User:Jdorje/Energy

Concept

Currently there are two methods of measuring hurricane intensity. Both are useful, but have drawbacks.

Top wind speed.
Minimum pressure.

Top wind speed isn't a good measure on its own because it is too localised. The top wind speed will show the level of damage a hurricane may cause at landfall, but not the scale of damage. A typical tornado has stronger winds than any hurricane, but does much less damage because it is so much smaller. This seems obvious, but we forget that hurricanes also vary vastly in size. A high-wind-speed small hurricane like Hurricane Camille will do more catastrophic damage, but over a much smaller scale than a lower-wind-speed giant hurricane like Hurricane Katrina. And this is before we consider storm surge, which is affected heavily by storm size as well as hydrology.

For several reasons minimum pressure is preferred as an absolute measure of a tropical cyclone's intensity. Since pressure differential is the "engine" that keeps hurricanes spinning, it is a good barometer of overall intensity. The drawback here is that it does not correspond directly to destructiveness of the storm at all - so while it is a good measure of hurricane "healthiness" it is not a good measure of hurricane destructiveness.

I therefore propose a new system of measuring hurricane intensity: energy. Energy is a natural measure of the power of both natural and man-made systems: earthquakes and nuclear bombs are both measured by their energy output. Applying the concept to hurricanes is a little harder but should yield good results. Energy is measured in joules but can be converted to the moment magnitude scale to give a nice friendly number that's probably between 1 and 10.

Explanation

I believe total kinetic energy of a hurricane can be measured as

E = 0.5mv^2 = 0.5 * (pi * r^2 * h * p * d) * v^2

m is mass (the mass of the moving air)
pi is pi, 3.14
r is the radius of the hurricane, in meters (1600 meters = 1 mile)
h is the height of the hurricane, in meters. This is probably the height of the cloud tops.
p is the pressure of the hurricane, over the entire volume (in % of sea level pressure).
d is the density of air, in kg/m^3. This is 1.2.
v is the velocity of the hurricane, over the entire volume (in meters/second; 3600 seconds = 1 hour).

Note that v and p assume that the pressure and wind velocity are constant throughout the system. Obviously this is never the case. Using an average is not correct here, but without knowing an exact wind-speed distribution (i.e., cutoff radii for different velocities) and pressure distribution (pressure varies mostly with height) we can only estimate here. In certain cases an exact measure of windspeed distribution may be available and should allow much more exact calculations.

We can then determine the moment magnitude of the hurricane via the energy-to-magnitude calculation

  $M_{\mathrm {e} }={2 \over 3}\log _{10}{\frac {\mathrm {E} }{\mathrm {N} \cdot \mathrm {m} }}-2.9$

where E is the energy, in joules (Newton-meters), as calculated above.

Examples

Katrina, landfall

For Katrina at landfall, r=120 miles, h=3000m (just a guess, margin of error 1000m), p of 0.8 (just a guess...pressure drops greatly with height...margin of error 0.1), v of 100 mph (just a guess...margin of error 20 mph). This gives a kinetic energy of about 3*10^17 joules, with a margin of error of about a factor of 2.

E = 0.5mv^2 = 0.5 * 3.14 * (120 * 1600)^2 * 0.8 * 1.2 * 3000 * (100 * 1600 / 3600)^2

and the moment magnitude is thus

M = (2/3)log(3*10^17) - 2.9 = 8.8

Thus, Katrina at landfall had a moment magnitude of 8.8, with a margin of error of about 0.3.

Wilma, peak strength

For Wilma at peak strength, r=15 miles, h=3000m (margin of error 1000m), p of 0.8 (margin of error 0.1), v of 175 mph (upper limit). This gives a kinetic energy of 1.5 * 10^16 joules and a moment magnitude of 7.9, with a margin of error of about 0.3.