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

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!

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 can’t see Rossby waves??

-Well, Rossby could see them - at least on Christmas Day 1940-Well, Rossby could see them - at least on Christmas Day 1940

2

2

4πβLUc −=

C= phase speed, U= zonal flow at 500 hPa, L=wave C= phase speed, U= zonal flow at 500 hPa, L=wave length, length, ββ=df/dy=df/dy

c < 0 for large L c >0 for small Lc < 0 for large L c >0 for small L

Rossby’s wave formula (inspired by Ekman, 1932)Rossby’s wave formula (inspired by Ekman, 1932)

How the Rossby wave How the Rossby wave was initially was initially

misunderstood by misunderstood by Rossby himselfRossby himself

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

H H

L

Conv Div

Jack Bjerknes´ 1937gradient wind explanation of the

progression of waves

Short waves - the curvature effect dominates

H H

L

Div Conv

Long waves - the latitude effect dominates

Carl Gustaf Rossby et al (1939) used Bjerknes´ gradient wind idea to

illustrate the retrogression of waves

Low latitude

High latitude

A very common misunderstanding:A very common misunderstanding:This is NOT a Rossby wave!This is NOT a Rossby wave!

……but a but a CConstant onstant AAbsolute bsolute VVorticity Trajectory!orticity Trajectory!

+f==constlow high f

high low f

There are 5-6 other misleading There are 5-6 other misleading or erroneous explanations of or erroneous explanations of

the Rossby wave before it the Rossby wave before it finally was explained in a finally was explained in a

kinematically consistent waykinematically consistent way

Rossby (1940), Petterssen (1956), Rossby (1940), Petterssen (1956), Persson (1993)Persson (1993)

Very few seem to have taken notice of a Rossby (1940) correction - and even fewer understood what he meant

(Trajectories represented by PV isolines)

H H

L

Relation between stream lines and trajectories in a progressive flow

Larger amplitudes and wave lengths

H H

L

Relation between stream lines and trajectories in a

retrogressive flow

Shorter amplitudes and wave lengths

Let us go back to the Constant Absolute Vorticity Let us go back to the Constant Absolute Vorticity Trajectory Trajectory (which is NOT a Rossby wave)(which is NOT a Rossby wave)

Rossby asked: Rossby asked: -Which non-stationary -Which non-stationary streamlines streamlines would correspond to this trajectory?would correspond to this trajectory?

+f==const

+f==const

One and the same CAV trajectory One and the same CAV trajectory satisfies two types of streamlines (waves)satisfies two types of streamlines (waves)

Long retrogressive waves

Short progressive waves