Hurricane Categories Depending on Their Winds in Context of Warming Climate: Using a Right-Tail L-Probability Distribution Function

The super-hurricane generally may be also mainly characterized as violent winds (too much strong whirling wind or gusts), so here it may be supposed that hurricane winds(usually sustained winds in one minutes or ten minutes interval) is good index to represents strength and power of tropical cyclone, such as Saffir-Simpson hurricane wind scale, generally, from commonsensible scene , the more power of hurricane; the more stronger winds take places; but from professional and technical aspects, the fundamental and comprehensive mathematical tools should be ability and available to study those kind questions of categories for super tropical cyclone, Especially, at current trend of today hurricanes power has been increasing decade by decade（or year by year）, the new categories for super-hurricanes will be urgent for in adoption to globe warming and meet growing requirements to calibrate increasingly super-hurricane in tropical or subtropical cyclone-prone region, in particular, using the intensified destructive winds the super-hurricane lead to, because hurricane violent wind often severely damaged infrastructure of some low-latitude and coastal cities today, such as Tropical Storm Hato did in Macao 23,Aug,2017, in Zhuhai of Guangdong province, for Hato, Hong Kong in five years shut down schools and financial markets, warned with the first Signal 10 typhoon.

Using how stronger wind of tropical cyclone or subtropical cyclone to give the category of strength of hurricane is one of many approaches to delineate What power of tropical cyclone is, at these points, obviously，the degree to whose mean of long term, the wind the hurricane will lead to, is important indicator of how much the hurricane has taken place, in other words, this degree is also in proportion to how much intensity (wind) the hurricane will bring to the area, or potential damage it will cause , at this time precisely speaking, the intensified wind the hurricane bring, the more stronger the hurricane is! here it is assumed that "stronger wind" event occurring is more than "weaker wind" event is for all wind-oriented events of any hurricane in future, same meaning, the distribution of the wind event of hurricane should be right-skewness distribution, and ‘weaker wind’ events is "scarce" but ‘ stronger wind’ events of hurricane is "often" ,even "abundant" and "plentiful", this means that right-distribution can suitable for the trend of the hurricane wind being growingly greater in future, In the other words, "below boundary" of wind of hurricane is limited and expected or averaged value , however, its "up-boundary” will be approaching + ∞ or unlimited, this is just main feature of right-tail distribution, Therefore, at this time, one the skew-distribution is needed to delineate the distribution of hurricane wind does and similarly using this distribution to categorize the strength of hurricane. Although, this right-skew distribution is required that it owns those ability to describe extreme wind velocity of hurricanes, but here it is required at same time that its standard variable formation should be identical and stability or remain same in whole defining interval(x_min,+∞) , and the boundary is limited in its “weaker wind” interval, however, the boundary is unlimited in its “intensified wind” interval, at this time, the theory of this right-skew distribution should be perfect , accurate; strict, even rigorous.

Here it deserve stress, from extreme event (wind) perspective, although Normal Distribution also somewhat have ability to delineate extreme precipitation, however, unfortunately Gaussian Distribution is not skew-distribution but only symmetric distribution. Its standard variable also can not keep same in(-∞,+∞).

In deed, the wind of hurricane generally is above 17m/s or 32 km/h (Saffir-Simpson hurricane scale), so it should be paid attention to that positive skew distribution gives broaden width in which extreme wind velocity can develop from its long term averaged value x_A to + ∞ (unlimited), thus under of this condition, wind of hurricane more than 32m/s or 63 km/h can not impact the main quality that enable wind velocity vary from its mean point until to its + ∞ point , just this point meets requirement of extreme unlimited biggest wind velocity for duration of studying extreme events of wind velocity for tropical or subtropical cyclone.

Wanli Wang right-skew L distribution function meets those basic requirements above, What property of approach being used to measure wind is key step to chose to its ability to describe to extreme wind event, here, it is recommended that wanli wang positive L probability distribution function may be suitable for category of the hurricane in term of wind , wanli wang Positive-Skew L probability distribution function is also called right- tail or right- skew L distribution function, in fact , wanli Wang right-skew L distribution function is just combined wanli wang L standard (0,1) distribution function (symmetry) with Standard(0,1) Gaussian Distribution ,also called as “Wang Wanli- Gaussian” Distribution”, and finally let Wang wanli right-skew L distribution function become asymmetry distribution and right-skew distribution.

Its intrinsic quality is that its standard random variable interval is from x_min to + ∞ , here x indicates wind, x_min is low boundary value, it may be one minute sustained wind ; ten minute sustained wind etc, also several second maximum gusts ,x_A indicates respective mean wind for historical data, therefore, standard random variable must be written as u=[ ( x-x_A) / ( x_A -x_min ) ] depending on boundary condition of the probability density function: f(-1) =0 or f(+∞) =0, both equal to zero , below, the formula is probability density function of wang wanli right-skew L distribution (Wang Wanli- Gaussian” Distribution)， finally， Fig-1 standard variable u;

Fig-2 is the explanation for what is wanli wang right-tail L probability distribution for in imagination; Fig-3 is consequence of categories of Hurricane or Typhoon in the term of wind strength in fixed sustain interval times.