Thresholds, Timing, and Teleconnections: A coupled water-power-economic analysis

Previous studies have failed to capture critical dynamics stemming from overlapping hydrological, power, and economic networks when assessing the economic impacts of future water stress on the power system. In this paper, we employ a coupled water-power-economy model to capture these important interactions. We identied three channels that are key to assessing economic impacts – thresholds, teleconnections, and timing. We nd that not all reductions in reserve electricity generation capacity result in impacts (thresholds), and that when they occur, intermittent interruptions in electricity supply occurring at critical times of the day, week, and year account for most of the economic impacts (timing). Lastly, we nd that impacts may be in different locations from the original water stress (teleconnections). This work underscores the importance of a coupled modeling approach that captures interactions across systems while retaining spatial, temporal, and sectoral detail. prior study to the authors’ knowledge has propagated climate forcing scenarios through water and power systems models with hourly resolution in the power grid to estimate unmet electricity demand. This paper builds on previous efforts by quantifying the potential economic losses from a set of climate forcing scenarios, applying a multisector dynamic modeling framework that integrates a hydrological model, a detailed power system model with high spatial and temporal resolution, and a state-level economy-wide model of the U.S. We present a case study for the Western U.S. based on the Western Electricity Coordinating Council (WECC) reliability system. This corresponds to the twelve U.S. states west of the Rocky Mountains as well as portions of British Columbia, Alberta, and northern Mexico. We estimate the regional economic and sectoral productivity losses from a sample set of future annual hydrological conditions and we quantify the impacts that result from both the increased cost of electricity, and the lost productivity from unmet electricity demand. Finally, we distinguish between the direct impact of water temperature stress on the power system, and the impact after accounting for economic adjustment in response to the higher energy costs. This study makes three contributions to the existing on this topic. First, we demonstrate that Second, when while Third,

power if needed, is one critical link in the causal chain. Others have estimated the effect on the broader economy from electricity demand that cannot be met because of a supply disruption. 5,6,7 These studies have shown that the economic costs depend not so much on the average or aggregate amount of unmet electricity demand but on the speci c temporal and spatial pattern of discrete outage events: the number of events, their duration, and the magnitude of each. The high-voltage transmission network is a centuryold solution to increase resilience by moving power over long distances. A consequence of the grid is that supply shortages in one location may result in unmet demand in a different location.
Multisector dynamical systems, such as the coupled water-power-economy system in this study, are composed of overlapping and intersecting networks. The regional network of watersheds and basins is one layer. In the same geographic region, the electric power grid is another layer. The regional economy forms a third layer. The water and power networks intersect where generators draw water for cooling and use water for hydropower. The electricity transmission network then transfers energy from generators to demand centers. Economic sectors, such as manufacturing, use the electricity to produce goods and services for consumption. An external shock, such as higher temperatures or water scarcity, is transformed and transported through these interconnected networks, which may dampen or amplify the impacts in the process. In the absence of explicit analysis, it is di cult to predict how a shock is translated through the interconnected networks and where the most signi cant impact will occur.
No prior study to the authors' knowledge has propagated climate forcing scenarios through water and power systems models with hourly resolution in the power grid to estimate unmet electricity demand. This paper builds on previous efforts by quantifying the potential economic losses from a set of climate forcing scenarios, applying a multisector dynamic modeling framework that integrates a hydrological model, a detailed power system model with high spatial and temporal resolution, and a state-level economy-wide model of the U.S. We present a case study for the Western U.S. based on the Western Electricity Coordinating Council (WECC) reliability system. This corresponds to the twelve U.S. states west of the Rocky Mountains as well as portions of British Columbia, Alberta, and northern Mexico. We estimate the regional economic and sectoral productivity losses from a sample set of future annual hydrological conditions and we quantify the impacts that result from both the increased cost of electricity, and the lost productivity from unmet electricity demand. Finally, we distinguish between the direct impact of water temperature stress on the power system, and the impact after accounting for economic adjustment in response to the higher energy costs.
This study makes three contributions to the existing literature on this topic. First, we demonstrate that reductions in reserve capacity, power plants that are unavailable because of cooling water restrictions, may or may not result in actual physical and economic impacts (thresholds). Second, when economic impacts do occur, they primarily result from intermittent periods of electricity demand that cannot be fully met, while the higher cost of electricity has a smaller effect (timing). Third, the locations where impacts are experienced may be geographically distant from the location of the water stress and may be the result of bottlenecks at some other locations in between (teleconnections).

Capacity outages from increased water temperatures
A set of one-year samples of hydrological conditions were produced from the climate elds from GFDL-CM3 and CCSM4, two of the models in CMIP5 RCP 8.5, which were bias-corrected and adjusted to a ner grid cell resolution and used to drive the Water Balance Model (WBM), a spatially distributed hydrological model for 2006-2099. Of the existing power plants in WECC, 478 are identi ed that require water for cooling, and their geographic locations were mapped to grid cells within WBM. We assume the U.S. federal standard temperature threshold of 32 °C, above which generators requiring water for cooling at those locations are not available on that day. 2,8,9 We focus on water temperature because it integrates the impacts of increased surface temperatures and reduced water volumes, and because the regulatory threshold is well de ned. The annual hydrological samples from WBM provide the daily water temperatures at each power plant location, from which any generator outages are determined. There are many possible ways to aggregate the hourly outages of 478 plants over the entire year for one scenario. In the Supplemental Information (SI) we show the generation capacity outages for each of 118 annual hydrological samples in terms of the number of hours of the year that one or more generators were unavailable because the water temperature threshold was reached and the average total capacity unavailable for those hours with non-zero capacity outage. These annual samples result in capacity reductions ranging from 0 to over 12 GW of generation capacity for durations ranging from 0 to 3312 hours within a year. These results correspond to the capacity reserve reductions estimated in prior studies. 1,2,3,4 The generation outage patterns resulting from the WBM water temperatures are imposed in the Power System Model (PSM). We nd that for all cases analyzed, annual samples with average capacity outages of 2200 MW or less and/or occurring for 1400 or fewer hours of the year do not result in any meaningful changes in the cost of electricity relative to the base case nor in any unmet electricity demand ( Figure S3 in SI). This is an example of a critical threshold in the coupled system. Many regions of the U.S. have excess generating capacity because of the legacy effects from traditional utility cost regulation and from reliability standards. 10 An important implication of this result is that a reduction in available generation capacity does not necessarily indicate any signi cant cost.

Impacts on Power System from Increased Water Temperatures
We focus the remainder of the analysis on 18 of the annual water temperature scenarios that induce nonzero impacts in the power system model. We rst present the potential impacts of each annual sample by showing results from the rst iteration of the power system model, before any economic adjustment has occurred. For each scenario, we solve the power system model for the 8736 hours of the year, excluding any o ine generators from the water temperature constraint in each hour, and obtain the hourly output of each generator at each location in the network, the prices at each location, and whether any portion of electricity demand was not met in each hour at each location. The shadow prices from the optimization model on the supply-demand balance constraint at each of the 312 buses (nodes in the electrical network) in each hour represent the marginal cost of electricity.
Power system impacts on the hourly time scale must be aggregated to annual impacts to enable feedbacks with the economic model. We average the marginal costs over all buses in each hour and average these values over the year to obtain an annual average of the marginal cost. The effect of having some generators unavailable, which are often the lower marginal cost units, is increased generation cost in those hours. In Figure 1a, we show the increase in the marginal cost of electricity relative to the baseline (no water temperature-induced capacity outages) that results from the capacity outage patterns induced by each hydrological sample. Each point in the scatter plot represents a oneyear simulation of the power system model for one annual sample of the daily spatial distribution of water temperatures. If there were no economic adjustment, the annual average increase in electricity cost would range from less than 1% to nearly 7%, depending on the water scenario.
In addition to the increased cost of electricity, a major concern about water impacts on the power system is the inability to meet all electricity demand at every location in every hour of the year. Estimation of the spatial and temporal pattern of any unmet electricity demand requires a model that explicitly represents the transmission network, the chronological hourly demand, and inter-temporal constraints on generators that cannot turn on or off instantaneously. In Figure 1b, we present the total unmet electricity demand in MWh for each annual hydrological sample, summed over all network locations and all hours of the year. The amount of total unmet demand ranges from zero to over 50 GWh across these 18 annual hydrological samples.
Note that for samples with relatively similar average capacity outage amounts in the 9 to 11 GW range, there is considerable variation in the amount of unmet demand. The magnitude of impacts from capacity outages depends critically on the co-occurring pattern of demand and renewable generation during the hours when some capacity is unavailable and the on/off state of slow-start power plants. This is an example of importance of timing in determining the impacts of different shocks to the system. These results indicate that estimates of aggregate capacity outages alone may not be su cient for estimating the consequences.
The total annual unmet demand for each water temperature scenario is the sum of unmet demand over all hours and locations, which aggregates a spatial and temporal pattern of discrete events. These events vary in duration, magnitude, and location. We show the distribution of unmet demand events for one annual hydrological sample, (GFDL-CM3, year 2089; circled in Figure 1b), in terms of the number of events of different durations in hours (Figure 1c) and the distribution of the average per-event magnitude of the unmet demand for all events of each duration as box-and-whisker plots (Figure 1d).

Impacts from power on economic activity without adjustment
Higher electricity costs and unmet electricity demand estimated from the power system model are propagated through the economic model to estimate resultant losses to the economy. The Regional Economic Model (REM) captures the response of consumers and producers to the increases in the annual cost of electricity (from Figure 1a). To measure the productivity losses from unmet electricity demand, we build on prior work 6 which provides electricity customer interruption costs from a survey of ~12,000 U.S. rms and ~8,000 U.S. households. We use the rm-level interruption costs developed in Sullivan et al., 6 which vary by economic sector, season, day of week, time of day, and duration of outage, and apply these to the temporal pattern of unmet demand events over all hours in each annual hydrological sample. The resulting sum of aggregate losses for each sector is then represented as a productivity loss for that sector in the REM. A useful metric of economic loss is the reduction in total nal consumption, which we present in Figure 2 for the 18 annual hydrological samples simulated.
To measure the relative importance of higher electricity costs versus unmet electricity demand to total economic loss from higher water temperatures, we compare the results from two versions of the model: 1) one that represents impacts from both higher electricity cost and unmet electricity demand, and 2) one that represents only the impact of higher electricity cost. From Figure 2, we see that the consumption loss due to unmet electricity demand is signi cantly larger than the consumption loss due to higher electricity cost and constitutes the primary driver of impacts on the broader economy. Quantitative estimates of the losses to industry from insu cient electricity supply emphasize that the damages depend on when the unmet demand occurs and how long it goes unmet for each event, another example of timing as critical factor. It is not possible to quantify these losses without a chronological hourly analytical framework.
The increase in electricity cost and the decrease in productivity due to unmet electricity demand has differential impacts across the sectors of the economy. This is a result of differences in the relative dependence on electricity vs. other inputs to production in each sector and variation in sectoral damages costs from electricity outage events. Figure 3b shows the reduction in output (%) by sector for one annual hydrological sample (GFDL-CM3, year 2089). The largest reduction occurs in the manufacturing sector.
We also show the resulting reduction in manufacturing output in all simulated scenarios (Figure 3a). The productivity loss for all sectors for the 18 water temperature scenarios are provided in Table S2 in the SI.

Feedbacks between economy and power system
The impacts presented above from climate forcing to water temperatures to capacity outages to electricity costs and unmet demands represent the potential impacts in the absence of an economic response. Economic agents respond to changes in prices and quantities to modify their behavior, and this response must also be represented. Demand for electricity will fall in response to higher electricity prices, which encourage substitution away from electricity use. Demand for electricity will also fall because the economy has contracted due to the economic losses from higher electricity costs and productivity losses due to unmet electricity demand. Feeding these adjustments in electricity demand back to the power system model will reduce the estimated impacts because less generation will be required to meet the lower demand level.
We iterate between the PSM and the REM after estimating the impacts from the higher water temperatures to capture this demand feedback. Speci cally, the higher water temperatures from the WBM result in increased electricity costs and unmet demand in the PSM, which leads to lower demand for electricity in the economic model. This lower electricity demand from the economic model is fed back to the PSM, and the resulting electricity cost and unmet demand impacts will be lower than the previous iteration. The adjusted electricity costs and unmet demand estimates from PSM are then fed back to the economic model, which may further adjust the electricity demand. The two models iterate until changes between the two models reach zero.
The results from the nal iteration, after equilibrium is achieved, is a useful indication of the likely impacts from the original water temperature scenario because it accounts for the economic response feedbacks. The dampening of the impacts by economic adjustment is illustrated in Figure 4, which presents the range of impacts before and after economic adjustments in the form of box-and-whisker plots. Economic substitution is most effective at reducing the cost of electricity (Figure 4b). In response to the higher cost, production shifts to other inputs and the economy contracts, leading to a reduction in the demand for electricity. The reduction in unmet demand and in consumption loss after economic adjustments are not as large as the initial estimate before adjustment.

System stress in coupled networks
For any given external shock, the interconnected networks in the water-power-economic system mitigate the impact by providing redundancy and transferring the impact spatially. As an illustration, Figure 5 shows the geographic relationships between impacts in the WECC region from a given week in one of the annual hydrological samples (GFDL, year 2097; week 29). The generators that are unavailable because the water temperature threshold is exceeded are primarily located in Southern California, Southern Nevada, Arizona, and New Mexico (blue circles in Figure 5). When these generators are unavailable, other generators elsewhere in the network must compensate. This shift in generation causes congestion on some of the transmission lines, de ned as the power ows on those lines are at their maximum capacity (red lines in Figure 5). Congestion causes the cost of electricity to increase in some locations, because lower cost generation is unable to be transported to where the demand is, and in some cases may also lead to unmet demand at other locations (teleconnections). In this example, the net effect of the generation outages is that some portion of electricity demand in Colorado and some in Arizona cannot be met for some hours of the week (red circles in Figure 5). The episodes of power outages in turn disrupt economic activity, reducing productivity and increasing costs. The differing spatial patterns of generator outages vs. unmet demand is robust across the water scenarios that induce impacts (see Table S3 in SI). The locations where the unmet demand occurs is driven by the bottlenecks in the transmission network and the particular spatial patterns of electricity demand and renewable generation in this set of experiments. In general, knowing the location of generator outages because of increased water temperatures would not by itself provide much guidance for where the impacts on consumers will be experienced.

Discussion
Our analysis of the impacts of a range of climate forcing patterns on the coupled water-power-economic system has demonstrated that higher water temperatures can lead to a causal chain of events from electric power generators o ine because of cooling water discharge temperature limits to higher electricity costs and unmet electricity demand to economic adjustment to higher electricity costs and productivity reductions in electricity using sectors. These impacts can be up to a consumption loss of 0.3% across the broader regional economy, up to a 3% increase in the average cost of electricity, and more than a 1% loss of production from regional manufacturing. The key insights are that many climate patterns that result in generator outages from higher water temperatures do not result in any signi cant impacts (thresholds), that the majority of the economic impacts result from electricity demand that cannot be met at speci c times and locations (timing), and that these unmet demand events may occur at geographically distant locations from the generator outages (teleconnections).
The results underscore the importance of accounting for feedbacks between overlapping and interacting system networks. Importantly, this type of coupled model approach allows investigators to retain the spatial, temporal, and sectoral richness represented in each of these individual models that would be unachievable in one comprehensive model where detail is usually sacri ced for computational tractability. In particular, the chronological hourly resolution of the power system is critical to be able to represent discrete events of intermittent power disruptions, the largest factor affecting economic cost. Similarly, sectoral detail allows us to differentiate between those industries that are hardest hit by these disruptions and those that are not, providing further evidence that impacts are not likely to be uniform across space, time, and sector.
For public and private sector organizations focused on increasing resilience to natural stressors from weather and climate, our analysis reinforces the importance of institutions for managing regional interdependent infrastructures. High water temperatures may prevent generators in Southern California or Arizona from operating, but the consequence could be felt elsewhere such as in Colorado. Regional coordination from organizations such as WECC or the Western Governors Association will be required to identify network vulnerabilities that can transmit impacts spatially and develop reinforcements that do not cause new unintended problems.
This work is just the rst step in developing what is needed to support such planning for resilient systems. Future work must rigorously investigate how potential adaptations will change the risk pro le. Any investments in the power or water infrastructure will modify the network structure and ows, which may alter how external shocks are dampened or ampli ed and transferred geographically. A rigorous assessment of the tradeoffs between these alternative strategies will require advances in computational methods for managing high-dimensional data. The authors hope that the analysis presented here will motivate and accelerate this agenda in the larger research community.

Methods
We simulate the impacts from a set of climate forcing scenarios through the coupled model as follows.
We propagate several CMIP5 climate forcings through the WBM. WBM is a process-based, gridded model that simulates both the vertical exchange of water, and the horizontal transport of water through runoff and the river network, developed at the University of New Hampshire 11,12 and includes estimated river temperature calculations. 13 The results in this paper are based on the RCP8.5 scenarios from GFDL-CM3 and from CCSM4. WBM uses downscaled climate elds to drive simulations 2006-2099 with daily timesteps. The gridded daily hydrological conditions from each simulated year in WBM constitutes one annual sample. We treat the annual samples of hydrological conditions from the WBM results for 2041-2099 from GFDL-CM3 and CCSM4 as 118 independent plausible samples of hydrological patterns for the purposes of this study.
All thermal power plants in the WECC system that require water for cooling are mapped to speci c grid cells in WBM. For the impacts on electric power supply, we assume the U.S. federal standard temperature threshold of 32 °C, 2,8,9 above which generators requiring water for cooling at those locations are not available on that day. We then solve for the hourly dispatch of generators to meet demand in the Power System Model (PSM), a model of the WECC system that represents the high-voltage transmission network (consisting of 312 locations and 654 transmission lines) developed by Hobbs and colleagues at Johns Hopkins University 14,15,16,17 and intertemporal operational constraints of generators, as well as a given scenario of hourly availability of all generators over the year based on the WBM input.
The resulting cost of electricity and hourly patterns of unmet electricity demand (if any) provide input to the REM, a static inter-regional computable general equilibrium (CGE) model of the United States. The regional economic model is based on the modeling framework of Rausch and Rutherford, 18 which calibrates the model to the IMPLAN U.S. state-level accounts. Finally, to represent the economic adjustment to the initially higher electricity costs from the external stressor, we iterate between the PSM and regional economic model using the coupling methodology of Böhringer and Rutherford 19 to nd the equilibrium reduction in electricity demand. Impacts of each scenario are presented as the nal equilibrium results for reductions in regional consumption and in sectoral output from the regional economic model. Detailed descriptions of the methods, including all models and data, are provided in the Supplemental Information (SI) available online.