IAC ETHZ
Cloud Dynamics
Assignment 5
Alexander Umbricht
17th May 2010
Erlinsbacherstrasse 62
5000 Aarau
Switzerland
Tel: +4162 823 61 66
a.umbricht@gmx.ch
http://alexander.umbricht.li/
Shinnecock Inlet and the widening of the Moriches
1 Long Island Express
Inlet to the west.” (Mandia, 2010)
The Long Island Express was the first major hurricane
which stroke New England for almost 70 years. “The
storm formed near the coast of Africa in September of
Saffir-Simpson hurricane scale
the 1938 Atlantic hurricane season, becoming a Category
It depends where we want to determine the category
5 hurricane on the Saffir-Simpson Hurricane Scale before
of the storm. Since the classification of TC according
making landfall as a Category 3 hurricane on Long Island
to the Saffir-Simpson Hurricane Scale only depends on
on September 21.” Several 100 people were killed, over
wind speed1 , it only takes this measurement. (Wikipedia,
57,000 homes destroyed and property losses are estima-
2010c)
ted at $ 4.7 billion (in 2009 dollars). “To date it remains
But there are some difficulties:
the most powerful, costliest and deadliest hurricane in
New England history.” (Wikipedia, 2010a)
• We need an instrument which sustains high windspeeds for a long enough time without getting damaged.
Specialities
• Long Island is far from the warm, tropical oceans
that feed hurricanes. Therefore one often does not
expect hurricanes in New York. But they happen. A
category 3 storm has a return period of roughly 75
years. (Mandia, 2010)
• Especially on the ocean there are (and were) only
few measurements. There is no guarantee, that this
measurements really capture the most relevant part
of the TC.
But, if we have a landfall of a TC, chances to get
enough measurements at the right spots increases
• “Except for Charlie Pierce, a junior forecaster in the
U.S. Weather Bureau who predicted the storm but
was overruled by the chief forecaster, the Weather
Bureau experts and the general public never saw it
coming.” (Mandia, 2010)
• Since the last severe Hurricane in New England large
influxes of European immigrants settled in cities and
largely.
Therefore it is quite possible, that the Long Island Express really was of category 3 at its landfall. If it really
was a category 5 TC over the ocean is probably more
debatable.
towns throughout New York and New England, many
Damage in today’s context
of whom knew little, if anything, about hurricanes.
The Long Island Express was devastating, the damage
By 1938, most of the earlier storms were remembered.
(Wikipedia, 2010a)
Therefore, the people were not prepared at all for such
a storm.
lot of wealth, many more people live there and every
up down of the ‘Wall Street’seems to have effect on
the world economy. Not surprisingly, the chances that a
• Such a strong storm in this area is luckily very rare.
“Case studies have shown that the next time a storm
like the Long Island Express roars through, it might
be the greatest disaster in U.S. history.”
‘epic’. Since then the same region has accumulated a
(Mandia,
2010)
Long Island Express type Hurricane would be disastrous
beyond imagination are given.2
To get more specific: According to Mandia (2010) the total cost of a category 3 hurricane to residential and commercial properties ranges between $ 11 and $ 14 billion
• The geological impact is noticeable until today: “Per-
while the damage to these structures in a category 4
haps the greatest long-term impact on Long Island of
storm would be $ 68 to $ 73 billion. And this are only
the Great Hurricane of 1938 was its creation of the
the estimated costs for Suffolk County (Fig. 1).
1 average
winds over a period of one minute, measured at 10.1 m height
2 In 2001 only two towers in New York were hit by planes. Look what happened to the economy. No compare this to the damage a hurricane
can inflict. . . Although I have to admit that the psychological factors in these two cases are profoundly different.
Cloud Dynamics: Assignment 5
Page 1 of 6
Maximal windspeed of a hurricane
We also know the following relations
TB − T0
TS − T0
=
T
T0
0 κ
p̂
θ = TS
p
(2)
=
(3)
L·q
(4)
θe = θ · e cp ·TS
q=
RH 0 · psat (TS )
100 %
p
(5)
pS = p̂ − 2000 Pa
(6)
If we insert (2) in (1), we get
Fig. 1: This map shows the state of New York. Marked in
red is Suffolk County. (Benbennick, 2006)
2
vmax
=
θ∗
Ck TS − T0
· cp · TS · ln es
C
T0
θe
{z
}
|D
(7)
C1
We already know all values of C1 , hence we have to
2 Maximal windspeed of a
∗
investigate θes
and θe
hurricane
θe
Using (3), (4) and (6), we get
The maximal wind speed vmax can be determined according to (1)
2
vmax
=
Ck
θ∗
· cp · TS · ln es
CD
θe
(1)
with
sat. equiv. potential temperature at TS
∗
θes
Sea surface temperature
TS = TB
Temperature boundary layer
TB
equiv. potential temp. boundary layer
θe
Ck
= 1.2
CD
L·q
θe = θ · e cp ·TS =
κ
L·q
p̂
= TS
· e cp ·TS =
p
κ
·p (T )
L
p̂
· RH 0 sat
= TS
· e cp ·TS 100 % p̂−2000 Pa
p̂ − 2000 Pa
∗
θes
∗
The saturation equivalent potential temperature θes
is
almost the same as θe . But instead of a RH of 78 % we
are in saturated conditions, hence RH = 100 %:
Using again (3), (4) and (6), we get
exchange coefficients
L·q
∗
θes
= θ · e cp ·TS =
κ
L·q
p̂
= TS
· e cp ·TS =
p
κ
·p (T )
L
p̂
· 0 sat
= TS
· e cp ·TS p̂−2000 Pa
p̂ − 2000 Pa
Carnot (2)
cp = 1005
specific heat with p = const.
J
K kg
Furthermore, we need
L = 2.53 · 106
R = 287.04
J
kg
J
K kg
latent heat of vaporisation
gas constant
(8)
(9)
Results
If everything is calculated (with Matlab), we get
0 = 0.622
p̂ = 105 Pa
pressure
T0 = 210 K
outflow temperature
κ=
R
= 0.286
cp
Page 2 of 6
psat (T ) (Pa)
∗
θes
(K)
θe (K)
vmax (m s-1 )
293
0.395
2318
334
325
62.3
298
0.419
3142
355
342
74.7
303
0.443
4210
381
362
88.9
TS (K)
Cloud Dynamics: Assignment 5
P o l a r L ow
A brief visualisation of the results (Fig. 2, deviation from
Formation
the blue to the red line) shows, that vmax increases more
PLs form in cold polar or arctic air advected over
then linear with higher TS .
relatively warmer water (weatheronline.co.uk, n.d.). Baroclinic and/or barotrope instability also can give rise
90
for a PL (Wikipedia, 2009). And at last but not least,
simple convection is also a suggested trigger (weathe-
85
ronline.co.uk, n.d.).
The formation of a TC is complex. In most situations,
vmax (m s-1 )
80
water temperatures of at least 26.5 °C are needed down
75
to a depth of at least 50 m. Another factor is rapid
cooling with height (release of the heat of condensation
70
to power a TC). When there is a great deal of moisture
in the atmosphere, conditions are more favourable for
65
disturbances to develop. Low amounts of wind shear
60
293
294
295
296
297
298
299
300
301
302
303
Sea Surface Temperature TS (K)
Fig. 2: Maximal wind speeds of hurricanes depending on sea
surface temperature. The red line represents a linear
extrapolation based on the first two points.
are needed, as high shear is disruptive to the storm’s
circulation. Lastly, a formative TC needs a pre-existing
system of disturbed weather. (Wikipedia, 2010d)
Both systems tend to decay rapidly with landfall, mostly
3 Polar Low
The most obvious similarity between a Tropical Cyclone
(TC) and a Polar Low (PL) is that both have the lowest
pressure in their centres (where also both usually form
an ‘eye’). Hence they both are low pressure systems
due to the lack of warm moisture supply from the relatively warm sea. (weatheronline.co.uk, n.d.)
Impact
PLs produce severe weather, heavy precipitation – usually
falling as snow, and strong surface winds (weatheronline.co.uk, n.d.).
Spatial Pattern
TCs often have a much larger impact, not only because
A PL is usually smaller then 1,000 km and can be found
they are larger and last longer, but also because they
poleward of the main polar front in both the Northern
and Southern Hemispheres. On the other hand, a TC
originates near the equator (usually about 10 ° away from
it) and its size is often larger then 670 km with an upper
limit near 1,800 km. (Wikipedia, 2010b,d)
Temporal Pattern
In the Northern Hemisphere PL are most common during
winter but also appear in autumn and spring. Apparently, there is no seasonal variability in the Southern
hemisphere (weatheronline.co.uk, n.d.). TCs usually are
formed near the end of the summer and in the early
autumn (Wikipedia, 2010d).
release much more energy. TCs out at sea cause large
waves, heavy rain, and high winds, disrupting international shipping and, at times, causing shipwrecks. On land,
strong winds can damage or destroy vehicles, buildings,
bridges, and other outside objects, turning loose debris
into deadly flying projectiles. The storm surge, or the
increase in sea level due to the cyclone, is typically the
worst effect from landfalling tropical cyclones, historically
resulting in 90 % of tropical cyclone deaths. The broad
rotation of a landfalling TC, and vertical wind shear at
its periphery, spawns tornadoes. (Wikipedia, 2010d)
Forecasting
“Polar lows are very difficult to forecast and a nowcasting
Typically a PL last for anything between 12 to 36 hours,
approach is often used, with the systems being advected
which is much less then the time a TC lasts – Hurricane
with the mid-tropospheric flow. Numerical weather pre-
John is the longest-lasting tropical cyclone on record,
diction models are only just getting the horizontal and
lasting 31 days in 1994.(weatheronline.co.uk, n.d., Wiki-
vertical resolution to represent these systems.” (Wiki-
pedia, 2010d)
pedia, 2010b)
A. Umbricht
Page 3 of 6
References
Combining forecast models with increased understanding
of the forces that act on TCs, as well as with a wealth
of data from e. g. satellites, scientists have increased the
accuracy of track forecasts over recent decades. However, predicting the intensity of tropical cyclones is still
quite problematic. (Wikipedia, 2010d)
Wikipedia: 2009, Polartief — Wikipedia, Die freie Enzyklopädie.
[Online; Stand 16. Mai 2010].
URL:
http: // de. wikipedia. org/ w/ index. php? title=
Polartief&oldid= 65387348
Wikipedia: 2010a, New England Hurricane of 1938 — Wikipedia,
The Free Encyclopedia. [Online; accessed 15-May-2010].
URL:
http: // en. wikipedia. org/ w/ index. php? title=
New_ England_ Hurricane_ of_ 1938&oldid= 360446567
4 References
Benbennick, D.: 2006, Map of New York highlighting Suffolk
County. [Online; accessed 15-May-2010].
URL:
http: // commons. wikimedia. org/ wiki/ File:
Map_ of_ New_ York_ highlighting_ Suffolk_ County. svg
Mandia, S. A.: 2010, The Long Island Express – The Great
Hurricane of 1938. [Online; accessed 15-May-2010].
URL:
http: // www2. sunysuffolk. edu/ mandias/
38hurricane/
weatheronline.co.uk: n.d., Polar low – the arctic hurricane.
[Online; accessed 17-May-2010].
URL:
http: // www. weatheronline. co. uk/ reports/
wxfacts/ The-Polar-low---the-arctic-hurricane. htm
Page 4 of 6
Wikipedia: 2010b, Polar low — wikipedia, the free encyclopedia.
[Online; accessed 16-May-2010].
URL:
http: // en. wikipedia. org/ w/ index. php? title=
Polar_ low&oldid= 353133027
Wikipedia: 2010c, Saffir-Simpson Hurricane Scale — Wikipedia,
The Free Encyclopedia. [Online; accessed 15-May-2010].
URL:
http: // en. wikipedia. org/ w/ index. php? title=
Saffir-Simpson_ Hurricane_ Scale&oldid= 361503316
Wikipedia: 2010d, Tropical cyclone — Wikipedia, The Free
Encyclopedia. [Online; accessed 31-March-2010].
URL:
http: // en. wikipedia. org/ w/ index. php? title=
Tropical_ cyclone&oldid= 353193087
Cloud Dynamics: Assignment 5
M at l a b - C o d e
Appendix A Matlab-Code
Used Matlabcode for task 2
5
%
%
%
%
%
Cloud Dynamics
AS 5
Alexander Umbricht
−−−−−−−−−−−−−−−−−−−
clc ;
clear
10
all;
%Dateipfad
p at h = ’C :\ Users \ Alexander Umbricht \ Documents \ ETH \ Cloud Dynamics \ Assignments \ A5 \ ’;
path_grafik = ’C :\ Users \ Alexander Umbricht \ Documents \ ETH \ Cloud Dynamics \ Assignments \ A5 \ graph \ ’;
path_functions = ’C :\ Users \ Alexander Umbricht \ Documents \ ETH \ Risk \ neu \ functions \ ’;
addpath ( path , path_grafik , path_fu nctions ) ;
15
% load colors
farben ;
20
25
%% constants
c . L = 2.53 e6 ;
c . R = 287.04;
c . cp = 1005;
c . epsilon . n u l l = 0.622;
c . p . hat = 1 e5 ;
c . coef = 1.2;
c . kappa = c . R / c . cp ;
c . p . hat = 1 e5 ;
c . p . s = c . p . hat - 2000;
c . RH = 0.78;
30
35
%% functions
f . p . sat = @ ( temperature ) exp (54.842763 - 6763.22/ temperature - 4.210 * l o g ( temperature ) + 0.000367 *
temperature + t an h (0.0415 * ( temperature - 218.8) ) * (53.878 - 1331.22/ temperature - 9.44523 * l o g (
temperature ) + 0.014025 * temperature ) ) ;
f . epsilon = @ ( temperature ) ( temperature - v . T . n u l l ) / v . T . n u l l ;
f . t . es = @ ( temperature , p_sat ) temperature * ( c . p . hat / c . p . s ) ^ c . kappa * exp (( c . L * c . epsilon . n u l l * p_sat )
/( c . cp * temperature * c . p . s ) ) ;
f . t . e = @ ( temperature , p_sat ) temperature * ( c . p . hat / c . p . s ) ^ c . kappa * exp (( c . L * c . RH * c . epsilon . n u l l *
p_sat ) /( c . cp * temperature * c . p . s ) ) ;
f . v = @ ( epsilon , temperature , potes , pote ) (1.2 * epsilon * c . cp * temperature * l o g ( potes / pote ) ) ^.5;
40
45
50
%% values
v . T . S = 293:5:303;
v . T . n u l l = 210;
au . p . sat = z e r o s (1 ,3) ;
au . epsilon = z e r o s (1 ,3) ;
au . v = z e r o s (1 ,3) ;
au . t . es = z e r o s (1 ,3) ;
au . t . e = z e r o s (1 ,3) ;
f o r i_ts =1:3
au . p . sat ( i_ts ) = f . p . sat ( v . T . S ( i_ts ) ) ;
au . epsilon ( i_ts ) = f . epsilon ( v . T . S ( i_ts ) ) ;
au . t . es ( i_ts ) = f . t . es ( v . T . S ( i_ts ) , au . p . sat ( i_ts ) ) ;
au . t . e ( i_ts ) = f . t . e ( v . T . S ( i_ts ) , au . p . sat ( i_ts ) ) ;
55
au . v ( i_ts ) = f . v ( au . epsilon ( i_ts ) , v . T . S ( i_ts ) , au . t . es ( i_ts ) , au . t . e ( i_ts ) ) ;
end
c l e a r i_ts ;
A. Umbricht
Page 5 of 6
M at l a b - C o d e
70
% Ausgabe LaTeX
f o r i_ts =1:3
f p r i n t f ( ’ \\ midrule \ n %4.0 f \ t & %4.3 f \ t & %4.0 f \ t & %4.0 f
v . T . S ( i_ts ) , ...
au . epsilon ( i_ts ) , ...
au . p . sat ( i_ts ) , ...
au . t . es ( i_ts ) , ...
au . t . e ( i_ts ) , ...
au . v ( i_ts ) )
end
c l e a r i_ts ;
75
%% plot
au . linear = au . v (1) + ( au . v (2) - au . v (1) ) /( v . T . S (2) -v . T . S (1) ) * ( v . T . S (3) -v . T . S (1) ) ;
p l o t ( v . T .S ,[ au . v (1:2) au . linear ] , ’ -. ’ , ...
’ color ’ , IBAdarkred ) ;
60
65
\ t & %4.0 f
\ t & %4.1 f \\\\ \ n ’ , ...
h o l d on ;
p l o t ( v . T .S , au .v , ’ -- ’ , ...
’ color ’ , MyLightBlue ) ;
80
85
90
95
100
105
110
115
120
h o l d on ;
p l o t ( v . T .S , au .v , ’o ’ , ...
’ color ’ , MyDarkBlue , ...
’ MarkerSize ’ ,8 , ...
’ Marke rF a ce Co lo r ’ , MyDarkBlue ) ;
ax2 = gca ;
s e t ( ax2 , ...
’ XGrid ’ , ’ off ’ , ...
’ YGrid ’ , ’ on ’ , ...
’ Ycolor ’ , Gray , ...
’ Xcolor ’ , Gray , ...
’ TickDir ’ , ’ out ’ , ...
’ box ’ , ’ off ’ , ...
... ’ Xlim ’ ,[ -1200 1200] ,...
... ’ Ylim ’ ,[ -1200 1200] ,...
... ’ Yscale ’ , ’ log ’ ,...
... ’ Xscale ’ , ’ log ’ ,...
... ’ YTickLabel ’ , v . buyo . pressure ,...
... ’ Color ’ , ’w ’ , ...
’ Box ’
, ’ off ’
, ...
’ TickDir ’
, ’ out ’
, ...
’ TickLength ’ , [.02 .02] , ...
’ XMinorTick ’ , ’ on ’
, ...
’ YMinorTick ’ , ’ on ’
, ...
’ XColor ’
, [.3 .3 .3] , ...
’ YColor ’
, [.3 .3 .3] , ...
’ LineWidth ’
, 1 );
y l a b e l ( ’ $v_ { max } $ ( m \ , s \ te xt su p er sc ri p t { -1}) ’ , ...
’ FontSize ’ ,14 , ...
’ Interpreter ’ , ’ latex ’) ;
x l a b e l ( ’ Sea Surface Temperature $T_S$ ( K ) ’ , ...
’ FontSize ’ ,14 , ...
’ Interpreter ’ , ’ latex ’) ;
s e t ( g c f , ’ PaperUnits ’ , ’ centimeters ’) ;
s e t ( g c f , ’ P a p e r O r i e n t a t i o n ’ , ’ landscape ’) ;
s e t ( g c f , ’ PaperPosition ’ ,[1 1 27.7 19]) ;
%speichern(gcf,path_grafik,[’v_max’]);
close a l l ;
Page 6 of 6
Cloud Dynamics: Assignment 5