Evaluation of the VIKOR and FOWA Multi-Criteria Decision Making Methods for Climate-Change Adaptation of Agricultural Water Supply

Abstract

Confronting climate change is a daunting challenge that requires policies for climate adaptation in the field of water resources management. This paper proposes a method for reservoir operation associated with climate-change projections aimed at ensuring the sustainability of agricultural water supply. The method is applied to the Aidoghmoush reservoir in East Azerbaijan province (Iran) employing climate-change projections for 2040–2069, and compares the future-period results with those calculated for the baseline period (1971–2000). The water-supply system depending on the Aidoghmoush reservoir is simulated using the climate-change projections. The water-supply system simulations are ranked with two multi-criteria decision-making (MCDM) methods according to their suitability for satisfying agricultural water demands and sustain cropping patterns. These are the multi-criteria optimization and compromise resolution (VIKOR) and the Fuzzy Order Weighted Average (FOWA) MCDM methods. The MCDM methods identify the best water-supply management alternatives for climate-change adaptation.

Appendix

Seven indexes, each corresponding to a decision criterion, are employed in this study. Their equations and intervening variables are presented in this section.

1.1 Time Reliability Criteria

This index measures the capacity of a reservoir system to satisfy downstream water demands (Hashimoto et al. 1982):

$$ \alpha =\frac{N}{T} $$

(13)

$$ N=\sum \limits_{t=1}^T count\left({R}_t\ge {D}_t\right) $$

(14)

where: α = time reliability index; N = the number of periods (months) in which the reservoir release is equal or greater than the downstream water demand (the number of satisfactory states); count = a counting function (it counts periods when releases are equal to or larger than water demand during the operational period); D_t = the volume of downstream water demand in period t; R_t = the reservoir release in period t; T = the number of operational periods (number of months).

1.2 Vulnerability Index

This index measures the average volumetric severity of failure to meet downstream water demands by reservoir system releases (Hashimoto et al. 1982):

$$ \nu =\frac{\sum_{t=1}^{N_D}\mid {R}_t-{D}_t\mid }{T\cdot {D}_{\mathrm{max}}} $$

(15)

in which ν = vulnerability index; D_max = the maximum water demand among all the monthly water demands in the operational period; N_D = the number of months in which the reservoir release is less than the downstream water demand, i.e., the summation on the right-hand side of Eq. (15) applies to reservoir releases and water demands in months such that R_t < D_t.

1.3 Resiliency Index

Measures how quickly a reservoir system recovers from a water-supply deficit (water-supply deficit is an unsatisfactory state whereby the monthly reservoir release is less than the downstream monthly water demand) to a situation whereby the monthly water release satisfies the monthly water demand (a satisfactory state) (this is a modified definition of resiliency of that by Hashimoto et al. 1982):

$$ \beta =\frac{N^{\prime }}{N_D} $$

(16)

where β = resiliency index; N^′ = the number of months in which a satisfactory state occurs immediately after an unsatisfactory state; N_D = the number of months in which the reservoir release is less than the downstream water demand (this is the number of unsatisfactory states).

1.4 Sustainability Index

The sustainability index combines the reliability, vulnerability, and resiliency indexes and is defined by the following equation (Loucks 1997):

$$ \gamma =\alpha \beta \left(1-\nu \right) $$

(17)

in which γ = sustainability index.

1.5 Supply to Demand Index

This index is a ratio of the actual water supply to the total water demand and is expressed as follows (ASCE 1998):

$$ S=\frac{\sum_{t=1}^TS{u}_t}{\lambda } $$

(18)

$$ S{u}_t=\Big\{{\displaystyle \begin{array}{l}{D}_t\kern0.5em if\begin{array}{c}\end{array}{R}_t>{D}_t\\ {}{R}_t-{D}_t if\begin{array}{c}\end{array}{R}_t<{D}_t\end{array}} $$

(19)

$$ \lambda =\sum \limits_{t=1}^T{D}_t $$

(20)

where S = supply to demand index; Su_t = equals the water demand if the reservoir release exceeds the water demand in period t, otherwise it equals the reservoir release minus the water demand in period t; λ = the total volume of downstream water demand.

1.6 Volumetric Reliability

This index measures the volume of water supplied divided by the total water demand (McMahon et al. 2006):

$$ {R}_V=1-\frac{\sum_{t=1}^T\left({D}_t-{R}_t\right)}{\sum_{t=1}^T{D}_t}\kern0.5em 0\le {R}_v\le 1 $$

(21)

where R_V = volume reliability index.

1.7 Availability Index

This index estimates the probability of a reservoir system supplying the downstream water demand (Jiménez-Cisneros 1996):

$$ \xi = prob\left[{R}_t\ge {D}_t|{D}_t>0\right]\cong \frac{N}{N_0} $$

(22)

in which ξ = availability index; prob = probability of release is more than demand, provided that demand is greater than zero; N = the number of periods in which the reservoir release equals or exceeds the water demand, given that the water demand is nonzero; N₀ = the number of months in which the water demand is nonzero.