Adapting Water Allocation to Irrigation Demandsto Constraints in Water Availability Imposedby Climate Change

Adriadna Chavez-Jimenez & Alfredo Granados &Luis Garrote & Francisco Martín-Carrasco

Received: 19 January 2014 /Accepted: 7 November 2014# Springer Science+Business Media Dordrecht 2014

Abstract Climate change projections predict a rise in temperatures which may result in areduction in water resource availability. Irrigation is both the most demanding water use andthat which is the lowest priority. Consequently, adaptation measures regarding irrigationdemands are required in coping with such a resource decrease. As improvement in waterefficiency use could not be enough to counteract strong stream flow reductions, managementactions regarding demands may be implemented. This paper proposes a methodology foridentifying the required reductions and sequence in which water allocation is to be reduced inorder to meet satisfactory system behaviour. Such a methodology could help basin managers indecision making in meeting irrigation demands which, accordingly, could offer better perfor-mance in terms of both reliability and productivity. The methodology is applied at theGuadalquivir Basin in Spain, under eight hydrological projections which represent futureclimate change scenarios. The results show that it is possible to reduce future water scarcityproblems and, hence, improve system performance. In addition to this, it is found that optimalreduction sequence is not only affected by water productivity, but also by the system topologywhich influences reliability. In the case study, the most sensitive demands are those located atthe river head. As such demands have no alternative sources, they typically offer the lowestdegree of reliability.

Water Resour ManageDOI 10.1007/s11269-014-0882-x

A. Chavez-Jimenez (*)Department of Civil Engineering, University of Piura, Piura, Perue-mail: adriadna.chavez@udep.pe

A. Chavez-Jimenez : A. Granados : L. Garrote : F. Martín-CarrascoDepartment of Civil Engineering: Hydraulic and Energy Engineering, Technical University of Madrid,Madrid, Spain

A. Granadose-mail: a.granados@upm.es

L. Garrotee-mail: l.garrote@upm.es

F. Martín-Carrascoe-mail: f.martin@upm.es

Keywords Climate change .Adaptationmeasures . Irrigationdemand .Water resources system .

Reliability indicators .Water productivity

1 Introduction

Studies have predicted a reduction in the availability of water resources at the end of thetwenty-first century that would intensify current water scarcity problems (Alcamo et al. 2007;Alcamo et al. 2003; IPCC 2013). As a consequence of this, a redistribution of water resourcestowards the highest priority uses will be necessary (Iglesias et al. 2011a; Pahl-Wostl 2007),with agriculture being the most affected sector given that it is a lower-value use and that itmakes a strong use of water resources (Fischer et al. 2007). Therefore, the proposal ofadaptation measures to minimise the effects of climate change on water resources systems isnecessary, with such measures being either demand-side or supply-side oriented (Cheng andHu 2011; Garrote et al. 2014; Tarjuelo et al. 2010). Of the several adaptation measures someare specific for the agricultural sector such as: water pricing, water use restrictions, improve-ment of water use efficiency, incentives to facilitate adaptation, water reuse, shifting to lesswater-requiring crops and fallowing, among others (Howden et al. 2007; Iglesias et al. 2011b;Purkey et al. 2007; Wheida and Verhoeven 2007; Yilmaz et al. 2008). The joint application ofadaptation measures may result in both a higher water saving and an improvement in theefficiency of each one (El Chami et al. 2011; Dworak et al. 2007; Mehta et al. 2013). Watersaving measures could be insufficient to cope with the strong reductions in wateravailability anticipated in climate change scenarios. One immediate action to addresssuch a decrease in water availability is the reduction of irrigation-demand volumes.For instance, an analysis of the Apulia Region (Italy) shows that the irrigated areaunder climate change projections would be reduced from 31% to 22% of the totalagricultural land (D’Agostino et al. 2014).

This paper is focused on such an immediate action through offering a methodologyfor identifying the required reduction of water allocated to irrigation demands to reacha satisfactory behaviour of the system, as well as the sequences in which allocationsare required to be reduced. The assessment of this behaviour is performed through useof reliability indicators. The demand satisfaction index (I1) and the demand reliabilityindex under climate change (I2p) (Chavez-Jimenez et al. 2013) are used. As thereduction of water allocation entails an economic impact, the proposed methodologyincludes not only the functional validation but also an economic approach thatconsiders water productivity. Water productivity is widely used as an indicator forassessing the economic value of water (Behera et al. 2012; García-Vila et al. 2008;George et al. 2011; Molden et al. 2010). Identification of the required reduction ofwater allocation to irrigation demands would make it possible to determine the impactof climate change on agriculture and provide criteria to set the most convenientsocioeconomic adaptation measures.

2 Methodology

The methodology is based on an iterative procedure that identifies the sequence for reducingwater allocation to irrigation demands, towards satisfactory system behaviour under a climatechange scenario. The system behaviour is estimated by assessing water scarcity problems inthe system through the use of indicators and water productivity.

A. Chavez-Jimenez et al.

2.1 Step 1: Generation of a Set of Future Hydrologic Projections

The selection of a set of future hydrologic projections aims to represent the climate changeeffect on future streamflows. The methodology selected to obtain these projections is thatproposed in Chavez-Jimenez et al. (2013). In this methodology, the projections are builtthrough perturbing the streamflows that characterise the current control period. Alterationfactors of the mean and the coefficient of variation (Δμ, ΔCV) result from comparison of thePRUDENCE (2007) future streamflows with the control period ones.

For the future period scenarios the long-term streamflow series change, though the currentstorage volumes and water demands remain constant. In the water scarcity regions of Spain itis held that total allocation to irrigation in the future will not rise, as it is linked to long-termadministrative concessions that are not envisaged to increase. If there were a modification inthe crop water requirements or in the water availability, the crop patterns or the cultivated areawould be adapted to the volume of water allocated. For urban demands, the increment in thefuture would imply a relatively small change in total requirement that would not alter theresults in the distribution of water resources.

2.2 Step 2: Generation of Alternatives

At the beginning of each iteration a set of alternatives is computed. Each alternative isgenerated by reducing water allocated to one of the irrigation demands by a small fraction.System behaviour is then assessed and the alternative which leads to best system performanceis chosen.

The economic aspect also influences the selection of the most appropriate alternative. Thisaspect is measured through the water productivity (WP) indicator which is usually expressedas the agricultural production per unit volume of water (van Halsema and Vincent 2012;Playán and Mateos 2006). This could be calculated by different methods, depending on theavailability of data and the objectives of the researcher. Water productivity is influenced byseveral variables, including climate change (Chen et al. 2010; Molden et al. 2010), by whichfuture values may vary with respect to the present ones. This study is based on current waterproductivity values for assessing future scenarios, given that projecting future changes in waterproductivity is outside the scope of the analysis.

Given a water resource system which has to meet "n" irrigation demands (IDs), thegeneration of alternatives is provided by Eq.1, with the number of generated alternativesbeing equal to the number of irrigation demands of the system.

IDmodtc ¼ IDt

c−VWRc

∀IDtc≥VWRc

ð1Þ

where ID is the initial allocated volume, VWR is the volume of water reduction and IDmod isthe allocated volume after applying the reduction measures. The scripts c and t identify thealternative (c=1,2,..,n) and the number of the iteration, respectively. VWR is given by Eq.2:

VWRc ¼ C

WPcð2Þ

whereWPc is water productivity (€/m3) for the ID. VWR varies depending on the WP. The IDs

with low-productivity values are penalised with greater reductions than those with high ones.C is the reference cost, which sets the size of VWR. Given that large values of C produce largeVWR, intermediate reduction steps are lost which results in a non-optimal sequence. On the

Water Allocation to Irrigation Demands under Climate Change

contrary, small values of C result in small VWR, which extends the iteration process withoutadding any relevant information. The value of C depends on the analysis scale.

2.3 Step 3: Water Resource Allocation

The allocation of water resources considers the physical characteristics of the water resourcesystem and the criteria set by the basin manager, such as the priorities in meeting the systemdemands and the operational restrictions set by the regulations. This simulation was carried outwith the OPTIGES model which is an optimisation module of the program AQUATOOL(Andreu et al. 1996). The allocation of water resources is made for the complete set of “n”generated alternatives, resulting in a set of "n" series of monthly supply volumes for each wateruse.

2.4 Step 4: Selection the best Behaviour

Selection of the best behaviour is performed as follows:

a) Characterisation of the system behaviour for each alternative is based on the analysis ofthe reliabilities with which demands are met. To that end, two performance metrics wereused: the demand satisfaction index (I1) and the demand-reliability index under climatechange (I2p) (Chavez-Jimenez et al. 2013). I1 allows assessing the system capability tomeet demands (Eq.3), while I2p quantifies the reliability of the system to satisfy demands(Eq.7). The determination of these indicators is based on information obtained from thedemand reliability (DR) curve. This curve represents the accumulated volume suppliedwith a given or greater reliability. For more information about this curve and how it is builtsee Martin-Carrasco et al. (2012) and Chavez-Jimenez et al. (2013).

I1 ¼Xk¼1

K

αkβk I1k ð3Þ

Where k identifies a water use (k=1,2,3,…,K), K is the number of water uses in thesystem, I1k is the indicator of satisfaction of each water use “k” (Eq.4); αk is the relativeweight of each water use “k” (Eq.5); and βk is the relevance weight. The relevance weightis assigned subjectively, depending on the importance given by the basin manager. βkvalues are assigned with the restriction that the aggregation of all relative and relevanceweight has to be one (Eq.6).

I1k ¼ SkDk

ð4Þ

αk ¼ DkXk¼1

K

Dk

ð5Þ

Xk¼1

K

αkβk ¼ 1 ð6Þ

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With Sk being the average amount of water supplied to water use “k”, regardless ofreliability (Mm3/yr), and Dk the average amount of water required by water use “k”(Mm3/yr)

I2p ¼Xk¼1

K

αkβk I2pk ð7Þ

Where I2pk is the demand-reliability index under climate change for each water use k(Eq.8):

I2pk ¼

Z0

Rk

F Gð ÞkdRk

Dk � Rk¼ ARk

DRkð8Þ

Where F(G)k is the DR curve function, ARk the area below the DR curve forreliabilities ranging from 0% to acceptable reliability (Rk), and DRk is the product ofthe demand Dk and the acceptable reliability Rk. The reliability is understood as theprobability that the system will be able, adequately, to satisfy the demand. An acceptablelevel of reliability is set for each water use “k”.

The joint use of these indicators (I1 and I2p) allows the identification of water scarcityproblems and their classification depending on their intensity by accounting for therelation between the amount and the quality of water supply to the system. Problemscan range from very serious (I1 and I2p below 0.6) to a system without water scarcityproblems (I1 and I2p equal or close to one).

b) Quantification of improvements in system behaviour by calculating the module (Mct)

(Eq.9). This module compares the current iteration t and the immediately previous one t-1.

Mtc ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiI t1c−I

t−11

� �2 þ I t2pc−It−12p

� �2r

∀ I t1c−It−11

� �> 0; I t2pc−I

t−12p

� �> 0 ð9Þ

where Mct is the module for alternative c in iteration t, I1c

t is the value of I1 for alternativec in iteration t, I1

t-1 is the value of I1 in iteration t-1, I2pct is the value of I2p for alternative c

in iteration t and I2pt-1 is the value of I2p for iteration t-1.

c) Selection of best behaviour. The alternative c with maximum Mct (Max(Mc

t )) is that inwhich the reduction of allocation to irrigation demand (IDc) minimizes the climate changeeffects.

2.5 Step 5: Assessment of the System Behaviour Under Criterion of Satisfactory Performance

It may be asserted that a given system presents satisfactory performance when it does not haveto address water scarcity problems, that is to say, when I1 and I2p are equal to one. However,due to the system characteristics and intensity of the climate change effects, among others, thisoptimal behaviour may vary according to the basin manager criteria and the assumable risks,with it being possible to consider flexible limits under water shortages (Shao et al. 2008), thussatisfactory performances (SP) with values of I1 and I2p lower than one could also be used.

The analysis ends when the indicator I1ct , which corresponds to the selected alternative,

reaches a value I1ct ≥SP. On the contrary, if I1c

t <SP a new iteration has to be performed.

Water Allocation to Irrigation Demands under Climate Change

Once the analysis finishes, the reduction sequence of the IDs is given by the selectedalternatives in each iteration. The percentage of reduction that leads to satisfactory perfor-mance is the sum of the reductions performed at each iteration in relation to the total irrigationdemand at the beginning.

The reduction of the IDs produces variation in the total production (TP) of the basin. ThisTP is determined as the sum of the multiplication of the supplied volume for each ID by theWP at each iteration (Eq.10):

TP ¼Xj¼1

t Xi¼1

n

Si j �WPi j ð10Þ

where i represents the ID (i=1,2…n), j represents the iteration number (j=1,2…t), Sij representsthe supply with which IDi is met in iteration j and WPij is water productivity of IDi in iterationj. Under the assumption that the basin has reached its maximum water saving efficiency,current demanded water is the required volume to reach the maximum water productivity(WPmax). The reduction of allocation to this demand entails a reduction of water productivity.This effect is characterised with a logistic function (Eq.11) (Fig. 1), (Geerts and Raes 2009;Hanks 1974). Three different sections may be distinguished in the curve:

& Section a: ID is met with low reliability. In this section the WP does not improvesignificantly regarding improvements in the reliabilities.

Fig. 1 Logistic function

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& Section b: Once a minimum reliability is over the WP grows significantly when reliabilityincreases.

& Section c: ID is met with high reliability, as WP is close to WPmax.

WP ¼ WPmax1

1þ e−24� Rk−CPð Þ

� �ð11Þ

where the CP is the central point of the logistic function. The selection of the CP value isrelated to the minimum reliability levels. For example, as shown in Fig. 1, CP values higherthan 0.6 (Curve 1) entails that for a given WP the IDs must be met with higher reliabilities,while values smaller that 0.6 (Curve 2) are required to satisfy the IDs with lower reliabilities.This point depends on the crop pattern, since drought-sensitive crops behave as Curve 1 doesand drought-tolerant crops as Curve 2.

3 The Case Study

The methodology has been applied to the Guadalquivir Basin. This basin, located in the southof Spain (Fig. 2), covers an area of 5.75 Mha. Currently, natural surface water resources in thebasin yield up to 6840 Mm3/yr from which only 40% is available for use (Martin-Ortega et al.2011). In the year 2002 the gross consumption of water (for urban and irrigation uses) wasestimated at 2858 Mm3, which is higher than the available resources (Berbel et al. 2011). Theimbalance between water resource availability and demand produces water scarcity problems

Fig. 2 Location of the Guadalquivir Basin. Spatial distribution and water productivity (€/m3) of the IDs. G-WP 1represents WP between 0 and 0.09, G-WP 2 between 0.25 and 0.26, G-WP 3 between 0.29 and 0.37, and G-WP4 between 0.48 and 0.49

Water Allocation to Irrigation Demands under Climate Change

(Bhat and Blomquist 2004; Chavez-Jimenez et al. 2013). One of the main reasons for thisimbalance is the high percentage of water resources used in agriculture, up to 90% on average(Montesinos et al. 2011).

There are 883,000 ha of equipped irrigable area in the basin, of which an average of846,000 ha are at present irrigated. The main crops are cotton, maize, olives, rice, vegetablesand winter cereals. The irrigation systems are drip irrigation (66%), surface irrigation (22%)and sprinkler irrigation (12)% (MAGRAMA-CHG 2013). Regarding irrigation efficiency,several irrigation districts are undergoing a modernisation process (Rodríguez Díaz et al.2007).

The required information for modelling the basin was taken from the River BasinManagement Plan (MAGRAMA-CHG 2013). The model topology is made up of 48 pointsthat represent the hydrological inflow (the mean annual value is 6840 Mm3/yr), 35 dams with areservoir capacity of 6495 Mm3, 23 points of agricultural demand (2583 Mm3/yr) and fivepoints of urban demand (275 Mm3/yr). The monthly streamflow data for the control period(1960 to 1990) were taken from the Modelling Rainfall-Streamflows Integrated System(SIMPA) (Estrela and Quintas 1996).

The last assessments of climate change in the twenty-first century for the GuadalquivirBasin suggest an increment in temperature and reduction in rainfall (IPCC 2013; García-Ruizet al. 2011; Martin-Ortega et al. 2011). García-Ruiz et al. (2011) predict an increase of 2.2°C intemperature and a 14% reduction in rainfall for the period 2040–2070. As a consequence, thereduction in discharges from numerous rivers in the basin accelerated towards the turn of thecentury (García de Jalón et al. 2013). Furthermore, a study on the Guadiana Menor sub-basinpredicts that a mean temperature rise of 1°C would produce an increment between 15-20% inseasonal irrigation requirements by the year 2050, depending on the location and the croppingpattern (Pulido-Calvo et al. 2012; Rodríguez Díaz et al. 2007). These changes would produce areduction in water resources availability.

For this work, eight hydrologic projections (HPs) were selected from the 29 HPs generatedin the study of Chavez-Jimenez et al. (2013), to represent future streamflows under climatechange scenarios. The selected HPs are shown in Table 1. Six HPs correspond to the A2emissions scenario and the other two to the B2. The general trend is a reduction of the average

Table 1 Alterations for the mean and coefficient of variation of annual stream flow. Period 2071–2100. Source:(Chavez-Jimenez et al. 2013)

Acronym of models Δμ ΔCV

ICTP-A2 −8 26

MPI-A2 −43 14

DMI2-A2 −47 61

DMI1-A2 −50 −50ETH-A2 −61 93

SMHI-A2 −65 40

DMI1-B2 −41 −37SMHI-B2 −44 15

Regionalised climate projections though a single global model: PRUDENCE-HadAM3. ICTP=InternationalCentre for Theoretical Physics (RegCM)*; MPI= Max Planck Institute (REMO)*; DMI=Meteorological Instituteof Denmark (HIRHAM)*; ETH=Zurich Polytechnic School (CHRM)*; SMHI=Meteorological and HydrologicalInstitute of Sweden (RCAO)* * Regional climate model used A2 and B2 are Emission scenario (IPCC)

A. Chavez-Jimenez et al.

streamflows with an increment of their variability, with the exception of the projections DMI1(A2 and B2) which present a reduction in variability too.

The water productivity values were taken from a study performed by Rodríguez et al.(2008) (Table 2). These values were calculated as the net production per unit area divided bythe supplied volume per unit area. Fig 2 shows the spatial distribution of water productivitiesaccording to four groups (G-WP). Most of the IDs (71%) present a WP of 0.25 €/m3 (G-WP2), and most are supplied with water resources from the main river. The lowest WP (0.09 €/m3)belongs to ID-10 Bembezar, located on the right bank of the basin, while the highest WP (0.48to 0.49 €/m3) to ID-11 Cacin, ID7 Alto Genil and ID-14 Guadajoz, all on the left bank of theriver (Fig. 2). The low WP value is due to the low efficient use of water resources, lowagricultural performance and large extensions of low added-value crops (Rodríguez et al.2008).

4 Results

The results of applying the proposed methodology to the control and future periods arepresented below. The methodology was applied under the criteria that follow: 1) the assump-tion that the basin had reached its maximum efficiency in the use of water; 2) selection assatisfactory behaviour of a system without water scarcity problems (I1=1 and I2p=1); 3) actionson urban demand were not taken into account in identifying the improvement achieved byreducing only the water allocated to irrigation.

Figure 3 (left) shows the improvement of indicators I1 and I2p through the progressivereduction of the IDs according to the described methodology. The serious and highly seriouswater scarcity problems that could arise under future HPs can be reduced or even eliminated.Despite the achieved improvement on all HPs, it was not possible to meet the desiredsatisfactory behaviour in all cases.

Figure 3 (right) shows the improvement trajectory followed by I1 and I2p as a consequenceof the progressive ID reductions. As may be observed, this trajectory is highly similar for both

Table 2 Volume of irrigation demands, water productivity (WP) and volume of water reduction (VWR).C=1412500 €

ID Code Volume WP VWR ID Code Volume WP VWR

Mm3/yr €/m3 Mm3/yr Mm3/yr €/m3 Mm3/yr

Alto GuadianaMenor

DR-1 48.9 0.31 4.56 Guadalmellato DR-18 74 0.25 5.65

Alto Genil DR-7 100 0.48 2.94 Guadalmena DR-19 16.2 0.25 5.65

Bajo Genil DR-8 165.6 0.25 5.65 GuadianaMenor DR-20 13.3 0.25 5.65

Bajo Guadalquivir DR-9 976.1 0.25 5.65 Jándula-Guadajoz DR-21 156.8 0.25 5.65

Bembézar DR-10 135.7 0.09 15.69 Rumblar DR-22 39.8 0.29 4.87

Cacin DR-11 41 0.48 2.94 Salado de Morón DR-23 14 0.37 3.82

Fardes DR-12 33.7 0.26 5.43 Sierra Boyera DR-24 7.2 0.25 5.65

Genil Cabra DR-13 96.1 0.25 5.65 Valle Inferior DR-25 215 0.25 5.65

Guadajoz DR-14 24.2 0.49 2.88 Vegas Bajas DR-26 82.7 0.25 5.65

Guadajoz-Genil DR-15 58.5 0.25 5.65 Vegas Medias DR-27 53.8 0.25 5.65

Guadalentín DR-16 41.7 0.25 5.65 VegasAltas DR-28 41.9 0.25 5.65

Guadalimar DR-17 45.9 0.25 5.65 Viar DR-29 101 0.26 5.43

Water Allocation to Irrigation Demands under Climate Change

the control period and HP regardless of the initial point, which suggests that the trajectory isrepresenting the optimal improvement sequence for the basin.

Figure 4 (left) shows the percentage reduction of ID required to meet different values of I1.As may be appreciated, the required reduction varies within a wide range depending on the HPused. For example, if at the end of the twenty-first century the basin is required to have asimilar behaviour to the present (point A), a reduction between 20% and 45% (points B and C)will be required. These ID reductions will be necessary for average streamflow decreases thatrange from 8% to 50%, given by the selected HPs (Table 1) with the exception of ETH-A2 andSMHI-A2. In such cases, average streamflow decrease is so strong, 61% and 65%, that it is notpossible to achieve behaviour similar to the present one (points D and E).

Considering projections where a performance similar to the present could be reached, thoserelated to the A2 emissions scenario required larger adjustments than those related to the B2.For example, the DMI1 projections required ID reductions of 31% and 21% for scenarios A2and B2 respectively.

Fig. 3 Water scarcity problems before and after the application of the ID reduction of water allocation. Blacksquares represent the value of I1 and I2p before reducing the ID (NO ADAPT) and grey circles the value of I1 andI2p after the reduction (ADAPT) (left), and Improvement trajectories followed by I1 and I2p, for control and futureperiod (right)

Fig. 4 The percentages reduction of water allocation of IDs for different I1 value (left) and Total production fordifferent I1 values (right)

A. Chavez-Jimenez et al.

Figure 4 (right) shows the variation of the total production in relation with I1 values. Theseresults were calculated based on a logistic function of CP=0.6 and Rk=85%. The general trendfor all projections responds to the organised reduction of water allocation towards bettersystem behaviour. As can be seen, there is an initial increase of the total production, that isrelated to the improvement of the reliability with which the IDs are met; then the maximumproduction remains constant as the improvement in reliability is balanced with the reduction inthe irrigated area; and finally there is a section of progressive decrease, because furtherimprovements in reliability do not produce a significant upturn in water productivity.

It was found that the reduction sequence shown in Fig. 4 is not only a function of the WP,but also of the reliabilities with which such IDs are met and the system topology.

The demands located in the upper course of the respective rivers, generally with lowerreliabilities, are the first that were reduced and the first that reached their maximum reductionvolume (MVR). This is because the sources for satisfying their demands are limited to their ownsub-basin. Additionally, the reduction in allocation to these demands benefits those others locateddownstream which may use the new resources to strengthen their reliability. On another note, IDslocated at the basinmouth are reduced in the latter iterations, given that a reduction in the allocationto demands produces only local benefits and does not improve the upstream areas. Therefore, thesystem topology plays an important role in the determination of the reduction sequence.

This effect is shown in Fig. 5. Figure 5 (a-f) presents the reduction sequences under theprojections DMI1-A2. As can be seen, the first ID that is reduced is ID-10 (Iter-1), because of alow reliability (55%-75%, G-R2) and high VWR (15 hm3) which results from its low WP(0.09 €/m3). As the iterative process continues, other IDs are then reduced, with some evenreaching their MVR. In the last iteration (Iter-241) it is observed that while almost all IDslocated on the upper course of the river network reached their MVR, those located on the maincourse and at the basin mouth (ID-9 and ID-23) remained unchanged.

Figure 5 (g-l) presents how reliabilities improved throughout the iterative process. SeveralIDs started with low and significantly low reliabilities of under 55% (G-R1) or of between55% and 70% (G-R2), and ended in reliabilities of over 85% (G-R4) in iteration 241.

5 Discussion

The discussion on the proposed methodology should be interpreted considering that this hassome simplifications and limitations. The optimisation procedure does not follow a pure jointoptimization formulation, where economic impacts of water shortages are directly taken intoaccount. An iterative sequential approach is followed which combines the water resourcesoptimization model based on water shortages with economic considerations based on availablevalues of water productivity in the irrigation districts. Despite this limitation, the methodologyallows identification of the reduction levels that provides an improvement in the systemperformance towards better water resources management. Climate change scenarios have beenintroduced in a highly simplified way, since only changes in runoff have been considered.Many other factors would also change under future climate scenarios. These include not onlynatural variables relevant for agriculture, such as temperature or potential evapotranspiration,but also socioeconomic variables, like population, per capita water consumption, environmen-tal awareness, land use, irrigated area, cropping pattern and international food markets, whichwould affect water allocation and agricultural productivity. The study has been undertakenunder strong simplifying assumptions. Maximum water efficiency in agricultural use has beenassumed, achieving the optimum production with the available water. Under Spanish regula-tion, the use of water is linked to administrative concessions. Farmers develop adaptive

Water Allocation to Irrigation Demands under Climate Change

practices to manage the water allocated to them, depending on various factors, like climate,subsidies and markets. If there were a modification in the amount of water allocated, cropalternatives and the size of cultivated area would be adapted to the volume of water provided tomaximise benefit. Moreover, the methodology assumes that water productivities will remainconstant in the future (with the known values of the control period) and that water useefficiency is the highest possible, with the consequence being that reduction measures arenecessary to cope with the resources decrease. Given that the basin is currently undergoing a

Fig. 5 Figures a to f show the reduction sequence of water allocation the IDs in different iterations (Iter), underthe HP-DMI1-A2. IDs affected by reductions are marked with grey rhombus, those that reached their MVR withblack rhombus, and those which remained unchanged with white squares. Figures g to I show, the reliabilities ofeach ID in different iterations

A. Chavez-Jimenez et al.

modernisation process to accomplish better use of water resources (Berbel et al. 2011;Rodríguez Díaz et al. 2007), water productivities may change. It should also be noted thatthe reduction of water allocation for irrigation not only has an economic aspect but also asocial one (Berbel and Gómez-Limón 2000) which is not considered in this study. All of thisaside, it could be argued that the results provide relevant information for identifying adaptationmeasures under climate change and that the methodology may be used as a helpful tool for thedecision-making process in water resources management.

Due to water scarcity problems existing in several regions, mainly the imbalance betweenwater resource availability and demands, the necessity of water saving is evident (Dworaket al. 2007). According to Strosser et al. (2007) the water saving potential reachable in 2030 inthe Guadalquivir Basin is 35%. However, at the end of the twenty-first century thesereductions could be insufficient in facing the impact of climate change on streamflows.

Chavez-Jimenez et al. (2013) analysed 29 possible future streamflow scenarios (for theperiod 2071–2100), with the results showing that the Guadalquivir Basin may face reductionsof between 8% and 81% depending on the climate model used. One immediate action forcoping with such strong reductions, once the maximum water efficiency is reached, is toreduce the water allocated to irrigation demands. The proposed methodology makes it possibleto determine the required reduction and the sequence to be followed. The analysis of differentHPs enables consideration of the uncertainty coming from the climate models

The reduction sequences under distinct projections follow a similar trend in which twotendencies may be noted (Fig. 4-left). The first is a continued improvement of the indicator I1while allocations to demands were reduced. This improvement is almost linear and lasts untilI1 is located either close to or in the favourable section. Then the marginal improvement decaysand the path tends to be vertical. In this section, further ID reductions are not as effective as theprevious ones. It may also be observed that the slopes for the diverse projections were slightlydifferent. The differences arise due to the coefficient of variation that characterised eachprojection, which influenced the reliability with which the IDs were met, resulting in a fasteror slower I1 improvement.

The maximum I1 values that could be achieved on the basin are between 0.90 and 0.96,requiring different percentages of ID reductions. While these improvements led to a satisfac-tory system performance, they did not reach absolutely satisfactory behaviour (I1=1 whichrepresents a null deficit). Such behaviour cannot be reached for the control period either. Thisis due to the characteristics of the Guadalquivir Basin. The strong reductions obtained are notparticularly different from the actions taken in 1995, when farmers were obliged to stopirrigating after a prolonged drought that lasted from 1992 to 1996 (Camacho Poyato 1995).

The reduction of the IDs that led to an improvement in system behaviour (see Fig. 4-left) isrequired to follow a certain sequence. This sequence is influenced not only bywater productivitiesbut also by the system topology which affects the reliabilities with which demand may be met.

In order to assess this effect, an additional procedure (AMP) was performed, where the IDswere reduced on the sole basis of water productivity, that is to say, the IDs with lower waterproductivities are those reduced first (Fig. 6-left). Under the AMP methodology the pathchanges, including another tendency which deviates from the optimal. In such a case, threetendencies were observed: a first part where the reduction of the IDs produce progressiveimprovements of I1 (similar to that of the proposed methodology); a second part where theimprovement is negligible despite the strong reductions; and a third part which presentssignificant improvements for small reductions. This change in shape under the AMPmethodology, from concavity to convexity, shows that the sequence does not followan optimal trajectory because it prioritises reductions which do not result in anyimprovement in performance.

Water Allocation to Irrigation Demands under Climate Change

As can be observed by comparing the results of Fig. 4 (left) and Fig. 6 (left), the proposedmethodology required a smaller reduction of the IDs than the AMP to accomplish a certain I1value. For example, to reach a similar behaviour to the current one, with the proposedmethodology a reduction of the IDs of between 20% and 45% is required (points B and C),while with the AMP the reduction would be between 21% and 90% (points L and M).

The advantages of the proposed methodology with respect to the AMP are also clear whencomparing Fig. 4 (right) and Fig. 6 (right). In addition to this, the AMP results present a similarinitial behaviour, but after the maximum undergo a sudden drop as a consequence of the strongvolume reductions due to targeting only the WP goal. For example, for accomplishing systemperformance similar to the present one, under the proposed methodology, the total productiondecrease is limited on average to 26% (for six out of the eight hydrologic projections), whileunder the AMP methodology it falls to 59% on average (points O and P).

Figure 7 shows the accumulated reduction volumes according to the improvement of I1 forthe proposed methodology and the AMP for three different HPs, distinguishing the produc-tivity groups. The methodologies show a similar behaviour at the beginning, which is due inmany cases to the ID-10 being reduced first. After reducing this ID, the trends start to divergeand become highly different for the two procedures. As can be appreciated in Fig. 7 (left),under the ICTP-A2 for I1 between 0.83 and 0.85, only the IDs from G-WP 4 are reduced,despite the presence of IDs with a lower productivity (G-WP 2 and G-WP 3). This behaviour isalso present in different parts of the DMI1-A2 (I1 between 0.90 and 0.92) and the SMHI-B2 (I1between 0.71 and 0.73). It can be also observed that, under the proposed methodology, G-WP2 demands did not suffer a strong allocation reduction at the end of the process, while G-WP 3and G-WP 4 demands were completely reduced. On another note, under the AMP methodol-ogy (Fig. 7 right), the allocations to lower water productivity demands were reduced first,resulting in a sudden drop with no improvement on I1. These results indicate that adequatewater resources management should not focus only on water productivity but also on thereliabilities with which the demands were met and on the basin topology. In a similarway, the importance of the topology was stated by Berbel et al. (2010), whodetermined that the measures for reducing impact on water bodies depend on thelocation of demands and river interconnection.

Fig. 6 The percentages reduction of water allocation of IDs for different I1 value under AMP (left) and Totalproduction for I1 values under AMP (right)

A. Chavez-Jimenez et al.

6 Conclusions

This paper presents a methodology for identifying the optimal sequence of reduction of waterallocation to irrigation demands, in responding in the best manner to water resources reductionunder climate change. The identification of this sequence is performed through assessment of

Fig. 7 Accumulated reduction volumes related to I1 for three HPs. Proposed methodology (left) and AMPmethodology (right). G-WP 1 represents WP between 0 and 0.09, G-WP 2 between 0.25 and 0.26, G-WP 3between 0.29 and 0.37, and G-WP 4 between 0.48 and 0.49

Water Allocation to Irrigation Demands under Climate Change

water scarcity problems by means of reliability indicators and economic analysis of theadaptation measures using the water productivity.

The novelty of the approach consists on the combination of an indicator-based system forevaluation of the performance of water resources systems with economic considerations basedon the productivity of water in different irrigation districts. The methodology allows theidentification of the optimal path of progressive adaptation to climate change in complexwater resource systems with a majority of agricultural demands. Results have shown that thetopology of the river network and the irregular distribution of water resources, reservoirs anddemands may modify the intuitive solution of reducing first those demands with lessproductivity.

This methodology was applied at the Guadalquivir Basin, one of the largest in Spain, andconsiders eight future hydrologic projections with average streamflow reductions ranging from8% to 61%. As a result, it was found that the predicted resource reductions may be addressedby reducing the allocation to current irrigation demands. Furthermore, it was observed that thisadaptation process may entail increasing the total production by means of improving thesystem performance and reliability with which demands were met.

The analysis of the sequence for reducing allocation to irrigation demands for the hydro-logic projections showed that such a sequence depends not only on the water productivity butalso on the reliabilities and system topology. For the Guadalquivir Basin it was found that theirrigation demands located at the riverheads were reduced first (given that they are moresensitive to generating improvements than the rest of basin), while those located at the basinmouth are the last (with only local improvements).

While it is acknowledged that it does have certain limitations, the methodology could beapplied to other systems given that it is based on easily understandable indicators. In additionto this, as it requires only general data for characterising the system studied, it could also beapplied to regions where information is incomplete.

Acknowledgments The authors wish to express their gratitude for financial support received from VIAGUA(410AC0399), funded by the Ibero-American Program for Scientific and Technological Development(CYTED)and from the European Commission BASE project (Grant agreement no: ENV-308337) of the 7thFramework Programme. The help of Andrew Selby in the proofreading of the manuscript is gratefullyacknowledged.

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