Spatial regression identifies socioeconomic inequality in multi-stage power outage recovery after Hurricane Isaac

Power outages are a common outcome of hurricanes in the USA with potentially serious implications for community wellbeing. Understanding how power outage recovery is influenced by factors such as the magnitude of the outage, storm characteristics, and community demographics is key to building community resilience. Outage data are a valuable tool that can help to better understand how hurricanes affect built infrastructure and influence the management of short-term infrastructure recovery process. We conduct a spatial regression analysis on customers experiencing outages and the total power recovery time to investigate the factors influencing power outage recovery in Louisiana after Hurricane Isaac. Our interest was in whether infrastructure damage and recovery times resulting from a hurricane disproportionately affect socioeconomically vulnerable populations and racial minorities. We find that median income is a significant predictor of the time it takes to restore 50%, 80%, and 95% of the total outages within a ZIP Code Tabulation Area, even after controlling for hurricane characteristics and total outages. Higher income geographies and higher income adjacent geographies experience faster recovery times. Our findings point to possible inequities associated with income in power outage recovery prioritization, which cannot be explained by exposure to outages, storm characteristics, or the presence of critical services such as hospitals and emergency response stations. These results should inform more equitable responses to power outages in the future helping to improve overall community resilience.


Introduction
Socioeconomically vulnerable communities often experience worse recovery outcomes compared to less vulnerable communities (Fothergill and Peek 2004;Tselios and Tompkins 2019;Ulak et al. 2020). These communities can take longer and, in some cases, even fail to return to the pre-disaster baseline. Increased risk exposure and fewer available resources for recovery or rebuilding tend to delay recovery (Fothergill and Peek 2004;Masozera et al. 2007;Rufat et al. 2015;Tate et al. 2021). Prolonged lack of access to infrastructure services, such as power, after a disaster, can also have negative health, social, economic, and mental consequences (Chang 2016;Mostafavi 2018;Coleman et al. 2020). Therefore, a poorly managed recovery process can perpetuate the disempowerment of marginalized groups and increase income inequality (Sovacool et al. 2018). Understanding and addressing uneven recovery efforts are critically important for equitable resilience and disaster management (Flanagan et al. 2011;Doorn et al. 2019).
Hurricanes frequently produce power outages in the USA. Outage data can signal how the short-term infrastructure recovery process is managed in the aftermath of a disaster . When faced with widespread outages, utilities often take a standardized and utilitarian approach by prioritizing repairs restoring power to the greatest number of clients as quickly as possible (Xu et al. 2007), or in some cases, restoring outages that affect the provision of vital services. The result of the latter approach is that neighborhoods on the same feeder as local emergency services or major grocery stores are likely to experience faster restoration times than others in the community (Chang et al. 2007;Maliszewski and Perrings 2012). It is also possible that vulnerable populations may have less access to adaptation methods such as backup generators or temporary relocation, in which case even an "objective" recovery prioritization approach may fail to address restoration vulnerabilities (Chandrasekhar et al. 2019). Regardless of the approach, there is a level of subjectivity inherent to the decision-making process that can potentially produce inequalities in restoration outcomes.
We conduct a spatial analysis of customers experiencing outages and power recovery time in Louisiana after Hurricane Isaac (2012). Our interest is in whether the infrastructure damage and long recovery times that resulted from this hurricane disproportionately affected socioeconomically vulnerable populations and, if so, whether recovery unevenness is the result of vulnerable populations living in more hazard-prone areas. Our primary research questions are (1) in the case of Hurricane Isaac, does socioeconomic inequality contribute to more severe impacts from a natural disaster in terms of proportion of customers experiencing power outages? If so, to what extent are the effects explained by differences in the spatial variation in storm strength? (2) Are spatial variations in socioeconomic inequality associated with differences in recovery speeds after Isaac? If so, can these effects be explained by differences in storm strength and/or presence of high priority infrastructure (e.g., hospitals and emergency services)? These questions guide our multi-stage approach at three different power recovery thresholds.
Our work is novel in several key ways. First, we use spatial regression, accounting for spatial autocorrelation, to identify the direct, indirect, and total effects of each variable on power outages and recovery times. Organizing results into direct, indirect, and total effects lends insight into the unique ways that socioeconomic conditions interact with power outage recovery across space. While spatial regression has been used to study the magnitude of power outages (Ulak et al. 2018), it has not been applied to examine the recovery process after those outages occur. Our research is also unique in that we conduct analysis on both the magnitude of power outages (represented by proportion of customers experiencing outages) and recovery times, meaning time for customers to have access to power again, across multiple stages (50%, 80%, and 95% recovery). Much of the previous quantitative work on post-disaster power outages has focused on either magnitude of disruptions (such as number of customers reporting outages) or the time to recovery as outcomes of interest, but not both. This also provides us with a more complete and nuanced view of how Hurricane Isaac affected the power system in Louisiana and how recovery efforts were subsequently administered.

The electric system, power outages, and restoration
In 2021, US customers experienced an average of 1.4 power interruptions and lost power for approximately 475 min, or almost 8 hours (EIA 2022). Major environmental events such as storms and floods can cause disruptions to power systems, and extended periods of time without power can contribute to significant economic losses (U.S. Department of Energy 2013; Sanstad et al. 2020). Natural disaster-related outages often result in multiple faults and disruptions occurring concurrently in generation, transmission, and distribution. The interdependence between power and other infrastructure systems such as transportation and telecommunication networks can present additional obstacles to power restoration (Wang et al. 2016).
While power outages are a common outcome of natural hazard events, they can be very disruptive and dangerous. Access to reliable power is critical for both short-and longterm recovery efforts, as well as the normal functioning of nearly every sector of society. Although some customers have backup generators, many others are left entirely without electricity during power outage periods (Darling and Hoff 2018;Chakalian et al. 2019). Even brief outages can cause negative health, social, and economic outcomes (de Nooij et al. 2007;Anderson and Bell 2012;Campbell 2012). This is especially true in areas that experience extreme heat, where loss of power and air-conditioning can pose serious health concerns for vulnerable populations (Riley et al. 2018;Dahl et al. 2019) and present equity and social justice issues (Karakoc et al. 2020;Lin et al. 2022).

Environmental justice and power outages
As mentioned, the effects of power outages can be severe. As with other impacts of environmental hazards, it is important to understand how power outages disproportionately affect populations based on characteristics such as income, race, age, gender, or disability (Zoraster 2010;Flanagan et al. 2011;Chakalian et al. 2019), and these characteristics are also likely to influence exposure and damages from storms. There are examples in the literature that indicate higher likelihood that low-income and otherwise disadvantaged communities are in areas with a higher risk of experiencing extreme hurricane damages, like flooding after Hurricane Sandy in New York City (Lieberman-Cribbin et al. 2021). Increased flood exposure by vulnerable groups was also seen after Hurricane Harvey in Houston, Texas (Bodenreider et al. 2019;Collins et al. 2019) andHurricane Katrina in New Orleans (2006;Cutter et al. 2006;McKenzie and Levendis 2010;Zoraster 2010). In these cases, disproportionate disaster outcomes were likely, in part, due to disproportionate exposure.
The uneven effects of power outages after a storm can also be related to unequal recovery after an outage. Although differential outage rates may be explained by differences in storm strength, the structural relationship between inequality and the built environment is well established (Pandey et al. 2022). For example, initial studies have suggested that lower-income areas experienced slower recovery from power outages after Winter Storm Uri in Texas in 2021. Counties with higher rates of white residents and higher median incomes experienced significantly fewer power outages, and a statistically significant and positive relationship existed between the percentage of linguistic minorities (linguistically isolated groups), public transport users, and outages throughout stages of recovery (Nejat et al. 2022). Socioeconomic disparities in the scale and duration of power outages were seen in Harris County, Texas (Lee et al. 2021), and in Puerto Rico after Hurricane Maria, where every 10% increase in population in poverty was associated with a 2% increase in power outage recovery time (Azad and Ghandehari 2021).
Despite the serious justice implications of power outages, many past quantitative studies of power outages and power outage recovery have not considered the underlying socioeconomic context in which recovery occurs. For example, in work to predict the duration of power outages after Hurricane Ivan, data related to the power service system, hurricane characteristics, land use, and local environmental/climatic conditions were used without controlling for socioeconomic factors (Nateghi et al. 2011. Including relevant socioeconomic variables can provide insights into both vulnerability to power outages and limitations to equitable recovery. For example, Mitsova et al. (2021) found that insurance status and access to health services were significant predictors of household recovery after Hurricane Irma (Mitsova et al. 2021). Ulak et al. (2018) found that higher populations of older (65 +) residents corresponded to higher rates of outages after Hurricane Hermine (Ulak et al. 2018).
We contribute to this literature by using median income as a measure of socioeconomic vulnerability and the percent of the population that is white as a measure of racial composition. We also include the presence of critical services such as health and emergency services to control for the effect that many lower income, and racial minority communities may have less access to and live further away from such services (Archibald and Putnam Rankin 2013; Guo et al. 2022).

Case study: Hurricane Isaac
Hurricane Isaac began in the Atlantic Ocean as a tropical storm on August 21, 2012. The tropical storm was upgraded to a hurricane on the 28th of August, and a few hours later it made its first US landfall on Louisiana's southeast coast in Plaquemines Parish (Berg 2013). The following day, Isaac made landfall for a second time west of Port Fouchon. The storm moved slowly through the state, with rain and high winds persisting for 56 h (Miles and Jagielo 2014;Miles et al. 2016). High winds resulted in power outages throughout Louisiana peaking on August 30 when 43% of utility customers were without power. In total, 900,000 customers experienced power outages. This is on par with the number of outages following Hurricane Katrina in 2005 and Hurricane Gustav in 2008. Some of the parishes hit hardest by Hurricane Isaac experienced up to a 90% power loss and restoration efforts took over 10 days (Miles et al. 2016).
Even though Hurricane Isaac resulted in power outages comparable to some of the region's most destructive storms, its other impacts were relatively mild. Wind damage to buildings was minor, and although some flooding did occur, the federal levee system, which was put to the test for the first time since Hurricane Katrina, protected the more populated areas from high waters, resulting in isolated and minimal water damage. Most people stayed in their homes for the duration of the storm and recovery period (Miles et al. 2016). Hurricane Isaac is a unique case study in that the electric system was severely damaged, but other infrastructure systems survived the storm relatively unscathed (Miles and Jagielo 2014). This suggests that, as a case study, Hurricane Isaac allows us to investigate the factors influencing power outages and restoration independent of compounding or cascading interactions with other infrastructure systems. The power restoration process involved over 12,000 utility workers and 4000 support personnel from 25 states, 20 mutual aid companies and 138 contractor companies (Miles et al. 2016). Restoration efforts started slowly; federal regulations prohibit utilities from using bucket trucks when winds are above the wind ratings provided by the truck manufacturers. The hurricane lingered over the state for an extended period of time; wind speeds did not abate for 2.5 days (Miles et al. 2016).
Hurricane Isaac ultimately caused five direct deaths in the USA, three of which were in Louisiana (Berg 2013). Even with a limited geographical scope, the storm was estimated to have caused $2.35 billion in damages across the US, of which $970 million was insured (Miles and Jagielo 2014;Miles et al. 2016). The National Flood Insurance Program paid out $407 million. The storm damaged or destroyed 4500 distribution poles, 2000 distribution transformers, 95 transmission lines, and 144 substations, costing an estimated $500 million in repairs (Miles and Jagielo 2014).

Data
We use power outage data scraped from utility websites in Louisiana in the aftermath of Hurricane Isaac. During major outages, utilities are required to regularly update their website with the number of customers without power in each region. The team retrieved these data from Entergy, the electrical utility that provides power to much of the state of Louisiana, providing a detailed view of power restoration following Hurricane Isaac. The data provide the number of households in a given ZIP code without power in 15-min intervals. The utility web site was scraped for a total of 13,760 min beginning on August 27, 2012, at 12:00 pm. This is equal to 229 h or roughly 9.5 days.
Our data included observations for 389 ZIP codes. Our analysis uses the spatial unit of Zip Code Tabulation Area (ZCTA) rather than the ZIP code. The process of converting ZIP codes to ZCTAs and dropping observations for which no demographic data were available reduced the total number of observations to N = 289. Exclusions included ZIP codes that did not reach the benchmark of 50%, 80%, or 95% restoration by the time the outage scraping ceased, so it is only known that the restoration time was greater than 13,760 min. In total, nine of the 289 observations did not reach 95% restoration during the data collection period. Of those, seven did not reach 50% restoration during this time frame, indicating significant remaining power outages. Without lack of accurate tie to recovery data, these observations were dropped from the analysis.
Variable selection is reflective of the relevant literature on modeling power outages and restoration (Han et al. 2009;Guikema et al. 2010;Quiring et al. 2011;Mcroberts et al. 2016). Modeling power outages as a result of hurricanes is complex, and past work has included a range of input variables including geographic characteristics, hazard-related variables, and information about the grid structure Nateghi et al. 2014). As mentioned, many models focused on prediction of outages do not incorporate socioeconomic factors. We use variables sorted into three categories: hazard, priority, and socioeconomic (Table 1). Hazard variables include those related to storm intensity such as maximum wind velocity and 5-day precipitation. Priority variables are related to common factors that are likely to influence a utility's recovery prioritization process including the number of outages and the locations of high-priority infrastructure such as health and emergency services. The literature indicates that emergency services like fire stations and hospitals may be prioritized for recovery, meaning that customers living in proximity to these priority facilities may experience shorter recovery times (Maliszewski and Perrings 2012). For this analysis, emergency services include ambulance services, emergency response facilities, fire stations, law enforcement stations, etc. Health services include hospitals and medical centers (Table S2). Lastly, to reflect potential structural inequities (Cutter et al. 2003;Wisner 2016) in the relationship between the number of outages and socioeconomics, we use median household income and percent of the population that is white and non-Hispanic as these variables capture two key components of vulnerability to natural hazards that have been most widely studied in the literature: wealth and race (Fothergill et al. 1999;Fothergill and Peek 2004).
Our analysis is conducted in two steps. First, we assess whether median income and racial composition are related to the proportion of customers experiencing outages in a ZCTA. In the second analysis, we examine the time to recovery by median income, race, and high-priority infrastructure such as emergency and health service locations.

Spatial analysis
Similar to Ulak et al. (2018), we begin with a spatial analysis to assess spatial autocorrelation in the data. We first use the spdep (Spatial Dependence: Weighting Schemes, Statistics) package in R (Bivand et al. 2022a) to define each ZCTA's neighbors based on Queen's contiguity criteria, which defines neighbors as all those with a common corner or boundary (Waller and Gotway 2004;Duncan et al. 2012). Each neighboring ZCTA is then assigned an equal weight, which is used to generate a spatially lagged value of the variable of interest. Using our neighboring weights and lagged variables, we can calculate a Global Moran's I value, the most commonly used method to identify spatial autocorrelation by testing the degree to which data is clustered or dispersed (Waller and Gotway 2004). Moran's I values and significance levels are reported in Sect. 4.
After identifying spatial autocorrelation in the data of proportion of customers reporting outages as well as recovery time data, we specify a spatial autoregressive model. Models that do not consider spatial relationships (such as Ordinary Least Squares models) have been shown to yield systematically varying residuals (i.e., residuals that are also spatially autocorrelated) when applied to data with spatial autoregression (Lesage 1999;Ulak et al. 2018). We use the Spatial Durbin Model (SDM) (LeSage 2014) which is appropriate when resources are shared across a system such as highways, rivers, or, in this case, power systems (LeSage 2014). In the SDM model, both the outcome variable and independent variables are lagged spatially, thus accounting for spatial autocorrelation in the outcome (Anselin 1988; Chi and Zhu 2008). The model is defined as where Y is the outcome variable, X is the set of explanatory or independent variables, W is the set of spatial weights, and is the error. WY is the set of spatially lagged Y values and WX is the spatially lagged X. is the vector of fitted coefficients associated with each independent variable and is the spatial autoregressive parameter or spatial dependence parameter (Lesage 1999;Chi and Zhu 2008). With SDM models, the total effect of the explanatory variable on the outcome variable can be split into direct and indirect effects, where the direct effect is the effect of the own variable value (i.e., the value in a given ZCTA), and the indirect effect is the average effect of the "spatial spillovers" or neighboring values (i.e., the values of neighboring ZCTAs) (LeSage and Pace 2014). We estimate our SDM models using the lagsarlm() function found in the spatialreg package in R (Bivand et al. 2022b). We assess the effectiveness of the SDM model in addressing spatial autocorrelation by then testing for spatial autocorrelation in the model residuals. If the model addresses the spatial correlation, then the model residuals should not be spatially related.

The effects of income and race on outages
Here, our interest is in identifying the relationship between the median household income and the proportion of customers experiencing power outages at the ZCTA level. We specify two models: one controlling for the storm strength and one omitting control variables to assess whether differential effects occur because communities of a given socioeconomic status live in areas experiencing more intense weather from the hurricane (i.e., higher exposure). The data for maximum outages are a count measure, and as is often the case with count variables, it is both right-skewed and long-tailed, meaning that the conditional variance is greater than the conditional mean. We also have data for the number of total housing units from the American Community Survey and businesses within a given ZCTA from the U.S. Census Bureau's ZIP Codes Business Patterns (ZBP) data. This serves as an approximation of the total number of electric customers within the unit of analysis. The actual number of customers is not publicly available, which is why we deploy a reasonable proxy. We calculate an estimated proportion of customers without power as the ratio of the maximum outages divided by the number of customers in the ZCTA. We omit observations with an estimated proportion of outages significantly greater than 1 (N = 2), which we believe may be due to certain customers experiencing multiple outages and/or error in the estimate of the number of customers. For observations in which the ratio is very close to, but above one (N = 60) we set the ratio to 1, representing 100% of customers experiencing outages.
We use a SDM spatial regression with an outcome variable as the proportion of customers without power in the ZCTA. In our first model, we include data related to income and race as independent variables. In our subsequent model, in addition to income and race, we also include a series of hazard variables reflecting Hurricane Isaac's varying levels of force (Table S1). We expect that power outages will be significantly and positively related to the intensity of hurricane effects.

Determinants of recovery time
Our aim in the second analysis is to examine the time to power restoration. For this, we use times to 50%, 80%, and 95% power restoration to compare differentials in basic levels of power restoration across ZCTAs. Recovery can be influenced by many factors including antecedent conditions, the extent of the damage to the system being recovered, obstacles to recovery such as flooding or debris, the point at which the recovery process can begin in a given spatial unit, and the extent to which a given unit is prioritized within the broader recovery operations (Cutter et al. 2008(Cutter et al. , 2014Tierney 2014). We use a SDM spatial regression for each model where the dependent variable is time to 50%, 80%, or 95% recovery. We again build our model specifications to reflect our research questions. We start by using median income in the ZCTA along with our total number of outages and then progress to introducing storm-related measures. Finally, we include the number of emergency service and health service locations to capture the possible effects of faster restoration due to the presence of high-priority infrastructure.

Spatial analysis
The mean number of outages at the ZCTA level was 2282, and the median was 620, indicating a strong right skew. The mean proportion of customers experiencing outages was 0.38, with a standard deviation of 0.31 and a median of 0.49. A series of maps were produced to visualize and better understand the way that Hurricane Isaac's damages and impacts were distributed across Louisiana. When examining the distribution of peak wind gust speeds across the state (Fig. 1), we observe that the most extreme winds were in the southeastern region of the state, and the wind speeds decreased as the storm moved north and west. This is consistent with official reporting on the storm's path. However, when a map is created tracking the proportion of customers experiencing outages at the ZCTA level, the results show a less clear spatial pattern (Fig. 2).
We find a Global Moran's I index of 0.62 with a z-score of 14.19 and a p-value < 2.2E−16 for the proportion of customer outages in a ZCTA, indicating that we can confidently reject the null hypothesis of no spatial correlation in the data. For our outcome variables of time to 95% recovery, time to 80% recovery, and time to 50% recovery, we find Global Moran's I values of 0.72 (z-score = 16.46), 0.71 (z-score = 16.18), and 0.63 (z-score = 14.53), respectively, all with a p-value < 2.2E−16. All our outcome variables exhibit strong spatial relationships, which indicates that a spatial autoregression model is necessary.

Analysis 1: the effects of income and race on outages
Our model specification for the proportion of customers affected by outages as a function of income and race does not control Hurricane Isaac's meteorological conditions ( Table 2). The spatial lag effects include direct (within the ZCTA), indirect (effect of neighboring ZCTAs), and total effects of each variable ( Table 2). The spatial autoregressive coefficient ρ has a value of 0.62 with a p-value < 2.22E−16, indicating our model specification is 1 3 correct. The model residuals have a Moran's I index of − 0.049 (p-value of 0.85), which indicates that the SDM model addresses the spatial autocorrelation in the data. We find that both median household income and percent white have significant indirect and total effects, but neither has significant direct effects (Table 2). This suggests that the income and race of neighboring ZCTAs are significantly related to the proportion of customer outages, while the income and race specific to a given ZCTA are not significant. Higher median household incomes are positively associated with proportion of customer outages, while a higher percentage of white population is associated with a lower proportion of customer outages. Table 3 shows the results for our SDM regression specification for the effects of median income and race on the ZCTA proportion of customer outages while controlling for the meteorological characteristics of the storm and local soil conditions. The spatial autoregressive coefficient ρ has a value of 0.35 with a p-value of 2.21E−06, suggesting that the SDM model specification is appropriate. The model residuals have a Moran's I index of − 0.0029 (p-value of 0.49), indicating that the SDM model addresses the spatial autocorrelation in the data. For this model, we see that the effects of race and income are no longer significant, while percent clay, precipitation, and maximum flood gauge ratio have significant total effects. All three significant variables have positive significant effects, indicating that larger values of these hazard-related variables are related to higher rates of power outages. We also see a slight increase in model R 2 (from 0.53 to 0.57) when we include storm and soil conditions. For both models, z-scores can be found in Supplementary Materials.

Analysis 2: determinants of recovery time
Results of models to test the effects of median income and race on recovery time, controlling for the total number of customer outages, are presented in Table 4. Again, for each independent variable, we present the direct, indirect, and total effects. Median income is not significant for any of the recovery thresholds. The percent of the community that is white has a significant and negative total effect for the 95% and 80% recovery models, suggesting that communities with greater minorities experience longer recovery times. The models are consistent and indicate that the maximum number of customer outages has a significant and overall positive effect on the restoration time. We extended our model specifications to control for storm weather conditions (Table 5). In earlier models, the maximum number of customer outages consistently had a positive and statistically significant effect on the restoration time. Here, this relationship is weaker in models that control for soil and storm conditions. The maximum customer outages has a positive and significant total and indirect effect on restoration time for 95% restored and only a significant indirect effect on 50% restored. In terms of hurricane-related variables, the only consistently significant variables are gust duration and percent clay, and gust duration is positively related to 95% and 80% recovery thresholds, while percent clay is negatively related. For the model of 95% recovery, the direct and indirect effects of the maximum flood gauge ratio are also significant, but in opposite directions such that the total effect is not significant. Precipitation has a significant direct and positive effect for time to 80% recovery. When considering our socioeconomic variables, we see that race is no longer significant for predicting recovery times. However, the ZCTA median income is consistently significant and negative in terms of both indirect and total effects. This suggests that ZCTAs with wealthier neighbors experience faster recoveries. For the 50% and 80% recovery models, we see that income is the most significant predictor (lowest p-value). Time to 50% recovery also exhibits a significant direct effect of income.

3
Finally, Table 6 shows the results for our model specification that controls for the presence of high-priority infrastructure such as hospitals (health services) and police stations (emergency services). The total number of customer outages is now significant and positively related to recovery time for all levels of recovery models. In the 95% recovery model, gust duration and maximum flood gauge ratio both have significant direct effects, though only the gust duration has a significant total effect (direct and indirect). Precipitation also has a significant and positive total effect on time to 95% recovery, while percent clay has a negative and significant indirect and total effect. Percent clay remains significant and negatively related in the 80% recovery model. Percent clay has a slightly significant (p < 0.1) direct effect but insignificant total effect for the 50% recovery model. No other hazard or local variables are significant in the 50% recovery model. In terms of socioeconomic variables, income remains significant and negative for all models. When considering the addition of essential services, we see that the number of emergency services (police stations) has a significant and positive direct effect on predicting time to 95% recovery, though the total effect is not significant. The number of health services (hospitals) has a significant indirect and total effect (both negative) on time to 80% recovery. This model also has the highest R 2 across all recovery stages. Again, for all models analyzing time to recovery, z-scores can be found in Supplementary Materials.

Determinants of outages
In this work, we employ a spatial regression analysis to assess the interactions between socioeconomic indicators including wealth and racial composition, storm severity indicators, and the presence of critical services such as emergency and health services on the overall proportion of customers in a ZCTA experiencing outages and time to three thresholds of power recovery (50%, 80%, and 95%). In Fig. 3, we summarize our findings of the total (indirect plus direct) effects of these variables on each outcome (originally presented in Tables 3, 6).
Our first analysis finds that the impact of Hurricane Isaac, measured as the proportion of customers experiencing outages within a given ZCTA, is closely related to the severity of the hazard. We find, reasonably, that the hazard severity in a ZCTA, measured by five-day precipitation and flooding, has a significant and positive effect on the proportion of customers without power, meaning that the proportion of outages will increase as the severity of the hazard increases (Table 3). However, socioeconomic vulnerability, as measured by the ZCTA median income and percent of the population that is white, only has a significant effect on the proportion of customers without power when not controlling for storm and local soil conditions ( Table 2). As median income increases, the proportion of customers without power also increases. This suggests that, for this analysis and particular storm event, socioeconomically disadvantaged populations did not experience more severe impacts. As the percent of the population that is white increases, the proportion of customers experiencing outages decreases, indicating that primarily white communities experience fewer storm effects. The fact that these socioeconomic and racial relationships go away when controlling for storm severity suggests that, in general, differences in customer outages are primarily explained by exposure to the hazard. The literature suggests that one reason why socioeconomically disadvantaged populations can experience more Table 6 SDM results of determinants of median income and race as determinants of recovery time with storm/soil characteristics and high-priority infrastructure analysis for times to 95%, 80%, and 50% recovery Standard errors in parentheses ***p < 0.001, **p < 0.01, *p < 0.05, p harm during disasters is because of increased exposure (Tierney 2014;Fielding 2018). Our work suggests that this may be the case with Hurricane Isaac, where minority populations were in higher areas of exposure. The relationship between our variables of interest and time to recovery was the focus of our second analysis in which time to recovery was modeled as the time for a ZCTA to reach 50%, 80%, and 95% power restoration. We found the maximum number of ZCTA outages had a significant and positive relationship with the time it takes for a ZCTA to reach 50%, 80%, and 95% restoration, meaning that impact and recovery are closely related when considering total recovery and that higher outages result in higher restoration times. However, the maximum number of outages has less of an effect on the time that it takes for a ZCTA to reach 80% and 50% restoration (Table 6). However, the total number of outages is only slightly significant (p < 0.1) for the 80% and 50% recovery thresholds. One possible explanation is that, in the early stages of recovery, prioritization of is based on a range of factors other than the maximum number of outages, and then later in the restoration process the number of outages left to restore plays a larger role. Importantly, these results signal that restoration is not simply based on the number of outages.

Hazard characteristics and recovery time
We introduce the effects of storm severity using a range of storm-related variables. We find that wind duration has a positive effect on recovery time for 80% and 95% recovery levels (Table 5). Wind duration measures the length of time until sustained wind speeds drop below 30 miles per hour, which is the federally mandated wind speed above which power restoration crews are not allowed to use elevated trucks for power line repair. However, none of the storm-related variables were consistently significant in predicting recovery times across time to recovery models.
In our customer outage models, 5-day precipitation and maximum flood-gauge ratio were significant and positive predictors of the proportion of customers experiencing outages (Table 3). Maximum wind gust velocity was not significant for any level of recovery time, including when controlling for priority service locations (Tables 5, 6). For the model of 95% recovery, the direct effects of maximum flood-gauge ratio are also significant, but the total effect is not significant (Tables 5, 6). Interestingly, when health and emergency services data are added to the analysis, only the model predicting time to 95% recovery has any significant hazard-related variables. As mentioned, maximum flood-gauge ratio has positive direct effects in this model, but not a significant total effect (Table 6). Precipitation has a positive and significant indirect and total effect. This suggests that early prioritization of power restoration is not driven by hazard outcomes or even the severity of the outages.
Soil type and soil characteristics have been demonstrated to be useful predictors of hurricane-related power outages, as they offer information about soil stability . Our analysis confirms the importance of soil type with our inclusion of percent clay, though results are mixed. In predicting the proportion of outages, we find that percent clay has a significant and positive relationship with outages (Table 3). However, in our models of recovery times, the percent clay is negatively related to 80% and 95% recovery times (Table 6). More work is needed to understand the specific role of soil type in this setting and what it means for both outages and recovery. It is possible that soil composition could be a proxy for other important local characteristics such as proximity to the coast and elevation.

Socioeconomic inequalities and recovery
We also investigated the effects of socioeconomic inequalities on power restoration times, focusing on the median household income and percent white population (as a proxy for racial composition). This model does not control for any hazard or priority variables, and income is not significant in predicting any of the recovery times (Table 4). In this model, however, our variable for racial composition total effect is significant and negative at the 95% and 80% recovery levels; this indicates that ZCTAs with higher proportions of white population experience shorter recovery times (or conversely, that communities with higher rates of minorities experience longer recovery times). When we introduce storm severity variables into our model, we see that ZCTA median income is consistently significant and negative in terms of both indirect and total effects (Table 5). Our 50% recovery model also exhibits a significant direct effect of income. Even when priority service variables are incorporated, all of our recovery time models retain a significant total effect of median income. This indicates that wealthier ZCTAs experience shorter recovery times across all stages of recovery (Table 6). This finding is important and striking, as it suggests that prioritization of recovery efforts is more related to community socioeconomic status than to the scale of outages, the severity of storm, or the presence of priority services.

Prioritization characteristics and recovery
The literature suggests that emergency and health services infrastructure are targets for early recovery efforts. Our model results show that the number of emergency services has a significant and positive direct effect on predicting time to 95% recovery, though the total effect is not significant. Somewhat counterintuitively, this suggests that the presence of more emergency service locations corresponds to longer times to 95% recovery. One possible explanation is that emergency services are often presumed to have backup generator access. Future research is required to understand what may be underlying these findings, but at the very least, our results suggest that emergency services were not prioritized in power recovery after Hurricane Isaac. Conversely, the number of health services (hospitals) has a significant indirect and total effect (both negative) on time to 80% recovery, suggesting that the presence of hospitals decreases recovery times to 80%. This could indicate that health services may be prioritized at later stages of recovery. However, these results may be specific to Hurricane Isaac which was a relatively weak storm. Other storms in other locations may exhibit different responses.

Conclusions
In this study, we use spatial regression to investigate determinants of both the scale of power outages and speed of recovery in Louisiana after Hurricane Isaac. To do so, we use power outage data scraped from the utility website in 15-min intervals. These data provide accurate and high-resolution information about both the hurricane's impacts on the power system in Louisiana and the outage recovery process across multiple stages. Studying both the magnitude of outages and the recovery process allows us to glean unique insights into Hurricane Isaac's impacts on the area. Our results suggest that the degree of power outages, as measured by the proportion of customers reporting outages in each ZCTA, is largely explained by the hurricane's meteorological conditions such as five-day precipitation and flood gauge levels. When controlling for these storm characteristics, we do not see a significant effect of the socioeconomic variables. However, when we consider times to recovery, we see that median income is a highly significant variable, even when controlling for storm variables and priority services. As expressed previously, the connections between social vulnerability, exposure, and risks associated with natural disasters are complex, but these results raise concerns for equity in the post-disaster response and suggest that wealthier ZCTAs, and those also surrounded by wealthy neighboring ZCTAs, experienced significantly shorter recovery times. These findings should be considered by the local utility to ensure that wealthier areas are not prioritized in power recovery at the expense of lower income and more vulnerable communities.
A key insight from this paper is that judging recovery outcomes by looking at a single threshold, such as 95% recovered, is insufficient. Recovery is a process, not an endpoint, and researchers and policymakers must consider the path that communities take to reach full recovery. Even if two communities reach a recovery endpoint at the same time, one cannot assume that the paths they took to arrive at this point in the recovery process were the same. The industry standard threshold for power restoration is 95% restored, but if this analysis had been limited to that threshold, some of the nuances in the discussion above would have been lost. Therefore, comparing results across different levels of recovery is a methodological contribution of this work. For example, we see that income was an especially important indicator at the 50% recovery threshold, suggesting that wealthier communities were more likely to be prioritized at the early stages of recovery as well as later stages.
One of the limitations of this study is that it did not control for infrastructure characteristics such as the percentage of power lines in each ZCTA that are undergrounded. This could have a significant effect on both the rate of outages and recovery time, but these data are not available. Greater transparency on the part of utilities regarding this information would improve the quality of the research that is possible on this important subject. Similarly, data related to the age of the grid components could improve the models. It is also important to note that, in part due to data limitations, this work only investigated one storm event. Further research is needed to identify whether these findings are unique to power restoration following Hurricane Isaac, a problem that is specific to the state of Louisiana and Entergy, or a more widespread phenomenon. However, it is difficult to apply these models to other hurricanes due to challenges in acquiring detailed, publicly available outage data from electric utilities. Researchers are often required to scrape the data themselves, and utilities will sometimes change the format in which the data are presented midrestoration. This poses a real challenge for the scraping algorithms, which are programmed to be able to navigate a set layout. These data are crucial to further define these recovery disparities, both the extent to which they exist and what motivates the decision-making that prioritizes some communities over others, so that processes can be improved and made more equitable in the future.