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Variation in microclimateMicroclimate at the tower varied across the daily sampling period with temperatures highest and relative humidity lowest around midday and the early afternoon hours, although the time of peak temperature and nadir humidity varied by height (Fig. 3a, b). Mean temperature was highest at ground level at 11:30 (30.0 °C) when it was on average 0.2 °C hotter than at 9 m, whereas at 5 m and 9 m, it was highest at 13:30 (29.7 °C and 30.3 °C, respectively). The inverse was true for mean relative humidity, which was lowest at ground level at 11:30 (83.8%) and lowest at 5 m and 9 m at 13:30 (80.1% and 76.4%, respectively). Both variables showed substantial overlap in means and standard errors across the sampled heights during the morning hours, before diverging in the afternoon. For comparison, we extracted microclimate data from the corresponding sampling period in the BG-Sentinel trap study15, which revealed clear differences in temperature and humidity at each height sampled (Fig. 3c, d). BG-Sentinel traps were often hung beneath the forest canopy where it was considerably cooler and more humid than at the treefall gap, particularly at ground level.Figure 3Variation in microclimate by height and collection method. (a) and (b) show the mean temperature (temp,°C) + / − 1 standard error (S.E.) and relative humidity (RH, %) + / − 1 standard error (S.E.) for net collections made at the tower between 10:00 and 15:00 in this study. (c) and (d) show corresponding data extracted from the BG-Sentinel trap study15.Full size imageCommunity composition of diurnally active, anthropophilic mosquitoesA total of 2146 adult mosquitoes representing seven genera and 34 species were collected using nets (Fig. 4a), of which 99.8% (2142/2146) were female and 99.7% (2140/2146) were identified to species level. Mosquito abundance was similar at ground level and 9 m but was slightly lower at 5 m, while species richness was higher at ground level (28 species), than at 5 m (18 species) and 9 m (22 species). Psorophora was the most abundant genus (1231 mosquitoes, 57.4% of the total catch), followed by Haemagogus (32.3%), and Sabethes (6.6%). The genera Limatus (1.4%), Culex (1.2%), Wyeomyia (1.0%), and Onirion ( 0.1 for both comparisons). A linear regression showed that, across all heights, lag to first approach decreased significantly as Hg. janthinomys abundance increased (DF = 1, F = 52.1, P  More

More detailed methods can be found in the supplementary material. Data from this experiment on the characterisation of the microbial community and its response to climate change has been previously published in Scanes et al.12, therefore, the present study focussed on the interaction of metabolic processes with the microbiome. We examined the links between climate change, metabolism, genotype and microbiome of the Sydney rock oyster, Saccostrea glomerata20. Nine oyster aquacultural breeding lineages (labelled as genotype-lines A–I) of S. glomerata, which are known to differ in their resilience to climate change12 were exposed to ambient and elevated temperature and PCO2 treatments. All seawater used in acclimation and experimental exposure was collected from Little Beach, Port Stephens (152°9′30.00″E, 32°42′43.03″S), filtered through canister filters to a nominal 5 µm, and stored onsite in 38,000 L polyethylene tanks as a stock of filtered seawater.Approximately 72 individual S. glomerata, from each of the nine families (A-I) were collected from intertidal leases in Cromarty Bay, Port Stephens (152° 4′0.69″E, 32°43′19.69″S). Oysters were held on private leases so a collection permit was not required. Oysters were collected in September 2019 for experiments, meaning all oysters were 22 months old when experiments began. Oysters were placed into a 2000 L fibreglass tank and maintained at 24 °C, a salinity of 35 ppt and ambient PCO2 (pH 8.18) for two weeks to acclimate to laboratory conditions. Following acclimation, oysters from each genotype-line were divided among twelve 750 L polyethylene tanks filled with 400 L of filtered seawater (5 µm) at a density of 54 oysters per tank, with each genotype-line represented by six replicate individuals. Treatments consisted of orthogonal combinations of two PCO2 concentrations (ambient [400 µatm]; elevated [1000 µatm]) and two temperature treatments (24 and 28 °C). Each combination was replicated across three tanks. Treatments were selected to represent temperatures and PCO2 concentrations predicted for 2080–2100 by the IPCC27 and reflect measured changes in estuary temperatures reported from south eastern Australia20.Once oysters were transferred to experimental tanks, the PCO2 level and temperature were steadily increased in elevated exposure tanks over one week until the experimental treatment level was reached. The elevated CO2 level was maintained using a pH negative feedback system (Aqua Medic, Aqacenta Pty Ltd, Kingsgrove, NSW, Australia; accuracy ± 0.01 pH units) bubbling food grade CO2 (BOC Australia) through a mixing chamber and into each tank, previously described in18. These PCO2 levels corresponded to a mean ambient pHNBS of (8.18 ± 0.01) and at elevated CO2 levels a mean pHNBS of (7.84 ± 0.01). Temperature was increased and then maintained using 1000 W aquarium heaters in each tank. Oysters were then exposed to their respective treatments for a further four weeks. Oysters were checked daily for mortality; no dead oysters were found in any tanks during the four-week exposure period.Haemolymph sampling for DNA extractionFollowing exposure to experimental conditions, haemolymph was taken from two replicate oysters, from each genotype-line, from each tank for microbial analysis following the methods previously described in Scanes et al.,12. This amounted to six individuals from each genotype-line, in each treatment. Each oyster was opened using an autoclave sterilised shucking knife, ensuring that the pericardial cavity was not ruptured. Excess fluid was tipped off the tissue surface and 200–300 µL of haemolymph was extracted from the pericardial cavity using a new sterile 1 mL needled syringe (Terumo Co.). Samples from two oysters were transferred to two new pre-labelled DNA/RNA free 1 mL tubes (Eppendorf Co.) and immediately frozen at − 80 °C where they were stored until DNA extraction.We used 16 s rRNA amplicon sequencing to characterise the bacterial microbiome of S. glomerata haemolymph following the methods previously described in Scanes et al.12. DNA was extracted from 216 oyster haemolymph samples (9 genotype-lines × 4 treatments × 3 replicate tanks × 2 replicate oysters per tank) using the Qiagen DNeasy Blood and Tissue Kit (Qiagen Australia, Chadstone, VIC), according to the manufacturer’s instructions. The bacterial microbiome of the oyster haemolymph was characterised with 16S rRNA amplicon sequencing, using the 341F (CCTACGGGNGGCWGCAG) and 805R (GACTACHVGGGTATCTAATCC) primer pair28 targeting the V3-V4 variable regions of the 16S rRNA gene with the following cycling conditions: 95 °C for 3 min, 25 cycles of 95 °C for 30 s, 55 °C for 30 s and 72 °C for 30 s, and a final extension at 72 °C for 5 min. Amplicons were sequenced on the Illumina Miseq platform (2 × 300 bp) following the manufacturer’s guidelines at the Ramaciotti Centre for Genomics, University of New South Wales. Raw data files in FASTQ format were deposited in NCBI Sequence Read Archive (SRA) under Bioproject number PRJNA663356.Sequence analysisRaw demultiplexed data was processed using the Quantitative Insights into Microbial Ecology (QIIME 2 version 2019.1.0) pipeline. Briefly, paired-end sequences were imported (qiime tools import), trimmed and denoised using DADA2 (version 2019.1.0). Sequences were identified at the single nucleotide threshold (Amplicon Sequence Variants; ASV) and taxonomy was assigned using the classify-sklearn QIIME 2 feature classifier against the Silva v138 database29. Sequences identified as chloroplasts or mitochondria were also removed. Cleaned data were then rarefied at 6,500 counts per sample.Physiological analysisWe measured physiological variables relating to oyster haemolymph metabolic function. These were: extracellular pH (pHe), extracellular CO2 concentrations (PCO2e) and the whole oyster metabolic rate (MR) measured as a standardised rate of oxygen consumption. Physiological measurements were taken from two oysters from each genotype-line in each tank (methods followed that of Parker et al.16,30 and Scanes et al.18). Oysters were immediately opened without rupturing the pericardial cavity. Haemolymph samples were drawn from the interstitial fluid filling the pericardial cavity chamber of an opened oyster using a sealed 1 mL needled syringe. A 0.2 mL sample was drawn carefully to avoid aeration of the haemolymph. Half of the sample was then immediately transferred to an Eppendorf tube where pHe of the sample was measured at 20 °C using a micro pH probe (Metrohm 827 biotrode). The remaining haemolymph was transferred to a gas analyser (CIBA Corning 965) to determine total CO2 (CCO2). The micro pH probe was calibrated prior to use with NBS standards at the acclimation temperature and the gas analyser was calibrated using manufacturer guidelines. Two oysters were sampled per genotype-line in each replicate tank. Partial pressure of CO2 in haemolymph (PCO2e) was calculated from the CCO2 using the modified Henderson-Hasselbalch equation according to Heisler31,32. Metabolic rate (MR) was determined using a closed respiratory system as previously described in Parker et al.16 and Scanes et al.18. Briefly, MR was measured in two oysters per genotype-line, per tank by placing oysters in a closed 500 mL glass chamber containing filtered seawater (5 µm) set at the correct treatment conditions. Oxygen concentrations were then measured within the chamber using a fibre optic dipping probe (PreSens dipping probe DP-PSt3, AS1 Ltd, Regensburg, Germany) and recorded (15 s intervals) until the oxygen concentration had been reduced by 20%, the time taken to reduce oxygen by 20% was recorded. Oysters were removed from the chambers, opened and the tissue was dried at 70 °C for 72 h. Tissue was then weighed on an electronic balance (± 0.001 g), and MR was calculated using Eq. (1):$$MR = frac{{left[ {V_{r} times Delta {text{C}}_{W} O_{2} } right]}}{{Delta t times {text{bw}}}}$$
(1)

where MR is oxygen consumption normalised to 1 g of dry tissue mass (mg O2 g−1 dry tissue mass h−1), Vr is the volume of the respiratory chamber minus the volume of the oyster (L), ΔCWO2 is the change in water oxygen concentration measured (mg O2L−1), Δt is the measuring time (h), bw is the dry tissue mass (g). Equation is modified from Parker et al.16.Data analysisIt was not possible to measure all variables in each oyster, but rather three individuals were needed to fulfil one replicate set of measurements. PCO2e and pHe could be measured in the same individual however, MR and the microbiome were measured in separate individuals. This meant that measurements were taken from 6 oysters per genotype-line, per replicate tank (each measurement replicated twice). To align physiological data with microbiome data we took a conservative approach where data from PCO2e and pHe, MR and the microbiome were randomly matched to individuals from the same genotype-line and replicate tank. This gave us the best approximation and is conservative because it increased variability compared to taking all measurements from the same individual. ANOVA was used to determine the significant (n = 210; P  More

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Crop production, water productivity, and virtual waterA method to calculate the water needed for crops is the water footprint (WF). The WF has a color-based classification: green water (precipitation), blue water (ground and surface water), and grey water (water to dilute polluted water to accepted water quality standards). A manual on how to calculate WFs has been published12. Calculations of WFs integrate green and blue crop water use (evapotranspiration by crops) over the growing period of specific crops and express results per unit of yield (m3 kg−1). The difference between crop-water use and effective rainfall is applied as a proxy for blue WFs when no data on actual irrigation water supply are available. WFs of specific crops vary greatly among countries, and even within countries45. This means that water can be saved when crops are smartly traded. This may also be possible within a country if crops are grown where water productivity is the highest.Calculation of the water footprintWater footprints (WFs) are calculated as green and blue water footprints (WFgreen, WFblue, respectively) adopting the method from the WF manual12. This study assumes that the difference between crop water requirement and evapotranspiration of green water (ETGreen) in crops is equal to the evapotranspiration of blue water (ETblue); therefore, crop water requirements are met with irrigation water. The crop water requirements are estimated with the Food and Agriculture Organization’s CROPWAT model46. The selected methods for calculating the reference evapotranspiration (ET0) and effective precipitation (Peff) are the FAO Penman–Monteith method47,48 and the USDA’s SCS method48, respectively. Calculations were performed at the provincial scale for each crop. Equations (1) through (4) are applied to calculate WFgreen and WFblue for the crops included in this study:Actual crop evapotranspiration from reference evapotranspiration:$$ ET_{c} = sum_{t} {ET_{0} times K_{c} } $$
(1)
Reference evapotranspiration:$$ ET_{0} = frac{{0.408Delta left( {R_{n} – G} right) + gamma frac{900}{{T + 273}}U_{2} left( {e_{a} – e_{d} } right)}}{{Delta + gamma left( {1 + 0.34U_{2} } right)}} $$
(2)
$$ WF_{green} = 10 times frac{{min left[ {ET_{c} ,P_{eff} } right]}}{Y} $$
(3)
$$ WF_{blue} = 10 times frac{{max left[ {0,ET_{c} – P_{eff} } right]}}{Y} $$
(4)
where ETc denotes the actual crop evapotranspiration (mm) during the growth period (t), ET0 represents the reference evapotranspiration (mm day−1), and Kc denotes the crop coefficient based on crop type and development stages (initial, middle, and late stages). In Eq. (2) ea (kPa), ed (kPa), Δ (kPa °C−1), G (MJ m−2 day−1), T (°C), Rn (MJ m−2 day−1), U2 (m s−1), and γ (kPa °C−1) denote the saturation vapor pressure, the actual vapor pressure, the slope of the saturation-vapor pressure curve, the soil heat flux, the average air temperature, the net radiation on the crop surface, the wind speed measured at a height of 2 m above ground level, and the psychrometric constant, respectively. Equations (3) and (4) calculate the green and blue water footprints (m3 ton−1), in which Peff (mm), Y (ton ha−1), and 10, are represent effective precipitation, the crop yield, and a conversion factor from mm to m3 ha−1, respectively. WFgreen and WFblue occur in irrigated cultivation; however, there is only WFgreen in rainfed cultivation.Optimization of crop productionAll the steps of the methods used in this work were coded in MATLAB for use by decision-makers, planners, and interested organizations.Balancing the agricultural systemAn internal trade network was created to organize and remedy the weaknesses of the trade network. The lack of a comprehensive trade network has caused the crops to be exported regardless of the country’s demands, which eventually leads to the import of the same crops. The production and demand amounts of each crop in each province and their WFgreen and WFblue are determined with the following equations applied to N = 51 crops in J = 31 provinces:$$ {CP}_{(i,j)} = {ICP}_{(i,j)} + {RCP}_{(i,j)} $$
(5)
$$ {ICP}_{(i,j)} = left( {{BCY}_{(i,j)} times {ICA}_{(i,j)} } right) $$
(6)
$$ {RCP}_{(i,j)} = left( {{GCY}_{(i,j)} times {RCA}_{(i,j)} } right) $$
(7)
$$ {CD}_{(i,j)} = left( {{PCD}_{i} times {POP}_{J} } right) $$
(8)
$$ {TWF}_{blue(i,j)} = {ICP}_{(i,j)} times {WF}_{blue(i,j)} $$
(9)
$$ {TWF}_{green(i,j)} = {ICP}_{(i,j)} times {WF}_{green(i,j)} $$
(10)
where (i=1, 2,ldots , N;j=1, 2, ldots, J,) CP(i,j) (ton), ICP(i,j) (ton), RCP(i,j) (ton), BCY(i,j) (ton.ha−1), GCY(i,j) (ton.ha−1), ICA(i,j) (ha), RCA(i,j) (ha), CD(i,j) (ton), PCDi (ton.person−1), POPj (person), TWFblue(i,j) (m3), and TWFgreen(i,j) (m3) denote the production of crop i in province j, crop production of irrigated land, crop production in rainfed cultivation, irrigated crop yield, rainfed crop yield, irrigated acreage, rainfed areas acreage, demand for crop i in province j, per capita diet, population of province j, the blue WF of crop i in province j corresponding to irrigated cultivation, and the green WFs of crop i in province j corresponding to irrigated cultivation, respectively.TWFblue(i,j) equals zero in rainfed cultivation, and TWFgreen(i,j) is calculated with Eq. (10) based on RCP(i,j). The deficit or surplus over the demand of the provinces were determined by comparing CP(i,j) and CD(i,j) for each crop in each province. Equation (11) implies that CS(i,j) is the amount of crop i supplied in province j (ton), which involves the export and import of crops:$$ {CS}_{(i,j)} = {CP}_{(i,j)} – {CD}_{(i,j)} $$
(11)
where (i=1, 2,ldots , N;j=1, 2, ldots, J) .The internal trade network is formed once the deficit and surplus for each crop in the provinces is determined, and crops are traded based on the shortest distance between the provinces. The developed trade network would improve the country’s agricultural system and reduce transportation costs between the provinces. Each province adds to or subtracts Ti,j (ton) from its crop amounts, where imports imply an addition and exports a subtraction of crop amounts. The internal exports and imports of WFs and the net water footprints trade (NWFT) in each province are calculated as follows:$$ {WFT}_{(x,r,i)} = T_{(x,r,i)} times left( {{WF}_{green} + {WF}_{blue} } right)_{(x,i)} $$
(12)
$$EW{F}_{(x)}={sum }_{r,i}WF{T}_{(x,r,i)}$$
(13)
$$ IWF_{(r)} = sumlimits_{x,i} {WFT_{(x,r,i)} } $$
(14)
$$ {NWFT}_{(j)} = IWF_{(j)} – EWF_{(j)} $$
(15)
where (i=1, 2,ldots , N;j, x=1, 2, ldots, J, r=x-1), WFT(x,r,i) (m3), T(x,r,i) (ton), (WFgreen + WFblue)(x,i) (m3 ton−1), EWF(x) (m3), IWF(r) (m3), and NWFT(j) (m3) denote the WFs traded for crop i from exporting province x to importing province r, the amount of crop i exported from province x to province r, the blue and green WFs related to crop i in exporting province x, the WFs exported from province x by the trade of crops, the WFs imported into province r by the trade of crops, and the net water footprints trade in province j, respectively.The positive and negative values ​​of NWFT(j) represent the import and export of WFs to province j, respectively. The calculation of the internal trade between provinces with Eq. (11) permits determining the deficits and surpluses for each crop in the provinces nationally. At this juncture the provinces may resort to international trade to cope with deficits and surpluses. However, from this work’s premise of improving food security and self-sufficiency the cropping patterns of surplus crops in the provinces are modified as described in the next section.Modifying exports to optimize the cropping patternThe multi-objective optimization approach to increase food security and self-sufficiency redirects the resources to be used to cultivate export crops to the cultivation of crops that are in deficit (i.e., whose production is less than demand). This modification of cropping patterns in the provinces is based on their traditional cropping patterns. For this purpose, the internal trade network is linked to the optimization method to manage cropping patterns of the regions based on the output of the trade network, and on the goals of achieving food security and preventing water crisis. These two goals are pertinent in many countries where water scarcity is a limiting factor to achieve food security49. Therefore, concerning available agricultural water it is imperative to pay attention to the type of water (green or blue) used. Specifically, WFblue can be used in several areas of consumption; however, WFgreen is not controllable in the same manner. The usage of WFgreen by crops depends on the growing season, and the maximum use can be achieved by choosing the optimal crops. Therefore, this work treats WFgreen and WFblue as indicators of water crisis and food security, which were chosen as objective functions. In other words, controlling and managing WFs prevent its waste (thus reducing the water deficit and crisis). Selecting optimal crops based on WFs will increase production and food security. The water crisis and food security serve as the benchmark for comparison between the reference situation (without optimization) and the results of this new method. The reference situation refers to the initial state of food security and water crisis, which occurs before optimizing the cropping patterns.The food-security objective function is expressed as follows:$$F{S}_{i}=frac{{sum }_{j=1}^{J}C{P}_{(i,j)}}{{sum }_{j=1}^{J}C{D}_{(i,j)}}$$
(16)
The water-crisis objective function is written as follows:$${WC}_{j}=frac{sum_{i=1}^{N}{TWF}_{blue(i,j)}}{{RWR}_{j}}$$
(17)
where (i=1, 2,ldots, N=51;j=1, 2, ldots, J=31,) FSi, CP(i,j) (ton), CD(i,j) (ton), WCj, TWFblue(i,j) (m3), and RWRj (m3) denote the food security for crop i, production of crop i in province j, the demand of crop i in province j, the water crisis in province j, the blue WFs of crop i in province j, and the renewable water resources in province j, respectively.Maximizing the FS index and minimizing the WC index represent the ideal situation. The maximizing function was converted to a minimization function for the purpose of multiobjective optimization. The final form of the objective functions i given by the following equations:$$Min({Z}_{1})=frac{1}{N}{sum }_{i=1}^{N}(1-F{S}_{i})begin{array}{cc},& where,, F{S}_{i}end{array}=Minleft(frac{{sum }_{j=1}^{J}C{P}_{(i,j)}}{{sum }_{j=1}^{J}C{D}_{(i,j)}},1right)$$
(18)
$$Min({Z}_{2})=frac{1}{J}{sum }_{j=1}^{J}W{C}_{j}$$
(19)
where (i=1, 2,ldots , N=51;j=1, 2, ldots, J=31.) The objective function Z1 is calculated based on the food security index expressed as an average for all crops, and the objective function Z2 is calculated as the average of the water crisis indexes in the 31 provinces. Both objective functions are affected by cropping patterns and cultivation areas. The water and land used must be calculated prior to modifying the cropping patterns. The amounts of surplus crops in the provinces and their equivalent water and land are calculated using the following equations:$$ {SCP}_{(i,j)} = Max({CP}_{(i,j)} – {CD}_{(i,j)} + T_{(i,j)} ,0) $$
(20)
$$ {BCY}_{(i,j)} times (X_{1(i,j)} times ICA_{(i,j)} ) + {GCY}_{(i,j)} times (X_{2(i,j)} times RCA_{(i,j)} ) = {SCP}_{(i,j)} $$
(21)
where (i=1, 2,ldots, N;j=1, 2, ldots, J,) SCP(i,j), (X_{1(i,j)}), (X_{2(i,j)}) denote the surplus crop i in province j (ton) determined based on demand and trade in the province, and the percentage of crop i in province j that must be removed from irrigated and rainfed cultivation, respectively. The amount of water and land available for new cultivation are calculated as follows:$$ ICA_{j}^{free} = sumlimits_{i = 1}^{51} {X_{1(i,j)} times ICA_{(i,j)} } $$
(22)
$$ RCA_{j}^{free} = sumlimits_{i = 1}^{51} {X_{2(i,j)} times RCA_{(i,j)} } $$
(23)
$$ TWF_{blue,j}^{free} = sumlimits_{i = 1}^{51} {{WF}_{blue(i,j)} times BCY_{(i,j)} } times ICA_{j}^{free} $$
(24)
where (i=1, 2,ldots , N;j=1, 2, ldots, J,) ICAjfree and RCAjfree denote the total available area of ​​irrigated and rainfed cultivation (ha) in province j, respectively, and TWFblue,jfree represents the total amount of blue WFs available in province j (m3). It is noteworthy that the water and land available in irrigated cultivation can be altered. On the other hand, only the available land is controllable under rainfed cultivation.The objective functions of the proposed method [Eqs. (18) and (19)] were subjected to a set of constraints introduced next.

(i)

Modification of the cropping patterns

The available land in each province is allocated to crops that feature a deficit in the country and are part of the traditional cropping patterns of the provinces. The set of cultivable crops is determined using the following equation:$$ P = left{ {pleft| {p in i,sum_{j = 1}^{31} {SCP_{(p,j)} < 0} } right.} right} $$ (25) where p denotes the set of crops with deficit conditions in the country and SCP(i,j) was defined above. Letting traditional irrigated and rainfed cropping patterns be denoted by Aj and Bj in province j, respectively, the set of irrigated and rainfed crops cultivable in province j was calculated as follows:$$ IC_{j} = P cap A_{j} begin{array}{*{20}c} {} & {(j = 1,2,3,ldots,31)} \ end{array} $$ (26) $$ RC_{j} = P cap B_{j} begin{array}{*{20}c} {} & {(j = 1,2,3,ldots,31)} \ end{array} $$ (27) where (j=1, 2, ldots, J), ICj and RCj denote the irrigated and rainfed crops cultivable in province j, respectively. (ii) Constraint on cultivation area A fraction of ICAjfree can be used in irrigated lands:$$ 0 le M times sumlimits_{i = 1}^{51} {{(X}_{1(i,j)} times ICA_{(i,j)} ) le ICA_{j}^{free} } begin{array}{*{20}c} , & {0 le M le 1} & {} \ end{array} $$ (28) where (j=1, 2, ldots, J), and M denotes the fraction of blue water available. (iii) Constraint on water use The amount of water used to modify the cropping pattern in the provinces is limited:$$ sumlimits_{i = 1}^{51} {TWF_{blue(i,j)}^{m} le RWR_{j} - sumlimits_{i = 1}^{51} {TWF_{blue(i,j)} + } } TWF_{blue,j}^{free} $$ (29) where (left(j=1,2,3,ldots,Jright),) TWFmblue(i,j) denotes the blue WFs used to modify the cultivation in province j, and TWFblue(i,j) represents the initial blue WFs consumed in province j to cultivate crops before changing the cropping pattern.Ideal solution and pareto optimalityThis work applied the multi-objective optimization Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The NSGA is based on the Genetic Evolutionary Algorithm and the Selection, Crossover, and Mutation operations50. The NSGA was introduced by Deb et al.51,Srinivas and Deb52, then improved to the NSGA-II51. The NSGA-II has been widely studied in water resources management53,54,55.The NSGA-II produces a Pareto front of solutions, in which, each point represents a management scenario. The decision-maker selects a scenario based on the objective functions and situational analysis. Multi-criteria decision-making methods (MCDM) can be applied to select an efficient point on the Pareto front curve56,57. This work implements the technique for order preference by similarity to ideal solution (TOPSIS) as the MCDM employed for that purpose. A description of the TOPSIS method is presented in the appendix.The NSGA-II parameters were determined based on a trial-and-error process. Multiple runs of the algorithm were used to adjust the parameters to reduce uncertainty. For this purpose, the population size and maximum iteration were set equal to 400 and 500, respectively, and the crossover and mutation rates were set equal to 0.8 and 0.1, respectively. The flowchart of the proposed approach is displayed in Fig. 1.Figure 1Flowchart of the methodology.Full size image More

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