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Crops and their landrace study areasFood crops whose genetic resources are researched and conserved by CGIAR international agricultural research centres or by the CePaCT of the SPC were included in this study. Crop landrace distributions were modelled and conservation analyses conducted within recognized primary and, for some crops, secondary regions of diversity, where these crops were domesticated and/or have been cultivated for very long periods, and where they are, thus, expected to feature high genetic diversity and adaptation to local environmental and cultural factors (Supplementary Tables 1 and 2)9,13. These regions were identified through literature review (Supplementary Information) and confirmed by crop experts.Occurrence dataOur crop landrace group distribution modelling and conservation gap analysis rely on occurrence data, including coordinates of locations where landraces were previously collected for ex situ conservation and reference sightings. For ex situ conservation records, occurrences marked as landraces were retrieved from two major online databases: the Genesys Plant Genetic Resources portal33 and the World Information and Early Warning System on Plant Genetic Resources for Food and Agriculture (WIEWS) of the Food and Agriculture Organization of the United Nations34. Occurrences were also obtained directly from individual international genebank information systems: AfricaRice, the International Transit Centre and Musa Germplasm Information System of Bioversity International35, CePaCT, International Center for Tropical Agriculture (CIAT), International Maize and Wheat Improvement Center (CIMMYT), International Potato Center (CIP), International Center for Agricultural Research in the Dry Areas (ICARDA), International Crops Research Institute for the Semi-arid Tropics (ICRISAT), International Institute of Tropical Agriculture (IITA) and International Rice Research Institute (IRRI), as well as from the United States Department of Agriculture (USDA) Genetic Resources Information Network (GRIN)–Global36 and the Comisión Nacional para el Conocimiento y Uso de la Biodiversidad (CONABIO)37. Occurrences were compiled from the Global Biodiversity Information Facility (GBIF), with ‘living specimen’ records classified as ex situ conservation records and the remaining serving as reference sightings for use in distribution modelling. Reference occurrences were also drawn from published literature (Supplementary Information). Duplicated observations within or between data sources were eliminated, with a preference to utilize the most original data. Coordinates were corrected or removed when latitude and longitude were equal to zero or inverted, located in water bodies or in the wrong country or had poor resolution ( 10 (ref. 60). The predictors and whether they were selected for the modelling of each landrace group are presented in Supplementary Table 4.We generated a random sample of pseudo-absences as background points in areas that (1) were within the same ecological land units61 as the occurrence points, (2) were deemed potentially suitable according to a support vector machine classifier that uses all occurrences and predictor variables and (3) were farther than 5 km from any occurrence62. The number of pseudo-absences generated per crop group was ten times its number of unique occurrences.MaxEnt models were fitted through five-fold (K = 5) cross-validation with 80% training and 20% testing. For each fold, we calculated the area under the receiving operating characteristic curve (AUC), sensitivity, specificity and Cohen’s kappa as measures of model performance. To create a single prediction that represents the probability of occurrence for the landrace group, we computed the median across K models. Geographic areas in the form of pixels with probability values above the maximum sum of sensitivity and specificity were treated as the final area of predicted presence13.Ex situ conservation status and gapsThree separate but complementary metrics were developed to compare the geographic and environmental diversity in current ex situ conservation collections to the total geographic and environmental variation across the crop landrace group distribution model and, thus, to identify and quantify ex situ conservation gaps13.A connectivity gap score (SCON) was calculated for each 2.5-arc-minute pixel within the distribution model by drawing a triangle63,64 around each pixel using the three closest genebank accession occurrence locations as vertices and then deriving normalized values for the pixel based on distance to the triangle centroid and vertices13. The SCON of a pixel is high—closer to 1 on a scale of 0–1—when its corresponding triangle is large, when the pixel is close to the centroid of the triangle or when the distance to the vertices is large. A high SCON represents a greater probability of the pixel location being a gap in existing ex situ collections.An accessibility gap score (SACC) was calculated for each 2.5-arc-minute pixel in the distribution model by computing travel time from each pixel to its nearest genebank accession occurrence location based both on distance and the speed of travel, defined by a friction surface13,45. Travel time scores were normalized by dividing pixel values by the longest travel time within the distribution model, with the final score ranging from 0 to 1. A high SACC value for a pixel reflects long travel times from existing genebank collection occurrences and, thus, represents a higher probability of the pixel location being a gap in existing ex situ collections.An environmental gap score (SENV) was calculated for each 2.5-arc-minute pixel in the distribution model by conducting a hierarchical clustering analysis using Ward’s method with all the predictor variables from the distribution modelling. The Mahalanobis distance between each pixel and the environmentally closest genebank accession occurrence location was then computed13. Environmental distance scores were normalized between 0 and 1. A high SENV value for a pixel reflects a large distance to areas with similar environments where landraces have previously been collected for genebank conservation and, thus, represents a higher probability of the pixel location being a gap in existing ex situ collections.Spatial ex situ conservation gaps were determined from the conservation gap scores using a cross-validation procedure to derive a threshold for each score. We created synthetic gaps by removing existing genebank occurrences in five randomly chosen circular areas with a 100 km radius within the distribution model. We then tested whether these artificial gaps could be predicted by our gap analysis, identifying the threshold value of each score that would maximize the prediction of these synthetic gaps. Performance for each of the five gap areas was assessed using AUC, sensitivity and specificity. The average cross-area threshold value was calculated for each score to discern pixels with a high likelihood of finding ex situ conservation gaps and that, thus, were higher priority for further field sampling. These were pixels with combined gap scores above the threshold, assigned a value of 1, as opposed to the relatively well-conserved areas below the threshold, which were assigned a value of 0.The three binary conservation gap scores were then mapped in combination, resulting in pixels across the distribution model with gap values ranging from 0 to 3. Pixels with a value of 0 display no connectivity, accessibility or environmental gaps and are considered well represented ex situ. Pixels with a value of 1 indicate a conservation gap in connectivity, accessibility or the environment; we consider these ‘low-confidence’ gaps. Pixels with a value of 2 indicate gaps in two metrics or ‘medium-confidence’ gaps, and values of 3 indicate gaps across all metrics or ‘high-confidence’ gaps. High-confidence gap areas are displayed on crop-conservation-gap maps (Fig. 2b and Supplementary Information) and conservation hotspot maps across crops (Fig. 4 and Extended Data Figs. 5–8).The representation of crop landrace groups in current ex situ conservation collections was calculated based on the final 1–3 value conservation-gap maps. The complement of the proportion of the modelled distribution considered as a potential conservation gap by any single gap score represents the minimum estimate of current representation; the complement of the proportion considered by all three scores as a gap, which is to say high-confidence gap areas, represents the maximum estimate (Supplementary Tables 1 and 2).While distribution modelling and conservation gap analyses were conducted at the crop landrace group level and results are presented in full in the Supplementary Information, for ease of comparison of results across crops, and to avoid bias towards crops with many landrace groups, we also calculated summary results at the crop level. Crops that had been assessed with geographic differentiations, including maize in Africa and Latin America and yams in the New World and the Old World, were also combined. For spatial results, the pixels in crop landrace group models were summed—that is, constituent landrace group models were combined. The minimum and maximum current conservation representation estimations at the crop level were then calculated based on combined spatial models.GBIF occurrence downloadsThe following occurrence downloads from the Global Biodiversity Information Facility (GBIF; https://www.gbif.org/, 2017−2021) were used: 10.15468/dl.rrntfr, 10.15468/dl.2f2v4h, 10.15468/dl.2ywlb7, 10.15468/dl.lnfelh, 10.15468/dl.ryrmfj, 10.15468/dl.8adf61, 10.15468/dl.nff5ys, 10.15468/dl.erxs6e, 10.15468/dl.vbfgho, 10.15468/dl.mjjk3x, 10.15468/dl.uppz1n, 10.15468/dl.938bgm, 10.15468/dl.hr87hm, 10.15468/dl.k1va80, 10.15468/dl.coqpu2, 10.15468/dl.lkoo9u, 10.15468/dl.e998mp, 10.15468/dl.vfbmm7, 10.15468/dl.tnp478, 10.15468/dl.6zxsea, 10.15468/dl.0lray8, 10.15468/dl.5sjgsw, 10.15468/dl.wkju6h, 10.15468/dl.7xzfvc, 10.15468/dl.autlf5, 10.15468/dl.fe2amw, 10.15468/dl.2zblvz, 10.15468/dl.ddplkj, 10.15468/dl.jbzejg, 10.15468/dl.ej5bha, 10.15468/dl.905pxd, 10.15468/dl.pim1vs, 10.15468/dl.vdridc, 10.15468/dl.b43gyv, 10.15468/dl.nnw3z7, 10.15468/dl.bnt9jc, 10.15468/dl.f5x2cg, 10.15468/dl.ub7zbg, 10.15468/dl.sggf2v, 10.15468/dl.ath5ve, 10.15468/dl.23k3ug, 10.15468/dl.cym376, 10.15468/dl.53bwzk, 10.15468/dl.fsad7h and 10.15468/dl.fm6p7z.Reporting SummaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

This work formulates a general framework of the WFE Nexus at the national level, which includes all pertinent interactions between water, food, and energy sources and demands. Figure 1 depicts the feedbacks involving resource availability and consumption. The causal loops of the developed model for national-scale assessment are shown in Fig. 2. The model depicted in Fig. 2 proposes reducing consumption to reduce the water crisis to the extent possible. By reducing water use and pollution the environmental water requirement can be reduced, thus alleviating the water crisis. This paper’s objective is sustainable management by reducing per capita water use (in the residential section) and per capita energy use (in the domestic, public, and commercial section). The WFE nexus is modeled as a dynamic system for demand management applied to the stocks of energy, surface water, and groundwater resources to calculate their input and output rates (flows) at the national level while providing for environmental flow requirements (Fig. 3). The national modeling approach is of the lumped type, meaning that inputs and outputs to the stocks of water and energy represent totals over an entire country (in the case study, Iran); therefore, the models does not consider intra-country regional variations. The units of water resources and energy resources are expressed in cubic meters and MWh, respectively.Figure 1Feedbacks between resources and uses in the WFE nexus taking into account environmental considerations.Full size imageFigure 2The causal loops of the model developed for simulating the WFE nexus.Full size imageFigure 3Flow diagram of the WFE Nexus system.Full size imageBalance of water resourcesThe study of water exchanges in a country is based on the law of conservation of matter. The following sections present calculations pertinent to the annual balance of surface and groundwater resources.Surface water resourcesThe national runoff generated in a country’s high-elevation areas (or high terrain) and low-elevation areas (plains) is quantified with the following equations:$${preheight}_{t}=HeightCotimes {Precipitation}_{t}$$
(1)

in which ({preheight}_{t}) = volume of precipitation that falls in high-elevation areas during period t, (HeightCo) = the percentage of total precipitation that falls in high-elevation areas, and ({Precipitation}_{t}) = volume of precipitation during period t.$${preplain}_{t}=PlainCotimes {Precipitation}_{t}$$
(2)

in which ({preplain}_{t}) = volume of precipitation that falls in the plains during period t, and (PlainCo) = the percentage of total precipitation that falls in plains (low elevation areas).$${SInflow}_{t}=HeighSInflowCotimes {preheight}_{t}+PlainSInflowCotimes {preplain}_{t}+{OutCSW}_{t}+{Dr}_{t}$$
(3)

in which ({SInflow}_{t}) = the total volume of surface flows during period t, (HeighSInflowCo) = the runoff coefficient in high-elevation areas, (PlainSInflowCo) = the runoff coefficient in the plains, ({OutCSW}_{t}) = the difference between the volume of surface inflow and outflow through a country’s border during period t; and ({Dr}_{t}) = the flow of groundwater resources to surface water resources (i.e., baseflow) during period t.It is possible to calculate the water use after calculating the annual surface water originating by precipitation. Some of the water use by the agricultural, industrial, and municipal sectors becomes return flows. Equations (4) through (9) show how to calculate the surface water use and the water return flows to the surface water sources.$${DomWD}_{t}={Population}_{t}times PerCapitaWatertimes 365$$
(4)

in which ({DomWD}_{t}) = the volume of water use in the municipal sector during period t, ({Population}_{t}) = the population of the country during period t, and (PerCapitaWater) = per capita drinking water use (cubic meters per person per day).$${IndDomWD}_{t}={DomWD}_{t}+{IndWD}_{t}$$
(5)

in which ({IndDomWD}_{t}) = the volume of water use in the municipal and industrial sectors during period t, and ({IndWD}_{t}) = the volume of water use in the industrial sector during period t.The water use by the agricultural sector accounts for the water footprint of agricultural products, which measures their water use per mass of produce, and adjusting the water use by including water losses and agricultural return flows. A separate sub-agent (AGR agent) is introduced to perform the calculations related to the agricultural sector to simplify the dynamic-system model (main model), and the required outputs (BWAgr, GWAgr) of the dynamic system model are called by the agent in the main model (see Figs. 3 and 4). The BWAgr is given by the expression within parentheses in Eq. (6).Figure 4Agricultural subsystem modeled in the AGR agent (shows how to calculate the blue and gray water footprints of agricultural products).Full size image$${AgrWD}_{t}=left(sum_{iin A}{BW}_{i}times {Product}_{i,t}right)times frac{1}{{E}_{Agr}}+OtherAgrWD$$
(6)

in which ({AgrWD}_{t}) = the volume of agricultural water use during period t, ({BW}_{i}) = blue water footprint of agricultural product i (cubic meters per ton), ({Product}_{i,t}) = the amount of production of agricultural product i during period t (tons), ({E}_{Agr}) = the overall irrigation efficiency, (OtherAgrWD) = the volume of water consumed by agricultural products not included in the set A of agricultural products (in cubic meters). The set A includes those agricultural products with the largest yields and shares of the national food basket.$${AgrReW}_{t}={AgrWD}_{t}times AgrReCo$$
(7)

in which ({AgrReW}_{t}) = the volume of water returned from agricultural water use during the period t, and (AgrReCo) = the coefficient of water returned from agricultural water use.$${IndDomReW}_{t}={IndDomWD}_{t}times IndDomReCo$$
(8)

in which ({IndDomReW}_{t}) = the volume of water returned from industrial and municipal water use during period t, and (IndDomReCo) = the coefficient of water returned from industrial and municipal water uses.$${ReSW}_{t}=IndDomReSWCotimes {IndDomReW}_{t}+AgrReSWCotimes {AgrReW}_{t}$$
(9)

in which ({ReSW}_{t}) = the volume of water returned from water uses to surface water resources during period t, (IndDomReSWCo) = the percentage of water returned from municipal and industrial water use to surface water resources, and (AgrReSWCo) = the percentage of water returned from agricultural water use to surface water resources.Water is applied to produce energy, and Eqs. (10) through (15) perform the related calculations. The ({WEIF}_{t}) variable in Eq. (14) is necessary to account for the volume of water saved as a result of the energy savings. A PR model is introduced to account for such water savings (see Fig. 3).$${Diff}_{t} ={OutputE}_{t}-{OutputE}_{t}^{P}$$
(10)

in which ({Diff}_{t})= the difference between the energy used in the main model during period t and the energy used in period t in the PR model, ({OutputE}_{t}) = the sum of energy uses during period t in the main model (the method of calculating ({OutputE}_{t}) is described in detail in “Energy uses”), and ({OutputE}_{t}^{P}) = the sum of energy uses during period t in the PR model. Equations (11) and (12) account for the case when energy use exceeds energy production under current conditions, in which case energy exports are reduced. This prevents additional energy production to meet excess demand, and, consequently, there would not be increases in water use.$${Diff}_{t} le 0,,,{if,,func}_{t}=0$$
(11)
$${Diff}_{t} >0,,,{ if,,func}_{t}={Diff}_{t}$$
(12)

in which ({ iffunc}_{t}) = the amount of energy saved during period t.Equation (13) calculates the water required to produce energy:$${{TotalWE}_{t}=Coal}_{t}times ENwateruseC+{Gas}_{t}times ENwateruseG+{OilPetroleumP}_{t }times ENwateruseO+{Nuclear}_{t}times ENwateruseN+{Elec}_{t}times ENwateruseE$$
(13)

in which ({TotalWE}_{t}) = the volume of water required to produce the energy demand during period t,({Elec}_{t}) = the amount of electricity production during period t (MWh), and (ENwateruseE) = the water required per unit of energy generated by electricity (cubic meters per MWh), all other terms were previously defined.Equation (14) calculates the water savings:$${WEIF}_{t}=sum_{t=1}^{T}frac{{TotalWE}_{t}}{{OutputE}_{t}^{0}}times {if,,func}_{t}$$
(14)

in which ({WEIF}_{t})= the volume of water saved as a result of the energy saved during period t, T = the number of periods of simulation (T = 5 years).Part of the water used to produce energy from coal, oil, petroleum products, and nuclear fuel is accounted for in the industrial sector water use. For this reason, the volume of water to produce energy calculated with Eq. (15) is reduced by that part of water already accounted for in the industrial water use to avoid double accounting.$${WE}_{t}={Coal}_{t}times ENwateruseC+{Gas}_{t}times ENwateruseG+{OilPetroleumP}_{t }times ENwateruseO+{Nuclear}_{t}times ENwateruseN-INDEtimes {IndWD}_{t}-{WEIF}_{t}$$
(15)

in which ({WE}_{t}) = the volume of water required to produce different types of energy (except those included in the industrial sector) during period t, ({Coal}_{t}) = the energy produced with coal during period t (MWh), (ENwateruseC) = the water required per unit of energy produced with coal (cubic meters per MWh),({Gas}_{t}) = the amount of energy produced with natural gas during period t (MWh), (ENwateruseG) = the water required per unit of energy produced with natural gas (cubic meters per MWh), ({OilPetroleumP}_{t}) = the amount of energy produced with crude oil and other petroleum products during period t (MWh), (ENwateruseO) = the water required per unit of energy produced with crude oil and petroleum products (cubic meters per MWh),({Nuclear}_{t}) = the amount of nuclear energy produced during period t (MWh), (ENwateruseN) = the water required per unit of nuclear energy produced (cubic meters per MWh), and (INDE) = the percentage of industrial water use already accounted for in Eq. (5) (which pertains to water used in the coke coal, oil refineries, and nuclear fuel industries).Part of the discharge of springs enters the surface water sources, and this enters the calculation of the input to the surface water-resources stock in Eq. (16):$${InputSW}_{t}= SInflow+{ReSW}_{t}{+ Fountain}_{t}$$
(16)

in which ({InputSW}_{t}) = the volume of inflow water to surface water sources during period t, and ({Fountain}_{t}) = discharge of springs to surface water sources during period t, other terms previously defined.The output of the surface water resources includes water use and the infiltration of surface water into groundwater, the latter calculated with Eq. (17):$${SInflowInf}_{t}={SInflow}_{t}times SInflowInfCo$$
(17)

in which ({SInflowInf}_{t}) = the infiltration volume of surface water during period t, and (SInflowInfCo) = the infiltration coefficient of surface water.The output of the surface water resources stock is calculated using Eq. (18):$${OutputSW}_{t}={AgrSWDCo}_{t}times {AgrWD}_{t}+{IndSWDCo}_{t}times {IndWD}_{t}+{DomSWDCo}_{t}times {DomWD}_{t}+{mathrm{ WE}}_{t}+{SInflowInf}_{t}-{EvSwSea}_{t}$$
(18)

in which ({OutputSW}_{t}) = the output volume of surface water during period t, ({AgrSWDCo}_{t}) = the percentage of gross agricultural water use from surface water resources during period t, ({IndSWDCo}_{t}) = the percentage of industrial water use from surface water resources during period t, ({DomSWDCo}_{t})= the percentage of gross drinking water consumption from surface water sources during period t, and ({EvSwSea}_{t}) = the total volume of evaporation from surface water plus the discharge of surface water to the sea during period t.The balance of surface water resources is calculated based on Eq. (19):$$SWaterleft(tright)=underset{{t}_{0}}{overset{t}{int }}left[{InputSW}_{t}left(Sright)-{OutputSW}_{t}(S)right]dt+SWater(0)$$
(19)

in which (SWaterleft(tright)) = the stock of surface water resources at time t, (SWater(0)) denotes the stock of surface water at the initial time (t = 0).Groundwater resourcesGroundwater resources gain water from deep infiltration of precipitation in the plains and elevated areas from (1) inflows from outside of the study area, (2) infiltration from surface flows and return waters. Groundwater output factors also include the discharge of groundwater resources (wells, springs, and aqueducts), groundwater flow that moves outside the study area and evaporation. Infiltration of precipitation in the plains and in high terrain into groundwater resources is calculated with Eq. (20):$${Inf}_{t}=PrePInfCotimes {preplain}_{t}+PreHInfCotimes {preheight}_{t}$$
(20)

in which ({Inf}_{t}) = the volume of water entering groundwater sources through infiltration of precipitation during period t, (PrePInfCo) = the infiltration coefficient of precipitation in the plains, and (PreHInfCo) = the infiltration coefficient of rainfall in high terrain.Equation (21) calculates the volume of return water that accrues to groundwater resources:$${ReGW}_{t}=IndDomReGWCotimes {IndDomReW}_{t}+AgrReGWCotimes {AgrReW}_{t}$$
(21)

in which ({ReGW}_{t}) = the volume of water returned from water use that accrues to groundwater resources during period t, (IndDomReGWCo) = the percentage of water returned from municipal and industrial water use accruing to groundwater resources, and (AgrReGWCo) = the percentage of water returned from agricultural water use accruing to groundwater resources.The volume of groundwater input is calculated with Eq. (22):$${InputGW}_{t}={Inf}_{t}+{ReGW}_{t}+{SInflowInf}_{t}+{OutCGw }_{t}$$
(22)

in which ({InputGW}_{t}) = the volume of groundwater input during period t, and ({OutCGw }_{t}) = the difference between the volume of groundwater leaving and that entering the country during period t.The volume of groundwater output is calculated with Eq. (23):$${OutputGW}_{t}={AgrGWDCo}_{t}times {AgrWD}_{t}+IndGWDCotimes {IndWD}_{t}+DomGWDCotimes {DomWD}_{t}+{EvGwDr}_{t}$$
(23)

in which ({OutputGW}_{t}) = the volume of groundwater output during period t, ({AgrGWDCo}_{t}) = the percentage of gross agricultural water use from groundwater resources during period t, IndGWDCo = the percentage of industrial water use from groundwater resources during period t, DomGWDCo = the percentage of municipal water use from groundwater resources during period t, and ({EvGwDr }_{t}) = the total volume of evaporation from groundwater plus the drainage of groundwater resources to surface water resources at time t.Equation (24) calculates the annual balance of groundwater resources:$$GWaterleft(tright)=underset{{t}_{0}}{overset{t}{int }}left[{InputGW}_{t}left(Sright)-{OutputGW}_{t}left(Sright)right]dt+GWater(0)$$
(24)

in which GWater(t) = the groundwater resources stock at time t, (GWater(0)) denotes the stock of groundwater at the initial time (t = 0).Energy usesEnergy uses are calculated with Eqs. (25)–(27). The total national energy use includes the agricultural, industrial, transportation, and exports sectors’ energy demands. The energy uses by these sectors do not change during the implementation of the policy, and, consequently do not change the WFE Nexus in that period; therefore, they are not included in the calculations.$${WDTP}_{t}={DomWD}_{t}times {CEIntensity}_{t}$$
(25)

in which ({WDTP}_{t}) = the energy used in the extraction, transmission, distribution, and treatment of water in the water and wastewater system during period t, and ({CEIntensity}_{t}) = the energy intensity in the extraction, transmission, distribution, and treatment of water in water and wastewater systems during the period t (MWh per cubic meter).$${ResComPubED}_{t}=ResComPubPerCapitatimes {Population}_{t}$$
(26)

in which ({ResComPubED}_{t}) = the energy use by the domestic, commercial, and public sectors during period t, and (ResComPubPerCapita) = the per capita energy consumption by the domestic, commercial, and public sectors (MWh per person per year).$${OutputE}_{t}={ResComPubED}_{t}+{WDTP}_{t}$$
(27)
Environmental water needsThe gray water footprint is defined as the volume of freshwater that is required to assimilate the load of pollutants based on natural background concentrations and existing ambient water quality standards. The estimation of the gray water footprint associated with discharges from agricultural production is based on the load of nitrogen fertilizers, which are pervasive in agriculture. The gray water footprint in terms of nitrogen concentration has been estimated by Mekonnen and Hoekstra24,25, as written in Eq. (28):$${GW}_{t}^{Agr}=sum_{iin A}{GW}_{i}times {Product}_{i,t}$$
(28)

in which ({GW}_{t}^{Agr})= the volume of gray water in the agricultural sector during period t, and ({GW}_{i}) = the volume of gray water associated with the production of one ton of agricultural product i (cubic meters per ton)(.)There are no accurate estimates of the concentrations of pollutants per unit of industrial production, or of the concentration of pollutants in municipal wastewater. Therefore, the conservative dilution factor (DF), which is equal to 1 for untreated returned water from the municipal and industrial sectors, is applied in this work. Equation (29) is a simplified equation of the gray water footprint26. The fraction appearing on the right-hand side of Eq. (29) is equal to the DF.$${GW}_{t}^{IndDom}= frac{{C}_{eff}-{C}_{nat}}{{C}_{max}-{C}_{nat}}times {IndDomReW}_{t}times IndDomReUT$$
(29)

in which ({GW}_{t}^{IndDom}) = the gray water footprint of the municipal and industrial sectors during period t, ({C}_{eff}) = the nitrogen concentration in return water (mg/L), ({C}_{nat}) = the natural concentrations of contaminant in surface water (mg/L), ({C}_{max}) = the maximum allowable concentration contaminant in surface water (mg/L), and (IndDomReUT) = the percentage of untreated returned water from the municipal and industrial sectors.The total gray water footprint is obtained by summing the footprints associated with the municipal/industrial and agricultural sectors:$${TotalGW}_{mathrm{t}}={GW}_{t}^{IndDom}+{GW}_{t}^{Agr}$$
(30)

in which ({TotalGW}_{mathrm{t}}) = the volume of gray water from all sectors during period t.This work considers qualitative and quantitative environmental water needs. Equation (31) is used to calculate the total environmental water need. The Tennant method for calculating the riverine environmental flow requirement (or instream flow) stipulates that, based on the conditions of each basin, between 10 to 30% of the average long-term flow of rivers represents the environmental flow requirement27. The sum of these requirements across all the basins equals the environmental requirement of the entire region or country. Yet, by providing 10 to 30% of the average long-term flow of rivers the riverine ecosystem barely emerges from critical conditions, and is far from optimal ecologic functioning. The total environmental water need is equal to the sum of the environmental flow requirement plus the volume of water needed to dilute the contaminants entering the surface water sources:$${ENV}_{t}={TotalGW}_{t}+Tennant$$
(31)

in which ({ENV}_{t}) = the environmental flow requirement during period t, and Tennant = the environmental flow requirement calculated by the Tennant (1976) method.The policy evaluation indexThe available renewable water is calculated with Eq. (32):$${IN}_{t}={OutCGW }_{t}+ {SInflow }_{t}+{ Inf}_{t}-{EvGwDr}_{t}$$
(32)

in which ({IN}_{t})= the renewable water available before the application of environmental constraints during period t.The volume of manageable water is calculated with Eq. (33):$$REWleft(tright)=underset{{t}_{0}}{overset{t}{int }}left[INleft(tright)-ENVleft(tright)right]dt$$
(33)

in which REW (t) = the (cumulative) manageable and exploitable renewable water in the period t-t0.Equation (34) calculates the total water withdrawals by the agricultural, industrial, municipal, and energy production sectors:$${WDW}_{t}={OutputSW }_{t}+ {OutputGW}_{t}- {cheshmeh}_{t}$$
(34)

in which ({WDW}_{t}) = the sum of the withdrawals by the agricultural, industrial, municipal, and energy production sectors during period t.The cumulative water withdrawals are calculated with Eq. (35):$$withdleft(tright)=underset{{t}_{0}}{overset{t}{int }}WDWleft(tright)dt$$
(35)

in which (withdleft(tright)) = the sum of the withdrawals by the agricultural, industrial, municipal and energy production sectors in the horizon t-t0.Equation (36) calculates the water stress index:$${index}_{{t}_{f}}^{MRW}=frac{withd({t}_{f})}{REWleft({t}_{f}right)}times 100$$
(36)

in which ({index}_{{t}_{f}}^{MRW}) = the renewable water stress index at the end of the study period, and ({t}_{f}) = the period marking the end of the study horizon.Once the water and energy model is developed it must be calibrated with observational data prior to its use in predictions, as shown below. More