Strategic Distribution of Water Conservation Incentives under Drought-Prone Conditions: A case study in the Red River Basin U.S

Hamed Zamani Sabzi1, Rachel Fovargue2, Shabnam Rezapour-Behnagh3, Hernan A. Moreno4, Thomas M. Neeson5 (1, 2, 4, and 5)University of Oklahoma Norman Campus, Department of Geography and Environmental Sustainability, Norman, OK, United States, (3) Florida International University, Department of Engineering and Computing, Miami, FL, United States, AGU 2018 H51H-1411

We want to optimize the water release decisions in all the reservoirs over Abstract Background of Research the planning horizon to simultaneously maximize the average satisfaction levels Many societies around the world face fresh water shortages that require strategic decision making in of the network’s agriculture and municipal sectors and ecosystems. Thus, for allocating resources between human uses and environmental ecosystems. In many regions, water the network model the objective functions are: 푑 퐷퐴푡 σ∀푑∈퐷 σ∀푡∈푇 1− policy makers are investigating potential water conservation plans that rely on incentivizing water 푇퐴푑 Max 푍퐴 = 푡 (16) 푇 . 퐷 users to reduce the consumption rather than governing regulations. However, in large watersheds, 푑 퐷퐹푡 σ∀푑∈퐷 σ∀푡∈푇 1− 푇퐹푑 such as Red River of South (USA) with 38 major dams, finding the most cost-effective locations and Max 푍퐹 = 푡 (17) 푇 . 퐷 appropriate time is a challenging step for water policy makers and conservation planners. In this We now extend the network model to the case where conservation study, we develop a spatiotemporal framework that strategically enables conservation practitioners to organizations wish to incentivize water users to use less water. We assume that there is a given budget that may be used to incentivize water conservation and apply incentives for water conservation actions in balancing societal and environmental water 푑 reduce the total water needed for societal use ( σ∀푑∈퐷 σ∀푡∈푇 푇퐴푡 ) up to 휃 demand. We apply this model to the Red River Basin, and highlight the challenges involved with percentage. To determine when and where a conservation group should simultaneously meeting societal and environmental water goals. We draw two main conclusions. incentivize water conservation actions, we have to determine how the budget First, modest decreases in societal water usage can significantly lower water conflicts through the should be allocated in space and time (i.e., among reservoirs and months). 푑 basin while these water conservation actions are strategically and spatiotemporally allocated. Second, We represent water conservation actions by adding new variables 훼푡 (∀푡 ∈ 푇 푑 we develop trade-off analyses between ecosystem and societal demands to find the most applicable and ∀푑 ∈ 퐷) to the network model. The variable 훼푡 represents the reduction made Fig. 2. An example network of six reservoirs. Inflows and outflows to each 푑 in the societal water need of reservoir 푑 at time step 푡 푇퐴푡 by incentivizing reduction in societal water usage that is required to fully satisfy both societal and environmental reservoir are given by the network water balance equation (Eq. (1)). water conservation. Thus, societal water needs after accounting for water 푑 푑 water goals. Our general approach through this study is readily transferable to many drought-prone 푆푡−1 + 퐼푡 + 푃푟푡 − 퐸푡 − 푃푡 − 퐴푡 − 퐹푡 = 푆푡 (1) conservation incentives are equal to 푇퐴푡 − 훼푡 . Using these new variables, watersheds worldwide to find water conservation strategies that simultaneously balance multiple constraint (10) in the optimization model should be modified as follows:

푑 푑 푑 푑 competing water users. where, (푆푡) is the storage at each time step, (푆푡−1) is the water storage left from 퐴푡 + 퐷퐴푡 ≥ 푇퐴푡 − 훼푡 (∀푡 ∈ 푇 and ∀푑 ∈ 퐷) (18) the previous time step, 퐼 is the ground and surface water inflow at that time ( 푡) Given the total budget 휃, we also add a budget constraint that stipulates that the step, (푃푟 ) is the precipitation amount in the reservoir’s basin, (퐸 ) is the Motivating Questions and objectives 푡 푡 total reduction in societal water needs achieved via conservation incentives evapotranspiration loss, (푃푡) is the seepage loss, (퐴푡) is the water release for across all reservoirs and time steps should be less than or equal to this budget: ● Investigating trade-offs analysis between societal water demands and environmental agriculture and municipal use, and (퐹푡) is the water release to the reservoir’s 푑 푑 σ∀푑∈퐷 σ∀푡∈푇 훼푡 ≤ 휃 ∙ σ∀푑∈퐷 σ∀푡∈푇 푇퐴푡 (19) demands (instream flow needs) downstream ecosystem at that time step. 퐴푡 + 퐷퐴푡 ≥ 푇퐴푡 (2) In addition, the following constraints should be added to the model:

퐴푑 훼푑 퐹푡 + 퐷퐹푡 ≥ 푇퐹푡 (3) 푡 푡 ● Optimal allocation of limited water resources among competing water using sectors in 푑 + 푑 ≤ 1 (∀푡 ∈ 푇 and ∀푑 ∈ 퐷) (20) 푇퐴푡 푇퐴푡

(푇퐴푡) is the targets for societal water needs and (푇퐹푡) is the environmental water 푑 a network of multiple dams in Red River Basin (RRB) 훼푡 ≥ 0 (∀푡 ∈ 푇 and ∀푑 ∈ 퐷) (21) Fig. 5. Spatial distribution of total annual water conservation actions when θ= 21%. needs. We quantify the deficiencies in the water volume assigned to the societal Fig. 4. Average annual satisfaction levels for societal flow targets (A) and Panel (A) shows reduction societal water needs of each reservoir in units of acre-feet 퐷퐴 퐷퐹 uses ( 푡) and the water released to meet environmental flow targets ( 푡). Constraint (20) calculates the societal satisfaction levels of reservoirs after environmental flow targets (B), overlain on reservoir network topology. 푑 ● Feasibility assessment of water conflict resolution by providing the efficient allocation (i.e.,σ푡 푎푡 ∀d ∈ D). Panel (B) shows the same data as a percentage reduction of the The satisfaction levels of meeting societal water targets and environmental flow water conservation actions that can be 100 percent at most. Part of the Reservoir locations in this layout are approximate (see Fig. 1) but have been original societal water target. Reservoir locations in this layout are approximate (see 훼푑 퐷퐴 퐷퐹 푡 퐴 푡 퐹 푡 satisfaction is due to reduction in the water needs ( 푑) while the rest is defined slightly modified for legibility. targets at the time step 푡 (∀푡 ∈ 푇) are 푍푡 = (1 − ) and 푍푡 = (1 − ) respectively. 푇퐴푡 Fig. 1) but have been slightly modified for legibility. 푇퐴푡 푇퐹푡 of water conservation actions across the RRB 퐴푑 퐴 푡 Therefore, the average satisfaction levels over the planning horizon are 푍 = as previously by the water release assigned to the societal needs ( 푑). 푇퐴푡 퐷퐴푡 퐹 퐷퐹푡 σ∀푡∈푇 1 − ൗ 푇 and 푍 = σ∀푡∈푇 1 − ൗ 푇 . Here, the notation 푇 indicates the Constraint (21) ensures that the water reduction of each reservoir is a non- ● Quantifying the substantial reduction in societal water usage that is required to fully 푇퐴푡 푇퐹푡 size of the set T, i.e. the number of time periods in the planning horizon. negative value. So, the average satisfaction level of the societal needs in the Conclusions whole network over the planning horizon , 푍퐴, should be modified as follows: satisfy societal and environmental flow goals. The mathematical model for this optimal decision making is as follows: 푑 푑 퐴푡 훼푡 We developed a new optimization framework that enables water managers to: σ∀푑∈퐷 σ∀푡∈푇 푑+ 푑 퐴 퐷퐴푡 퐴 푇퐴푡 푇퐴푡 Max 푍 = σ∀푡∈푇 1 − ൗ 푇 (4) Max 푍 = (22) Study Basin with a network of multiple dams 푇퐴푡 푇 . 퐷 퐹 퐷퐹푡 Max 푍 = σ∀푡∈푇 1 − ൗ 푇 (5) 푇퐹푡 1) delineate optimal trade-offs between societal water goals and instream flow needs, but also Subject to: 푆푡−1 + 퐼푡 + 푃푟푡 − 퐸푡 − 푃푡 − 퐴푡 − 퐹푡 = 푆푡 ∀푡 = 2, 3, … , 푇 (6)

푆 + 퐼 + 푃푟 − 퐸 − 푃 − 퐴 − 퐹 = 푆 (7) 12 1 1 1 1 1 1 1 2) optimally allocate water conservation actions to reduce societal water consumption across the river network.

퐹 푆푡 ≤ 퐶 (∀푡 = 1, 2, … , 푇 ) (8) Optimal allocation of water conservation Our application to the Red River basin highlighted the challenges of simultaneously meeting societal and 푆 ≥ 퐶푀 (∀푡 = 1, 2, … , 푇 ) (9) 푡 incentives 퐴푡 + 퐷퐴푡 ≥ 푇퐴푡 (∀푡 = 1, 2, … , 푇 ) (10)

퐹푡 + 퐷퐹푡 ≥ 푇퐹푡 (∀푡 = 1, 2, … , 푇 ) (11) environmental water goals there, but also illustrated how efficient allocation of water conservation actions

퐴푡, 퐹푡, 퐷퐴푡, 퐷퐹푡, 푎푛푑 푆푡 ≥ 0 (∀푡 = 1, 2, … , 푇 ) (12)

In a network of reservoirs, in addition to the water inflow to each reservoir across the basin might considerably reduce water conflicts. This approach should be readily transferable to 푑 from its own basin (퐼푡 ), the released water from its upstream reservoirs 푑ሖ σ푑ሖ ∈퐷 푑 퐹푡 for environmental needs is also added to the reservoir’s water storage left from the previous time step (푆푑 ). So, the mass balance equation 푡−1 drought-prone river networks worldwide to resolve conflicts between competing water users. for a single reservoir (Eq. 1) is modified to include the contributions from upstream reservoirs:

Fig. 1. Study area, Red River Basin with the location of the 38 major reservoirs within the Red River basin. 푆푑 + σ 퐹푑ሖ + 퐼푑 + 푃푟푑 − 퐸푑 − 푃푑 − 퐴푑 − 퐹푑 = 푆푑 ∀푡 ∈ 푇 푎푛푑 ∀푑 ∈ 퐷 푡−1 푑ሖ ∈퐷 푑 푡 푡 푡 푡 푡 푡 푡 푡 Acknowledgements (13) • Red River’s headwater is located in New Mexico, and it flows across Texas through the Texas- We thank the LCLUC and SRL research groups at OU for advice and feedback on our modeling approach. The Deficiencies in the water volume released from reservoir 푑 (∀푑 ∈ 퐷) at time Oklahoma border, enters the Arkansas, then reaches the Mississippi River in Louisiana. 푑 step 푡 (∀푡 ∈ 푇) for societal needs (퐷퐴푡 ) and the water released for the project described in this publication was supported by the Science Applications division of the Southwest environment (퐷퐹푑) are calculated analogously to the single-reservoir model: 푡 Region of the U.S. Fish and Wildlife Service, and by Grant No. G17AP00120, Balancing Water Usage and • Red River of the south is considered as fourth long river in terms of navigation and economic 푑 푑 푑 퐴푡 + 퐷퐴푡 ≥ 푇퐴푡 ∀푡 ∈ 푇 푎푛푑 ∀푑 ∈ 퐷 (14) importance in the United States. Ecosystem Outcomes Under Drought and Climate Change: Enhancing an Optimization Model for the Red 퐹푑 + 퐷퐹푑 ≥ 푇퐹푑 ∀푡 ∈ 푇 푎푛푑 ∀푑 ∈ 퐷 (15) 푡 푡 푡 River, from the United States Geological Survey. • The spatial map of the study area illustrates the stream networks across the RRB, real time gauge The satisfaction level of meeting societal water targets and environmental 퐴,푑 flow targets for reservoir 푑 (∀푑 ∈ 퐷) at time step 푡 (∀푡 ∈ 푇) would be: 푍푡 = (1 − stations, and major dams 푑 푑 퐷퐴푡 퐹,푑 퐷퐹푡 푑) and 푍푡 = (1 − 푑) respectively. Therefore, the average satisfaction levels References 푇퐴푡 푇퐹푡 푑 퐴,푑 퐷퐴푡 of reservoir 푑 over the planning horizon are: 푍 = σ∀푡∈푇 1 − 푑 ൗ 푇 Fig. 3. Pareto curves between meeting societal flow targets (ZA) and 푇퐴푡 Sabzi, Hamed Zamani, Shabnam Rezapour, Rachel Fovargue, Hernan Moreno, and Thomas M. Neeson. "Strategic allocation of water • The watershed area of the Red River Basin is about 89,970 square miles. 푑 퐹,푑 퐷퐹푡 ecosystem flow targets (ZF) in the Red River. Points show actual model and 푍 = σ∀푡∈푇 1 − 푑 ൗ 푇 . In the whole network of reservoirs, the average 푇퐹푡 solutions, and the curves are lines of best fit to these points. The lowest conservation incentives to balance environmental flows and societal outcomes." Ecological Engineering 127 (2019): 160-169. 푑 퐷퐴푡 σ∀푑∈퐷 σ∀푡∈푇 1− 푇퐴푑 curve represents the tradeoff in meeting societal and ecosystem water • It passes through about 1,600 miles from its headwater in New Mexico to the Mississippi River. satisfaction levels would be: 푍퐴 = 푡 and 푍퐹 = 푇 . 퐷 McPherson, R., et al., 2016. Impacts of climate change on flows in the Red River Basin.Final report to the South Central Climate Science 푑 goals given current societal water usage and no water conservation (i.e., 퐷퐹푡 σ∀푑∈퐷 σ∀푡∈푇 1− 푇퐹푑 θ= 0%). The remaining curves give the Pareto tradeoff given some 푡 . Center. Available at: http://www.southcentralclimate.org/content/documents/RedRiverClimateChange_Final Report.pdf. (accessed April 푇 . 퐷 percentage reduction in aggregate annual societal water needs (i.e., values of θ) across the basin. 26, 2018). Contact information: [email protected]