In the shadow of wind energy: Predicting community exposure and annoyance to wind turbine shadow flicker in the United States

The moving shadows caused by wind turbines, referred to as “shadow flicker” (“SF”), are known to generate annoyance in a subset of the exposed population. However, the relationship between the level of modeled SF exposure and the population's perceived SF and SF annoyance is poorly understood. Improved understanding of SF exposure impacts could provide a basis for exposure thresholds and, in turn, potentially improve community acceptance of and experience with wind power projects. This study modeled SF exposure at nearly 35,000 residences across 61 wind projects in the United States, 747 of which were also survey respondents. Using these results, we analyzed the factors that led to perceived SF and self-reported SF annoyance. We found that perceived SF is primarily an objective response to SF exposure, distance to the closest turbine, and whether the respondent moved in after the wind project was built. Conversely, SF annoyance was not significantly correlated with SF exposure. Rather, SF annoyance is primarily a subjective response to wind turbine aesthetics, annoyance to other anthropogenic sounds, level of education, and age of the respondent. We also examined regulations governing SF in the sample project areas and compared them to SF exposure in the surrounding population. Additionally, we found that noise limits could serve as a proxy for SF exposure, as 90% of those exposed to wind turbine sound of no more than 45 dBA L1h had SF exposure of less than 8 h per year (a prototypical EU regulatory threshold).


Background
Targets to decarbonize the US electricity sector rely on increasing the installed capacity of wind energy in the United States from approximately 110 gigawatts (GW) today [1] to nearly 600 GW by 2035 [2]. Many European countries have similarly ambitious goals [3,4]. Meeting these targets could necessitate thousands of new wind projects and, therefore, many willing host communities. Several common annoyances-such as opaque planning and approval processes, and sound, visual/aesthetic, and shadow flicker (SF) impacts [5]-have been identified by community members living near existing wind projects. These annoyances affect individuals living near existing wind projects and raise questions of distributive fairness. Concerns about these impacts also influence a local community's attitudes toward newly proposed wind projects [6]-affecting wind project permitting timelines and outcomes. To balance these competing goals, some communities have opted to enact highly restrictive siting ordinances or moratoria on wind projects until such concerns and impacts are better understood (e. g., recent US examples from Kansas [7] and Indiana [8]). While overly restrictive wind energy siting ordinances have been shown to increase electricity costs and emissions [9], ignoring social impacts could also result in negative societal outcomes.
Rarely, however, have perceived SF, exposure, or annoyance levels been the focus of rigorous research. Perhaps as a result of this research void, regulations around SF in the United States and in Europe are variable and unstandardized-if they exist at all. A better understanding of the magnitude, drivers, and potential mitigation strategies of SF annoyance is needed for the wind industry, policymakers, and potential host communities to better understand this concern and be able to properly regulate it, if desired.

What is shadow flicker?
Shadow flicker, or SF, is an effect of pulsating light and shadow caused by the sun shining through rotating wind turbine blades. The intensity of SF diminishes with increasing distance from a wind turbine, which means it is typically most noticeable near the wind turbine. The area where SF occurs is largest when the sun is relatively close to the horizon, thus it is most common in the morning and evening hours to the west and east of the turbine, respectively. Similarly, the area of impact is typically larger at higher latitudes, where the sun spends more time at lower angles from the horizon (i.e., at large solar zenith angles). SF is expressed as either the maximum number of hours/year or minutes/day. It is modeled either assuming the "worst case" (e.g., turbines always operating, no intervening clouds), or what is termed "real case" that considers mitigating factors related to meteorology and project operation. A detailed discussion of these models and methods is provided in Section 2.1.3.

What is annoyance?
Lindvall et al. [21] define annoyance as "a feeling of displeasure associated with any agent or condition believed to affect adversely an individual or group." Lindvall et al. recognize that feelings of annoyance are not necessarily pathogenic and may or may not result in negative health consequences. Hübner et al. [22] go further to define "annoyance stress" by evaluating self-reported annoyance in the presence of additional stress indicators such as sleep disturbance, irritability, and coping responses. As such, there is a distinction between self-reported annoyance and annoyance stress, in that the former could be considered an attitude while the latter may lead to health impacts. In this study, we focus on self-reported annoyance on a five-point scale, with the highest annoyance category being "very annoyed." This is distinct from the highest category of annoyance stress of "strongly annoyed" [22].

Wind neighbor survey background
Lawrence Berkeley National Laboratory's National Survey of Attitudes of Wind Power Project Neighbors ("LBNL Neighbor Survey") was conducted by many of the same authors as this paper [6,10,22,23]. This survey collected data in 2016.
Hübner et al. [22] demonstrated that self-reported annoyance to SF, although lower than that of turbine noise, was similar to annoyance to traffic and more prevalent than annoyance to agricultural machinery, turbine lighting, or landscape changes. 1 From this same survey data, we found that of those who could experience the effects, though, SF emoted a high negative reaction. Twenty percent of the 1705 respondents indicated they noticed SF on their property, and 7% reported being very annoyed by it. However, of those that experienced SF in their residence, approximately one-third reported being very annoyed. Further, wind project developers often rank SF as one of the top concerns of communities. 2 However, the role of SF in the experience of neighbors of wind projects has not been well studied in the United States or abroad.
Statutorily, there is no US national SF regulation, and regulatory limits on SF in states, counties, and towns vary or are often nonexistent [24,25]. Several countries have guidelines or standards, most of which use the same thresholds as or reference the German national guidelines for the evaluation of SF [24,26] (as will be discussed in Section 1.3 and Section 3.4.2). However, there are currently no international standards for how to model SF exposure levels around turbines.
To examine how SF exposure affects perception and annoyance, we conducted a mixed-methodology (both quantitative and qualitative) study using surveys of people living around US wind turbines and combined this data with SF modeling. We modeled SF for 61 unique wind projects across 17 states and 50 counties. These sites included approximately 750 survey respondents and more than 34,000 additional homes (non-survey respondents) from the surrounding population within 2 km of a wind turbine, making this the largest SF dataset analyzed for perceived SF and annoyance that we are aware of. From respondents, we collected survey data on whether they perceived SF in their home and the degree to which they were annoyed by it. We also collected a suite of demographic characteristics and attitudes toward the nearby project.

Research objectives
The present analyses of modeled SF exposure and survey-reported annoyance were intended to investigate the following research objectives: 1. Quantify SF exposure across a large and geographically diverse sample of residences to develop a general understanding of SF experienced in populations living near wind turbines. 2. Use a mixed-method approach to examine the correlation between modeled SF exposure and individuals' reported levels of perceived SF and annoyance to help inform regulations in the United States and abroad. 3. Create a model to predict individual perceived SF and SF annoyance to better understand the magnitude, drivers, and potential mitigation strategies for SF impacts.

Previous shadow flicker research
As early as 1984, SF from turbines was recognized for its potential to be an adverse community impact. Verkuijlen and Westra [27] found that to avoid nuisance, the SF frequency should remain below 2.5 Hertz (Hz) (50 rotations per minute [RPM] for a three-bladed wind turbine). These conclusions were primarily based on previous research related to the onset of epileptic, nausea, and dizziness symptoms [28]. However, the authors conceded that the prior literature was not specific to wind turbines, and that further study was needed. In a later study specific to wind turbines, Harding et al. confirmed that to protect against epileptic impacts, wind turbines should not exceed 60 RPM [28]. For context, modern utility-scale wind turbines rotate at less than one-third of this rate; the fleetwide simple average for US turbines from 1998 to 2019 is 17.4 RPM. 3 In 1999, Pohl et al. [29] conducted a survey of 223 residents in Germany who lived around wind projects, to determine the impacts of SF and to examine whether the proposed regional SF limit was reasonable with respect to impacts. They found that SF exposure alone did not explain SF annoyance. However, when adding in weighing to account for SF sensitivity of different types of rooms and SF exposure of those rooms in individual homes, they found a clear linear relationship between this weighted shadow duration and SF annoyance. They also found that certain residents with high levels of exposure "spent less time in the shaded living spaces and in open spaces around the house and felt…activities indoors and outdoors as well as in their leisure time were severely disturbed as compared to people who were not exposed to shadows" (translation). They concluded that the proposed limit of 30 h of SF per year was likely to prevent most cases of substantially annoyed individuals. The hours estimate was based on a model of purely astronomical shading duration ("worst case"), which gives an upper limit to the duration of periodic shading to which a dwelling is exposed. This model can then be adjusted down by meteorological and turbine operation corrections to mimic actual operating conditions ("real case"). Germany later adopted the 30 h/year (and 30 min/day) worst case and an 8 h/year real case limits for its guidelines for wind projects [26].
Koppen et al. summarized US and EU SF standards in 2017 and found that when SF limits existed, the 30 h/year (and 30 min/day) limit was consistently applied [24]. Many of these in the EU were expressed as a worst case. They observed real case limits in some jurisdictions as well (e. g., Germany, Australia, Belgium, Denmark, and Sweden), with maximums of either 8 or 10 h/year (and 8 to 10 min/day). This suggests a worst-toreal-case relationship of roughly 3 to 1 and a rough equivalent between hours/year and maximum minutes/day. The metric in the three US examples cited did not differentiate between real or worst-case metrics.
In one of the largest and most comprehensive studies of its kind to date, Health Canada surveyed 1,238 people living between 0.25 km and 11.22 km from existing wind turbines in two Canadian provinces [30]. Among other important findings, the researchers found that SF exposure, expressed in maximum minutes per day, improved the ability to estimate high annoyance from wind turbines when combined with other factors such as noise, concern with physical safety, and noise sensitivity. For the lowest level of wind turbine SF exposure (0 to 10 min/day worst case), 3.8% of the population was highly annoyed by SF, while of those experiencing the highest level of exposure (>30 min/day worst case), 21.1% were highly annoyed by SF. However, when modeling SF without additional observable and subjective variables, the predictive strength of the model was weak (R 2 of 0.1). The authors concluded, "In addition to addressing some of the aforementioned shortcomings, future research may also benefit by considering variables that were not addressed in the current study. These may include, but not be limited to, personality traits, attitudes toward WTs [wind turbines], and the level of community engagement between WT developers and the community." This research addresses some of these variables.
Frieberg et al. [31] conducted a systematic literature review on the influence of wind turbine visibility, including indirect effects such as SF, on health. They recommended that additional high-quality research be conducted on the subject, including, "the combined impact of visual and audible aspects of wind turbines on residents' health, and the complex interdependency with other variables (e.g., attitude toward wind energy, economic benefit) should be taken into consideration." This research attempts to address some of these areas of study.

Data
A wide range of data were collected and generated for this research effort. The following sections describe these data in additional detail. One of the key variables was modeled duration of SF exposure at each home (Section 2.1.3). The inputs for those models included the following: • Wind turbine and project data (Section 2.1.1).
Those modeled SF data were, in turn, key inputs to both the perceived SF and SF annoyance models (Section 2.2.2). The models required survey response data such as demographics, self-reported perceived SF and SF annoyance levels, and other response data (Section 2.1.4). Finally, we collected data on SF ordinances (whether they existed, and if so, the relevant limit) for all 50 counties represented in our analysis (Section 2.1.5).

Wind turbine and project data
The 61 wind projects used for modeling encompassed 2,982 wind turbines spread across 17 US states and 50 counties (Fig. 1). Data on each of these wind turbines were obtained from the US Wind Turbine Database (USWTDB) [1,32]. These data included turbine location (i.e., latitude/longitude), rated capacity, hub height, rotor diameter, manufacturer, model, total height, total project capacity, and number of turbines in the project. Table 1 shows summary statistics on the wind turbines.
Additional turbine data that are not available from the USWTDB-such as power curves for operational profiles-were applied from data built into the SF modeling software described in Section 2.1.3.
The wind projects included in this analysis ranged from a 1.5-megawatt (MW) wind project with a single wind turbine to a 515 MW project with 222 turbines. The median project capacity and number of turbines were 180 MW and 87, respectively.

Receiver (residence) data
The residence location data were obtained from CoreLogic. 4 Data comprised all single-family homes, condominiums, duplexes, and apartments with complete addresses located within 2 km of one of the 61 wind projects. Initially, this yielded a sample of 46,175 receivers (i.e., residences).
A variety of quality control measures were used to verify the receiver location data, including removing duplicate location records, validating via an alternative source of location data, and visually inspecting using aerial imagery. 5 Of the total sample, we found 34,117 unique locations and 12,058 duplicates. Some of these duplicates were multi-family housing units, but most were determined to be inaccurately geocoded and grouped into centroids of subdivisions or blocks. The duplicated locations were evaluated for geospatial accuracy. We visually examined all locations with >100 receivers using satellite imagery (n = 9), as well as a random sample of 25 additional duplicate sites, and the 100 locations with the highest modeled SF using satellite imagery. We matched each receiver location to the nearest "building" location from Microsoft's open-source building footprint data [33], flagging any locations found to be more than 40 m from the nearest structure. If the flagged location was a survey receptor, it was visually inspected with satellite imagery and then relocated (n = 157). The remaining (non-survey respondent) receiver locations were removed from the analysis. We additionally removed excess duplicate receivers for locations with 10 or more records (keeping any survey respondents, if applicable). This process resulted in a final set of 34,940 receivers, which included the 747 survey respondents.

Modeled shadow flicker data
In this study, two aspects of SF were quantified-the annual number of SF hours (and daily SF minutes) at each home and their distributions 4 See https://www.corelogic.com/find/property-data-solutions/ for more info on their data products. 5 All survey respondents' residence locations were manually verified with aerial photography.
by time of day and over the year. These were modeled using the SHADOW module in windPRO Version 3.3. Predicting SF at residences surrounding a wind project is achieved through calculations of sun angles at different times of day and periods of a year at a given latitude; this is done while accounting for turbines' heights and intervening topography. This enables estimates of the maximum cumulative number of hours in a year (or hours per day) that a home will experience SF. SF can be modeled (and, for that matter, regulated) in terms of "real" or "worst" case. Worst case modeling is the astronomical maximum SF, assuming turbines are always operating (i.e., rotating) and there is no cloud cover. Real case modeling includes meteorology (e.g., cloud cover [34]), turbine operational factors (e.g., downtime), wind speed and direction [35], and potentially land cover [34], each of which can reduce worst-case levels. Real case modeling, therefore, results in fewer hours of calculated SF, all else being equal. We posit the real case model is a better approximation of actual conditions experienced by wind project neighbors, and therefore it is the metric we primarily use in the analysis.
The model outputs the periods of every SF event for each residence. Using these data, we estimated other parameters like maximum number of SF minutes in any day, as well as seasonality and time-of-day impacts.
The most SF occurs close to a wind turbine and (in the northern hemisphere) primarily to the northeast and northwest of a turbine, and to a lesser extent, to the north ( Fig. 2A). When multiple turbines are between the sun and a home, a combination of SF from those turbines is possible (Fig. 2B). The farther one moves away from a turbine, the greater the decrease in SF intensity. At 15 rotor diameters from a wind turbine (roughly 1.3 km for the median turbine in this analysis) the SF intensity is diffuse enough that little observable light flicker occurs. Therefore, for this study, SF beyond that limit was not modeled.
Physical obstructions from structures and land cover such as trees or other vegetation were not included in the SF models. Although these objects can significantly reduce SF at a shadow receiver, reliable highresolution data were not consistently available across the full set of modeling areas. To test the potential model impacts of land cover, though, six of the study's modeling areas-those which had survey respondent shadow receivers receiving high amounts of annual SF hours-were modeled again with the 30-m gridded 2011 National Land Cover [34] included. Most receivers were unaffected: 94% of receivers with modeled SF had the same annual SF hours for the land-cover and no-land-cover scenarios. Because we found most receivers were unaffected by land cover's inclusion, and because of the relatively coarse grid of obstructions, we did not otherwise include the effect of land cover in this study.

Survey data
Survey data were obtained from the LBNL Neighbor Survey [20]. This survey asked respondents 50 questions about their experience living in proximity to existing utility-scale wind energy projects. Details on that survey's methods, including sample selection, the survey instrument, and multimodal (phone, mail, internet) data collection, are reported at length elsewhere [6,10,22,23], and therefore are only briefly discussed here.
The survey frame encompassed all US residences within 8 km of any utility-scale wind turbine (≥1.5 MW in nameplate capacity) constructed through the end of 2015. This resulted in a population of 1.29 million residences around 604 wind projects, comprising 29,848 individual turbines. To ensure an adequate sample of residents most likely to experience SF and other impacts, the sample was stratified and some oversampling was conducted-most notably among residences closest to turbines (<1.6 km). Oversampling also occurred at 15 wind project sites (representing a diversity of turbine models, geographies, project sizes, population densities, and topographies) where sound modeling was initially planned; these sites also formed the basis for the present SF analysis. After data collection, we selected 15 additional wind project sites for a total of 30 sites, that included 61 wind projects, which were used for the corresponding sound modeling analysis [10] and this SF analysis.  Survey data collection occurred in 2016. Ultimately, a total of 1705 valid responses were received from residents living within 8 km of 250 US wind projects, with the majority (1121) of respondents living within 1.6 km of a turbine. For this study, SF exposure was modeled for a total of 747 survey respondents living within 2 km of 61 wind projects.
The survey data provided basic demographic data (e.g., age, sex, education level) and data about respondents' potential relationship with the local wind project (e.g., whether they received compensation), and self-reported data on perceived SF and level of SF annoyance.
For perceived SF, respondents were asked if "the blades of a wind turbine ever cast a shadow on your property, outside your home?" An affirmative answer to this question triggered the follow-up of "Do the blades of a wind turbine ever cast a shadow in your home?" We use the latter response as our dependent variable, for several reasons. First, SF is regulated at homes. Second, a home is a single point rather than a large area. Finally, most human exposure is in or around a home.
To determine SF annoyance, respondents were asked: "To what extent do you feel annoyed by the following effects of the local wind project?" Where "shadow flicker" was listed as an option, they could respond "Not at all," "Slightly," "Somewhat," "Moderately," "Very," or "Don't Know."

Shadow flicker ordinance data
Wind energy siting ordinances were collected and reviewed for all 50 US counties represented in this analysis. From these ordinances, we collected data on whether SF exposure was regulated, and if so, what the SF limit was, what metric was used (i.e., real or worst case, hours per year or minutes per day), and what location(s) the limit applied to (e.g., "non-participating dwelling"). These data were used to contextualize our discussion around SF exposure.

Analysis methods
This section describes the analysis methods. We briefly discuss the perceived SF and SF annoyance (dependent variable) response categories and the regression models used to validate and predict them with a variety of covariates (i.e., controlling variables).

Dependent variable categories
Two dependent variables are considered in the regression model analysis: perceived SF and SF annoyance. 6 These were created by combining responses from the survey (Section 2.1.4) and modeled annual real-case SF exposure (Section 2.1.3) to represent a doseresponse relationship of perceived SF and SF annoyance. The response groups for perceived SF include "no perceived SF in home" and "perceived SF in home." The former includes two survey response levels: "no perceived SF" and "perceived SF on property but not in home." For SF annoyance, the respondents were categorized as "not," "mildly," or "very" annoyed. "Mildly" annoyed includes the three survey response levels: "slightly," "somewhat," and "moderately."

Regression models
To examine the relationships between various covariates and the dependent variable (perceived SF and SF annoyance, with perceived SF ["PSF"] used in this example), we assume the following relationship: Specifically, we estimate the following basic logistic regression model. 7 where: PSF i represents perceived SF in the home for respondent I (binary yes/no). α is the constant or intercept across the full sample.
MSF i is the modeled SF for respondent i, (hours/year real case). R i is a vector of characteristics for respondent i, including their age, gender, if they attended college, and if they received compensation from the wind project. WP i is a vector of characteristics of the nearby wind project for respondent i, including the size of the project, the distance the nearest turbine was from the respondent, and if it was oversampled for the survey or not. 8 ε i is a random disturbance term for respondent i.  6 For a survey respondent to be included in both models, their homes must have had at least 1 min per year of worst case (astronomical) SF. In addition, for the annoyance model, only those who reported observing SF in their home were included. 7 R: A language and environment for statistical computing (Version 4.0.2) was used for the statistical analysis herein. https://www.R-project.org/. 8 The two categories of oversampling are dominant or discrete. The former refers to under-sampling because the project was located in a high population area, while the latter refers to oversampling because it was the focus of additional detailed analyses (like this study).
The model is then repeated using SF annoyance (i.e., SFA i ) as the dependent variable. In either case, the vector of parameter estimates β 1 , β 2 , and β 3 are used to determine the odds ratio of each variable, calculated as e β . The odds ratio signifies that a one-unit change in a covariate will lead to a decrease (values between 0 and <1) or an increase (values > 1) in the likelihood that a respondent will move to the next response level. For example, for perceived SF, it might indicate a change from not perceiving SF in their home to perceiving SF in their home, or for SF annoyance, from being "not" to "mildly" annoyed or "mildly" to "very" annoyed. When the range of the odds ratio's 95% confidence interval (CI) is completely less than one (representing lower odds of moving to the next response level) or completely greater than one (representing higher odds of moving to the next response level), the variable is considered a significant predictor; this is equivalent to the standard method of assigning variable significance for variables with a p-value of <0.05.
Because the units of the various covariates differ, we analyze the strength of the correlations via the Akaike information criterion (AIC). The AIC represents the impact on the model fit when it is removed from the regression. A higher AIC value indicates a stronger relationship between the covariate and the dependent variable.
The overall fit of the model is measured using Nagelkerke's R 2 (R N 2 ), which is a "pseudo-R 2 " used as an index of overall model quality [36]. It is calculated as a measure of the improvement of the log likelihood of the model compared to that of a null model. To ensure the independence of the variables included in each model, multi-collinearity is assessed with the variance inflation factor (VIF) [37]; the maximum VIF for each model is reported with the results in Section 3.3. Typically, a VIF above four warrants further investigation into the collinearity among model variables.
To indicate the efficacy of each model in predicting responses, the proportion of responses that the regression model correctly predicts is determined using a "leave-one-out cross validation" procedure. For each sample, the regression model is calculated without one respondent. Then, using the model's results, we predict the missing response (either PSF i or SFA i ), repeating for each respondent, and compare those predicted results to those of the respondents.
Three parallel models for each dependent variable are estimated, each with progressively more covariates: Basic, Observable, and Subjective. These covariates are shown in Table 2, and are grouped into functional classification groups. Column 3 denotes which of the three models the covariates are used in. The Basic model ("B") contains all stratification, controlling, relationship, and stimulus variables. The Observable model ("O") adds wind turbine and project characteristics covariates specific to each individual respondent (i.e., objective variables). The Subjective model ("S") expands the scope of covariates to personal variables, including the degree to which respondents liked the look of the nearby wind project, and their general annoyance to community nuisances. In addition to the model and covariate distribution, Table 2 also contains summary statistics for the covariates, means for continuous variables, and percentages for categorical variables.

Population exposure to shadow flicker
This research utilized a large population with modeled SF and a robust sample of those that perceive SF across a wide range of modeled SF hours. Fig. 3 shows the number of receivers (homes) in our sample with (dark grey) and without (orange) modeled SF as a function of distance to the nearest wind turbine. The total number of residences in the sample increases with increasing distance from the nearest turbine. The total number of residences with any modeled SF (grey bars) peaks near 1000 m to the nearest turbine because modeled SF fades considerably beyond that distance. 9 The proportion of the sample population with modeled SF (green line) is highest at distances closest to the turbine. Greater than 50% of the sample residences within 550 m of the nearest turbine have some modeled SF hours. Fig. 4 includes only those receivers with modeled SF. It shows the different levels of modeled SF hours per year by distance from the nearest turbine producing SF. (Note that this may differ from the "nearest turbine" as used in Fig. 3). It also includes the percentage of the sample that has >8 h/year real-case SF (blue line)-a maximum limit used in some SF standards (see discussion in Section 1.3). A majority of residences within 750 m were modeled with real case SF exposure above 8 h per year. Within 500 m, 90% have more than 8 h of modeled real case annual SF.

Survey respondent shadow flicker summary
This section presents survey responses used to build perceived SF and SF annoyance categories and compares them to modeled annual SF exposure. Fig. 5 presents the distribution of perceived SF among survey respondents. Each bar represents the proportion of respondents in each response group and modeled SF exposure category. The width of each bar is proportional to the sample size in that category. Fig. 5A provides the full survey sample of SF receivers, while Fig. 5B presents only those with some modeled SF exposure. Both include three respondent categories: perceived SF in home, perceived SF on property, and no perceived SF. The proportion of respondents that notice SF in their homes increases as the number of annual hours increase. This is expected, as the more SF a home is modeled to have, the more likely it is that the resident will report perceiving SF in their home. For individuals with some modeled SF (>0) at their home, roughly 15% report that they can perceive SF only on their property but not in their home (shown in Fig. 5 as "On Property"). This percentage is consistent regardless of SF exposure levels.

Perceived shadow flicker
Of those that have modeled SF in the range of 4 to 8 h/year real case, only about half (52%) reported perceiving SF in their home. We believe that this disparity is due to other factors that are not considered in this study that mitigate SF exposure, particularly land cover, the use of rooms that may be exposed to the SF, whether windows face the wind turbines, draperies and other window covers, and whether the occupants are home during the SF events. Fig. 6 presents parallel results for reported annoyance to SF. Fig. 6A appears to indicate that the distribution of SF annoyance increases with SF exposure across all respondents. However, it is notable that roughly half of the respondents in the figure had no modeled SF exposure (and thus cannot be annoyed by SF in their home). When limited to only respondents with some modeled SF (Fig. 6B), the distributions between annoyance levels do not vary appreciably across exposure levels. This suggests two things: 1) the apparent increase in SF annoyance for all respondents is driven by the inclusion of the do-not-perceive-SF-in-theirhome category; and 2) there is an insignificant relationship between modeled SF and SF annoyance in the sample once they are excluded. This was tested directly and is described in Section 3.3.

Distribution of responses, by exposure
To directly compare SF exposure to perceived SF and SF annoyance, Fig. 7 shows box plots representing all survey respondents. The "box" provides the 75th, 50th (median [dark line]), and 25th percentile of the distribution of the sample. The "tails" on the boxes represent the range of 95% of the data. The plot reaffirms that the prevalence of perceived SF in one's home increases with modeled SF exposure. However, the number of modeled SF hours alone is insufficient to explain reported SF annoyance among survey respondents.

Regression results
The results from the three (Basic, Observable, and Subjective) logistic regression (logit) models for perceived SF and SF annoyance, as described in Section 2.2.2 and Table 2, are presented in Table 3 and Table 4. 10

Perceived shadow flicker
The basic perceived SF model (  Table 3) and about 60% of respondents that did not perceive SF in their home.
Turning to the regression results, the real-case annual SF hours is the strongest predictor of perceived SF, with an AIC about four times greater than the next covariate (22.6 vs. 7.6). Across all three models, a onehour increase in annual real-case wind turbine SF is associated with an increase in the odds of perceiving SF in the home by 12% to 13%. Logically, quantifiable SF exposure should be a good predictor of whether a respondent perceives SF or not. The model indicates that, indeed, a significant dose-response relationship is present. Further, respondents farther than 800 m (~0.5 miles) from the nearest wind turbine had 65% to 66% lower odds of perceiving SF than respondents within 800 m (see the Distance Bin variable in Table 3). The odds of perceiving SF in one's home were at least 75% lower for those who moved into the area after the project was built compared with those who lived in the area prior to the project's construction (see the move-in-after variable in Table 3). Project participation did not significantly contribute to the prediction of perceived SF in one's home.

Shadow flicker annoyance
The SF annoyance results (Table 4) differ substantially from those of perceived SF. For SF annoyance, the Basic and Observable models are relatively weak predictive models, with R N 2 < 0.27 and less than 49% of the total responses correctly predicted. Adding subjective variables considerably increases the model's effectiveness, increasing R N 2 to 0.58 and correctly predicting 65% of the responses overall.
In the Basic SF annoyance model, respondent participation in the project is the most influential predictor (AIC = 25.1); participants had about 81% lower odds of being annoyed by SF than non-participants. Annoyance was comparable among project participants that hosted wind turbines on their properties and those that were compensated without hosting a turbine, relative to non-participants. After project participation, a respondent's college education (AIC = 6.6) was the strongest predictor of SF annoyance; respondents who had completed college had 57% lower odds of moving to a higher annoyance level than those that did not attend college. Modeled SF exposure was the thirdstrongest correlate: a one-hour annual increase in real case SF was associated with a 4% increase in the odds of SF annoyance. Age (AIC = 6.0) was the fourth-strongest predictor in the Basic model, with decreased odds of SF annoyance among older respondents.
Adding objective variables did not increase predictive strength of the model (see "Observable" model). In fact, none of the observable vari-  The decrease in "without modeled SF" beyond 1,900 meters is a result of not modeling SF beyond distances 15 times total turbine height (see Section 2.1.3). The small increase in SF level for respondents at 1,600 m is due to a small sample size (n = 8); one of these receivers had three distinct wind turbines contributing SF annually. Of the three wind turbines, the farthest turbine at 1,620 meters contributed the most SF; the other two turbines contributing SF were within 800 meters of the receiver. 10 Although we present multivariate correlation results in the regression tables, we did examine univariate correlations as well. Contact the authors for more information on those.
ables were significant in predicting SF annoyance. In contrast, all Subjective model variables were significant in predicting the SF annoyance outcomes. The respondents' stated attitudes toward the aesthetics of the   local wind project (i.e., if they did or did not like the look of it vs. a neutral response) was by far the strongest correlate (AIC = 62.3). 11 The respondents' general annoyance to environmental nuisances (AIC = 9.7), if they attended college (AIC = 9.2), their age (AIC = 6.9), the age of the nearest wind project (AIC = 4.3), and if the respondent was compensated but not a host were all statistically significant. With subjective variables considered, modeled SF exposure was not a statistically significant predictor of SF annoyance. The Subjective model correctly predicted 65% of annoyance levels overall, 73% of the very annoyed responses, and 79% of not-at-all-annoyed responses.
Moving in after the project was built was found to be a strong predictor of perceived SF in this study and in previous literature for: attitudes toward wind projects [23]; perceptions of the planning process [6]; and both the audibility of wind turbine noise in the home and wind turbine noise annoyance [10]. However, we found moving in after a project was built was not significantly correlated with SF annoyance.
In summary, although this study found a strong relationship between modeled SF exposure and perceived SF reported by survey respondents, the relationship between SF exposure and SF annoyance is much weaker, indicating other factors are likely at play that cause annoyance. 12

Exposure to shadow flicker compared with existing guidelines and sound levels
The combined survey data, SF exposure data, and data on US countylevel SF exposure limits allow us to examine other relationships. We first calculate a ratio between worst and real-case SF estimates and compare that to the 3:1 ratio commonly used in EU SF standards (see Section 1.3). We then assess modeled exposure against the most commonly enforced SF limits in our sample (see Section 2.1.5) and examine them relative to project participation. Finally, we look at the relationship between SF exposure and sound exposure by comparing SF exposure categories and modeled sound-level categories.

US state-and county-level shadow flicker ordinances
The data from wind energy siting ordinances for all 50 US counties represented in this analysis were revealing: most counties in this analysis (62%) do not enforce any limit on SF exposure. Two states (New York and Ohio) have enacted statewide SF limits (30 h/year), and only 13 other county-level ordinances were identified (10 at 30 h/year, 2 at 0 h/year, and 1 at 40 h/year). Of the 15 authorities that do specify any limit on SF exposure, 30 h/year was by far the most common limit.  11 Although not discussed here in detail, liking the look of the turbines was nuanced among respondents. Those who did like the look did not believe the turbines were "attractive" but did feel they represented "progress." Alternatively, those that did not like the look believed they "did not fit" with the landscape and were "unattractive". 12 One reviewer pointed out that perceptions of the planning process have been found to be a strong predictor of wind turbine annoyance [6] and strongly annoyed individuals [21]. As noted later in the document, this might be a useful variable to study in future analyses.  Notably, only two of those regions specify a modeling metric (real or worst). In the authors' experience, where there is ambiguity as to the metric, in most circumstances the 30 h/year limit is modeled during permitting as real case.

Real vs. worst-case ratio and modeled exposure
As described in Section 1.3, Koppen et al. [24], document a common three-to-one ratio between worst and real case SF guidelines. That is, a 30 h/year real-case limit would allow about three times more SF exposure than a 30 h/year worst-case limit. In this section, we test if those relationships were borne out in our data and also examine the relationship between hours/year and minutes/day, which are sometimes apparently used interchangeably in regulations [24]. Fig. 8 plots the modeled maximum number of minutes of SF in a day against the annual SF hours for each respondent with any modeled SF in our sample population (n = 4825). Both the real case (orange) and worst case (dark grey) modeled values are provided, and a trendline fitted to the data is superimposed over the scattered data. Horizontal dotted lines denote 30 and 8 min/day, and, separately, vertical lines denote 30 and 8 h/year. These dotted lines nearly intersect on the solid trendlines of the scattered worst and real case modeled SF values. This indicates that a ratio of 30 worst case hours/year is roughly equivalent in our data to the 30 worst case minutes/day, as is 8 real case hours/year and 8 min/day. Further, the ratio in our data of worst to real case is roughly three to one (r 2 = 0.93), which is equivalent to the German guidelines and others outlined by Koppen et al. [24].
The data from Fig. 8 also indicate that approximately 7% of all modeled residences in the sample population (including both survey respondents and non-respondents) exceed either 30 h/year worst case or 8 h/year real case (the "30/8 limit"). Although we do not show distance in the figure, the data indicate that 21% of residences within 1 km of any turbine exceed the 30/8 limit. As discussed in Section 3.4.1, the majority of counties in our sample do not apply SF exposure limits, and those that do fail to specify whether those limits are real or worst case limits. Fig. 8 elucidates that if those limits were in force, compliance would not be achieved at many residences. However, we found that only 2.3% of those with modeled SF exceeded 30 h/year real case. This supports our interpretation that real case is used with 30 h/year standards where the metric is ambiguous.

Survey respondent exposure summary
Considering the sample of survey respondents (n = 717), 27% exceed the 30/8 limits. This percentage is above the 7% of the full sample population discussed in Section 3.4.2 because the respondents are, by design, closer to turbines than the general population and have a higher preponderance of exceeding the limits. Considering the 404 survey respondents with any modeled SF, 50% exceeded either of the 30/8 limits, with 37% exceeding both.
Individuals living closest to wind turbines are also likely to host a turbine or are otherwise being compensated, which could accommodate higher levels of SF as part of that agreement. Table 5 shows that at least 70% of the turbine hosts experience SF above either limit, 55% or more of the compensated neighbors exceed the limits, and at least 34% of the non-participants have modeled SF that are above both limits.
Importantly, in line with the findings above, the group that exceeds the 30/8 limits is no more likely to be annoyed by SF than respondents who are under the limit.

Combined wind turbine noise and shadow flicker exposure
We examine if sound-level limits can be used as a proxy for SF limits, which, as discussed in Section 3.4.1, are rarely applied. Noise exposure, for our purposes here, is modeled as a one-hour equivalent continuous A-weighted sound level (L 1h ). 13 In the US jurisdictions we reviewed, 45 dBA and 50 dBA are commonly applied noise limits (or greater for participating homes), although metrics and averaging times vary considerably. Fig. 9 shows the proportion of the population in real-case SF categories with respect to wind turbine sound-level categories. For homes with modeled wind turbine sound level 40 dBA or below, 98% do not exceed the 8-hour real-case SF limit, while between 40 and 45 dBA, 90% do not exceed the limit. Alternatively, for those between 45 and 50 dBA or greater than 50 dBA, only 40% and 25% are below the 8-hour realcase SF limit, respectively. These results indicate that a sound limit of 45 dBA is a decent proxy for meeting a SF limit of 8 h/year real case. Paradoxically, low SF exposure limits are not a good a predictor of low noise exposure, as very low (or no) SF occurs across all sound-level categories.
The relationships are different for SF annoyance. Fig. 10 shows the distribution of respondent SF annoyance by turbine sound-level category. Fig. 10A appears to show a relationship between SF annoyance and sound level. Higher proportions of respondents exposed to sound at progressively higher sound levels reported some level of SF annoyance at higher rates. However, as outlined in Section 2.1.4, only those experiencing SF in their home can be annoyed by it in their home. Considering that cohort, we find the absence of a correlation between sound level and SF annoyance: SF annoyance levels are roughly equally distributed across sound-level categories (Fig. 10B). The survey data also indicate that noise and SF annoyance are similar among survey respondents: 71% of those very annoyed by SF (n = 72) indicated that they are also very annoyed by noise from the wind turbines (data not shown).

Conclusions
Although SF has been identified in multiple national surveys as a potential source of annoyance among wind project neighbors, the magnitude of SF exposure and drivers of SF annoyance have remained significantly understudied, leaving both developers and communities in need of science-based guidance. To help fill that research gap, this study modeled SF exposure at nearly 35,000 residences, 747 of which were also survey respondents, and developed models to predict the respondents' stated perceived SF and SF annoyance. In so doing, we provide information not only on the levels and extent of SF exposure around US wind projects, but also identify variables that do (and, of equal importance, do not) predict perception and annoyance to SF. The research also reports on findings about SF modeling and metrics, including the relationship between noise, SF exposure, and SF annoyance.  13 Specifically, A-weighted decibels (dBA) are the level of sound weighted to mimic the perception of the human ear. In this study, we estimate the maximum expected equivalent continuous sound level over one-hour (L 1h ), using the ISO 9613-2 sound propagation standard with mixed ground porosity (G = 0.5), four-meter receptor heights, and + 2 dB (dB) uncertainty (see [10] for explanation of these terms and more details).
Perceived SF is found to be largely influenced by observable characteristics, including SF exposure, distance to the nearest turbine, and whether a respondent moved in after the project was built. Notably, only about half of those with SF exposure in the range of 4 to 8 h per year real case reported perceiving SF in their home. When applied to a predictive model of an individual's perceived SF in their home, up to 71% of the perceived SF regression model predictions were correct.
Of respondents with modeled SF at their home, 17% reported being highly annoyed. SF annoyance is found to be correlated with one's subjective response to the look of the wind turbines, general annoyance to other anthropogenic sounds, level of education, and age. With subjective factors included, an individual's annoyance to SF was correctly predicted 65% of the time, with 73% of the "very annoyed" responses predicted correctly by the model. Importantly, when individual subjective factors were considered, modeled SF exposure was not significantly correlated with SF annoyance.
In summary, we find modeled SF levels predict one's perceived SF, but once perceived, higher levels of SF are not a predictor of higher levels of self-reported annoyance. These concepts are similar to findings we previously observed for wind turbine noise-that modeled wind turbine sound level was a robust predictor of wind turbine audibility but not annoyance to wind turbine noise [10,22]. SF exposure is regulated in relatively few jurisdictions across the US analysis area. The most commonly enforced limit across the United States in the project areas evaluated in our study is 30 h/year, similar in value to German worst-case guidelines and other standards found in the EU. However, in the United States, the metric is rarely defined as real or worst case, and, in our experience, is most often interpreted during the application process as real case. Of the full sample population, 7% exceed 30 h worst case or 8 h real case. Of the 404 survey respondents with any modeled SF, 50% exceeded the 30/8 worst-case/real-case limits, though a majority are project participants, and 2.3% exceeded 30 h/year real-case. Respondents exceeding those limits were no more likely to be very annoyed by SF than other respondents. Regulated SF exposure limits are designed to mitigate annoyance, yet we find no clear dose-response relationship between SF exposure and self-reported annoyance when subjective variables are considered.
However, several of our findings can be helpful to inform SF regulatory standards. Overall, we found that an average relationship of worst to real case of roughly 3 to 1, following the relationship enforced in many EU jurisdictions. Including land-cover data in the analysis, has little effect on modeled levels for most residences, but could be used to obtain more realistic estimates of SF at individual locations, especially if high-resolution ground cover data are available. Finally, more than 90% of homes exposed to wind turbine sound levels below a typical limit of 45 dBA L 1h also received less than 8 h/year real-case SF. These results  imply that sound-level limits might act as a decent proxy for SF limits.
This paper looks at self-reported annoyance, which is more of an attitudinal variable than annoyance stress. Accordingly, SF emissions could reduce the community acceptance of wind turbines and thus should be reduced to the extent feasible.
We offer several suggestions for future research: (1) Future research should further examine the interactive impacts of SF, sound, and visual perception on wind project neighbors and their perceived levels of annoyance. (2) Although SF is typically regulated by exposure (i.e., minutes or hours), we find that SF exposure is not significantly correlated with annoyance. If a goal is set to reduce SF annoyance, though, future research, in the United States and in Europe, should study other approaches, metrics, or standards to mitigate SF annoyance. (3) Wind energy is rapidly expanding on a global scale, yet, to our knowledge, in-depth studies of SF exposure and annoyance have been conducted in few regions. Researchers should seek to replicate these types of analyses in more regions where wind energy is deployed. Additional survey questions could reveal more factors leading to annoyance such as time-of-day impacts, work and sleep schedules, activity interruptions, and measures taken to mitigate SF, such as shutting down the wind turbines during periods of intense SF. 14 (4) Pohl et al. [29] used a weighted shadow duration (WSD) variable, which accounted for modeled SF hours and the number of shaded rooms and outdoor areas in a home. They found a consistent significant relationship between WSD and SF annoyance; these data were not available for this study. Future case studies, though, could seek to replicate Pohl et al.'s methodology to test if that relationship is robust, as well as, potentially, exploring other variables that might modify modeled SF. These variables include: the prevalent time-of-day SF is experienced, the intensity of the SF based on the turbine's distance and the number of turbines creating the SF. (5) The annoyance stress scale (AS-scale) as developed by Hübner et al. [22], may provide an improved metric from a policy or regulatory perspective to protect public health over self-reported annoyance. Self-reported annoyance (without accounting for stress and coping mechanisms, for example) may miss the full weight of the responses of unique individuals. Indeed, this is a promising area for future study for wind turbine SF, noise, and public acceptance in general.

Declaration of competing interest
The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript.   14 Shutting down the turbines was suggested by a reviewer who is familiar with a German requirement to limit SF hours below a certain threshold.