Modeling the evolution of climates over long period: the Planetary Evolution
Model
R. Vandemeulebrouck, F.Forget, L.Lange, E.Millour, A.Spiga, A.Bierjon, A.Delavois, J.Naar, Laboratoire de
Météorologie Dynamique, Institut Pierre-Simon Laplace (LMD/IPSL), Sorbonne Université, Centre National de
la Recherche Scientifique (CNRS), École Polytechnique, École Normale Supérieure (ENS), Paris, France
romain.vandemeulebrouck@lmd.ipsl.fr.

Introduction:
Studies show that the variation of orbital
parameters can deeply impact the climate [Hays et
al., 1976]. On Earth, small variations of ±1.3° of
obliquity are responsible for ice ages [Imbrie and
Imbrie, 1979]. Laskar et al. [2004] indicate that the
obliquity of Mars can vary between 0° and 60°, this
suggests that huge climatic variations could have
happen on Mars in the last Myr.

Fig.1 : Martian obliquity for the last and next Millions
of years (Laskar et al. [2004])

The usual tool to model and study Mars climate
is a Global Circulation Model (GCM here the
LMDZ). It is able to adequately simulate a vast
impact of phenomenon with a good precision.
However, the drawback of this accuracy is that it
requires a relatively long computing time. For a low
resolution simulation of a martian year it can take up
to 2 hours. Therefore it is impossible to study the
long timescale variation of orbital parameters (order
of magnitude Myr). The new and innovative way to
couple physical processes with very different
timescale
(cloud
microphysics,
atmospheric
dynamics, evolution of glacier accumulation,
atmospheric
collapse)
is
a
new
“asynchronous-coupling” model called Planetary
Evolution model (PEM)
Philosophy of the PEM:
The idea of the PEM is to take as input different
tendencies from the GCM and extrapolate them. It
would be able to simulate long variation and should
not consider subyear on interannual variability.
There is two possibility of use of the PEM :

●

Find a steady state for a given external
forcing (example : perineal ice reservoir at a
given obliquity)
● Realistic simulation of climate and fate of
volatiles for thousands of years
Concretely, the GCM is used as a subroutine of
the PEM. The GCM is called for two martian years
(only one year is also tested for validation), it
simulates Mars precisely using a vast variety of
physical processes. From these two years, different
information can be extracted at a given frequency;
such as sublimation and condensation of water and
CO2 ice, precipitation, volume mixing ratio of the
atmosphere component etc… Given these
informations we are able to compute tendencies.
These tendencies can be applied to the output state of
the GCM. Once we have applied them, we use this
new state as the initial state of the GCM and
continue like this for as long as necessary.
To illustrate, we present the first two kinds of
processes that have been implemented : the evolution
of water and CO2 ice.
We are only interested in perennial ice. For each
point we compute the minimum of ice over each
year; the difference gives the tendency. One has to
carefully take into account the change of mass of the
atmosphere as the martian atmosphere is mainly
composed of CO2. This change of pressure is taken
back into account as a feedback on the tendency as
the condensing temperature depends on the pressure
and volume mixing ratio. We also assume the
relative humidity to be constant.
The extrapolation of the tendency is valid until
the climate has changed too much. We created a
stopping criterion that is supposed to characterize the
amplitude of the change of climate. This stopping
criterion depends on the surface of ice sublimating
that disappeared and the global average pressure, it
can be adapted.
This configuration has been validated by some
experiments.
Fig.2 Schematic view of the PEM

Validation:
A run at 5° obliquity has been performed, the
opacity of the atmosphere is fixed, and we only
consider two tracers in the atmosphere: one called
CO2 and the other one called noCO2. Water is not
modeled here. We assume that the CO2 ice thickness
can not exceed 10 m on slopes, and must flow if this
thickness is reached. Values of albedo, emissivity for
CO2 and H2O ices, as well as ice tables are set to the
current values used in the LMD GCM. The
resolution is 3.75° latitude, 5.625° longitude. The
PEM is compared to the GCM.

First we can conclude that the PEM behaves as
expected and follows the GCM run very nicely. It
often calls the GCM in the first moment of the
simulation as expected since this is the time where
the climate changes the most and the most rapidly.
Then, it does longer time steps and extrapolates
tendencies for longer which will be very useful to do
longer run.
Secondly we see that the evolution seems
realistic as the atmosphere condens as co2 ice. The
ice is mainly present near the North pole as it should
theoretically be at 5° of obliquity.
Computing time acceleration:
Another possible way to accelerate the running
time is to accelerate the time needed to run the
GCM. This has been achieved by using mix
MPI-OMP parallelism. Results and performance can
be seen in Fig. 4

Preliminary applications to the study of ice
evolution:
Another work has been performed most focused
on H2o ice. We start from an aritrary initial state : all
the water ice form a patch around the equator. We
take present day Mars configuration and let the PEM
run. We expect to see the ice progressively move to
the present ice patch that we observe on Mars. This
is exactly what happen and first the ice increase
along Tharsis before moving to the poles.

Ongoing work and perspective:
Next part of the work will be to implement a
subslope parametrisation in order to accurately
simulate glaciers flow and all the physical processes
taking place on slope such as the different radiative
transfer according to the North-South orientation of
the slope.
Then it will also be possible to simulate a
variation of orbital parameters such as a descent of
obliquity.
Reference:
Hays, J. D., Imbrie, J., and Shackleton, N. J.
(1976). Variations in the earth’s orbit: Pacemaker of
the ice ages. Science, 194(4270):1121–1132.
Imbrie, J. Z. and Imbrie, K. P. (1979). Ice ages:
Solving the mystery
Forget, F., Hourdin, F., Fournier, R., Hourdin, C.,
Talagrand, O., Collins, M., Lewis, S. R., Read, P. L.,
and Huot, J.-P. (1999). Improved general circulation
models of the Martian atmosphere from the surface
to above 80 km. , 104(E10):24155–24176.
Laskar, J., Correia, A., Gastineau, M., Joutel, F.,
Levrard, B., and Robutel, P. (2004). Long term
evolution and chaotic diffusion of the insolation
quantities of mars. Icarus, 170(2):343–364.
Acknowledgement :
This project has received funding from the
European Research Council (ERC) under the
European Union’s Horizon 2020 research and
innovation program (grant agreement No 835275).