Accumulated cyclone energy

Accumulated cyclone energy (ACE) is a metric used to compare overall activity of tropical cyclones, utilizing the available records of windspeeds at six-hour intervals to synthesize storm duration and strength into a single index value. The ACE index may refer to a single storm or to groups of storms such as those within a particular month, a full season or combined seasons. It is calculated by summing the square of tropical cyclones' maximum sustained winds, as recorded every six hours, but only for windspeeds of at least tropical storm strength (≥ 34 kn; 63 km/h; 39 mph); the resulting figure is divided by 10,000 to place it on a more manageable scale.

The calculation originated as the Hurricane Destruction Potential (HDP) index, which sums the squares of tropical cyclones' maximum sustained winds while at hurricane strength, at least 64 knots (≥ 119 km/h; 74 mph) at six-hour recorded intervals across an entire season. The HDP index was later modified to further include tropical storms, that is, all wind speeds of at least 34 knots (≥ 63 km/h; 39 mph), to become the accumulated cyclone energy index.

The highest ACE calculated for a single tropical cyclone on record worldwide is 87.01, set by Cyclone Freddy in 2023.

History
The ACE index is an offshoot of Hurricane Destruction Potential (HDP), an index created in 1988 by William Gray and his associates at Colorado State University who argued the destructiveness of a hurricane's wind and storm surge is better related to the square of the maximum wind speed ($$v_\max^2$$) than simply to the maximum wind speed ($$v_\max$$). The HDP index is calculated by squaring the estimated maximum sustained wind speeds for tropical cyclones while at hurricane strength, that is, wind speeds of at least 64 knots (≥ 119 km/h; 74 mph). The squared windspeeds from six-hourly recorded intervals are then summed across an entire season. This scale was subsequently modified in 1999 by the United States National Oceanic and Atmospheric Administration (NOAA) to include not only hurricanes but also tropical storms, that is, all cyclones while windspeeds are at least 34 knots (≥ 63 km/h; 39 mph). Since the calculation was more broadly adjusted by NOAA, the index has been used in a number of different ways such as to compare individual storms, and by various agencies and researchers including the Australian Bureau of Meteorology and the India Meteorological Department. The purposes of the ACE index include to categorize how active tropical cyclone seasons were as well as to identify possible long-term trends in a certain area such as the Lesser Antilles.

Calculation
Accumulated cyclone energy is calculated by summing the squares of the estimated maximum sustained velocity of tropical cyclones when wind speeds are at least tropical storm strength (≥ 34 kn; 63 km/h; 39 mph) at recorded six-hour intervals. The sums are usually divided by 10,000 to make them more manageable. One unit of ACE equals 10−4 kn2, and for use as an index the unit is assumed. Thus:


 * $$\text{ACE} = 10^{-4} \sum v_\max^2$$    (for $$v_\max$$ ≥ 34 kn),

where $$v_\max$$ is estimated sustained wind speed in knots at six-hour intervals.

Kinetic energy is proportional to the square of velocity. However, unlike the measure defined above, kinetic energy is also proportional to the mass $$m$$(corresponding to the size of the storm) and represents an integral of force equal to mass times acceleration, $$F = m \times a$$, where acceleration is the antiderivative of velocity, or $$v_\max$$. The integral is a difference at the limits of the square antiderivative, rather than a sum of squares at regular intervals. Thus, the term applied to the index, accumulated cyclone energy, is a misnomer since the index is neither a measure of kinetic energy nor "accumulated energy."

Atlantic Ocean


Within the Atlantic Ocean, the United States National Oceanic and Atmospheric Administration and others use the ACE index of a season to classify the season into one of four categories. These four categories are extremely active, above-normal, near-normal, and below-normal, and are worked out using an approximate quartile partitioning of seasons based on the ACE index over the 70 years between 1951 and 2020. The median value of the ACE index from 1951 to 2020 is 96.7 x 104 kt2.

Individual storms in the Atlantic
The highest ever ACE estimated for a single storm in the Atlantic is 73.6, for the San Ciriaco hurricane in 1899. A Category 4 hurricane which lasted for four weeks, this single storm had an ACE higher than many whole Atlantic storm seasons. Other Atlantic storms with high ACEs include Hurricane Ivan in 2004, with an ACE of 70.4, Hurricane Irma in 2017, with an ACE of 64.9, the Great Charleston Hurricane in 1893, with an ACE of 63.5, Hurricane Isabel in 2003, with an ACE of 63.3, and the 1932 Cuba hurricane, with an ACE of 59.8.

Since 1950, the highest ACE of a tropical storm was Tropical Storm Philippe in 2023, which attained an ACE of 9.4. The highest ACE of a Category 1 hurricane was Hurricane Nadine in 2012, which attained an ACE of 26.3. The record for lowest ACE of a tropical storm is jointly held by Tropical Storm Chris in 2000 and Tropical Storm Philippe in 2017, both of which were tropical storms for only six hours and had an ACE of just 0.1225. The lowest ACE of any hurricane was 2005's Hurricane Cindy, which was only a hurricane for six hours, and 2007's Hurricane Lorenzo, which was a hurricane for twelve hours; Cindy had an ACE of just 1.5175 and Lorenzo had a lower ACE of only 1.475. The lowest ACE of a major hurricane (Category 3 or higher), was Hurricane Gerda in 1969, with an ACE of 5.3. The following table shows those storms in the Atlantic basin from 1851–2021 that have attained over 50 points of ACE.

Historical ACE in recorded Atlantic hurricane history
There is an undercount bias of tropical storms, hurricanes, and major hurricanes before the satellite era (prior to the mid–1960s), due to the difficulty in identifying storms.

Classification criteria {{legend|Salmon|Extremely active|border=solid 1px #AAAAAA}} {{legend|Gold|Above-normal|border=solid 1px #AAAAAA}} {{legend|White|Near-normal|border=solid 1px #AAAAAA}} {{legend|Cyan|Below-normal|border=solid 1px #AAAAAA}}

Eastern Pacific
Within the Eastern Pacific Ocean, the United States National Oceanic and Atmospheric Administration and others use the ACE index of a season to classify the season into one of three categories. These three categories are above-, near-, and below-normal and are worked out using an approximate tercile partitioning of seasons based on the ACE index and the number of tropical storms, hurricanes, and major hurricanes over the 30 years between 1991 and 2020.

For a season to be defined as above-normal, the ACE index criterion and two or more of the other criteria given in the table below must be satisfied.

The mean value of the ACE index from 1991 to 2020 is 108.7 x 104 kt2, while the median value is 97.2 x 104 kt2.

Individual storms in the Pacific
The highest ever ACE estimated for a single storm in the Eastern or Central Pacific, while located east of the International Date Line is 62.8, for Hurricane Fico of 1978. Other Eastern Pacific storms with high ACEs include Hurricane John in 1994, with an ACE of 54.0, Hurricane Kevin in 1991, with an ACE of 52.1, and Hurricane Hector of 2018, with an ACE of 50.5.

The following table shows those storms in the Eastern and Central Pacific basins from 1971 through 2023 that have attained over 30 points of ACE.

† – Indicates that the storm formed in the Eastern/Central Pacific, but crossed 180°W at least once; therefore, only the ACE and number of days spent in the Eastern/Central Pacific are included.

Historical ACE in recorded Pacific hurricane history
Data on ACE is considered reliable starting with the 1971 season.

Classification criteria {{legend|Gold|Above-normal|border=solid 1px #AAAAAA}} {{legend|White|Near-normal|border=solid 1px #AAAAAA}} {{legend|Cyan|Below-normal|border=solid 1px #AAAAAA}}

Historical ACE in recorded Western Pacific typhoon history
There is an undercount bias of tropical storms, typhoons, and super typhoon before the satellite era (prior to the mid–1950s), due to the difficulty in identifying storms.

Classification criteria {{legend|Salmon|Extremely active|border=solid 1px #AAAAAA}} {{legend|Gold|Above-normal|border=solid 1px #AAAAAA}} {{legend|White|Near-normal|border=solid 1px #AAAAAA}} {{legend|Cyan|Below-normal|border=solid 1px #AAAAAA}}

North Indian
There are various agencies over the North Indian Ocean that monitor and forecast tropical cyclones, including the United States Joint Typhoon Warning Center, as well as the Bangladesh, Pakistan and India Meteorological Department. As a result, the track and intensity of tropical cyclones differ from each other, and as a result, the accumulated cyclone energy also varies over the region. However, the India Meteorological Department has been designated as the official Regional Specialised Meteorological Centre by the WMO for the region and has worked out the ACE for all cyclonic systems above 17 kn based on their best track analysis which goes back to 1982.