Innsbruck University

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Seven sins in dynamical meteorological education
The mathematics is always correct, the
computers are given the right equations, but the
explanations do not only contradict Nature but
also the mathematics they are supposed to
illuminate
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Seven sins in dynamical meteorological education
Professor Richard Reed, Univ. Of Seattle
1988 -Our understanding of the cyclogenesis
process has increased tremendously during the
last 40 years at least the computers seem to
understand!
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1. Air passing mountains
Although this conceptual model seems to work
well for westerly flow over topography, an
attempt to apply it to easterly flow quickly
leads to an absurdity. Prof. James Holton, Bull
AMS 1994
4
? 0
North higher f
H
South lower f
5
? 0
North higher f
H
? lt 0
H
South lower f
6
? 0
North higher f
? lt 0
? 0
South lower f
7
? lt 0
North higher f
? lt 0
? 0
South lower f
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The Second Haurwitz Memorial Lecture Stationary
Planetary Waves James R. Holton Atmospheric
Sciences Department University of Washington,
Seattle, Washington
According to this reasoning, no air stream will
ever be able to pass a mountain range from the
east! Bull AMS 1994
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The Second Haurwitz Memorial Lecture Stationary
Planetary Waves James R. Holton Atmospheric
Sciences Department University of Washington,
Seattle, Washington
Since the standard conceptual model does not
work for easterly flow it is reasonable to ask
whether it is appropriate for westerly
flow. Bull AMS 1994
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The Second Haurwitz Memorial Lecture Stationary
Planetary Waves James R. Holton Atmospheric
Sciences Department University of Washington,
Seattle, Washington
Acknowledgements Anders Persson and Prof. Dale
Durran for correspondence and discussions on some
of this material. Bull AMS 1994
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The Second Haurwitz Memorial Lecture Stationary
Planetary Waves James R. Holton Atmospheric
Sciences Department University of Washington,
Seattle, Washington
Acknowledgements Anders Persson and Prof. Dale
Durran for correspondence and discussions on some
of this material. Bull AMS 1994
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2. Group velocity The energy is the atmospheric
flow is moving much faster downstream than the
individual waves
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in ocean waves
Group velocity
Holton, 1972, 1979, 1992
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Group velocity
in the atmosphere
Persson, 1993
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James R. Holton, Fourth edition, 2004
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Email exchange 22 December 2003 Jim, It's
great - but the dashed line in fig. 7.4b is
slightly displaced. It should lie along the
crests in the waves. But the main points come
through well. Anders You are right about that
-- unfortunately it may be a bit late to change
it for the first printing. Jim
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3. The Rossby Wave -I have never understood
what a Rossby waves is Professor Harold
Jeffreys on his deathbed 1987 Lunch discussion
at ECMWF 1995 Scientist -How is the weekend
going to be? AP -Fine, a Rossby wave is seen
coming in! Scientist -But you cant see Rossby
waves??
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-Well, Rossby could see them - at least on
Christmas Day 1940
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Rossbys wave formula (inspired by Ekman, 1932)
C phase speed, U zonal flow at 500 hPa, Lwave
length, ?df/dy c lt 0 for large L c gt0 for
small L
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How the Rossby wave was initially misunderstood
by Rossby himself
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The isobaric channel illustration used by Rossby
et al (1939)
Only when the paper was published did Rossby
realize that he could not use gradient wind
balance - it is only applicable on stationary
patterns
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Jack Bjerknes 1937 gradient wind explanation of
the progression of waves
L
Conv
Div
H
H
Short waves - the curvature effect dominates
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Carl Gustaf Rossby et al (1939) used Bjerknes
gradient wind idea to illustrate the
retrogression of waves
High latitude
L
Div
Conv
H
H
Low latitude
Long waves - the latitude effect dominates
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A very common misunderstanding This is NOT a
Rossby wave!
low ? high f
?f?const
high ? low f
but a Constant Absolute Vorticity Trajectory!
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There are 5-6 other misleading or erroneous
explanations of the Rossby wave finally was
explained in a kinematically consistent
way Rossby (1940), Petterssen (1956), Persson
(1993)
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Very few seem to have taken notice of a Rossby
(1940) correction - and even fewer understood
what he meant
(Trajectories represented by PV isolines)
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Relation between stream lines and trajectories
in a progressive flow
L
H
H
Larger amplitudes and wave lengths
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Relation between stream lines and trajectories
in a retrogressive flow
L
H
H
Shorter amplitudes and wave lengths
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Let us go back to the Constant Absolute Vorticity
Trajectory (which is NOT a Rossby wave)
?f?const
Rossby asked -Which non-stationary streamlines
would correspond to this trajectory?
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One and the same CAV trajectory satisfies two
types of streamlines (waves)
?f?const
Short progressive waves
Long retrogressive waves
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4. The Coriolis Effect -The serious students
should rebel against theories that have been
repeatedly shown to be seriously
incomplete! Professor W.M.Davis on the
explanation of the Coriolis effect in a speech
at the Royal Meteorological Society in 1899
(QJRMS 1899)
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The Coriolis Effect
- 2 ? ? V
The Coriolis parameter f 2?sin?
V
The radius of the inertia circle RV/f
fV
The inertia circle motion
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The woollen cap effect
The effect of the earths rotation is to stop or
delay air mass exchanges
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George Hadleys (but also Immanuel Kants)
explanation of the Coriolis effect
0 m/s
30?
400 m/s
460 m/s
60 m/s
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The carousel explanation of the Coriolis
effect If only the Coriolis force was present
the object would move around in a circle
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The carousel explanation of the Coriolis
effect But here also the centrifugal force is
present and prevents the object to ever return
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but if we combine these two erroneous
explanations...
we might get the right answer. That is indeed
what the French Academy approved of in 1847!
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Joseph Bertrands 1847 simplified derivation
of the Coriolis effect Two
common errors compensate each other
?
R
?R
?S
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The beta-effect
The Coriolis parameter f 2?sin? depends on
latitude
? the radius of the inertia circle RV/f depends
on latitude
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The beta-effect gives rise to a slow westward
propagation of mass
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The subtropical high pressure area (The Azores
High)
Europe
USA
H
Africa
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The beta effect would drive the water westward
Europe
USA
H
Africa
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The asymmetric Gulf Stream circulation
Europe
USA
H
G
Africa
S Am
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5. Angular momentum Hadleys erroneous
explanation yielded excessive winds (50-80 m/s),
the correct concept of angular momentum yields
the double!
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Hadleys explanation of the Trade winds
(conservation of absolute motion) is not only
physically unrealistic ...
30?
400 m/s
60 m/s
460 m/s
0 m/s
.it only explains half of the Coriolis
deflection and yields too high winds
46
Conservation of angular momentum seems to yield
even more unrealistic results, double wind speeds
6000 km x (400130) m/s
30?
130 m/s
6370 km x 460 m/s
0 m/s
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The problem with angular momentum conservation
Latitudinal displacement for different initial
velocities at different latitudes
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The problem with angular momentum conservation
Angular momentum conservation does not need
information about the speed which the ring must
be displaced in order to reach as far north as
30? latitude without being turned by by the
Coriolis force.
130 m/s
The initial impetus must give an initial
poleward speed of exactly those 130 m/s which at
30? latitude is pointing eastward
What prevents any excessive winds from developing
is not friction, but pressure gradient forces
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6. Geostrophic adjustment The common
visualization is not only wrong, the teachers
miss chances to link to jet streams, both
nocturnal and upper tropospheric
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The school book image of geostrophic adjustment
in a constant pressure field
Low pressure
Vg
High pressure
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The real image of motion of an air parcel in a
constant pressure field
Low pressure
2Vg
2Vg
V0
V0
This is also the mechanism behind nocturnal jet
streams
High pressure
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We rarely see inertia circles in the
atmosphere But they are there, disguised in
cycloid shapes
Motion rotation cycloids
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In particular this type of cycloid
We rarely see inertia circles in the
atmosphere But they are there, disguised in
cycloid shapes
Translation rotation cycloids
max
max
min
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The pressure field and the winds will mutually
adjust to each other and stretch the cycloid
Low pressure
lt2Vg
Vgt0
V0
High pressure
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The jet streams look like stretched cycloids
J
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7. Indirect circulation and negative
work Textbooks ignore almost half of the
energetic processes in the atmosphere
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Typical relation between isobars and winds in the
frictional layer
H
L
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Typical relation between isobars and winds above
frictional layer
H
L
H
L
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Work force x distance
When the roller skater goes down potential energy
converts into kinetic and gravity is doing
positive work, when he goes up kinetic energy
goes back into potential energy when gravity is
doing negative work
Highest potential energy No kinetic energy
Highest potential energy No kinetic energy
mg
friction
Lowest potential energy Highest kinetic energy
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The previous isotach chart converted into a
vector image
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The typical flow
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and the typical energy conversions
Potential to kinetic energy
Kinetic to potential energy
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Direct circulation potential energy is
converted to kinetic
Cold window
Warm oven
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Indirect circulation kinetic energy is
converted to potential
Cold window
Wind wheel
Warm oven
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The typical energy conversions
Cyclo- genesis
Cyclo- genesis
Cold air rising warm air sinking kinetic
energy is destroyed
Warm air rising cold air sinking kinetic
energy is produced
How can we then have the most violent
storms develop in the left exit region?
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The energy budget
P
K
F
This is how the energy conversions in the
atmosphere is often portrayed - as an
irreversible process
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The goings on in the atmosphere
P
K
F
The energy conversions in the atmosphere are
partly reversible
And only a small residual is lost in friction
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• So
• The same physical-dynamic processes can often be
  described by different mathematical formalisms
  
  
• The text-books authors do not always chose the
  most pedagogic mathematical formalism
• Whilst their mathematical derivations are always
  correct, this is not always the case for their
  interpretation of the mathematics

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4. This is because in physics the easiest bit is
the maths Cest beaucoup plus facile de voir
si un calcul est juste que de voir si une
observation est fineles maths, cest la méthode
économique pour fair des concours Pierre
Gilles de Gennes, 1991 Nobel Prize in physics
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4. This is because in physics the easiest bit is
the maths  It is much easier to judge if a
mathematical derivation is all right, than to
judge if a observation is correct... Maths,
thats the cheap way to do examinations.  Pierr
e Gilles de Gennes, 1991 Nobel Prize in physics
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C-G Rossby The problems in meteorology only
appear complicated to us, just because we have
not tackled them in the right way Guy Dady,
La Météorologie no 37, 1955
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END
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1851 and Foucaults famous experiment
The decisive proof that the earth rotates?
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According to the logic of the common explanation
it would take almost 24h to complete a full
turn-around in reality it takes
24h/sin(latitude)
because the Foucault pendulum does not move
unaffected by any forces (what about gravity?)
Consequently the plane of swing does not keep
its orientation in absolute space!
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The eighth sin The Ferrel Cell
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The general circulation according to Ferrel
Ferrel Cell
Ferrel Cell
Hadley Cell
Hadley Cell
Ferrel Cell
Ferrel Cell
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Direct Hadley cell sinking cold air, rising
warm air
Indirect Ferrel cell rising cold air, sinking
warm air
Indirect Ferrel cell rising cold air, sinking
warm air
Temp
Temp
Equator
S
N
But the Ferrel Cell is a statistical illusion!
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A snapshot of a NH map
W
Rising warm air
C
W
L
L
W
W
L
C
C
Sinking cold air
C
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A non-snapshot of a NH map
On average northerly latitudes with rising air
are also colder
On average southerly latitudes with sinking air
are also warmer
After Riehl and Fultz, QJRMS 1957
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So there is no Ferrel circulation in the real
atmosphere
It exists only in some peculiar statistical space
where we map
..which seems to indicate indirect circulation
We should really have looked at
which indicates direct circulation