Proposal for an Intensity scale for rogue waves

1. The case for Rogue Wave Intensity scale
2014Selim.Stahl@gu.se

2. Rogue Wave
Rogue waves (aka freak waves, monster waves, killer waves, extreme waves, and abnormal waves) are
relatively large and spontaneous ocean surface waves that occur far out at sea, and are a threat even to
large ships and ocean liners.
Oceanography Definition: H > 2 x SWH
A rogue waves is NOT a storm wave and NOT necessarily the BIGGEST wave found at sea; nor it is a
hundred-year wave*. Rogue waves are, rather, unusually large waves for a given sea state. Rogue waves
seem NOT to have a single DISTINCT cause, but occur where physical factors such as high winds and
strong currents cause waves to merge to create a single exceptionally large wave.
* a statistically projected water wave, the height of which, on
average, is met or exceeded once in a hundred years for a given
location

3. Rogue Waves are:
1. NEWLY observed
2. NOT well understood
3. Intensity Scale or Magnitude YET to be developped
4. KILLING people* and DESTROYING infrastructures
*131 fatalities in 2006-2010

4. Where Rogue Waves occured 2006-2010

5. Some Existing emergency-related scales
Introduction Date Name Phenomena
1805 Beaufort Scale Wind
1935 Richter Scale Earthquake
1969 Saffir-Simpson Scale Hurricane
1971 Fujita Scale Tornadoes
1982 Volcanic Explosivity
Index
Volcanic Eruption
1990 International Nuclear
Even Scale
Nuclear accident
1999 Air Quality Index Air Pollution
1999 Torino Scale Asteroid Impact
2012 ITIS Scale Tsunamis

6. First proposal: a 12 division Rogue Wave Intensity scale I based on impacts on infrastructures
(Fujita style)
I Not felt
II Scarcely felt
III Weak
IV Largely observed
V Strong
VI Slightly damaging
VII Damaging
VIII Heavily damaging
IX Destructive
X Very destructive
XI Devastating
XII Completely devastating

7. Second proposal: a Rogue Wave Intensity scale based on Wave height (Richter style)
i = 2.5526 log H + 0.4632
i = 1..6
Though we assume a log function (hence linearizable) we still used a general optimisation method with 8 points
corresponding to 8 rogue waves recently observed, in case we want to change to a more advanced formula later.
With the generic intensity scale formula:
I(h) = a + log(h)/log(b) where a and b are constant numbers.
And our rogue waves vector set (I(hi), hi) i =1..8 so we could find (a,b )
With c= 1/log(b) to simplify the wording, and u=SUM((log(h_k))^2, k=1..8) and v= SUM((I(log(h_k))^2, k=1..8) and
w=SUM(log(h_k), k=1..8) and r=SUM(I(log(h_k)), k=1..8) and s=SUM(log(h_k) x I(log(h_k), k=1..8).
The problem is to find a value for (a,c) that minimise f(a,c), where f(a,c)= SUM((a+c.log(h_k)-I(log(h_k))^2, k=1..8) A
necessary and sufficient condition for f to have a minimum at (a,c) is that the gradient of f is zero at (a,c) and that
the Hessian of f in (a,c) is positive-definite, which translates in that the partial derivatives of f with respect to the
variable a and c be zero in (a,c) and that the determinant and the trace of the Hessian of f in (a,b) be strictly
positive-definite. This means:
a= (ru-sw) / (8u-w^2)
c= (8s-wr) / (8u-w^2)
with the conditions 8u-w^2>0 and 8+u>0 for the problem to have a solution.