefficiency. This becomes especially important if estimates of reliability, resilience, and vulnerability are used to optimize decisions, as many estimates of these criteria may be required, depending on the optimization algorithm used.In this paper, an approach using the First-Order Reliability Method (FORM) is developed as an alternative to simulation for obtaining probabilistic estimates of reliability, vulnerability, and resilience. The approach is illustrated for an example water quality case study based on the Willamette River, Oregon. The remainder of the paper is organized as follows. In section 2, details of FORM are given, and the relative advantages and disadvantages of the method are discussed. In section 3, the approach that uses FORM to estimate reliability, vulnerability, and resilience is outlined, and th e case study is introduced in section 4. The results of the case study are presented and discussed in section 5, and conclusions are given in section 6. Reliability Analysis IntroductionThe performance of any engineered system can be expressed in terms of its load (demand) and resistance (capacity). Use of the load resistance analogy for water resources problems has been discussed by a number of authors, including Duckstein end Bernier [1986] and Kundzewicz [1989]. For example, in the water supply case, water demand corresponds to system load and supply capacity to system resistance, whereas in the water quality case, pollution load and a given water quality standard correspond to the system's load and resistance, respectively.

Identification of resilience factors, variables and indicators for sustainable management of urban drainage systems

“…This factor evaluates the capacity to recover and is associated with the time of failure, reliability and recovery speed of a system from the perspective of risk management. Flexibility has been quantified through semi-quantitative indices that measure the capacity to provide a service [20], mathematical functions that quantify the probability of system failure [23][24][25][26][27]29,32], system reliability [30,31] and indicators based on performance curves of a system that provide information on its behaviour before and after a disturbance [17,18,28,33,34].…”

“…The indicators proposed for this variable are the failure index, which quantifies the probability of system failure [23][24][25][26][27]29]; the gradualness, which measures the change in the response of a system with respect to the change of magnitude in a flood surge [17,18]; the recovery duration, which quantifies the time it takes for a system to recover from an unsatisfactory condition [17]; the recovery rate, which measures the recovery rate of the system after a flood [18]; the recovery loss, which quantifies the loss of quality in a system [28]; the environmental load capacity, which quantifies the amount of pollutant emissions that a system can endure [32]; and the recovery indicator, which measures the recovery time from a flood at each node of the system [33,34].…”

Water Supply, Demand, and Quality Indicators for Assessing the Spatial Distribution of Water Resource Vulnerability in the Columbia River Basin

“…b Vulnerability Index: Overview In general, vulnerability is defined as a measure of the magnitude of a system's potential for failure (Maier, Lence, Tolson, & Foschi, 2001). In a more elaborate definition, vulnerability is the exposure of a system to shocks, stresses, and disturbances, or the degree to which a system is susceptible to adverse effects (Leurs, 2005;McCarthy, 2001;Turner et al, 2003), or the degree to which a system is likely to experience harm from perturbation or stress (De Sherbinin, Schiller, & Pulsipher, 2007).…”

“…In a more elaborate definition, vulnerability is the exposure of a system to shocks, stresses, and disturbances, or the degree to which a system is susceptible to adverse effects (Leurs, 2005;McCarthy, 2001;Turner et al, 2003), or the degree to which a system is likely to experience harm from perturbation or stress (De Sherbinin, Schiller, & Pulsipher, 2007). Vulnerability can be calculated using sophisticated approaches (e.g., Maier et al, 2001). In this study, however, to identify the current state of water vulnerability at the county scale of the CRB, we employed the indexbased approach of Sullivan (2011) that quantifies water vulnerability as an integration of several indicators representing the socio-economic and environmental status of the water resources system.…”

Non-Uniform Flow Effect on Optimal Waste Load Allocation in Rivers

“…Enhanced Stream Water Quality Model (QUAL2E) (Brown and Barnwell, 1987) is a comprehensive and versatile stream water quality model which has been used as the water-quality simulation model (simulation engine) in the recent water quality management models developed by Carmichael and Strzepek (2000), Gabriel et al (2000), Burn and Yulianti (2001), Dai and Labadie (2001), Maier et al (2001), and Mujumdar and Vemula (2004). It is a one-dimensional, advection-dispersionreaction model which is capable of simulating the transport of up to 15 water quality constituents such as DO, Biochemical Oxygen Demand (BOD), temperature, algae, and conservative constituents.…”