3.1 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 Plaqumines 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 hours (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 2006 and Hurricane Gustav in 2008. Some of the hardest hit parishes 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). The power restoration process involved over 12,000 utility workers and 4,000 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 United States, 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 4,500 distribution poles, 2,000 distribution transformers, 95 transmission lines, and 144 substations, costing an estimated $500 million in repairs (Miles and Jagielo 2014).
3.2 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 this 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 provides the number of households in a given ZIP code without power in 15-minute intervals. The utility website was scraped for a total of 13,760 minutes beginning on August 27, 2012 at 12:00 pm. This is equal to 229 hours 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 minutes. 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.
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. To control for the speed of recovery, we use variables sorted into three categories: hazard, priority, and socioeconomic (Table 1). Variable selection is reflective of the relevant literature on modelling power outages and restoration (Han et al. 2009; Guikema et al. 2010; Quiring et al. 2011; Mcroberts et al. 2016). Our analysis is conducted in two steps. First, we assess whether median income and racial composition are related to the number of outages experienced in a ZCTA. In the second analysis, we examine the time to recovery by median income, race, and critical infrastructure.
Table 1
Independent variables used in Analysis 1 (effects of income and race on outages) and Analysis 2 (effects of income, race, and priority infrastructure on recovery time) with data sources and descriptive statistics
Variable name
|
Variable source
|
Variable type
|
Analysis
|
Min
|
Mean (SD)
|
Max
|
Median household income (USD)
|
American Community Survey
|
Socioeconomic
|
1,2
|
17,300
|
44,100 (13,270)
|
91,464
|
Percent white population
|
American Community Survey
|
Socioeconomic
|
1,2
|
1.1
|
61.0 (24.9)
|
100
|
Maximum wind velocity (m/s)
|
Stormwindmodel(Anderson et al. 2018)
|
Hazard
|
1,2
|
15.8
|
34.6 (8.8)
|
51.2
|
Gust duration
|
Stormwindmodel
|
Hazard
|
1,2
|
0
|
788.4 (626.0)
|
1,605
|
5-Day Precipitation
|
NASA Giovani([CSL STYLE ERROR: reference with no printed form.])
|
Hazard
|
1,2
|
1.4
|
80.1 (68.7)
|
217.4
|
Flood Gauge Ratio
|
USGS Storm Gauges(USGS 2022)
|
Hazard
|
1,2
|
0.023
|
0.36 (0.24)
|
1.38
|
Percent Clay in Soil
|
USDA SSURGO Soil Data([CSL STYLE ERROR: reference with no printed form.])
|
Hazard
|
1,2
|
10.9
|
28.1 (11.2)
|
59.0
|
Maximum outages
|
Scraped
|
Priority
|
2
|
25
|
2,643 (4,080)
|
21,343
|
Emergency Services
|
USGS(National Geospatial Technical Operations Center 2021)
|
Priority
|
2
|
0
|
3.3 (2.5)
|
13
|
Health Services
|
USGS(National Geospatial Technical Operations Center 2021)
|
Priority
|
2
|
0
|
0.50 (0.88)
|
6
|
3.3 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. 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 to identify spatial autocorrelation. Moran’s I values and significance levels are reported in the Results section.
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
\(Y=\rho WY+ X\beta +WX\theta + \epsilon\) (Eq. 1)
where Y is the outcome variable, X is the set of explanatory or independent variables, W is the set of spatial weights, and \({\epsilon }\) is the error. WY is the set of spatially lagged Y values and \(WX\theta\) is the spatially lagged X. \(\beta\) is the vector of fitted coefficients associated with each independent variable and \(\rho\) is the spatial autoregressive parameter or spatial dependence parameter (Lesage 1999; Chi and Zhu 2008). 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.
3.4 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 the differential effects occur because communities of a given socio-economic status live in areas experiencing more intense weather from the hurricane (i.e., higher exposure).
The data for maximum outages is 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 and businesses within a given ZCTA. 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 greater than 1 (N = 2), and 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 (Model 1), we include median income as an independent variable. Model 2, in addition to median income, also includes 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.
3.5 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, 2014; Tierney 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. As discussed earlier, utilities have formal policies in place for determining high-priority areas for power restoration. Finally, we include the number of emergency service and health service locations to capture the effects of faster restoration due to the presence of high-priority infrastructure. The literature indicates that emergency services like fire stations and hospitals may be prioritized (Table S2).