Hurricane Wind Speed Formulas I Found In Bryan Norcross's Bo

[Ptarmigan]

Here are some formulas I found in Bryan Norcross's most recent book, Hurricane Almanac: The Essential Guide to Storms Past, Present, and Future. It is used in Hurricane Re-Analysis.

Sustained Wind (MPH) = 9.615 * (1015 - Central Pressure in Millibars) ^ 0.6143

Another formula is:
Sustained Wind (MPH) = 1375 - (1.315 * Central Pressure in Millibars)

Examples (902 millibars is Katrina's peak at 1800 UTC on August 28, 2005)

9.615 * (1015 - 902) ^ 0.6143 = 175.4 mph
1375 - (1.315 * 902) = 188.9 mph

The first formula is about right and the second formula is off as described in the book, about 10 to 15 mph either way.

Hurricane Almanac: The Essential Guide to Storms Past, Present, and Future

[vmax135]

Those are really cool! Using Katrina's peak as the example, the first formula seems to do a really good job... my only question is that is seems to assume a constant of "1015" as the ambient environmental pressure (1015mb) that the storm is embedded in, which is highly variable for each individual storm and is likely too high for the Katrina scenario.

I've personally always used Fletcher's formula... Vmax = 16 * sqrt(Pn - Po)

Vmax: Maximum wind in knots
Pn: Pressure(mb) outer closed isobar
Po: Pressure(mb) minimum central

...as this formula allows for the ambient/environmental pressure (Pn) to be variable, it probably does a better overall job of describing a standard pressure/wind relationship than using the constant of 1015.

If we assume Katrina's outer closed isobar to be around 1000mb, with the Fletcher formula we get:

16 * sqrt(1000-902) = 158.3 kts (158.3*1.1513 = 182.2 mph) ...a little on the high side for Katrina, but not too far off.


If we take the initial formula's constant of 1015 and use it in the Fletcher formula we get:

16 * sqrt(1015-902) = 170.1 kts (170.1*1.1513 = 195.8 mph) ...way too high for Katrina, but probably about right for a 902mb storm embedded in a much higher ambient environment, resulting in a tighter gradient.

-=Michael=-
http://www.tropmet.com

[Berwick Bay]

I have a question concerning this topic of formulas and pressure gradients. Its easy for me to see the importance of pressure gradient when referring to a weaker system. For example (excuse my old fashioned inches of mercury) a storm of 29.44 embedded within a surrounding air mass of 30.20 as opposed to a storm of 29.44 embedded within an air mass of 29.95. The percentage differential between the two is substantial enough. But when we get to major hurricanes, whose inner pressures are ungodly low compared to that of any surrounding air mass, it would seem that the differential with the surrounding air mass would not be as important in determining wind speed. For example the percentage differential between the next two examples would appear to be rather negligible. A storm with pressure of 26.85 embedded within an air mass of 30.20 or one of 26.85 embedded within an air mass of 29.95. Just wondering?? Oh, and one other question. Has there been any research done as far as what "highest absolute wind speed" might be? I've never heard anyone mention this before, but is there such a thing? Referring to the physics of the situation, so that no matter what the pressure gradient, our atmosphere can only support a wind speed of x and no higher. Maybe its silly, just wondering?

[vmax135]

I have a question concerning this topic of formulas and pressure gradients. Its easy for me to see the importance of pressure gradient when referring to a weaker system. For example (excuse my old fashioned inches of mercury) a storm of 29.44 embedded within a surrounding air mass of 30.20 as opposed to a storm of 29.44 embedded within an air mass of 29.95. The percentage differential between the two is substantial enough. But when we get to major hurricanes, whose inner pressures are ungodly low compared to that of any surrounding air mass, it would seem that the differential with the surrounding air mass would not be as important in determining wind speed. For example the percentage differential between the next two examples would appear to be rather negligible. A storm with pressure of 26.85 embedded within an air mass of 30.20 or one of 26.85 embedded within an air mass of 29.95. Just wondering??

Hi Berwick - Actually, for the most part, the "differential" (i.e. gradient) is all that really matters in determining the maximum potential gradient wind... not the actual "values" of the ambient/environmental pressure and the storm's central pressure. So basically, the greater the pressure drop over a defined distance, the stronger the wind will be. That said, as you start getting into extremely large pressure drops (i.e. over 100mb/2.95in), the "rate of increase" in the gradient wind is not quite as fast. Using the Fletcher formula, in your "weak" storm comparative example:

1023mb (30.20in) - 997mb (29.44in) = 26mb (0.77in) = 81kts (93mph)
1014mb (29.95in) - 997mb (29.44in) = 17mb (0.50in) = 65kts (75mph)

As you anticipated, a significant difference in the resulting gradient wind, but all that really matters is the 26mb pressure drop and the 17mb pressure drop, respectively, to determine the resulting wind. Between the two scenarios, the 9mb (0.27in) gradient pressure drop difference results in about an 18mph difference in resulting gradient wind.

With your "intense" storm scenario...

1023mb (20.20in) - 909mb (26.85in) = 114mb (3.37in) = 171kts (197mph)
1014mb (29.95in) - 909mb (26.85in) = 105mb (3.10in) = 160kts (184mph)

Again, all that matters to determine the gradient wind are the 114mb and 105mb pressure drops, respectively. The gradient pressure drop difference between the two is still the same 9mb (0.27in) but, in this case, that results in about a 13mph difference in gradient wind. Still a significant difference.

As a final example, to reiterate that it's really just the gradient difference that is of most importance... if I take your last example, the storm had a central pressure of 909mb (26.85in) and was embedded in a relatively high ambient environment of 1014mb (29.95in) resulting in a 105mb (3.10in) drop, yielding a gradient wind of 160kts (184mph)... if we look at three additional scenarios where the values for ambient and central pressure change drastically, but still produce the same 105mb pressure drop... the result is the same gradient wind... 160kts (184mph)

1004mb (29.65in) - 899mb (26.55in) = 105mb (3.10in) = 160kts (184mph)
1024mb (30.24in) - 919mb (27.14in) = 105mb (3.10in) = 160kts (184mph)
1050mb (31.00in) - 945mb (27.91in) = 105mb (3.10in) = 160kts (184mph)

In my opinion, where these type of formulas are somewhat flawed is two-fold... 1. Basically they assume a linear decrease in pressure from the ambient environment to the storm's center... which often times is not the case, as the gradient usually becomes steeper towards the center of stronger storms (especially really small ones like Andrew and Charley) 2. They don't really account well for the great differences in distance that can occur, from storm to storm, between the "ambient" environment and the storm's center (i.e. small compact storms vs. large expansive systems).

Regardless... as formulas to basically describe a "rule of thumb" method for determing maximum gradient wind, the Fletcher equation and the ones highlighted by Ptarmigan in Bryan Norcross' book are pretty good... the user just has to evaluate the results on a case-by-case basis.

Oh, and one other question. Has there been any research done as far as what "highest absolute wind speed" might be? I've never heard anyone mention this before, but is there such a thing? Referring to the physics of the situation, so that no matter what the pressure gradient, our atmosphere can only support a wind speed of x and no higher. Maybe its silly, just wondering?

I'll defer to anyone with a greater understanding of fluid dynamics and/or a potential planetary maximum wind... but as far as I know, no... "theoretically" there is no limit (other than the gradient) that atmospheric physics impose, that would "cap" Earth's maximum wind speed at a certain value. But again, this is not really my area of expertise.


-=Michael=-
http://www.tropmet.com

[Ptarmigan]

I used that same formula and found that Wilma formed in an ambivient pressure of 1005 millibars, which is rather low.

October 19, 2005 (1200 UTC)
9.615 * (1005 - 882) ^ 0.6143 = 184.8 mph

Wilma had a pressure pof 892 mb and winds of 155 mph, which is the lowest recorded for a non-category 5 hurricane. It is ver likely, that typhoons have had pressures of 890 mb and winds of 150 mph, but those are never actually measured. It is a combination of low ambivient pressure and eyewall replacement cycle Wilma was undergoing at the time. Feel free to correct me on that part because 892 mb is low for a Category 4 hurricane and I though that might be an error. I know at the time, Wilma had hurricane force winds extending up to 70 miles from the eye.
October 20, 2005 (0000 UTC)
9.615 * (986 - 892) ^ 0.6143 = 154.6 mph

[Berwick Bay]

Thanks a lot Michael. So as I suspected the difference in wind speed in a powerful storm relative to its surrounding enviroment is not quite as significant as a weaker storm relative to its environment. (13mph compared to 18mph). But as you say, 13mph is really still a significant number. Especially since any increase in the winds of a powerful storm increase its strength according to the geometric formula. As far as my question on max absolute wind speed, it makes me think of tornadoes. It wasn't that long ago that powerful tornadoes were believed to have winds of 400 or even 500 mph. That has since been reduced, with the Fujita Scale showing 260-318 mph for an F5 the strongest of tornadoes. What I find amazing though is that Cat 5 Hurricanes have been reported to have gusts of up to 220 Mph!!This is on the level of an F4 and not too far from the strength of an F5 tornado. Incredible that a storm of the scope and breadth of a hurricane could have winds in the range of the most powerful of tornadoes. Kinda blows my mind (pun definitely intended!) Thanks again Michael.

[Ptarmigan]

Those are really cool! Using Katrina's peak as the example, the first formula seems to do a really good job... my only question is that is seems to assume a constant of "1015" as the ambient environmental pressure (1015mb) that the storm is embedded in, which is highly variable for each individual storm and is likely too high for the Katrina scenario.

I've personally always used Fletcher's formula... Vmax = 16 * sqrt(Pn - Po)

Vmax: Maximum wind in knots
Pn: Pressure(mb) outer closed isobar
Po: Pressure(mb) minimum central

...as this formula allows for the ambient/environmental pressure (Pn) to be variable, it probably does a better overall job of describing a standard pressure/wind relationship than using the constant of 1015.

If we assume Katrina's outer closed isobar to be around 1000mb, with the Fletcher formula we get:

16 * sqrt(1000-902) = 158.3 kts (158.3*1.1513 = 182.2 mph) ...a little on the high side for Katrina, but not too far off.


If we take the initial formula's constant of 1015 and use it in the Fletcher formula we get:

16 * sqrt(1015-902) = 170.1 kts (170.1*1.1513 = 195.8 mph) ...way too high for Katrina, but probably about right for a 902mb storm embedded in a much higher ambient environment, resulting in a tighter gradient.

-=Michael=-
http://www.tropmet.com

Interesting formula. I wonder if these formulas take into accoun pressure gradient and size of hurricane? Some hurricanes have really low pressure, but wind is not as high.
Wilma-882 mb 185 mph 50 miles (Maximum extent of hurricane force winds at peak)
Gilbert-888 mb 185 mph 150 miles
Labor Day 1935-892 mb 190 mph 15 miles
Rita-895 mb 180 mph 80 miles
Allen-899 mb 190 mph 120 miles
Katrina-902 mb 175 mph 105 miles
Camille-905 mb 190 mph 50 miles
Mitch-905 mb 180 mph 60 miles
Andrew-922 mb 175 mph 30 miles
Charley-941 mb 150 mph 25 miles

[Derek Ortt]

wilma formed form a monsoon trough. The ambient pressures were very low. Remember, when it had a 989mb pressure, it only had sustained winds of 45KT

[Berwick Bay]

Ptarmigan, when I look at the chart that you just posted, including diameter of hurricane winds along with max wind speed, I would have to conclude that Gilbert is still boss.

[vmax135]

I used that same formula and found that Wilma formed in an ambivient pressure of 1005 millibars, which is rather low.

October 19, 2005 (1200 UTC)
9.615 * (1005 - 882) ^ 0.6143 = 184.8 mph

Wilma had a pressure pof 892 mb and winds of 155 mph, which is the lowest recorded for a non-category 5 hurricane. It is ver likely, that typhoons have had pressures of 890 mb and winds of 150 mph, but those are never actually measured. It is a combination of low ambivient pressure and eyewall replacement cycle Wilma was undergoing at the time. Feel free to correct me on that part because 892 mb is low for a Category 4 hurricane and I though that might be an error. I know at the time, Wilma had hurricane force winds extending up to 70 miles from the eye.
October 20, 2005 (0000 UTC)
9.615 * (986 - 892) ^ 0.6143 = 154.6 mph

Hi Ptarmigan - Wilma's 892mb value is indeed extremely low for only 155mph... but that wasn't an error. The nuances to Wilma's specific pressure/wind relationship (and many other storms) is extremely complex and is not something that these simple gradient formulas handle (or were intended to handle) very well. They're much better at describing "standard" sized, steady-state storms. Of course, our natural instinct is to immediately apply these formulas to the most extreme cases we can think of... haha.

That said, I'm pretty sure these formulas are not intended to be reversed to derive the ambient environmental pressure using the central pressure and the operationally reported wind speed. Is that how you came to the ambient value of 1005mb for Wilma's peak, or did you get that value somewhere else? If you did just reverse the formula, using the reported wind speed to derive the ambient environmental pressure will probably yield an unreliable result, since the operationally reported wind speed is not solely based on the "gradient"... which are the sole basis for these formulas.

-=Michael=-
http://www.tropmet.com

[vmax135]

Thanks a lot Michael. So as I suspected the difference in wind speed in a powerful storm relative to its surrounding enviroment is not quite as significant as a weaker storm relative to its environment. (13mph compared to 18mph). But as you say, 13mph is really still a significant number. Especially since any increase in the winds of a powerful storm increase its strength according to the geometric formula. As far as my question on max absolute wind speed, it makes me think of tornadoes. It wasn't that long ago that powerful tornadoes were believed to have winds of 400 or even 500 mph. That has since been reduced, with the Fujita Scale showing 260-318 mph for an F5 the strongest of tornadoes. What I find amazing though is that Cat 5 Hurricanes have been reported to have gusts of up to 220 Mph!!This is on the level of an F4 and not too far from the strength of an F5 tornado. Incredible that a storm of the scope and breadth of a hurricane could have winds in the range of the most powerful of tornadoes. Kinda blows my mind (pun definitely intended!) Thanks again Michael.

Anytime BB! Glad I could help.

-=Michael=-
http://www.tropmet.com

[vmax135]

Interesting formula. I wonder if these formulas take into accoun pressure gradient and size of hurricane?

Yeah, unfortunately these simple formulas don't really take size of the pressure field into consideration... which is why they should only be used for "rule of thumb" applications. I had mentioned in my mammoth (sorry about the length) response to Berwick, that this was one of the two areas where these equations are flawed... 1. Size of the pressure field and 2. A non-linear decrease in pressure... which are not really accounted for.

-=Michael=-
http://www.tropmet.com

[Ptarmigan]

wilma formed form a monsoon trough. The ambient pressures were very low. Remember, when it had a 989mb pressure, it only had sustained winds of 45KT

That sure explains it all. I remember where Wilma formed, that area was a real mess of clouds. I wonder how many hurricanes form from monsoon troughs in the Atlantic. I rarely think of monsoon troughs over the Caribbean and Atlantic. Worldwide, most tropical cyclocnes form from monsoon troughs. That would explain why typhoons have lower pressure than Atlantic and East Pacific Hurricanes.

[Ptarmigan]

Hi Ptarmigan - Wilma's 892mb value is indeed extremely low for only 155mph... but that wasn't an error. The nuances to Wilma's specific pressure/wind relationship (and many other storms) is extremely complex and is not something that these simple gradient formulas handle (or were intended to handle) very well. They're much better at describing "standard" sized, steady-state storms. Of course, our natural instinct is to immediately apply these formulas to the most extreme cases we can think of... haha.

That said, I'm pretty sure these formulas are not intended to be reversed to derive the ambient environmental pressure using the central pressure and the operationally reported wind speed. Is that how you came to the ambient value of 1005mb for Wilma's peak, or did you get that value somewhere else? If you did just reverse the formula, using the reported wind speed to derive the ambient environmental pressure will probably yeild an unreliable result, since the operationally reported wind speed is not solely based on the "gradient"... which are the sole basis for these formulas.

-=Michael=-
http://www.tropmet.com

The 1005 mb was my estimate. As Derek said, Wilma formed from a monsoonal trough, which is why at 989 mb it had 45 knot winds. Like I said, typhoons and tropical cyclones in South Pacific and Indian Ocean probably have 890 mb and 155 mph or less because they often form from monsoonal troughs.

[DanKellFla]

Berwick Bay,

I will ask some of the fluid dynamicists that I work with but, from my basic Aerodynamics course, I would say that the maximum windspeed could be 0.7 X the speed of sound (remember, the speed of sound varies with teperature). That is where compresibility effects start to become significant. If you add in frictional effects near the surface, I would GUESS that the maximum windspeed would be about 0.5 X the speed of sound.

[Tampa Bay Hurricane]

Very Interesting formulas. I'm going to
use them the next time we are tracking
storms.

[Berwick Bay]

Dankell Fla wrote this

will ask some of the fluid dynamicists that I work with but, from my basic Aerodynamics course, I would say that the maximum windspeed could be 0.7 X the speed of sound (remember, the speed of sound varies with teperature). That is where compresibility effects start to become significant. If you add in frictional effects near the surface, I would GUESS that the maximum windspeed would be about 0.5 X the speed of sound.

Dan, Berwick here, thanks for responding to my inquiry about a possible max wind speed on planet earth. I know that you are speculating, you say "could be", but I find the numbers you mention interesting. You say with frictional effects perhaps .5 X the speed of sound is a possibility. Like you say the speed of sound varies, but lets call it on the neighborhood of 660 mph or a little higher (toward 700 mph). Not exactly sure but I think thats about right. Well if the .5 X the speed of sound is correct, then you get a max wind speed not a whole lot greater than an F5 tornado. Makes you wonder if what happens in an F5 tornado is not at or very near a max of what is possible on the planet, and if the estimated speed of 318 mph is a function of the formula you mention. Its all speculation here, but let me know if you find out something concrete. Thank you DanKellFla and take care, I mean that, too.

[windstorm99]

I read bryans first book but this issue is even more informative on all issues.

Ive actually had the opportunity of meeting bryan on several occasions and is really a great guy.His continues coverage during hurricane andrew almost 34 hours live during the storm separates him from the rest in my opinion.He's number one on my list across south florida for hurricane coverage.Adrian