Water allocation, return flows, and economic value in arid basins: Results from a coupled natural-human system model

Water allocation, return flows, and economic value in arid basins: Results from a coupled natural-human system model | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Water allocation, return flows, and economic value in arid basins: Results from a coupled natural-human system model Cameron Wobus, Eric Small, Jared Carbone, Ben Livneh, William Szafranski, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1485992/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 3 You are reading this latest preprint version Abstract The allocation of water in the arid western United States is governed by complex water laws that dictate who receives water, how much they receive, and when. Because these rules are generally based on the seniority of water rights, they are not necessarily focused on maximizing economic value across the entire economy. The maximization of value from water use economy-wide is a complex optimization problem that must explicitly consider each user’s peak water demand, willingness to pay function, and the feedbacks among users in a coupled natural-human system model. In this study, we distill these complexities into a simple model of a two-user economy that allows us to explore the relationships among water availability, water use, and value in water-limited systems. We find that the total economic value generated from water-dependent users depends primarily on the total water available in the system. However, for a given volume of water available, the way that water is allocated between the two users also has a significant effect on economic value. The degree to which this allocation affects value depends primarily on the relative willingness to pay for water between the two users, and on the return flows generated from each sector’s water use. While our simple two-user model is an abstraction of the complexities inherent in natural systems, our study provides important insights into the coupled natural-human system dynamics of water allocation and use in water-limited environments. Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. Introduction Across the arid western United States, water is typically allocated by some version of a prior appropriations doctrine, wherein those with the most senior water rights – typically agricultural users –receive their full allocation of water prior to any other user being able to draw from the resource (e.g., MacDonnell, 2015 ; Zellmer & Amos, 2021 ). This “rigid” allocation of water remains in place today, even though the vast majority of recent economic growth in the West has been driven by other sectors who may have a higher value for water (e.g., Griffin and Boadu 1992 ; Howe and Goemans 2003 ; Brewer 2007;Schilling, 2018 ; Weber et al., 2020 ). Importantly, in many cases the initial water allocation rules did not account for return flows - water that is not fully consumed by an upstream user and is, therefore, available for downstream use - since prior appropriations rules are typically based on the volume of water withdrawn rather than the volume of water consumed (e.g., Johnson et al., 1981 ; Gould 1988 ; Huffaker et al. 2000 ). The overall result is a mismatch between water policy, allocation, and value. Identifying a better alternative, however, requires an improved understanding of the coupled natural-human system dynamics between water allocation and return flows in river basins. Specifically, individual decisions about where and how to use water affect the volume of water available at other points in the watershed, which create feedbacks that influence the total social value the water can generate (Fig. 1 ). Identifying allocations that best serve society’s needs therefore requires consideration of human decision-making, the physical constraints on water availability, and the feedbacks between them. We developed a coupled natural-human system model that simulates streamflow, water allocation, return flows, and economic value in an idealized basin with two water users. The users differ in the total volume of water they require, their marginal value per unit of water, and the magnitude of their return flows. We use the model to test the hypothesis that natural-human system coupling is particularly strong, and opportunities for improving water allocation efficiency are increased, when return flows are significant and when water is scarce. Our simple model shows that economic value depends primarily on the total water available in the system. However, for a given volume of water available, the way that water is allocated between the two users can also have a significant effect. The degree to which this allocation matters depends on both the relative willingness to pay for water between the two users (a measure of economic value), as well as on the physical constraints on the system. These physical constraints include the relative position of each user within the basin, and the return flows generated from each sector’s water use. We contrast the general results of these model outputs with the economic outcomes that would be expected in real systems across the arid western United States (e.g., Burness and Quirk, 1979 ; Libecap 2007 ; Leonard et al., 2019 ). Our model thus provides a means to evaluate the gains in economic output that could be achieved by explicitly considering the value that each user places on water as a resource, as well as the return flows from each user. This latter component – consideration of return flows – has largely been ignored from existing physical-economic modeling analyses, with a few notable exceptions (e.g., Weckström et al., 2020 ; Pérez-blanco et al. 2020 ). This represents an important knowledge gap, since additional water supply from return flows could significantly ameliorate water shortages, particularly during drought conditions. 2. Methods Our simple system includes two water users, and water allocation is tracked between these users using a coupled economic-physical modeling framework. While we abstract away from many institutional details, the two water users in the system differ in ways that are meant to capture key features of agricultural and industrial users in western basins. Specifically, production in the agricultural sector requires more water overall, and more water per dollar of output, than in the industrial sector (e.g., Brewer et al., 2007 ). However, the value of access to additional water is also generally lower for the agriculture sector than it is for the industrial sector, at the typical allocation of water determined from prior appropriations (Griffin and Boadu 1992 ; Howe and Goemans 2003 ; Brewer et al. 2007 ). In the economic component of our model, we impose linear willingness to pay (WTP) functions to represent each sector’s marginal value per unit of water. A WTP function describes the maximum amount a user would be willing to pay to obtain an additional unit of water, as a function of that user’s total allocation of water. In the context of an agricultural or industrial user, for example, this would correspond to the user’s increase in profits due to the expanded output/sales the extra water would make possible. The maximum total economic value across users occurs at the allocation where all users have the same the WTP (Fig. 1 c-d). If one user has a higher WTP – for example the industrial user under prior appropriations – then total economic value can be increased by transferring a unit of water from the lower-value to the high-value user, holding total water availability constant. The physical component of the model tracks consumptive use for each sector, and ensures that the overall water balance includes return flows from each user. If each use of water in the basin were 100% consumptive (i.e., if there were no return flows), identifying the optimal allocation based on the two users’ WTP functions would be straightforward because the total water available in the system would be fixed (e.g., Fig. 1 a). However, because a change in water use upstream also affects the return flows available for downstream uses in the basin, identifying the optimal water allocation becomes significantly more complex (e.g., Fig. 1 b). Our contribution is to consider not only how total value from water use can be maximized, but also how these changes in return flows affect the total value of different water allocations. We use the model to sequentially vary the total supply of water available, each user’s relative WTP for water, and the return flows from each sector (Table 1). For each of these experiments, we assume that the maximum water demand from each sector is fixed. We set peak demand for the agricultural user at 500 acre feet (AF) and peak demand for the industrial user at 200 AF. We then loop through a series of allocations between users in which the upstream user takes anywhere from 0–100% of its total demand, subject to constraints from the total inflow. For example, if the total water available in the basin is only 300 AF, the maximum possible use by the agricultural sector is only 60% of its peak demand (300 AF/500 AF). For each of the possible water withdrawals and return flows from the upstream user, we assume that the downstream user will take as much water as remains up to its peak demand. Note that throughout these experiments we set actual values for agricultural and industrial uses, return flows, and other parameters for ease of interpretation. The absolute magnitude of peak demand values are of no significance because the system dynamics are driven by the relative values of each of these parameters. Our experiments result in a series of plausible water allocations between upstream and downstream users, which we combine with the WTP functions for each sector to calculate the total economic value for each scenario. We then identify the single water allocation that maximizes economic value for each scenario of total water availability, allowing us to examine how total economic value is affected by the interplay between water shortages, return flows, and willingness to pay. Finally, we compare the maximum value attainable for each scenario to the value that would be achieved under a prior appropriations allocation, in which the upstream, senior user maximizes its own output without regard to optimizing total value economy-wide. 3. Results Our analysis focused on three types of experiments: varying the total volume of water available in the system; varying the relative willingness to pay for water between the two sectors; and varying the return flows from each sector (Table 1). Table 1 . Summary of experiments designed to evaluate system response to total water, WTP ratios, and return flow fractions. Run # Tot Water WTP Ratio Ag Return Total Water 1 100 2:1 30% 2 300 2:1 30% 3 500 2:1 30% WTP Ratio 4 300 1:1 30% 5 300 2:1 30% 6 300 4:1 30% Return Flow 7 300 3:1 15% 8 300 3:1 45% 9 300 3:1 60% 3.1 Variation in total water available Our first set of experiments focused on varying the total volume of water available in the system. In each of these experiments, the industrial sector has a willingness to pay for water that is double that of the agricultural sector, per unit of water. As expected, these experiments illustrate that economic value increases as the total volume of water increases. However, the relative allocation of water that maximizes value also varies as the total volume of water changes. This leads to a shift in water usage relative to a prior appropriations case in which the allocations are fixed. Figure 2 illustrates this effect for three scenarios where agriculture is the upstream user, and where water is scarce relative to the total peak demand of the entire economy of 700 AF. In the scenario where water is most scarce (100 AF total), value is maximized when agriculture uses no water, and all of the water is allocated to the higher-valued industrial user downstream (Fig. 2a). In a scenario with an intermediate level of scarcity (300 AF total), economic value is maximized when agriculture uses just over half of its peak demand (Fig. 2b), leaving the remaining water and its return flows for the industrial user downstream. And finally, in a scenario with enough water to just meet agriculture’s peak demand, value is maximized when agriculture uses 100% of its peak demand and the industrial user relies entirely on agricultural return flows (Fig. 2c). In each of these scenarios, water is scarce relative to the total demands of the two users. However, even though industry is willing to pay twice the amount per unit of water as agriculture, the maximum value is not always achieved when this sector simply takes all of the water it requires to maximize its own output. This underscores the importance of considering return flows, which can be seen in Fig. 2b, where there is 300 AF of total water available. If the upstream agricultural user were to take only 150 AF of this water (red dot in Fig. 2b), allowing industry to maximize its output by using the remaining 150 AF plus agricultural return flows, total economic value is actually lower than a scenario in which agriculture uses all 300 AF of the available water (60% of its peak demand; blue dot in Fig. 2b). This is because the latter scenario still allows return flows to be used by the downstream industrial user, so that the value of the industrial sector, while smaller than in the first allocation, does not go to zero. This is also true in the scenario where there is 500 AF of total water available (Fig. 2c). In this case, even when agriculture withdraws all of the water from the system, its return flow (30% of 500 AF, or 150 AF) is almost enough to meet the industrial user’s peak demand as well. Thus, even though the economic output per unit of water is half as large for agriculture as it is for industry, and there is not enough water to meet the full demand of both users, total economic value is still maximized when agriculture withdraws enough water to meet its full demand. 3.2 Variation in relative value of water Our second set of experiments focused on understanding the relationship between the value that each sector places on water and the optimal allocation of water between the two sectors. In these experiments, we varied the relative willingness to pay for water between the two users. To do this, we varied the slope of the demand curve for the (downstream) industrial user relative to the (upstream) agricultural user, and examined how the optimal allocation of water and total value changes for each of these scenarios. We characterized these differences as “willingness to pay ratios” of 1, 2, and 4, where the industrial user valued water the same, a factor of two higher, or a factor of four higher than the upstream user, per unit of water. Figs 3a through 3c illustrate how the optimal allocation of water changes as the WTP ratio increases from 1 (Fig. 3a) to 4 (Fig. 3c), when the total water available is 300 AF (approximately 60% of the upstream agricultural user’s total demand). As shown in Fig. 3, when the WTP ratio is less than or equal to 2:1, value is maximized when the agricultural sector draws all of the available water and maximizes its output (blue dots in Fig. 3a and 3b). In both of these scenarios, because agriculture is withdrawing its total maximum allocation, the downstream industrial user has access only to the return flow from the upstream agricultural user, which in these experiments is held fixed at 30% of agricultural withdrawals. If the WTP ratio is increased to 4:1, economic value is maximized when the downstream industrial user is allowed to take the full 200 AF of water it requires to maximize the its own output (a sum of direct streamflow plus return flows from ~ 150 AF of agricultural use; blue dot in Fig. 3c). In this scenario, the agricultural user’s output is limited to what it can produce with only 100AF of water, or 30% of its total demand. However, because the value of water is substantially higher for the industrial user, total value in this scenario is approximately 50% higher than the total value in either of the previous scenarios. Thus, total output is determined not only by the total water available, but also by the differences in WTP for parties at different points within the basin. 3.3 Variation in return flows In our final set of experiments, we examined the impact of varying the return flow from the agricultural user’s withdrawals on the optimal allocation of water. As with the other parameters we explored, return flows exert the most leverage on economic outcomes when there is a water shortage. Thus, we focused these experiments on scenarios where the total water available (300 AF) is insufficient to meet the needs of both users. Figures 4a through 4c illustrate how the optimal allocation of water changes as the return flows from the upstream use increase from 15% (Fig. 4a) to 45% (Fig. 4b) to 60% (Fig. 4c). The lower return flow values of 15% and 45% approximately reflect the range of irrigation efficiencies for sprinkler and flood irrigation in agricultural systems in the Western United States, respectively (CWCB, 2017). In each of these experiments, the WTP ratio is set at 3:1, representing a 3x higher value per unit of water for the downstream industrial user than for the upstream agricultural user. The increase in return flow creates two effects, as shown in Fig. 4. First, although the total volume of water available in all three of these experiments is fixed at 300 AF, the maximum economic value increases as the return flow fraction increases: the maximum attainable output with a 60% return flow is approximately 35% higher than it is when return flow is only 15%. This is simply a result of a higher total water availability for the downstream user, as return flows from the upstream user increase. The second effect of increasing return flows is a shift in the optimal allocation of water between the upstream and downstream users. When agricultural return flows are lowest at 15%, total economic value is maximized when the agricultural sector uses only 25% of its total demand, or approximately 125 AF (Fig. 4a), leaving the rest of the water for the higher-value downstream user. As agricultural return flows increase, however, the upstream agricultural sector can use a higher and higher fraction of its peak demand until at a 60% return flow it can use all of the water available (300 AF, or 60% of its peak demand) while still maximizing value for the whole economy. This scenario is possible because the lost revenue due to the water shortage for the industrial sector (200 AF – 0.6*300AF = 20 AF shortage) is more than compensated for by the increased production from the agricultural sector upstream. 3.4 Comparison to a prior appropriations scenario For each of the evaluations above, we sought to find the allocation of water that maximized economic output, assuming that water could be freely re-allocated between users. In our final set of experiments, we compared two scenarios. The first is a “maximum value” scenario in which water can be freely traded to maximize overall economic output. The second is a “rigid” scenario in which the upstream user focuses on maximizing its own production. This latter scenario is similar to the way water is currently allocated across the Western United States: where a “senior” user makes decisions to optimize their own output, ignoring the needs of others. This system exists both because of the prior appropriations doctrine, and because mechanisms for water trade are currently limited (e.g., Chong and Sunding 2007; Howe and Goemans 2003 ; Howitt and Hansen 2005 ; Leonard et al., 2019 ). Figure 5 shows the difference in total output between these “rigid” and “maximum-value” scenarios. In all cases, the user with the lower demand but higher value per unit of water (“industry”) is downstream, and the user with the higher demand but lower value per unit of water (“agriculture”) is upstream. The blue curves (rigid) represent the attainable total value for each scenario if the upstream user focuses on maximizing its own production, and the red curve represents the maximum attainable total economic value. The benefits of re-allocation of water away from the prior appropriations regime are highest when water is scarce, as shown by the grey shaded regions highlighting the difference between the two allocations. Figures 5 a and 5 b compare model results where the WTP ratio is 3:1 (5a) vs 6:1 (5b). In both cases, the agricultural return flow is 30%. In each of these scenarios, the most rapid divergence between the “rigid” and “free trade” scenarios occurs between 0-200 AF of total water. Here, the added value from water re-allocation is a result of the upstream agricultural user releasing all of its water to the downstream industrial user, who places a higher value on each unit of water. Beyond 200 AF, the downstream industrial user’s peak demand is fully satisfied, and agricultural production resumes. The difference between the rigid and trade optimized scenarios shrinks from this point up to a total water availability of ~ 400 AF (3:1 WTP ratio) or ~ 550 AF (6:1 WTP ratio), where the curves re-join. The location along the x-axis at which the rigid and optimized scenarios meet (400 AF vs 550 AF) reflects the difference in optimal allocation of water between the two sectors under these different WTP ratios (see Fig. 3). In our initial model runs, we also modified the location of the two users in the system: placing the higher-valued industrial user upstream, rather than downstream from the lower-valued agricultural user. However, in these experiments where the higher-valued industrial user was upstream, economic value was almost always maximized when this user took its full allocation of water. The exception to this rule occurs when the WTP ratio is small and the return flow from the industrial user is also small. Fig. 6 illustrates this effect for three scenarios where the industrial user is upstream. In the first two scenarios, the industrial user’s WTP is twice that of the agricultural user and its return flow ranges from 10% (Fig. 6a) to 40% (Fig. 6b). In the third scenario, the industrial user’s WTP is three times higher than the agricultural user and its return flow is 10% (Fig. 6c). In each of these cases, there is additional economic value to be added only over a very narrow range of total water availability, if the industrial user allows all of the water to be used by the agricultural user downstream. The peak increase in economic value from trade occurs at 500 AF of total water, where the complete transfer of water from industry allows the agricultural user to generate its maximum value. On either side of this peak, the range of total water availability over which trade increases economic value is sensitive to the return flow from industry and the WTP ratio. This is because the total economic value is universally higher with higher return flows or a higher WTP ratio, which limits the gains from trading downstream (compare the total value of “rigid” allocations between Figs. 6a-6b). The same effect occurs when the WTP ratio is higher (compare Figs. 6a-6c). For WTP ratios or industrial return flows much larger than the values shown in Fig. 6, the advantages of water re-allocation disappear altogether. 4. Discussion And Conclusions Our simple model demonstrates two key points related to water allocation and use in water-scarce environments: First, we show that return flows cannot be ignored in analysis of economic value from these systems, because the optimal allocation of water depends on how much of the water is returned and can be used downstream. Second, we show that when water is scarce relative to total demand, the total economic value from water-intensive industries can be increased when water is re-allocated relative to a “rigid” prior appropriations system. While this result is consistent with prior research on the topic (Chong and Sunding 2006 ; Ghosh et al.; Hagerty 2019 ), our model also illustrates several new points about the dynamics of this coupled natural-human system. When water is re-allocated between users relative to a “rigid” allocation, we find that the change in total economic value is sensitive to at least three conditions: the scarcity of water relative to the total demand across all sectors (see Figs. 2 and 5 ); the difference in willingness to pay for water between sectors (Fig. 3); and the return flows from the upstream user (Fig. 4). Our model also shows that the maximum economic value for the entire economy is not always achieved when a lower-valued, upstream user sacrifices all of its output in favor of a higher-valued, downstream user. This is because a fraction of the upstream user’s withdrawals remain available to the downstream user as return flows, allowing some of the water in the system to be extracted twice. Depending on the return flow fraction from the upstream user and the relative willingness to pay for water between the two users, the downstream user may be able to maximize its value in a water-scarce scenario even if the upstream user takes a fraction of the water for its own use (see Figs. 3–4). Our economic analysis is idealized, in that we used a partial equilibrium analysis rather than a more complete, computable general equilibrium (CGE) analysis to simulate the value placed on water. Because of this, our current framework implicitly assumes that no other prices in the economy (like wages of workers in each sector) are impacted by the allocation changes described here. We further assume that there are no other market failures (tax distortions, non-market goods, etc.) that would be impacted by changes in water allocation. These additional complexities are best explored in a CGE framework, which is a focus of ongoing research. Our physical model is clearly an abstraction of real water systems, which are characterized by multiple users with a range of demands, values and seniority. While our modeling framework is a simplification of the many processes, interactions, and feedbacks among multiple users in real systems, it is also easily interpreted, allowing us to explore the key factors that control the dynamics of this coupled human-natural system. Future work will be focused on gradually adding complexity to the model, so that we can begin to explore time-varying water demand and supply among multiple user groups in a more realistic system. Declarations Ethical Approval: Not applicable Consent to Participate : Not applicable Consent to Publish : All authors consent to publication of this manuscript. Authors Contributions : C. Wobus, E. Small, J. Carbone, B. Livneh, B. Szafranski, H. Kamen and P. Modi all contributed to the study conception and design. Model development and analysis were completed by C. Wobus, with support from E. Small. The first draft of the manuscript was written by C. Wobus, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. Funding : This work was supported by US National Science Foundation Grant #2009922, awarded to B. Livneh. Competing Interests : The authors have no relevant financial or non-financial interests to disclose. Availability of data and materials : Data and materials used in the preparation of this manuscript will be made available upon request from the corresponding author. 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J Hydrol 584(February):124676 Schilling K (2018) Addressing the Prior Appropriation Doctrine in the Shadow of Climate Change and the Paris Climate Agreement.Seattle Journal of Environmental Law, 8(1) Weber GS, Harder JL, Bearden BL (2020) Cases and materials on water law (Tenth edition). West Academic Publishing Weckström MM, Örmä VA, Salminen JM (2020) An order of magnitude: How a detailed, real-data-based return flow analysis identified large discrepancies in modeled water consumption volumes for Finland. Ecol Ind 110:105835. https://doi.org/10.1016/j.ecolind.2019.105835 Zellmer SB, Amos AL (2021) Water law in a nutshell. West Academic Publishing Cite Share Download PDF Status: Under Review Version 1 posted Reviewers invited by journal 06 Apr, 2022 Editor assigned by journal 28 Mar, 2022 First submitted to journal 24 Mar, 2022 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-1485992","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":96497465,"identity":"1bd1d90a-64d7-40e1-819a-4cbc21d1444e","order_by":0,"name":"Cameron Wobus","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAArklEQVRIiWNgGAWjYHACNiC2AWLGxgOkaEkDaWkgScthMIs4Lfwzko895vlz3m5t+2GgLTU20QS1SNxISzfmbbudvO1MIlDLsbTcBkJaDKRzzKR5G24nmx0AamFsOEykFp4/55LNzj8kSQvbATuzG8TaInH/Wbrh3LbkBLMbQFsSiPELf8/hYw/e/LGzNzuf/vDBhxobwlpgIBGsMoFY5SBgT4riUTAKRsEoGGEAANBHRKNr4Q5+AAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-9654-1738","institution":"Lynker","correspondingAuthor":true,"prefix":"","firstName":"Cameron","middleName":"","lastName":"Wobus","suffix":""},{"id":96497466,"identity":"9cdfda2b-abd9-413c-8616-847e64c4eae9","order_by":1,"name":"Eric Small","email":"","orcid":"","institution":"University of Colorado Boulder College of Arts and Sciences","correspondingAuthor":false,"prefix":"","firstName":"Eric","middleName":"","lastName":"Small","suffix":""},{"id":96497467,"identity":"c3fb5caa-49cb-42a2-9368-be24ef701c9a","order_by":2,"name":"Jared Carbone","email":"","orcid":"","institution":"Colorado School of Mines Division of Economics and Business","correspondingAuthor":false,"prefix":"","firstName":"Jared","middleName":"","lastName":"Carbone","suffix":""},{"id":96497468,"identity":"fc338f2d-2f10-4265-a233-95530b40f643","order_by":3,"name":"Ben Livneh","email":"","orcid":"","institution":"University of Colorado Boulder College of Engineering and Applied Science","correspondingAuthor":false,"prefix":"","firstName":"Ben","middleName":"","lastName":"Livneh","suffix":""},{"id":96497469,"identity":"761fd5d8-55a0-4e40-8ae1-d616689995a9","order_by":4,"name":"William Szafranski","email":"","orcid":"","institution":"Lynker","correspondingAuthor":false,"prefix":"","firstName":"William","middleName":"","lastName":"Szafranski","suffix":""},{"id":96497470,"identity":"b6eef616-161e-42e7-bc48-5c4834565206","order_by":5,"name":"Hannah Kamen","email":"","orcid":"","institution":"Colorado School of Mines Division of Economics and Business","correspondingAuthor":false,"prefix":"","firstName":"Hannah","middleName":"","lastName":"Kamen","suffix":""},{"id":96497471,"identity":"74cfd1a4-d15b-4283-b471-46634b347f41","order_by":6,"name":"Parthkumar Modi","email":"","orcid":"","institution":"University of Colorado Boulder College of Engineering and Applied Science","correspondingAuthor":false,"prefix":"","firstName":"Parthkumar","middleName":"","lastName":"Modi","suffix":""}],"badges":[],"createdAt":"2022-03-24 15:11:43","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1485992/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1485992/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":20129431,"identity":"fb4fc116-fbef-4284-b690-e53b24a1b037","added_by":"auto","created_at":"2022-04-08 17:47:13","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":53423,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic illustrating the relationships between water availability, water use, and economic output. A) In a system with no return flows, stream depletion is a simple sum of all users’ water withdrawals. B) When return flows are considered, stream depletion depends on both water withdrawals and return flows, generating additional water that can be allocated for beneficial use. C-D) Total economic output is the sum of areas under the production curves for agriculture and industry. Note that more output is possible with return flows (D) relative to a system without return flows (D).\u0026nbsp;\u003c/p\u003e","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-1485992/v1/e428c206a4bf9ea80465924c.png"},{"id":20129435,"identity":"79445ec3-d65f-49bd-abac-01477b5ab9ce","added_by":"auto","created_at":"2022-04-08 17:47:14","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":87579,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of water allocation between agriculture and industry and total economic output, for total water availability varying from 100 to 500 AF. Maximum output (blue dots) is achieved for different relative allocations of water depending on the total water available. Note differences in x-axis between plots\u003c/p\u003e","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-1485992/v1/c0f02c79c066a15d346b077a.png"},{"id":20129524,"identity":"93a73175-d9b3-4f79-88a1-ce9e8e91ea0e","added_by":"auto","created_at":"2022-04-08 17:52:14","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":54082,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of optimal water allocation for 300 AF of total water, for WTP ratios of a) 1:1, b) 2:1, and c) 4:1 between industrial and agricultural use. Maximum GRP (blue dots) is achieved for different allocations depending on relative WTP between the two sectors.\u003cstrong\u003e \u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Figure3.png","url":"https://assets-eu.researchsquare.com/files/rs-1485992/v1/af00a0d5415a071f30b2f7e6.png"},{"id":20129525,"identity":"67c060a2-c42f-46d4-8155-7910f2afcf63","added_by":"auto","created_at":"2022-04-08 17:52:14","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":48416,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of optimal water allocation for 300 AF of total water, for upstream (agricultural) return flows of a) 15%, b) 45%, and c) 60%. Maximum GRP (blue dots) increases, and optimal allocation shifts towards agricultural use, as return flow fraction increases.\u003cstrong\u003e \u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Figure4.png","url":"https://assets-eu.researchsquare.com/files/rs-1485992/v1/1a2904e86b12f6f6819b4c74.png"},{"id":20129433,"identity":"1e54d6e5-f369-4ef5-810d-2d674c846535","added_by":"auto","created_at":"2022-04-08 17:47:14","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":44372,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of attainable economic output under “maximum value” scenarios (red) vs a scenario in which the upstream user focuses only on maximizing its own output (blue). In all cases, the downstream user generates higher economic output per unit of water than upstream user. A: WTP ratio of 3:1, agricultural return flow 30%. B: WTP ratio of 6:1, agricultural return flow 30%. C: WTP ratio of 6:1, agricultural return flow 15%.\u0026nbsp;\u0026nbsp;\u003c/p\u003e","description":"","filename":"Figure5.png","url":"https://assets-eu.researchsquare.com/files/rs-1485992/v1/31e5174ad8e71fe3e4f20f5e.png"},{"id":20129432,"identity":"293b7e96-352b-4545-bc25-b455da5fac4b","added_by":"auto","created_at":"2022-04-08 17:47:13","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":36481,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of attainable economic output under free trade scenarios (red) vs a scenario in which the upstream user focuses only on maximizing its own output (blue) when industry is upstream. In all cases, the industrial user generates higher economic output per unit of water than upstream user. A: WTP ratio of 2:1, industrial return flow 10%. B: WTP ratio of 2:1, industrial return flow 40%. C: WTP ratio of 3:1, industrial return flow 10%.\u0026nbsp;\u0026nbsp;\u003c/p\u003e","description":"","filename":"Figure6.png","url":"https://assets-eu.researchsquare.com/files/rs-1485992/v1/5822620b0d7acf74399c9613.png"},{"id":20129526,"identity":"d8e791f7-ec92-49da-b3d4-c383a87508c1","added_by":"auto","created_at":"2022-04-08 17:52:21","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":373092,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1485992/v1/99e3fb48-a280-4b59-adeb-bffcee5187cc.pdf"}],"financialInterests":"","formattedTitle":"Water allocation, return flows, and economic value in arid basins: Results from a coupled natural-human system model","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eAcross the arid western United States, water is typically allocated by some version of a prior appropriations doctrine, wherein those with the most senior water rights \u0026ndash; typically agricultural users \u0026ndash;receive their full allocation of water prior to any other user being able to draw from the resource (e.g., MacDonnell, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Zellmer \u0026amp; Amos, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). This \u0026ldquo;rigid\u0026rdquo; allocation of water remains in place today, even though the vast majority of recent economic growth in the West has been driven by other sectors who may have a higher value for water (e.g., Griffin and Boadu \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1992\u003c/span\u003e; Howe and Goemans \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Brewer 2007;Schilling, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Weber et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Importantly, in many cases the initial water allocation rules did not account for return flows - water that is not fully consumed by an upstream user and is, therefore, available for downstream use - since prior appropriations rules are typically based on the volume of water \u003cem\u003ewithdrawn\u003c/em\u003e rather than the volume of water \u003cem\u003econsumed\u003c/em\u003e (e.g., Johnson et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e1981\u003c/span\u003e; Gould \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e1988\u003c/span\u003e; Huffaker et al. \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2000\u003c/span\u003e). The overall result is a mismatch between water policy, allocation, and value.\u003c/p\u003e \u003cp\u003eIdentifying a better alternative, however, requires an improved understanding of the coupled natural-human system dynamics between water allocation and return flows in river basins. Specifically, individual decisions about where and how to use water affect the volume of water available at other points in the watershed, which create feedbacks that influence the total social value the water can generate (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Identifying allocations that best serve society\u0026rsquo;s needs therefore requires consideration of human decision-making, the physical constraints on water availability, and the feedbacks between them.\u003c/p\u003e \u003cp\u003eWe developed a coupled natural-human system model that simulates streamflow, water allocation, return flows, and economic value in an idealized basin with two water users. The users differ in the total volume of water they require, their marginal value per unit of water, and the magnitude of their return flows. We use the model to test the hypothesis that natural-human system coupling is particularly strong, and opportunities for improving water allocation efficiency are increased, when return flows are significant and when water is scarce.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eOur simple model shows that economic value depends primarily on the total water available in the system. However, for a given volume of water available, the way that water is allocated between the two users can also have a significant effect. The degree to which this allocation matters depends on both the relative willingness to pay for water between the two users (a measure of economic value), as well as on the physical constraints on the system. These physical constraints include the relative position of each user within the basin, and the return flows generated from each sector\u0026rsquo;s water use.\u003c/p\u003e \u003cp\u003eWe contrast the general results of these model outputs with the economic outcomes that would be expected in real systems across the arid western United States (e.g., Burness and Quirk, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1979\u003c/span\u003e; Libecap \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Leonard et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Our model thus provides a means to evaluate the gains in economic output that could be achieved by explicitly considering the value that each user places on water as a resource, as well as the return flows from each user. This latter component \u0026ndash; consideration of return flows \u0026ndash; has largely been ignored from existing physical-economic modeling analyses, with a few notable exceptions (e.g., Weckstr\u0026ouml;m et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; P\u0026eacute;rez-blanco et al. \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). This represents an important knowledge gap, since additional water supply from return flows could significantly ameliorate water shortages, particularly during drought conditions.\u003c/p\u003e"},{"header":"2. Methods","content":"\u003cp\u003eOur simple system includes two water users, and water allocation is tracked between these users using a coupled economic-physical modeling framework. While we abstract away from many institutional details, the two water users in the system differ in ways that are meant to capture key features of agricultural and industrial users in western basins. Specifically, production in the agricultural sector requires more water overall, and more water per dollar of output, than in the industrial sector (e.g., Brewer et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). However, the value of access to additional water is also generally lower for the agriculture sector than it is for the industrial sector, at the typical allocation of water determined from prior appropriations (Griffin and Boadu \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1992\u003c/span\u003e; Howe and Goemans \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Brewer et al. \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2007\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn the economic component of our model, we impose linear willingness to pay (WTP) functions to represent each sector\u0026rsquo;s marginal value per unit of water. A WTP function describes the maximum amount a user would be willing to pay to obtain an additional unit of water, as a function of that user\u0026rsquo;s total allocation of water. In the context of an agricultural or industrial user, for example, this would correspond to the user\u0026rsquo;s increase in profits due to the expanded output/sales the extra water would make possible. The maximum total economic value across users occurs at the allocation where all users have the same the WTP (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec-d). If one user has a higher WTP \u0026ndash; for example the industrial user under prior appropriations \u0026ndash; then total economic value can be increased by transferring a unit of water from the lower-value to the high-value user, holding total water availability constant.\u003c/p\u003e \u003cp\u003eThe physical component of the model tracks consumptive use for each sector, and ensures that the overall water balance includes return flows from each user. If each use of water in the basin were 100% consumptive (i.e., if there were no return flows), identifying the optimal allocation based on the two users\u0026rsquo; WTP functions would be straightforward because the total water available in the system would be fixed (e.g., Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea). However, because a change in water use upstream also affects the return flows available for downstream uses in the basin, identifying the optimal water allocation becomes significantly more complex (e.g., Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb). Our contribution is to consider not only how total value from water use can be maximized, but also how these changes in return flows affect the total value of different water allocations.\u003c/p\u003e \u003cp\u003eWe use the model to sequentially vary the total supply of water available, each user\u0026rsquo;s relative WTP for water, and the return flows from each sector (Table\u0026nbsp;1). For each of these experiments, we assume that the maximum water demand from each sector is fixed. We set peak demand for the agricultural user at 500 acre feet (AF) and peak demand for the industrial user at 200 AF. We then loop through a series of allocations between users in which the upstream user takes anywhere from 0\u0026ndash;100% of its total demand, subject to constraints from the total inflow. For example, if the total water available in the basin is only 300 AF, the maximum possible use by the agricultural sector is only 60% of its peak demand (300 AF/500 AF). For each of the possible water withdrawals and return flows from the upstream user, we assume that the downstream user will take as much water as remains up to its peak demand. Note that throughout these experiments we set actual values for agricultural and industrial uses, return flows, and other parameters for ease of interpretation. The absolute magnitude of peak demand values are of no significance because the system dynamics are driven by the \u003cem\u003erelative\u003c/em\u003e values of each of these parameters.\u003c/p\u003e \u003cp\u003eOur experiments result in a series of plausible water allocations between upstream and downstream users, which we combine with the WTP functions for each sector to calculate the total economic value for each scenario. We then identify the single water allocation that maximizes economic value for each scenario of total water availability, allowing us to examine how total economic value is affected by the interplay between water shortages, return flows, and willingness to pay. Finally, we compare the maximum value attainable for each scenario to the value that would be achieved under a prior appropriations allocation, in which the upstream, senior user maximizes its own output without regard to optimizing total value economy-wide.\u003c/p\u003e"},{"header":"3. Results","content":"\u003cp\u003eOur analysis focused on three types of experiments: varying the total volume of water available in the system; varying the relative willingness to pay for water between the two sectors; and varying the return flows from each sector (Table 1).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 1\u003c/strong\u003e. Summary of experiments designed to evaluate system response to total water, WTP ratios, and return flow fractions.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable border=\"1\" id=\"Taba\"\u003e\n \u003ccolgroup cols=\"5\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eRun #\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eTot Water\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eWTP Ratio\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAg Return\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eTotal Water\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2:1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e300\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2:1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2:1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eWTP Ratio\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e300\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1:1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e300\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2:1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e300\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4:1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003eReturn Flow\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e300\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3:1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e15%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e300\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3:1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e45%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e300\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3:1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e60%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec4\"\u003e\n \u003ch2\u003e3.1 Variation in total water available\u003c/h2\u003e\n \u003cp\u003eOur first set of experiments focused on varying the total volume of water available in the system. In each of these experiments, the industrial sector has a willingness to pay for water that is double that of the agricultural sector, per unit of water. As expected, these experiments illustrate that economic value increases as the total volume of water increases. However, the relative allocation of water that maximizes value also varies as the total volume of water changes. This leads to a shift in water usage relative to a prior appropriations case in which the allocations are fixed.\u003c/p\u003e\n \u003cp\u003eFigure\u0026nbsp;2 illustrates this effect for three scenarios where agriculture is the upstream user, and where water is scarce relative to the total peak demand of the entire economy of 700 AF. In the scenario where water is most scarce (100 AF total), value is maximized when agriculture uses no water, and all of the water is allocated to the higher-valued industrial user downstream (Fig.\u0026nbsp;2a). In a scenario with an intermediate level of scarcity (300 AF total), economic value is maximized when agriculture uses just over half of its peak demand (Fig.\u0026nbsp;2b), leaving the remaining water and its return flows for the industrial user downstream. And finally, in a scenario with enough water to just meet agriculture\u0026rsquo;s peak demand, value is maximized when agriculture uses 100% of its peak demand and the industrial user relies entirely on agricultural return flows (Fig.\u0026nbsp;2c).\u003c/p\u003e\n \u003cp\u003eIn each of these scenarios, water is scarce relative to the total demands of the two users. However, even though industry is willing to pay twice the amount per unit of water as agriculture, the maximum value is not always achieved when this sector simply takes all of the water it requires to maximize its own output. This underscores the importance of considering return flows, which can be seen in Fig. 2b, where there is 300 AF of total water available. If the upstream agricultural user were to take only 150 AF of this water (red dot in Fig. 2b), allowing industry to maximize its output by using the remaining 150 AF plus agricultural return flows, total economic value is actually lower than a scenario in which agriculture uses all 300 AF of the available water (60% of its peak demand; blue dot in Fig. 2b). This is because the latter scenario still allows return flows to be used by the downstream industrial user, so that the value of the industrial sector, while smaller than in the first allocation, does not go to zero. This is also true in the scenario where there is 500 AF of total water available (Fig. 2c). In this case, even when agriculture withdraws all of the water from the system, its return flow (30% of 500 AF, or 150 AF) is almost enough to meet the industrial user\u0026rsquo;s peak demand as well. Thus, even though the economic output per unit of water is half as large for agriculture as it is for industry, and there is not enough water to meet the full demand of both users, total economic value is still maximized when agriculture withdraws enough water to meet its full demand.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec5\"\u003e\n \u003ch2\u003e3.2 Variation in relative value of water\u003c/h2\u003e\n \u003cp\u003eOur second set of experiments focused on understanding the relationship between the value that each sector places on water and the optimal allocation of water between the two sectors. In these experiments, we varied the relative willingness to pay for water between the two users. To do this, we varied the slope of the demand curve for the (downstream) industrial user relative to the (upstream) agricultural user, and examined how the optimal allocation of water and total value changes for each of these scenarios. We characterized these differences as \u0026ldquo;willingness to pay ratios\u0026rdquo; of 1, 2, and 4, where the industrial user valued water the same, a factor of two higher, or a factor of four higher than the upstream user, per unit of water.\u003c/p\u003e\n \u003cp\u003eFigs 3a through 3c illustrate how the optimal allocation of water changes as the WTP ratio increases from 1 (Fig. 3a) to 4 (Fig. 3c), when the total water available is 300 AF (approximately 60% of the upstream agricultural user\u0026rsquo;s total demand). As shown in Fig. 3, when the WTP ratio is less than or equal to 2:1, value is maximized when the agricultural sector draws all of the available water and maximizes its output (blue dots in Fig. 3a and 3b). In both of these scenarios, because agriculture is withdrawing its total maximum allocation, the downstream industrial user has access only to the return flow from the upstream agricultural user, which in these experiments is held fixed at 30% of agricultural withdrawals.\u003c/p\u003e\n \u003cp\u003eIf the WTP ratio is increased to 4:1, economic value is maximized when the downstream industrial user is allowed to take the full 200 AF of water it requires to maximize the its own output (a sum of direct streamflow plus return flows from ~\u0026thinsp;150 AF of agricultural use; blue dot in Fig.\u0026nbsp;3c). In this scenario, the agricultural user\u0026rsquo;s output is limited to what it can produce with only 100AF of water, or 30% of its total demand. However, because the value of water is substantially higher for the industrial user, total value in this scenario is approximately 50% higher than the total value in either of the previous scenarios. Thus, total output is determined not only by the total water available, but also by the differences in WTP for parties at different points within the basin.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec6\"\u003e\n \u003ch2\u003e3.3 Variation in return flows\u003c/h2\u003e\n \u003cp\u003eIn our final set of experiments, we examined the impact of varying the return flow from the agricultural user\u0026rsquo;s withdrawals on the optimal allocation of water. As with the other parameters we explored, return flows exert the most leverage on economic outcomes when there is a water shortage. Thus, we focused these experiments on scenarios where the total water available (300 AF) is insufficient to meet the needs of both users.\u003c/p\u003e\n \u003cp\u003eFigures\u0026nbsp;4a through 4c illustrate how the optimal allocation of water changes as the return flows from the upstream use increase from 15% (Fig.\u0026nbsp;4a) to 45% (Fig.\u0026nbsp;4b) to 60% (Fig.\u0026nbsp;4c). The lower return flow values of 15% and 45% approximately reflect the range of irrigation efficiencies for sprinkler and flood irrigation in agricultural systems in the Western United States, respectively (CWCB, 2017). In each of these experiments, the WTP ratio is set at 3:1, representing a 3x higher value per unit of water for the downstream industrial user than for the upstream agricultural user.\u003c/p\u003e\n \u003cp\u003eThe increase in return flow creates two effects, as shown in Fig. 4. First, although the total volume of water available in all three of these experiments is fixed at 300 AF, the maximum economic value increases as the return flow fraction increases: the maximum attainable output with a 60% return flow is approximately 35% higher than it is when return flow is only 15%. This is simply a result of a higher total water availability for the downstream user, as return flows from the upstream user increase.\u003c/p\u003e\n \u003cp\u003eThe second effect of increasing return flows is a shift in the optimal allocation of water between the upstream and downstream users. When agricultural return flows are lowest at 15%, total economic value is maximized when the agricultural sector uses only 25% of its total demand, or approximately 125 AF (Fig.\u0026nbsp;4a), leaving the rest of the water for the higher-value downstream user. As agricultural return flows increase, however, the upstream agricultural sector can use a higher and higher fraction of its peak demand until at a 60% return flow it can use all of the water available (300 AF, or 60% of its peak demand) while still maximizing value for the whole economy. This scenario is possible because the lost revenue due to the water shortage for the industrial sector (200 AF \u0026ndash; 0.6*300AF\u0026thinsp;=\u0026thinsp;20 AF shortage) is more than compensated for by the increased production from the agricultural sector upstream.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"Section2\" id=\"Sec7\"\u003e\n \u003ch2\u003e3.4 Comparison to a prior appropriations scenario\u003c/h2\u003e\n \u003cp\u003eFor each of the evaluations above, we sought to find the allocation of water that maximized economic output, assuming that water could be freely re-allocated between users. In our final set of experiments, we compared two scenarios. The first is a \u0026ldquo;maximum value\u0026rdquo; scenario in which water can be freely traded to maximize overall economic output. The second is a \u0026ldquo;rigid\u0026rdquo; scenario in which the upstream user focuses on maximizing its own production. This latter scenario is similar to the way water is currently allocated across the Western United States: where a \u0026ldquo;senior\u0026rdquo; user makes decisions to optimize their own output, ignoring the needs of others. This system exists both because of the prior appropriations doctrine, and because mechanisms for water trade are currently limited (e.g., Chong and Sunding 2007; Howe and Goemans \u003cspan class=\"CitationRef\"\u003e2003\u003c/span\u003e; Howitt and Hansen \u003cspan class=\"CitationRef\"\u003e2005\u003c/span\u003e; Leonard et al., \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e\n \u003cp\u003eFigure\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e shows the difference in total output between these \u0026ldquo;rigid\u0026rdquo; and \u0026ldquo;maximum-value\u0026rdquo; scenarios. In all cases, the user with the lower demand but higher value per unit of water (\u0026ldquo;industry\u0026rdquo;) is downstream, and the user with the higher demand but lower value per unit of water (\u0026ldquo;agriculture\u0026rdquo;) is upstream. The blue curves (rigid) represent the attainable total value for each scenario if the upstream user focuses on maximizing its own production, and the red curve represents the maximum attainable total economic value. The benefits of re-allocation of water away from the prior appropriations regime are highest when water is scarce, as shown by the grey shaded regions highlighting the difference between the two allocations.\u003c/p\u003e\n \u003cp\u003eFigures\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003ea and \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003eb compare model results where the WTP ratio is 3:1 (5a) vs 6:1 (5b). In both cases, the agricultural return flow is 30%. In each of these scenarios, the most rapid divergence between the \u0026ldquo;rigid\u0026rdquo; and \u0026ldquo;free trade\u0026rdquo; scenarios occurs between 0-200 AF of total water. Here, the added value from water re-allocation is a result of the upstream agricultural user releasing all of its water to the downstream industrial user, who places a higher value on each unit of water. Beyond 200 AF, the downstream industrial user\u0026rsquo;s peak demand is fully satisfied, and agricultural production resumes. The difference between the rigid and trade optimized scenarios shrinks from this point up to a total water availability of ~\u0026thinsp;400 AF (3:1 WTP ratio) or ~\u0026thinsp;550 AF (6:1 WTP ratio), where the curves re-join. The location along the x-axis at which the rigid and optimized scenarios meet (400 AF vs 550 AF) reflects the difference in optimal allocation of water between the two sectors under these different WTP ratios (see Fig.\u0026nbsp;3).\u003c/p\u003e\n \u003cp\u003eIn our initial model runs, we also modified the location of the two users in the system: placing the higher-valued industrial user upstream, rather than downstream from the lower-valued agricultural user. However, in these experiments where the higher-valued industrial user was upstream, economic value was almost always maximized when this user took its full allocation of water. The exception to this rule occurs when the WTP ratio is small and the return flow from the industrial user is also small. Fig. 6 illustrates this effect for three scenarios where the industrial user is upstream. In the first two scenarios, the industrial user\u0026rsquo;s WTP is twice that of the agricultural user and its return flow ranges from 10% (Fig. 6a) to 40% (Fig. 6b). In the third scenario, the industrial user\u0026rsquo;s WTP is three times higher than the agricultural user and its return flow is 10% (Fig. 6c).\u003c/p\u003e\n \u003cp\u003eIn each of these cases, there is additional economic value to be added only over a very narrow range of total water availability, if the industrial user allows all of the water to be used by the agricultural user downstream. The peak increase in economic value from trade occurs at 500 AF of total water, where the complete transfer of water from industry allows the agricultural user to generate its maximum value. On either side of this peak, the range of total water availability over which trade increases economic value is sensitive to the return flow from industry and the WTP ratio. This is because the total economic value is universally higher with higher return flows or a higher WTP ratio, which limits the gains from trading downstream (compare the total value of \u0026ldquo;rigid\u0026rdquo; allocations between Figs.\u0026nbsp;6a-6b). The same effect occurs when the WTP ratio is higher (compare Figs.\u0026nbsp;6a-6c). For WTP ratios or industrial return flows much larger than the values shown in Fig.\u0026nbsp;6, the advantages of water re-allocation disappear altogether.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4. Discussion And Conclusions","content":"\u003cp\u003eOur simple model demonstrates two key points related to water allocation and use in water-scarce environments: First, we show that return flows cannot be ignored in analysis of economic value from these systems, because the optimal allocation of water depends on how much of the water is returned and can be used downstream. Second, we show that when water is scarce relative to total demand, the total economic value from water-intensive industries can be increased when water is re-allocated relative to a \u0026ldquo;rigid\u0026rdquo; prior appropriations system. While this result is consistent with prior research on the topic (Chong and Sunding \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Ghosh et al.; Hagerty \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), our model also illustrates several new points about the dynamics of this coupled natural-human system.\u003c/p\u003e \u003cp\u003eWhen water is re-allocated between users relative to a \u0026ldquo;rigid\u0026rdquo; allocation, we find that the change in total economic value is sensitive to at least three conditions: the scarcity of water relative to the total demand across all sectors (see Figs.\u0026nbsp;2 and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e5\u003c/span\u003e); the difference in willingness to pay for water between sectors (Fig.\u0026nbsp;3); and the return flows from the upstream user (Fig.\u0026nbsp;4). Our model also shows that the maximum economic value for the entire economy is not always achieved when a lower-valued, upstream user sacrifices all of its output in favor of a higher-valued, downstream user. This is because a fraction of the upstream user\u0026rsquo;s withdrawals remain available to the downstream user as return flows, allowing some of the water in the system to be extracted twice. Depending on the return flow fraction from the upstream user and the relative willingness to pay for water between the two users, the downstream user may be able to maximize its value in a water-scarce scenario even if the upstream user takes a fraction of the water for its own use (see Figs.\u0026nbsp;3\u0026ndash;4).\u003c/p\u003e \u003cp\u003eOur economic analysis is idealized, in that we used a partial equilibrium analysis rather than a more complete, computable general equilibrium (CGE) analysis to simulate the value placed on water. Because of this, our current framework implicitly assumes that no other prices in the economy (like wages of workers in each sector) are impacted by the allocation changes described here. We further assume that there are no other market failures (tax distortions, non-market goods, etc.) that would be impacted by changes in water allocation. These additional complexities are best explored in a CGE framework, which is a focus of ongoing research.\u003c/p\u003e \u003cp\u003eOur physical model is clearly an abstraction of real water systems, which are characterized by multiple users with a range of demands, values and seniority. While our modeling framework is a simplification of the many processes, interactions, and feedbacks among multiple users in real systems, it is also easily interpreted, allowing us to explore the key factors that control the dynamics of this coupled human-natural system. Future work will be focused on gradually adding complexity to the model, so that we can begin to explore time-varying water demand and supply among multiple user groups in a more realistic system.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthical Approval:\u0026nbsp;\u003c/strong\u003eNot applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to Participate\u003c/strong\u003e: Not applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to Publish\u003c/strong\u003e: All authors consent to publication of this manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors Contributions\u003c/strong\u003e: C. Wobus, E. Small, J. Carbone, B. Livneh, B. Szafranski, H. Kamen and P. Modi all contributed to the study conception and design. Model development and analysis were completed by C. Wobus, with support from E. Small. The first draft of the manuscript was written by C. Wobus, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e: This work was supported by US National Science Foundation Grant #2009922, awarded to B. Livneh.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interests\u003c/strong\u003e: The authors have no relevant financial or non-financial interests to disclose.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e: Data and materials used in the preparation of this manuscript will be made available upon request from the corresponding author.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003e\u003cspan\u003eBrewer J, Glennon R, Ker A, Libecap GD (2007) Water markets in the west: prices, trading, and contractual forms. NBER Working Paper 13002. Available: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.nber.org/papers/w13002\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eBurness SH, Quirk JP (1979) Appropriative Water Rights and the Efficient Allocation of Resources. Am Econ Rev 69(1):25\u0026ndash;37\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eChong H, Sunding D (2006) Water markets and trading. 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West Academic Publishing\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eWeckstr\u0026ouml;m MM, \u0026Ouml;rm\u0026auml; VA, Salminen JM (2020) An order of magnitude: How a detailed, real-data-based return flow analysis identified large discrepancies in modeled water consumption volumes for Finland. Ecol Ind 110:105835. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ecolind.2019.105835\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eZellmer SB, Amos AL (2021) Water law in a nutshell. West Academic Publishing\u003c/span\u003e\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"water-resources-management","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"warm","sideBox":"Learn more about [Water Resources Management](https://www.springer.com/journal/11269)","snPcode":"11269","submissionUrl":"https://submission.nature.com/new-submission/11269/3","title":"Water Resources Management","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-1485992/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1485992/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe allocation of water in the arid western United States is governed by complex water laws that dictate who receives water, how much they receive, and when. Because these rules are generally based on the seniority of water rights, they are not necessarily focused on maximizing economic value across the entire economy. The maximization of value from water use economy-wide is a complex optimization problem that must explicitly consider each user\u0026rsquo;s peak water demand, willingness to pay function, and the feedbacks among users in a coupled natural-human system model. In this study, we distill these complexities into a simple model of a two-user economy that allows us to explore the relationships among water availability, water use, and value in water-limited systems. We find that the total economic value generated from water-dependent users depends primarily on the total water available in the system. However, for a given volume of water available, the way that water is allocated between the two users also has a significant effect on economic value. The degree to which this allocation affects value depends primarily on the relative willingness to pay for water between the two users, and on the return flows generated from each sector\u0026rsquo;s water use. While our simple two-user model is an abstraction of the complexities inherent in natural systems, our study provides important insights into the coupled natural-human system dynamics of water allocation and use in water-limited environments.\u003c/p\u003e","manuscriptTitle":"Water allocation, return flows, and economic value in arid basins: Results from a coupled natural-human system model","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-04-08 17:47:11","doi":"10.21203/rs.3.rs-1485992/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewersInvited","content":"","date":"2022-04-06T06:34:46+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2022-03-28T23:52:27+00:00","index":"","fulltext":""},{"type":"submitted","content":"Water Resources Management","date":"2022-03-24T11:03:05+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"water-resources-management","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"warm","sideBox":"Learn more about [Water Resources Management](https://www.springer.com/journal/11269)","snPcode":"11269","submissionUrl":"https://submission.nature.com/new-submission/11269/3","title":"Water Resources Management","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"5ea5a4e0-ddba-4183-a57a-d98e26b43129","owner":[],"postedDate":"April 8th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2022-04-08T17:47:12+00:00","versionOfRecord":[],"versionCreatedAt":"2022-04-08 17:47:11","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-1485992","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-1485992","identity":"rs-1485992","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}