### Case study

The Zayandeh-Rud basin (Fig. 1), a arid region of Iran, was selected to evaluate the SPIs. The Zayandeh-Rud basin is located in the central part of Iran. It has an area of 26,972 km^{2} area, where there are multiple water stakeholders such as agriculture, industry, urban and the environment sectors, with agriculture being the main user of the basin. Water resources in the basin are divided into surface water and groundwater. Approximately 100,000 ha among 113,000 ha of the agricultural area is irrigated by Zayandeh-Rud dam, and 3100 mm^{3} of water resources are used in the agricultural sector. The main surface water source in the basin, Zayandeh-Rud River originates in the Zagros Mountains and is about 350 km long in a west to east direction passing by the city of Isfahan. The Zayandeh-Rud River is an important water source for the agricultural, industrial, health, and urban sectors in Central Iran and the Chaharmahal-Bakhtiari and Isfahan provinces.

### Multi-criteria decision making

Multi-criteria decision making includes two categories of multi-objective decision making and multi-criteria decision making, which are implemented to select the best decision among several alternatives or to evaluate decisions. This work applies decision making as a multi-criteria decision to achieve a goal. Each decision includes objectives, alternatives, and criteria. A problem’s goal is first defined. Alternatives are different options for wastewater management in this instance that are assigned weights based on their contribution to achieving the goal. Criteria are also factors that are measured by the purpose of the alternatives^{23}. The AHP method helps achieve a defined goal after completing the steps outlined below.

### The AHP method

The Analytical Hierarchy Process (AHP), developed by Saaty^{24}, is a multi-criteria decision-making method for solving complex problems. It combines objective and quantitative evaluation in an integrated manner based on multi-level comparisons, and helps organize the essential aspects of a problem into a hierarchical format. It regularly organizes tangible and intangible factors and offers a structured and a relatively simple solution to decision problems. The AHP method ranks alternatives propose to tackle a decision-making problem. The ranking is based through a sequence of pairwise comparisons of evaluation criteria and sub-criteria.

#### The AHP structure

In a hierarchical structure the communication flow is top-down. First, indicators and evaluation criteria are defined from experts who are asked for their expert opinions. The criteria serve the purpose of determining the relative worth of alternatives entertained to solve a multi-criteria decision-making problem. Thereafter, the problem is divided into criteria and sub-criteria for the evaluation of alternatives. Figure 2 depicts a generic AHP structure depicting a goal to be met with (n) = 4 evaluation criteria, and (m=3) alternatives to cope with a problem (in our case SIPs).

#### The pairwise comparison matrix

The pairwise comparison matrix ((A)), called the Saaty Hierarchy Matrix, measures the importance of each criterion (or sub-criterion) relative to other criteria based on a numeric scale ranging from 1 to 9. Criteria that are extremely preferred, very strongly preferred, strongly preferred, moderately preferred, and equally preferred are assigned the values 9, 7, 5, 3, and 1, respectively, in the scale of preference; intermediate values are assigned to adjacent scales of preference. Thus, the values 8, 6, 4, and 2 are assigned respectively to the adjacent scales (9,7), (7,5), (5,3), and (3,1)^{24}. These numerical assignment of values is made based on the opinion of experts^{25}. The pairwise comparison matrix ((A)), therefore, represents a set of relative weights assigned to the criteria^{23}. The general form of a pairwise comparison matrix when there are (n) evaluation criteria is written in Eq. (1):

$$A=left[{a}_{ij}right]=left[begin{array}{cccc}{1=w}_{1}/{w}_{1}& {w}_{1}/{w}_{2}& dots & {w}_{1}/{w}_{n} {w}_{2}/{w}_{1}& 1={w}_{2}/{w}_{2}& dots & {w}_{2}/{w}_{n} .& .& dots & . .& .& dots & . .& .& dots & . {w}_{n}/{w}_{1}& {w}_{n}/{w}_{2}& …& 1={w}_{n}/{w}_{n}end{array}right]$$

(1)

where ({w}_{i}/{w}_{j}) denotes the weight assigned to the (i)-th criterion relative to the (j)-th criterion^{24}. Clearly, ({a}_{ji}=1/{a}_{ij}), with ({a}_{ji}={a}_{ij}=1) when (i=j).

#### The ratio matrix

The ratio matrix ((R)) has elements ({r}_{ij}) is calculated by Eq. (2):

$$R=left[{r}_{ij}right]=left[begin{array}{cccc}1& {a}_{12}& dots & {a}_{1n} 1/{a}_{12}& 1& dots & {a}_{2n} .& .& .& . .& .& .& . .& .& .& . 1/{a}_{1n}& 1/{a}_{2n}& dots & 1end{array}right]$$

(2)

clearly, ({r}_{ij}={a}_{ij}) when (jge i), and ({r}_{ij}=1/{a}_{ji}) when (j<i). The 4 × 4 ratio matrix obtained for the criteria of relevance, measurability, data availability, and comparability is given by Eq. (3):

$$R=left[begin{array}{cccc}1& 2& 2& 2 1/2& 1& 1& 3 1/2& 1& 1& 2 1/2& 1/3& 1/2& 1end{array}right]$$

(3)

The ratio matrix is instrumental in calculating the criteria weights.

#### Determining the criteria weights

The weights assigned to the criteria must be determined. For this purpose the ratio matrix is multiplied by the vector of weights (({varvec{w}})) as shown in Eq. (4):

$$R {varvec{w}}= {lambda }_{i} w or left[begin{array}{cccc}1& {a}_{12}& dots & {a}_{1n} 1/{a}_{12}& 1& dots & {a}_{2n} .& .& .& . .& .& .& . .& .& .& . 1/{a}_{1n}& 1/{a}_{2n}& dots & 1end{array}right]left[begin{array}{c}{w}_{1} {w}_{2} . . . {w}_{n}end{array}right]={lambda }_{i}left[begin{array}{c}{w}_{1} {w}_{2} . . . {w}_{n}end{array}right]$$

(4)

where ({lambda }_{i}) is denotes a component of the vector of eigenvalues (lambda). The system of Eqs. (4) represents the classic eigenvalue problem that is solved for (lambda) from the equation (left|R-lambda Iright|)= 0 were (I) represents the (n bullet n) identify matrix and | | denotes the determinant of a matrix. For each element ({lambda }_{i}) of (lambda) there is a corresponding vector ({{varvec{w}}}_{{varvec{i}}}), (i=1, 2, dots ., n.) The largest eigenvector is denoted by ({lambda }_{max}) and its corresponding vector ({varvec{w}}) contains the weights assigned to the criteria. The weights so developed are normalized to add to one as discussed in the Results and Discussion section. Weighting vectors were also calculated for 17 sustainability performance indicators (SPIs) with respect to the evaluation criteria. The procedure to calculate the weights for each SPI is the same as described in this section. See the calculated weights in the Results and Discussion section.

#### The consistency ratio

The consistency ratio ((CR)) is calculated to determine the acceptability of the weights determined according to the previous section. First calculate the consistency index ((CI)) as Eq. (5):

$$CI= frac{{lambda }_{max}-n}{n-1}$$

(5)

According to Eq. (6), the consistency rate ((CR)) is also obtained by dividing the consistency index by the random index ((RI)):

$$CR= frac{CI}{RI}$$

(6)

The consistency rate is an indicator that shows possible inconsistencies in the pairwise comparison matrix. It takes the value 0 (complete consistency) when ({lambda }_{max}=n). The random index takes the values 0, 0, 0.58, 0.9, 1.12, 1.24, 1.32, 1.41, 1.45, 1.49 corresponding to the number of criteria *n* = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, respectively^{24}. The acceptable *CR* level should not exceed 10%, but some studies have suggested that the acceptable *CR* levels may be up to 20%^{27,28}.

### Selection of the sustainability performance indicators (SPIs)

One of the most important elements of agricultural systems is water resources^{29}. Various indicators of the sustainability of agricultural systems were considered. As mentioned earlier, the United Nations (UN) has classified sustainability indicators into three categories: economic, social, and environmental. Sustainable development has been widely used since the 1980s to address the negative consequences of development and policies on the environment and society^{30}. Also, the UN has defined 17 Sustainable Development Goals (SDGs) in 2015 to achieve 2030 sustainable development program, which address global challenges such as poverty, environmental degradation, justice, and more. In this research, sustainable indicators involve the water, energy, and food sectors to embed sustainable development concept in the water-energy-food nexus.

Seventeen SPI were selected; 10, 3, and 4 corresponding to the water, energy, and food, sectors, respectively. The selected SPIs are listed in Table 1. Sustainability performance indicators were identified considering multiple attributes of sustainability (sustainable water resources, sustainable agriculture, sustainable development, environment, yield sustainability, food sustainability, and energy sustainability). In fact, the sustainability performance indicators of the Table 1 are connected to the UN SDGs. According to the UN Sustainable Development Goals (https://sdgs.un.org/goals), the SDGs include access to safe water and sanitation for all, food supply and eradication of poverty, job creation and income for young people, social welfare, the provision of affordable and clean energy, and more. The indicators in Table 1 are also a set of assessment criteria for assessing water, food, income, and energy supply, as well as assessing the environment by examining water stress, reliable water supply, available water, groundwater level sustainability, and greenhouse gas emissions. Calculating each of the sustainable indicators is described at the following, and all these indicators are used in different parts of an agricultural system.

#### Water stress

The water stress index ({HWSI}_{i,t}) is given by Eq. (7), which quantitatively evaluates the stress on water resources:

$${HWSI}_{i,t}= frac{{Supply}_{i,t}}{{Population}_{i,t}}$$

(7)

where, (i): consumer number, (t): time of consumption, Supply: the amount of meeting the needs of the consumer (i) at time (t) (MCM), population: consumer (i) population at time (t).

#### River flow index in the dry season

This index was developed by the World Resources Institute^{31} to describe water conditions in a river basin. This index calculates the timing of changes in water access in different seasons, such as the dry and wet seasons. Basins in a dry season have less than 2% of the surface runoff in four months of the driest months of the year (the sum of the lowest runoff during four consecutive months). This index is expressed by Eq. (8):

$$River,flow, index ,in ,the ,dry ,season = frac{Runoff ,volume, in, the, dry ,season }{Population}$$

(8)

#### Reliable water supply

Reliable access to safe drinking water is essential for social and economic sustainable development. The water supply reliability is defined as the ratio of the amount actually supplied to what is provided in the absence of failure (the demand)^{32}, and is calculated with Eq. (9):

$$Rel=frac{number ,of ,satisfactory, conditions}{total, number ,of ,conditions}$$

(9)

#### Groundwater level sustainability

The groundwater level sustainability index (SI), a function of performance indices^{33}, is calculated with Eq. (10):

$$SI , = Rel, times , Res , times , left( {1 – Vul} right)$$

(10)

where (Rel), (Res), and (Vul) denote reliability. resiliency, and vulnerability, respectively, of groundwater supply^{33,34}.

#### Irrigation performance index

The irrigation performance index (SGVP) or “Standardized Gross Value of Production” (SGVP) is calculated with Eq. (11):

$$SGVP= left(sum Crops {A}_{i}{Y}_{i}frac{{P}_{i}}{{P}_{b}}right){P}_{world}$$

(11)

where, A_{i} = Area under plant cultivation (i), Y_{i} = Crop yield (i), P_{i} = Local crop (i) price, P_{b} = Local price of the base crop (dominant crop of a region that has an international market), P_{world} = International price of the crop base. The SGVP allows the performance of irrigation schemes to be compared regardless of the location and type of crop planted.

#### Water consumption per kg of product

Water is an essential environmental factor that contributes to sustainable economic growth. Water, being limited resource, is a key input that must be included in the sustainability assessment of water use in agriculture. An effective factor in water efficiency can play a significant role in estimating the level of sustainability. Therefore, the level of water use was estimated through irrigation. The water footprint indicator shows the amount of water consumed per unit of product obtained. The lower the value of this index, the more sustainable production is^{35}.

#### Available water index

Temporal changes in available water were calculated by Meigh et al.^{36}. This index includes surface water and groundwater resources, and their differences in terms of demand for all urban, industrial and agricultural sectors. This index is calculated with Eq. (12) and its value ranges between 1 and − 1.

$$Available ,water, index = frac{(S + G-D) }{(S+ G+D)}$$

(12)

where (S)= surface water volume, (G) = groundwater volume, and (D) = the sum of the water demands of all sectors. An index equal to zero means supply and demand are equal.

#### Water efficiency index (kg m^{−3})

This index is obtained with Eq. (13):

$$WPC=frac{1}{VWC}=frac{CY}{CWR}=frac{CY }{{mathrm{Ir}}_{mathrm{c}}+{mathrm{p}}_{mathrm{ec}}}$$

(13)

where (Irc) , p_{ec}, and (CY) denote respectively the water requirement for plant irrigation, the amount of water that comes from rainfall during the growing season, the crop yield.

#### Water economic efficiency index

Economic efficiency refers to the concept of the value of the product material per cubic meter of water applied; it is calculated b Eq. (14):

$$BPD=frac{{I}_{N}}{CWR}$$

(14)

where (BPD), (CWR), and (IN) denote respectively the economic productivity of water (Rials per cubic meter), the gross income obtained from the sale of a crop grown in a season (in Rials), and the amount of water applied to grow the crop.

#### Water resources vulnerability index

Gleick^{37} developed this index for basins in the United States as part of an assessment of the effects of climate change on water resources and systems. This index describes the vulnerability of water resources systems based on five criteria and thresholds, each of which is briefly described below. A number of vulnerable regions are identified in each area. This approach emphasizes parts of the basin that are at risk.

This index is obtained by dividing the excess runoff in 5% of a period of study by the excess runoff in 95% in the period of study. Low levels of this ratio indicate low runoff changes and therefore a low risk of floods or droughts. A value greater than 3 indicates the basin is vulnerable to floods and drought.

#### Energy performance index (EPI)

EPI is the energy used per unit area per year or per per capita per year, and is measured in kWh/m^{2}/year or kWh/person/year.

#### Energy sustainability index (ESI)

Brown and Sovacool^{8} developed an energy sustainability index based on 12 indicators including four dimensions of oil security, electricity reliability, energy efficiency, and environmental quality. This index is an attempt to measure the sustainability in environmental and energy systems.

#### GHG emissions from energy use

Greenhouse gas emissions per farm (tonnage equivalent to carbon dioxide, for example, tCO2) are a major target, and using the Level 1 and Level 2 procedures of the Intergovernmental Panel on Climate Change—IPCC, it is estimated that the index desirable value must be low, in which a farm produces efficiently insofar as greenhouse gases emissions is concerned. The emission index provides useful information on applied production methods and, more broadly, on agricultural systems. In addition, it supports long-term greenhouse gas emissions assessments, and it contributes to the Common Agricultural Policy (CAP) to reduce climate change.

#### Food security index

The FSI was introduced by IFAD^{38}. In general, this index is used to estimate food security at the national level. The FSI is calculated by Eq. (15):

$$FSI=0.77 times left[left{frac{{x}_{1}}{1+ {x}_{6}}right}{left(1+ {x}_{2}right)}^{n}right]+0.23 times left[{x}_{4}left{frac{{x}_{s}}{left(1+ {x}_{s}right)}right}right]$$

(15)

where, ({x}_{1}), ({x}_{2})*,* ({x}_{3}), ({x}_{4}), and ({x}_{5}), and ({x}_{65}) denote the per capita supply of calories per day relative to the required calories, the annual growth rate of calories per capita per day, the food production index, the self-sufficiency index, changes in production, and changes in food consumption, respectively.

#### Revenue index

The revenue index is calculated with Eq. (16):

$$Revenue ,Index= frac{Income ,from ,agricultural, consumer ,i, at, time ,t ,(currency)}{Expected, income, from ,agricultural, consumer, i ,at, time, t, (currency)}$$

(16)

Revenue index equal to or larger than 1 means income equals or exceeds expectations**.**

#### Price Index

The price index is calculated based on the Laspeyres formula, which means that the prices of selected goods in the current period are compared with their prices in the base period (i.e., average annual price in the base year)^{39}.

#### Farm Net Value Added (FNVA)

The farm’s net value added index is the reward for the use of fixed factors of production (labor, land, and capital). A profitable farm has a large value of this index^{40}.

### Criteria for ranking the SPIs

The criteria of relevance (importance), measurability, data availability, and comparability were applied to ranking the SPIs^{41,42,43}. A description of the criteria is found in Table 2.

Source: Ecology - nature.com