How to Quantify Sustainable Development: A Risk-Based Approach to Water Quality Management

Abstract

Since the term was coined in the Brundtland report in 1987, the issue of sustainable development has been challenged in terms of quantification. Different policy options may lend themselves more or less to the underlying principles of sustainability, but no analytical tools are available for a more in-depth assessment of the degree of sustainability. Overall, there are two major schools of thought employing the sustainability concept in managerial decisions: those of measuring and those of monitoring.

Measurement of relative sustainability is the key issue in bridging the gap between theory and practice of sustainability of water resources systems. The objective of this study is to develop a practical tool for quantifying and assessing the degree of relative sustainability of water quality systems based on risk-based indicators, including reliability, resilience, and vulnerability.

Current work on the Karoun River, the largest river in Iran, has included the development of an integrated model consisting of two main parts: a water quality simulation subroutine to evaluate Dissolved Oxygen Biological Oxygen Demand (DO-BOD) response, and an estimation of risk-based indicators subroutine via the First Order Reliability Method (FORM) and Monte Carlo Simulation (MCS). We also developed a simple waste load allocation model via Least Cost and Uniform Treatment approaches in order to consider the optimal point of pollutants control costs given a desired reliability value which addresses DO in two different targets.

The Risk-based approach developed herein, particularly via the FORM technique, appears to be an appropriately efficient tool for estimating the relative sustainability. Moreover, our results in the Karoun system indicate that significant changes in sustainability values are possible through dedicating money for treatment and strict pollution controls while simultaneously requiring a technical advance along change in current attitudes for environment protection.

Appendix

The following symbols are used in this paper:

• C: The major state of a system such as water quality in context of the environment component which based on it we can measure the reliability, resilience and vulnerability of the system

• C(t): The time series of the state C

• C(t+1): The state of C at time t+1

• W_Rel , W_Res , and W _vul,v : Different relative weights for reliability, resilience and v-th type of vulnerability indicators respectively

• RS: Relative Sustainability

• X = (X₁, X₂,...,X _n ): Indicates the vector of the random variables of the system

• G: The Performance function of the system

• R and L: The resistance and load functions of the system

• β: Reliability index

• α: Reliability of the system

• S: System survival or System success

• F: System failure

• ν: Vulnerability Indicator

• e _j : Probability of the load of the system, L, is in discrete failure state

• w _j : A numerical indicator of the severity of failure state j

• R _j : Hierarchy of failure levels

• D _L : The CDF of the load, L

• ϕ: The pdf of standard normal

• Φ: The standard normal CDF

• β _j : The reliability index for resistance level R _j

• γ: The system resilience

• p_f1 and p_f2:The probabilities of failure modes 1 and 2 respectively

• p_f12: Joint probability of failure modes 1 and 2

• ϕ(;ρ): The CDF for a bivariate normal vector with zero mean values, unit variance, and correlation coefficient ρ

• Ψ(;ρ): The corresponding PDF of ϕ(;ρ)

• $Z^{ * }_{1}$ and $Z^{ * }_{2}$: The design points in standard normal space of failure modes 1 and 2 respectively

• $F_{{X_{i} }} (x_{i} )$: CDF of the X _i

• R₀: Correlation matrix of the vector Z

• Z: Correlated standard statistical variables

• $\rho _{{Z_{i} Z_{j} }}$: Correlation coefficients of vector Z

• $\rho _{{X_{i} X_{j} }}$: Correlation coefficients of vector X

• $\Gamma _{0}$: Lower triangular matrix

• U: Uncorrelated variables based on converted vector Z

• $P(X_{{1p}} ,X_{{2p}} ,...,X_{{np}} )$: A specific point in performance function

• $X^{ * }_{i} = (X^{ * }_{1} ,X^{ * }_{2} ,...,X^{ * }_{n} )$: Design point

• E(Z): Mean or expected value of Z

• σ _Z : Standard deviation of Z

• WQ _a (X): The ambient water quality given a realization of X

• WQ _t : A pre-determined water quality target at a desired check point

• V: The difference between the DO target and the amount of ambient DO

• f: The water quality function

• x: Percentage of treatment level or removal percentage

• w: Emission loads or effluent

• Q: Input and output flows

• T: Water temperature

• K: Coefficients of aeration and deoxygenating

• D: Diffusion coefficient

• WQ _t : Water quality target