Spatial planning for water sustainability projects under climate uncertainty: balancing human and environmental water needs

We focus on the Red River, a major river basin in the south-central USA where water availability follows a strong spatial gradient from west to east. Historical precipitation follows this gradient from the RRB's headwaters in the arid Texas panhandle (less than 600 mm yr⁻¹) to wet Mississippi river lowlands (greater than 1500 mm yr⁻¹) (figure 1(A)). More than 3 million people currently live within the RRB (US Census Bureau n.d.) with a high economic dependence on water. Just outside the basin boundaries, growing metropolitan areas like Oklahoma City, OK and Dallas, TX rely on RRB water and have approved construction projects to expand withdrawals (114th Congress 2016). Water quantity also plays a key role in regulating ecosystem services related to water quantity and quality (e.g. salinity, algal blooms, and pathogens), which strongly impact residents (Green et al 2015). Water availability is also critical for endangered species of fish and mussels (e.g. Ouachita rock-pocketbook Arkansas wheeleri) (Vaughn and Pyron 1995). Reservoirs have been constructed throughout the basin for flood control mechanisms and water storage. While most reservoirs play a key role in ensuring societal water supplies, a subset dry during drought conditions or are anticipated to dry with future groundwater mining and climate change (Brikowski 2008). These engineering interventions each create a decision point at which humans can choose how much water to store for future uses and how much water to release downstream to maintain instream flows (Guo et al 2019).

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Three GCMs from the Coupled Model Intercomparison Project Phase 5 (Taylor et al 2012) were selected based on their historical performance over the region and climate sensitivity as described in Bertrand and Mcpherson (2019). These GCMs (i.e. Max Planck Institute for Meteorology Earth System Model-Low Resolution (MPI-ESM-LR) (Giorgetta et al 2013), Community Climate System Model, version 4 (CCSM4) (Kluzek 2010), and Model for Interdisciplinary Research on Climate, version 5 (MIROC5) (Watanabe et al 2011)) were found to capture a representative range of temperature and precipitation biases and climate sensitivities across the larger GCM ensemble. Including only three GCMs was necessitated by the computational demand of the subsequent downscaling and hydrologic modeling. Downscaled versions of these GCMs under multiple representative concentration pathways (RCP 2.6, 4.5, 8.5) (van Vuuren et al 2011) illustrate diverging projections for annual precipitation and thus water availability. CCSM4 generally predicts the drier conditions, MIROC5 is more moderate in its precipitation shifts, and MPI-ESM-LR predicts increased precipitation across large parts of the basin (figure 1(B)).

Downscaled future climate projections over the RRB were produced for each GCM/RCP combination for a future period (2011–2099) using the Cumulative Density Function transform (Vrac and Michelangeli 2009) to create a new spatial scale of 1/8 degree for all models (Bertrand and Mcpherson 2019). Transfer functions used to predict future regional parameters were calibrated using daily temperature and precipitation observations sourced from Livneh et al (2013) over the historical period (1961–2005). Daily precipitation values from these projections were used to estimate monthly precipitation contributions to each reservoir in our network model (section 2.3).

Estimates of runoff and streamflow under historical (1961–2011) and future (2011–2099) climate scenarios were derived from a variable infiltration capacity (VIC) model parameterized with land cover and future climate data (Xue et al 2016). Details of the VIC calibration process are given by Xue et al (2016). Briefly, Livneh data were used as observations to benchmark VIC outputs (version 4.1.2.h.), and all data were re-gridded to 1/8°. A digital elevation model (DEM) was derived from the 30 arcsec DEM (HydroSHEDS) and flow direction fields were obtained from the river-routing network data set produced by Wu et al (2011). Calibration was via multi-site cascading calibration over an abbreviated time period (1983–1990). Model validation used Livneh data (1991–2011), and assessment scores included the Nash-Sutcliffe model efficiency coefficient (calibration: 0.62, validation: 0.59), correlation coefficient (c: 0.8, v: 0.79) and percent bias (c: 7%, v: 11%).

The parameterized VIC model computed unit-area based runoff across the RRB under all climate projections described above for historical and predictive time periods. These model results informed reservoir inflow and evaporation estimates for the optimization model described in the next section. Inflow was derived from naturalized streamflow estimates of the reservoir's basin. Daily evaporation rates were converted to monthly evaporation volumes per reservoir by summing across days and multiplying by the typical surface area of the reservoir. For more details on the hydrologic modeling process, see Xue et al (2016) and Zamani Sabzi et al (2019a).

We used a mathematical model to optimize water allocation in a network of reservoirs to meet both societal and ecosystem water needs. Using a water balance approach, we model the inflows and outflows of each reservoir in the RRB network at monthly timesteps, and a total time horizon $T = \left\{ {t = 1,\,2,\, \ldots ,\,\left| T \right|} \right\}$. In the RRB, a monthly timestep is the shortest frequency at which instream flow and reservoir release decisions might realistically be made; indeed, the current version of the Oklahoma Comprehensive Water Plan advocates seasonal, not monthly, flow targets (Oklahoma Water Resources Board 2012). Reservoir (d) receives a given inflow ($I_t^d$) from ground and surface water sources as well as a total estimated precipitation amount (${\text{Pr}}_t^d$). These sources are combined with water stored in the reservoir from the previous time step ($S_{t - 1}^d$) before the model subtracts losses: evapotranspiration ($E_t^d$), releases for agriculture and municipal use ($A_t^d$), and water released downstream ($F_t^d$). The downstream releases from reservoirs directly upstream are also added into the inflow for each reservoir $\left( {\sum\limits_{\mathop {{\textrm{ }}d} \in {D^{\left( d \right)}}} {F_t^{\mathop {{\textrm{ }}d} }} } \right)$. Equation (1) gives the full water balance equation.

$$\begin{align}& S_{t - 1}^d + {\text{ }}\left( {\sum\limits_{d \in {D^{\left( d \right)}}} {F_t^d} } \right) + I_t^d + {\text{Pr}}_t^d - E_t^d - A_t^d - F_t^d = S_t^d{\text{ }}\notag\\ &\qquad\ \left( {\forall t \in T{\text{ and }}\forall d \in D} \right)\end{align} \tag{ 1 }$$

At each time step, the key management decision is to determine the total quantity of water to withdraw from each reservoir for societal uses (${A_t}$) and the quantity to release downstream to support ecology and ecosystem services (${F_t}$). Water withdrawn from the reservoir or released downstream should be as close as possible to target values for societal water needs, $T{A_t}$, and environmental water needs, $T{F_t}$, respectively. When water supply is limited, simultaneously satisfying both targets will be infeasible. In these circumstances, we quantify water deficiencies as $D{A_t}$ and $D{F_t}$ with the following constraints:

$$\begin{equation}A_t^d + DA_t^d \ge TA_t^d{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {\forall t \in T\ \mathrm{{and}}\ \forall d \in D} \right)\end{equation} \tag{ 2 }$$

$$\begin{equation}F_t^d + DF_t^d \ge TF_t^d{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {\forall t \in T\ \mathrm{{and}}\ \forall d \in D} \right)\end{equation} \tag{ 3 }$$

The 'satisfaction' for meeting consumptive use and instream flow targets for reservoir $d$ ($\forall d \in D$) at time step $t$ ($\forall t \in T$) is defined as $Z_t^{A,d} = \left( {1 - \frac{{DA_t^d}}{{TA_t^d}}} \right)$ and $Z_t^{F,d} = \left( {1 - \frac{{DF_t^d}}{{TF_t^d}}} \right)$ respectively. By averaging these satisfaction levels across all time steps and all reservoirs we can define the two objective functions:

$$\begin{equation}{\textrm{Max }}{Z^A} = \frac{{\sum\limits_{\forall d \in D} {\left( {\sum\limits_{\forall t \in T} {\left( {1 - \frac{{DA_t^d}}{{TA_t^d}}} \right)} } \right)} }}{{\left| T \right|.\left| D \right|}}\end{equation} \tag{ 4 }$$

$$\begin{equation}{\textrm{Max }}{Z^F} = \frac{{\sum\limits_{\forall d \in D} {\left( {\sum\limits_{\forall t \in T} {\left( {1 - \frac{{DF_t^d}}{{TF_t^d}}} \right)} } \right)} }}{{\left| T \right|.\left| D \right|}}\end{equation} \tag{ 5 }$$

Subject to:

$$\begin{equation}S_{t - 1}^d + {\text{ }}\left( {\sum\limits_{d \in {D^{\left( d \right)}}} {F_t^d} } \right) + I_t^d + {\text{Pr}}_t^d - E_t^d - A_t^d - F_t^d = S_t^d\end{equation} \tag{ 6 }$$

$$\begin{equation}S_t^d \le C_d^F\end{equation} \tag{ 7 }$$

$$\begin{equation}A_t^d + DA_t^d \ge TA_t^d\end{equation} \tag{ 8 }$$

$$\begin{equation}F_t^d + DF_t^d \ge TF_t^d\end{equation} \tag{ 9 }$$

$$\begin{equation}A_t^d,{ }F_t^d,{ }DA_t^d,{ }DF_t^d,\ \mathrm{{and}}\ S_t^d \ge 0.\end{equation} \tag{ 10 }$$

$$\begin{equation*}(\forall t \in 1,{ }2, \ldots ,{ }\left| T \right|\ \mathrm{{ and}}\ \forall d \in 1,2, \ldots ,\left| D \right|)\end{equation*}$$

Constraint (6) reinforces the water balance equation (equation (1)) at each time step. Constraint (7) ensures that the water quantity per reservoir does not exceed capacity ($C_d^F$). Constraints (8)–(10) estimate water deficiencies and keep all values of water quantities positive.

To parameterize this model, we calculated the set of upstream reservoirs (${D^{\left( d \right)}}$) and identified a maximum capacity ($C_d^F$) for each reservoir node in the network from the National Hydrography Data set (U.S. Geological Survey 2017). Parameter estimates representing climatic conditions ($I_t^d$, ${\text{Pr}}_t^d,$ and $E_t^d$) are drawn from downscaled climate projections and VIC modeling described in previous sections (Xue et al 2016, Bertrand and Mcpherson 2019). Water withdrawal target values $\left( {TA_t^d} \right)$ are derived from water rights data using data from Texas Commission on Environmental Quality, the OWRB, and the US Geological Survey (for Arkansas and Louisiana) and are summarized in the Bertrand and Mcpherson (2019) RiverWare model for the basin. Initialization conditions for the reservoirs were also drawn from this RiverWare model. Target volumes for downstream releases $\left( {TF_t^d} \right)$ were calculated as 60% of the average annual flow in each reach based on instream flow recommendations from Tennant (1976). Alternate target-setting methods could be implemented within the same modeling framework. The optimization ran over 240 timesteps (20 years) with all years' subject to the same parameterized conditions. In this way, we could assess any burn-in period due to initial conditions or incongruous behavior at the terminal end of the time period, sometimes observed in dynamic optimizations. The first and last 12 timesteps were disregarded from analysis for this reason. Our optimization model is a linear programming model coded and solved using LINGO software. More details on the optimization method and model can be found in Zamani Sabzi et al (2019b).

We performed several analyses using optimal water allocation solutions from the RRB network model to explore tradeoffs in water management objectives as well as spatiotemporal water scarcity trends under climate change.

First, we delineated tradeoff curves using Pareto-optimal solutions that balance consumptive societal withdrawals and downstream environmental flows targets. Figure 2 displays the average satisfaction of societal water targets (${Z^A}$) across all time steps and all reservoirs (horizontal axis) against the average satisfaction of environmental water targets (${Z^F})\,$across all time steps and reservoirs (vertical axis). Each climate projection curve (i.e. the set of points that belongs to a particular combination of climate projection and future time period) was created by systematically varying the relative importance (i.e. weight) of meeting societal vs. environmental water targets. To create figure 2, the relative weights of the two objectives ${Z^A}$ and ${Z^F}\,$were varied inversely from 0 to 1. Eighteen curves are illustrated, representing all combinations of nine climate scenarios and two time periods: near present (2010–2030) and future (2031–2050).

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For the remaining analyses (figures 3 and 4), we assigned equal weight to meeting societal and environmental water goals (0.5 weight for ${Z^A}$ and ${Z^F}$). We then calculated total satisfaction for a particular reservoir in a particular month as the average of the societal satisfaction (0 < ${Z^A}$ < 1) and environmental satisfaction (0 < ${Z^F}$ < 1). To compare basin-wide total satisfaction across months, we calculated mean total satisfaction in each month (i.e. the vertical axis in figure 3) by averaging total satisfaction across all reservoirs in the network. To further aggregate to seasonal satisfaction, we averaged satisfaction values within a three-month period following standard meteorological definitions of seasons (Winter = December, January, February; Spring = March, April, May; Summer = June, July, August; Fall = September, October, November). To spatially compare average annual satisfaction across all reservoirs, the total satisfaction solution to each reservoir was averaged across all monthly solutions (figure 4).

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Water resource managers in the RRB invest in a wide range of projects to enhance water sustainability, including voluntary incentives to water users to reduce consumption; retrofitting of existing infrastructure; wastewater reuse and recycling; invasive species removal (e.g. salt cedar); artificial recharge of aquifers; and the potential construction of new reservoirs (Oklahoma Water Resources Board 2012). Our identification of three classes of reservoirs (sometimes, often, and rarely water scarce) illustrates how joint consideration of spatiotemporal patterns of both water scarcity and future climate uncertainty might guide decision-makers' efforts to distribute investments among these various project types and across the RRB (figure 5). For reservoirs and regions classified as 'often water scarce' water resource planners can be confident that investments in water sustainability will boost water availability under all projections. Therefore, planners in this region may make 'secure investments' in high cost, high reward infrastructure projects (e.g. reservoirs, pipelines or desalination structures (Mashburn and Sughru 2003)) because there is relatively low risk that they will become stranded assets. Nevertheless, infrastructure projects at some 'often water scarce' locations may not be cost-effective; further return-on-investment analysis may be needed to site infrastructure projects among these locations (Rodriguez et al 2012, Neeson et al 2015) or prioritize locations for economic incentives to reduce demand (Qureshi et al 2010).

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Similarly, persistent water availability in regions deemed 'rarely water scarce' allows for a 'secure resource' strategy (figure 5). Assuming that societal water needs do not increase dramatically, and that water is efficiently allocated across the RRB, there should be enough surface water in these regions to satisfy future societal and ecological needs. Therefore, 'status quo' management may be appropriate, including careful monitoring of current consumption and evaluation of proposals for expanded societal use.

Regions classified as 'sometimes water scarce' require careful planning: under-investment in water sustainability may have dire consequences if future water availability declines, but investments have the potential to become stranded assets in a wetter future. Thus, decision-makers may prefer 'low regret' (flexible, low-cost or temporally targeted) investments (figure 5). Here, flexibility is a priority. For example, short-term grants or renewable incentives for water-use reduction would allow investments to shift among regions as climate patterns change. Indeed, economic incentives have been shown to be effective tools for reducing water demand (Qureshi et al 2010, Nikouei et al 2012) and the costs of reallocating them are minimal compared to those of infrastructure projects. Similarly, lease programs for high-efficiency irrigation infrastructure would enable equipment to be moved to locations with greatest benefit (Robertson et al 1982). For smaller dams, flexible designs would enable dam height to be raised to increase storage without incurring the up-front costs of a single large reservoir (Fletcher et al 2019). In the residential sector, investments in water sustainability programs (e.g. incentivizing efficient appliances and low-flow toilets) (Oklahoma Water for 2060 Advisory Council 2015) involve relatively little financial outlay, but the aggregate water savings could be substantial if widely adopted.

Our approach employs top-down modeling (i.e. the use of downscaled hydrologic projections to map uncertainty) to enable bottom-up, location-specific decision-making (Dessai and van der Sluijs 2007) to address IPCC recommendations to consider climate uncertainty in planning efforts (IPCC 2014). For example, the application of our conceptual framework (figure 5) to the RRB (figure 4) provides a basis for a diverse set of stakeholders to evaluate a range of water resource projects with different levels of risk. With large investments in water sustainability expected over the coming decades (Hartman and Kober 2020), our framework may be most useful for choosing among candidate projects at a regional level. For example, the OWRB and the Texas Water Development Board have both identified the reuse of wastewater as an important strategy for boosting water availability (Oklahoma Water Resources Board 2012). Given that wastewater reuse infrastructure is both expensive and inflexible, our climate uncertainty map could be used to identify locations where water reuse infrastructure has low potential of becoming a stranded asset over the coming decades. While this study used relatively few GCMs, this climate uncertainty map approach could be implemented with additional GCMs and downscaling techniques (if feasible for interested stakeholders) to capture a broader range of the climate uncertainties. For locations with greater climate uncertainty, more flexible investments, such as education or economic incentives to change water users' behavior, may be more appropriate.

Our analysis highlights locations where the value of information from additional data and modeling may be high. Notably, regions with the highest uncertainty in future water scarcity may highlight research investment opportunities where there is value for reducing uncertainty in climate projections. For example, the northernmost reservoir, Foss, has <20% water satisfaction under the CCSM4, RCP 8.5 projection; in this possible future, serious water conflicts will occur unless investments in water sustainability are made. Yet Foss exhibits 100% water satisfaction under two other climate projections, in which case investments would become stranded assets. Thus, information from additional climate and water modeling would be highly valuable if it enables decision-makers to better compare risks and consequences of water shortages (under dry projections and little investment) vs. stranded assets (under wet projections and large investment). Specifically, there is a need for improved understanding of groundwater-surface water interactions across the basin. Many Great Plains rivers have diminished hydrological connectivity with aquifers due to groundwater pumping (Perkin et al 2017), but groundwater-surface water interactions are poorly understood in key sub-basins (Oklahoma Water Resources Board 2012).

We identified strategies for allocating sustainability investments among different types of projects and across space by coupling climate projections with a basin-scale water planning model. We focused on the nine projections most representative of future climate over the RRB; nevertheless, estimates of future uncertainty in water scarcity may shift with consideration of additional climate projections. Further, we examined outcomes for the near future (up to 30 years), but consideration of longer time horizons may be important for certain management strategies or infrastructure types. Our analysis also allowed the planning model to have perfect foresight over future climate conditions; repeating our analysis with non-perfect foresight would increase future uncertainty but our conceptual framework (figure 5) would still apply.

We also assumed that societal water demand remained constant in all future projections; future work could integrate uncertain water demand projections (Oklahoma Water Resources Board 2012) into our conceptual framework (figure 5) by replacing the vertical axis with a more comprehensive estimate of water uncertainty stemming from all sources. We also assumed that environmental flow targets were equally important in all reaches; future analyses could place greater weight on meeting flow targets in reaches where species are projected to be highly impacted by climate change (Gill et al 2020) or where ecosystem services are highly valued (Castro et al 2016, Burch et al 2020). Alternatively, by considering our results in combination with studies about human actors in the basin, such as the stakeholder perceptions of water management decisions (Kharel et al 2018) and the influence of irrigation on low flow events (Krueger et al 2017) future research could focus on further refinement of feasible water management strategies and model feedback loops of such strategies on water availability.