| title | author | date | output | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
Analysis of Which American Weather Events Cause the Most Damages to Human Life and Private Property, 1950 - 2011 |
Bryan Murphy |
2023-04-04 |
|
library(tidyverse)
library(R.utils)
library(lubridate)
library(forcats)
library(stringdist)# This is our initial setup block, named setup, with include = TRUE so it will show up.
# First we'll set any global variables we care about...
options(scipen=999) # This stops knitr from displaying 5 digit numbers as Scientific Notation.
options(cache = TRUE)
# And then we'll use a seperate code chunk to load our data.#Here we download our dataset, if it's not already downloaded, and read it as a tibble into RStudio.
fileUrl <- "https://d396qusza40orc.cloudfront.net/repdata%2Fdata%2FStormData.csv.bz2" # Set the DL link url.
if(!file.exists("./Proj2data/Stormdata.csv.bs2")) {download.file(fileUrl,destfile="./Proj2data/StormData.csv.bz2",method="curl")} # Actually download the file.
gunzip(filename = "./Proj2data/StormData.csv.bz2", destname = "./Proj2data/StormData.csv",
skip = TRUE, ext = "bz2")## [1] "./Proj2data/StormData.csv"
## attr(,"temporary")
## [1] FALSE
stormdata <- as_tibble(read.csv(file = "./Proj2data/StormData.csv", stringsAsFactors = FALSE, strip.white = TRUE))Adverse weather events are a significant cause of damage to human health as well as private and public property in the United States. This report analyzes the effects of weather events on the United States, with a focus on the health and economic consequences of adverse weather. The data used in this analysis is derived from the U.S. National Oceanic and Atmospheric Administration’s (NOAA) storm database from the years 1950 to 2011.
This report concludes that adverse weather events have significant health and economic consequences in the United States, but that the weather patterns which cause the most damage to human life are not the same as those which cause the most damage to property. In particular, Tornadoes, Heat and Lightning cause the most human injuries and fatalities, while in general, water-related weather events, particularly Floods and Hurricanes/Typhoons, cause by far the most economic damage to the United States. Tornadoes, however,despite not being dependent on water, tend to cause a great deal of damage to both private property as well as human lives.
This report concludes by noting that further study is necessary, and that it would be particularly worthwhile expanding the analysis to the present day. For example, it is highly probable heat-related weather events have been more consequential in the last decade, with wildfires becoming more common as global climate change leads to drier weather in some U.S. states, particularly California.
After loading our data, we look at some general descriptive statistics of the data set. We see it has
stormdata$BGN_DATE <- mdy_hms(stormdata$BGN_DATE)
stormdata$BGN_DATE <- as.Date(stormdata$BGN_DATE)
range(stormdata$BGN_DATE)## [1] "1950-01-03" "2011-11-30"
Out of curiosity, we decide to look up the most fatal weather incident in this dataset. A quick subsetting of the dataset by the row which has the maximum number of fatalities tells us that the event with the most fatalities recorded in this dataset is the 1995 Chicago heatwave, with
maxfatal <- stormdata[stormdata$FATALITIES == max(stormdata$FATALITIES), ]
glimpse(maxfatal[c(2,7,8,23)])## Rows: 1
## Columns: 4
## $ BGN_DATE <date> 1995-07-12
## $ STATE <chr> "IL"
## $ EVTYPE <chr> "HEAT"
## $ FATALITIES <dbl> 583
However, a quick look at the Hurricane Katarina data shows us that the incident is set to
stormdata[stormdata$REFNUM == 577615,23]## # A tibble: 1 × 1
## FATALITIES
## <dbl>
## 1 0
Katrina <- stormdata[stormdata$REFNUM == 577615,]
Katrina$REMARKS## [1] "Hurricane Katrina was one of the strongest and most destructive hurricanes on record to impact the coast of the United States. It will likely be recorded as one the worst natural disaster in the history of the United States to date resulting in catastrophic damage and numerous casualties in southeast Louisiana and along the Mississippi coast. Damage and casualties resulting from Hurricane Katrina extended as far east as Alabama and the panhandle of Florida. Katrina developed from a tropical depression southeast of the Bahamas on August 24th. After moving through the Bahamas as a tropical storm, Katrina strengthened to a category 1 hurricane prior to landfall in south Florida around the Miami area on the 25th of August. Katrina crossed south Florida and entered the Gulf of Mexico and began to strengthen. Hurricane Katrina strengthened to a category 5 storm on August 28th about 250 miles south southeast of the mouth of the Mississippi River with winds reaching their peak intensity of 175 mph and a central pressure of 902 mb. Post event analysis by the National Hurricane Center indicates that Katrina weakened slightly before making landfall as a strong category 3 storm in initial landfall in lower Plaquemines Parish. Maximum sustained winds were estimated at 110 knots or 127 mph and a central pressure of 920 mb around 610 AM CDT on August 29th in southeast Louisiana just south of Buras in Plaquemines Parish. The storm continued on a north northeast track with the center passing about 40 miles southeast of New Orleans with a second landfall occurring near the Louisiana and Mississippi border around 945 AM CDT as a Category 3 hurricane on the Saffir Simpson scale with maximum sustained winds estimated around 105 knots or 121 mph. Katrina continued to weaken as it moved north northeast across Mississippi during the day, but remained at hurricane strength 100 miles inland near Laurel, Mississippi. Katrina weakened to a tropical depression near Clarksville, Tennessee on August 30th.\r\n\r\nDamage in southeast Louisiana, especially in the New Orleans area and the coastal parishes, was catastrophic. Hurricane protection levees and floodwalls were overtopped and/or breached resulting in widespread and deep flooding of homes and businesses. Much of Orleans and Plaquemines Parishes and nearly all of St. Bernard Parish were flooded by storm surge. Approximately 80 percent of the city of New Orleans was flooded. Thousands of people were stranded by the flood waters in homes and buildings and on rooftops for several days and had to be rescued by boat and helicopter. In Jefferson Parish, levees were not compromised, however many homes were flooded by either heavy rain overwhelming limited pumping capacity or storm surge water moving through in-operable pumps into the parish. Severe storm surge damage also occurred along the north shore of Lake Pontchartrain from Mandeville to Slidell with storm surge water moving inland as far as Old Towne Slidell with water up to 6 feet deep in some locations. Hurricane force winds also caused damage to roofs, power lines, and downed trees. Windows were broken in large buildings in the metro New Orleans area from wind and wind driven debris. In areas away from storm surge flooding, wind damage was widespread with fallen trees taking a heavy toll on houses and power lines, especially over St. Tammany and Washington Parishes. Excluding losses covered by the Federal Flood Insurance Program, insured property losses in Louisiana were estimated at 22.6 billion dollars. Overall uninsured and insured losses combined were estimated to exceed 100 billion dollars along the entire Gulf Coast.\r\n\r\nFatalities occurring in Louisiana as a result of Hurricane Katrina numbered approximately 1097 people as of late June 2006. The majority of the victims were in the New Orleans area. 480 other Louisiana residents died in other states after evacuating..\r\n Detailed information on the deaths, locations, and indirect or direct fatalities will be described in updates to Storm Data. \r\n\r\nDue to the failure of power and equipment prior to the peak of the storm, data for wind, storm surge, pressure, and rainfall are incomplete. A university portable weather unit measured the lowest pressure of 920.2 mb near Buras around 0616 AM AM CDT on Aug 29th. with 934 mb being measured at the National Weather Service Office in Slidell at 938 AM CDT. \r\n\r\nThe highest wind gust recorded in Louisiana and the adjacent coastal waters was 99 knots (114 mph) at the Grand Isle CMAN station (338 AM CDT on August 29th) before the gage failed, though higher wind gusts certainly occurred. While most of the metro New Orleans escaped the extreme winds, the extreme eastern portions of the metro area from St Bernard Parish into extreme east New Orleans experienced the western portion of the hurricane eyewall. Wind gusts between 120 to 125 mph were recorded at a couple of locations in East New Orleans. Wind gust to hurricane force (64 kt or 74 mph) were also recorded at New Orleans Louis Armstrong Intl Airport by an FAA wind instrument. In eastern St. Tammany Parish, wind gusts to 87 knots (100) mph were measured at Slidell by a wind tower deployed by a university. An estimated wind gust of 105 kt (120 mph) was taken at a hospital in Slidell. \r\n\r\nPost storm high water surveys of the area conducted by FEMA indicated the following storm surge estimates: Orleans Parish - 12-15 feet in east New Orleans to 9 to 12 feet along the Lakefront; St. Bernard Parish - 14 to 17 feet; Jefferson Parish - 6 to 9 feet along the lakefront to 5 to 8 feet from Lafitte to Grand Isle; Plaquemines Parish - 15 to 17 feet; St. Tammany Parish - 11 to 16 feet in southeast portion to 7 to 10 feet in western portion. All storm surge heights are still water elevations referenced to NAVD88 datum. \r\n\r\nStorm total rainfall amounts generally ranged from 7 to 14 inches with lower amounts observed farther west toward the Atchafalaya River. A rainfall total of 11.63 inches was measured at the National Weather Service Office in Slidell."
This is a baffling omission, so we'll fix that.
There might be other errors in the dataset, but it seemed very relevant to this analysis to ensure that the single most fatal weather event in the time period that dataset comprises was recorded accurately.
stormdata[stormdata$REFNUM == 577615,23] <- 1097
max(stormdata$FATALITIES)## [1] 1097
That accomplished, we can now begin to look at the dataset to answer the following two questions:
**1: Across the United States, which types of events kill and injure the most people??**
**2: Across the United States, which types of events have the greatest economic consequences?**
In order to look at these questions in more detail, and to avoid the unwieldyness of dealing with an enormous dataset, we are going to subset our initial data, named stormdata, into two smaller datasets, human_events, comprising only those weather-related incidents which resulted in at least
human_events <- filter(stormdata, FATALITIES > 0 | INJURIES > 0)
property_events <- filter(stormdata, PROPDMG > 0 | CROPDMG > 0)
crops <- filter(property_events, CROPDMG > 0)
range(crops$BGN_DATE)## [1] "1993-01-04" "2011-11-28"
We'll start by focusing on weather events in the United States from 1950 until 2011 that had a direct impact on human health - in other words, the data contained within our subset human_events.
Before we go any further, we are going to want to try to group human_events by the column EVTYPE, so we can try and look at the cumulative effect on human health for specific types of weather incidents.
human_events %>% group_by(EVTYPE) %>%
summarise(FATALITIES = sum(FATALITIES), INJURIES = sum(INJURIES))%>%
arrange(desc(FATALITIES + INJURIES)) -> summed_human_eventsHowever, when we do this, we notice our dataset covers $220$ different supposed event types. This is a lot less than the apparently $985$ different type of weather events in the original data set, but according to the NOAA itself, the Storm Events Database should only include
length(unique(summed_human_events$EVTYPE))## [1] 220
length(unique(stormdata$EVTYPE))## [1] 985
head(unique(stormdata$EVTYPE),40)## [1] "TORNADO" "TSTM WIND"
## [3] "HAIL" "FREEZING RAIN"
## [5] "SNOW" "ICE STORM/FLASH FLOOD"
## [7] "SNOW/ICE" "WINTER STORM"
## [9] "HURRICANE OPAL/HIGH WINDS" "THUNDERSTORM WINDS"
## [11] "RECORD COLD" "HURRICANE ERIN"
## [13] "HURRICANE OPAL" "HEAVY RAIN"
## [15] "LIGHTNING" "THUNDERSTORM WIND"
## [17] "DENSE FOG" "RIP CURRENT"
## [19] "THUNDERSTORM WINS" "FLASH FLOOD"
## [21] "FLASH FLOODING" "HIGH WINDS"
## [23] "FUNNEL CLOUD" "TORNADO F0"
## [25] "THUNDERSTORM WINDS LIGHTNING" "THUNDERSTORM WINDS/HAIL"
## [27] "HEAT" "WIND"
## [29] "LIGHTING" "HEAVY RAINS"
## [31] "LIGHTNING AND HEAVY RAIN" "FUNNEL"
## [33] "WALL CLOUD" "FLOODING"
## [35] "THUNDERSTORM WINDS HAIL" "FLOOD"
## [37] "COLD" "HEAVY RAIN/LIGHTNING"
## [39] "FLASH FLOODING/THUNDERSTORM WI" "WALL CLOUD/FUNNEL CLOUD"
For example, in only the
Before we start, we're also going to correct two particularly problematically misentered event type observations - one event type was listed as "cold" when the official weather formatting should be "Extreme Cold/Wind Chill", which will cause that observation to be mismatched as "flood" simply because flood has the letters O,L and D and is a short word, and one observation is listed as the unnecessarily loquacious "unseasonably warm and dry," which we'll amend to the official event type, "Heat".
Having corrected these outliers, we'll create a vector, dictionary, of the NOAA's
summed_human_events[47,1] <- "extreme cold"
summed_human_events[67,1] <- "heat"
dictionary <- c("Astronomical Low Tide","Avalanche","Blizzard","Coastal Flood","Cold/Wind Chill","Debris Flow","Dense Fog","Dense Smoke","Drought","Dust Devil","Dust Storm","Excessive Heat","Extreme Cold/Wind Chill","Flash Flood","Flood","Freezing Fog","Frost/Freeze","Funnel Cloud","Hail","Heat","Heavy Rain","Heavy Snow","High Surf","High Wind","Hurricane","Typhoon","Ice Storm","Lakeshore Flood","Lake-Effect Snow","Lightning","Marine Hail","Marine High Wind","Marine Strong Wind","Marine Thunderstorm Wind","Rip Current","Sleet","Storm Tide","Strong Wind","Thunderstorm Wind","Tornado","Tropical Depression","Tropical Storm","Tsunami","Volcanic Ash","Waterspout","Wildfire","Winter Storm","Winter Weather")
dictionary <- tolower(dictionary)
summed_human_events$EVTYPE <- tolower(summed_human_events$EVTYPE)
summed_human_events$EVTYPE_MATCHED <- dictionary[amatch(summed_human_events$EVTYPE,dictionary,method="lcs", maxDist=40)]
length(unique(summed_human_events$EVTYPE_MATCHED))## [1] 41
You can see we're now down to just
summed_human_events$EVTYPE <- NULL
head(summed_human_events,10) -> human10
human10## # A tibble: 10 × 3
## FATALITIES INJURIES EVTYPE_MATCHED
## <dbl> <dbl> <chr>
## 1 5633 91346 tornado
## 2 1903 6525 excessive heat
## 3 504 6957 strong wind
## 4 470 6789 flood
## 5 816 5230 lightning
## 6 937 2100 heat
## 7 978 1777 flash flood
## 8 1161 1275 hurricane
## 9 89 1975 ice storm
## 10 133 1488 thunderstorm wind
Before we do anything else, we're going to recapitalize our event types, as we put them all into lower case for the sake of making our approximate matching work better.
capwords <- function(s, strict = FALSE) {
cap <- function(s) paste(toupper(substring(s, 1, 1)),
{s <- substring(s, 2); if(strict) tolower(s) else s},
sep = "", collapse = " " )
sapply(strsplit(s, split = " "), cap, USE.NAMES = !is.null(names(s)))
}
summed_human_events$EVTYPE_MATCHED <- capwords(summed_human_events$EVTYPE_MATCHED)
head(summed_human_events,10) -> human10Now we can try actually plotting the
ggplot(data = human10) +
geom_col(mapping = aes(x = fct_reorder(EVTYPE_MATCHED, FATALITIES + INJURIES, .desc = TRUE), y = FATALITIES, fill = "Fatalities")) +
geom_col(mapping = aes(x = fct_reorder(EVTYPE_MATCHED, FATALITIES + INJURIES, .desc = TRUE), y = INJURIES, fill = "Injuries", alpha = 0.5), show.legend = FALSE) +
scale_fill_manual(values = c("Fatalities" = "red", "Injuries" = "yellow")) +
theme(plot.title = element_text(hjust = 0.5), plot.caption = element_text(hjust = 0.5))+
theme(axis.text.x = element_text(angle = 45, size = 6, margin = margin(10)))+
labs(x = "Event Type", y = "Weighted Human Suffering Index", title = "10 U.S. Weather Events Which Most Affect \nHuman Health", fill = "Human Health \nImpact Type")
We see that the event which causes the most injuries by far is Tornado (the original event type which the NOAA began tracking in 1950). Next is Excessive Heat, a perennially overlooked source of human misery, suffering and death, followed by Strong Wind, Flood, and Lightning. Of particular interest are the next three event types, Heat, Flash Flood and Hurricane, because we notice their bars are almost entirely orange; this is because the graph was "stacked" by placing the Injuries bar on top of the Fatalities bar (which was invariably smaller for all event types in the top
It hardly seems fair to weight Fatalities and Injuries equally, so we can create what we might call a "Weighted Index of Human Suffering" by assigning injuries a weight of
Now, if we plot our data again, we see the following:
human10_adj <- human10
human10_adj$FATALITIES <- human10$FATALITIES*10
human10_long_adj <- human10_adj %>%
pivot_longer (cols = c(INJURIES, FATALITIES), names_to = "type", values_to = "value")
ggplot(data = human10_long_adj) +
geom_col (mapping = aes (x = fct_reorder(EVTYPE_MATCHED, value, .desc = TRUE), y = value, fill = type)) +
theme(plot.title = element_text (hjust = 0.5), plot.caption = element_text (hjust = 0.5))+
theme(axis.text.x = element_text(angle = 45, size = 6, margin = margin(10))) +
labs(x = "Event Type", y = "Weighted Index of \nHuman Suffering", title = "10 U.S. Weather Events Which Most Affect \nHuman Health, Weighted", fill = "Human Health \nImpact Type") +
theme(axis.text.y = element_blank())
Now we see that while Tornado still leads the pack (being a storm type that tends to cause a fair number of fatalities, even though it causes far more injuries), we see that Hurricane jumps from
In conclusion, we can see that in the United States from 1950 to 2011, the weather events which most impacted human health were Tornadoes, Heat waves, Lightning storms (probably correlated somewhat with tornadoes), and then Hurricanes, Strong Winds and Flash Floods. Ice Storms, as annoying as they might be to drivers in northern states, tend not to cause many fatalities, as well as comparatively few injuries compared to the higher ranked event types.
One final thing to note is that splitting up Excessive Heat from Heat seems to end up undercounting the effects of both events, but the NOAA itself explicitly draws this distinction, so we maintained it in our analysis.
From here, we can go on to analyze weather events with economic consequences, defined as those weather events in the NOAA Storm Data set which contained an explicitly recorded value for either the variable PROPDMG or CROPDMG. PROPDMG is typically defined as damage inflicted to private property as well as public infrastructure and facilities; beginning in 1993, the NOAA began including estimates of damage to crops as well, hence the inclusion of the variable CROPDMG.
A quick calculation shows us that there are actually
stormdata %>%
filter(CROPDMG > 0 & PROPDMG == 0) -> cropsonly
nrow(cropsonly)## [1] 5857
range(cropsonly$BGN_DATE)## [1] "1993-01-19" "2011-11-27"
One quirk of the NOAA dataset we have is that the values for property and crop damage are recorded as relatively short numbers, with the unit of measurement of that number recorded in a seperate column called PROPDMGEXP and CROPDMGEXP. Thus, an event that causes
Before proceeding further in our analysis, it would help to create variables called PROPDMG_TOTAL and CROPDMG_TOTAL by actually multiplying those PROPDMG values by the appropriate number (
We have accomplished this neatly and quickly using case_when() from the dplyr package, as seen below.
property_events$PROPDMG_TOTAL <- case_when (
property_events$PROPDMGEXP == "K" ~ property_events$PROPDMG * 10^3,
property_events$PROPDMGEXP == "M" ~ property_events$PROPDMG * 10^6,
property_events$PROPDMGEXP == "B" ~ property_events$PROPDMG * 10^9,
TRUE ~ 0
)
property_events$CROPDMG_TOTAL <- case_when (
property_events$CROPDMGEXP == "K" ~ property_events$CROPDMG * 10^3,
property_events$CROPDMGEXP == "M" ~ property_events$CROPDMG * 10^6,
property_events$CROPDMGEXP == "B" ~ property_events$CROPDMG * 10^9,
TRUE ~ 0
)
property_events$TOTALDMG <- (property_events$PROPDMG_TOTAL + property_events$CROPDMG_TOTAL)This accomplished, we now group by EVTYPE again so we can see the cumulative economic consequences of particular weather events.
property_events %>% group_by(EVTYPE) %>%
summarise(TotalDamage = sum(TOTALDMG)) %>%
arrange(desc(TotalDamage)) -> summed_property_events
length(unique(summed_property_events$EVTYPE))## [1] 431
Unfortunately, we see we have
We will also re-capitalize our Event Type names again, and delete the now unnecessary EVTYPE column.
dictionary <- c("Astronomical Low Tide","Avalanche","Blizzard","Coastal Flood","Cold/Wind Chill","Debris Flow","Dense Fog","Dense Smoke","Drought","Dust Devil","Dust Storm","Excessive Heat","Extreme Cold/Wind Chill","Flash Flood","Flood","Freezing Fog","Frost/Freeze","Funnel Cloud","Hail","Heat","Heavy Rain","Heavy Snow","High Surf","High Wind","Hurricane","Typhoon","Hurricane/Typhoon","Ice Storm","Lakeshore Flood","Lake-Effect Snow","Lightning","Marine Hail","Marine High Wind","Marine Strong Wind","Marine Thunderstorm Wind","Rip Current","Sleet","Storm Tide","Strong Wind","Thunderstorm Wind","Tornado","Tropical Depression","Tropical Storm","Tsunami","Volcanic Ash","Waterspout","Wildfire","Winter Storm","Winter Weather")
dictionary <- tolower(dictionary)
summed_property_events$EVTYPE <- tolower(summed_property_events$EVTYPE)
summed_property_events$EVTYPE_MATCHED <- dictionary[amatch(summed_property_events$EVTYPE,dictionary,method="lcs", maxDist=60)]
summed_property_events$EVTYPE_MATCHED <- case_when(
summed_property_events$EVTYPE_MATCHED == "hurricane" ~ "Hurricane/Typhoon",
summed_property_events$EVTYPE_MATCHED == "hurricane/typhoon" ~ "Hurricane/Typhoon",
summed_property_events$EVTYPE_MATCHED == "typhoon" ~ "Hurricane/Typhoon",
TRUE ~ summed_property_events$EVTYPE_MATCHED
)
summed_property_events$EVTYPE_MATCHED <- capwords(summed_property_events$EVTYPE_MATCHED)
summed_property_events$EVTYPE <- NULL
head(summed_property_events, 10)## # A tibble: 10 × 2
## TotalDamage EVTYPE_MATCHED
## <dbl> <chr>
## 1 150319678250 Flood
## 2 71913712800 Hurricane/Typhoon
## 3 57340613590 Tornado
## 4 43323541000 Storm Tide
## 5 18752904170 Hail
## 6 17562128610 Flash Flood
## 7 15018672000 Drought
## 8 14610229010 Hurricane/Typhoon
## 9 10148404500 Flood
## 10 8967041310 Ice Storm
Looking at our
summed_property_events %>% group_by(EVTYPE_MATCHED) %>%
summarise(TotalDamage = sum(TotalDamage)) %>%
arrange(desc(TotalDamage)) -> summed_property_events_refined
head(summed_property_events_refined,10)## # A tibble: 10 × 2
## EVTYPE_MATCHED TotalDamage
## <chr> <dbl>
## 1 Flood 161071361250
## 2 Hurricane/Typhoon 90732527810
## 3 Tornado 57345502190
## 4 Storm Tide 47965589000
## 5 Hail 19145902670
## 6 Flash Flood 18439139760
## 7 Drought 15091766600
## 8 Ice Storm 8968208310
## 9 Wildfire 8895482130
## 10 Thunderstorm Wind 8685898490
Finally, our data looks like it's in a format where we can analyze it using a plot!
neat10 <- summed_property_events_refined[1:10,]
ggplot(data = neat10) +
geom_col(mapping = aes(x = fct_reorder(EVTYPE_MATCHED, TotalDamage, .desc = TRUE), y = TotalDamage/1000000000, fill = TotalDamage)) +
theme(axis.text.x = element_text(angle = 45, size = 8, margin = margin(12))) +
theme(plot.title = element_text(hjust = 0.5), plot.caption = element_text(hjust = 0.5))+
scale_fill_gradient(low = "sienna", high = "red2")+
theme(legend.position = "none")+
labs(title = "The Most Economically Consequential Weather Events,\n Ordered", y = "Cumulative Damage in Billions of Dollars,\n from 1950 to 2011",
x = "Type of Weather Event")
We can see clearly that the weather events that cause the most economic damage in the United States share some similarities with the weather events that cause the most impact on human health, but there is not a
It is important to note, however, that being as this data set ends in 2011, it misses the effect of recent global-warming mediated wildfires that have caused so much havoc in the United States in the last