What the M stands for
Piet Termonia
5 October 2012
50 years of the
Institute for Theoretical Physics
Leuven
During my postdoc years in theory, 1997-1999:
Ed Witten, 1998: Magic, Mystery, and Matrix, Notice of the AMS, 45, 1124-1129
Witten did not specify what the M stood for:
"M can stand variously for magic, mystery or
matrix, according to ones taste”
In 1999 I got a job in the research department of
the Royal Meteorological Institute (RMI)
“Congratulations, and,
At least you, will know what the M stands for ...”
Walter Troost
The Mother of all study objects
Meteorologists like to zoom in on the planet
Planetary waves
107 m
synoptic cyclones
106 m
hurricanes
105 m
fronts
Individual
thunderstorm cells
tornado’s
104 −105 m
103 m
100 m
Wind gust
10−100 m
Turbulence
10−2−10 m
Molecular scale
10−7 m
Bjerknes, 1904: weather prediction is a
problem of mathematical physics
1: The condition of the atmosphere
must be known at a specific time with
sufficient accuracy
2: The laws must be known, with
sufficient accuracy, which determine
the development of one weather
condition from another.
Bjerknes, V. (1904) Das Problem der
Wettervorhersage, betrachtet vom
Standpunkte der Mechanik und der
Physik. Meteorol. Z., 21, pp. 1–7
Planetary waves
107 m
synoptic cyclones
106 m
hurricanes
105 m
fronts
Individual
thunderstorm cells
tornado’s
Write the equations somewhere here
104 −105 m
103 m
100 m
Wind gust
10−100 m
Turbulence
10−2−10 m
Molecular scale
10−7 m
Effective theories?
Explaining the atmosphere as an
application of mathematical physics?
BUT, there are no analytical solutions of the full 3D system,
Even if we idealize the problem by “forgetting” moisture.
So, historically, one needed to wait for two ingredients:
smart simplifications and computers (the ENIAC)
Charney, J. G., Fjørtoft, R.
and Von Neumann, J. (1950)
Numerical integration of the
barotropic vorticity
equation. Tellus, 2, pp. 237–
254
The point of view of a modeler, today
(I brutally simplify here)
Planetary waves
107 m
synoptic cyclones
106 m
hurricanes
105 m
fronts
Numerical discretization,
cut off, is here somewhere
Individual
thunderstorm cells
tornado’s
Wind gust
Dynamical equations
(filtered)
104 −105 m
103 m
100 m
10−100 m
Parameterizations:
●Turbulent diffusion
●Radiation
Turbulence
10−2−10 m
●Subgrid convection
●Microphysics
−7
Molecular scale
10 m
●Clouds
●Interactions with the surfac
Parameterizations are either empirical relations or brutal approximations,
so VERY inaccurate!
A Mystery ...
The global energy cycle in the atmosphere
Unit = W/m²
342
107
235
The equations
(u²+v²)/2
37
2.5
2.5
78
198
Cp.T+φ
78
30
24
324
390
Lectures
Atmospheric
Modeling,
J.-F. Geleyn,
UGent
Mystery
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In the atmosphere, the energy conversions in the parameterizations are one
or two orders of magnitude larger than conversion of potential energy into
kinetic energy of the dynamical equations.
Why is the planet inhabitable? Why is life not blown away? Or put in a more
scientific way, why is the atmosphere so inefficient in converting energy?
One can apply a Darwinist reasoning here: it is a matter of fine tuning (gas
constant, gravitation, rotation of the planet, ...), but this, nevertheless, poses
a serious problem if one wants to make weather forecasts and climate
scenario's (small errors in the conversions could blow the system)!
For a long time it was thought that forecasts beyond two days (the time
scale of synoptic systems) would not be possible because of this.
The pessimists proved to be wrong ...
Atmospheric Modeling, Jean-François Geleyn, UGent
Some Magic
Evolution in forecast skill: roughly every ten
years we look 1 day further into the future
WHY?: more observations and higher resolution, BUT also
a steady process of mastering the fine tuning of our atmosphere
and the feedbacks in the system!
Grad (RT) with water vapour only; dx = 2.3km
Grad (RT) with all species included
Contributors: S. Malardel & Y. Bouteloup (sensitivity),
R. Brožková & P. Smolíková (DFI problem)
More theory
Poincaré
« Une cause très petite, qui nous échappe,
détermine un effet considérable que nous ne
pouvons pas ne pas voir, et alors nous disons
que cet effet est dû au hasard. Si nous
connaissions exactement les lois de la nature et
la situation de l'univers à l'instant initial, nous
pourrions prédire exactement la situation de ce
même univers à un instant ultérieur. Mais, lors
même que les lois naturelles n'auraient plus de
secret pour nous, nous ne pourrions connaître la
situation qu'approximativement. Si cela nous
permet de prévoir la situation ultérieure avec la
même approximation, c'est tout ce qu'il nous
faut, nous disons que le phénomène a été prévu,
qu'il est régi par des lois ; mais il n'en est pas
toujours ainsi, il peut arriver que de petites
différences dans les conditions initiales en
engendrent de très grandes dans les
phénomènes finaux ; une petite erreur sur les
premières produirait une erreur énorme sur les
derniers. La prédiction devient impossible et
nous avons le phénomène fortuit. »
Application to meteorology: Lorenz, 1963
Lorenz, Edward N., 1963: Deterministic Nonperiodic Flow. J. Atmos. Sci., 20, 130–141.
Today we perturb the model runs to make probabilistic forecasts to
make early warnings (ill. Pukkelpop run) and to increase their
economic value (e.g. wind for energy production)
Our model
(ALADIN)
adds skill
to ECMWF's
ECMWF
Smet, G., P. Termonia and A. Deckmyn, 2012:
Added economic value of limited area multi-EPS
weather forecasting applications Tellus , A , 64 ,
18901
Summary
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In essence, one can see atmospheric modeling as an exercise in
mathematical physics (already put forth in 1904 by Bjerknes and many
others later), but approached with a firm dosis of pragmatism.
A second main innovation in our field is the introduction of probabilistic
forecasts (based on theoretical insights of Poincaré and Lorenz and many
others later) quantifying the inherent predictability of the system.
The complexity of the models is strongly increasing (linked to the increased
resolutions and new assimilated data) and this increasingly demands unique
skills. A training in theoretical physics is an excellent basis!
In our research department in the RMI we are actively recruiting theorists.
And finally, Walter, you were right: in the past 13 years, according to my
taste ...
The M stands for
Meteorology