CERFACS CERFACS Scientific Activity Report Jan. 2010 – Dec. 2011

3 Large scale atmospheric composition
3.1 Introduction of chemistry into large-scale atmospheric models
(D. Cariolle, R. Paoli)
.
All the models that include atmospheric chemistry need to adopt a numerical solver to integrate the
transport-chemical continuity equations. This is usually done by the integration of successive operators
working on the integration of the transport equation followed by the calculation of the evolution of the
chemical species. For instance, with the MOCAGE CTM from Météo-France, the model first solves the
evolution of the species due to advection with a semi-lagrangien scheme, followed by the chemical evolution
of species solved using a semi-implicit solver. Both of those schemes do not assure mass conservation and
hence may introduce drifts in the numerical integration which could become large for long term multi-year
simulations. To study the properties of some advection and chemical solvers we have developed within
the SOLSTICE project a reduced 2D model that mimic the evolution of the atmospheric composition on a
latitude-longitude plane from pole to pole. On that geometry the model solves the coupled set of continuity
equations :
dC i /dt = ... − div(V.C i ) − K ij C j C i + ... (3.1)
Where C i are the species concentrations and V the velocity. To integrate the transport part of the above
equation, the divergence of the fluxes, we have used the so called ’slope scheme’ which adopts a volume
finite formulation, is characterised by its mass conservation, and assures the positivity of the solution if a
slope limiter is used. For the integration of the chemistry par of the equation we have developed a semiimplicit
scheme which is mass conserving and is preconditioned to insure positivity in most cases. The
discretisation writes as follow :
(C t+1
i − C t i)/dt = −δK ij C t jC t+1
i − (1 − δ)K ij C t+1
j C t i (3.2)
The C t+1 concentrations are obtained by inversion of the matrix obtained from the above equation. The
matrix is of the order on the number of species. On scalar computers we use the direct DGES software
from the Scalapack library to invert the system. In a preliminary version the value of δ was fixed according
to the user’s knowledge of the stiffness of the system, but il was found that a much stable solution was
obtained by evaluating its value using the species concentrations at time t. Best results were obtained with
the formulation : δ = Cj t/(Ct j + Ct i ), coupled to the determination of the time step dt function of the
curvature of the solution.
We have first tested the above choices in the framework of the reduced model. The chemical system is
composed of 30 species representative of the Ox, HOx, NOx and Clx chemistry in the stratosphere.
The model performed very well, Fig. 3.1 shows for instance the concentration of the HOCl radical after
more than 1000 iterations of the system. As can be seen the solution exhibits filamentations of the field,
which are a result of the combination of advection and chemistry. In the atmosphere this sort of situation is
encountered for air masses at the boundary of the ozone hole in the stratosphere. The chemical solver was
then introduced in the CNRM general circulation model. Preliminary results show a satisfying behaviour,
although with a numerical cost which will be only affordable if the model is integrated in parallel mode
on a scalar computer. The solver was also tested with success in the LATMOS chemical transport model
applied to the atmosphere of Mars.
CERFACS ACTIVITY REPORT 187