Priority Water Rights for Irrigation at the River Basin Level. Do They Improve Economic Efficiency During Drought Periods?

This paper assesses the potential efficiency gains of reforming the water rights regime in the Spanish agricultural sector by replacing current allocation procedures based on the proportional rule with a priority allocation procedure based on two tiers of security-differentiated water rights. This assessment is useful for evaluating whether said change in water rights can be considered a suitable policy instrument to improve water management during droughts events. For this purpose, a mathematical programming model is built to simulate the performance of the proposed reform. The empirical analysis is implemented at the basin scale, where water rights holders are highly heterogeneous, considering different climate scenarios accounting for changes in water supply reliability. The Guadalquivir River Basin (GRB) in southern Spain is used as a case study. The results obtained show that this change in the water allocation regime would yield only modest economic efficiency gains under the current climate scenario. However, it is also evidenced that this policy instrument could play a more relevant role as an efficiency enhancer in a climate change scenario, given that more frequent and intense drought episodes are expected. Moreover, priority rights represent an interesting risk management instrument for farmers, allowing the most vulnerable farmers to reduce income volatility. These findings suggest that the combined implementation of the proposed shift in the allocation regime with spot or allocation water markets would lead to successful outcomes, significantly improving drought management in the irrigation sector.


Introduction and Objectives
Existing water rights allocation regimes are the result of local historical trajectories, which often go back centuries (OECD 2015). This is why these allocation regimes do not usually align with society's current priorities, which reflect the growing demand for water for urban and economic 1 3 uses, and a focus on ecosystem services (e.g., ecological flows), as opposed to the traditional allocation where agriculture is the largest user. This mismatch of current water allocation and society's priorities is an important source of inefficiency that policy-makers and water managers must seek to minimize. For this reason, various international organizations have raised the need to reform these allocation regimes to achieve a more efficient and sustainable allocation of increasingly scarce water resources (e.g., Bruns et al. 2005;Hodgson 2006;OECD 2015).
Inefficiency in water use becomes especially acute during cyclical scarcity events (i.e., droughts), when matching supply and demand is a major challenge (Hanemann 2006). Under these circumstances, water managers have to ration water allocations until aggregate water supply equals water availability. There are two main alternative approaches to water rationing (Sechi and Zucca 2015;Degefu and He 2016;OECD 2016): proportional and priority rules. The proportional rule is the most widely-used procedure for water rationing among water rights holders, especially in countries with more traditional water institutions. According to this rule, all water rights holders receive a quantity of water proportional to their water rights, calculated so that total allocations equals total water availability. This is the rule currently applied in Spain to ration water among agricultural water rights holders (i.e., farmers) during drought periods. On the other hand, the priority rule is used to ration water in the Western US and Australia. This rule ensures the demands of the highest priority rights holders are met first, and once they are fully satisfied, the remaining resource is allocated to the other rights holders in decreasing order of priority. Gómez-Limón et al. (2020) discuss the advantages and disadvantages of both allocation rules. They present a wide range of empirical evidence pointing to the implementation of the proportional rule as a source of inefficiency in the irrigation sector (e.g., Alarcón et al. 2014;Martínez and Esteban 2014;Goetz et al. 2017;Rightnar and Dinar 2020). In fact, the literature suggests that allocation regimes based on priority rights (or security-differentiated water rights) are a suitable alternative to proportional rights since they enable more efficient and sustainable water use (e.g., Freebairn and Quiggin 2006;Lefebvre et al. 2012).
The abovementioned evidence points to the need to reform water allocation regimes currently based on the proportional rule, introducing water rights regimes with different priority levels. Theoretically, this reform would enhance water use efficiency since the aggregate profit gains obtained by water rights holders with higher priority (more reliable supply) would outweigh the aggregate losses suffered by holders with lower priority (less reliable supply). These efficiency gains would be especially critical during drought periods, allowing the scarce resources to be allocated to the highest value-added users. For this reason, security-differentiated water rights are considered an adaptation measure to climate change (Xu et al. 2014;Mallawaarachchi et al. 2020), given that more frequent and intense cyclical water shortages are expected (Bisselink et al. 2018).
However, there is scarce empirical evidence of the efficiency gains that can be achieved by shifting away from proportional allocation towards a priority rule allowing the implementation of security-differentiated water rights. To the best of the authors' knowledge, the only relevant study in this sense is the one by Gómez-Limón et al. (2021), who assessed the efficiency gains achieved through the implementation of the priority rule with two priority rights levels within an irrigation district. However, the improvement in economic efficiency compared to the proportional rule was almost negligible. They conclude that this disappointing result could be due to the lack of heterogeneity in water rights holders (i.e., farmers) within a single irrigation district and the fact that the supply of irrigation water allocations in the irrigation district considered as a case study is fairly reliable (in more than 70% of the years, annual water allocations meet farmers' demands for their crop mixes).
In light of the situation described above, this paper aims to contribute to the existing literature by testing two hypotheses regarding the implementation of priority rights in the irrigation sector. The first is the hypothesis that replacing a water allocation regime based on proportional rights with another regime based on two levels of priority rights would significantly increase economic efficiency when this change is implemented at the basin level, where there is large heterogeneity among agricultural water rights holders. The second hypothesis is that the less reliable the irrigation water supply (i.e., under more frequent and intense droughts due to climate change), the more significant the efficiency gains achieved due to the implementation of priority rights.
Therefore, the main objective of this paper is to test the two abovementioned hypotheses empirically. For this purpose, a mathematical programming simulation exercise is performed to assess the improvement in economic efficiency that could be achieved by replacing the current proportional rule with a priority allocation procedure based on two tiers of security-differentiated water rights. Moreover, the empirical analysis is implemented at the basin scale (i.e., heterogeneous rights holders), considering different climate scenarios (i.e., varying water supply reliability). To that end, we focus on the Guadalquivir River Basin (GRB) in southern Spain as a case study.

Water Allocation in Spain: a Proposal for Reform
All water resources in Spain are legally in the public domain. Water use for private activities is allowed through water rights granted by the river basin authorities (RBAs) under the terms of the River Basin Management Plans (RBMPs), according to which rights holders can extract water from a specific water body (river, aquifer, or reservoir) up to a maximum annual volume (full water allotment). However, the RBAs do not guarantee the availability of said maximum water volume every year. The volume of water actually available for each rights holder (annual water allocation) is set every year depending on the hydrological situation (water availability).
Annual water allocations granted to irrigation districts are managed as a common property resource through water user associations, where all farmers obtain the same amount of water per irrigated hectare. However, these farmers can distribute the water as they choose within their own farms.
When a drought occurs in Spain, the RBAs limit water allocations as stipulated by the RBMPs. Since urban uses have absolute priority over agricultural use (ranked as the second priority level), during drought periods, proportional water rationing is only applied to agricultural water rights holders, which account for most of the water rights in the Spanish basins.
This paper proposes a shift away from proportional allocation in agriculture towards a priority rule allowing the implementation of security-differentiated water rights at the basin level, similar to the Australian case. Thus, two priority classes are proposed, with a distinction between high-security or 'priority' rights and low-security or 'general' water rights. Farmers would be able to combine these two priority rights, creating a portfolio of water rights to achieve any desired level of reliability while minimizing the transaction costs involved in dynamically adapting to the optimal mix (Young and McColl 2003).
Initially, all farmers would be considered to hold general water rights, and only a certain share of total rights would be eligible for upgrade into priority rights through an auction procedure. In these auctions, the rights holders would bid to upgrade their rights through a surcharge on the annual payment to their basin authority. The total amount of money collected through these surcharges would be set aside to compensate all general rights holders in the basin for the decline in their supply reliability. Moreover, under the proposal simulated here, those who win the bid in the auction can hold priority rights forever, enabling long-term investment planning (e.g., fruit orchards or irrigation technology). In any case, our proposal also assumes that there would be a local water rights market allowing a dynamic allocation of these priority rights.
For the proposed change to be successful, the increase in farm profitability achieved by reliability winners must be higher than the surcharges they would have to pay, and the compensation received by reliability losers must outweigh their farm profitability losses. This condition would be met only if the change in allocation rule leads to an increase in economic efficiency, that is, if the aggregate profitability at the basin level increases.

The Irrigation Sector in the Guadalquivir River Basin
The Guadalquivir is a 650 km-long river in the south of the Iberian Peninsula. Its basin, which covers an area of 57,527 km 2 , has a typical Mediterranean climate (i.e., mild, wet winters and warm, dry summers) suitable for profitable irrigated agriculture (i.e., olives, other fruits, and vegetables). Annual precipitation usually ranges between 500 and 700 mm, although there are frequent drought episodes (less than 500 mm/year).
After several decades of intensive infrastructure construction to increase the availability of water resources, the basin is now administratively closed to new users (Berbel et al. 2013). As a result, the average water use in the GRB amounts to 3815 hm 3 per year, of which approximately 3357 hm 3 is used for irrigation (88% of the total water demand) and 379 hm 3 is used by households and for other urban demands (10%) (CHG 2015). Spanish water law stipulates that urban demands are served first in the event of a water shortage (priority rule), meaning such demands are always covered. However, during drought episodes, the scarce water resources available for agriculture are rationed among farmers, according to the proportional rule.
According to the most recent data available (MAPA 2020), the irrigated areas in the GRB can be classified into four different categories: a) Traditional irrigated areas with extensive annual crops (5% of the irrigated area in the GRB); b) Modern irrigated areas with intensive annual crops (40%); c) Olive groves (51%); and d) Rice paddies (4%). Considering these categories, we selected seven representative irrigation districts (IDs) in the GRB. Table 1 provides information about the main relevant features (area, number of farmers, main crop, and irrigation technology) of each ID. The next step after selecting the IDs was to identify the different production profiles at the farm level. In order to characterize the 1624 farms located in these IDs, primary information was obtained from a survey of 355 farmers selected using random route sampling. Data were collected on the farms' main production features (size, crop mix, production technology, yields, prices, and costs by crops) and the farmers' socio-demographic characteristics. Farms within each ID were divided into farm types (f), accounting for the heterogeneity in terms of profitability and productivity of water. This farm typology was determined by performing cluster analyses in each ID, using the percentage of the area devoted to each crop as differentiating variables. Table 1 shows the most relevant data for each farm type.
Complete primary information on farm types and crop data can be found in the supplementary material, along with other secondary sources also supporting the findings of this study. Table 2 presents data related to the irrigated area and full water allotment per ID category (Traditional, Modern, Olive, and Rice). It is worth noting that water rights are granted to each ID, allowing their farmers to receive water allocations that fully cover crop water needs in 'normal' hydrological years.

Annual Water Allocations in the GRB
However, because the GRB is located in a drought-prone region (the Mediterranean basin), water availability varies widely across hydrological years. This means that annual water allocations in each ID ( wa id ) are frequently lower than the full water allotments ( fwa id ) established in the water rights. In fact, annual water allocations in the GRB are stochastic variables, which Gómez-Limón (2020) characterized based on a stochastic hydrological model considering current water availability (rainfall, water run-off, and water storage in dams), water demands (existing water rights), and water management rules (e.g., minimum ecological flows) set out in the Guadalquivir RBMP (CHG 2015). This characterization yields the histogram shown in Fig. 2a.
Notwithstanding, the stochastic hydrological model developed by Gómez-Limón (2020) is only suitable for simulating near-future hydrological years, since it does not account for  feasible impacts of climate change at the basin level. In fact, the present study uses the outputs from that hydrological model solely to simulate the performance of the proposed priority rights regime under the 'current climate' scenario. Developing a hydrological model accounting for climate change is a complex task involving the use of simulated climate data reflecting different climate change scenarios for updated hydrological modeling estimating new distributions of rainfall and water inflows (e.g., Raju and Kumar 2018) and revised agronomic modeling estimating new irrigation water needs (e.g., Ewert et al. 2015). However, it is a challenge that goes far beyond the scope of this paper. The present study seeks to explore whether feasible changes in the climate would make priority rights a more suitable policy instrument to improve economic efficiency during drought episodes, assessing the role of this instrument in facilitating adaptation to climate change. For this exploratory assessment, we modified the hydrological model from Gómez-Limón (2020) in order to generate a feasible "climate change" scenario for the Spanish case according to the specialized literature (CEDEX 2017). To that end, we assumed climate change will involve more frequent drought episodes, thus increasing the probability of hydrological years with water shortages ( wa id < fwa id ) by 30%; and more intense drought episodes, increasing the gap fwa id − wa id in every hydrological year with a water shortage by 30%. In any case, it is worth noting that while the climate change scenario built by changing the abovementioned parameters is feasible, it is still hypothetical and its probability of occurrence is unknown. This modified modeling has allowed us to characterize the distribution of annual water allocations under the climate change scenario as shown in the histogram displayed in Fig. 2b. Table 2 presents data related to water allocations and gross margins per ID category and climate scenarios considering the implementation of the current proportional allocation rule for water rationing. It is worth noting here that recurrent drought episodes involve average water allocations below the full water allotments. This is especially true for the climate change scenario, where water resources become scarcer. The decrease in average water allocations also leads to lower gross margins, although the impact on farms' profitability is heterogeneous among IDs. Table 2 also shows the coefficients of variation of both

Modeling Approach
A mathematical programming model is built to simulate farmers' behavior under the proposed water rights regime. The simulation exercise enables a comparison of the potential performance of the proposed allocation regime with that of the current proportional allocation rule in terms of economic efficiency.

Proportional and Priority Allocation Rules
The basin (subscript b) taken as a case study is represented by a sample of seven IDs (subscript id), each of which has a different number of farm types (subscript f) which are considered as the decision-making units. Each farm type represents a number of farms nf id,f with an average size of s id,f irrigated hectares, with s id being the total irrigated area in each Moreover, each ID in the sample represents m id irrigation districts with similar features within the GRB, and s b is the total irrigated area in the basin Under current management rules, the annual aggregate volume of water available for irrigation at the basin level ( WA b measured in cubic meters) is shared among IDs proportionally according to the water rights granted to each district. In hydrological years when WA b is higher than or equal to the sum of water rights granted to every rights holder in the basin (full water allotment, FWA b ), the volume of water allocated to each ID is equal to the water rights granted ( FWA id ). In years when WA b is lower than FWA b , the volume allocated to each ID ( WA id ) is proportionally reduced as follows: Similarly, IDs share the water annually allocated proportionally among all their farm types, i.e., water allocations in cubic meters per hectare ( wa id,f ) are the same for all farm types within   (2020) the ID ( wa id,f = wa id , ∀f ), such that wa id = WA id ∕s id . Thus, the annual water allocation for farm type f measured in cubic meters is WA id,f = wa id ⋅ s id,f . Under the proposed new distribution rules, each farm type would hold water rights defined as portfolios of two different types of water rights, priority and general rights. Thus, the annual water allocation to each farm type measured in cubic meters would be calculated as the sum of the annual water allocation for holding priority and general water rights, as follows: where wapr id is the annual water allocation per hectare for every farm type within an ID for priority rights and wagr id is the same for general rights, while PR id,f and GR id,f are the shares of priority and general rights held by farm type id, f , which add up to one ( PR id,f + GR id,f = 1 ) for every farm type. This implies that the same identity applies at the ID level ( PR id + GR id = 1 ) and the basin level ( PR b + GR b = 1).
According to the latter expression, the volume of water annually allocated to each farm type measured in cubic meters per hectare is: It is worth explaining that the maximum or full water allotments per hectare and year for priority ( fwapr id ) and general ( fwagr id ) water rights are the same for every farm type within an ID, according to the water rights granted at the ID level. This means that fwa id = fwapr id = fwagr id .
The aggregate volume of water needed to satisfy all priority rights holders is denoted as FWAPR b , and is calculated as the sum of all priority rights in the basin: while the quantity annually available to allocate among priority rights holders ( WAPR b ) is: Likewise, FWAGR b and WAGR b denote the volume of water needed to fully meet water demands from all general rights holders and the water annually available to be allocated among these rights holders, respectively: The share of priority rights at the basin level ( PR b ) relates the aggregate volume of water needed to satisfy all priority rights holders ( FWAPR b ) to the aggregate volume of water needed to satisfy all water rights ( FWA b = FWAPR b + FWAGR b ) as follows: Priority rights are served first with the full water allotment granted to the corresponding ID ( fwa id ) as long as the water availability WA b is enough to cover all water demands from priority rights holders ( WA b ≥ FWAPR b or, following Eq. (8), WA b ≥ FWA b ⋅ PR b ). After that, the remaining water available for sharing is allocated proportionally among general rights holders. In years when there is not enough water to meet full allotments for priority rights, the available water is rationed among priority rights holders following the proportional rule according to their full water allotments. In these years, general rights holders would not receive any water.
The abovementioned priority allocation rules can be expressed mathematically considering the following formulae: In Eq. (9), when the aggregate volume of water available for irrigation at the basin level ( WA b ) is greater than or equal to the water requirements to satisfy all priority rights holders ( FWAPR b or FWA b ⋅ PR b ), priority rights holders receive allocations corresponding to the full water allotment for the ID ( fwa id ). General rights holders receive a proportion of their full water allotments. This proportion depends on how much water remains available for general rights related to the total volume of water needed to cover them ( ). Similarly, when there is not enough water available at the basin level to satisfy the demand from priority rights holders (Eq. (10)), they receive a proportion of their full water allotment ( fwa id ), while general rights holders receive no water at all. The optimal share of priority rights at the river basin level is initially unknown, so it will be parametrized to determine the PR b that yields the most efficient outcome.

Farmers' Decision-making
We assume that farmers try to maximize farming profits as a function of their water allocation ( id,f = f wa id,f ). As explained above, farmers' annual water allocations vary depending on the availability of irrigation water. Thus, since W A b is a stochastic variable, water allocations wa id , wapr id , wagr id , and wa id,f are also stochastic variables ranging from fwa id to 0, which in turn means that farming profits are stochastic variables (̃i d,f ). Within this stochastic framework, it is assumed that farmers make decisions about whether to upgrade their water rights to maximize their expected (or average) profit. To simulate the risk from water supply variability, N = 1000 probabilistic values for W A b,n are considered (the subscript n denotes each irrigation water availability scenario). For the current climate scenario, these values have been taken from the hydrological simulation model built by Gómez-Limón (2020). For the climate change scenario, the values for W A b,n have been obtained by modifying the values taken for the current climate scenario to reflect more frequent and intense drought episodes, as explained in Sect. 3.2. In both cases, these scenarios (n = 1, …,1000) have been considered equally probable.
We use the expected total gross margin ( GM id,f ,n ) as a proxy of profit in the short run. Gross margin is a mathematical function of the area covered by the different crops (i.e., farmers' decision variables), denoted by X c,id,f ,n , where c denotes the crop. In addition, farmers can decide what percentage of their water rights will become priority rights ( PR id,f ), with the remaining rights being kept as general water rights ( GR id,f = 1 − PR id,f ). However, it is worth noting that these last two decision variables do not depend on the water availability scenario n , since both denote long-run decision-making (i.e., this farmer's choice is considered to remain the same for the ⋅ fwa id wagr id = 0 N = 1000 scenarios). Thus, the simulation of farmers' decision-making maximizes the expected total gross margin considering both kinds of decision variables, GM id,f ,n = f X c,id,f ,n , PR id,f .
The modeling approach is based on the standard Positive Mathematical Programming (PMP) formally introduced by Howitt (1995) and the average cost approach proposed by Heckelei and Britz (2005).
In case of drought, it is assumed that farmers react by changing their cropping pattern, replacing water-intensive crops with others that have lower water needs or even rainfed crops (i.e., no irrigation water is required). Thus, three rainfed alternatives (wheat and sunflower plus olive when this permanent crop is present in a farm type) have also been considered as decision variables for simulations under drought scenarios.
Considering the priority allocation rule proposed, decision-making for the different farm types can be integrated into a single model at the basin level, where optimum values for the variables X c,id,f ,n and PR id,f (and GR id,f ) are to be found for every value considered for the parameter PR b : In the above expressions, GM id,f ,n represents the farm's expected gross margin for farm type id, f in scenario n calculated as the sum of total income, including both ∑ c wr c,id,f ⋅ X c,id,f ,n ≤ wa id,f ,n ⋅ s id,f ∀id, f , n (15) wa id,f ,n = wapr id,n ⋅ PR id,f + wagr id,n ⋅ GR id,f ∀id, f , n ) X c,id,f ,n ≥ 0; PR id,f ≥ 0; GR id,f ≥ 0 ∀c, id, f , n product sales (expected crop price, p c,id , multiplied by expected crop yield, y c,id,f ) and coupled subsidies ( s c,id ), minus the variable cost function ( c,id,f + 1∕2⋅ c,id,f ⋅ X c,id,f ,n ) for every crop c , where c,id,f and ⋅ c,id,f are the PMP calibrating parameters.
The objective function (11 and 12) allows the joint maximization of the average gross margin at the basin level (i.e., maximum economic efficiency solution), as a result of the optimum decision-making regarding the crop mixes in each scenario n and the long-run choices about the upgrade into priority rights. Constraint (13) is related to land availability and limits the total area covered by the different crop alternatives to the farm size ( s id,f ). Equations (14-18) are related to water availability. Equation (14) establishes that irrigation water use cannot exceed water availability, with the former being the sum of water requirements per crop ( wr c,id,f ) and the latter the water allocation per farm type ( wa id,f ,n ⋅ s id,f ), while Eqs. (15-18), derived from Eqs. (9) and (10) explained above, describe how water availability is shared among farm types according to the priority rules proposed. Constraint (19) just limits the maximum share of rights that can be upgraded to priority rights at the basin level, as fixed by the parameter PR b . Equation (20) denotes the rest of the constraints defining the feasible solution set, which constitute agronomic (rotational and frequency requirements) and policy (cotton and sugar beet quotas) factors, with X id,f ,n being the matrix containing all variables X c,id,f ,n , A id,f the technical coefficient matrix for every variable and constraint of the irrigation district id and farm type f , and B id,f the vector of limit values for each constraint for the irrigation district id and the farm type f . Finally, non-negativity constraints are imposed for X c,id,f ,n , PR id,f and GR id,f (Eq. (21)).
Considering the current proportional allocation rule, farm type decision-making can also be simulated for N = 1000 water availability scenarios using a simplified version of model (11), replacing Eq. (15-19) with a single expression (22) representing how the proportional rule works for every irrigation district id and farm type f .
Simply by comparing the simulated results obtained for the two allocation rules, we are able to calculate variations in gross margins and water use at the farm, ID, and basin level, as well as other indicators, allowing an assessment of the proposed analysis.

Aggregate Economic Efficiency Gains at the Basin Level
For the current climate scenario, the results from model (11−21) show that the maximum efficiency solution for the proposed priority allocation regimen is achieved with 44.5% of priority rights over total water rights at the basin level ( PR b ). As can be seen in Table 3, compared to the baseline values of the current proportional water rights regime (i.e., results from model considering Eq. (22)), for this value of the parameter PR b , aggregate gross margins at the basin level increase in every water availability scenario (i.e., drought events), with these increases ranging from 0.0% to 6.1%.
Similar results are obtained for the climate change scenario considered. In this case, the maximum efficiency solution is reached when 46.0% of total water rights at the basin level are upgraded into priority ones. This share of priority rights would result in an increase in economic efficiency ranging from 0.0% to 6.6%, depending on the water availability scenario. This is evidence that changing the allocation regimen to replace current proportional rules with the priority rule would enhance economic efficiency in any drought situation and climate scenario.
For light hydrological droughts (i.e., water availability higher than 75% of full water allotments), the improvements in economic efficiency are almost negligible (less than 1% of current aggregate gross margin at the basin level). However, the increase in aggregate gross margins becomes significant for mild droughts (i.e., water availability between 75 and 50% of full water allotments). In fact, for drought scenarios where water availability is lower than 50% of full water allotments (i.e., severe and extreme droughts), priority rights become a valuable policy instrument to enhance overall economic efficiency, raising aggregate gross margins above 4.0%.

Heterogeneity in Priority Rights Allocation
It is worth noting that the optimum upgrade into priority rights according to the results from model (11−21) is fairly heterogeneous among ID categories and farm types, as shown in Table 4. In this sense, it can be observed that those ID categories and farm types with higher value-added crops and water productivity (modern irrigated areas) upgrade a higher proportion of water rights than those with lower value-added crops and water productivity (traditional irrigated areas). Among the former, Olive and Modern ID categories stand out. In the current climate scenario, farmers in Olive IDs upgrade 56.6% of their water rights into priority ones, while farmers in Modern IDs upgrade almost half (48.2%) of their water rights. Similar upgrade rates are obtained for both ID categories (61.1% and 48.6%, respectively) when the climate change scenario is considered. Conversely, farmers in Traditional IDs upgrade just 28.0% and 28.8% of their water rights in the current climate and climate change scenarios, respectively, while those operating in Rice IDs do not upgrade any rights in either of the climate scenarios considered. Moreover, as shown in Table 4, there is also significant heterogeneity among farm types within each ID category in terms of the optimum share of priority water rights. These shares depend on farms' production orientation and water productivity; the higher the value-added of the crops and the higher the water productivity, the greater the share of priority rights. Table 5 shows more detailed results for the maximum efficiency solution of model (11−21) considering the current climate scenario (i.e., based on a 44.5% share of priority water rights at the basin level). As indicated in rows using a blue color spectrum, the heterogeneity in the share of priority rights granted to the various farm types for this climate scenario would lead to a relevant change in water allocation regime for the different scenarios of water availability ( WA b ∕FWA b ). As expected, for those ID categories with a higher share of priority rights (i.e., Olive and Modern IDs), water allocations increase for every drought scenario when a regime based on priority rights is implemented compared to the current situation (i.e., implementation of proportional water rights). In fact, as can be seen in Table 7, these ID categories increase their average water allocations (+ 4.9% in the case of Olive IDs and + 3.8% in the case of Modern IDs), while their water allocations . On the other hand, allocations to ID categories with a lower share or no share of priority rights (i.e., Traditional and Rice IDs) are reduced in every drought scenario. These ID categories thus get worse both in terms of the average  1380  1375  1365  1309  1225  1106  952  762  535  Modern  2003  2000  1960  1906  1821  1684  1520  1341  1125  824  Olive  930  930  930  930  893  836  780  724  667  611  Rice  1471  1333  1196  1058  921  783  646  508  371  233  Basin  1397  1390  1368  1340  1279  1186  1081  968  839  674  Gross margin implementing priority water rights (€/ha)  Traditional 1384  1382  1380  1324  1210  1033  856  729  590  438  Modern  2003  2000  1993  1965  1906  1829  1700  1490  1246  908  Olive  930  930  930  930  930  898  842  770  698  627  Rice  1471  1223  975  728  480  232  96  96  96  96  Basin  1397  1386  1372  1347  1308  1241  1147  1022  882  allocations (decreases of -6.6% and -17.9%, respectively) and their stability over time (increases of + 27.1% and + 85.3%, respectively, in their coefficients of variation). Moreover, it is worth noting that the overall volume of water allocated at the basin level when the priority rights are implemented remains the same as in the proportional water rights baseline. This constraint is implicitly assumed in the proposal for the reform, evidencing that this change in the allocation regime has no impact on water abstractions (i.e., on the environment).

Changes in Water Allocation and Gross Margin by ID Categories
The changes in water allocations discussed above also lead to changes in gross margins, as shown at the bottom of Table 5 (see rows using a yellow color spectrum). The improvement in water supply reliability compared to the current situation means farmers in Olive and Modern IDs achieve higher levels of profitability for every drought scenario when priority rights are implemented. This leads to an increase in their average gross margins (+ 1.4% and + 2.3% for Olive and Modern ID categories, respectively), and a decrease in volatility (-20.2% and -18.3% in their coefficients of variation, respectively), as shown in Table 7. On the contrary, under the new water allocation regime based on priority rights, farmers in Traditional and Rice IDs see a decline in their profitability indicators: reduced average gross margins (-3.7% and -16.5%, respectively) and increased profit volatility (+ 47.3% and + 82.1% in the coefficients of variation, respectively).
The key point worth highlighting is that aggregate average profitability gains by the farmers who upgrade their rights into priority ones are larger than aggregate average losses affecting farmers who maintain their general rights; i.e., the average variation in gross margins at the basin level is positive overall. This fact has two important implications. First, the priority allocation regime is more economically efficient than the proportional allocation regime. As shown in Table 7, this average improvement in economic efficiency is 1% of the current aggregate gross margin at the basin level. And second, these changes in average profitability allow the farmers to upgrade their rights into priority ones (reliability/profitability winners) to compensate those holding general rights (reliability/profitability losers) through the auction procedure suggested (i.e., annual surcharges to be paid by those upgrading their rights). This suggests that the proposed change in allocation rules is a win-win solution for every farmer in the basin. Table 6 shows detailed results for the maximum efficiency solution of model (11−21) considering the climate change scenario (i.e., a 46.0% share of priority water rights at the basin level). These results are similar to those described above for the current climate scenario, leading to enhanced water reliability and farm profitability for irrigators operating in the Olive and Modern IDs and a deterioration in reliability and profitability for those farming in Traditional and Rice IDs. In any case, it is worth noting that under this climate scenario, changes in water allocations and gross margins are more pronounced than in the current climate scenario; thus, the proposed allocation regime leads to a bigger improvement in economic efficiency. In fact, under the climate change scenario, the average efficiency increase at the basin level is 1.9% of the current aggregate gross margin, almost doubling the increase achieved in the current climate scenario (see Table 7). This means priority rights will be more useful for increasing economic efficiency when the effects of climate change on the availability of irrigation water become more perceptible.
For the sake of brevity, the analysis of the abovementioned heterogeneous effects of the proposed priority rights regime on water allocations and gross margins has focused solely on the results by ID categories. However, it is worth pointing out that this heterogeneity is even larger when the various farm types are considered. Interested readers can confirm this by checking the results provided in the supplementary material, both for the current climate scenario and the climate change scenario. As noted in the previous section, the different impacts on farm types depend on their production orientation and water productivity; the higher the value-added of the crops and the higher the water productivity, the greater the share of priority rights, and the greater the improvement in water reliability and farm profitability.

Discussion and Concluding Remarks
The results show modest average economic efficiency gains from the proposed change in the water allocation regime: just 1% of the average aggregate gross margin for the current climate scenario. The improvements in economic efficiency estimated in this paper are much greater than those reported by Gómez-Limón et al. (2021) for a similar change in the allocation regime at the irrigation district level (0.2% of the average aggregate gross margin). This confirms the first hypothesis presented in the introduction, supporting the idea that the implementation of priority rights in a real-world setting only makes sense if there is enough heterogeneity in water productivity among the rights holders involved.
In any case, the simulated performance of priority rights at the basin level is somewhat disappointing, raising doubts about the suitability of this instrument for reducing the inefficiency of water allocation caused by proportional water allocation in cyclical scarcity events. In fact, it may be reasonable to assume that the potential economic gains would not be enough to cover the transaction costs associated with implementing the proposed allocation regime in a real-world setting (McCann 2013;McCann and Garrick 2014); namely, the costs incurred for the auction to upgrade water rights through auctions and the procedure to compensate reliability losers.
This unsatisfactory performance is mainly explained by the fact that priority rights do not reflect the marginal value of water across users in a timely manner (OECD 2016); like any other allocation regime, the implementation of priority rights is a rigid instrument that cannot be adapted depending on the level of water scarcity (i.e., drought or water availability scenarios). In fact, since water scarcity is a dynamic phenomenon, droughts must be managed by implementing sufficiently flexible instruments capable of modifying allocations in the short term, just as the spot water markets do (Chong and Sunding 2006).
However, there are several reasons for implementing the proposed change in the allocation regime. First, because annual efficiency gains become relevant in severe and extreme droughts, indicating that this policy instrument can play a valuable role in minimizing the negative impact of water shortages. Moreover, as evidenced in this paper, this role could be more important for the climate change scenario, given that more frequent and intense drought episodes are expected in the Mediterranean irrigated areas. This confirms the second hypothesis set out in the introduction, which posits that priority rights could achieve higher efficiency gains considering feasible climate change scenarios. Therefore, the proposed regime can be considered an instrument for adaptation to climate change (Xu et al. 2014;Mallawaarachchi et al. 2020).
Second, it is also worth noting that priority rights represent an interesting risk management instrument for farmers. As shown in the simulation results, the farmers who are most vulnerable to drought risk can use priority rights as a hedging mechanism, reducing gross margin volatility. In the context of climate change, where farmers are eager to stabilize their income, these priority rights constitute a useful adaptation instrument.
The third and probably most relevant reason is that the proposed shift in the allocation regime can be successfully implemented in combination with other economic instruments aimed at improving water management during scarcity periods, such as allocation water markets and temporary water banks. As pointed out by Freebairn and Quiggin (2006) and Lefebvre et al. (2012) and demonstrated by the Australian experience, the combined implementation of priority water rights and spot water markets can lead to significant improvements in drought management in the irrigation sector.

Author Contribution
All authors contributed to the study conception and design. Material preparation, data collection, and modeling were performed by Carlos Gutiérrez-Martín and Nazaret M. Montilla-López. Result analysis and discussion were performed by Carlos Gutiérrez-Martín and José A. Gómez-Limón. The first draft of the manuscript was written by José A. Gómez-Limón, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Funding Open Access funding provided thanks to the Universidad de Córdoba and the CRUE-CSIC agreement with Springer Nature. This work was financially supported by the Spanish Ministry of Science, Innovation, and Universities, the Andalusian Department of Economy and Knowledge, and the Euro- Data Availability The data that support the findings of this study are openly available in the supplementary material.