Accumulated Cyclone Energy (ACE)

Tim Trice

June 27, 2017

library(dplyr)
library(ggplot2)
# library(HURDAT)
library(lubridate)
library(readr)
library(rrricanes)
#library(rrricanesdata)

ACE or Accumulated Cyclone Energy is a method of measuring energy of a cyclone or for an entire season. It is calculated by the formula

\[ \text{ACE} = 10^{-4}\sum{v^2_\text{max}} \]

where \(v_\text{max}\) is the wind speed in knots. Values may only be used when a storm is a tropical system with winds of at least 35 knots. Additionally, only six-hour intervals are used.

To calculate ACE you would want to use the fstadv dataset and apply the following rules:

• since forecast/advisory products are typically issued at 03:00, 09:00, 15:00 and 21:00 UTC filter out odd hours
• Status is Tropical Storm or Hurricane.
• Wind is not NA
• group by Key
• select Wind

fstadv <- fstadv %>% 
    filter(hour(Date) %in% c(3, 9, 15, 21), 
           Status %in% c("Tropical Storm", "Hurricane"), 
           !is.na(Wind)) %>% 
    group_by(Key) %>% 
    select(Name, Wind)

Now let’s summarise our dataset with new variable ACE.

fstadv %>% 
    summarise(Name = last(Name), 
              ACE = sum(Wind^2) * 1e-04) %>% 
    arrange(desc(ACE)) %>% 
    top_n(10)

This matches somewhat well with Wikipedia and other sources. But, you may notice we’re missing some storms. rrricanes currently only holds data back to 1998; this data is considered “real-time”.

A companion package, HURDAT is available in CRAN that has data for all cyclones dating back as far as 1851. This package has less data than rrricanes. But, as it is based on a post-storm reanalysis project, the data is more accurate.

Let’s revisit the top 10 using HURDAT: Note:HURDAT is currently archived on CRAN.

AL %>% 
    filter(hour(DateTime) %in% c(0, 6, 12, 18), 
           Status %in% c("TS", "HU"), 
           !is.na(Wind)) %>% 
    group_by(Key) %>% 
    summarise(Name = last(Name), 
              ACE = sum(Wind^2) * 1e-04) %>% 
    arrange(desc(ACE)) %>% 
    top_n(10)

A couple of things to notice here:

1. in HURDAT, the common times used are 00:00, 06:00, 12:00 and 18:00 UTC
2. Our list is more comprehensive than the Wikipedia list as that list only measures storms after 1950.

ACE is slightly higher and that could be for a number of reasons. For example, on re-analysis the Hurricane Research Division may have determined a cyclone was actually tropical (shown in HURDAT) when initially it was believed to be extratropical (as shown in rrricanes). Or, and more likely, they determined through additional data that a storm was actually stronger than originally though.

You can also calculate ACE for a season. Instead of grouping by Key we group by Year. I’ll stick with HURDAT in this example.

(df <- AL %>% 
    mutate(Year = year(DateTime)) %>% 
    filter(hour(DateTime) %in% c(0, 6, 12, 18), 
           Status %in% c("TS", "HU"), 
           !is.na(Wind)) %>% 
    group_by(Year) %>% 
    summarise(ACE = sum(Wind^2) * 1e-04) %>% 
    arrange(desc(ACE))) %>% 
    top_n(10)

This also matches relatively well with that on Wikipedia and other sources.

ggplot(df, aes(x = Year, y = ACE)) + 
    geom_bar(stat = "identity") + 
    theme_bw()

It would certainly seem that tropical cyclone activity ebbs and flows over time.