Hurricanes, Integrated Kinetic Energy

In the western hemisphere, hurricanes are all rated on the Saffir-Simpson scale.. To compute a storm's category rating, you have to measure the highest speed sustained by a gust of wind for an entire minute.. Based on how large this maximum speed is, a storm is assigned to one of five different categories [1].

The problem with this number is that it only captures one aspect of a storm's intensity - the highest speed that it can sustain. Not only is it tricky to measure this peak speed, but different organizations may come to different conclusions about it, depending on their coverage of the wind data. This number doesn't tell you anything about the size of the storm, nor about how the wind-speeds are distributed overall.

Consider a tale of two storms - the first is fierce but more contained, whereas the second is larger, and though it has lower peak wind speed, these wind speeds are spread over a larger area. The SS scale would give the first storm a higher score, even though the latter may be more destructive. Based on the rating, people might have expected Katrina to be about as destructive as Camille...

Integrated Kinetic Energy

We can get a sense of a storms' strength with a little bit of high school physics. You might remember that every object in motion carries a certain amount of energy, known as its kinetic energy. The kinetic energy of an object depends on the square of its speed, and is directly proportional to the mass of the object..

Well, think of a storm as being built out of moving parcels of air. Each of these parcels has a certain amount of kinetic energy.

IKE is calculated as

$$ IKE = \int_v \frac{1}{2} \rho U^2 dV $$

$v$ is volume, $\rho$ is density, $U$ is speed. This is the familiar kinetic energy calculation, a variation of $1/2 m v^2$ (here $v$ is speed). Mass is of the pocket of air, a grid cell of 1 meter high. Since numerically 1m height, and air density of 1 kg/m3 is assumed, jut the cell area calculation is sufficient since times 1 wld give volume times 1 wld give weight. Wind speed from NOAA comes in $u,v$ components, $u^2+v^2$ will give square speed. Multiply by 0.5 and sum all cells, this gives total energy. Wind speed is retrieved from a NOAA for each grid cell.

Hurricane Katrina

import impl as u

u.ike_ncei(lat=25,lon=-90,day=30,month=8,year=2005,hour=10)

Out[1]: 340.975708798976

Hurricane Sandy

u.ike_ncei(lat=39,lon=-74,day=29,month=10,year=2012,hour=13)

Out: 213.90759

Hurricane Ivan

u.ike_ncei(lat=30.302,lon=-87.751,day=16,month=9,year=2004,hour=10)

Out: 175.953368

All results are in terrajoules.

References

[1] Wired

[2] WaPo

[3] Powell, Reinhold Paper

[4] NOAA Python Code