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.
