AbstractIncreased prevalence, lower cost, and reduced environmental impacts have granted natural gas status as a bridge fuel over the past decade in place of coal-fired heat and power generation across the United States. As a result, some coal facilities are retrofitting their systems to combust natural gas for heating and power. However, data and economic criteria surrounding these decisions are not widely available. Wright-Patterson Air Force Base (WPAFB) invested approximately $25 million, from 2014 to 2016, to retrofit two coal-fired steam-heat-generating plants with natural gas equipment. Economic analyses used to inform these long-term infrastructure decisions rarely consider the uncertainty of climate change. As the uncertainty of climate change projects is large, there is a distinct need to incorporate these forecasting models in large-scale infrastructure investments to facilitate robust decision-making. In this case study, we evaluate the uncertainty surrounding infrastructure decision-making through a Monte Carlo simulation. The case study evaluates the sensitivity of cost savings and payback period for the fuel switch relative to climate predictions. In this analysis, we characterize uncertainty of the retrofit as a function of its payback period length. The payback period is expected to increase by nearly 6 years (∼20%) when factoring climate change and uncertainty into the economic analysis. This case study showcases the uncertainty surrounding large infrastructure decisions with climate change implications.IntroductionThe projected and current impacts of climate change are forcing national and local policy makers and asset managers to evaluate the status of their infrastructure and address adaptation under different climate and environmental regimes. Warming of the climate system is unequivocal, as illustrated by increases in global average air and ocean temperatures (Gray 2007; Rhamstorf et al. 2017). The rising mean global temperature is primarily caused by the increase in atmospheric greenhouse gases (GHGs) from the onset of the industrial era to the present. The burning of fossil fuels in the transportation and energy sector contributed between 70% and 75% of total global CO2 emissions each year since 1990 (WRI 2021). As a result, the industrial and commercial energy production sectors, which have a strong impact on both the environmental and economic landscapes, need to adjust and adapt current practices. On US military installations, base civil engineers are tasked with the management and operation of infrastructure. Infrastructure operation and maintenance costs have been under scrutiny in recent years as an avenue to optimize the US Department of Defense (DoD) budget.The US Department of Defense is among the largest energy resource consumers in the world and the largest single consumer in the United States (Lengyel 2007). As a result, fossil fuel energy resources are an important and significant, albeit variable, portion of the budget consisting of up to 3% of total defense spending (Dimotakis 2016). While the two previous studies are relatively dated, it is unlikely that these proportions have changed significantly over the past decade due to increasing energy demands of buildings and mission support. Climate change is expected to increase the variability of energy consumption, largely for space conditioning, and lead to an increase in cooling demand and decrease in heating demands (Huang and Gurney 2016; Wenz et al. 2017). Military installations worldwide have investigated opportunities to reduce their overall energy and resource demands as well as their environmental impact to drive a more sustainable enterprise into the future. However, the DoD does not currently weigh the impacts of climate change in its long-term economic planning and infrastructure investment strategy. For a large-scale project, such as converting centralized heating facilities, it is important to consider the impacts of climate change. In this research, we present a case study that evaluates uncertainty in the decision-making process. Here, we pair an empirical, climate-informed energy use prediction model with Monte Carlo simulations to account for fuel price variability and temperature change projections to evaluate the payback period for a major heating infrastructure project at Wright-Patterson Air Force Base (WPAFB) near Dayton, Ohio.Using a unique data set of energy cost and consumption specific to WPAFB’s boilers, we investigate the fuel accounting data of the heating facilities for the years before and after conversion. Monthly data from October 2010 to September 2018 for the WPAFB boilers are available. These data include short tons of coal, 100 cubic feet (CCF) of natural gas, and total costs of energy purchased. To determine climate uncertainty, we compare three climate scenarios: a stationary assumption, moderate climate change [Representative Concentration Pathway 4.5 (RCP4.5)], and extreme climate change (RCP8.5). Using these data, we characterize the uncertainty surrounding the selected retrofit alternative using a Monte Carlo simulation to determine the expected payback period with different climate change scenarios. As a result, we answer the following question: what is the uncertainty surrounding the expected payback period of this retrofit and how does it change when including variable climatic conditions and nonstatic fuel prices?BackgroundRenewable energy sources are becoming increasingly prevalent; however, fossil fuels remain the backbone of our national power generation due to availability, efficiency, and reliability, producing 63% of US electricity (Grubert 2020). In recent years, falling prices and increased abundance have made natural gas an attractive alternative to coal (Liang et al. 2012). Because of the US shale gas revolution, natural gas prices are well below the price per unit of coal across most of the country (Carley et al. 2018). Additionally, natural gas–fired plants are more operationally flexible than similar coal plants, which may benefit energy grids as policies and economics evolve and change (Grubert et al. 2012). As a result, retrofit projects for plant conversions from coal to natural gas as a primary fuel are being considered (Liang et al. 2012).Natural gas was described as a bridge fuel by policy makers in the first decades of the 2000s and a better alternative to coal until near-zero-emission technologies become more feasible (Zhang et al. 2014). However, emissions from combustion of natural gas will not fully enable the decarbonization of society to meet climate goals. Additionally, this bridge fuel status was intended until renewable sources like solar and wind become more economical, which they have. In the meantime, national GHG emissions policy changes have been forcing modernization of energy production infrastructure (Gerrard 2012). For the last decade, coal use has been declining as natural gas has been on the rise, due to increased availability from hydraulic fracturing technology and infrastructure development (Capuano 2019). For example, the Marcellus Shale formation located in New York, Pennsylvania, and Ohio became available as a result of hydraulic fracturing and is believed to hold a natural gas supply equivalent to 45 years of US national consumption (Sovacool 2014).Beyond resource availability and economics, environmental regulation contributes a central role in fuel selection. In April 2012, the EPA anticipated the final publishing of the Boiler Maximum Achievable Control Technology (MACT) regulations under the Clean Air Act. These regulations dictated that generating sources had 3 years to demonstrate compliance. Section 112 of the Clean Air Act maintains that the EPA will regulate emissions of hazardous air pollutants from source categories including industrial, commercial, and institutional boilers that include the systems utilized at WPAFB (EPA 2021).Prior to the EPA’s regulations on boiler MACT, WPAFB was primarily heated by two coal-fired steam heat plants with some natural gas used year-round for heating and dehumidification of essential facilities. However, the policy requirement forced the modernization of the existing centralized heating system to remain in regulatory compliance (WPAFB 2011). To meet regulations, WPAFB conducted an economic analysis across three alternatives: (1) upgrading the existing infrastructure to MACT compliance while maintaining coal as the primary fuel, (2) conversion of the central systems to 100% natural gas, or (3) decentralization of the primary facilities to provide individual facility systems that utilize natural gas heating. The considerations within the economic analysis included feasibility, environmental impacts, short-term capital cost, and long-term fuel and maintenance costs (WPAFB 2011). Despite the long-term implications of this retrofit, there were no considerations of climate change variability and its impact on the utilization of the heating facility in either alternative. In this study, we develop and present an analysis of the selected Option 2 to investigate how uncertainty and climate change could potentially influence decision-making on infrastructure investments.A simple life-cycle cost (LCC) analysis of the alternatives, such as the one used by WPAFB in this case, might not be sufficient to capture the payback period of the retrofit. LCC analyses evaluate the total cost of ownership of a particular asset including construction, operation, and rehabilitation costs. The LCC performed by WPAFB was relatively simple, not factoring in long-term change. The primary weakness of using a simple LCC is the improper treatment of uncertainty when there is sparse and imprecise information available (Lo et al. 2005). Lo et al. (2005) noted that using a Monte Carlo simulation categorizes uncertainty and provides results that allow for a better-informed decision and a clearer comparison of alternatives. Similarly, Bhargava et al. (2017) utilized Monte Carlo to understand infrastructure project risk to cost deviation. Arnold and Yildiz (2015) also utilized Monte Carlo simulation for energy infrastructure to determine life-cycle project risk of decentralized renewables. In this case, climate change was not considered, despite linkages of climate change to reduced heating demand in the winter, when the central boilers of WPAFB are most used (Delorit et al. 2020). Additionally, fuel prices in the WPAFB economic analysis were treated as static, ignoring the uncertainty of price variability for both coal and natural gas resources. In colder climates, models suggest a decrease in annual site energy demands for heating (Wang and Chen 2014). Van Ruijven et al. (2019) modeled climate change temperature projections in 2050, showing the highest decline to cold weather exposure in the midlatitudes, which includes Ohio. Additionally, global impacts of climate change could have significant effects on fossil fuel resource extraction and production, resulting in uncertain fuel price trends going into the future (Parry et al. 2007; Schaeffer et al. 2012). This evidence, when considered, could result in a longer payback period for this or similar conversion projects and uncertainty in the final decision based on evaluated alternatives.Case StudyWPAFB, located in southwestern Ohio, provides an interesting case study due to its size [3,200 hectares (8,000 acres)], population (>27,000 personnel), and geographic location (WPAFB 2019). Prior to 2015, WPAFB in Ohio utilized three primary hot water and steam heating plants to supply the base with both hot water and facility heating (WPAFB 2011). Among the three primary heat plants, two utilized coal-fired systems. These facilities provided heat to approximately 245 buildings, making up more than 86% of the installation’s heating demand (WPAFB 2011). While the heating plants both utilized natural gas throughout the year, coal was the primary fuel during peak heating season and provided more than 60% of the annual heating demand to the service area. These conditions and the access to data provide an interesting opportunity to investigate how climate can affect economic analysis uncertainty.The WPAFB economic analysis produced initial capital costs for all three alternatives. The installation ultimately decided to select the alternative with the lowest initial capital cost, the second alternative: conversion of primary facilities to natural gas. Despite the annual operating costs being slightly higher than those expected with the decentralization alternative, the 20-year net present value of known costs for Option 2 was the lowest ($388 million versus $420 million for Option 3). Based on the findings of the economic analysis, WPAFB’s decision was to pursue a complete conversion to natural gas within the two primary heating facilities on the installation to maintain EPA compliance. The impetus for this major infrastructure upgrade was driven by environmental regulation; however, the decision to pursue natural gas was situated economically because gas is relatively cheap and natural gas–fired plants are cheaper to construct and operate (EIA 2019).Due to a large population, industrial economy, and wide seasonal temperature variations, Ohio is among the top 10 states in total energy consumption (EIA 2020). Ohio is also among the top 10 coal-consuming states, and, while Ohio is the 15th largest coal-producing state, more than three times as much coal is consumed as is produced there (EIA 2020). Due to advancements in natural gas extraction technology, Ohio’s natural gas production was more than 30 times greater in 2019 than in 2012. Almost all of the state’s natural gas comes from the Utica Shale wells where horizontal drilling and hydraulic fracturing are required to extract the gas (EIA 2020). Ohio’s natural gas production surpassed consumption for the first time in 2015, and, in 2018, the electric power sector became the state’s largest natural gas consumer (EIA 2020). WPAFB and Dayton, Ohio, fall within International Energy Conservation Code (IECC) Climate Zone 5, also known as the cold zone (US DOE 2015). Within this zone, the area can expect that the effects of climate change will result in a significant reduction in heating demand projected into the future (Van Ruijven et al. 2019).MethodsThe methodology of this research consisted of two overarching categories (Fig. 1): (1) data collection and model training, and (2) Monte Carlo simulation to determine uncertainty. Uncertainty was introduced into the model through variable coal and natural gas prices and variability in different climate models.Data Collection and Model TrainingFuel accounting data and conversion project data were provided by the 88th Civil Engineer Group at WPAFB (personal communication, 1988). Fuel accounting data were obtained for both coal and natural gas from 2010 to 2018, before and after the conversion (Fig. 1). Due to the construction period, fuel data during the retrofit were not included as part of the model training data. The fuel data were analyzed in MATLAB version 2020a with October 2010–May 2014 designated as preconstruction and July 2016–September 2018 as postconstruction. The data from within the construction period were ignored due to the uncertainty and error introduced as the coal-fired equipment was replaced by natural gas equipment in phases. By analyzing the periods before and after the construction window, we were able to develop projections of coal and natural gas consumption into the future.WPAFB has monthly fixed-rate contracts for natural gas and annual fixed costs for coal. Therefore, historical prices for each fuel provided appropriate distributions to both coal and natural gas costs. While this assumption does ignore future energy cost growth, it was a necessary assumption to focus on data available to the decision makers. Coal prices were assigned a uniform distribution from $120 to $166  ton−1, largely due to the few data points available (Fig. S2). Natural gas prices were fit with three different distributions: normal, log-normal, and Weibull. A log-normal distribution was the closest fit with a Kolmogorov-Smirnov statistic of 0.063. The mean natural gas price was $0.47  CCF−1, with a log-mean of 4.91 and log-standard deviation of 0.29. Sensitivity of these parameters are evaluated at the end of the results. The log-normal fit of the natural gas prices are shown in Fig. S1.Preliminary analyses performed a multivariate linear regression predicting heating energy consumption as a function of heating degree-days (HDDs), monthly extreme high and low temperature, and monthly average of daily high and low temperatures. HDDs were determined to be the single best indicator for heating energy demand on WPAFB, which is consistent with previous studies (Alola et al. 2019). HDD is measured as the difference in daily temperature from a comfort threshold, generally 18.3°C (65°F). Therefore, a day with an average temperature of 4.4°C (40°F) would equal 25 HDD. To determine payback period for the retrofit, three future HDD scenarios were generated from (1) historical temperature data (estimating climate stationarity), (2) RCP4.5 projections (a moderate climate change projection), and (3) RCP8.5 projections (extreme climate change projection). RCP projections were obtained at the daily scale for 2015–2070 from the Coupled Model Intercomparison Project (CMIP5) (Maurer et al. 2007; Pierce et al. 2014, 2015; US Bureau of Reclamation 2013, 2014; Vano et al. 2020). The mean monthly temperature of all ensembles for each RCP (70 ensembles for both RCP4.5 and RCP8.5) were then calculated and HDDs were aggregated to the monthly scale.To produce a stationary climate scenario, the historical monthly temperature data from 2010 to 2015 were used to create monthly distributions. Fig. S3 provides a breakdown of HDD by month during this time. These distributions were then sampled to produce a random monthly average temperature projection from 2015 to 2070, assuming a normal distribution (Fig. 2). For the climate change scenarios based on RCP4.5 and RCP8.5 projections, all ensembles were averaged into a single scenario assuming a normal distribution. As a result, each month in the data set had three corresponding distributions of HDDs: a stationary mean and standard deviation from historical data (Fig. 2), a normal distribution for RCP4.5 (Fig. 2), and a normal distribution for RCP 8.5. Upon further analysis, there were negligible differences between HDDs for the RCP4.5 and RCP8.5 scenarios. As a result, RCP8.5 is not shown in Fig. 2. Utilizing the defined pre- and postconstruction timelines, regression models for both fuel types were created using an ordinary least-squares method in MATLAB. These models were then validated using a bootstrap method to determine confidence intervals of the regression parameters. Bootstrapping validation was completed in R using the caret package (Kuhn 2008).Monte Carlo Simulation and Sensitivity AnalysisFollowing the building, training, and validation of the linear models, three scenarios (stationary climate, RCP4.5, and RCP8.5) were modeled in MATLAB using a Monte Carlo simulation beginning in 2015 and ending in 2070 (Fig. 1). The Monte Carlo simulation sampled across each climate scenario for HDD in a given month and sampled from the requisite coal or natural gas costs. The study simulated 100,000 Monte Carlo iterations for each of the scenarios to create a robust distribution of results. Within each simulated iteration, monthly savings were calculated as a function of the cost of doing nothing and the cost of the retrofit. Monthly savings were calculated based on Eq. (1) (1) sm=[cng×fngpre(HDD)+ccoal×fcoalpre(HDD)]−[cng×fngpost(HDD)]where sm = savings at each month; cng = cost per unit of natural gas (consistent for both pre- and postconstruction); ccoal = cost per unit of coal; fngpre(HDD) = resultant linear model for preconstruction natural gas as a function of HDD; fcoalpre(HDD) = model for preconstruction coal; and fngpost(HDD) = model for postconstruction natural gas consumption. These monthly savings were then normalized to a 2015 present value considering 2% discount rate per year [Eq. (2)] (2) where y = year of analysis; and i = discount rate. Using this discount-adjusted monthly savings, the breakeven year was calculated by determining the year in which cumulative savings met or exceeded the project cost. Total project cost for the retrofit was $25 million.To further understand the uncertainty of the problem, a sensitivity analysis was performed across four variables: coal price, natural gas price, project cost, and discount rate. These variables were chosen based on the inherent nature of their uncertainty. Each of these variables was adjusted by ±10% to uniformly address and compare each variable. A one-way sensitivity analysis required the reexecution of the Monte Carlo for each adjustment to determine the expected change in a breakeven year.ResultsLinear Modeling and ValidationFig. 3 illustrates the strong correlation between energy consumption and heating degree-days, with the exception of preconstruction natural gas. Preconstruction natural gas versus HDD showed no relationship because coal was the primary fuel for the base. Natural gas was consumed year-round for humidity control and to supplement coal shortages or temporary shutdowns due to environmental air permits, a relatively static consumption. To keep the baseline natural gas pre- and postconstruction consumption values consistent, the preconstruction natural gas intercept was fixed through the same intercept as postconstruction at a baseline of 241,481 CCF per month. Both the postconstruction natural gas and preconstruction coal models explain a significant amount of the variability in energy consumption using HDD (Table 1). However, these data sets are relatively small with a limited number of data points, suggesting a level of uncertainty for the linear models. To validate each model, we performed a bootstrapping cross validation with 100 samples to determine the confidence of our linear models. These models, though trained with small amounts of data, show strong correlation through similar residual standard errors in the model to root-mean-squared errors in the validation (Table 1).Table 1. Results of bootstrapping cross-validation of linear modelingTable 1. Results of bootstrapping cross-validation of linear modelingModelβ1β0R2Residual standard errorModel p-valueBootstrap root-mean-squared errorNatural gas preconstruction (CCF)27.79241,481*0.00185,0000.68187,800Coal preconstruction (short tons)7.41*0 (forced)0.941,181<0.0011,216Natural gas postconstruction (CCF)1,822*241,481 (forced)0.98161,800<0.001101,447Payback Period with Monte Carlo SimulationThe Monte Carlo simulation provided distributions of the payback period for each of the three scenarios (Fig. 4). As previously stated, there were minimal differences between the future HDDs of RCP4.5 and RCP8.5. This similarity manifested in no significant difference in expected payback periods. A pair sample t-test on RCP4.5 and RCP8.5 distributions failed to reject the null hypothesis that the distributions were different. Therefore, RCP8.5 results are not shown in Fig. 4. First, the mean value for the stationary climate scenario was 28.3 years, equating to approximately 150,000 HDD. The RCP4.5 scenario has an expected payback length of 34.7 years, yielding a 20% increase (+6.4  years) to the breakeven point. The increased payback period for RCP4.5 projections requires approximately 165,000 HDDs due to discount rate. Second, there is an increased variance in the distribution for the climate change–informed models compared to the stationary climate scenario. The standard deviation of the stationary climate scenario distribution is 2.5 years, compared to 3.2 years for both climate change models. These differences highlight the importance of factoring a nonstationary climate into long-term infrastructure decisions, especially those with a high temperature dependency, like energy.Sensitivity AnalysisA sensitivity analysis for the four uncertain variables is shown in Fig. 5. The simulation has a high level of sensitivity to fuel price and comparatively low sensitivity to total project cost and discount rate. For a 10% decrease in coal price under both the stationary and RCP4.5 climate scenarios, the payback period increases 27 and 21 years (a 96% and 60% increase), respectively. Conversely, a 10% increase in natural gas price increases the payback period by 21 years for both scenarios. Additionally, there is an apparent a skewness, which suggests a tendency for the model to increase in payback period versus reduce. The stationary model shows a higher level of sensitivity and a higher degree of skewness when compared to the climate change model. These sensitivity results inform the level of uncertainty surrounding not only our climate-informed models, but also the original economic analysis performed by WPAFB. The reliance on the cost of fossil fuels to inform the economic viability of the option is another factor for decision-making in the model, potentially making other options, such as electrification or decentralization, more viable.DiscussionThe economic assessment to retrofit the coal-fired boilers by WPAFB utilized a simple economic analysis, relying on current fuel price rates without considering change in temperature or climate over time. In this way, the installation decision makers were given a limited view of the payback period without any evaluation of uncertainty within the assessment. As Lo et al. (2005) established, a Monte Carlo simulation that introduces uncertainty can provide for a better-informed decision based on clearer and more complete comparison of options. This research does not contend that WPAFB made an incorrect decision; however, it does assert that similar projects could benefit from a Monte Carlo analysis that considers uncertainty in climate change and fuel pricing through the lifetime of the infrastructure. Additionally, it is shown that, for this case study, savings associated with fuel cost alone are sufficient to pay back the investment within a reasonable amount of time.The mean breakeven year of the conversion project under climate change was 6 years longer than the payback period under stationary conditions. This information was not considered in WPAFB’s economic analysis of alternatives, which might have changed the overall decision or made other alternatives such as electrification more viable. Electrifying space heating through electric heat pumps offers some environmental benefits over conventional natural gas heating in many parts of the country, but offers a potentially higher heating cost (Vaishnav and Fatimah 2020). These additional demands to the electric grid will substantially require the increase of overall grid capacity (White et al. 2021). The sensitivity analysis (Fig. 5) illustrates the high uncertainty of the model. For example, a 10% decrease in the mean coal price increases the payback period by more than 20 years. The economic analysis is also contingent on the cost of natural gas. The sensitivity of these two values is much greater than the standard deviation of the models, which incorporate climate variability. Therefore, the most uncertainty in the model comes from a reliance on fossil fuels and their costs. As a result, WPAFB has high uncertainty in its decision and could have benefited from analyzing alternatives that were not reliant on fossil fuels to have more certainty in the infrastructure decision-making process.There are a number of limitations to this research, with the foremost being the limited data set available for historic fuel prices at Wright-Patterson Air Force Base. For example, long- and short-term dependent relationships likely exist between natural gas and coal prices that were not modeled. Additionally, any long-term economic projections for coal and natural gas availability and price were not considered. In this model, we utilize RCP data from downscaled climate models, which might not correctly characterize local climate accurately, inducing model bias (Jang et al. 2020). Finally, this model and analysis only examine the payback period for the capital investment on the conversion project based on fuel price and climate projection uncertainty. Variation in other operations and maintenance costs such as equipment service life, recurring maintenance costs, coal ash disposal, and required labor for operation were not considered in this model and would likely play a significant role in a full economic analysis of the alternatives. Because operations and maintenance costs of natural gas plants are often much lower than those of coal-fired plants, the inclusion of these variables would likely reduce the overall payback period of the infrastructure conversion (Grubert et al. 2012), yet those would be somewhat uniform across the scenarios analyzed. Future research could evaluate counterfactuals such as the other evaluated alternatives by WPAFB (coal retrofit, decentralized heating) and decentralized electrification to facilitate comparisons across decisions with uncertainty using similar methods.ConclusionA large amount of research is available on the impacts of the commercial energy sector and fossil fuel usage on climate change. However, minimal research has investigated effects of climate change on commercial energy capital investment returns and how incorporating climate change impacts infrastructure decision-making with uncertainty. This research provides important insights on the benefits of uncertainty modeling through Monte Carlo simulation to inform decision makers on retrofits of energy infrastructure as assets approach the end of their useful life. A simple deterministic economic analysis without considering fuel price and climate uncertainty might not provide an accurate projection of investment return. In this case study, a positive 6-year shift in mean expected payback for WPAFB is seen when climate change is considered within the analysis. This shift in expected return potentially affects the selection of the most economical alternative, such as electrification or decentralized heating.Compared to a deterministic approach, a Monte Carlo analysis produces values of uncertainty for independent scenarios. These data provide decision makers additional information and a clearer and more complete comparison of options to aid in infrastructure economic assessments. These energy projects have large up-front costs and large environmental and economic implications, which should be considered with any models. Decision makers will benefit from a quantification of uncertainty as infrastructure conflicts with environmental policy or nears the end of its service life. A Monte Carlo analysis provides the potential to account for uncertainty such as climate change to inform federal, state, and local infrastructure policy makers and decision makers.Data Availability StatementAll data used during the study were provided by the 88th Air Base Wing Civil Engineer Squadron. Direct request for these materials may be made to the provider. Models and code used to support the findings are available from the corresponding author upon request.AcknowledgmentsFunding for the research was provided by the Air Force Civil Engineer Center as part of a broader funding program for the Department of Systems Engineering and Management. Data for the analysis were provided by the 88th Air Base Wing Civil Engineer Squadron. T.A.F performed the analysis. J.D.D. supervised the research. C.M.C. conceived the project and supervised the research. T.A.F., J.D.D., and C.M.C. all contributed to the writing of the manuscript.References Alola, A. A., S. Saint Akadiri, A. C. 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